Solid-Liquid Phase Equilibria and Crystallization of Disubstituted Benzene Derivatives

Home , Cooling bath, Supersaturation

Royal Institute of Technology School of Chemical Science and Engineering Department of Chemical Engineering and Technology Division of Transport Phenomena

Fredrik Nordström

Doctoral Thesis

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie doktorsexamen den 30:e Maj 2008, kl. 10:00 i sal D3, Lindstedtsvägen 5, Stockholm. Avhandlingen försvaras på engelska.

Cover picture: Crystals of o-hydroxybenzoic acid (salicylic acid) obtained through evaporation crystallization in solutions of ethyl acetate at around room temperature.

Solid-Liquid Phase Equilibria and Crystallization of Disubstituted Benzene Derivatives

Doctoral Thesis © Fredrik L. Nordström, 2008 TRITA-CHE Report 2008-32 ISSN 1654-1081 ISBN 978-91-7178-949-5

KTH, Royal Institute of Technology School of Chemical Science and Engineering Department of Chemical Engineering and Technology Division of Transport Phenomena SE-100 44 Stockholm Sweden

Paper I: Copyright © 2006 by Wiley InterScience Paper II: Copyright © 2006 by Elsevier Science Paper III: Copyright © 2006 by the American Chemical Society Paper IV: Copyright © 2006 by the American Chemical Society

In loving memory of my grandparents Aina & Vilmar Nordström

iii

i v Abstract

The Ph.D. project compiled in this thesis has focused on the role of the solvent in solid-liquid phase equilibria and in nucleation kinetics. Six organic substances have been selected as model compounds, viz. ortho-, meta- and para-hydroxybenzoic acid, salicylamide, meta- and para-aminobenzoic acid. The different types of crystal phases of these compounds have been explored, and their respective solid-state properties have been determined experimentally. The solubility of these crystal phases has been determined in various solvents between 10 and 50 oC. The kinetics of nucleation has been investigated for salicylamide by measuring the metastable zone width, in five different solvents under different experimental conditions. A total of 15 different crystal phases were identified among the six model compounds. Only one crystal form was found for the ortho-substituted compounds, whereas the meta-isomeric compounds crystallized as two unsolvated polymorphs. The para-substituted isomers crystallized as two unsolvated polymorphs and as several solvates in different solvents. It was discovered that the molar solubility of the different crystal phases was linked to the temperature dependence of solubility. In general, a greater molar solubility corresponds to a smaller temperature dependence of solubility. The generality of this relation for organic compounds was investigated using a test set of 41 organic solutes comprising a total of 115 solubility curves. A semi-empirical solubility model was developed based on how thermodynamic properties relate to concentration and temperature. The model was fitted to the 115 solubility curves and used to predict the temperature dependence of solubility. The model allows for entire solubility curves to be constructed in new solvents based on the melting properties of the solute and the solubility in that solvent at a single temperature. Based on the test set comprising the 115 solubility curves it was also found that the melting temperature of the solute can readily be predicted from solubility data in organic solvents. The activity of the solid phase (or ideal solubility) of four of the investigated crystal phases was determined within a rigorous thermodynamic framework, by combining experimental data at the melting temperature and solubility in different solvents and temperatures. The results show that the assumptions normally used in the literature to determine the activity of the solid phase may give rise to errors up to a factor of 12. An extensive variation in the metastable zone width of salicylamide was obtained during repeated experiments performed under identical experimental conditions. Only small or negligible effects on the onset of nucleation were observed by changing the saturation temperature or increasing the solution volume. The onset of nucleation was instead considerably influenced by different cooling rates and different solvents. A correlation was found between the supersaturation ratio at the average onset of

v nucleation and the viscosity of the solvent divided by the solubility of the solute. The trends suggest that an increased molecular mobility and a higher concentration of the solute reduce the metastable zone width of salicylamide.

Keywords: Salicylic acid, m-hydroxybenzoic acid, p-hydroxybenzoic acid, salicylamide, m-aminobenzoic acid, p-aminobenzoic acid, solubility, solid-liquid equilibria, thermodynamics, activity of the solid phase, ideal solubility, activity coefficient, van't Hoff enthalpy of solution, solid state, solution properties, metastable zone width, primary nucleation, nucleation kinetics.

v i Popular Scientific Summary

Compounds in nature exist as gases, liquids and solids. These states are separated by temperature and pressure. When the temperature of a liquid decreases at constant pressure, it forms a solid. As an example, ice forms on a lake on a cold winter day. When a solid is placed in contact with a liquid, the solid will start to dissolve into the liquid. This is something we see when we for example add sugar to a cup of coffee. As we continue to add a solid to the liquid the solid will at some point no longer dissolve into the liquid. The solution is then said to be saturated and the concentration of the saturated solution is called solubility. In science, we refer to this condition as a state of equilibrium between the solid and the solution. When the solid is in contact with a liquid we also often call the liquid a solvent. The solubility depends on several factors. When we change the solvent or the solid, the solubility will also change. However, we have an additional factor to consider when looking at the solid. The structure of the solid is sometimes different. The element carbon is for example found in nature in different solid forms such as graphite and diamond. These two forms, or phases, of course are very different and also have different solubility. In the pharmaceutical industry, the drug is often found in different solid forms. When we make a tablet of the drug and administer it to humans it will dissolve when it comes in contact with the fluids in the intestines. The drug then travels into the blood's circulatory system giving its purposed medical effect. Since the solid forms of the drug have different solubility they will also dissolve at different rates. This will affect the medical response of the drug, sometimes dramatically. It is therefore very important that we know what the different solid forms of the drug are and how fast they dissolve. When a drug has been discovered it is produced through a series of chemical reactions. To purify the drug from side-products it goes through several industrial purification and separation processes. One of the last and very important processes is the crystallization process. This is when the drug is formed in a solid form from a solution. Crystallization is almost like the opposite of dissolution. We can perform a crystallization process in different ways, but usually we saturate a solution at a certain temperature and then lower the temperature until the solid starts to appear in the form of crystals. Depending on how we perform the crystallization different solid forms of the crystals may appear. The shape and size of these crystals may also be very different. Just as the solubility is important when the drug is given to humans, the solubility is also the most important factor in the crystallization process. To be able to control a crystallization process we need to know the solubility of the different solid forms and how they are related to the solvent and temperature.

vii In this research project, six different solid compounds have been investigated together with up to nine different solvents at different temperature. In the first part of the project, we have looked at what different solid forms, or phases, are found among these compounds. We have found that two of the compounds only crystallize as one solid form, whereas the other four compounds crystallize in two to five different solid forms. The solubility of these different solid forms has been determined in different solvents from 10 to 50 oC. It soon became clear that the solubility of these solid forms is directly related to how solubility is dependent on temperature. This connection has not been explored much in the past. To understand why we see this relationship, we used thermodynamic theory, which describes how solubility is related to the properties of the solid and the properties of the solution. Although the science of this connection is interesting to explore we also obtain several practical applications that we can use as an aid in the crystallization process. We can for example more easily estimate how much of the drug is formed as solid depending on what solvent we use. We can also identify different solid forms just by looking at the solubility data. Since the relationship between the solubility and how it depends on temperature was so strong it was decided to investigate whether this connection is something that appears for organic compounds in general. In order to do that, we used a total of 41 different compounds and their solubility data in different solvents. We could verify this behavior and also construct a model that allows us to estimate what the solubility is at different temperature. In addition, it was observed that the solubility at different temperature was predictable to the extent that we could estimate the melting point of the solid. A common problem in the field of crystallization is not being able to measure how the properties of the solid and the properties of the solution affect the solubility. By using this connection and thermodynamic theory it was possible to separate these two properties from each other. This gave us a clearer picture of what is actually responsible for the value of the solubility for different solid forms and solvents. In the last part of this research project, the crystallization behavior was investigated for one of the compounds. As of today, the crystallization process is not thoroughly understood and the theory that is used is not always consistent with what is observed. In this study, we measured the temperature at which the crystals first began to be visible in the solution by slowly lowering the temperature of the solution. The experiments were performed to provide us with information on how the crystallization is affected by a) how fast we cool the solution, b) the temperature at which we saturate the solution, c) the volume of the solution and d) the type of solvent. It was found that the solvent and the cooling rate were the most important factors whereas temperature and solution volume posed a small effect. We also obtained different results even though the experiments were performed in exactly the same way. It is suggested from the data that the collision of molecules are responsible for when we see crystals start to form in the solution.

v iii List of papers

The thesis is based on the following papers, which are referred to by Roman numerals.

Main papers: I. Nordström, F.L.; Rasmuson, Å.C. (2006) Phase Equilibria and Thermodynamics of p-Hydroxybenzoic acid, J. Pharm. Sci., 95(4), 748-760.

II. Nordström, F.L.; Rasmuson, Å.C. (2006) Polymorphism and Thermodynamics of m-Hydroxybenzoic acid, Eur. J. Pharm. Sci., 28, 377- 384.

III. Nordström, F.L.; Rasmuson, Å.C. (2006) Solubility and Melting Properties of Salicylic acid, J. Chem. Eng. Data, 51, 1668-1671.

IV. Nordström, F.L.; Rasmuson, Å.C. (2006) Solubility and Melting Properties of Salicylamide, J. Chem. Eng. Data, 51, 1775-1777.

V. Nordström, F.L.; Rasmuson, Å.C. Determination of the Activity of the Solid of Molecular Compounds, in submission process.

VI. Nordström, F.L.; Rasmuson, Å.C. Prediction of Solubility Curves and Melting Properties of Organic and Pharmaceutical Compounds, in submission process.

VII. Nordström, F.L.; Rasmuson, Å.C. Metastable Zone Width of Salicylamide, manuscript.

Crystal structure determinations: VIII. Aziz, B.; Nordström, F.L.; Fischer, A. (2/1) p-Aminobenzoic acid-Acetone Solvate, manuscript.

IX. Fischer, A.; Nordström, F.L. (2/1) p-Hydroxybenzoic acid-1,4-Dioxane Solvate, manuscript.

ix Conference contributions (not included): X. Nordström, F.L.; Rasmuson, Å.C., (2005) Phase Equilibria and Thermodynamics of Hydroxybenzoic acid Isomers, Proceedings of the 16th International Symposium on Industrial Crystallization, Dresden, Germany.

XI. Nordström, F.L.; Rasmuson, Å.C. (2006) Metastable Zone Width of Salicylamide, 7th, Conference on Crystal growth of Organic Materials, Rouen, France.

XII. Nordström, F.L.; Rasmuson, Å.C. (2008) Thermodynamics and Prediction of Solubility, Oral Presentation at the Swedish Academy of Pharmaceutical Sciences, Lund, Sweden.

XIII. Nordström, F.L.; Rasmuson, Å.C. (2008) Primary Nucleation of Salicylamide, submitted to the Proceedings of the 17th International Symposium on Industrial Crystallization, Maastricht, The Netherlands.

Related work (not included): XIV. Nordström, F.L.; Rasmuson, Å.C.; Sheikh, A.Y. (2004) Analysis of Solution Nonideality of a Pseudomorphic Drug System through a Comprehensive Thermodynamic Framework for the Design of a Crystallization Process, J. Pharm. Sci., 93(4), 995-1004.

XV. Nordström, F.L. (2005) Technical Licentiate Thesis: Phase Equilibria and Thermodynamics of Hydroxybenzoic acid Isomers and Salicylamide, Royal Institute of Technology, ISSN 1104-3466.

x Notation

A Coefficient in regression equation of solubility AS Surface area of the nucleus m2 a Activity of the solid phase mol·mol-1 ai Activity of component i mol·mol-1 anucleus Activity of the nucleus mol·mol-1 asolute Activity of the solute mol·mol-1 solute -1 aeq Activity of the solute at equilibrium mol·mol B Coefficient in regression equation of solubility C Coefficient in regression equation of solubility c Activity coefficient constant Cm Concentration mol·m-3 Cp Isobaric heat capacity J·mol-1·K-1 L -1 -1 C p Isobaric heat capacity of the liquid J·mol ·K S -1 -1 C p Isobaric heat capacity of the solid J·mol ·K D Coefficient in regression equation of solubility d Activity coefficient constant K N ET Polarity G Gibbs free energy J·mol-1 H Enthalpy J·mol-1 HL(T) Enthalpy of the liquid at temperature T J·mol-1 HL(Tm) Enthalpy of the liquid at the melting J·mol-1 temperature HS(T) Enthalpy of the solid at temperature T J·mol-1 HS(Tm) Enthalpy of the solid at the melting J·mol-1 temperature J Nucleation rate No·s-1·m-3 Jo Pre-exponential factor in the nucleation No·s-1·m-3 rate K1 Solid-state property constant

K2 Solid-state property constant

K3 Solid-state property constant

xi K4 Solid-state property constant k1 Heat capacity constant of the solid J·mol-1·K-2 k2 Heat capacity constant of the solid J·mol-1·K-1 M Molar mass kg·mol-1 Nf Number of degrees of freedom n Number of moles mol nj Number of moles of substance j mol p Pressure Pa q Heat capacity constant J·mol-1·K-1 R Gas constant, 8.314 J·mol-1·K-1 r Heat capacity constant J·mol-1·K-2 rcrit Critical radius of nucleus m rnucleus Radius of nucleus m S Entropy J·mol-1·K-1 s Supersaturation ratio savg Supersaturation ratio at the average onset of nucleation sMZW Supersaturation ratio at the onset of nucleation T Temperature K Tbp Boiling temperature (boiling point) K Teq Saturation temperature K Texp Experimental temperature K Tm Melting temperature (melting point) K Tm,exp Experimentally determined melting K temperature Tm,pred Predicted melting temperature K Ttr Transition temperature K T1 Temperature at point 1 K T3 Temperature at point 3 K u Heat capacity constant J·mol-1·K-3 V Volume m3 Vm Molar volume m3·mol-1 Vsoln Solution volume m3 x Molar concentration mol·mol-1 xA Molar concentration of solvent A mol·mol-1

xii xB Molar concentration of solute B mol·mol-1 xeq Molar solubility (molar concentration at mol·mol-1 equilibrium) xeq,exp Experimental molar solubility mol·mol-1 xi Molar concentration of component i mol·mol-1 id -1 xeq Ideal solubility mol·mol x1 Molar concentration at point 1 mol·mol-1 x3 Molar concentration at point 3 mol·mol-1

α Regression curve coefficient β Regression curve coefficient γ Activity coefficient γA Activity coefficient of solvent A

γB Activity coefficient of solute B

γeq Activity coefficient at equilibrium

γi Activity coefficient of component i γsl Interfacial energy between the solid and J·m-2 the solution γ1 Activity coefficient of the solute at point 1 γ2 Activity coefficient of the solute at point 2 γ3 Activity coefficient of the solute at point 3 ΔCp Heat capacity difference between J·mol-1·K-1 the supercooled liquid and solid ΔCp(T) Heat capacity difference between J·mol-1·K-1 the supercooled liquid and solid at temperature T ΔCp(Tm) Heat capacity difference between J·mol-1·K-1 the supercooled liquid and solid at the melting temperature ΔGcrit Critical free energy of nucleus J ΔGf(T) Gibbs free energy of fusion at J·mol-1 temperature T ΔGf(Tm) Gibbs free energy of fusion at the J·mol-1 melting temperature ΔGmix Partial molar free energy of mixing J·mol-1

xiii ΔGnucleus Free energy change of growth of the J nucleus surface ΔGnucleus Excess free energy between the surface J of the nucleus and the bulk of the nucleus volume ΔGnucleus Volume excess free energy of the J nucleus ΔGsoln Gibbs free energy of solution J·mol-1 Δgmix Free energy of mixing J volume -3 Δg nucleus Volume excess free energy of the J·m nucleus per unit volume ΔHf(T) Enthalpy of fusion at temperature T J·mol-1

ΔHf(Tm) Enthalpy of fusion at the melting J·mol-1 temperature ΔHmix Partial molar enthalpy of mixing J·mol-1

ΔHSoln Enthalpy of solution J·mol-1 vH -1 ΔH So ln van’t Hoff enthalpy of solution J·mol ΔSf(T) Entropy of fusion at temperature T J·mol-1·K-1 ΔSf(Tm) Entropy of fusion at the melting J·mol-1·K-1 temperature ΔSmix Partial molar entropy of mixing J·mol-1·K-1 ΔT Degree of undercooling K ΔTavg Average degree of undercooling K ΔTmax Maximum degree of undercooling K ΔTmix Minimum degree of undercooling K Δx Concentration difference at the onset of mol·mol-1 nucleation Δµ Difference in chemical potential of the J·mol-1 solute ρ Density of the solid kg·m-3 ε Coefficient in solubility model η Viscosity Pa·s µ Chemical potential J·mol-1 µo Chemical potential at the reference state J·mol-1 µA Chemical potential of solvent A J·mol-1 S -1 µB Chemical potential of solid B J·mol solute -1 µB Chemical potential of solute B J·mol µi Chemical potential of component i J·mol-1

xi v µj Chemical potential of component j J·mol-1 µL Chemical potential of the pure liquid J·mol-1 µnucleus Chemical potential of the nucleus J·mol-1 µS Chemical potential of the pure solid J·mol-1 µsolute Chemical potential of the solute J·mol-1 solute µeq Chemical potential of the solute at J·mol-1 equilibrium σ Coefficient in solubility model φ Coefficient in solubility model φ* Coefficient in solubility model mol·mol-1 (normalized) χ2 Minimization parameter mol·mol-1

xv xvi Abbreviations, Acronyms and Expressions

ACN Acetonitrile Ansolvate Solid phase only comprising solute molecules ATR Attenuated Total Reflectance CSD Crystal size distribution DSC Differential Scanning Calorimetry Enantiotropy Polymorphs with a transition temperature below the melting temperature EtAc Ethyl acetate FCP Frequency of consistent predictions FTIR Fourier Transform InfraRed HAc Acetic acid Isomers Substances with the same molecular weight and functional group where the functional groups are situated in either ortho-, meta- or para-position MABA m-Aminobenzoic acid MeOH Methanol MHBA m-Hydroxybenzoic acid Monotropy Polymorphs with no transition temperature below the melting temperature OHBA o-Hydroxybenzoic acid PABA p-Aminobenzoic acid PHBA p-Hydroxybenzoic acid Polymorph Substance with ability to crystallize in more than one molecular structure 2-PrOH 2-Propanol RMS Residual mean square SA Salicylamide Solvate Solid phase incorporating solvent molecules in the crystal lattice Std. dev. Standard deviation XRD X-Ray Diffraction

xvii xviii Table of Contents

Abstract ...... v Popular Scientific Summary ...... vii List of papers...... ix Notation ...... xi Abbreviations, Acronyms and Expressions ...... xvii

1. Introduction...... 1 1.1 Scope ...... 2 1.2 Objectives...... 3 2. Theory...... 5 2.1 The Solid State...... 5 2.2 Thermodynamics of Solid-Liquid Equilibria...... 6 2.2.1 Fundamentals ...... 6 2.2.2 Fusion of the Solid Phase...... 7 2.2.3 Liquid-Liquid Mixing ...... 9 2.2.4 Solid-Liquid Equilibria...... 10 2.2.5 The Temperature Dependence of Solubility...... 12 2.2.6 Experimental Determination of Thermodynamic Parameters .....13 2.3 Development of a Semi-empirical Solubility Model ...... 17 2.3.1 Boundary Conditions ...... 17 2.3.2 Approximations ...... 18 2.3.3 Behavior of (∂lnγ/∂lnx)T in Solvents of Various Solubility...... 19 2.3.4 Solubility Model ...... 21 2.3.5 Influence of Temperature on Solubility...... 23 2.4 Extrapolation of Solubility Data...... 25 2.4.1 Theoretical Interpretation of RES...... 26 2.4.2 Prediction of Melting Temperature of the Solute...... 27 2.5 Determination of the Activity of the Solid Phase...... 28 2.5.1 Procedure ...... 29 2.6 Nucleation of the Solid Phase...... 31 2.6.1 The Classical Nucleation Theory ...... 31 2.6.2 The Metastable Zone Width...... 35 3. Experimental ...... 39 3.1 Materials...... 39 3.2 Identification of Crystal Phases and Crystal Morphology...... 41 3.3 Determination of Solid-State Properties ...... 41 3.4 Solubility ...... 42 3.5 Metastable Zone Width of Salicylamide...... 43

xix 4. Results...... 45 4.1 Crystal Phases and Crystal Morphology...... 45 4.2 Solid-State Properties of the Crystal Phases...... 51 4.3 Solubility ...... 53 4.4 Metastable Zone Width of Salicylamide...... 55 5. Evaluation and Discussion...... 59 5.1 Crystal Phases ...... 59 5.2 Experimental Relation between Solubility and the ...... Temperature Dependence of Solubility...... 60 5.2.1 Yield in Cooling Crystallization...... 61 5.2.2 Influence of Solubility on Enantiotropic Polymorphism ...... 62 5.2.3 Distinguishing Crystal Phases from Solubility Data ...... 64 5.3 Evaluation of the Semi-empirical Solubility Model...... 65 5.4 Prediction of Solubility Curves ...... 67 5.5 Experimental Evaluation of RES and Prediction of the ...... Melting Temperature of the Solute ...... 69 5.6 Experimental Determination of the Activity of the Solid Phase ...... 72 5.6.1 Evaluation of ΔCp...... 72 5.6.2 Evaluation of Solid-state Activity and Activity ...... Coefficients at Equilibrium...... 74 5.7 Influence of Solid-state and Solution Properties on Solubility...... 76 5.7.1 Influence of Solid-state Properties on Solubility...... 76 5.7.2 Influence of the Solution on Solubility...... 77 5.8 The Metastable Zone Width of Salicylamide...... 80 5.8.1 Saturation Temperature and MZW ...... 80 5.8.2 Relation between Cooling Rate and MZW ...... 81 5.8.3 Role of the Solvent...... 81 5.8.4 Effect of Solution Volume...... 84 5.8.5 Influence of Solvent Evaporation during Cooling ...... Crystallization ...... 85 5.8.6 Distribution in the MZW ...... 87 6. Conclusions...... 89 7. References...... 91 Acknowledgements...... 97 Appendix 1. Total Differentials with Temperature of the Activity, Concentration and Activity Coefficient at Equilibrium. Appendix 2. Solubility and Melting Properties of m-Aminobenzoic acid. Appendix 3. Thermodynamic Properties of p-Aminobenzoic acid. Appendix 4. Coefficients α and β of the Model Compounds.

xx 1. Introduction

A molecular compound exists in three general states, i.e. gas, liquid and solid. These states are separated by temperature and pressure. While the movement of molecules in a gas is random the molecular motion in liquids is more restricted. In the solid state the molecules are fixed. Unlike the gaseous and liquid state, the solid phase may differ in the structural arrangement of molecules. Solid phases can either be crystalline or amorphous or in some cases exhibit both crystalline and amorphous properties. A crystalline phase is comprised of an ordered arrangement of molecules that is repeated in three dimensions. Crystalline phases can be formed directly from a gas (reversed sublimation or deposition) or from a liquid (freezing). Crystals can also be formed from a solution. This process is called crystallization and is frequently employed in the industry, particularly in the pharmaceutical sector. Crystallization is used to separate and purify a product and can be invoked in four different ways, viz. cooling crystallization, evaporation crystallization, reaction crystallization and finally drowning-out crystallization. The crystals that are formed during a crystallization process may differ in shape, size and size distribution. Different crystalline phases may also appear for the same compound. Crystal phases are normally classified in two categories. A compound may crystallize as several so-called polymorphs in which the molecular structure differs. A well-known polymorphic compound is carbon, which in the solid state is found as both graphite and diamond. When a compound is crystallized from a solution it may also form a so-called solvate. A solvate is a crystalline phase in which the solvent molecules are incorporated into the crystal lattice. The properties of crystals differ, sometimes dramatically, depending on their shape, size and crystal structure. Controlling these properties is of utmost importance in the pharmaceutical industry as they affect the formulation and tableting processes and once administered to humans the dissolution rate and therapeutic response of the drug. Two vital parameters in crystallization are temperature and solvent. The solvent affects the solubility of the crystals, which constitutes the basis for any crystallization process. The solubility concentration and its dependence on temperature determine the yield of the process and the generation of supersaturation. Solubility reflects a thermodynamic equilibrium in which the chemical potential of the solute is equal to the chemical potential of the solid phase. Different crystal phases exhibit different equilibrium concentrations, commonly referred to as phase equilibria. The solvent also influences the rate of the crystallization, i.e. the kinetics of crystallization. Crystallization takes place in two steps, viz. by nucleation followed by growth of the crystals. Nucleation occurs at a certain level of supersaturation, which is directly related to the solvent. The number of nuclei formed during nucleation normally increases with increasing supersaturation. Hence, controlling the onset of nucleation enables control of the number of crystals that is obtained from the

1 crystallization process. When crystals have formed they start to grow and consume the supersaturation until equilibrium is established. The growth rate is different at different crystal surfaces, which results in the different shapes of crystals that we observe in nature. The solvent affects the growth rate of the different crystal surfaces and thus influences the final morphology of the crystals. As of today, the kinetics of crystallization is not clearly understood. But it is believed that the interfacial energy between the crystal surface and the solution governs the rate of nucleation, as well as, the rate of crystal growth. Finally, different crystal phases, i.e. polymorphs and solvates, can be formed from a crystallization process depending on what solvent is used. These crystal phases exhibit different degrees of stability, which is related to the temperature. Polymorphs can either be monotropic or enantiotropic, where the latter exhibits a transition in stability prior to the melting temperature while the former does not. Solvates may also shift in stability at different temperatures but are always solvent-specific. In contrast to unsolvated polymorphs, the crystal structure of solvates may collapse (and often does) after being brought from the solution. These polymorphic and solvated crystal phases all exhibit different solid-state properties, such as melting temperature, solubility and dissolution rate, which ultimately lead to different bioavailability of the drug.

1.1 Scope This Ph.D. project has been focused on the role of the solvent in the crystallization of organic compounds. Primarily four organic compounds have been investigated, viz. salicylic acid, m-hydroxybenzoic acid, p-hydroxybenzoic acid and salicylamide. In addition, two related compounds were explored, i.e. p-aminobenzoic acid and m- aminobenzoic acid. These model compounds are all structurally similar and comprise a benzene ring having two functional groups. Up to nine pure solvents were used in this project, of which eight are organic and one is water. Crystallization was predominately invoked by cooling crystallization at constant cooling rate. The influence of the solvent in crystallization was investigated experimentally by i) exploring the prevalence of crystal modifications for each compound and solvent, ii) establishing phase equilibria diagrams of these compounds in each solvent, and iii) study the onset of nucleation in different solvents. Furthermore, the solid-state and melting properties of the obtained crystal phases were determined experimentally. The results were analyzed using thermodynamic theory where the relationship between solubility, temperature dependence of solubility and melting properties of the solute was explored. The analysis is used to increase the understanding of how solubility curves emerge in different solvent and how they are related to the melting properties of the solute. Examples of applications are presented, which delineates the role of the solvent in the field of crystallization and may contribute to a reduction in the need for collection of experimental data.

2 A fundamental problem in the chemistry of solutions, and in crystallization, is to differentiate between the influence of the solvent and the influence of the solute on the properties of the non-ideal solution. This distinction is crucial when attempting to account for the sole role of the solvent in crystallization, in particular since essentially all solutions are non-ideal to more or less extent. In the literature, the solubility of the ideal solution has always been determined using approximations and simplifications, which inevitably leads to erroneous results and misconceptions regarding the influence of the solvent. Moreover, the driving force of nucleation has frequently been simplified to only account for cases where the properties of the non-ideal solution are assumed equal at equilibrium and in the supersaturated solution. In this project, the influence of the solvent was separated from the influence of the solute by employing a comprehensive thermodynamic framework using standard experimental data. The data is subsequently used to investigate the influence of the solvent in systems at equilibrium, i.e. for phase equilibria, and in systems at non-equilibrium conditions, e.g. during nucleation in solution.

1.2 Objectives The overall goal of this project is to investigate the role of the solvent in crystallization of organic molecular compounds. The specific aim of the project is to explore the influence of the solvent on i) the prevalence and type of crystal phases, ii) phase equilibria, and finally iii) nucleation from solution.

4 2. Theory

A molecular compound exists in three general physical states, i.e. solid, liquid and gas. Unlike liquids and gases, solid compounds may appear in different molecular structures. The dissolution of a solid into a liquid, or solvent, can be considered to appear in two steps, viz. fusion of the solid, followed by mixing with the solvent.

Solid ⎯Fusion⎯→⎯ Supercooled liquid ⎯Mixing⎯→⎯ Solute

At equilibrium and constant pressure, the concentration of the solution depends on the activity of the solid phase, the properties of the solvent and temperature. When the solution is not at equilibrium, the system will move towards equilibrium either through dissolution of the solid (undersaturated solution) or via nucleation of the solid (supersaturated solution).

2.1 The Solid State When molecules are arranged in a solid form, they can either be disordered, i.e. amorphous, or ordered, i.e. crystalline, or in some cases exhibit both amorphous and crystalline properties. The molecular structure of a crystalline compound may also differ. These different crystal structures are denoted as crystal phases and can be classified according to their molecular constituents. A crystal phase comprising only one molecular component is referred to as an ansolvate whereas crystal phases having more than one molecular component are denoted as co-crystals and solvates (occasionally also referred to as pseudo-polymorphs). A solvate incorporates solvent molecules into the crystal lattice. Several different crystal structures may sometimes appear of a compound having the same molecular constituents. This phenomenon is referred to as polymorphism. Even though polymorphism has been observed in solvates it is more frequently encountered for ansolvates. Polymorphs can either be monotropic or enantiotropic. Enantiotropic polymorphs exhibit a transition in stability below the melting temperature. Monotropic polymorphs do not shift in stability prior to the melting temperature. A scheme of the classification of solids is given in Figure 2.1.

Solid

Amorphous Crystalline

Solvate Ansolvate

Monotropic Enantiotropic polymorph polymorph

Figure 2.1. Classification of solid phases.

The chemical and physical properties of the different solid phases may vary, sometimes dramatically. Crystal phases of the same molecular component may e.g. exhibit different melting temperature, crystal morphology, crystal size, solubility, dissolution rate and even taste.

2.2 Thermodynamics of Solid-Liquid Equilibria

2.2.1 Fundamentals The free energy, G, at temperature T, is a function of enthalpy, H, and entropy, S:

⋅−= STHG (2.1)

The change in the free energy is described by the fundamental equation of chemical thermodynamics.

SdTVdpdG +−= ∑ μ dn jj (2.2) j

In a closed system where no work is added and the pressure remains constant the change in free energy with temperature is:

⎛ ∂G ⎞ ⎜ ⎟ −= S (2.3) ⎝ ∂T ⎠ ,np and from Eq. 2.1 we may derive the Gibbs-Helmholtz relation:

⎛ ∂ ⎛ G ⎞⎞ H ⎜ ⎟ −= ⎜ ⎜ ⎟⎟ 2 (2.4) ⎝ ∂T ⎝ T ⎠⎠ ,np T

The change in the corresponding enthalpy and entropy at constant pressure is given by the isobaric heat capacity, Cp:

⎛ ∂H ⎞ ⎜ ⎟ = CP (2.5) ⎝ ∂T ⎠ P

⎛ ∂S ⎞ C p ⎜ ⎟ = (2.6) ⎝ ∂T ⎠ P T

2.2.2 Fusion of the Solid Phase By using the supercooled liquid as the reference, the chemical potential of the solid, µS, is given as:

LS += ln aRTµµ (2.7) where µL is the chemical potential of the supercooled liquid, and a is the activity of the solid. The free energy of fusion (or melting) at temperature T, ΔGf(T) is:

f )( −=Δ µµTG SL (2.8)

The superscripts S and L represent henceforth the solid and (supercooled) liquid phase, respectively, and the superscript f denotes the fusion process. Thus, by Eq. 2.7 and 2.8 the activity of the solid phase can be expressed as:

− µµ LS Δ f TG )( ln a = −= (2.9) RT RT

The free energy of fusion at temperature T, ΔGf(T), is by Eq. 2.1 given as:

f f Δ⋅−Δ=Δ f TSTTHTG )()()( (2.10)

7 Hence:

Δ f TS Δ f TH )()( ln a = − (2.11) R RT where ΔSf(T) and ΔHf(T) represent the entropy and enthalpy of fusion, respectively. The enthalpy of fusion equals:

f L −=Δ S THTHTH )()()( (2.12) which by integration of Eq. 2.5 from the melting temperature, Tm, to temperature T at constant pressure affords:

T T f f )()( L −+Δ=Δ S dTCdTCTHTH m P ∫∫ P (2.13) Tm Tm

L S where C p and C p denote the heat capacity of the supercooled liquid and solid, respectively. Introducing

L S Pp −=Δ CCC P (2.14) gives:

T f f )()( Δ+Δ=Δ dTCTHTH m ∫ p (2.15) Tm

The corresponding equation of the entropy of fusion, ΔSf(T) at constant pressure is obtained via integration of Eq. 2.6:

T ΔC f f TSTS )()( +Δ=Δ p dT (2.16) m ∫ T Tm

By definition, at the melting temperature the chemical potential of the solid, µS, is equal to the chemical potential of the liquid (or melt), µL. Hence, at Tm the activity of the solid is unity and ΔGf(Tm) is zero, and by Eq. 2.11 we can write:

f f Δ TH m )( TS m )( =Δ (2.17) Tm

8 Thus, Eq. 2.10, 2.15, 2.16 and 2.17 give for the free energy of fusion at constant pressure:

T T f f ⎡ T ⎤ ΔC p Δ=Δ THTG m ⎢1)()( − ⎥ p −Δ+ TdTC dT (2.18) T ∫∫ T ⎣ m ⎦ Tm Tm and the activity of the solid phase at constant pressure is obtained from Eq. 2.9 and 2.18:

f T T Δ TH m )( ⎡ ⎤ 111 1 ΔC p ln a = ⎢ − ⎥ p dTC +Δ− dT (2.19) RTTTR R ∫∫ T ⎣ m ⎦ Tm Tm

The relationship between the thermodynamic parameters ΔGf(T), ΔHf(T) and T·ΔSf(T) and temperature is illustrated in Figure 2.2.

T·ΔSf(T)

Energy ΔHf(T)

f ΔH (T=0)

Tm T

f ΔG (T)

Figure 2.2. Illustration of the relationship between ΔGf(T), ΔHf(T) and T·ΔSf(T) and temperature.

2.2.3 Liquid-Liquid Mixing By using the pure liquid as the reference, the chemical potential of component i in a liquid mixture is:

L ii += ln aRTµµ i (2.20) where the activity of component i is given by:

9 = γ xa iii (2.21) and γi represents the activity coefficient and xi the molar concentration of component i. According to Euler's theorem, the free energy of mixing at constant temperature and pressure for a two-component system, Δg mix (J), can be expressed as:

⎛ Δ∂ g ⎞ ⎛ Δ∂ g ⎞ =Δ ng ⎜ mix ⎟ + n ⎜ mix ⎟ (2.22) imix ⎜ ∂n ⎟ j ⎜ ∂n ⎟ ⎝ i ⎠ n j j ⎝ ⎠ ni

If nj is constant then the partial molar free energy of mixing of component i, ΔGmix (J/mol), equals:

mix =Δ γxRTG )ln( (2.23)

(Prausnitz et al., 1999). By differentiation of Eq. 2.23 via the Gibbs-Helmholtz relation (Eq. 2.4) we obtain at constant pressure and concentration:

2 ⎛ ∂ lnγ ⎞ mix −=Δ RTH ⎜ ⎟ (2.24) ⎝ ∂T ⎠ x where ΔHmix is the partial molar enthalpy of mixing. The corresponding partial molar entropy of mixing, ΔSmix, is obtained through Eq. 2.1, 2.23 and 2.24:

⎛ ∂ lnγ ⎞ mix γ )ln( −−=Δ RTxRS ⎜ ⎟ (2.25) ⎝ ∂T ⎠ x

For an ideal liquid mixture the activity coefficient is unity and the partial molar enthalpy of mixing is zero.

2.2.4 Solid-Liquid Equilibria If the supercooled liquid is used as the reference (Raoult's law reference) the chemical potential of the solid is equal to the chemical potential of the solute at equilibrium. Hence, the activity of the solid is equal to the activity of the solute at solute equilibrium, aeq , and:

solute eq == γ xaa eqeq (2.26) where γeq and xeq represent the activity coefficient and molar concentration of the solute at equilibrium.

10 The free energy change associated with fusion of the solid and mixing with the solvent at equilibrium is henceforth denoted as the free energy of solution, ΔGSoln, and is given by:

f So ln Δ+Δ=Δ GGG mix (2.27) which by e.g. Eq. 2.9, 2.23 and 2.26 affords:

GSo ln =Δ 0 (2.28)

In Figure 2.3 is depicted the free energy change associated with the fusion of the solid and mixing with the solvent at equilibrium.

Chemical potential

µL Supercooled liquid

ΔGf ΔG Fusion mix Mixing

S solute ΔGSoln µ = µ Solid phase Solute at equilibrium

Figure 2.3. Change in free energy at constant temperature upon moving from a pure solid phase to a supercooled liquid to a solute at equilibrium.

The enthalpy of solution, ΔHsoln, is obtained by combining Eq. 2.15 and 2.24:

T ⎛ ∂ lnγ ⎞ f f )( −Δ+Δ=Δ+Δ=Δ RTdTCTHHHH 2 ⎜ ⎟ (2.29) So ln mix m ∫ p ∂T Tm ⎝ ⎠ x and the entropy of solution, ΔSsoln, is (from Eq. 2.16 and 2.25):

T ΔC p ⎛ ∂ lnγ ⎞ f f TSSSS )( +Δ=Δ+Δ=Δ − γ )ln( − RTxRdT ⎜ ⎟ (2.30) So ln mix m ∫ T eqeq ∂T Tm ⎝ ⎠ x

The solubility of the solute, xeq, can be derived from Eq. 2.19 and 2.26:

11 f T T Δ TH m )( ⎡ ⎤ 111 1 ΔC p xeq lnln γ eq +−= ⎢ − ⎥ p dTC +Δ− dT (2.31) RTTTR R ∫∫ T ⎣ m ⎦ Tm Tm

2.2.5 The Temperature Dependence of Solubility An expression of the temperature dependence of solubility can be obtained by allowing the activity of the solute in the solution to be a function of temperature and concentration. ln solute = xTfa )ln,( (2.32)

The total differential of the activity of the solute is then:

solute solute solute ⎛ ∂ ln a ⎞ ⎛ ∂ ln a ⎞ ln ad = ⎜ ⎟ dT + ⎜ ⎟ ln xd (2.33) ⎝ ∂T ⎠ x ⎝ ∂ ln x ⎠T which when divided by dT at equilibrium yields:

⎛ ∂ ln a solute ⎞ ⎛ ∂ ln a solute ⎞ ⎛ ∂ ln a solute ⎞ ⎛ ∂ ln x ⎞ ⎜ ⎟ = ⎜ ⎟ + ⎜ ⎟ ⎜ ⎟ (2.34) ⎝ ∂T ⎠eq ⎝ ∂T ⎠ x ⎝ ∂ ln x ⎠T ⎝ ∂T ⎠eq

By Eq. 2.26 we derive:

⎛ ∂ ln a ⎞ ⎛ ∂ lnγ ⎞ ⎡ ⎛ ∂ lnγ ⎞ ⎤⎛ ∂ ln x ⎞ ⎜ ⎟ = ⎜ ⎟ ⎢1++ ⎜ ⎟ ⎥⎜ ⎟ (2.35) ⎝ ∂ ⎠ ⎝ ∂TT ⎠ x ⎣ ⎝ ∂ ln x ⎠T ⎦⎝ ∂T ⎠eq

By combining Eq. 2.4 and 2.9 we can identify the first partial derivative in Eq. 2.35:

⎛ ∂ ln a ⎞ Δ f TH )( ⎜ ⎟ = (2.36) ⎝ ∂T ⎠ RT 2

The second partial derivative in Eq. 2.35 corresponds to -ΔHmix/RT2 (Eq. 2.24), and the third partial derivative is according to the Gibbs-Duhem equation for a binary system equal for the solute (B) and solvent (A) at constant pressure and temperature:

⎛ ∂ lnγ ⎞ ⎛ ∂ lnγ B ⎞ ⎛ ∂ lnγ A ⎞ ⎜ ⎟ = ⎜ ⎟ = ⎜ ⎟ (2.37) ⎝ ∂ ln x ⎠T ⎝ ∂ ln xB ⎠T ⎝ ∂ ln x A ⎠T

12 The last partial derivative in Eq. 2.35 describes the change in solubility of the solute with temperature and can be expressed with an enthalpic term, denoted as the van’t vH 1 Hoff enthalpy of solution, ΔH So ln :

vH ⎛ ∂ ln x ⎞ ΔH So ln ⎜ ⎟ = 2 (2.38) ⎝ ∂T ⎠eq RT

The van't Hoff enthalpy of solution can be determined from the slope of the solubility curve in a so-called van't Hoff plot by plotting lnxeq versus the reciprocal of the absolute temperature. Combining Eq. 2.35, 2.36 and 2.38 yields:

⎡ ⎤ ⎡ ⎤ ⎢ ⎥ vH f 2 ⎛ ∂ lnγ ⎞ ⎢ 1 ⎥ So ln ⎢ )( −Δ=Δ RTTHH ⎜ ⎟ ⎥ ⋅ (2.39) ⎣ ⎝ ∂T ⎠ x ⎦ ⎢ ⎛ ∂ lnγ ⎞ ⎥ ⎢1+ ⎜ ⎟ ⎥ ⎣ ⎝ ∂ ln x ⎠T ⎦

The van't Hoff enthalpy of solution can also be expressed in different forms (relationships are given in appendix 1). Another form is obtained by combining Eq. 2.26, 2.36 and 2.38:

vH f 2 ⎛ ∂ lnγ ⎞ So ln )( −Δ=Δ RTTHH ⎜ ⎟ (2.40) ⎝ ∂T ⎠eq

vH f For an ideal solution (when γeq is unity at all temperatures) So ln Δ=Δ THH )( .

2.2.6 Experimental Determination of Thermodynamic Parameters Experimental determination of the thermodynamic parameters that are used to determine the fusion of solids and the activity of the solid phase (Eq. 2.19) can essentially only be carried out at the melting temperature. The melting temperature and enthalpy of fusion at the melting temperature can usually be determined using e.g. thermal analysis, such as Differential Scanning Calorimetry, DSC. However, polymorphism and solvation of crystal phases may prevent direct measurements. Polymorphic crystal phases may be, or become metastable at elevated temperature, resulting in a transformation into other crystalline modifications prior to the melting temperature. Solvated crystal structures are typically only stable in solution or in an atmosphere that is nearly saturated by the same solvent component that is incorporated in the solvated crystal lattice. As these solvated crystals are brought out

1 The denotation "van't Hoff enthalpy of solution" is used since this enthalpic term can be obtained from solubility data in a van't Hoff plot. It is normally not equal to the enthalpy of solution, as pointed out by Hollenbeck (1980).

13 from these environments the crystal structure may start to collapse and transform into an unsolvated crystal phase. The solid compound may also be sensitive to higher temperatures and decompose or sublime before reaching the melting temperature. A comparably greater difficulty emerges with the experimental determination of the difference in heat capacity between the liquid and solid. The heat capacity of the solid can in practice only be determined below the melting temperature whereas the heat capacity of the liquid can essentially only be determined above the melting temperature. The approach to avoid this problem has in the literature been to introduce approximations of ΔCp. The greatest simplification has been to assume that ΔCp can be neglected all together. In that case, the activity of the solid is reduced to:

f Δ TH m )( ⎡ 11 ⎤ ln a = ⎢ − ⎥ (2.41) ⎣ m TTR ⎦

Another approximation has been suggested by Hildebrand et al., 1970, stating that the ΔCp can be assumed equal to ΔSf(Tm) at all temperatures, giving for the activity of the solid:

f Δ TH m )( ⎛ T ⎞ ln a = ln⎜ ⎟ (2.42) RTm ⎝ Tm ⎠

The estimation of the activity of the solid can be improved when experimental data is available of the heat capacity of the solid and liquid phases. In Figure 2.4 is shown an illustration of two approaches in the estimation of ΔCp.

L CP b

ΔCP(Tm) a ΔCP(T) Heat capacity C S P

T Tm Temperature

Figure 2.4. Illustration of the approximations of ΔCp from experimental data of the heat capacity of the solid and liquid phases.

The first approximation assumes that ΔCp is constant and equal to ΔCp at the melting temperature, ΔCp(Tm) (line a in Figure 2.4), in which case we derive for the activity of the solid:

f Δ TH m )( ⎡ 11 ⎤ Δ TC mp )( ⎡ ⎛ T ⎞ Tm ⎤ ln a = ⎢ − ⎥ + ⎢ln⎜ ⎟ −+ 1⎥ (2.43) ⎣ m TTR ⎦ R ⎣ ⎝ Tm ⎠ T ⎦

L The second approximation is based on an extrapolation of CP down to temperature T (curve b in Figure 2.4). The expression of the activity of the solid phase then depends on how ΔCp is described as a function of temperature. The determination of ΔCp is crucial in obtaining accurate data of the activity of the solid and in the determination of the thermodynamic parameters describing fusion of the solid. Frequently in the literature, the importance of the ΔCp terms has been neglected, which in turn may lead to serious errors in the value of the activity of the solid phase. Moreover, in solid-liquid equilibria the activity coefficient of the solute at equilibrium is normally calculated from the activity of the solid phase and solubility data (Eq. 2.26). The introduction of errors in the activity of the solid leads to errors in the activity coefficient of the solute and thus reduces the understanding of how the solvent influences the solubility of solid compounds. Experimental determination of the thermodynamic parameters involved in non- ideal liquid-liquid mixing is also fraught with difficulties. For a real non-ideal solution the activity coefficient and the change in the activity coefficient with temperature at constant concentration must be accounted for. There are several types of theories in the literature that deal with non-ideal behavior of solutions. These theories are theoretical, semi-empirical and empirical and listed as e.g. the Wohl's expansion, the

15 equations by Margules, van Laar and Wilson, and the NRTL, UNIQUAC and UNIFAC equations. These expressions typically require several interaction parameters at constant temperature between the involving components. Two additional theories, viz. the theory of regular solutions and the theory of athermal solutions, have been derived based on theoretical simplifications and are comparably more straightforward. Scatchard and Hildebrand have independently of each other developed a theory based on a simplification of the van Laar's theory, commonly referred to as the regular solution theory (Prausnitz et al., 1999). This theory regards the non-ideal contribution to the mixing of liquids as only stemming from a change in enthalpy, i.e. the excess entropy of mixing is zero. This assumption leads to:

mix =Δ RTH lnγ (2.44)

mix −=Δ ln xRS (2.45)

The regular solution theory can only account for non-ideal behavior when the activity coefficient exceeds unity (Prausnitz et al., 1999) and is typically expected for mixing of liquids of similar molecular size (Klotz and Rosenberg, 2000). The regular solution approximation has been shown to provide a reasonable representation of the activity coefficients for a solution containing non-polar components, in particular at greater positive deviations from Raoult's law (Prausnitz et al., 1999). Another theory of non-ideal solution was developed by Flory and Huggins and assumes that the non-ideal contribution during mixing of liquids is only present in the entropic term. Since this assumption implicates that the enthalpy of mixing is zero (i.e. the activity coefficient is constant with temperature at constant concentration), these solutions are often referred to as athermal. Using this approximation, the entropy of mixing of one component becomes:

mix −=Δ γxRS )ln( (2.46)

The Flory-Huggins theory is frequently applied to polymer solutions in which the chemical characteristics of the involving components normally are similar. A general empirical equation of the change in the activity coefficient with temperature at constant concentration has been given by Prausnitz et al., 1999,

d lnγ c += (2.47) T where c and d are empirical constants at constant concentration. A regular solution is then obtained when c = 0, and an athermal solution is obtained when d = 0.

16 2.3 Development of a Semi-empirical Solubility Model The general behavior of solubility curves at all solubility concentrations can be explored by investigating the thermodynamic parameters comprising the equation describing solubility (Eq. 2.31) and the equation describing the temperature dependence of solubility (e.g. Eq. 2.39).

2.3.1 Boundary Conditions The melting temperature of the solute constitutes a boundary condition of Eq. 2.31 and 2.39. At this point the chemical potential of the solid is equal to the chemical potential of the liquid and we can via Eq. 2.9 establish that:

SL µµ −==− m ln0 aRT (2.48) implicating that the activity of the solid is unity at the melting temperature. When the activity approaches unity the activity coefficient also approaches unity (asymptotically), according to a Raoult's law behavior. Hence, at the melting temperature:

xeq = 1 (2.49)

Thus, regardless of solvent, all solubility curves intersect at the melting temperature of the solute. From Eq. 2.39 we can also establish at the melting temperature:

vH f So ln Δ=Δ THH m )( (2.50)

Ergo, all solubility curves, irrespective of solvent, exhibit the same slope at the melting temperature, the value of which is directly dependent on the melting enthalpy of the solute. Another boundary condition appears in the region where Henry's law applies, i.e. at very dilute concentration of the solute. At constant temperature, when the concentration of the solute approaches zero the activity coefficient is constant with concentration. Hence,

⎛ ∂ lnγ ⎞ ⎜ ⎟ = 0 (2.51) ⎝ ∂ ln x ⎠ xT →0, and by Eq. 2.39 and 2.40:

⎛ ∂ lnγ ⎞ ⎛ ∂ lnγ ⎞ ⎜ ⎟ = ⎜ ⎟ (2.52) ⎝ ∂T ⎠ x ⎝ ∂T ⎠eq

17 which through Eq. 2.29 and 2.39 shows that:

vH So ln Δ=Δ HH So ln (2.53) in the Henry's law region. In addition, since solubility, with very few exceptions2, increases with increasing temperature, we further expect that:

vH H So ln ≥Δ 0 (2.54)

2.3.2 Approximations At constant temperature, the activity and enthalpy of fusion of the solid phase are invariant. Hence, the thermodynamic parameters responsible for a change in lnxeq vH and ΔH So ln are only found in the terms describing the influence of the solvent. These thermodynamic parameters are lnγeq (in Eq. 2.31) and the partial derivatives vH (∂lnγ/∂T)x and (∂lnγ/∂lnx)T (in Eq. 2.39), or alternatively (∂lnγ/∂T)eq when ΔH So ln is given by Eq. 2.40. When the temperature changes the solution properties and the solid-state properties change. The activity of the solid phase and the enthalpy of fusion are both based on the integral terms of ΔCp. Of all the thermodynamic parameters describing solubility curves (Eq. 2.31 and 2.39), only the melting temperature and the melting enthalpy are normally experimentally accessible (it is however possible to determine γeq, (∂lnγ/∂T)eq and ΔCp using the approach outlined in section 2.5). In the development of a semi-empirical model of how solubility relates to temperature, it is therefore necessary to introduce approximations. When no data of the heat capacity of the solid and liquid forms of the solute are available it has been suggested by Hildebrand, 1970, and shown by Neau et al., 1997, that a better approximation is made if ΔCp is assumed constant and equal to the entropy of fusion at the melting temperature, ΔSf(Tm). In this model we insert an empirical coefficient, σ:

f p σ Δ⋅≈Δ TSC m )( (2.55) and allow σ to be general regression coefficient equal for all solutes. The change in the activity coefficient, γ, with temperature at constant concentration, (∂lnγ/∂T)x, can be simplified according to the regular solution theory (Eq. 2.24 and 2.44), giving at equilibrium:

2 A decreasing solubility with increasing temperature can according to Eq. 2.39 only occur when f ΔHmix>ΔH (T).

18 ⎛ ∂ lnγ ⎞ lnγ eq ⎜ ⎟ −= (2.56) ⎝ ∂T ⎠ x T

Inserting Eq. 2.31, 2.55 and 2.56 in Eq. 2.39 affords:

⎛ ⎞ ⎜ ⎟ ⎡ ⎤ vH f T ⎛ ⎛ T ⎞⎞ ⎜ 1 ⎟ ⎢Δ=Δ THH ⎜ + σ ln1)( ⎜ ⎟⎟ − ln xRT ⎥ (2.57) So ln m T ⎜ ⎜ T ⎟⎟ eq ⎜ ∂ lnγ ⎟ ⎣⎢ m ⎝ ⎝ m ⎠⎠ ⎦⎥ ⎛ ⎞ ⎜1+ ⎜ ⎟ ⎟ ⎝ ⎝ ∂ ln x ⎠T ⎠

The last term in Eq. 2.57, i.e. the change in the activity coefficient with concentration at constant temperature, (∂lnγ/∂lnx)T, can be estimated by considering solvents of different solubility.

2.3.3 Behavior of (∂lnγ/∂lnx)T in Solvents of Various Solubility At constant temperature, the activity coefficient is constant with concentration at very low concentration (Henry's law region) and approaches Raoult's law when the molar concentration approaches unity. To account for how (∂lnγ/∂lnx)T changes for a solute in different solvent a schematic representation of lnγ versus lnx is given in Figure 2.5.

Henry’s law region lnγ

E lna

D γ > 1

Raoult’s law, γ=1 C (0,0) lnx

γ < 1

lnγeq = lna

Figure 2.5. Illustration of how the activity coefficient changes with concentration at constant temperature. The solid curves correspond to different solvents displaying positive and negative deviations from Raoult's law. The dashed line represents the boundary of Henry's law, and the dot- dashed line depicts the activity of the solid phase.

Inserted in Figure 2.5 is also the activity of the solid phase, which is constant at constant temperature. Since lnγeq = lna - lnxeq (Eq. 2.26), a line with the slope -1 is obtained in Figure 2.5 (dot-dashed line). At equilibrium, the activity of the solid phase is equal to the activity of solute and hence along this line the solutions are saturated. The partial derivative (∂lnγ/∂lnx)T of saturated solutions is obtained from the slope of the solid curves in Figure 2.5 at the intersection with the line representing the activity of the solid phase. To describe how (∂lnγ/∂lnx)T is related to solubility five points are inserted in Figure 2.5 (A, B, C, D and E) representing different solubility concentrations. Starting in the right side in Figure 2.5 (high solubility) and moving left (to low solubility): When xeq is unity it follows that (∂lnγ/∂lnx)T is infinite. At point A, (∂lnγ/∂lnx)T is a positive finite value. When the solubility decreases (∂lnγ/∂lnx)T also decreases but still is a positive finite value (point B). When the solution is ideal (point C) then (∂lnγ/∂lnx)T is zero. At positive deviations from Raoult's law (point D), i.e. γeq > 1, (∂lnγ/∂lnx)T exhibits a negative finite value. When the solubility concentration reaches Henry's law region (point E) the (∂lnγ/∂lnx)T is again zero. Thus, we can conclude for the partial derivative (∂lnγ/∂lnx)T:

20 • lnxeq → 0 ⇒ (∂lnγ/∂lnx)T → ∞ • lnxeq > lna ⇒ (∂lnγ/∂lnx)T > 0 • lnxeq = lna ⇒ (∂lnγ/∂lnx)T = 0 • lnxeq < lna ⇒ (∂lnγ/∂lnx)T < 0 • lnxeq in Henry's law region ⇒ (∂lnγ/∂lnx)T = 0

The corresponding behavior of the last term in Eq. 2.57, i.e. 1/(1 + (∂lnγ/∂lnx)T), is depicted in Figure 2.6.

−1 Raoult’s law, γeq = 1 ⎛ ⎛ ∂ lnγ ⎞ ⎞ ⎜1+ ⎜ ⎟ ⎟ ⎜ ⎟ D ⎝ ⎝ ∂ ln x ⎠T ⎠

1 C E Henry’s law region B

A 0

0 1 lnx /lna eq

Figure 2.6. Expected behavior of the term 1/(1 + (∂lnγ/∂lnx)T) at different solubility concentrations. The solubility is normalized with respect to the activity of the solid state.

By normalizing lnxeq on lna, different solutes are expected to fall on the same curve. It can be deduced from the previously stated condition of lnxeq → 0 ⇒ (∂lnγ/∂lnx)T vH → ∞ (and Figure 2.6), that the ΔH So ln approaches zero as xeq approaches unity.

2.3.4 Solubility Model In the development of how the temperature dependence of solubility is related to solubility we assume that the curve between point A and C (at negative deviations from Raoult's law) is a linear function of lnxeq/lna. Hence,

1 ⎛ ln x ⎞ ln xeq = ⎜ ⎟ ≈ (2.58) ⎛ ∂ lnγ ⎞ ⎝ ln a ⎠ ln a 1+ ⎜ ⎟ T ⎝ ∂ ln x ⎠T

21 so that the condition (∂lnγ/∂lnx)T → ∞ when lnxeq → 0 is fulfilled. For positive deviations from Raoult's law we employ the mathematic function

⎡ 2 ⎤ 1 ⎛ ∂ ln x ⎞ ⎛ ln xeq ⎞ ⎛ ln xeq ⎞ = ⎜ ⎟ ε⎜ −≈ ⎟ exp1 ⎢ ϕ⎜ −−⋅ ⎟ ⎥ +11 (2.59) ⎛ ∂ lnγ ⎞ ⎝ ∂ ln a ⎠ ln a ⎢ ln a ⎥ 1+ ⎜ ⎟ T ⎝ ⎠ ⎣ ⎝ ⎠ ⎦ ⎝ ∂ ln x ⎠T to describe how (∂lnγ/∂lnx)T is related to solubility. The coefficients ε and φ describe the height and width, respectively, of the peak in Figure 2.6. The height of the peak (point D) in Figure 2.6 is dependent on the activity of the solid. This can be seen from Figure 2.5, where a lower activity of the solid (the dot-dashed line is moved left in the diagram) results in a smaller peak. Should the activity of the solid be low enough so that γeq ≤ 1 in Henry’s law region, then the peak disappears all together. For this situation to appear, however, requires that the activity of the solid is exceptionally low, which is not frequently encountered for organic molecular compounds. To compensate for the effect of different activity of the solid on the coefficient φ, we introduce a normalized coefficient:

ϕ ϕ ⋅−= ln* a (2.60) giving for positive deviations from Raoult's law:

⎡ 2 ⎤ 1 ⎛ ∂ ln x ⎞ ⎛ ln xeq ⎞ ⎛ ln xeq ⎞ = ⎜ ⎟ ε⎜ −≈ ⎟ ⎢ϕ ⋅⋅ ln*exp1 a⎜ − ⎟ ⎥ +11 (2.61) ⎛ ∂ lnγ ⎞ ⎝ ∂ ln a ⎠ ln a ⎢ ln a ⎥ 1+ ⎜ ⎟ T ⎝ ⎠ ⎣ ⎝ ⎠ ⎦ ⎝ ∂ ln x ⎠T

Thus, we summarize for negative deviations from Raoult's law:

⎡ T ⎛ ⎛ T ⎞⎞ ⎤ ln xeq vH ⎢ f THH ⎜ +⋅Δ=Δ σ ln1)( ⎜ ⎟⎟ − ln xRT ⎥ (2.62) So ln m T ⎜ ⎜ T ⎟⎟ eq ln a ⎣⎢ m ⎝ ⎝ m ⎠⎠ ⎦⎥ and for positive deviations from Raoult’s law:

⎡ ⎡ 2 ⎤ ⎤ ⎡ T ⎛ ⎛ T ⎞⎞ ⎤ ⎛ ln xeq ⎞ ⎛ ln xeq ⎞ vH ⎢ f THH ⎜ +⋅Δ=Δ σ ln1)( ⎜ ⎟⎟ − ln xRT ⎥ ⎢ε⎜ −⋅ ⎟ ⎢ϕ ⋅⋅ ln*exp1 a⎜ − ⎟ ⎥ +11 ⎥ So ln m T ⎜ ⎜ T ⎟⎟ eq ⎢ ⎜ ln a ⎟ ⎜ ln a ⎟ ⎥ ⎣⎢ m ⎝ ⎝ m ⎠⎠ ⎦⎥ ⎣ ⎝ ⎠ ⎣⎢ ⎝ ⎠ ⎦⎥ ⎦ (2.63) where lna is obtained from Eq. 2.31 and 2.55:

22 f Δ TH m )( ⎡ − 11 − σσσ ⎛ T ⎞⎤ ln a = ⎢ − + ln⎜ ⎟⎥ (2.64) ⎣ m TTTR m ⎝ Tm ⎠⎦

Eq. 2.62 and 2.63 describe the temperature dependence of solubility at constant temperature. As the temperature approaches the melting temperature all solubility curves approach xeq = 1 (section 2.3.1) and thus we can expect that the terms representing the non-ideal solution properties are reduced (i.e. approaches a Raoult's law behavior) as we approach the melting temperature. Based on the expected behavior of solubility curves in real solvents at different concentration and temperature, a generalized van't Hoff plot is depicted in Figure 2.7 for an arbitrary crystalline organic compound.

1/Tm 1/T 0 γ < 1 eq

Id eal s olut ion, Rao ult’ s law

γeq > 1

ln(x ) Henry’s law region eq

Figure 2.7. Illustration of a generalized van't Hoff plot of an arbitrary organic solute in several solvents.

2.3.5 Influence of Temperature on Solubility Figure 2.7 indicates that the solubility of a solute is related to the temperature dependence of solubility. A lower molar solubility corresponds to a greater dependence on temperature and thus to a greater van't Hoff enthalpy of solution. We may explore this relation based on the equations given above. In the Henry's law region (∂lnγ/∂lnx)T is zero and the van't Hoff enthalpy of solution is given by Eq. 2.53. The regular solution theory states that (∂lnγ/∂T)x is given by the approximate form -lnγeq/T (Eq. 2.56). In this case, the van't Hoff enthalpy of solution is via Eq. 2.26 reduced to:

23 T vH f )( +−Δ+Δ=Δ lnln xRTaRTdTCTHH So ln m ∫ p eq (2.65) Tm

Thus, at constant temperature we obtain the following relationship between the temperature dependence of solubility (i.e. the van't Hoff enthalpy of solution) and molar solubility:

vH H So ln α +=Δ ln xRT eq (2.66) where α is a constant drawn from the solid-state properties of the solute. Hence, for regular solutions in the Henry's law region we expect that the temperature dependence of solubility is linearly related to the molar solubility, at constant temperature. When the solubility curve is not in the Henry's law region the analysis becomes more complex. Our starting point is Eq. 2.62, which in the solubility curve model is used for negative deviations from Raoult's law. This equation is based on the approximation that (∂lnx/∂lna)T is equal to lnxeq/lna (Eq. 2.58). Hence, at constant temperature we can infer:

vH 2 H So ln =Δ α()ln xeq + β ln xeq (2.67) where α and β are constants referring to the solid-state properties of the solute. Combining Eq. 2.66 and 2.67 in their respective concentration regions for a solid vH phase results in the relation between ΔH So ln and lnxeq, as depicted in Figure 2.8.

Henry’s law

[kJ/mol]

Raoult’s law

0 ln(xeq) [mol/mol] 0 Figure 2.8. Expected relation between the temperature dependence of solubility (van't Hoff enthalpy of solution) and molar solubility, at constant temperature for a solute in different regular solutions. The orange curve is based on Eq. 2.62 (negative deviations from Raoult's law) and the green curve is based on Eq. 2.63 (positive deviations from Raoult's law). The grey circle represents the activity of the solid phase (Raoult's law).

2.4 Extrapolation of Solubility Data When solubility data has been determined experimentally in one solvent at different temperatures, it is convenient to use a regression equation of solubility, RES. The RES coefficients are fitted to the solubility data in order to enable determination of the solubility at different temperatures, through interpolation or extrapolation. In the literature, the mathematical form of the RES is often arbitrarily selected but normally based on the fit of the RES to the experimental solubility. However, the RES also conveys information of the thermodynamic properties of the solid phase and the solution. As is illustrated in Figure 2.7, the temperature exerts different influences on solubility in different concentration regions. This in turn affects the selection of a suitable RES. In order to explore the relationship between solubility data and thermodynamic properties a total of 15 different empirical RES have been investigated. These RES comprise two to four RES coefficients and are of different mathematical form. Each RES can through Eq. 2.38 be derived to express the corresponding van't Hoff enthalpy of solution. In Table 2.1 is listed the 15 RES and the associated van't Hoff enthalpy of solution.

Table 2.1. Investigated RES. A, B, C and D are RES coefficients and T is given in K. vH Category RES lnxeq Δ So ln / RH A A1 AT-1 + B -A A2 A + BT BT2 A3 A + Bln(T) BT B B1 AT-2 + BT-1 + C -2AT-1 - B B2 AT-1 + B + CT -A + CT2 B3 A + BT + CT2 BT2 + 2CT3 B4 AT-2 + B + CT2 -2AT-1 + 2CT3 C C1 AT-2 + BT-1 + Cln(T) -2AT-1 – B + CT C2 AT-1 + B + Cln(T) -A + CT C3 A + BT + Cln(T) BT2 + CT C4 AT + BT2 + Cln(T) AT2 + 2BT3 + CT D D1 AT-2 + BT-1 + C + DT -2AT-1 – B + DT2 D2 AT-1 + B + CT + DT2 -A + CT2 + 2DT3 D3 AT-2 + BT-1 + C + Dln(T) -2AT-1 – B + DT D4 AT-1 + B + CT + Dln(T) -A + CT2 + DT

2.4.1 Theoretical Interpretation of RES From Table 2.1 it is seen that the selection of RES directly implicates a certain relationship between the van't Hoff enthalpy of solution and temperature. RES A1 vH for example assumes that ΔH So ln is constant with temperature (corresponds to a linear regression of solubility data in a van't Hoff plot). Although frequently employed, this RES can only be substantiated thermodynamically when the solution is ideal and ΔCp is zero (see Eq. 2.31). The RES in the literature are predominately based on empirics. From the equations describing the molar solubility (Eq. 2.31) and the associated van't Hoff enthalpy of solution (e.g. Eq. 2.39), we may derive expressions that are based on thermodynamics. In the Henry's law region, the temperature dependence of solubility for a regular solution was shown to follow Eq. 2.65. By approximating ΔCp as being constant with temperature we obtain the following differential equation through Eq. 2.38 and 2.65:

⎛ ln xd ⎞ T⎜ ⎟ 21 −+= lnln xTKK eq (2.68) ⎝ dT ⎠eq where K1 and K2 are constants given by the solid-state properties of the solute. Solving this differential equation yields:

26 ln eq += lnTBAx (2.69)

which is equal to RES A3 (Table 2.1). Thus, RES A3 can be thermodynamically derived in the Henry's law region based on the approximation of a regular solution and a constant ΔCp with temperature. This form of RES was suggested by Hildebrand (1952) when fitting solubility data of non-electrolytes at different temperatures. At negative deviations from Raoult's law our starting point is Eq. 2.62, which together with Eq. 2.38 results in the following differential equation:

⎛ ln xd ⎞ Tdh )( 2 Th )( ⋅⎜ ⎟ ln xeq −⋅= eq )(ln Rx (2.70) ⎝ dT ⎠eq dT where the function h(T) is

)( 43 ++= 2 lnTTKTKKTh (2.71) and K2, K3 and K4 are constants drawn from the melting properties of the solute. Solving this differential equation gives:

++ lnTCTBTA ln x = (2.72) eq RT + D where A, B and C are constants referring to the solid-state properties of the solute and D is an integration constant, which is specific for each solvent. Thus, Eq. 2.72 can be derived from rigorous thermodynamics under the assumption of (∂lnx/∂lna)T ≈ lnxeq/lna (Eq. 2.58), for regular solutions and when ΔCp is constant with temperature. Grant et al. (1984) suggested that RES C2 (in Table 6.2) should be used when fitting solubility data at different temperatures based on the assumption of a linear vH temperature dependence of ΔH So ln . This RES has subsequently been used in the literature on frequent occasions. When comparing Eq. 2.72 and RES C2, we see that RES C2 is obtained when the solvent-related integration constant D is zero.

2.4.2 Prediction of Melting Temperature of the Solute Solubility data is often extrapolated to temperatures outside the temperature of measurements, and the selection of RES then determines the value of the solubility at this temperature. This is e.g. of importance when attempting to estimate the transition temperature of enantiotropic polymorphs or when the solid phase undergoes transformation or decomposition at higher temperatures. Since solubility curves obey the boundary condition xeq = 1 at the melting temperature (Eq. 2.49), the

27 accuracy in extrapolating solubility data to higher temperatures can be explored for different RES using solubility data and the melting temperature of the solute. For example, applying RES A1 at the melting temperature gives through Eq. 2.49:

−1 0 m += BAT (2.73) and hence the melting temperature of the solute can be predicted using only the coefficients A and B determined from solubility data. In Table 2.2 is listed the corresponding equations of the RES for prediction of the melting temperature of the solute.

Table 2.2. Prediction of melting temperature of the solute from RES coefficients. Category RES Tm,pred A A1 -A/B A2 -A/B A3 exp(-A/B) B B1 2A/(-B + (B2 – 4AC)0.5) B2 (-B + (B2 – 4AC)0.5)/(2C) B3 (-B + (B2 – 4AC)0.5)/(2C) B4 [(-B + (B2 – 4AC)0.5)/(2C)]0.5 C C1 Numeric or C2 graphic approach C3 C4 D D1 D2 D3 D4

2.5 Determination of the Activity of the Solid Phase The solubility of a solute stems from the properties of the solid and the properties of the solution. Using a Raoult's law reference, the properties of the solid are represented by the activity of the solid, while the properties of the solution are given by the activity coefficient. Distinguishing between the influence of the solid and the influence of the solvent on solubility must be made on accurate determination of either the activity of the solid, a, or the activity coefficient at equilibrium γeq (Eq. 2.26). The activity of the solid phase (or ideal solubility) is a function of the integral terms of ΔCp (Eq. 2.19). Since the ΔCp at T < Tm cannot be determined properly, many

28 approximations have been introduced in the literature leading to more or less poor estimations of the activity of the solid (see section 2.2.6). The activity coefficient can be determined experimentally from e.g. vapor pressure measurements above the solution (fugacity must be used when the vapor is not ideal)3. However, since the solute is typically non-volatile and the concentration of the solute in the solution normally low, it is often more convenient to determine the activity coefficient of the solvent. The activity coefficient of the solute is then determined from the activity coefficient of the solvent using the Gibbs-Duhem equation (an example of this equation is given by Eq. 2.37). This requires that the activity coefficient of the solvent has been determined at several concentrations at constant temperature. An alternative approach to distinguish between the influence of the solid and the influence of the solvent on solubility is to use the thermodynamic equations describing the solubility and its dependence on temperature for an ideal and a non- ideal solution, as is developed below.

2.5.1 Procedure The basis for the approach is the thermodynamically rigorous equations of the solid-state properties, viz. the activity of the solid, a (Eq. 2.19), and the enthalpy of fusion at temperature T, ΔHf(T) (Eq. 2.15), and the thermodynamically rigorous equations of the solution properties, viz. solubility, xeq (Eq. 2.31), and the vH temperature dependence of solubility, ΔH So ln (Eq. 2.40). These equations are all functions of ΔCp, and to determine the solid-state properties we therefore need to determine ΔCp. In the simplest case, ΔCp as independent of temperature and equal to a constant q:

p =Δ qC (2.74)

Then, the integrations of Eq. 2.15 and 2.19 give for the solid-state:

f f m −+Δ=Δ TTqTHTH m )()()( (2.75)

f Δ TH m )( ⎡ 11 ⎤ q ⎡ ⎛ Tm ⎞ Tm ⎤ ln a = ⎢ − ⎥ − ⎢ln⎜ ⎟ +− 1⎥ (2.76) ⎣ m TTR ⎦ R ⎣ ⎝ T ⎠ T ⎦ and for non-ideal solutions at equilibrium:

3 Other experimental techniques to determine the activity coefficient of non-electrolytes are available using e.g. osmotic pressure and freezing point depression (Klotz and Rosenberg, 2000).

29 vH f 2 ⎛ ∂ lnγ ⎞ So ln m m )()( −−+Δ=Δ RTTTqTHH ⎜ ⎟ (2.77) ⎝ ∂T ⎠eq

f Δ TH m )( ⎡ 11 ⎤ q ⎡ ⎛ Tm ⎞ Tm ⎤ xeq lnln γ eq +−= ⎢ − ⎥ − ⎢ln⎜ ⎟ +− 1⎥ (2.78) ⎣ m TTR ⎦ R ⎣ ⎝ T ⎠ T ⎦

vH The relationship between ΔH So ln and lnxeq was shown theoretically in section 2.3.5. The equations of the solid-state (Eq. 2.75 and 2.76) can be plotted in the same graph vH as the relation between ΔH So ln and lnxeq. However, in order to do that we need the melting properties of the solid phase (Tm and ΔHf(Tm)) and the constant q. In this procedure it is assumed that the melting properties of the solute can be determined experimentally. The remaining parameter, the constant q, may for example be chosen as zero (Eq. 2.41 is obtained) or equal to the entropy of fusion at the melting temperature, ΔSf(Tm) (results in Eq. 2.42), which are two frequent approximations in the engineering literature. By assigning different values to q, we establish a relation f vH between the ΔH (T) and lna, which in a plot of ΔH So ln and lnxeq at constant temperature appears as a line, denoted here as a solid-state activity line. As shown in Figure 2.9, the solid-state activity line and the experimental correlation between vH ΔH So ln and lnxeq intersect for a certain value of q. This point of intersection corresponds to an ideal solution since Eq. 2.75 through 2.78 all apply (i.e. lnγeq and (∂lnγ/∂T)eq are zero). Ergo, this point represents the activity of the solid phase and the enthalpy of fusion at temperature T, and also provides us with the correct value of q at that temperature.

ΔH vH Soln q = 0 f ΔH (Tm)

f q = ΔS (Tm)

q = ΔCp f ΔH (T)

id 0 ln(xeq) = xa eq )ln()ln( 0

Figure 2.9. Schematic presentation of determination of the activity of the solid phase at constant temperature. The solid curve depicts the relation between the van't Hoff enthalpy of solution and molar solubility, the dashed curve the solid-state activity line.

The activity of the solid phase (as well as ΔHf(T) and ΔCp), is determined at constant temperature. When the procedure is repeated at several different temperatures, we obtain values of q as a function of temperature. Thus, we may use this information to corroborate or refute our first approximation, i.e. ΔCp = q (Eq. 2.74). Should the approximation of ΔCp being constant with temperature be incorrect, we can extend the expression of ΔCp as e.g. a polynomial equation on temperature:

2 p m m TTuTTrqC +−+−+=Δ ...)()( (2.79) and then based on Eq. 2.15 and 2.19 derive new expressions of the activity of the solid phase and the enthalpy of fusion at temperature T. The coefficients q, r, u,..., are thereafter determined by an optimization procedure based on the number of vH temperatures at which we have data of lnxeq and ΔH So ln . When the determined values of ΔCp at different temperatures are satisfactory described by the used expression of ΔCp then the approximation of the functional form of ΔCp is relaxed.

2.6 Nucleation of the Solid Phase Nucleation of the solid phase from a solution is normally classified as primary or secondary nucleation. Primary nucleation is used when nucleation takes place in a solution that contains no crystalline matter, whereas secondary nucleation results from nuclei formed in the vicinity of crystals already present in the supersaturated solution. Primary nucleation can either be homogeneous or heterogeneous. Homogeneous nucleation is the spontaneous formation of nuclei in the solution, whereas heterogeneous nucleation is induced by foreign particles in the solution (definition by Mullin, 2001).

2.6.1 The Classical Nucleation Theory The classical nucleation theory, CNT, was originally developed by Gibbs, Volmer and others in the 1930s and 1940s, intended to describe condensation of a vapor to a liquid. The theory has subsequently been extended to homogeneous nucleation of a solid phase from melts and solutions (Mullin, 2001). The CNT regards nucleation as a molecular addition process resulting in the formation of an unstable nucleus (often referred to as cluster). As the unstable nucleus continues to grow the nucleus reaches a critical size, which is thermodynamically stable. The free energy change, ΔGnucleus, associated with the formation of a nucleus is given as:

surface volume Gnucleus nucleus Δ+Δ=Δ GG nucleus (2.80)

surface where ΔGnucleus denotes the excess free energy between the surface of the nucleus and volume the bulk of the nucleus, and ΔGnucleus represents the volume excess energy, which is the difference in free energy between a nucleus of infinite size and the solute in solution. Hence for a prefect sphere,

4π 3Δgr volume G 4 r 2γπ +=Δ nucleus (2.81) nucleus sl 3

volume where Δg nucleus is the free energy change per unit volume, and γsl is the interfacial energy between the solid and the solution. The critical size of the nucleus, rcrit, is obtained when dΔGnucleus/dr = 0. Thus,

− 2γ sl rcrit = volume (2.82) Δg nucleus which when introduced into Eq. 2.80 gives for the critical free energy of the nucleus, ΔGcrit:

4πγ r 2 G =Δ critsl (2.83) crit 3

Thus, the critical free energy required for the formation of a stable nucleus is only dependent on the interfacial energy between solid and solution and the radius of the nucleus. The relationship between solubility and radii of small particles has been derived by Ostwald and Freundlich. The Ostwald-Freundlich relation (sometimes referred to as the Gibbs-Thomson or the Gibbs-Kelvin relationship) can be derived from the fundamental equation of chemical thermodynamics (Eq. 2.2) where the influence of the surface free energy is accounted for:

S += γ dAdnµdG Ssl (2.84) where AS is the surface area of the nucleus. Since for component i:

⎛ ∂G ⎞ ⎜ ⎟ µi = ⎜ ⎟ (2.85) ∂ni ⎝ ⎠ ,, nTp j

(ni ≠ nj) we obtain:

32 dA nucleus µµ S += γ S (2.86) sl dn which can be rewritten as:

γ dAM nucleus µµ S += sl S (2.87) ρ dV where V is the volume of the nucleus, M is the molar mass of the solid, and ρ is the density of the solid.. For a spherical nucleus of radius rnucleus:

dAS 8πrdrnucleus 2 = 2 = (2.88) dV 4π nucleus drr nucleus rnucleus giving:

2γ M nucleus µµ S += sl (2.89) ρrnucleus

The chemical potential of the nucleus can also be expressed in terms of activity, which when using the supercooled liquid as the reference yields:

nucleus L += ln aRTµµ nucleus (2.90)

The chemical potential of the solid is equal to the chemical potential of the nucleus when the radius of the nucleus is infinite. Hence,

nucleus LS (rµ nucleus ) +==∞→ ln aRTµµ (2.91)

Combining Eq. 2.90 and 2.91 gives:

nucleus nucleus S ⎛ a ⎞ += RTµµ ln⎜ ⎟ (2.92) ⎝ a ⎠ which combined with Eq. 2.89 results in a modified form of the Ostwald-Freundlich relation4 first derived thermodynamically by van Zeggeren and Benson (1957) and Enustun and Turkevich (1960).

4 The original Ostwald-Freundlich relation does not include the activity of the solid and nucleus, but uses the solubility concentration of the solid and nucleus in its place.

33 2Mγ ln a nucleus ln a += sl (2.93) ρrRT nucleus

Introducing Eq. 2.93 into the relationship of the critical free energy (Eq. 2.83) yields:

32 16 M γπ sl Gcrit =Δ 2 (2.94) ⎛ ⎛ a nucleus ⎞⎞ 222 ⎜ ⎜ ⎟⎟ 3 TR ρ ⎜ln⎜ ⎟⎟ ⎝ ⎝ a ⎠⎠

This expression can be simplified since the molar volume, Vm, (m3/mol) is given as:

M V = (2.95) m ρ

The driving force of nucleation and crystal growth, Δµ, is the difference in chemical potential between the solute in the supersaturated solution, µsolute, and the solute at solute equilibrium, µeq :

solute solute −=Δ µµµ eq (2.96) and can when using the same reference state be written:

⎛ a nucleus ⎞ =Δ RTµ ln⎜ ⎟ (2.97) ⎝ a ⎠

Eq. 2.94, 2.95 and Eq. 2.97 thus affords:

16 V γπ 32 G =Δ slm (2.98) crit Δµ)(3 2

Hence, the critical free energy required for the formation of a stable nucleus is according to the CNT governed by the interfacial energy between the nucleus and the solution, and the driving force of nucleation, Δµ. In the CNT, the rate of nucleation, J, (i.e. the number of formed nuclei per time and volume) is derived from an Arrhenius reaction velocity equation, which is normally used for the rate of a thermally activated process (Mullin, 2001):

⎛ ΔG ⎞ JJ 0 exp⎜−= crit ⎟ (2.99) ⎝ kT ⎠

34 The equation of the pre-exponential factor, J0, has been developed by several researchers (e.g. Zettlemoyer, 1969, Myerson and Izmailov, 1993, and Mersmann, 1996) using different models. It is expected that J0 is dependent on the interfacial energy between the solid and solution and on the movement of solute molecules to the nuclei. The influence of temperature and supersaturation on J0 is however believed to be small. The CNT predicts that the nucleation rate increases exponentially with supersaturation, as depicted in Figure 2.10.

rate Nucleation

Supersaturation ratio

Figure 2.10. Influence of supersaturation ratio on the nucleation rate according to the CNT.

The CNT has frequently failed to provide accurate prediction of real systems (Mullin, 2001). The CNT is applicable to homogeneous nucleation, which in practice can be hard to achieve in a laboratory environment. Small amounts of dust particles or other microscopic solids may provide surfaces in the solution for nuclei to grow on, resulting in heterogeneous nucleation. The CNT also assumes that the interfacial energy and density of the nuclei are constant and independent of the shape and size of the nucleus. Moreover, the driving force of nucleation is considered unchanged during nucleation, which implies that the concentration surrounding the nucleus is constant (Mokross, 2001). Finally, the shape of the nucleus and crystal phase may be different at the onset of nucleation than when grown into detectable size.

2.6.2 The Metastable Zone Width Primary nucleation occurs when the solution is supersaturated. The window from the solubility concentration to the onset of nucleation is referred to as the metastable zone width, MZW. The MZW is illustrated in Figure 2.11 using a cooling crystallization from the solubility curve (point 1 in Figure 2.11) to the onset of nucleation (point 2 in Figure 2.11).

ΔT Solubility

T3,x1,γ2 T1,x1,γ1 2 1

Δµ

Concentration, x T3,x3,γ3 3

Temperature, T

Figure 2.11. The metastable zone width during cooling crystallization.

For a cooling crystallization the MZW can be expressed in terms of concentration difference, Δx, degree of undercooling, ΔT, or supersaturation ratio, s. By using the notation in Figure 2.11, the concentration difference at the onset of nucleation is given as:

−=Δ xxx 31 (2.100) the degree of undercooling is:

−=Δ TTT 31 (2.101) and the supersaturation ratio is given as:

x s = 1 (2.102) x3

The thermodynamic driving force at the onset of nucleation is obtained through Eq. 2.21 and 2.96.

⎛ x γ ⎞ ⎜ 21 ⎟ =Δ RTµ 3 ln⎜ ⎟ (2.103) ⎝ x γ 33 ⎠

36 where x1 = x2. The ratio between the activity coefficients is often assumed to be unity, which leads to:

=Δ 3 ln sRTµ (2.104)

This assumption is however only valid when the solution is ideal (γ2 = γ3 = 1), or when the influence of temperature on γ at constant concentration is negligible, i.e. γ2 ≈ γ3 (the solution is athermal). Davey (1982) derived an expression of the MZW from the CNT by assigning the nucleation rate as 1 nuclei·cm-3·s-1, which when using the simplified form of Δµ (Eq. 2.104) gives:

⎛ 4V πγ 3 ⎞ s = exp⎜ m sl ⎟ (2.105) MZW ⎜ 0 ⎟ ⎝ RT ln3 JkT ⎠

The MZW is known to be affected by several factors. Among these are cooling rate, temperature and hydrodynamic conditions such as e.g. agitation rate, crystallizer and impeller design, as well as, properties of the solution, e.g. solvent, purity, presence of foreign particles, solution history, and external factors such as ultrasound. Hence, the MZW is normally not considered a physical property of the system. However, the MZW conveys information of the mechanism of nucleation. Since the size of the crystals in a cooling crystallization depends on the onset of nucleation, the MZW is also of great importance in the design of the crystallization process.

38 3. Experimental

A condensed summary of the experimental method is given in the present section. For a more detailed description, see experimental sections in paper I through IX.

3.1 Materials o-Hydroxybenzoic acid (purity > 99 %), m-hydroxybenzoic acid (purity > 99 %), p- hydroxybenzoic acid (purity > 99 %), salicylamide (purity > 99 %), m-aminobenzoic acid (purity > 98 %) and p-aminobenzoic acid (purity > 99 %) were purchased from Sigma-Aldrich and used as obtained. These compounds were chosen due to their low toxicity, crystalline properties and industrial applications. The selected model compounds exhibit similar molecular structures, molecular weight and functional groups, as shown in Figure 3.1 and Table 3.1.

O O O

OH OH OH

OHBA MHBA PHBA

O O O

NH2 OH OH

OH 2NH NH 2 SA MABA PABA

Figure 3.1. Investigated model compounds. From upper left to lower right: o-hydroxybenzoic acid: OHBA (salicylic acid), m-hydroxybenzoic acid: MHBA, p-hydroxybenzoic acid: PHBA, salicylamide: SA, m-aminobenzoic acid: MABA and p-aminobenzoic acid: PABA.

39 Table 3.1. Model compounds. Compound Acronym Molecular CAS Fields of application weight Registry (Kirk-Othmer, number Ullmann's, Palafox et al., 1996) [g·mol-1] o-hydroxybenzoic OHBA 138.12 69-72-7 Analgesic, intermediate acid (salicylic acid) in apirin production m-hydroxy- MHBA 138.12 99-06-9 Intermediate in benzoic acid production of germicides, preservatives and pharmaceuticals p-hydroxybenzoic PHBA 138.12 99-96-7 Liquid crystal polymers, acid preservatives Salicylamide SA 137.14 65-45-2 Anti-fungus protection in oils, soaps and lotions m-aminobenzoic MABA 137.14 99-05-8 Used in pharmaceutical acid synthesis of e.g. analgesics, antihipertensives and vasodilators. p-aminobenzoic PABA 137.14 150-13-0 Intermediate in acid production of pharmaceuticals, perfumes and dyes

Methanol (purity > 99.8 %), acetonitrile (purity > 99.9 %), acetic acid (purity = 96 %), acetone (purity > 99.6 %), ethyl acetate (purity > 99.8 %), iso-propanol (purity > 99.5 %) and 1,4-dioxane (purity > 99.5 %) were purchased from Merck/VWR and used as obtained. The water was distilled, deionized and filtered at 0.2 µm. Ethanol (purity = 99.7 %) was purchased from Solveco Chemical. These solvents are frequently used in industrial applications and vary in polarity from 0.16 to 1.00, according to Reichardt's polarity index (Reichardt, 2003). Some physical properties of the selected solvents are listed in Table 3.2.

40 Table 3.2. Selected solvents. Data of Tm, Tbp and polarity from Reichardt, 2003. Data of density from Beilstein data base at 20 oC (average values). Solvent Acronym M Tm Tbp Density Polarity, CAS N ET registry number [g·mol-1] [oC] [oC] [g·ml-1] Methanol MeOH 32.04 -97.7 64.5 0.792 0.762 67-56-1 Aceto- ACN 41.05 -43.8 81.6 0.783 0.460 75-05-8 nitrile Acetic acid HAc 60.05 16.7 117.9 1.049 0.648 64-19-7 Acetone 58.08 -94.7 56.1 0.791 0.355 67-64-1 Water H2O 18.02 0 100 0.998 1.000 7732-18-5 Ethyl EtAc 88.11 -83.6 77.2 0.900 0.228 141-78-6 acetate 2-propanol 2-PrOH 60.10 -88.0 82.2 0.786 0.546 67-63-0 1,4- 88.11 11.8 101.31.034 0.164 123-91-1 dioxane Ethanol EtOH 46.07 -114.5 78.3 0.789 0.654 64-17-5

3.2 Identification of Crystal Phases and Crystal Morphology Crystalline phases were identified primarily using Fourier Transform InfraRed with an Attenuated Total Reflectance (FTIR-ATR) module having a ZnSe window (Perkin Elmer Instruments, Spectrum One). Dry crystal samples or wet suspensions comprising crystals and solution were placed on the ATR module and spectra were collected between 650 and 4 000 cm-1. Visual identification and imaging of crystal morphology were conducted at around room temperature using Photo Microscopy (Olympus SZX12) and at elevated temperatures using Hot Stage Microscopy (Olympus BH-2). Crystal structures were resolved by Dr. Andreas Fischer, Dept. of Inorganic Chemistry, Royal Institute of Technology, Stockholm, using a Bruker-Nonius KappaCCD Single-Crystal X-ray Diffractometer. Crystals of approximately 0.1 to 0.5 mm were placed in the diffractometer and analyzed at around room temperature or in case of solvates at around 150 K.

3.3 Determination of Solid-State Properties Dry crystal samples were analyzed using Differential Scanning Calorimetry, DSC (TA Instruments, DSC 2920), from typically 10 oC up to approximately 30 oC above the melting temperature. The melting temperature and melting enthalpy of crystals

41 were determined at heating rates of 1, 2 and 5 K/min in hermetic Al-pans while being purged with nitrogen. The DSC thermograms also provided information of the presence of phase conversion and desolvation of crystal phases, as well as, the temperature and enthalpy change of the associated phase transformations. The heat capacity of the different crystal phases was determined from normally 10 oC up to approximately 30 oC above the melting temperature in 5 oC increments. All heat capacity measurements were conducted using modulated isothermal DSC with a modulation amplitude of ± 0.5 oC and a modulation period of 80 s. The DSC was calibrated against the melting temperature and melting enthalpy of Indium and the heat capacity of sapphire.

3.4 Solubility The solubility of crystal phases in different solvents was normally determined between 10 and 50 oC in 5 oC increments. The experimental procedure involved several steps. Initially, crystals were placed in contact with the solvent in 250 ml bottles at a certain temperature and the concentration of the solution was determined over time up to typically two weeks. The bottles containing the suspensions were placed in water baths and agitated at around 400 rpm using magnetic teflon spin bars. The temperature of the water baths was validated by a calibration mercury thermometer (accuracy of 0.01 oC). This part of the study allowed for the time to reach equilibrium to be estimated in order to ascertain that the system is at equilibrium. Moreover, by measuring the concentration over time it was also possible to investigate the presence of possible chemical reactions, phase transformations and contaminations of foreign substances (typically water), as these resulted in changes in the concentration and solubility. In the second step, the solubility concentration of the investigated phases was approached either by dissolution or recrystallization until equilibrium was established. Crystals of a pure crystal phase were partially dissolved at constant temperature in both 250 ml bottles and 20 ml test tubes and agitated at 400 rpm. The solubility concentration was determined when the time to reach equilibrium was exceeded from a minimum of four measurements per solvent and temperature. Recrystallization was performed by cooling crystallization at a constant cooling rate of approximately 1 K/min. The attaining of equilibrium was corroborated by continuous concentration measurements over time. The crystal phase in the suspension was identified by FTIR- ATR and DSC analyses and by photo microscopy. All concentration and solubility measurements were conducted gravimetrically. The suspension was allowed to sediment and a sample of the pure solution was collected and transferred into a pre-weighed vial. The weight of the clear solution was determined. Filters were used when sedimentation of the suspension was incomplete. All the syringes, needles and filters were pre-heated to exceed the temperature of the solution in order to prevent crystallization of the pure solution during the sample collection. The vials containing the clear solution were normally placed in a

42 laboratory hood at room temperature. The vials were weighed continuously throughout the drying process and complete dryness was determined when the weight of the vials remained constant over time. The solubility was determined from the weight of the empty vial, the weight of the clear solution and the weight of the vial containing the dried crystals.

3.5 Metastable Zone Width of Salicylamide Saturated solutions of salicylamide were prepared in 250 or 500 ml bottles using the organic solvents methanol, acetonitrile, acetic acid, acetone and ethyl acetate. The suspensions were equilibrated at 35, 40, 45 and 50 oC for a minimum of four hours. The solutions were then filtered at 0.2 µm and injected into 20 ml test tubes (solution volume of 15 ml), 250 ml bottles (solution volume of 150 ml) or 500 ml bottles (solution volume of 500 ml). Agitation was provided by magnetic teflon spin bars. The test tubes and bottles were properly sealed to prevent evaporation and contamination. (i) The test tubes and bottles containing the filtered solutions were placed in water baths at 10 oC above the saturation temperature of the solutions for a minimum of three hours while being agitated at 300 rpm. (ii) The solutions in the test tubes and bottles were moved to a cooling bath having a temperature equal to the saturation temperature of the solutions and agitated at 400 rpm. A total of 14 test tubes (solution volume of 15 ml) or 4 bottles (solution volume of 150 or 500 ml) were used simultaneously in the cooling bath. (iii) After 15 min, the solutions were cooled at the same time at a constant cooling rate of 5, 10 or 20 K/h until nucleation took place in all solutions. The onset of nucleation and the water temperature shown by the cooling bath display were recorded by a video camera. The experimental setup is illustrated in Figure 3.2. (iv) The test tubes or bottles containing the crystallized solutions were moved back to the water bath where the temperature corresponded to 10 oC above the saturation temperature of the solutions. The crystals in the solutions were dissolved completely. The procedure given by the steps (i) - (iv) were repeated for a maximum of 10 times giving around 50 to 200 nucleation events for each experimental condition. After the last cooling crystallization, the concentration of the solutions was determined gravimetrically.

D o ___ C C

A E

Figure 3.2. Experimental setup of the determination of the metastable zone width for a solution volume of 150 and 500 ml. The bottles (A) were placed on stirring plates (B) in the cooling bath (C) and cooled at constant cooling rate from the saturation temperature until all the solutions crystallized. The sequence was filmed by a video camera (D) and recorded by a VCR (E), which was connected to a TV monitor (F). The onset of nucleation, as given by the nucleation temperature, was determined using the recorded video tapes.

The metastable zone width of salicylamide was also investigated in jacked glass crystallizers having a volume of 250 ml. The crystallizer were placed on top of a magnetic stirring plate and connected to a cooling bath. A saturated solution of 150 ml were filtered at 0.2 µm and injected into the jacketed glass crystallizer. Agitation was provided by magnetic teflon stirrer bars at 400 rpm. The same procedure as previously outlined was employed in the cooling crystallizations, except in these experiments the crystallizer solution was in half the experiments left without the crystallizer lid leaving the solution exposed to the surrounding air. A total of 20 experiments for each solvent were conducted with a closed (10 crystallizations) and open system (10 crystallizations), where the sequence of the experiments were alternated between open and closed systems.

44 4. Results

4.1 Crystal Phases and Crystal Morphology The number of crystal phases varied significantly between the different model compounds. Only one monoclinic crystal structure of OHBA was observed. This structure is based on dimers and has been resolved by Cochran (1953), Sundaralingam and Jensen (1965), and Bacon and Jude (1973). OHBA crystallized in the form of needles during cooling and evaporation crystallization in the organic solvents MeOH, ACN, HAc, acetone and EtAc (paper III). Crystals of OHBA when crystallized from water however exhibited comparably different crystal morphology. These crystals appeared as hollow tubes with square cross-sections, as shown in Figure 4.1.

Figure 4.1. Microscopy photo of OHBA (32 times magnification) crystallized from water through evaporation crystallization at room temperature.

MHBA were found to crystallize as two unsolvated polymorphs only. The two polymorphs were found to be monotropically related (paper II). The crystal structures of the two polymorphs have been resolved by Gridunova et al., 1982. The stable crystal form crystallizes as a monoclinic structure, while the metastable form crystallizes in the orthorhombic crystal group. The structure of the monoclinic crystal form is based on dimers where intermolecular hydrogen bonds are present between the opposing carboxylic groups. This is not observed in the orthorhombic structure where monomers of MHBA form weaker intermolecular hydrogen bonds. The crystal structures of the two polymorphs are given in Figure 4.2.

MHBA: Figure 4.2. Crystal structure of monoclinic MHBA (left) and orthorhombic MHBA (right), viewed down the crystallographic b-axis (data from Gridunova et al., 1982).

The monoclinic polymorph normally crystallized during cooling and evaporation crystallization in MeOH. The pure metastable orthorhombic modification was typically obtained through cooling crystallization in ACN, HAc, Acetone and EtAc at approximately 1 K/min. Crystallization of MHBA in H2O resulted in the formation of the orthorhombic form followed by a rapid phase conversion into the monoclinic polymorph. At least five different crystal phases of PHBA exist. Two unsolvated polymorphs have been reported, by Heath et al., 1992, and by Kariuki et al., 2000. The polymorphic relationship between these two polymorphs was expected to be enantiotropic (paper I). In addition, solvated structures of PHBA were found in water, acetone and 1,4-dioxane. When PHBA came into contact or recrystallized from water a monohydrate formed, which exceeded the stability of the unsolvated PHBA. The crystal structure of this monohydrate has been resolved by Fukuyama et al., 1973, and Colapietro et al., 1979. The solvated structure of PHBA obtained from acetone was found to be stable up to approximately 50 oC at which a transition appeared in stability between the ansolvate and the solvate. The crystal structure of the solvate comprises two PHBA molecules for each acetone molecule and has been determined by Heath et al., 1992. Finally, a solvate of PHBA also emerged in 1,4- dioxane (paper IX). This new crystal structure was resolved using Single-Crystal XRD (paper IX) and consists of two PHBA molecules per molecule of 1,4-dioxane, as shown in Figure 4.3.

Figure 4.3. Crystal structure of (2/1) PHBA-1,4-dioxane solvate, viewed down the crystallographic b-axis.

SA has only been found to crystallize in a dimeric monoclinic structure. This structure has been determined by Sasada et al., 1964, and Pertlik, 1990. No new crystal phases of SA were found in the investigated solvents between 0 and 50 oC (paper IV). SA crystallizes as hexagonal plates in the organic solvents, whereas water typically yielded needles, as depicted in Figure 4.4.

Figure 4.4. Crystal morphology of SA obtained through evaporation crystallization at room temperature in water at 40 times magnification (left) and in ACN at 90 times magnification (right).

Similar to MHBA, MABA crystallizes in two polymorphic forms, which are expected to be enantiotropically related according to the heat of fusion rule by Burger and Ramberger, 1979 (appendix 2). The crystal structure of the metastable polymorph at room temperature (phase 2) has been determined by Voogd et al., 1980. This structure is based on dimers and crystallizes in the monoclinic crystal group. The crystal structure of the stable form at room temperature (phase 1) has hitherto not been resolved, which is likely due to that very small and agglomerated crystals are

47 formed during evaporation and cooling crystallization, irrespective of solvent. No solvates were found in the investigated solvents. The crystal morphology of the metastable polymorph is depicted in Figure 4.5.

Figure 4.5. Crystal morphology of the metastable polymorph of MABA at 50 times magnification. The crystals were obtained through evaporation crystallization at room temperature in EtAc.

The last of the model compounds, PABA, is a known enantiotropic polymorphic compound (Gracin and Rasmuson, 2004). The crystal structure of the so-called α- polymorph has been determined by Killean et al., 1965, and Lai and Marsh, 1967. The structure of the β-polymorph has been resolved by Alleaume et al., 1966, and most recently by Gracin and Fischer, 2005. The structure of the α-polymorph is based on dimers about an inversion center, whereas the structure of the β-polymorph is formed by a network of hydrogen bonds between the amino and hydroxy groups. The enantiotropic transition temperature has been estimated to be located around 16 oC (appendix 3). The β-polymorph exhibits a higher stability below the transition temperature and the α-polymorph is more stable at temperatures above the transition temperature. Two solvates of PABA in acetone and 1,4-dioxane were also found. The solvated structure of PABA in acetone comprises two PABA molecules for each acetone molecule and has been determined by Single-Crystal XRD (paper VIII). The oxygen atom in the acetone molecule is connected to the hydrogen of the amino group of PABA. The PABA-acetone solvate exhibits a comparably fast desolvation process when the crystals are brought from the solution and exposed to the atmosphere, as depicted in Figure 4.6.

Figure 4.6. Desolvation process of (2/1) PABA-acetone solvate, magnified 90 times. The images were captured in approximately 20 s intervals.

The solvate of PABA obtained from 1,4-dioxane comprises two PABA molecules and one 1,4-dioxane molecule in the asymmetric unit. Similar to the PHBA-1,4- dioxane solvate the PABA-1,4-dioxane contains two PABA molecules per molecule 1,4-dioxane in the crystal lattice. The different types of crystal phases of the model compounds are summarized in Table 4.1.

49 Table 4.1. Crystal phases of the model compounds. Model Ref. Crystal Crystal Space Crystal compound phase system group phase category notation OHBA Bacon and Unsolvated Monoclinic P 21/a OHBA-P1 Jude, 1973 MHBA Gridunova et Unsolvated Monoclinic P 21/b MHBA-P1 al., 1982 MHBA Gridunova et Unsolvated Orthorhombic P n a 21 MHBA-P2 al., 1982 PHBA Heath et al., Unsolvated Monoclinic P 21/a PHBA-P1 1992 PHBA Kariuki et al., Unsolvated PHBA-P2 2000 PHBA Colapietro et Monohydrate Monoclinic P 21/a PHBA-S1 al., 1979 PHBA Heath et al., (2/1) acetone Monoclinic P 21/a PHBA-S2 1992 solvate PHBA Paper IX (2/1) 1,4- Monoclinic P 21/n PHBA-S3 dioxane solvate SA Pertlik, 1990 Unsolvated Monoclinic I 2/a SA-P1 MABA Unsolvated MABA-P1 MABA Voogd et al., Unsolvated Monoclinic P 21/c MABA-P2 1980 PABA Killean et al., Unsolvated Monoclinic P 21/n PABA-α 1965 PABA Gracin and Unsolvated Monoclinic P 21/n PABA-β Fischer, 2005 PABA Paper VIII (2/1) acetone Triclinic P -1 PABA-S1 solvate PABA Fischer and (2/1) 1,4- PABA-S2 Nordström, dioxane 2008 solvate

50 4.2 Solid-State Properties of the Crystal Phases The solid-state properties of the investigated crystal phases have been determined using DSC at different heating rates. However, for some crystalline modifications the solid-state properties could not be determined experimentally as the crystal phase underwent a polymorphic transformation or desolvation before reaching the melting temperature. The unsolvated metastable polymorphs typically transformed into the stable phase prior to the melting temperature, and all the solvated crystal phases underwent desolvation (i.e. paramorphosis) when the crystals were brought out from the solution (as e.g. seen in Figure 4.6). In addition, several of the model compounds decomposed or evaporated considerably upon melting, preventing direct measurement of the properties of the melt. In Table 4.2 is listed the experimentally determined melting properties of crystal phases of the model compounds.

Table 4.2. Experimentally determined melting properties of the model compounds. Crystal phase Onset Tm ΔHf(Tm) ΔSf(Tm) Scans [K] [kJ·mol-1][J·mol-1·K-1] OHBA-P1 431.4 27.09 62.80 9 MHBA-P1 474.8 35.92 75.66 11 PHBA-P1 487.7 30.85 62.26 29 SA-P1 411.9 29.00 70.41 13 MABA-P1 445.1 36.04 80.96 8 MABA-P2 451.4 27.24 60.34 4 PABA-α 460.4* 24.1* 52.3 * Data from Gracin and Rasmuson, 2004.

The heat capacity of the solid forms of the model compounds was determined by isothermal modulated DSC. The heat capacity data at different temperatures was correlated to the function:

S p += kTkC 21 (4.1) where T is in absolute temperature and R2 exceeded 0.99 for all the investigated crystal phases. The regression coefficients, k1 and k2, are given in Table 4.3.

51 Table 4.3. Heat capacity regression coefficients of Eq. 4.1. Crystal phase k1 k2 Measured temperature interval [K] OHBA-P1 0.4023 14.88 280-405 MHBA-P1 0.4603 5.37 280-460 MHBA-P2 0.3415 33.86 280-385 PHBA-P1 0.4401 15.92 280-460 SA-P1 0.4942 -15.10280-395 PABA-α 0.4308 29.90 280-445 PABA-β 0.4685 -8.35 280-380

The density of a crystal phase can be retrieved through data obtained by the crystal structure determination. The density then corresponds to a crystal lattice in which the asymmetric unit is repeated in three dimensions. Hence, the crystal lattice is regarded as perfectly ordered and no dislocations in the lattice are accounted for. The density of the investigated crystal phases is given in Table 4.4.

Table 4.4. Density of the crystal phases obtained from crystal structure determination using Single- Crystal XRD. Crystal phase Density Temperature [g·cm-3] [K] OHBA-P1 1.444 283-303 MHBA-P1 1.469 283-303 MHBA-P2 1.469 283-303 PHBA-P1 1.497 283-303 PHBA-S1 1.398 283-303 PHBA-S2 1.315 283-303 PHBA-S3 1.416 173 SA-P1 1.351 283-303 MABA-P2 1.378 283-303 PABA-α 1.367 283-303 PABA-β 1.399 298 PABA-S1 1.306 148

52 4.3 Solubility The regression equation of solubility, RES,

A x )ln( ++= CTB (4.2) eq T was employed and the coefficients A, B and C were determined from the solubility data at different temperature (paper I-IV, appendix 2 and 3), using the computer software ®Origin, v6.1. T is given in absolute temperature, xeq is the mole fraction solubility concentration of the solute and A, B and C are regression coefficients. The RES coefficients of the investigated crystal phases are listed in Table 4.5 through 4.10.

Table 4.5. Solubility of OHBA. Crystal phase Solvent Temperature A B C interval [K] OHBA-P1 MeOH 283.15-323.15 -578.84 -3.1329 1.0124·10-2 OHBA-P1 ACN 283.15-323.15 -562.01 -8.2729 2.2262·10-2 OHBA-P1 HAc 283.15-323.15 358.27 -12.839 2.9307·10-2 OHBA-P1 Acetone 283.15-323.15 -1190.9 2.4355 -5.3585·10-4 OHBA-P1 H2O 283.15-323.15 5566.7 -56.253 9.8240·10-2 OHBA-P1 EtAc 283.15-323.15 -332.73 -4.0701 1.0684·10-2

Table 4.6. Solubility of MHBA. Crystal phase Solvent Temperature A B C interval [K] MHBA-P1 MeOH 283.15-323.15 338.48 -7.8499 1.4783·10-2 MHBA-P1 ACN 283.15-323.15 -1973.4 -0.3454 8.3233·10-3 MHBA-P1 HAc 283.15-323.15 -164.83 -8.7284 1.9398·10-2 MHBA-P1 Acetone 283.15-323.15 15.271 -5.3969 1.0752·10-2 MHBA-P1 H2O 283.15-323.15 965.03 -26.204 5.3807·10-2 MHBA-P1 EtAc 283.15-323.15 -3.1951 -7.9761 1.6805·10-2 MHBA-P2 ACN 283.15-323.15 189.68 -14.473 3.2070·10-2 MHBA-P2 HAc 283.15-323.15 1288.9 -17.525 3.3290·10-2 MHBA-P2 Acetone 283.15-323.15 1085.3 -12.326 2.2460·10-2 MHBA-P2 EtAc 283.15-323.15 1039.5 -14.287 2.7010·10-2

53 Table 4.7. Solubility of PHBA. Crystal phase Solvent Temperature A B C interval [K] PHBA-P1 MeOH 283.15-323.15 591.82 -8.7780 1.5514·10-2 PHBA-P1 ACN 283.15-323.15 -1385.7 -3.3611 1.2595·10-2 PHBA-P1 HAc 283.15-323.15 136.49 -8.5590 1.6899·10-2 PHBA-P1 Acetone 303.15-323.15 3192.5 -24.662 4.0531·10-2 PHBA-P1 EtAc 283.15-323.15 453.13 -9.1187 1.6665·10-2 PHBA-S1 H2O 283.15-323.15 3993.9 -49.165 9.5870·10-2 PHBA-S2 Acetone 283.15-318.15 608.99 -11.317 2.3980·10-2

Table 4.8. Solubility of SA. Crystal phase Solvent Temperature A B C interval [K] SA-P1 MeOH 283.15-323.15 924.33 -17.810 3.8580·10-2 SA-P1 ACN 283.15-323.15 -525.14 -9.9656 2.7950·10-2 SA-P1 HAc 283.15-323.15 -207.06 -7.9933 2.0770·10-2 SA-P1 Acetone 283.15-323.15 -312.21 -5.1669 1.3970·10-2 SA-P1 H2O 283.15-323.15 268.52 -22.971 4.6980·10-2 SA-P1 EtAc 283.15-323.15 312.02 -10.907 2.4390·10-2

Table 4.9. Solubility of MABA. Crystal phase Solvent Temperature A B C interval [K] MABA-P1 MeOH 283.15-323.15 -279.14 -11.934 2.8910·10-2 MABA-P1 ACN 283.15-323.15 2604.9 -36.068 7.1930·10-2 MABA-P1 H2O 283.15-323.15 1957.1 -29.224 5.1680·10-2 MABA-P1 EtAc 283.15-323.15 2471.8 -31.566 6.1340·10-2

Table 4.10. Solubility of PABA. Crystal phase Solvent Temperature A B C interval [K] PABA-α ACN 278.15-323.15 31.064 -12.095 2.7234·10-2 PABA-α HAc 278.15-323.15 1693.6 -18.579 3.3583·10-2 PABA-α EtOH 278.15-323.15 1989.1 -20.930 3.7783·10-2 PABA-α 2-PrOH 278.15-323.15 1180.9 -18.494 3.7213·10-2 PABA-β ACN 278.15-298.15 4348.1 -43.573 8.4432·10-2 PABA-β EtOH 278.15-298.15 871.83 -14.099 2.7517·10-2 PABA-β 2-PrOH 278.15-298.15 996.39 -18.361 3.8955·10-2 PABA-S1 Acetone 278.15-323.15 295.266 -11.5377 2.6550·10-2

54 4.4 Metastable Zone Width of Salicylamide Since no crystal phases were observed of SA other than SA-P1 it was determined to be a suitable compound for the investigation of the kinetics of primary nucleation. The results are summarized in Table 4.11 through 4.15 in terms of degree of undercooling, ΔT, at the onset of nucleation. Due to the significant variation in the data, ΔT is listed as the average degree of undercooling at the onset of nucleation, ΔTavg, standard deviation in ΔTavg, and minimum and maximum observed onset of nucleation, ΔTmin and ΔTmax, respectively. All together, a total of 2911 nucleation events have been recorded. Experiments given by denotation A1-A7 in MeOH, B1-B7 in ACN, C1-C4 in HAc, D1-D6 in acetone and E1-E4 in EtAc were performed in 20 ml sealed test tubes. Denotation A8 and A9 refer to experiments conducted in sealed 250 ml and 500 ml bottles, respectively. Denotation A10, B8, C5, D7 and E5 represent experiments performed in 250 ml crystallizers when no crystallizer lid was used (i.e. the solvent was allowed to evaporate during the cooling crystallization), and denotation A11, B9, C6, D8 and E6 refer to experiments in 250 ml crystallizers when a crystallizer lid was used (no solvent evaporation).

Table 4.11. MZW of salicylamide in methanol. Deno- Experimental parameters MZW No of tation exp. Teq -dT/dt Vsoln ΔTavg Std. dev. ΔTmin ΔTmax [K] [K/h] [ml] [K] [K] [K] [K] A1 323.15 5 15 11.2 7.0 2.0 31.5 128 A2 318.15 5 15 9.3 4.5 2.4 21.7 56 A3 313.15 5 15 15.1 7.6 4.3 32.7 56 A4 308.15 5 15 11.6 6.1 3.2 29.4 53 A5 303.15 5 15 11.3 4.5 5.0 25.9 56 A6 323.15 10 15 18.5 7.0 1.5 34.9 136 A7 323.15 20 15 21.4 7.6 3.9 35.8 126 A8 323.15 20 150 21.1 6.2 6.8 34.1 128 A9 323.15 20 500 22.7 5.7 8.9 36.2 125 A10 323.15 20 150 1.5 0.4 0.7 2.1 10 A11 323.15 20 150 11.9 5.4 4.4 21.3 10

55 Table 4.12. MZW of salicylamide in acetonitrile. Deno- Experimental parameters MZW No of tation exp. Teq -dT/dt Vsoln ΔTavg Std. dev. ΔTmin ΔTmax [K] [K/h] [ml] [K] [K] [K] [K] B1 323.15 5 15 9.9 5.8 1.3 23.1 133 B2 318.15 5 15 8.1 4.0 2.6 21.1 54 B3 313.15 5 15 9.7 5.1 3.2 24.2 55 B4 308.15 5 15 8.9 5.2 1.9 22.6 56 B5 303.15 5 15 7.0 3.6 2.9 18.0 56 B6 323.15 10 15 14.5 6.9 2.0 26.8 205 B7 323.15 20 15 14.2 6.8 2.9 27.2 138 B8 323.15 20 150 2.4 0.5 1.8 3.6 10 B9 323.15 20 150 9.1 3.2 5.2 14.2 10

Table 4.13. MZW of salicylamide in acetic acid. Deno- Experimental parameters MZW No of tation exp. Teq -dT/dt Vsoln ΔTavg Std. dev. ΔTmin ΔTmax [K] [K/h] [ml] [K] [K] [K] [K] C1 323.15 5 15 23.4 10.7 3.4 47.4 110 C2 318.15 5 15 24.4 9.3 6.9 41.7 84 C3 323.15 10 15 34.0 8.6 9.7 49.6 70 C4 323.15 20 15 35.9 8.1 11.1 49.5 112 C5 323.15 20 150 13.7 5.4 7.1 23.1 10 C6 323.15 20 150 20.8 5.2 14.9 34.0 10

56 Table 4.14. MZW of salicylamide in acetone. Deno- Experimental parameters MZW No of tation exp. Teq -dT/dt Vsoln ΔTavg Std. dev. ΔTmin ΔTmax [K] [K/h] [ml] [K] [K] [K] [K] D1 323.15 5 15 12.4 5.9 3.6 29.7 70 D2 318.15 5 15 15.7 6.5 3.7 31.9 70 D3 313.15 5 15 20.0 6.7 5.6 31.0 51 D4 308.15 5 15 17.7 9.1 3.8 33.9 54 D5 323.15 10 15 18.9 8.9 4.7 34.9 71 D6 323.15 20 15 20.6 7.0 6.7 31.7 87 D7 323.15 20 150 8.0 2.3 4.6 12.4 10 D8 323.15 20 150 10.4 2.0 7.9 14.1 10

Table 4.15. MZW of salicylamide in ethyl acetate. Deno- Experimental parameters MZW No of tation exp. Teq -dT/dt Vsoln ΔTavg Std. dev. ΔTmin ΔTmax [K] [K/h] [ml] [K] [K] [K] [K] E1 323.15 5 15 17.6 6.7 3.8 33.6 126 E2 318.15 5 15 21.5 8.5 7.2 42.3 65 E3 323.15 10 15 25.8 7.6 7.7 42.7 140 E4 323.15 20 15 23.5 8.5 5.7 45.1 140 E5 323.15 20 150 15.6 6.2 7.9 25.6 10 E6 323.15 20 150 18.0 6.4 5.9 27.2 10

58 5. Evaluation and Discussion

5.1 Crystal Phases A total of 15 different crystal phases were identified among the six investigated model compounds in a total of eight solvents. Most of these crystal phases belong to space group P 21/c, which can be expected as it is by far the most common space group for organic crystals (Hammond, 2006). Furthermore, none of these crystal phases were found in crystal systems other than the monoclinic (most common), orthorhombic or triclinic. It has been reported that these three crystal systems alone comprise about 95 % of all organic crystal phases (Baur and Kassner, 1992). The investigated compounds are structurally and chemically similar as they all comprise a benzene ring having two functional groups located in ortho, meta, or para-configuration. The number and type of crystal phases for each compound is to some extent linked to its isomeric configuration. Only one crystal phase was found for the ortho-isomers (i.e. OHBA and SA), in which the crystal structures are both based on dimers. These dimers are in the crystal lattice inversely connected through hydrogen bonds via the COOH (OHBA) and CONH2 (SA) groups. In addition, hydrogen bonds are established intramolecularly between the hydroxy groups in the crystal lattice of both OHBA and SA. This arrangement effectively reduces the ability for intermolecular hydrogen bonding leading to a decreased capacity for formation of solvated and polymorphic structures. The meta-isomeric compounds (i.e. MHBA and MABA) were only found to crystallize as two unsolvated polymorphs. However, whereas MHBA is expected to be monotropic, MABA is likely enantiotropic with a transition temperature close to the melting temperature of polymorph 1 of MABA (appendix 2). The para-substituted compounds (i.e. PHBA and PABA) both displayed several different crystal phases where the type of the crystal phase is similar for PHBA and PABA. Two (unsolvated) polymorphs are known of PHBA and PABA. In acetone and 1,4-dioxane, PHBA and PABA both crystallize as (2/1) solvates. Thus, the hydroxy and amino groups in PHBA and PABA, respectively, appear to exert a similar influence on the molecular packing arrangement of the crystal lattice. However, this structural similarity is not completely unambiguous as PHBA forms a (stable) monohydrate in water whereas no hydrate of PABA has been found.

59 5.2 Experimental Relation between Solubility and the Temperature Dependence of Solubility In Figure 5.1 is shown the experimental relation between the molar solubility and the temperature dependence of solubility, given as the van't Hoff enthalpy of solution (Eq. 2.38), for an unsolvated phase (normally the stable phase at room temperature) of each model compound in several solvents.

40 40 R2 = 0.983 30 R2 = 0.998 30 20 20 OHBA-P1 10 MHBA-P1 10 0 0 -6 -4 -2 0 -6 -4 -2 0 40 40

R2 = 0.999 30 R2 = 0.912 30

20 20 [kJ/mol] PHBA-P1 10 SA-P1 10 0 0 -6 -4 -2 0 -6 -4 -2 0 40 40

R2 = 0.955 30 R2 = 0.894 30 20 20 MABA-P1 10 PABA-α 10 0 0 -6 -4 -2 0 -6 -4 -2 0

ln(xeq) [mol/mol] Figure 5.1. Experimental relationship between molar solubility and the temperature dependence of molar solubility of six different compounds in three to five organic solvents at 35 oC.

Figure 5.1 clearly shows how a lower molar solubility corresponds to a higher van't Hoff enthalpy of solution (i.e. a greater temperature dependence of solubility) in the solubility region (-6 < lnxeq < 0) at 35 oC for these crystal phases. The same relation appears at other temperatures in the 10 to 50 oC interval. In this solubility region, the vH experimental relationship between lnxeq and ΔH So ln is well correlated by the function given in section 2.3.5 (Eq. 2.67):

vH 2 H SO ln =Δ α xeq + β ln)(ln xeq (5.1) where α and β are crystal phase specific coefficients (solid curves in Figure 5.1). The coefficients α and β of unsolvated crystal phases of the model compounds are listed

60 vH in appendix 4. The trend between lnxeq and ΔH So ln typically follow Eq. 5.1 at a solubility concentration above lnxeq = -6. At lower molar solubility the relationship vH between lnxeq and ΔH So ln begins to deviate from Eq. 5.1 and follows the general trend shown in Figure 2.8. This was frequently observed for solubility data in water, which exhibits a comparably lower solubility for all the model compounds. The relation between the molar solubility and its dependence on temperature emerges from the fact that all solubility curves converge at higher temperature and intersect at the melting temperature of the solute. At the melting temperature of the solute the slope of the solubility curve in a van't Hoff plot is dependent on the melting enthalpy of the solute, regardless of solvent (see section 2.3.1). Based on these boundary conditions at the melting temperature a generalized van't Hoff plot can be constructed for a solute in different solvents at higher molar solubility, as envisaged in Figure 5.2.

1/Tm 1/T 0

Solvent A

Solvent B f Δ⋅−= THRSlope m )(

Solvent C

Δ⋅−= HRSlope vH Soln ln(x ) eq

Figure 5.2. Illustration of a van't Hoff plot of a solid phase in three solvents at higher molar solubility.

vH Some general applications of the relationship between lnxeq and ΔH So ln in this solubility region are outlined below.

5.2.1 Yield in Cooling Crystallization Due to the relationship between solubility and its temperature dependence the yield obtained from a cooling crystallization is directly affected by the solubility concentration. A cooling crystallization conducted in a solvent of high molar solubility (solvent A) and a solvent of low molar solubility (solvent B) is illustrated in Figure 5.3.

Solvent A Solvent B

Solubility

T T T 2 1 2 T1 Temperature Temperature Figure 5.3. Influence of molar solubility on the yield in a cooling crystallization performed from temperature T1 to T2.

Since the solubility in solvent B is lower than in solvent A, the temperature dependence of the solubility in solvent B will be greater than in solvent A. Thus, the yield obtained from the cooling crystallization in solvent B will exceed the yield (in percentage) obtained from the cooling crystallization in solvent A.

5.2.2 Influence of Solubility on Enantiotropic Polymorphism Another effect that emerges as a result of how solubility is related to temperature can be seen in the case of an enantiotropic polymorphic system. The solubility of enantiotropic polymorphs is at the transition temperature equal and very similar in close proximity to the transition temperature. It can therefore be difficult to pinpoint the exact location of the transition temperature based on experimental solubility data. The accuracy in the identification of this transition temperature is drawn from the difference in solubility between the polymorphs close to the transition temperature and from the experimental uncertainty in the solubility measurements. As stated previously, the molar solubility of each polymorph approaches unity at the melting temperature of respective polymorph. Thus, when two enantiotropic polymorphs exhibit different melting temperature, the difference in lnxeq between the polymorphs close to the transition temperature becomes greater in solvents of low solubility as compared to solvents of high solubility. This effect is illustrated in Figure 5.4.

1/Tm(I) 1/Tm(II) 1/Ttr 1/T 0

Solvent A

ln(x ) eq

Polymorph I Polymorph II Solvent B

Figure 5.4. Illustration of a van't Hoff plot of an enantiotropic polymorphic system in two solvents. Due to the difference in melting temperature of the polymorphs, the difference in lnxeq between the polymorphs close to the transition temperature, Ttr, is greater in solvent B (low solubility) than in solvent A (high solubility).

Therefore, we can expect that it is easier to determine the transition temperature in solvents of lower solubility as compared to solvents of higher solubility. Of course, the experimental uncertainty in the solubility measurements may also affect the determination of the transition temperature. Of the investigated model compounds, the enantiotropic polymorphs of PABA (i.e. PABA-α and PABA-β) exhibit a transition temperature at approximately 16 oC (appendix 3). The solubility of the two polymorphs was determined between 5 and 25 oC in three solvents of different solubility. As shown in Figure 5.5, a greater difference in lnxeq between the two polymorphs more often appears in solvents of lower solubility, as can be expected.

63 0 5 ˚C 10 ˚C 15 ˚C 20 ˚C 25 ˚C

-1

-2 ) [mol·mol-1] α -3

-4 (PABA- eq

lnx -5 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 -1 lnxeq(PABA-α) – lnxeq(PABA-β) [mol·mol ] Figure 5.5. Relationship between lnxeq of PABA-α and the difference in lnxeq between the two enantiotropic polymorphs of PABA in EtOH (□), 2-PrOH (◊) and ACN (Δ). At constant temperature, the difference in lnxeq between the polymorphs close to the transition temperature is normally greater in solvents of lower solubility (ACN) when compared to solvents of higher solubility (EtOH).

5.2.3 Distinguishing Crystal Phases from Solubility Data At constant temperature the solid-state properties of the crystal phase are constant. When a different crystal phase is formed in one solvent (e.g. a solvate), then the solid- state properties (i.e. melting temperature, melting enthalpy and ΔCp) of that crystal phase will differ from the crystal phase in the other solvents. Thus, a trend vH disagreement is obtained when compared to the data of lnxeq and ΔH So ln in the other solvents. We may utilize this trend discrepancy using only solubility data when exploring the presence of crystal phases in different solvent. The solubility of PHBA was determined in five organic solvents at different vH temperatures. Upon plotting lnxeq versus ΔH So ln at constant temperature, a trend disagreement appears for the solubility in acetone, as depicted in Figure 5.6.

[kJ/mol]

0 -5 -4 -3 -2 -1 0

ln(x ) [mol/mol] eq Figure 5.6. Identification of a solvated crystal phase of PHBA in acetone from solubility data, vH o using the trend between lnxeq and ΔH So ln at 30 C of the unsolvated crystal phase in different solvents (grey diamond) and the solubility in acetone (white circle).

Thus, it is possible to distinguish crystal phases solely based on solubility data in different solvents. In the case of the acetone solvate of PHBA (PHBA-S2), the solvated crystals desolvated rapidly after being brought from solution. As a consequence, a detailed solid-state analysis of the crystals, using e.g. DSC, was fraught with difficulties and prevented the melting properties of the solvate to be determined. Many solvated crystal phases, similar to the PHBA acetone solvate, only retain the crystal structure in solution and once the crystals are removed from the solution are prone to desolvation during normal atmospheric conditions. In such cases, the crystal phase in the solution may be hard to resolve, leading to uncertainties as to what type of crystal phase is present in the solution.

5.3 Evaluation of the Semi-empirical Solubility Model To explore the generality of the relation between molar solubility and its temperature dependence at all solubility concentrations, a test set of 41 different organic and pharmaceutical compounds was employed comprising a total of 115 solubility curves (81 in organic solvents and 34 in water). The references to the test set are given in Paper VI. The regression equation of solubility, RES B2 (Table 2.1)

A ln x ++= CTB (5.2) eq T

65 was used and the coefficients A, B and C were determined from the solubility data. The corresponding experimental van't Hoff enthalpy of solution was calculated through Eq. 2.38:

vH 2 ΔH So ln (experimental +−= CTAR )() (5.3)

The van't Hoff enthalpy of solution given by the semi-empirical solubility model in section 2.3 (Eq. 2.62 and 2.63) contain the melting temperature and melting enthalpy of the solute, and three coefficients, viz. σ, ε and φ*. The melting properties of the investigated solutes are given in Paper VI. At constant temperature, the coefficients σ, ε and φ* are assumed to be equal for all solutes. The coefficients σ, ε and φ* were vH determined by non-linear regression using the 115 values of ΔH So ln at each temperature between 10 and 30 oC in 5 oC increments. The objective function used in the minimization is given by:

N vH vH 2 ∑()ΔH So ln (experimental i Δ− H So ln predicted)() i RMS = i (5.4) N where RMS denotes the residual mean square and N is the number of solubility curves. The results from the minimization are listed in Table 5.1.

Table 5.1. Coefficients and RMS for prediction of the van’t Hoff enthalpy of solution. T σ ε φ* RMS RMS [oC] [mol·mol-1] [kJ·mol-1] [kJ·mol-1] Organic solvents Water γeq<1 γeq>1 10 1.958 1.632 0.276 2.57 5.12 8.16 15 1.940 1.624 0.294 2.32 4.53 6.87 20 1.922 1.619 0.311 2.07 4.19 6.09 25 1.897 1.622 0.333 1.83 4.20 6.04 30 1.868 1.620 0.355 1.63 4.75 6.76

In Figure 5.7 is shown the accuracy of the prediction of the van't Hoff enthalpy of solution at 20 oC based on the values of the coefficients σ, ε and φ*, in Table 5.1.

66 50000

40000

30000

20000

10000

Experimental [J/mol] Experimental 0 0 10000 20000 30000 40000 50000 vH Predicted Δ H So ln [J/mol] Figure 5.7. Experimental versus predicted van't Hoff enthalpy of solution at 20 oC. The red and blue symbols depict organic solvents and water, respectively. The triangles and circles represent negative and positive deviations from Raoult's law, respectively.

Better predictions of the van't Hoff enthalpy of solution were obtained in organic solvents (red symbols in Figure 5.7) compared to water (blue symbols in Figure 5.7), and at negative deviations from Raoult's law, as seen in Table 5.1.

5.4 Prediction of Solubility Curves Through the semi-empirical solubility curve model, it is possible to predict the temperature dependence of solubility using the melting temperature and melting enthalpy of the solute and the solubility at one temperature. Thus, we may use this model in conjunction with the boundary condition of solubility (Eq. 2.49), to predict entire solubility curves in new solvents. When the solubility has been determined experimentally at temperature T (xeq,exp and Texp) we can e.g. use the RES given by Eq. 5.2 and the associated Eq. 5.3 for the temperature dependence of solubility. Applying Eq. 5.2 at the melting temperature gives:

A 0 ++= CTB m (5.5) Tm

The three equations 5.2, 5.3 and 5.5 contain three coefficients. Resolving these coefficients yields the following equations for A, B and C:

67 vH 2 ΔH So ln Tm mTT exp A = − xeq exp, )ln( 2 (5.6) R exp − TT m m − TT exp )(

vH 2 2 2 2 ΔH So ln m − TT exp )( m + TT exp )( B = 2 + xeq exp, )ln( 2 (5.7) RTexp m − TT exp )( m − TT exp )(

vH ΔH So ln Tm C = − xeq exp, )ln( 2 (5.8) expexp − TTRT m )( m − TT exp )(

The van't Hoff enthalpy of solution can be predicted through the above model using the melting properties of the solute and solubility at one temperature. Hence, we can conclude that for a crystal phase for which the melting temperature and melting enthalpy has been determined (e.g. via DSC analysis), we need only one value of the solubility between 10 and 30 oC (xeq,exp and Texp) to predict a solubility curve in that solvent. To illustrate, in Figure 5.8 is shown a predicted solubility curve of MABA-P1 in acetonitrile, based on the experimental solubility at 20 oC.

solvent] [g solute/kg Solubility 0 0 102030405060 Temperature [oC] Figure 5.8. Predicted solubility curve of MABA-P1 in ACN (solid black curve), based on the experimental solubility at 20 oC (grey diamond). The blue triangles represent the experimental solubility at temperatures between 10 and 50 oC, the dashed green and red curves the 68 % and 95 % confidence limits in the prediction.

The model compound MABA was not included in the test set used in the development of the solubility curve model. The experimental solubility at other temperatures is also inserted in Figure 5.8 to demonstrate the accuracy in the prediction for this particular case. From the uncertainty in the prediction of the van't Hoff enthalpy of solution, we may establish confidence limits in which we expect the

68 solubility curve to be located. 68 and 95 % confidence limits are inserted in Figure 5.8 corresponding to one and two standard deviations in the prediction of the van't Hoff enthalpy of solution. An experimental solubility curve that appears outside the 95 % confidence limits of the predicted solubility curve may be due to statistical reasons (5 %), indicate that equilibrium is not achieved in the solubility determination, or actually signal that the crystal phase at Texp differs from the crystal phase at the melting temperature.

5.5 Experimental Evaluation of RES and Prediction of the Melting Temperature of the Solute The 15 different regression equations of solubility, RES, in Table 2.1 were fitted to the 115 solubility curves (81 solubility curves in organic solvents and 34 in water), using non-linear regression in the computer program ®Origin, v6.1. The function:

2 1 2 χ BA ,...),( = ∑∑[]− 21 iijijeq BATTfx ,...),,...;,()(ln (5.9) N f ij was employed and the RES coefficients A, B, C and D were determined by a non- weighted least-square minimization of χ2. The minimization parameter χ2 thus represents the goodness of fit of the solubility data. In Table 5.2 is listed the average goodness of fit (104·χ2) in the regression of the 115 solubility curves divided into positive and negative deviations from Raoult's law (based on Eq. 2.64 and Table 5.1) and in organic solvents and water.

69 Table 5.2. Average goodness of fit (104·χ2) of 15 RES to 115 solubility curves. Category RES Negative deviations from Positive deviations from Raoult's law (γeq < 1) Raoult's law (γeq > 1) Organic Water Organic Water solvents (6 solubility solvents (28 solubility (38 solubility curves) (43 solubility curves) curves) curves) A A1 22.07 12.33 12.79 120.80 A2 12.54 11.55 27.87 68.95 A3 16.44 10.07 14.39 92.57 B B1 10.26 1.92 9.75 17.56 B2 9.43 1.97 10.00 18.07 B3 8.94 1.98 9.38 18.55 B4 9.27 1.95 10.42 18.35 C C1 10.20 1.93 9.92 17.58 C2 9.71 1.93 9.98 17.83 C3 9.28 1.97 9.78 18.19 C4 8.93 1.98 9.28 18.53 D D1 4.73 1.97 4.67 16.19 D2 4.37 2.03 4.86 16.52 D3 4.82 1.97 4.63 16.14 D4 4.55 2.00 4.76 16.36

As seen in table 5.2, the average goodness of fit differed between aqueous and organic solvents and to some extent between the RES belonging to different categories. For the organic solvents, the goodness of fit of the solubility data increased upon adding additional RES coefficients for both negative and positive deviations from Raoult's law. However, the difference in χ2 between the category B and C equations and within each category is small. It is therefore suggested that the number of adjustable coefficients in the RES is more important than the mathematical function in regression of solubility data. For solubility data in water, no significant increase in the average goodness of fit was observed when adding a fourth coefficient to the RES for both negative and positive deviations from Raoult's law. It has been suggested by Grant et al. (1984) that adding more than three coefficients to the RES is unnecessary. Based on these 115 solubility curves, only solubility data in water appears to conform to this conclusion. The ability to extrapolate solubility data was investigated for the 15 different RES by prediction of the melting temperature of the solutes through Table 2.2. The results are given in Table 5.3, in terms of the average difference between the predicted melting temperature, Tm,pred, and experimental melting temperature, Tm,exp, and the

70 associated standard deviation. In some cases and for some RES the prediction of the melting temperature failed. This occurred when the RES coefficients e.g. gave negative values within the root-square term in Table 2.2 or when an inflection point was obtained in the extrapolated solubility curve prior to the melting temperature. The frequency of how often the predictions succeeded is given in Table 5.3 and is denoted as frequency of consistent predictions, FCP.

Table 5.3. Prediction of melting temperature from extrapolation of solubility data. Category RES Organic solvents Water (81 solubility curves) (34 solubility curves) Tm,pred-Tm,exp std. dev. FCP Tm,pred-Tm,exp std. dev. FCP [K] [K] [%] [K] [K] [%] A A1 127.5 204.0 100 500.8 673.1 85.3 A2 -5.0 26.0 100 73.2 128.7 100 A3 25.2 53.0 100 160.9 168.6 97.1 B B1 18.2 54.0 92.6 70.5 113.0 88.2 B2 0.2 37.0 90.1 24.3 71.5 85.3 B3 -5.0 29.3 80.2 14.7 82.2 73.5 B4 -6.5 31.8 91.4 69.1 332.5 91.2 C C1 16.8 52.2 92.6 65.4 107.6 88.2 C2 4.6 38.1 90.1 36.1 78.0 88.2 C3 -2.4 29.6 87.7 21.2 75.7 79.4 C4 -6.1 27.1 76.5 11.8 81.8 70.6 D D1 -16.0 39.4 60.5 43.1 198.8 61.8 D2 -25.3 35.3 53.1 -3.1 78.7 55.9 D3 -13.1 42.3 61.7 77.7 322.5 64.7 D4 -17.6 39.5 59.3 5.9 104.4 55.9

As shown in Table 5.3 the melting temperature of the solute can be predicted from solubility data in organic solvents with a relatively high accuracy using several RES. Better predictions were made when the solubility was high and when the melting temperature was lower. This of course stems from a shorter extrapolation to the melting temperature. In general, adding more coefficients to the RES leads to a reduced ability for extrapolation to higher temperature, as seen in Table 5.3. It is instead the functional form of the RES that is of importance for the accuracy and precision of the prediction of the melting temperature. The perhaps most accurate RES for organic solvents appears to be A2 (average absolute error of 19.8 K) possibly followed by B2 (average absolute error of 21.7 K). The prediction of the melting temperature of the solute using aqueous solubility data was however rather poor. In Figure 5.9 is shown the accuracy and precision of the prediction of the melting

71 temperature of the solutes through RES A2 and B2 using solubility data in organic solvents.

550

500

450 [K]

m,pred 400 T 350

300 300 350 400 450 500 550 T [K] m,exp Figure 5.9. Prediction of the melting temperature of the solute from solubility data in organic solvents using RES A2 (blue circles) and B2 (red crosses).

Among the fundamental physical properties, the melting temperature is one of the most difficult to predict and standard deviations are typically obtained in the range of 17 to 35 oC (lower for narrow test sets) (Katrizky et al., 2001, Simamora et al., 1993 and Martin et al., 1979). Most of these approaches are based on more or less intricate group contribution methods or structure-property relationships. By using the comparably simple approach of extrapolating solubility curves in organic solvents to the melting temperature it is possible to estimate the melting temperature of organic solutes with a reasonable accuracy.

5.6 Experimental Determination of the Activity of the Solid Phase In the experimental evaluation of the approach to determine the activity of the solid phase (section 2.5), the activity of the solid phase has been determined using four of the crystal phases of the model compounds, i.e. OHBA-P1, MHBA-P1, PHBA-P1 and SA-P1. The melting properties of these crystal phases are available in Table 4.2, and the coefficients α and β of Eq. 5.1 are available in appendix 4.

5.6.1 Evaluation of ΔCp The activity of the solid phase was determined by treating ΔCp as constant with temperature (Eq. 2.74) or linearly dependent on temperature, according to:

p m −+=Δ TTrqC )( (5.10)

Eq. 5.10 was proven to adequately describe the temperature dependence of ΔCp in the investigated temperature interval and no grounds have been found to use a higher order function of ΔCp. Details of the procedure to determine the coefficients q and r are given in Paper V. In Table 5.4 is listed the values of q and r for the model compounds from ΔCp given by Eq. 2.74 and 5.10. The Residual Mean Square, RMS, in the optimization procedure is also included.

Table 5.4. Determined constants of ΔCp (J·mol-1·K-1) when assumed constant with temperature (Eq. 2.74) and when assumed linearly dependent on temperature (Eq. 5.10). ΔCp = f(T) ΔCp = q ΔCp = q + r(Tm-T) Crystal phase q RMS q r RMS [J·mol-1·K-1] [J·mol-1] [J·mol-1·K-1] [J·mol-1·K-2] [J·mol-1] OHBA-P1 93.3 481 143.3 -0.6201 36 MHBA-P1 105.9 1043 165.7 -0.5037 69 PHBA-P1 102.7 497 140.8 -0.2970 25 SA-P1 126.9 655 192.3 -0.9322 112

Since the heat capacity of the solid form of the model compounds has been determined experimentally (Table 4.3), it is possible to calculate the corresponding heat capacity of the supercooled liquid via the values of ΔCp in Table 5.4 and Eq. 2.14. The heat capacity of the solid and (supercooled) liquid of the model compounds is given in Figure 5.10.

400 400 OHBA-P1 MHBA-P1

300 300

]

-1 200 200

·K 100 100 -1 250 350 450 550 250 350 450 550

400 400

[J·mol PHBA-P1 SA-P1 p 300 300 C 200 200

100 100 250 350 450 550 250 350 450 550

Temperature [K] Figure 5.10. Experimental heat capacity of the solid (lower curve) and determined heat capacity of the supercooled liquid (upper curve) of OHBA-P1, MHBA-P1, PHBA-P1 and SA-P1.

The heat capacity of the solid and supercooled liquid forms of the model compounds decreases with decreasing temperature. For the hydroxybenzoic acid isomers, the heat capacity of the solid and liquid forms decreases in the order para-, meta- and ortho-isomer.

5.6.2 Evaluation of Solid-state Activity and Activity Coefficients at Equilibrium Based on Eq. 5.10, the activity of the solid phase is given by:

f 2 Δ TH m )( ⎡ 11 ⎤ q ⎡ ⎛ Tm ⎞ Tm ⎤ r ⎡ ⎛ Tm ⎞ Tm T ⎤ ln a = ⎢ − ⎥ − ⎢ln⎜ ⎟ +− 1⎥ − ⎢Tm ln⎜ ⎟ +− ⎥ (5.11) ⎣ m TTR ⎦ R ⎣ ⎝ T ⎠ T ⎦ R ⎣ ⎝ T ⎠ T 22 ⎦ where the values of q and r are available in Table 5.4. By using the solid-state activity through Eq. 5.11 as the reference we may estimate the error in the determination of the activity of the solid for other approximations. In Table 5.5 is listed the average error over the different temperatures of the solid-state activity for the approximations ΔCp = 0 (Eq. 2.41), ΔCp = ΔSf(Tm) (Eq. 2.42) and ΔCp = q (Eq. 2.76).

74 Table 5.5. Comparison of the average error in the estimation of the activity of the solid phase using three approximations of ΔCp. Approximation OHBA-P1 MHBA-P1 PHBA-P1 SA-P1 ΔCp = 0 62 % 85 % 85 % 62 % ΔCp = ΔSf(Tm) 36 % 57 % 60 % 42 % ΔCp = q 17 % 33 % 25 % 17 %

Table 5.5 reveals a significant error upon using the approximation of ΔCp = 0. By this assumption the estimated value of the activity may become as low as 1/12 of the correct value. The approximations ΔCp = ΔSf(Tm) underestimates the value of ΔCp by up to a factor of three. Although, a smaller error appears for the approximation ΔCp = q, where q is determined from the intersection between the solid-state activity line vH and the correlation between ΔH So ln and lnxeq, the estimated solid-state activity is consistently lower than the real value (up to a factor of 1.6). Thus, regarding ΔCp as constant with temperature is overly simplified for these compounds. The determination of the activity of the solid phase enables the determination of the activity coefficient at equilibrium, through Eq. 2.26. The activity coefficient at equilibrium of OHBA-P1 in five solvents is shown in Figure 5.11.

γ 2 eq

0 275 325 375 425 Temperature [K]

Figure 5.11. Relation between the activity coefficient at equilibrium, γeq, and temperature, for OHBA-P1 in MeOH; ◊, ACN; □, HAc; Δ, Acetone; o, and EtAc; +. The melting temperature of OHBA-P1 is also inserted (grey circle) representing the boundary condition where γeq is unity.

The activity coefficients of the solute at equilibrium appear for each solvent to converge towards unity and a Raoult's law behavior upon approaching the melting temperature of OHBA-P1, as can be expected.

75 5.7 Influence of Solid-state and Solution Properties on Solubility The solubility of four of the crystal phases in six solvents at 30 oC is given in Figure 5.12.

-1

] -2

-1 -3

-4

[mol·mol -5 eq -6 lnx -7

-8

-9 O

2 H HAc ACN EtAc MeOH Acetone

Figure 5.12. Solubility of OHBA-P1; ◊, MHBA-P1; □, PHBA-P1; Δ, and SA-P1; X, in six solvents at 30 oC.

The hydroxybenzoic acid isomers comprise the same molecular weight and functional groups. The difference between SA and the hydroxybenzoic acid isomers is present in the molecular weight (137.14 versus 138.12 g/mol) and in the amino group. Despite these small differences in the molecular structure, the solubility varies between the model compounds, in some solvents with several orders of magnitude. The value of the solubility in a real solvent depends on the ideal solubility and the extent of deviation from ideality. Within a Raoult's law reference, the ideal solubility is equal to the activity of the solid phase, while the extent of non-ideality is captured by the activity coefficient at equilibrium. In the preceding section, the activity of the solid phase of four crystal phases was determined and the activity coefficient at equilibrium was determined from solubility data using Eq. 2.26. Thus, the separation of the solid-state properties from the solution properties allows us to qualitatively investigate how the properties of the solid and the properties of the solution influence the solubility for different solutes and solvents.

5.7.1 Influence of Solid-state Properties on Solubility Based on the melting properties and determined coefficients q and r (Table 5.4), the ideal solubility of the crystal phases is shown in Figure 5.13.

0.20 ]

-1

0.15

0.10

0.05

[mol·mol Ideal Solubility 0.00 0 102030405060 Temperature [oC] Figure 5.13. Ideal solubility of OHBA-P1; ◊, MHBA-P1; □, PHBA-P1; Δ, and SA-P1; X, between 10 and 50 oC.

It is seen that SA-P1 exhibits the highest ideal solubility followed by OHBA-P1, PHBA-P1 and finally MHBA-P1. A lower ideal solubility is directly inferred from a higher melting temperature and melting enthalpy, whereas a greater magnitude of ΔCp increases the ideal solubility. The reason SA exhibits the highest ideal solubility of the investigated solutes is inherent in the low melting temperature (lowest of the solutes) and in the comparably high ΔCp.

5.7.2 Influence of the Solution on Solubility The properties of the solution are reflected by molecular interactions between the solute and solvent molecules. These interactions can be divided into solvent-solvent, solvent-solute and solute-solute interactions. An ideal solution is obtained when Raoult's law is obeyed, implicating that all the molecular interactions are identical and equal to the solute-solute interactions. When the solution is non-ideal the influence of the solvent is represented by solvent-solvent and solvent-solute interactions, which in terms of thermodynamic quantities are expressed by the activity coefficient of the solute. The solvent-solvent interactions are drawn from the cohesive energy of the solvent, which when compared to other solvents are elucidated by e.g. the boiling point, volatility and density. The solvent-solute interactions originate from the affinity of the solute for the solvent, which is dependent on the chemical properties of the solute and solvent, e.g. the involved functional groups. In Figure 5.14 is shown the activity coefficient of the solute at equilibrium at 30 oC of the different crystal phases in different solvents.

5 4 eq γ 3 ln 2

1 0 -1

-2 O 2 H HAc ACN EtAc MeOH

Acetone Figure 5.14. Activity coefficient at equilibrium of OHBA-P1; ◊, MHBA-P1; □, PHBA-P1; Δ, and SA-P1; X, at 30 oC in six solvents.

The influence of the solvent on the non-ideal contribution to the solubility can be observed by comparing the activity coefficients between different solvents. Although the activity coefficients at equilibrium differ with different solutes, some general trends can be identified between the solvents. The solvents displaying the highest affinity for the solutes OHBA, MHBA, PHBA and SA were acetone, followed by MeOH and EtAc. In these solvents the hydroxybenzoic acid isomers exhibit negative deviations from Raoult's law, indicating favorable interactions in the solution. In particular beneficial interactions are seen in solutions comprising acetone. In fact, for the solute SA, acetone was the only solvent which resulted in negative deviations from Raoult's law. The comparably higher affinity between the solutes and acetone can be expected to relate to the low cohesive energy of the pure acetone. Acetone exhibits the lowest boiling point (56.1 oC) and highest volatility of the investigated solvents. MeOH is capable of both hydrogen bond donation and acceptance and can accommodate the aromatic ring of the solute. MeOH also exhibits a lower boiling point (64.5 oC), indicative of a comparably lower cohesive energy. Although negative deviations from Raoult's law were primarily obtained for EtAc in solutions with the investigated solutes, EtAc does not exhibit a considerably lower cohesive energy in comparison to the other solvents, as observed though e.g. the boiling point and density, and has a lower hydrogen bonding capability. In solutions of ACN, HAc and H2O, only positive deviations from Raoult's law were observed for all the solutes. The lowest affinity between the solvents and solutes appears in water, which deviates considerably from the other solvents. Water is the only solvent, which lacks the functional groups involving carbon. Hence, the

78 interactions with the solutes takes place primarily through hydrogen bonding and the capability for accommodating the aromatic ring is significantly reduced. The second lowest affinity emerges in ACN followed by HAc. ACN is incapable of providing hydrogen bond donation, which restricts the ability for solute-solvent interactions. In solutions of HAc, an almost ideal behavior is obtained for all the solutes. It thus appears that the interactions between HAc and the solutes are similar to the solute- solute interactions. Overall, no clear correlation could be established between the activity coefficients at equilibrium and the properties of the pure solvents, such as e.g. melting temperature and boiling point, molar mass, density or polarity (Reichardt's polarity index, Reichardt, 2003). Instead, the extent of non-ideality is also dependent on what type of solute is present in the solution. Since the solvent-solvent interactions are unchanged regardless of solute at constant temperature, we may observe the influence of the solute on the solvent-solute interactions by comparing the activity coefficients between different solutes in the same solvent. OHBA and SA are both ortho-isomeric compounds which only differ in one functional group, viz. the hydroxy group in OHBA and the amino group in SA. In MeOH, acetone and EtAc the activity coefficient at equilibrium differs considerably between OHBA and SA. Replacing the hydroxy group with the amino group resulted in an increased activity coefficient at equilibrium and thus in a reduced affinity between the solute and the solvent. This tendency points towards beneficial interactions between the carboxylic group in OHBA and the solvents MeOH, acetone and EtAc in relation to the amino group in SA. However, it is surprising to find a higher activity coefficient at equilibrium for OHBA compared to SA in the solvent HAc, which is dominated by a carboxylic group. In ACN the activity coefficient at equilibrium of OHBA and SA is almost the same. It appears that the presence of the nitrogen in ACN does not contribute considerably in reducing the activity coefficient of SA in solutions with ACN. Similarly, almost equal activity coefficients at equilibrium of OHBA and SA were obtained in water. If beneficial interactions were to be present between the hydroxy group in OHBA and water it would be expected that water exhibits a greater affinity for OHBA than SA, which is not seen. The hydroxybenzoic acid isomers OHBA, MHBA and PHBA all comprise the same functional groups. Nevertheless, the activity coefficients at equilibrium of these solutes differ in all solvents. MHBA always exhibit the highest affinity for the investigated solvents. The meta-configuration thus appears as the isomer capable of constructing the most favorable interactions with all types of solvents. In the solvents MeOH, HAc and acetone OHBA displays a higher activity coefficient at equilibrium over PHBA, whereas the opposite applies in the solvents ACN and EtAc. Ergo, the isomeric configuration of the solutes is of importance in the molecular interactions with the solvents, and in case of the ortho- and para-substituted hydroxybenzoic acids appear to be solvent-specific. Although the numerical values of the activity of the solid (section 5.6) may carry some uncertainties, the influence of the isomeric configuration on the activity coefficient at equilibrium is elucidated in the case of

79 water. In solutions of water, OHBA exhibits an activity coefficient at equilibrium that exceeds the activity coefficient at equilibrium of MHBA by a factor of approximately 11 at 30 oC.

5.8 The Metastable Zone Width of Salicylamide The metastable zone width, MZW, constitutes an important experimental factor in the design of the crystallization process. Primarily nucleation can be induced at solution concentrations above the MZW and seeding crystallization can be performed in supersaturated solutions below the MZW. However, the MZW is known to be affected by numerous experimental factors.

5.8.1 Saturation Temperature and MZW The influence of saturation temperature on the MZW of SA was investigated in 5 oC increments between 30 and 50 oC in MeOH and ACN, between 35 and 50 oC in acetone and between 45 and 50 oC in HAc and EtAc. Comparably small differences in the average degree of undercooling, ΔTavg, were observed in all solvents between the investigated saturation temperatures. The MZW of SA in acetone is shown in Figure 5.15, at a cooling rate of 5 oC/h, a solution volume of 15 ml, and saturation temperatures between 35 and 50 oC.

0.22

0.2

0.18

0.16 ty ili ub 0.14 ol S

Concentration [mol/mol] 0.12

0.1 0 1020304050 Temperature [C] Figure 5.15. MZW of SA in acetone between 35 and 50 oC (D1-D4 in Table 4.14).

80 5.8.2 Relation between Cooling Rate and MZW In the literature a linear relationship is often obtained between the cooling rate and the degree of undercooling at the onset of nucleation (expressed as log(-dT/dt) and log(ΔT)) (Nyvlt, 1983, Mullin et al., 1970, Kubota, 2008). This relation has been used to estimate the apparent nucleation order by the method proposed by e.g. Nyvlt, 1968. The relation between the degree of undercooling at the average onset of nucleation of SA and cooling rate is given in Figure 5.16.

1.8 MeOH 1.7 ACN HAc 1.6 Acetone 1.5 EtAc

) 1.4 avg T

Δ 1.3 1.2 log( 1.1

1.0 0.9 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 log(-dT/dt) Figure 5.16. Relation between degree of undercooling at the average onset of nucleation of SA and cooling rate at a solution volume of 15 ml and a saturation temperature of 50 oC.

The greatest effect on the MZW of SA was observed when the cooling rate was increased from 5 to 10 oC/h, but levels out between 10 and 20 oC/h for all solvents. The correlation between log(ΔTavg) and log(-dT/dt) is weak in all solvents. A poor correlation is also obtained when using the value of undercooling at the maximum observed onset of nucleation.

5.8.3 Role of the Solvent Of the investigated experimental variables, the solvent exerted a comparably stronger effect on the MZW of SA. At a solution volume of 15 ml, saturation temperature of 50 oC, and a cooling rate of 5 oC/h, the supersaturation ratio at the average onset of nucleation, savg, ranged from 1.24 in acetone up to 1.76 in HAc. The corresponding driving force of nucleation (according to Eq. 2.104) at the average onset of nucleation, Δµavg, varied from 0.54 to 1.3 kJ/mol in acetone and HAc, respectively. Although, errors are introduced in the Δµavg by not accounting for the ratio of the activity coefficients, it appears that the driving force at the average onset of nucleation is not independent of the solvent. The distribution in the MZW of SA was also related to the solvent. A greater variation in the MZW was obtained in solvents when the supersaturation at the

81 average onset of nucleation was greater. At a solution volume of 15 ml, saturation temperature of 50 oC, and a cooling rate of 5 oC/h, the onset of nucleation of SA in solutions of acetone varied in supersaturation ratio from 1.06 to 1.67, while SA in solutions of HAc nucleated between 1.08 and 2.97. These differences in supersaturation ratio at the onset of nucleation between identically performed experiments in the same solvent, highlights the stochastic nature of nucleation of SA from solutions. In regards to the classical nucleation theory, the critical free energy is inversely related to the driving force of nucleation to the power of two (Eq. 2.98). The difference in the driving force of nucleation at the minimum and maximum observed supersaturation ratio for solutions of HAc then corresponds to a critical free energy that differs by a factor of approximately 150, if γsl can be assumed to be constant with temperature. This significant difference in the critical free energy between reproducibly conducted experiments suggests that the onset of nucleation of SA is governed by a different mechanism. The MZW of SA in different solvents is presented in Figure 5.17 as cumulated distribution with supersaturation ratio.

100%

50% Methanol Acetonitrile Acetic acid Acetone Ethyl acetate

Cumulated MZW distribution 0% 11.522.53 Supersaturation ratio

Figure 5.17. Cumulated distribution of MZW of SA at a solution volume of 15 ml, saturation temperature of 50 oC and a cooling rate of 5 oC/h.

In previous studies, the influence of the solvent on the kinetics of nucleation has been related to bulk properties of the solution. The main factor responsible for differences in nucleation kinetics between different solvents is within the classical nucleation theory found in the interfacial energy between the crystal surface and the solution, γsl, This parameter, which is experimentally difficult to determine, has been related to the solubility and enthalpy of solution by e,g, Nielsen and Söhnel, 1971, Davey, 1982, Mersmann, 1990 and Bennema and Söhnel, 1990. Furthermore, within the so-called equivalent wetting condition, bond energies at the surface of the crystals have been related to bond energies in the bulk (Liu and Bennema, 1993). In the

82 MZW study of SA, no evident relation appeared between solubility or enthalpy of solution and the supersaturation ratio or driving force at the average onset of nucleation for the investigated solvents. The viscosity has also been found to pose an influence on the kinetics of nucleation. In nucleation from melts a decrease in the nucleation rate has been observed above a certain level of supercooling, which was believed to originate from a sharp increase in viscosity (Mullin, 2001). This behavior has also been observed in viscous solutions of citric acid (Mullin and Leci, 1969) and in protein crystallization of lysozyme (Pan et al., 2005). The relation between the average onset of nucleation of SA and physical properties of the pure solvents has been explored and no clear correlation was found to the viscosity, boiling point, polarity (according to Reichardt's polarity index), pH, density or molecular weight of the pure solvents. However, when the viscosity of the pure solvents is divided by the concentration of the solution (expressed as mol solute per m3 solvent, denoted as Cm), a comparably stronger correlation emerges to the supersaturation at the average onset of nucleation. This relation is depicted in Figure 5.18 at three cooling rates, at a solution volume of 15 ml and saturation temperature of 50 oC.

2.4 2 2.2 R = 0.86

2 2.0 R = 0.95 1.8

avg R2 = 0.98 s 1.6 1.4

1.2

1.0 0.00.10.20.30.40.50.60.7 3 η/Cm [Pa·s·m /mol SA] Figure 5.18. Relation between supersaturation ratio at the average onset of nucleation and solvent viscosity divided by moles SA per m3 solvent, in five solvents at a cooling rate of 5 oC/h (blue diamonds), 10 oC/h (green squares) and 20 oC/h (red triangles). The error bars represent 95 % confidence limits in the supersaturation ratio at the average onset of nucleation.

As seen in Figure 5.18, a more or less linear relationship is obtained at all cooling rates. Following the trends, the onset of nucleation of SA thus appears to be linked to the viscosity of the pure solvent, η, and the number of solute molecules per unit volume, Cm. In terms of supersaturation ratio at the average onset of nucleation, a

83 narrower MZW is then obtained when the viscosity of the solvent is low and when the number of solute molecules per volume is high. The viscosity is inversely related to the diffusivity via the Stokes-Einstein equation. The diffusion of solute molecules is normally considered as an important and often rate-determining step in several mass transfer processes, e.g. dissolution and crystal growth. According to the relation in Figure 5.18 it is expected that the rate-limiting step in the onset of nucleation of SA is dependent on the molecular mobility of the solute and on the number of solute molecules per unit volume. The molecular movement of solute molecules in the solution is random in nature. As solute molecules in the supersaturated solution randomly collide they start to aggregate, which with continued addition of solute molecules leads to the formation of clusters and subsequent crystals. The collision frequency of the solute molecules is directly related to the molecular mobility of the solute and on the number of solute molecules per volume. Thus, the trends in Figure 5.18 suggest that the onset of nucleation of SA is governed by a collision frequency of the solute molecules per unit volume.

5.8.4 Effect of Solution Volume The influence of solution volume on the onset of nucleation was investigated in solutions of MeOH at a cooling rate of 20 oC/h, and saturation temperature of 50 oC, at solution volumes of 15, 150 and 500 ml. The results are shown in Figure 5.19 as a distribution histogram over the nucleation events at different supersaturation ratios.

84 20% 15 ml 150 ml 500 ml 15%

10%

Frequency [%] Frequency 5%

0% 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 Supersaturation ratio

Figure 5.19. Histogram over the distribution of the onset of nucleation of SA in solutions of MeOH with supersaturation ratio for three solution volumes (15, 150 and 500 ml).

The average onset of nucleation remained essentially constant for the investigated solution volumes. Although the variation in the onset of nucleation decreased slightly with increasing solution volume (standard deviation in savg; 15 ml: 7.6, 150 ml: 6.2, 500 ml: 5.7), the difference is not statistically significant. Thus, it appears that the solution volume does not affect the MZW of SA. This behavior is in accordance with what can be expected if the onset of nucleation is dependent on a collision frequency of the solute molecules per unit volume, which is an intensive parameter.

5.8.5 Influence of Solvent Evaporation during Cooling Crystallization The importance of solvent evaporation during the cooling crystallization was investigated in jacketed crystallizers by measuring the onset of nucleation in five solvents. In half the crystallizations (10 experiments per solvent) the solution was exposed to the surrounding atmosphere and in half the experiments (10 experiments per solvent), the crystallizer was sealed to prevent solvent evaporation. The results from the cooling crystallization at 20 oC/h in 250 ml crystallizers are shown in Figure 5.20.

85 2.2

2.0

1.8

1.6

1.4

Supersaturation ratio 1.2

1.0

HAc ACN EtAc

MeOH

Acetone Figure 5.20. MZW of SA in open (O) and sealed (X) crystallizers at a saturation temperature of 50 oC, a cooling rate of 20 oC/h and a solution volume of 150 ml.

The onset of nucleation of SA differed significantly in primarily MeOH and ACN upon not using a crystallizer lid during cooling crystallization. The supersaturation ratio at the average onset of nucleation decreased from 1.43 and 1.36 in sealed crystallizers, down to 1.05 and 1.08 in open crystallizers in MeOH and ACN, respectively. The variation in the onset of nucleation also decreased considerably in these solvents by allowing the solvent to evaporate during the cooling crystallizations. In the other solvents the change was not as notable, in terms of the average and variation in the onset of nucleation. A continuous evaporation of the solvent from the surface of the solution leads to an increasing concentration in the bulk, which can be expected to be particularly predominant at the solution surface. The overall decrease in supersaturation ratio at the average onset of nucleation in these solvents indicates that the emergence of concentration gradients in the solution facilitates the nucleation process of SA. However, the reduction in MZW in solutions of acetone, which exhibits the lowest boiling point and highest volatility, was smaller than in ACN and MeOH. The reduced MZW in MeOH and ACN is instead likely a result of a different nucleation mechanism. The onset of nucleation in solutions of MeOH and ACN when the crystallizer lid was removed was always preceded by a thin layer of crystals formed on the crystallizer walls adjacent to the solution surface. As this crystal layer was in contact with the solution it can be expected that these crystals induced the subsequent nucleation in the bulk. This process was never observed for the other solvents or when the containers were sealed.

86 5.8.6 Distribution in the MZW The MZW of SA was more or less confined to a certain supersaturation region, which differed with different solvents and experimental conditions. Within that region a Gaussian distribution with supersaturation ratio was normally obtained (as e.g. seen in Figure 5.19). Thus, the supersaturation ratio at the average onset of nucleation normally corresponds to the supersaturation having the most frequent nucleation events. The variation in the onset of nucleation was seen to be related to the average onset of nucleation. This relation is depicted in Figure 5.21 using data from all the investigated experimental conditions.

0.7

avg 0.6

0.5

0.4

0.3

0.2 Methanol Acetonitrile Acetic acid 0.1 Acetone Standard deviation in s in deviation Standard Ethyl acetate 0.0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 s avg Figure 5.21. Relation between the standard deviation and supersaturation ratio at the average onset of nucleation. Data from all investigated experimental conditions (Table 4.11 through 4.15).

The relation between the variation and average value in the onset of nucleation, as shown in Figure 5.21, more or less fall on the same trend line, where the slope of the trend line corresponds to the coefficient of variation (expressed as 100·std.dev./(savg - 1)), which equals 43.8. The onset of nucleation normally governs the average crystal size and crystal size distribution, CSD, during cooling crystallization. Data of the MZW is also important in finding the appropriate supersaturation for seeding crystallization. By selecting experimental conditions that increases the MZW, we can also expect a greater variation in the MZW of SA. If the nucleation kinetics of SA is representative for organic compounds in general then it is imperative that studies of the kinetics of nucleation are repeated during identical experimental conditions. Determination of the MZW from only a few measurements may give rise to substantial errors, which in the final crystallization process may lead to unexpected and unwanted crystallization kinetics resulting in significant alterations in crystal properties.

88 6. Conclusions

15 different crystal phases were identified among the six model compounds in a total of eight solvents. The ortho-substituted compounds were only found to crystallize in a single crystal structure, whereas the meta-isomeric compounds crystallized as two unsolvated polymorphs. The greatest number of crystal phases was observed for the para-substituted derivatives, which formed both unsolvated polymorphs and solvated crystal structures. At constant temperature, the molar solubility is directly related to the temperature dependence of solubility. For the model compounds, a lower molar solubility corresponds to a greater temperature dependence of solubility at solubility concentrations above lnxeq = -6. This connection leads to some general applications pertinent to the field of crystallization. A greater yield in cooling crystallization is expected in solvents having lower molar solubility as opposed to solvents exhibiting higher molar solubility. The difference in molar solubility close to the transition temperature of two enantiotropic polymorphs of different melting temperature is greater in solvents of lower molar solubility. Solubility data of a solute exhibiting different crystal phases in different solvents leads to discrepancies in the relation to the temperature dependence of solubility. This deviation can be used to identify new crystal phases solely based on solubility data in different solvents and at different temperature. Within a semi-empirical solubility model applied to a test set of solubility and melting property data comprising 41 organic solutes, it is found that the temperature dependence of solubility of organic solutes in general can be predicted from the melting properties of the solute and the molar solubility at one temperature. This in turn enables entire solubility curves to be established in new solvents from the measurement of the solubility at a single temperature, thus reducing the need for collecting solubility data at different temperatures. By examining 15 different regression equations of solubility and 115 different solubility curves, it is found that extrapolation of solubility data can readily be performed to predict the melting temperature of the solute in organic solvents. The optimum regression equation of solubility predicted the melting temperature of the solute with an average absolute error of 20 oC. The activity of the solid phase (or ideal solubility) can be determined from the melting properties of the solutes and solubility data in different solvents and temperatures using thermodynamic theory. The approach enables the heat capacity difference between the supercooled liquid and solid to be determined without using experimental measurements of the heat capacity of the solid and liquid phases. It was found that the assumptions that normally are used in the literature to determine the activity of the solid phase may give rise to errors up to a factor of 12.

89 By accurately determining the activity of the solid phase it was possible to differentiate between the influence of the solid and the influence of the solution on solubility. The influence of the solution on solubility was found to be dependent on the isomeric configuration of the model compounds. The metastable zone width of salicylamide varied considerably during identically performed experiments in the same solvent. An almost negligible influence of the saturation temperature on the onset of nucleation was observed in all solvents and an increased solution volume did not affect the average onset of nucleation. The greatest impact on the average onset of nucleation was instead found by changing the cooling rate and by using different solvents. A reduced metastable zone width was also obtained when the solvent was allowed to evaporate during the cooling crystallization. A correlation was found between the supersaturation ratio at the average onset of nucleation and the viscosity of the solvent divided by the solubility of the solute. The trends suggest that a greater molecular mobility and a greater concentration of solute molecules in the solution reduce the metastable zone width of salicylamide. Finally, the variation in the metastable zone width was normally found to be Gaussian distributed with supersaturation ratio. A greater variation in the onset of nucleation appeared with a greater average metastable zone width, irrespective of solvent and experimental condition.

90 7. References

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96 Acknowledgements

First and foremost, I would like to express my sincerest gratitude and appreciation to my supervisor Prof. Åke Rasmuson. During this Ph.D. project I have grown attached to the world of thermodynamics and to its applications in the field of crystallization (some would say too attached). Without his extensive support, and guidance throughout these years this project could not have been carried out. I have particularly enjoyed our numerous discussions.

Of course, my gratitude also extends to my colleagues in the crystallization group, past and present.

To Dr. Johan Westin, Dr. Osvaldo Pino-Garcia, Dr. Veronica Profir, Dr. Marie Ståhl, Dr. Ziyun Yu and Dr. Marketta Uusi-Penttilä for their help and contributions to the many discussions that took place during my first years as a Ph.D. student.

To Dr. Eva Ålander for putting up with my disorder in the lab and in the office, and for our many talks on crystallization.

To Jyothi Thati for making the office nicer (without you the flowers would have been dead a long time ago).

To Dr. Sandra Gracin for her critical eye. Her typical words “Fredrik, the problem is…” have helped me avoid many pitfalls and dead ends.

To Kerstin Forsberg for all our discussions during seminars, conferences and in the office. It has been great working with you during all these years. Best of luck in your new role as a mom.

And to Michael Svärd for our work together on the aberrantly devious MABA. I am going to miss the Friday kebabs, floorball games and all the betting.

I would also like to express my appreciation to two M.Sc. diploma students, Baroz Aziz and Baldur Malmberg, for whom I had the privilege of being their project adviser. You have done a great job with two rather complex projects.

97 I also extend many thanks to the other people in the department.

To everyone working with administration and economy. In particular, many thanks go to Jan Appelquist for all his help with every conceivable problem that arose throughout these years.

To Raimund von der Emden, for always finding time to help out with numerous computer problems.

To Dr. Joaquin Martinez, for the many floorball games (it can be a dangerous sport sometimes).

I would also like to express my gratitude to people outside the department.

To Dr. Ahmad Sheikh for introducing me to the field of crystallization.

To Dr. Andreas Fischer, Dept. of Inorganic chemistry, for his invaluable work on numerous XRD analyses.

Finally, my work could not have been carried out without the support from my family and friends.

To in particular the Nordström, Proffitt, Boström, Hansson, Burke and Runesson families, Elisabeth, Håkan, Shariar and others.

And of course, to my fantastic wife Lesli, for her continuous support and love throughout these years. I am indebted to you for all the late nights and weekends I have been away from home and for moving to Sweden to be by my side. I could not have done this without you. You're the best.

98 Appendix 1: Total Differentials with Temperature of the Activity, Concentration and Activity Coefficient at Equilibrium

The activity of the solute, asolute, is a function of the molar concentration, x, and activity coefficient, γ,

solute = xa γ (X1-1)

At equilibrium the activity of the solute is equal to the activity of the solid phase. Hence,

solute eq == xaa γ eqeq (X1-2)

At constant pressure we may express the total differential of Eq. X1-2 with temperature using either the activity of the solute, the molar concentration or the activity coefficient as the starting point:

1. lnasolute = f(T, lnx)

solute solute solute ⎛ ∂ ln a ⎞ ⎛ ∂ ln a ⎞ ln ad = ⎜ ⎟ dT + ⎜ ⎟ ln xd (X1-3) ⎝ ∂T ⎠ x ⎝ ∂ ln x ⎠T

Divided by dT at equilibrium:

⎛ ∂ ln a solute ⎞ ⎛ ∂ ln a solute ⎞ ⎛ ∂ ln a solute ⎞ ⎛ ∂ ln x ⎞ ⎜ ⎟ = ⎜ ⎟ + ⎜ ⎟ ⎜ ⎟ (X1-4) ⎝ ∂T ⎠eq ⎝ ∂T ⎠ x ⎝ ∂ ln x ⎠T ⎝ ∂T ⎠eq

Introducing

⎛ ∂ ln a solute ⎞ Δ f TH )( ⎜ ⎟ = ⎜ ⎟ 2 (X1-5) ⎝ ∂T ⎠eq RT

vH ⎛ ∂ ln x ⎞ ΔH So ln ⎜ ⎟ = 2 (X1-6) ⎝ ∂T ⎠eq RT and simplifying according to Eq. X1-2:

⎛ ∂ ln a solute ⎞ ⎛ ∂ lnγ ⎞ ⎜ ⎟ = ⎜ ⎟ (X1-7) ⎝ ∂T ⎠ x ⎝ ∂T ⎠ x

⎛ ∂ ln a solute ⎞ ⎛ ∂ lnγ ⎞ ⎜ ⎟ 1+= ⎜ ⎟ (X1-8) ⎝ ∂ ln x ⎠T ⎝ ∂ ln x ⎠T gives:

⎡ ⎤ ⎡ ⎤ ⎢ ⎥ vH f 2 ⎛ ∂ lnγ ⎞ ⎢ 1 ⎥ So ln ⎢ )( −Δ=Δ RTTHH ⎜ ⎟ ⎥ ⋅ (X1-9) ⎣ ⎝ ∂T ⎠ x ⎦ ⎢ ⎛ ∂ lnγ ⎞ ⎥ ⎢1+ ⎜ ⎟ ⎥ ⎣ ⎝ ∂ ln x ⎠T ⎦

2. lnasolute = f(T, lnγ)

⎛ ∂ ln a solute ⎞ ⎛ ∂ ln a solute ⎞ ⎛ ∂ ln a solute ⎞ ⎛ ∂ lnγ ⎞ ⎜ ⎟ = ⎜ ⎟ + ⎜ ⎟ ⎜ ⎟ (X1-10) ⎝ ∂T ⎠eq ⎝ ∂T ⎠γ ⎝ ∂ lnγ ⎠T ⎝ ∂T ⎠eq

Simplifying through Eq. X1-2:

⎛ ∂ ln a solute ⎞ ⎛ ∂ ln x ⎞ ⎡ ⎛ ∂ ln x ⎞ ⎤⎛ ∂ lnγ ⎞ ⎜ ⎟ = ⎜ ⎟ ⎢1++ ⎜ ⎟ ⎥⎜ ⎟ (X1-11) ⎜ ∂T ⎟ ∂T ⎜ ∂ lnγ ⎟ ∂T ⎝ ⎠eq ⎝ ⎠γ ⎣ ⎝ ⎠T ⎦⎝ ⎠eq which through Eq. X1-5 results in:

f 2 ⎛ ∂ ln x ⎞ 2 ⎡ ⎛ ∂ ln x ⎞ ⎤⎛ ∂ lnγ ⎞ )( =Δ RTTH ⎜ ⎟ RT ⎢1++ ⎜ ⎟ ⎥⎜ ⎟ (X1-12) T ⎜ lnγ ⎟ T ⎝ ∂ ⎠γ ⎣ ⎝ ∂ ⎠T ⎦⎝ ∂ ⎠eq

3. lnx = f(T, lnasolute)

⎛ ∂ ln x ⎞ ⎛ ∂ ln x ⎞ ⎛ ∂ ln x ⎞ ⎛ ∂ ln a solute ⎞ = + ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ solute ⎟ ⎜ ⎟ (X1-13) solute ⎝ ∂T ⎠eq ⎝ ∂T ⎠ a ⎝ ∂ ln a ⎠T ⎝ ∂T ⎠eq

Inserting Eq. X1-5 and X1-6 in Eq. X1-13 gives:

vH 2 ⎛ ∂ ln x ⎞ ⎛ ∂ ln x ⎞ f So ln =Δ RTH ⎜ ⎟ + ⎜ solute ⎟ Δ TH )( (X1-13) ⎝ ∂T ⎠ asolute ⎝ ∂ ln a ⎠T

ii 4. lnx = f(T, lnγ)

⎛ ∂ ln x ⎞ ⎛ ∂ ln x ⎞ ⎛ ∂ ln x ⎞ ⎛ ∂ lnγ ⎞ ⎜ ⎟ = ⎜ ⎟ + ⎜ ⎟ ⎜ ⎟ (X1-14) ⎝ ∂T ⎠eq ⎝ ∂T ⎠γ ⎝ ∂ lnγ ⎠T ⎝ ∂T ⎠eq

Combining Eq. X1-6 and X1-14:

vH 2 ⎛ ∂ ln x ⎞ 2 ⎛ ∂ ln x ⎞ ⎛ ∂ lnγ ⎞ So ln =Δ RTH ⎜ ⎟ + RT ⎜ ⎟ ⎜ ⎟ (X1-15) ⎝ ∂T ⎠γ ⎝ ∂ lnγ ⎠T ⎝ ∂T ⎠eq

5. lnγ = f(T, lnx)

⎛ ∂ lnγ ⎞ ⎛ ∂ lnγ ⎞ ⎛ ∂ lnγ ⎞ ⎛ ∂ ln x ⎞ ⎜ ⎟ = ⎜ ⎟ + ⎜ ⎟ ⎜ ⎟ (X1-16) ⎝ ∂T ⎠eq ⎝ ∂T ⎠ x ⎝ ∂ ln x ⎠T ⎝ ∂T ⎠eq

Eq. X1-6 and X1-16 gives:

⎡⎛ ∂ lnγ ⎞ ⎛ ∂ lnγ ⎞ ⎤ ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎝ ∂T ⎠ ⎝ ∂T ⎠ vH =Δ RTH 2 ⎢ eq x ⎥ (X1-17) So ln ⎢ ⎛ ∂ lnγ ⎞ ⎥ ⎢ ⎜ ⎟ ⎥ ⎣ ⎝ ∂ ln x ⎠T ⎦

6. lnγ = f(T, lnasolute)

⎛ ∂ lnγ ⎞ ⎛ ∂ lnγ ⎞ ⎛ ∂ lnγ ⎞ ⎛ ∂ ln a solute ⎞ = + ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ solute ⎟ ⎜ ⎟ (X1-18) solute ⎝ ∂T ⎠eq ⎝ ∂T ⎠a ⎝ ∂ ln a ⎠T ⎝ ∂T ⎠eq

Combining Eq. X1-5 and X1-18:

⎡⎛ ∂ lnγ ⎞ ⎛ ∂ lnγ ⎞ ⎤ ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎝ ∂T ⎠ ⎝ ∂T ⎠ solute f )( =Δ RTTH 2 ⎢ eq a ⎥ (X1-19) ⎢ ⎛ ∂ lnγ ⎞ ⎥ ⎢ ⎜ solute ⎟ ⎥ ⎣ ⎝ ∂ ln a ⎠T ⎦

Finally, combining Eq. X1-2 and X1-5 gives:

vH f 2 ⎛ ∂ lnγ ⎞ So ln )( −Δ=Δ RTTHH ⎜ ⎟ (X1-20) ⎝ ∂T ⎠eq

iii Appendix 2: Solubility and Melting Properties of m- Aminobenzoic acid

Solubility The solubility of m-aminobenzoic acid, phase I (MABA-P1) was determined gravimetrically between 10 and 50 oC in 5 oC increments in the solvents methanol, acetonitrile, water and ethyl acetate. Details of the experimental procedure and chemicals used are given in paper I through IV. The solubility measurements are summarized in Table X2-1 through X2-4:

Table X2-1. Solubility of MABA-P1in methanol. Temperature Solubility Standard deviation No of measurements [K] [g MABA/kg [g MABA/kg solvent] solvent] 283.15 38.56 0.03 4 288.15 44.31 0.28 4 293.15 51.73 0.24 4 298.15 60.74 0.50 4 303.15 73.63 0.07 2 308.15 88.05 1.30 8 313.15 100.51 0.65 6 318.15 118.12 0.88 4 323.15 138.55 1.98 4

Table X2-2. Solubility of MABA-P1in acetonitrile. Temperature Solubility Standard deviation No of measurements [K] [g MABA/kg [g MABA/kg solvent] solvent] 283.15 5.27 0.05 4 288.15 5.92 0.05 4 293.15 7.15 0.04 4 298.15 9.45 0.24 6 303.15 11.31 0.05 4 308.15 15.01 0.34 8 313.15 18.85 0.99 8 318.15 22.64 0.60 8 323.15 27.95 0.57 8

i Table X2-3. Solubility of MABA-P1in water. Temperature Solubility Standard deviation No of measurements [K] [g MABA/kg [g MABA/kg solvent] solvent] 283.15 3.50 0.10 4 288.15 4.07 0.13 4 293.15 4.66 0.11 4 298.15 5.40 0.09 4 303.15 6.24 0.08 4 308.15 7.30 0.10 4 313.15 8.58 0.05 4 318.15 10.10 0.08 4 323.15 11.80 0.08 6

Table X2-4. Solubility of MABA-P1in ethyl acetate. Temperature Solubility Standard deviation No of measurements [K] [g MABA/kg [g MABA/kg solvent] solvent] 283.15 6.71 0.13 4 288.15 7.66 0.19 4 293.15 8.78 0.17 4 298.15 10.50 0.31 8 303.15 13.02 0.59 8 308.15 15.28 0.48 8 313.15 18.42 0.31 8 318.15 21.49 0.32 4 323.15 26.18 0.64 4

The regression equation of solubility

A ln(x ) ++= CTB (X2-1) eq T was used and the coefficients A, B and C were determined from the solubility data using the computer software program ®Origin, v6.1 by minimization of the function:

2 1 2 χ BA ,...),( = ∑∑[− 21 iijijeq BATTfx ,...),,...;,()(ln ] (X2-2) N f ij

The coefficients A, B and C and the fit of the regression are given in Table X2-5:

Table X2-5. Regression coefficients and fit of Eq. X2-1. Crystal phase Solvent A B C 10-3·χ2 MABA-P1 MeOH -279.14 -11.934 2.8910·10-2 0.31 MABA-P1 ACN 2604.9 -36.068 7.1930·10-2 1.87 -2 MABA-P1 H2O 1957.1 -29.224 5.1680·10 0.03 MABA-P1 EtAc 2471.8 -31.566 6.1340·10-2 0.48

Melting properties The melting properties of the two polymorphs of MABA (i.e. MABA-P1 and MABA-P2) were determined using Differential Scanning Calorimetry at a heating rate of 2 and 5 K/min. The results are summarized in Table X2-6.

Table X2-6. Melting properties of MABA-P1 and MABA-P2. f Crystal Onset Std. dev. in onset ΔH (Tm) Std. dev. in No of f phase Tm Tm ΔH (Tm) scans [K] [K] [kJ/mol] [kJ/mol] MABA-P1 445.10 0.65 36.04 1.40 8 MABA-P2 451.38 0.67 27.24 0.37 4 Data from DSC analyses by T. Jasnobulka, M. Svärd and F. Nordström.

Polymorphic stability analysis DSC analyses revealed an endothermic transition from phase I to phase II at around 433 K. Based on the melting properties of these two phases and this solid-solid transformation it is expected that this polymorphic system is enantiotropic, where the transition temperature is located at a temperature below 433 K. From the melting properties of the two polymorphs it is possible to estimate the activity of the respective solid phases of the two polymorphs.

However, this estimation is based on the value of ΔCp, which has not been resolved. A ΔCp equaling zero for both polymorphs yields a polymorphic transition temperature of 426.7 K. MABA-P1 is then stable below this estimated transition temperature, while MABA-P2 is stable above this estimated transition temperature.

iii Appendix 3: Thermodynamic Properties of p-Aminobenzoic acid

Solubility The solubility of p-aminobenzoic acid was determined gravimetrically by B. Aziz. The solubility of PABA-α was determined between 5 and 50 oC in 5 oC increments in the solvents acetonitrile, acetic acid, ethanol and 2-propanol. The solubility of PABA-β was determined between 5 and 25 oC in 5 oC increments in the solvents acetonitrile, ethanol and 2-propanol. The solubility of PABA-β could not be determined above 25 oC due to polymorphic transformation into the α-polymorph. Details of the experimental procedure are given in paper I through IV. The solubility measurements are summarized in Table X3-1 and X3-2:

Table X3-1. Solubility of the α-polymorph of PABA in g PABA/kg solvent, based on the average of four measurements at each temperature. Standard deviations are given in parenthesis. Temperature/oC Acetonitrile Acetic acid Ethanol 2-Propanol 5 41.12 (0.11) 111.61 (0.26) 117.73 (0.21) 47.50 (0.43) 10 47.10 (0.06) 119.17 (0.40) 125.51 (0.22) 52.70 (0.47) 15 54.19 (0.35) 128.00 (0.33) 134.65 (0.21) 59.26 (0.53) 20 62.17 (0.34) 137.49 (0.05) 144.95 (0.16) 66.94 (0.48) 25 71.22 (0.39) 148.14 (0.39) 156.96 (0.17) 75.65 (0.49) 30 81.38 (0.42) 159.21 (1.42) 170.57 (0.11) 85.96 (0.50) 35 93.34 (0.07) 171.07 (0.42) 186.29 (0.25) 97.72 (0.36) 40 107.39 (0.06) 190.66 (0.33) 204.39 (0.33) 111.41 (0.34) 45 123.58 (0.12) 206.60 (0.99) 224.53 (0.36) 127.12 (0.24) 50 142.55 (0.20) 227.12 (1.32) 247.67 (0.65) 144.90 (0.02)

Table X3-2. Solubility of the β-polymorph of PABA in g PABA/kg solvent, including (standard deviation) and [number of measurements]. Temperature/oC Acetonitrile Ethanol 2-Propanol 5 39.21 (0.31) [10] 112.77 (0.60) [5] 45.14 (0.68) [6] 10 45.72 (0.34) [8] 122.74 (0.29) [6] 51.57 (0.46) [8] 15 52.94 (0.22) [5] 133.75 (0.30) [8] 58.75 (0.16) [6] 20 63.32 (0.33) [4] 147.14 (0.31) [4] 68.63 (0.22) [7] 25 75.15 (0.32) [6] 160.64 (2.68) [4] 78.12 (0.67) [8]

The regression equation of solubility

A ln(x ) ++= CTB (X3-1) eq T

was used and the coefficients A, B and C were determined from the solubility data using the computer software program ®Origin, v6.1 by minimization of the function:

2 1 2 χ BA ,...),( = ∑∑[− 21 iijijeq BATTfx ,...),,...;,()(ln ] (X3-2) N f ij

The coefficients A, B and C and the fit of the regression are given in Table X3-3:

Table X3-3. Regression coefficients and fit of Eq. X3-1. Crystal Solvent A B C 10-5·χ2 phase PABA-α ACN 31.064 -12.095 2.7234·10-2 0.63 PABA-α HAc 1693.6 -18.579 3.3583·10-2 4.0 PABA-α EtOH 1989.1 -20.930 3.7783·10-2 0.08 PABA-α 2-PrOH 1180.9 -18.494 3.7213·10-2 1.0 PABA-β ACN 4348.1 -43.573 8.4432·10-2 4.0 PABA-β EtOH 871.83 -14.099 2.7517·10-2 0.76 PABA-β 2-PrOH 996.39 -18.361 3.8955·10-2 7.0

Determination of the Polymorphic Transition Temperature The transition temperature was calculated from the RES coefficients in Table X3-3, and is given in Table X3-4.

Table X3-4. Polymorphic transition temperature of PABA-α and PABA-β. Solvent Transition temperature/oC ACN 17.6 EtOH 14.8 2-PrOH 16.2

Average 16.2 Std. dev. 1.4

Heat capacity The heat capacity of PABA-α and PABA-β was determined by B. Aziz and F. Nordström using modulated isothermal DSC. Details of the experimental procedure are given in paper V. The heat capacity data at different temperatures was correlated to the function:

S p += kTkC 21 (X3-3) where T is given in absolute temperature. The coefficients and fit of Eq. X3-3 are given in Table X3-5.

Table X3-5. Heat capacity coefficients of PABA-α and PABA-β. 2 Polymorph k1 k2 R Temperature interval/K PABA-α 0.4308 29.90 0.996 280-445 PABA-β 0.4685 -8.35 0.999 280-380

ii Appendix 4: Coefficient α and β of the Model Compounds

The molar solubility and temperature dependence of solubility, as given by the van't Hoff enthalpy of solution, was correlated by the function:

vH 2 H SO ln =Δ α xeq + β ln)(ln xeq (X4-1)

The coefficients α and β of unsolvated crystal phases of the model compounds are vH listed in Tables below, where ΔH So ln is given as J/mol.

Table X4-1. Coefficients of OHBA-P1 based on solubility data in MeOH, ACN, HAc, Acetone and EtAc. Temperature α β R2 [K] 283.15 77.82 -4675 0.986 288.15 141.4 -4819 0.983 293.15 194.2 -5028 0.978 298.15 266.2 -5236 0.972 303.15 377.6 -5399 0.964 308.15 461.9 -5660 0.951 313.15 617.5 -5835 0.939 318.15 796.6 -6039 0.924 323.15 935.6 -6388 0.903

Table X4-2. Coefficients of MHBA-P1 based on solubility data in MeOH, ACN, HAc, Acetone and EtAc. Temperature α β R2 [K] 283.15 572.5 -1593 0.998 288.15 581.3 -1820 0.998 293.15 598.2 -2046 0.998 298.15 612.9 -2286 0.998 303.15 644.4 -2514 0.997 308.15 670.9 -2760 0.997 313.15 686.2 -3075 0.995 318.15 668.4 -3479 0.993 323.15 680.4 -3824 0.990

i Table X4-3. Coefficients of MHBA-P2 based on solubility data in ACN, HAc, Acetone and EtAc. Temperature α β R2 [K] 283.15 603.1 -1238 0.993 288.15 619.4 -1568 0.992 293.15 638.9 -1921 0.993 298.15 658.1 -2303 0.993 303.15 685.0 -2680 0.994 308.15 728.0 -3042 0.994 313.15 769.7 -3429 0.995 318.15 820.0 -3822 0.995 323.15 858.6 -4271 0.994

Table X4-4. Coefficients of PHBA-P1 based on solubility data in MeOH, ACN, HAc and EtAc. Temperature α β R2 [K] 283.15 825.7 -380.0 0.999 288.15 860.4 -521.4 0.999 293.15 897.6 -689.0 0.999 298.15 961.6 -803.4 0.999 303.15 1025 -943.9 0.998 308.15 1041 -1215 0.999 313.15 1106 -1388 0.998 318.15 1168 -1607 0.998 323.15 1232 -1834 0.998

Table X4-5. Coefficients of SA-P1 based on solubility data in MeOH, ACN, HAc, Acetone and EtAc. Temperature α β R2 [K] 283.15 399.2 -3985 0.901 288.15 493.2 -4158 0.912 293.15 574.6 -4423 0.923 298.15 666.3 -4754 0.936 303.15 813.1 -4994 0.940 308.15 1019 -5189 0.941 313.15 1222 -5515 0.946 318.15 1507 -5746 0.950 323.15 1973 -5772 0.954

ii Table X4-6. Coefficients of MABA-P1 based on solubility data in MeOH, ACN and EtAc. Temperature α β R2 [K] 283.15 -183.6 -5121 0.622 288.15 -147.6 -5260 0.740 293.15 -103.5 -5399 0.827 298.15 -49.10 -5537 0.887 303.15 18.60 -5670 0.928 308.15 103.4 -5791 0.955 313.15 210.8 -5895 0.973 318.15 348.2 -5969 0.985 323.15 526.0 -5999 0.992

Table X4-7. Coefficients of PABA-α based on solubility data in ACN, HAc, EtOH, 2-PrOH and EtAc. Temperature α β R2 [K] 278.15 620.4 -962.2 0.826 283.15 626.9 -1295 0.842 288.15 634.1 -1657 0.856 293.15 638.7 -2054 0.867 298.15 639.6 -2492 0.878 303.15 634.5 -2978 0.887 308.15 625.9 -3514 0.894 313.15 608.3 -4125 0.902 318.15 589.9 -4765 0.906 323.15 565.3 -5476 0.910

Table X4-8. Coefficients of PABA-β based on solubility data in ACN, EtOH, 2-PrOH and EtAc. Temperature α β R2 [K] 278.15 122.7 -3554 0.847 283.15 131.6 -3952 0.830 288.15 134.8 -4399 0.812 293.15 138.8 -4916 0.788 298.15 131.0 -5489 0.763

iii Phase Equilibria and Thermodynamics of p-Hydroxybenzoic Acid

FREDRIK L. NORDSTRO¨ M, A˚ KE C. RASMUSON

Department of Chemical Engineering and Technology, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

Received 23 September 2005; revised 22 November 2005; accepted 4 December 2005 Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.20569

ABSTRACT: The prevalence of phases and associated solubilities of p-hydroxybenzoic acid have been investigated in methanol, acetonitrile, acetic acid, acetone, water, and ethyl acetate at temperatures from 10 to 508C. Thermodynamic data was acquired through determination of van’t Hoff enthalpy of solution, enthalpy of fusion, and melting temperature. Indications of polymorphic enantiotropy were found primarily through solubility analysis and FTIR-ATR. A comprehensive thermodynamic investigation disclosed correlation between the van’t Hoff enthalpy of solution and the solubility in different solvents. A higher solubility is linked to a lower van’t Hoff enthalpy of solution. A thermodynamic analysis to discriminate between different solid phases is presented. ß 2006 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 95:748–760, 2006 Keywords: p-hydroxybenzoic acid; 4-hydroxybenzoic acid; polymorphism; pseudo- polymorphism; solvate; complexation; solubility; desolvation; solid state stability; van’t Hoff

INTRODUCTION occurrence of different solid forms. Today, it is even a regulatory requirement to identify the The manufacture of pharmaceuticals often possible polymorphic forms of the product. involves crystallization from pure or mixed Solid-solid phase transitions are often studied organic solvents. The composition of the solvent by differential scanning calorimetry (DSC). Occa- determines the solubility and thus affects the sionally, phase transitions are difficult to capture method for supersaturation generation. Further- with purely thermodynamic solid-state analysis more, the solvent composition influences the due to small transition energies or similar melting product crystal size distribution, the shape of points.1 Furthermore, in DSC measurements the crystals, and the crystal structure. At least these phase transitions do not usually occur at one third of organic compounds exhibit poly- the thermodynamic transition temperature be- morphism and the occurrence of solvates are cause of kinetic limitations.2 Determination of about as frequent. The different solid forms of solubility with temperature provides important the substance display dissimilar solid-state prop- information for process development. The solubi- erties which lead to differences in handling and lity of a compound depends on the properties of the processing properties of the compound, and in the solid-state and therefore typically differs for shelf life and bioavailability of a drug. Hence, in different polymorphs and solvates of the same order for the pharmaceutical industry to ensure compound. Hence, in the determination of solubi- reliable and robust processes as well as confor- lity it is important to identify the particular solid mity with good manufacturing practice it is phase that is present. On occasion, the solid phase important to gather an understanding for the present in the solution is not sufficiently stable when brought out of the solution. It can in these ˚ Correspondence to:Ake C. Rasmuson (Telephone:þ46 8 cases be difficult to actually establish whether 7908227; Fax: þ46 8 105228) different solid phases do occur or not, during a Journal of Pharmaceutical Sciences, Vol. 95, 748–760 (2006) ß 2006 Wiley-Liss, Inc. and the American Pharmacists Association series of measurements. Thus, a combination of

748 JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 PHASE EQUILIBRIA AND THERMODYNAMICS OF p-HYDROXYBENZOIC ACID 749

Equipment and Procedures

Saturated solutions were prepared in test tubes and 250 mL bottles, and evaluated at 58C increments at 10–508C. The temperature was controlled by thermostat baths to 0.018C, and the true Figure 1. p-hydroxybenzoic acid (PHBA). temperature was validated by a calibration mercury thermometer (Thermo-Schneider, Wertheim, methods and experiments are required to establish Germany, accuracy of 0.018C). Preheated syringes the solubility and the phase relationships. were used to sample 3–6 mL of solution into This study attempts to uncover the predomi- preweighed glass vials. Preheating of the syringes nant phases and their associated solubilities of and needles was conducted when necessary in p-hydroxybenzoic acid (Fig. 1) encountered in six order to obstruct nucleation inside the syringes solvents, that is, methanol (MeOH), acetonitrile during sampling. Filters (PTFE, 0.2 mm) were (ACN), acetic acid (HAc), acetone, water, and ethyl utilized when sedimentation of the solution was acetate (EtAc) in the temperature range 10–508C. troublesome or when instant sampling was neces- The obtained phase equilibria are addressed sary. The filters were also preheated to exceed the within a comprehensive thermodynamic analysis. solution temperature. Suspensions of water and An analysis is presented that may contribute to PHBA were always filtered (nitrocellulose, 0.2 mm). disclose whether different solid phases do occur, However, filtration reduced the reproducibility of and to establish thermodynamic properties of the measurements and were avoided as much as unstable phases. It is shown that solubility data possible. The weight of the saturated (filtered) can contribute to gain knowledge of the occurrence clear solution and of the final dry residue after and stability of different solid phases of the solvent evaporation was recorded. Drying was compound. conducted primarily in ventilated laboratory p-hydroxybenzoic acid (PHBA) has previously hoods at room temperature. The vials containing been reported to exhibit polymorphism3,4 as well the samples were weighted continuously through- as a tendency to form solvated structures5. out the drying process, and complete dryness was Already characterized crystal structures of sol- determined as when the weight of the vial vates pertinent to this work are a monohydrate6,7 remained constant over time. Formed solvates and an acetone solvate with one acetone molecule were let to desolvate in a vacuum oven or an oven per two PHBA molecules.3 These crystal struc- set at 508C until completely free from solvent. tures have been investigated through X-ray dif- Fourier transform infrared spectroscopy with fraction analysis. However, thermodynamic data Attenuated Total Reflectance module, FTIR- of PHBA are scarce in the literature. ATR (Perkin Elmer Instruments, Spectrum One, Beaconsfield, Buckinghamshire, UK), having a ZnSe window, was used to help identify poly- EXPERIMENTAL SECTION morphic and solvated phases. A wavelength range of 4000–650/cm and a scanning frequency of eight The solubility of PHBA in six different pure per sample was used for each analysis. Crystal solvents has been determined gravimetrically in structure determination was conducted using a the temperature range 10–508C. Bruker-Nonius KappaCCD single-crystal X-ray diffractometer. Visual identification and imaging was carried out with a photo microscope, Olympus, Materials SZX12, and at elevated temperatures with a hot PHBA (CAS registry number 99-96-7) was pur- stage microscope, Olympus BH-2. DSC, TA Instru- chased from Sigma-Aldrich, purity > 99%, and ments, DSC 2920, provided information of melting was used as obtained. The five organic solvents points, enthalpy of fusion, and desolvation tem- were purchased from VWR/Merck; methanol peratures. The calorimeter was calibrated against (HiperSolv, >99.8%), ACN (LiChroSolv, Gradient the melting point and enthalpy of fusion of indium grade, >99.8%), acetic acid (Pro Analysi, 96%), at a nitrogen flow rate of 50 mL/min. Samples, 1– acetone (HiperSolv, >99.8%), and ethyl acetate 10 mg, were heated at 1, 2, or 58C/min from 10 to (HiperSolv, >99.8%). The water was distilled, 2508C in hermetic Al-pans while being purged deionized, and filtered at 0.2 mm. with nitrogen.

DOI 10.1002/jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 750 NORDSTRO¨ M AND RASMUSON

Equilibrium was established by dissolution to RESULTS saturation of solid material as well as by crystallization to saturation in a solution originally The behavior of PHBA in the six solvents is brought into a supersaturated state. The attaining addressed solvent by solvent in order of increas- of equilibrium was confirmed by repeated con- ing complexity of the phase diagram. All solubility centration measurements over time and from data are presented as gram of dry PHBA per kg different mother liquors. Similarly, the pseudo- solvent, that is, on a solute free basis and in equilibrium of metastable phases was validated unsolvated state. The solubility of the ansolvate is using repeated concentration measurements over given in Table 1 whereas the solubilities of the time. The occurrence of phase conversions was two solvated modifications are presented in observed as rapid decrease in concentration. In all Table 2. experiments where equilibrium is obtained by dissolution an excess amount of commercial PHBA was partly dissolved either in 250 mL glass bottles Water or 20 mL glass test tubes. The bottles/tubes were placed in a water bath and magnetic stirring was Only one solid phase was found in the tempera- used at 300 and 600 rpm, respectively. In the ture range from 10 to 508C. By single crystal X- crystallization experiments supersaturation was ray diffractometry the solid phase was proved to generated by cooling at 18C/min until the solution be the monohydrate having an identical crystal nucleated spontaneously. In some experiments the structure as that given by Fukuyama et al.6 and concentration of the solution was recorded for up to Colapietro et al.7 When excessive amounts of the 2 weeks to evaluate the time required for establish- commercial PHBA material were dispersed in ment of equilibrium. This also allowed for evalua- water the transformation to the monohydrate tion of possible chemical degradation and solid occurs within minutes, as observed by FTIR and phase stability. The solid phase in equilibrium solubility determination. Similarly, at crystal- with the solution was analyzed by sampling lization from a homogenous solution only the suspensions of crystals and solution. The suspen- monohydrate was obtained between 10 and 508C, sion samples were collected in conjunction to regardless of cooling or evaporation profile. No extracting the first and last solubility samples of signs of phase transitions were found when the the experiment. The suspension samples were solubility was recorded over a time period of filtered and analyzed with FTIR-ATR at room 2 weeks. temperature. IR spectra (4000–650/cm) were then The melting point of the monohydrate could not collected throughout the drying of the suspension be determined due to desolvation/transformation until complete dryness. Complete dryness was prior to reaching the melting point. The desolva- determined as when the obtained IR pattern tion peak occurs at approximately 678C in DSC remained constant over time. The dried crystals scans at 18C/min. obtained from the suspension were also examined The monohydrate displays clear and unambig- by DSC (heating rate of 1, 2, or 58C/min, ranging uous FTIR-ATR spectra with a characteristic from 10 to 2508C). absorption peak at 1651/cm. The monohydrate

Table 1. Solubility of PHBA (Ansolvate) in Five Solvents

T Solubility in g PHBA/kg Solvent (Standard Deviation) [Number of Samples]

[8C] MeOH ACN HAc Acetone EtAc 10 486.16 (2.71) [21] 31.47 (0.17) [5] 88.90 (0.15) [4] 101.93 (0.57) [4] 15 499.76 (4.84) [28] 35.95 (0.41) [6] 96.04 (0.23) [4] 107.96 (0.30) [8] 20 531.97 (1.82) [21] 41.54 (0.39) [9] 103.84 (0.09) [4] 114.32 (0.38) [7] 25 555.49 (3.93) [28] 48.75 (0.44) [10] 113.27 (0.09) [4] 122.04 (0.34) [11] 30 590.40 (0.98) [13] 57.00 (1.12) [8] 122.54 (0.08) [4] 447.36 (2.40) [2] 130.19 (0.45) [10] 35 618.17 (2.67) [20] 63.58 (0.96) [8] 132.54 (0.12) [4] 462.70 (1.55) [9] 138.39 (0.51) [12] 40 648.05 (5.38) [18] 73.44 (0.61) [18] 143.75 (0.58) [6] 487.46 (1.15) [5] 148.49 (0.43) [6] 45 691.82 (0.80) [16] 84.61 (0.65) [8] 156.58 (0.09) [4] 509.77 (1.23) [6] 158.03 (0.43) [6] 50 727.55 (1.37) [19] 96.58 (1.04) [10] 170.22 (0.23) [4] 541.67 (0.73) [4] 168.97 (0.53) [10]

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 DOI 10.1002/jps PHASE EQUILIBRIA AND THERMODYNAMICS OF p-HYDROXYBENZOIC ACID 751

Table 2. Solubility of Solvated PHBA in Acetone 258C yielded unequal IR spectra. Crystals pre- (Acetone Solvate) and Water (Monohydrate) cipitated at the lower temperature displayed a characteristic FTIR peak at 1672/cm. By single- Solubility in g PHBA/kg Solvent (Standard crystal X-ray diffractometry this solid phase was T Deviation) [Number of Samples] conﬁrmed to be identical to the structure given by 3 [8C] Acetone Water Heath et al. Crystals obtained at elevated temperatures exhibited characteristic FTIR 10 243.31 (0.44) [4] 2.786 (0.067) [4] peaks at 1740/cm. When these crystals were 15 267.12 (2.12) [5] 3.557 (0.126) [4] subjected to a very small weight of 100 g on the 20 292.44 (0.57) [6] 4.553 (0.062) [4] surface of the FTIR-ATR window (approximately 25 321.23 (0.12) [4] 5.796 (0.059) [4] 2 30 357.68 (0.77) [5] 7.521 (0.068) [4] 5cm), the 1740/cm peak gradually disappeared, 35 393.58 (1.75) [4] 9.764 (0.058) [4] and the 1672/cm peak gradually appeared in 40 435.43 (0.12) [13] 12.846 (0.016) [4] consecutive FTIR measurements. Similarly, 45 486.23 (0.83) [8] 17.089 (0.164) [3] grinding resulted in a total disappearance of the 50 22.721 (0.215) [3] 1740/cm peak and appearance of the 1672/cm peak. However, upon storing the crystals at 508C for several days the 1740/cm peak reappeared. crystals are formed as needles with a hexagonal Thus, this suggests an enantiotropically related base as depicted to the left in Figure 2. Removed polymorphism of PHBA (the commercially avail- from the solution, the monohydrate can attain its able PHBA displayed predominately the 1672/cm structure at ambient temperature and humidity but also the 1740/cm peak). However, there was for several days before dehydration commences. no signiﬁcant difference in the DSC curves nor However, if the monohydrate is stored at 508C, could the second polymorph be corroborated by dehydration will take place within minutes. The Single Crystal X-ray Diffractometry. No transfor- resulting crystals are white and chalky as shown to mation was observed in DSC scans up to the the right in Figure 2, signifying a transformation melting point. Furthermore, there was no obvious to an aggregate of crystallites of the anhydrate difference in the particle morphology as observed within the macroscopic boundaries of the original by microscopy. monohydrate crystals. The enthalpy of fusion at the melting tempera- f ture, DH (Tm), of the unsolvated PHBA was determined to 30.85 kJ/mol (average of 29 DSC Acetic Acid scans at 1, 2, and 58C, standard deviation: 1.09 kJ/ No solvates of PHBA has been found in acetic mol). The corresponding average melting tem- acid. However, the solubility curve of HAc is not perature was estimated to 215.88C (average onset entirely smooth. At approximately 25–308C there temperature 214.58C, standard deviation: melting is a slight indication of a phase transition. FTIR temperature 0.608C, onset melting temperature analysis of crystals obtained from cooling crystal- 0.458C). Heath et al.3 reported 31 kJ/mol and lization experiments (18C/min) above and below 2158C. The accuracy of the calorimetric data was

Figure 2. Left: monohydrate crystals, obtained through evaporation crystallization at 208C. Right: Dehydrated monohydrate crystals.

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tence of which has been reported previously by Heath et al.3 In the present work, the solvated form was shown to be the stable phase up to approximately 508C. The solubility of the ansolvate could be determined at higher temperature by dissolution up to equilibrium. Both acetone and PHBA had to be preheated to 508C in order to obstruct phase conversion into the solvate. The solubility of the ansolvate could only be measured down to 308C due to the gradually increasing tendency of phase conversion into the stable solvate. The phase diagram in Figure 3 suggests Figure 3. Solubility of PHBA ansolvate (empty cir- that the ansolvate is the stable phase above cles) and solvate (full circles) in acetone between 10 and approximately 508C. The solvate phase exhibits 508C. a steeper dependence with temperature than the ansolvate. obscured by considerable sublimation before melt- The melting point and associated enthalpy of ing and additional fusion peaks often appeared at fusion could not be determined for the solvate since around 220–2308C. The origin of these extra desolvation occurred rapidly upon contact with air fusion peaks was not resolved. at ambient temperature. The desolvation process is depicted in Figure 4 where each image is taken with ca 1 min intervals. As a direct consequence of the desolvation, Acetone FTIR and DSC analysis provided no direct infor- The predominant phase found in this tempera- mation concerning the solvated form. The desol- ture interval was an acetone solvate, the exis- vated crystals displayed similar characteristics as

Figure 4. Desolvation process of PHBA-acetone solvate at room temperature. The upper left image is taken just as all the free acetone has evaporated from the crystal surfaces. The upper right picture illustrates the initial part of the desolvation process, where white areas are building up and spreading (lower left photo) until all the acetone has left the crystal lattice (lower right photo).

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 DOI 10.1002/jps PHASE EQUILIBRIA AND THERMODYNAMICS OF p-HYDROXYBENZOIC ACID 753

Data have been obtained by employing dissolution up to saturation of the commercially available product at constant temperature. It can be seen that the solubility curve appears to have a discontinuity in the slope close to 308C. This suggests that the solid phase present above this temperature is not the same as the solid phase below. FTIR spectra of crystals obtained in these regions displayed the same characteristic peaks, that is, at 1672 and 1740/cm, respectively, as seen in the acetic acid system. However, recrystallization experiments gave inconsistent results. DSC scans revealed several desolvation peaks typically Figure 5. Desolvated acetone-PHBA solvate crystals, present between 120 and 1908C. In addition, there obtained through evaporation crystallization at 208C. were no differences in the external appearance of the crystals as observed in the microscope. A conceivable reason behind the scatter in solubility and possibly the DSC desolvation peaks is the effect of water contamination due to the hygro- the low temperature polymorph with a melting 8 point of 215–2168C and the typical FTIR peak at scopic nature of ACN. Deliberate water contam- 1672/cm. ination to the PHBA-ACN system in quantities The morphology of the acetone solvate crystals not exceeding 1 mass % of the solution amounted after drying is shown in Figure 5. Besides being an increase in solubility of approximately 30%. white because of the paramorphosis, the crystals Hence, the variation observed in the solubility have during desolvation lost the outer structure data may easily be explained by trace amounts of and the middle parts have fallen inwards to its water. The scatter in solubility data was also center, creating peculiar terraces downwards the found well organized within each series of gradu- middle of the crystal. ally increasing temperature. The presence of water in the solution may cause the formation of monohydrate crystals, thus explaining the appearance of desolvation peaks during DSC Acetonitrile scans. The behavior of PHBA in ACN was confounded by what appeared as additional phases in conjunc- Ethyl Acetate tion with a severe sensitivity to water contamination. Solubility results are shown in Figure 6. Similar to ACN, ethyl acetate also appeared as a difficult solvent. Solubility experiments exhibited poor repeatability, in particular those conducted through recrystallization. Commonly, solubility curves were acquired with dissimilar magnitudes but similar temperature dependences. DSC scans frequently displayed desolvation/transformation peaks in the temperature range of 90–1608C. However, the melting point was in general in the range of 215–2178C, regardless of desolvation/transformation prior to fusion. Crystals obtained through evaporation crystallization at 508C yielded FTIR spectra with the characteristic 1740/cm absorption peaks. Analo- gous to the ACN system, the ethyl acetate system was sensitive to water contamination as very Figure 6. Solubility of PHBA in acetonitrile between small quantities inflicted significant solubility 10 and 508C with 95% confidence limits. increases.

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Methanol not able to detect any disparities from analyses of the ansolvates. Only the previously observed 1740/ Methanol, proved to be the most complex of all cm absorption peak could be veriﬁed. solvents. In particular solubility data obtained A pronounced effect of the solvent appeared at lower temperatures, exhibited considerable through the shape of the crystals when recrystal- systematic deviations depending on the method lized from different solvents. The crystal morphol- used. These problems cannot be attributed to ogy of unsolvated PHBA differed markedly with water contamination since the presence of selection of solvent. Some examples of crystals small amounts of water only weakly decreases obtained from different solvents are depicted in the solubility. In addition, drying of the samples Figure 7. for gravimetric concentration determination required extended time at elevated temperature. At least 1 week at 508C was required in order to DISCUSSION reach a constant weight. DSC scans revealed several desolvation/trans- Solid Phases of PHBA formation peaks, however, seldom at consistent temperatures but typically at temperatures close This study has primarily utilized solubility, DSC, to 2008C. In several cases, crystals melted at 208– FTIR-ATR, and microscopy to probe the preva- 2138C, that is, prior to the melting point of PHBA lence of phases and solution properties of PHBA and displayed a contrasting enthalpy of fusion. in six solvents between 10 and 508C. The This deviating stability was never seen for crystals structures of two different PHBA polymorphs obtained from the other solvents. Moreover, after have been reported.4 The structure of polymorph I melting numerous additional fusion peaks were has four molecules in the unit cell and is based on observed. The origin of these extra peaks has not centrosymmetric dimers of molecules associated been resolved. The desolvation/transformation via the carboxylic acid groups.3 These dimers are peaks were still present in some batches occasion- then hydrogen bonded in hydroxylic group chains ally up to a month after precipitation and ﬁltra- along the b-axis. The structure of polymorph II is tion. Microscopy and FTIR analyses were however also based on centrosymmetric carboxylic acid

Figure 7. Crystals acquired through evaporation crystallization from open container from different solvents and temperatures. Upper left photo: ACN at 208C. Upper right photo: methanol at 408C. Lower left photo: ethyl acetate at 508C. Lower right photo: acetic acid at 508C.

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 DOI 10.1002/jps PHASE EQUILIBRIA AND THERMODYNAMICS OF p-HYDROXYBENZOIC ACID 755 bonded dimers. However, in this structure the points of two modifications are within 2–38Cof dimers are linked to one another by hydroxyl- each other or when the energy of transition is too carboxyl bonding.4 In the present work, the small, DSC cannot determine the transition presence of two polymorphs has been suggested temperature and existence of enantiotropy.1 through different observations. Hence, no safe conclusions concerning polymorph- In acetic acid and ACN, the slope of the ism can be drawn from the DSC data. solubility curve exhibit discontinuities of a kind The solubility study suggested that the poly- that is typical for the occurrence of two different morphs exhibit similar solubility and thus a small polymorphs and an enantiotropic transition. The driving force for phase conversion. Therefore, it is transition temperature for PHBA in both these indeed surprising to find this apparent tendency solvents is between 25 and 308C. In water and for phase transformation, in particular consider- acetone, this transition could not be detected due ing the ease in which phase conversion was to the formation of solvated modifications that are observed through inducing pressure on the crys- more stable than the unsolvated polymorphs. tals displaying the 1740/cm peak. It must be The solid forms obtained from acetic acid, at addressed that this study only encompasses a temperature above or below 308C, respectively, temperature range of 408C. Additional poly- expose FTIR spectra that are clearly different with morphs may be present at elevated temperatures. respect to absorption peaks at 1740 and 1672/cm. Numerous crystal samples display several fusion These two peaks were observed in crystals peaks after the initial melting point at 215–2168C. obtained from all solvents, even in the desolvated In hot stage microscopy, needle-shaped crystals crystals from acetone and water. Absorption peaks growing from desolvated monohydrate crystals in this frequency region originate from carbonyl were observed at elevated temperatures. group vibrations, and hence the peak change The previously reported acetone solvate and the points towards alterations primarily concerning hydrate were found in the present work and the carboxylic acid interactions in accordance with the corresponding solubilities have been determined. structural differences of the two known poly- In water, the monohydrate is more stable than the morphs. Furthermore, the peak shifts in the IR anhydrate over the entire temperature range. The spectra induced by pressure or grinding of the structure of the monohydrate is also based on high-temperature crystals as well as the reappear- the centrosymmetric carboxylic acid dimerisation ance of the 1740/cm peak upon heating above (Heath et al.3). The water molecules are, however, the conjectured transition temperature supports integrated into the hydroxyl group chains and bind the understanding of PHBA as enantiotropic. The to two hydroxyl groups and one carboxylic acid shift in the frequency of these peaks is in group of three different molecules. The water accordance with Burger and Ramberger’s infrared molecules thus contribute to a stronger intermo- rule, which states that the phase that absorbs at lecular bonding along the a-axis and this explains higher frequencies is also less stable at 0 K.9 On the higher stability. In acetone the solvate is more these grounds it may even be speculated that the stable than the ansolvate up to the transition high-temperature phase is in fact the phase temperature at approximately 508C. The presence reported by Kariuki et al.4 Unfortunately, the of the acetone solvate is shown by the emergence of structure of the high temperature polymorph the two solubility curves in conjunction with could not be resolved by single crystal X-ray particle properties of the desolvated solvate dif- diffractometry due to the stability sensitivity of ferent from those of the ansolvate. The structure of the high-temperature polymorph. the acetone solvate is based on the centrosym- The two polymorphs could not be affirmed in the metric carboxylic acid dimerisation (Heath et al.3). DSC measurements. No peaks of polymorphic The acetone molecule is hydrogen bonded to one transformation were found. However, on a few hydroxyl group and by this actually seems to occasions at the melting point two peaks appeared interrupt the hydroxyl bonded chain of the separated by 18C (at approximately 215.5 and ansolvate. Hence, the increased stability of the 216.58C), in accordance with reports of Heath solvate over the unsolvated form perhaps relates et al.3 Frequently, DSC scans of crystals acquired to increased van der Waals bonding. The rapid through evaporation crystallization at 508C, desolvation may occur through channels along the exhibited a somewhat higher melting point (216– c-axis. Indication of the presence of further 2178C). However, PHBA sublimes at temperatures solvates in ACN, ethyl acetate, and methanol far below the melting point, and when the melting was found but could not be verified. In methanol

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The slope of the van’t Hoff curve is given by

dlnx DHvH eq ¼ So ln ð1Þ dT RT2 vH where DHSo ln is the so-called van’t Hoff enthalpy of solution. It is seen from Figure 8 that with an increased solubility follows a decline in the slope of the curve and hence a reduction in van’t Hoff enthalpy of solution. The acetone solvate emerges as an exception to this trend as it differs considerably from the remaining curves by its steeper slope. Figure 8. van’t Hoff plot of the ansolvate phase of The van’t Hoff enthalpy of solution differs PHBA in methanol (--), ACN (-}-), acetic acid (-~-), from the calorimetric enthalpy of solution, and acetone (-*-), and ethyl acetate (-þ-) between 10 and to establish the relation we need to analyze 508C. The solvates are denoted by full symbols with the the thermodynamic fundamentals. From the acetone solvate and monohydrate as circles and squares, Gibbs–Helmholtz equation, for a pure component respectively. the Gibbs free energy of fusion, DGf(T) is related to the enthalpy of fusion, DHf(T), at temperature T as d DGf ðTÞ DHf ðTÞ endothermic peaks as well as lowered melting ¼ ð2Þ points and additional fusion peaks were observed dT T T2 during DSC scans. However, water contamination The activity of the pure solid phase, as, can be with associated monohydrate formation or solvent defined as inclusions may mislead. The centrosymmetric carboxylic acid dimerisation is found in all the RT ln aS ¼ moðlÞmðsÞ¼DGf ðTÞð3Þ modifications of PHBA, which perhaps explains why no solvate with acetic acid is found. where m(s) is the chemical potential of the pure solid and mo(l) is the chemical potential of the reference state in the definition of the activity. Thermodynamics Since the activity is defined on the free energy of Commonly, the temperature dependence of the fusion, mo(l) is the chemical potential of the pure solubility is described in a so-called van’t Hoff melt at temperature T. At the temperatures of plot, by plotting ln(xeq) versus the reciprocal of the interest in the present work the reference state is absolute temperature. The data of the present a hypothetical supercooled melt. If Equation 3 is work are presented in this way in Figure 8. inserted into Equation 2 we obtain: The van’t Hoff curves are well correlated by 2nd degree polynomials and the coefficients are listed dlnas DHf ðTÞ ¼ ð4Þ in Table 3. dT RT2

Table 3. Regression Curves of PHBA in Six Solvents Between 10 and 508C

2 Solvent Regression Curve ln(xeq) ¼ A*(1/T) þ B(1/T) þ C

Ansolvate ABC R2

Methanol 4.3201 105 3.6886 103 5.3439 0.998078 Acetonitrile 3.5127 105 4.8645 103 8.1099 0.999335 Acetic acid 4.6655 105 4.4995 103 6.7801 0.999907 Acetone 1.2435 106 8.7272 103 13.414 0.998500 Ethyl acetate 4.6287 105 4.1378 103 6.0428 0.999880 Solvates Acetone solvate 6.4779 105 5.8733 103 10.286 0.999865 Monohydrate 2.6425 106 2.2278 104 37.807 0.99993

Temperature, T, Refers to Absolute Temperature and xeq to Mole Fractions.

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 DOI 10.1002/jps PHASE EQUILIBRIA AND THERMODYNAMICS OF p-HYDROXYBENZOIC ACID 757

In a saturated solution the activity of the solute in Rearrangement of Equation 10 and insertion of the solution, aeq, equals that of the solid, if the Equations 4, 8, and 11 gives reference state is equal (called a Raoult’s law state of reference). Hence, for a saturated solution we @ ln x @ ln x DHf ðTÞ DHmix ¼ þ So ln may write: @T @ ln a RT2 RT2 eq T ð12Þ dlna DHf T @ ln x DHso ln eq ð Þ ¼ ¼ 2 ð5Þ 2 dT RT @ ln a T RT If we define the activity coefficient, g, in the If this equation is compared with the classical solution as van’t Hoff equation we find xeq ¼ aeq ð6Þ vH @ ln xeq DHSoln ¼ DHSo ln ð13Þ We derive at @ ln a f and it becomes clear that the reason why the van’t dlnxeq DH ðTÞ ¼ ðconstant xÞð7Þ Hoff enthalpy of solution differs from the true dT RT2 calorimetric enthalpy of solution is that the van’t which has clear resemblance to Equation 1. Hoff equation neglects the change in activity with However, a direct identification between the two composition. equations cannot be done since the Gibbs– @ ln a @ ln g Helmholz equation requires that the derivative ¼ 1 þ ð14Þ on the left hand side is at constant composition. If @ ln x T @ ln x T we consider the dissolution as proceeding in two steps we may write All van’t Hoff curves in Figure 8, display deviation

f mix from linearity, albeit to smaller extent. These DHSo ln ¼ DH ðTÞþDHSo ln ð8Þ deviations reflect the temperature dependence of the van’t Hoff enthalpy of solution. In particular, where DHso ln is the actual calorimetric partial mix the enthalpy of fusion, DHf(T), varies with tem- molar heat of solution. DHSo ln is the partial molar heat of mixing of the supercooled melt with the perature. The net enthalpy required to heat the solvent at concentration x, and can be written solid from temperature T to the melting point, where it melts and then cool the melt down as mix DHSo ln ¼ RT ln ð9Þ a supercooled liquid to temperature T can be expressed as For the ideal solution, the activity coefficient is unity and the solubility mole fraction can replace Tðm ðT the activity of the solid in Equation 4 and from DHf ðTÞ¼ CSdT þ DHf ðT Þþ CLdT ð15Þ the slope of the solubility curve we may deter- p m p mine the enthalpy of fusion. Since the enthalpy of T Tm mixing is zero for an ideal solution, we also obtain f where DH (Tm) represents the enthalpy of fusion the enthalpy of solution. Hence, for an ideal S L at the melting point and Cp and Cp the heat solution the van’t Hoff enthalpy of solution is capacities of the solid and the supercooled melt, the true calorimetric enthalpy of solution and is respectively. Combining Equations 8, 9, 14, and equal to the enthalpy of fusion at the temperature 15 yields of the solubility data. 10 11 " ! Hollenbeck, and Manzo, have contributed to Tðm ðT the analysis of the problem in case of a nonideal vH S f L DHSo ln ¼ CpdT þ DH ðTmÞþ Cp dT solution. For an intensive thermodynamic property like the activity we may write T # ! Tm @ ln x @ ln a @ ln a @ ln a @ ln x þðRT ln gÞ eq ð16Þ ¼ þ ð10Þ @ ln a @T eq @T x @ ln x T @T eq where If the heat capacity difference between the supercooled melt and the solid, DC , is regarded as @ ln DHmix p a So ln constant independent of temperature, the equa- ¼ 2 ð11Þ @T x RT tion is simplified into

DOI 10.1002/jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 758 NORDSTRO¨ M AND RASMUSON

DHvH ¼½DHf ðT ÞþDC ðT T Þ So ln m p m @ ln x ð17Þ þ RT ln eq @ ln a and by Equation 14 we may write DHvH ¼ DHf ðT ÞþDC ðT T Þ So ln m 0 p 1m @ 1 A ð18Þ þ RT ln geq 1 þ @ ln g Figure 9. Illustration of the effect of the solvent on @ ln xeq the van’t Hoff plot of an enantiotropic polymorphic system. Tm and Ttr correspond to the melting point and The magnitude of the DCp(T Tm) term in transition temperature, respectively. Equation 17 and 18, which regularly is negative, increases with decreasing temperature, which tends to govern the influence of the temperature Several different features can be observed from on the van’t Hoff enthalpy of solution, that is, the Figure 10. Firstly, consider the data for the curvature of the van’t Hoff plots. The first two expected unsolvated stable modification. For each terms on the right hand side are independent of temperature the values for the different solvents the solvent, and hence the dependence of DHvH on can be empirically correlated by 2nd degree So ln vH the solvent is fully exerted through the enthalpy regression curves originating at DHSo ln and ln(xeq) of mixing and the partial derivative of the activity equaling zero. with composition. As the temperature increases DHvH ¼ ðlnðx ÞÞ2 þ lnðx Þð19Þ the solubility increases. At the melting point the So ln eq eq DCp(T Tm) term vanishes. In addition, as the where a and b denote phase specific regression mole fraction approaches unity the activity coeffi- curve coefficients. The regression curves correlate vH cient as well as the partial derivative factor theDHSo ln, that is, the temperature dependence of approaches unity in the Raoult’s law definition the solubility, to the solubility at a certain of activity. Hence, we may envisage that regard- temperature for different solvents. The regression less of the solvent all van’t Hoff enthalpies for the curve coefficients are listed in Table 4 (giving same solid phase should approach DHf(T )asT vH m DHSo ln in kJ/mol). approaches Tm. These regressions can be used in different ways. Different polymorphs have different enthalpy of One important application is that the curve may fusion and also the second term may differ because of different heat capacities as well as different melting temperatures, and hence the slope of the van’t Hoff plot of different polymorphs in a particular solvent differs. Enantiotropic polymorphs display similar solubility in close proximity to the transition temperature. Establishing phase diagrams of such systems may therefore be problematic as experimental uncertainties exceed the solubility difference between the polymorphs. However, the difference between the polymorphs becomes more accentuated when using solvents of lower solubility rather than the opposite. This is illustrated in Figure 9. This may explain why, a discontinuity in the slope of the solubility curves, Figure 10. Temperature and solvent effect on solubi- only appear in ACN and possibly acetic acid. & * vH lity and of monohydrate ( ), acetone solvate ( ) (only In Figure 10 DHSo ln is plotted versus ln(xeq)at 30, 40, and 508C), and the ansolvate phase in MeOH (), 108C increments ranging from 10 to 508C for the ACN (}), HAc (~), acetone (*), and EtAc (þ)in108C different solids and solvents of the present work. increments between 10 and 508C. The Hf(Tm) of the vH The DHSo ln values are determined from the slopes ansolvate, as estimated to 30.85 kJ/mol from DSC is also of the van’t Hoff curves displayed in Figure 8. included (dashed).

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 DOI 10.1002/jps PHASE EQUILIBRIA AND THERMODYNAMICS OF p-HYDROXYBENZOIC ACID 759

Table 4. Regression Curve Coefﬁcients of Equation 19 for Unsolvated PHBA

T [8C] 10 15 20 25 30 35 40 45 50 a 0.8379 0.8651 0.8967 0.9570 1.0202 1.0361 1.1065 1.1768 1.2537 b 0.3015 0.4907 0.6928 0.8282 0.9739 1.2381 1.3872 1.5641 1.7323 R2 0.999 0.999 0.999 0.999 0.998 0.998 0.998 0.998 0.998 provide an estimation of the temperature depen- data in Figure 10 becomes 27.8 kJ/mol as com- dence of the solubility of the compound in a solvent pared to the value of 30.85 kJ/mol obtained by in which there is only one single solubility DSC measurements. If the data for the acetone measurement. Quite often solubility data reported solvate is extrapolated to ln(xeq) ¼ 0, we obtain f in the literature is limited to a value at, for DH (Tm) ¼ 27.4 kJ/mol. In the solubility study the example, 258C. If this value is inserted in Equation transition temperature of stability between the 19, an estimate of the van’t Hoff enthalpy is acetone solvate and the ansolvate was estimated vH obtained and thus of the temperature dependence. to 508C, and the difference in DHSo ln at this Another important feature becomes apparent temperature amounts to approximately 7 kJ/mol. when the data in water and in acetone are This value agreeswell with the calorimetric value 8 considered in relation to the regression curves of kJ/mol as determined by DSC.3 Since the esti- f the ansolvate. The monohydrate and the acetone mated DH (Tm) of the acetone solvate is close to the solvate do not fit into the relations discussed above corresponding value of the ansolvate, the differ- valid for the unsolvated phase. The acetone solvate ence in the van’t Hoff enthalpies may originate data are located clearly above the data of the from differences in the heat capacity term. The vH ansolvate, that is, the DHSo ln values are too high lower melting point of the solvate (1958C, Heath for the solubility values. The monohydrate data et al.3) suggests a lower heat capacity term, which vH are completely off, where the DHSo ln is high but not would explain the higher van’t Hoff enthalpy of high enough to match the low solubility. Hence, in solution. the plot we can easily distinguish these solid phases from the ansolvate, purely from the solubility data in different solvents and the CONCLUSIONS corresponding temperature dependence. This is of particular value, in the case where it is difficult Solubility of PHBA, as retrieved in six solvents in to prevent desolvation when bringing a sample of the temperature interval of 10–508C, portrayed a the solid to a more detailed identification. By very intricate and changeable behavior. Strong vH extrapolation of the regression curve of DHSo ln indications of an enantiotropic polymorphism of versus ln(xeq) for the unsolvated phase towards the PHBA were obtained from solubility measure- low solubilities in water, we can obtain a rough ments of acetic acid and especially ACN. The estimate of the solubility of this phase in water transition point was estimated to between 25 and even though it could not be determined experi- 308C. FTIR analysis corroborated these findings mentally. If this estimated value is compared with through contrasting spectra of crystals obtained the experimentally determined solubility of the from above and below the conjectured transition monohydrate we obtain a measure of the relative point. Solvation of PHBA was verified from water stability, and an explanation for why the anhy- and acetone, where the acetone solvate surpass drate is not found in water. the stability of the corresponding ansolvate up to Finally, the correlation between solubility and approximately 508C. Suggestions of additional vH DHSo ln for each solvent at increasing temperature solvated modifications from, in particular, metha- may also be utilized. As the temperature is nol were obtained through solubility and DSC vH increased for each solvent, DHSo ln and ln(xeq) analysis. increases towards the melting point where the A thermodynamic analysis disclosed a pro- vH f DHSo ln equals DH (Tm) regardless of solvent. nounced correlation at constant temperature f Hence, DH (Tm) can be estimated by extrapolating between the van’t Hoff enthalpy of solution and the unsolvated curves for each solvent to the natural logarithm of the mole fraction solubi- f ln(xeq) ¼ 0. The average of the DH (Tm) values lity of the ansolvate in different solvents. This obtained by linear extrapolation of the ansolvate correlation can be used for discrimination between

DOI 10.1002/jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 760 NORDSTRO¨ M AND RASMUSON different solvated and unsolvated solid phases in diffractometry analyses and Sandra Gracin, the experiments and for estimation of solubility Department Chemical Engineering and Technol- curves in new unexplored solvents. It is also shown ogy, Royal Institute of Technology, for scientiﬁc that van’t Hoff data can be extrapolated to obtain a discussions. ﬁrst estimate of the enthalpy of melting.

REFERENCES NOTATION 1. Giron D. 1995. Thermal analysis and calorimetric A Regression curve coefficient methods in the characterization of polymorphs and a Activity [mol/mol total] solvates. Thermochimica Acta 248:1–59. 2. Gu C-H, Grant DJW. 2001. Estimating the relative aeq Activity of solute in solution at equilibrium [mol/mol total] stability of polymorphs and hydrates from heats of solution and solubility data. J Pharm Sci 90:1277– s Activity of solid phase [mol/mol total] a 1287. B Regression curve coefficient 3. Heath EA, Singh P, Ebisuzaki Y. 1992. Structure of C Regression curve coefficient p-Hydroxybenzoic acid and p-hydroxybenzoic acid- L Cp Heat capacity of liquid [J/(mol K)] Acetone Complex (2/1). Acta Cryst C 48:1960–1965. S Cp Heat capacity of solid [J/(mol K)] 4. Kariuki BM, Bauer CL, Harris KDM, Teat SJ. R Gas constant, 8.314 [J/(mol K)] 2000. Polymorphism in p-Hydroxybenzoic acid: The T Temperature [K] effect of intermolecular hydrogen bonding in controlling proton order versus disorder in the car- Tm Fusion temperature [K] boxylic acid dimer motif. Angew Chem Int Ed Ttr Transition temperature [K] 39:24. xeq Solubility [mol/mol total] a Regression curve coefficient 5. Ebisuzaki Y, Askari LH, Bryan AM, Nicol MF. 1987. Phase transitions in resorcinal. J Chem Phys b Regression curve coefficient 87:11, 6659–6664. DCp Heat capacity difference between 6. Fukuyama K, Ohkura K, Kashino S, Haisa M. supercooled liquid and solid [J/(mol K)] 1973. The crystal and molecular structure of p- f DG (T) Gibbs free energy of fusion at tempera- hydroxybenzoic acid monohydrate. Bull Chem Soc ture T [J/mol] Japan 46:804–808. f DH (Tm) Enthalpy of fusion at the melting point 7. Colapietro M, Domenicano A, Marcianti C. 1979. [J/mol] Structural studies of benzene derivates. VI. Refine- DHf(T) Enthalpy of fusion at temperature ment of the crystal structure of p-hydroxybenzoic T [J/mol] acid monohydrate. Acta Cryst B35:2177–2180. 8. Ewing MB, Sanchez Ochoa JC. 2004. Vapor DHSoln Enthalpy of solution [J/mol] DHmix Enthalpy of mixing [J/mol] pressures of acetonitrile determined by compara- So ln tive ebulliometry. J Chem Eng Data 49:486–491. D vH van’t Hoff enthalpy of solution [J/mol] HSo ln 9. Burger A, Ramberger R. 1979. On the poly- g Activity coefficient morphism of pharmaceutical and other molecular o m (l) Chemical potential of liquid (reference) crystals. I. Theory of thermodynamic rules. II. phase Applicability of thermodynamic rules. MikroChim m(s) Chemical potential of solid phase Acta (Wien) II:259–271, 273–316. 10. Hollenbeck RG. 1980. Determination of differential heat of solution in real solutions from variation in solubility with temperature. J Pharm Sci 69:1241– 1242. ACKNOWLEDGMENTS 11. Manzo RH, Ahumada AA. 1990. Effects of solvent medium on solubility. V. Enthalpic and entropic The authors appreciate and acknowledge the contributions to the free energy changes of di- Swedish Research Council for financial support, substituted benzene derivatives in ethanol:water Andreas Fischer, Inorganic chemistry, Royal and ethanol:cyclohexane mixtures. J Pharm Sci Institute of Technology for single crystal X-ray 79:1109–1115.

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 95, NO. 4, APRIL 2006 DOI 10.1002/jps european journal of pharmaceutical sciences 28 (2006) 377–384

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Polymorphism and thermodynamics of m-hydroxybenzoic acid

Fredrik L. Nordstrom¨ ∗, Ake˚ C. Rasmuson

Department of Chemical Engineering and Technology, Royal Institute of Technology, Teknikringen 28, SE-100 44 Stockholm, Sweden article info abstract

Article history: Solution and solid-state properties of m-hydroxybenzoic acid have been investigated. Two Received 23 January 2006 polymorphs were found where the monoclinic modiﬁcation exhibits a higher stability Received in revised form than the orthorhombic form. The solubility of the monoclinic polymorph was determined 27 March 2006 between 10 and 50 ◦C in methanol, acetonitrile, acetic acid, acetone, water and ethyl acetate. Accepted 10 April 2006 The solubility of the orthorhombic polymorph was determined between 10 and 50 ◦Cin Published on line 29 April 2006 acetonitrile, acetic acid, acetone and ethyl acetate. A thermodynamic analysis revealed a marked correlation between the molar solubility and the van’t Hoff enthalpy of solution Keywords: at constant temperature. In addition, in each solvent increased temperature resulted in m-Hydroxybenzoic acid increased van’t Hoff enthalpy of solution. It is shown that the solubility data can be used 3-Hydroxybenzoic acid to estimate melting properties for both polymorphs. The solubility ratio of the two forms Polymorphism and the DSC thermogram of the orthorhombic form strongly suggest that the system is Monotropy monotropic. However, according to the polymorph rules of Burger and Ramberger, the esti- Enantiotropy mated higher melting enthalpy and lower melting temperature of the orthorhombic form Solubility points towards an enantiotropic system. Hence, this system appears to be an exception to van’t Hoff enthalpy of solution the Burger and Ramberger melting enthalpy rule, and the probable reason for this is found Thermodynamics in the difference in the heat capacity of the two solid forms. © 2006 Elsevier B.V. All rights reserved.

1. Introduction melting point and the enthalpy of melting may also be inaccessible due to phase conversion or decomposition prior to The prevalence of polymorphic modiﬁcations of a compound fusion. The aim of this paper is to address problems of this may cause alterations in solid-state properties. Variations in character for meta-hydroxybenzoic acid (abbreviated hence- e.g. solubility and dissolution rate may have a serious impact forth to MHBA) using a thermodynamic framework. It is shown in industrial crystallization processes and in the case of phar- that the solubility of MHBA follows patterns, which with ther- maceutics, bioavailability of drugs. Solubility, melting tem- modynamic theory, convey pertinent information of solid- perature and enthalpy of melting are experimental quantities state and solution properties as well as in estimating melting from which thermodynamic parameters for each polymorph properties. can be calculated. However, in polymorphic systems there are MHBA is used as an intermediate in the production of ger- often problems associated with the determination of the data micides, preservatives, plasticizer and pharmaceuticals (Kirk- for the metastable form. In the solubility determination, the Othmer’s Encyclopedia, 1997). MHBA has previously been solid phase may convert to the stable phase more rapidly than reported to exhibit polymorphism (Gridunova et al., 1982) the rate by which the pseudo-equilibrium is attained. The and exists as a monoclinic and as an orthorhombic crys-

∗ Corresponding author. Tel.: +46 8 7906402; fax: +46 8 105228. E-mail address: [email protected] (F.L. Nordstrom).¨ 0928-0987/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2006.04.008 378 european journal of pharmaceutical sciences 28 (2006) 377–384

tal structure. The monoclinic modification comprises cen- single-crystal X-ray diffractometer. Visual identification and trosymmetric carboxylic acid dimerisation. The orthorhombic imaging was carried out with a photo microscope, Olympus, phase lacks the typical dimer configuration of hydroxybenzoic SZX12, and at elevated temperatures with a hot stage micro- acids (Heath et al., 1992; Bacon and Jude, 1973; Cochran, 1953; scope, Olympus BH-2. Differential scanning calorimetry (DSC), Sundaralingam and Jensen, 1965). TA Instruments, DSC 2920, provided information of melting point and enthalpy of fusion at the fusion temperature. The calorimeter was calibrated against the melting point and 2. Materials and methods enthalpy of fusion of indium. Samples, 1–10 mg, were heated at 2 K/min from 10 to 230 ◦C in hermetic Al-pans while being The solubility of monoclinic MHBA has been determined purged with nitrogen. gravimetrically in the solvents methanol (MeOH), acetonitrile Equilibrium was established by dissolution to saturation of (ACN), acetic acid (HAc), acetone, water and ethyl acetate solid material as well as by crystallization to saturation in a (EtAc) in the temperature range 10–50 ◦C. The solubility of the solution originally brought into a supersaturated state. The orthorhombic MHBA has been determined gravimetrically in attaining of equilibrium was confirmed by repeated concen- ACN, HAc, acetone and EtAc in the 10–50 ◦C temperature inter- tration measurements over time and from different mother val. The melting point and enthalpy of fusion at the fusion liquors. Similarly, the pseudo-equilibrium of the metastable temperature of the monoclinic MHBA have been determined phase was validated using repeated concentration measure- by DSC. ments over time. The occurrence of phase conversion was observed as a rapid decrease in concentration. In experiments 2.1. Material where saturation was obtained by dissolution, an excess amount of commercial MHBA was partly dissolved either in MHBA (CAS registry number 99-06-9) was purchased from glass bottles or in glass test tubes. The bottles/tubes were Sigma–Aldrich, purity >99%, and was used as obtained. placed in a water bath and magnetic stirring was used at 300 The five organic solvents were purchased from VWR/Merck; and 600 rpm, respectively. In the crystallization experiments, ◦ methanol (HiperSolv, >99.8%), acetonitrile (LiChroSolv, Gra- supersaturation was generated by cooling at 1 C/min until the dient grade, >99.8%), acetic acid (Pro Analysi, 96%), acetone solution nucleated spontaneously. In some experiments the (HiperSolv, >99.8%) and ethyl acetate (HiperSolv, >99.8%). The concentration of the solution was recorded for up to 2 weeks water was distilled, deionized and filtered through a 0.2 ␮m to evaluate the time required for establishment of equilibrium. filter. This also allowed for evaluation of possible chemical degradation and solid phase stability. The solid phase in equilibrium 2.2. Equipment and procedures with the solution was analyzed by sampling suspensions of crystals and solution. The suspension samples were collected Saturated solutions were prepared in 20 ml test tubes and in conjunction to extracting the first and last solubility sam- 250 ml bottles and the concentration estimated at 5 ◦C incre- ples of the experiment. The suspension samples were filtered ments at temperatures ranging from 10 to 50 ◦C. The temper- and the crystals analyzed with FTIR-ATR at room temperature. − ature was controlled by thermostat baths and the true tem- IR spectra (4000–650 cm 1) were then collected throughout perature was validated by a calibration mercury thermometer the drying of the suspension until complete dryness. Com- (Thermo-Schneider, Wertheim, Germany, accuracy of 0.01 ◦C). plete dryness was determined as when the obtained IR pattern Pre-heated syringes (10 ml) and needles were used to sam- remained constant over time. The dried crystals obtained from ple 3–6 ml of solution into pre-weighed glass vials. Pre-heating the suspension were also examined by DSC. of the syringes and needles were conducted when necessary in order to obstruct nucleation inside the syringes during sampling. Filters (PTFE, 0.2 ␮m) were utilized when sedimentation 3. Results and discussion of the solution was troublesome or when instant sampling was necessary. The filters were also pre-heated to exceed the solu- MHBA emerged from the solvents investigated in two polymor- tion temperature. The weight of the saturated (filtered) clear phic forms. No solvates were encountered. The metastable, solution and of the final dry residue after solvent evaporation orthorhombic polymorph was obtained by cooling crystal- was recorded. From these weights the solubility was calcu- lization from a supersaturated solution. However, the pure lated. The weight was repeatedly recorded throughout the orthorhombic form could only be retrieved from ACN, HAc, drying process with complete dryness determined when the acetone and EtAc. Crystallization experiments from MeOH weight of the vials remained constant over time. Drying was consistently yielded the stable monoclinic form and crys- conducted primarily in ventilated laboratory hoods at room tallization from water resulted in the orthorhombic form temperature. followed by a rapid phase transition into the monoclinic Fourier transform infrared spectroscopy with attenuated polymorph. total reflectance module, FTIR-ATR (Perkin Elmer Instruments, Spectrum One), having a ZnSe window, was used to help 3.1. Polymorphism identify the two polymorphic phases. A wavelength range of 4000–650 cm−1 and a scanning frequency of eight per The polymorphism of MHBA was corroborated through anal- sample was used for each analysis. Crystal structure deter- yses by single-crystal X-ray diffractometry, FTIR, DSC, and as mination was conducted using a Bruker–Nonius KappaCCD well as through solubility data. In addition, crystal morphol- european journal of pharmaceutical sciences 28 (2006) 377–384 379

Fig. 2 – DSC thermograms of monoclinic (upper) and Fig. 1 – FTIR spectra of monoclinic (upper) and orthorhombic (lower) MHBA at 2 K/min. orthorhombic (lower) MHBA, obtained through eight consecutive scans.

201.6 ◦C (11 scans, standard deviation of 0.6 ◦C). Literature data reported melting enthalpy of 26.2 kJ/mol (Sabbah and Le, ogy of the polymorphs differed. The two polymorphs of MHBA 1993). were determined to be identical by single-crystal X-ray diffrac- The melting temperature and the melting enthalpy of the tometry as those given by Gridunova et al. (1982). orthorhombic form could not be determined by DSC. Instead, DSC scans of crystals of the orthorhombic polymorph exhib- 3.1.1. FTIR ited recrystallization peaks typically located around 160 ◦C The IR spectra of the monoclinic and orthorhombic form of with an exothermic transformation heat of 0.51 kJ/mol on MHBA are presented in Fig. 1. The IR spectra of the monoclinic average. Thermograms of both polymorphs are presented in − polymorph exhibit a speciﬁc absorption peak at 1683 cm 1 as Fig. 2. compared to a peak at 1727 cm−1 for the orthorhombic form. Absorption peaks in this region correspond to carbonyl group 3.1.3. Solubility vibrations of MHBA (Skoog et al., 1992). Other conspicuous dif- The determined solubility of the two forms of MHBA in ferences between the IR spectra of the polymorphs are present conjunction with single X-ray diffractometry implicated that − in the regions 740–760, 790–800, 915–940 and 1420–1460 cm 1. the monoclinic form is the stable polymorph between 10 The absorption peak relation between the two polymorphs and 50 ◦C. The mole fraction solubility of the metastable − located in the 1700 cm 1 region appears to be in accordance orthorhombic polymorph exceeded the corresponding sol- with Burger and Ramberger’s infrared rule, which states that ubility of the monoclinic form by approximately 20% over the phase that absorbs at higher frequencies is also less stable the entire investigated temperature interval. The solubility of at 0 K (Burger and Ramberger, 1979). the monoclinic MHBA in the solvents MeOH, ACN, HAc, acetone, water and EtAc are presented in Fig. 3 and are listed in 3.1.2. DSC Table 1. The average melting enthalpy of monoclinic MHBA was The solubility differs markedly depending on the sol- determined to 35.9 kJ/mol (11 scans, standard deviation of vent. The solubility of monoclinic MHBA in acetone exceeded 1.0 kJ/mol). The average peak fusion temperature was deter- 125 mmol/mol total whereas the solubility in water only mined to 202.8 ◦C (11 scans, standard deviation of 0.3 ◦C) amounted to 1.2 mmol/mol total, at 30 ◦C. Thus, MHBA is more and the corresponding average onset fusion temperature to than a 100 times more soluble in acetone than in water. Scarce

Table 1 – Solubility of monoclinic MHBA with associated standard deviations Temperature (◦C) Solubility (standard deviation) [number of samples] (g MHBA/kg solvent)

MeOH ACN HAc Acetone H2O EtAc

10 398.87 (0.38) [4] 24.07 (0.31) [6] 51.70 (0.018) [4] 265.85 (0.57) [8] 4.00 (0.040) [4] 64.72 (0.46) [4] 15 422.46 (0.12) [4] 27.93 (0.33) [6] 57.54 (0.014) [4] 281.27 (0.71) [7] 4.92 (0.011) [6] 70.55 (0.42) [5] 20 448.92 (0.27) [4] 32.59 (0.08) [6] 64.49 (0.18) [4] 298.90 (1.03) [6] 6.09 (0.13) [6] 77.04 (0.67) [8] 25 478.10 (0.11) [4] 37.89 (0.26) [7] 71.80 (0.13) [4] 315.96 (0.84) [8] 7.57 (0.054) [4] 83.73 (0.22) [4] 30 505.60 (0.15) [11] 44.96 (0.25) [11] 79.66 (0.67) [5] 336.94 (0.84) [8] 9.31 (0.0082) [4] 92.30 (1.00) [6] 35 537.75 (1.07) [5] 52.66 (1.41) [11] 89.77 (0.54) [6] 358.03 (0.28) [4] 11.64 (0.021) [4] 100.48 (0.52) [3] 40 575.20 (0.43) [7] 61.26 (0.10) [4] 99.66 (0.68) [6] 382.61 (0.45) [4] 14.62 (0.097) [4] 110.34 (0.99) [6] 45 616.31 (0.44) [6] 69.07 (0.10) [4] 111.52 (0.59) [6] 403.76 (0.53) [8] 17.97 (0.019) [4] 121.11 (0.69) [3] 50 653.68 (0.70) [6] 79.40 (0.15) [4] 124.23 (1.01) [8] 430.26 (0.71) [10] 22.62 (0.048) [4] 131.35 (1.60) [5] 380 european journal of pharmaceutical sciences 28 (2006) 377–384

♦ Fig. 3 – Solubility of monoclinic MHBA in methanol (×), Fig. 4 – Solubility of orthorhombic MHBA in acetonitrile ( ), acetonitrile (♦), acetic acid (), acetone (), water () and acetic acid ( ), acetone ( ) and ethyl acetate (+) from 10 to ◦ ethyl acetate (+) from 10 to 50 ◦C. 50 C.

reference solubility data of MHBA is available. The solubility of ior. If crystallized as the orthorhombic form in water, con- MHBA in water is in agreement with the value given by Nakai version occurred within minutes into the monoclinic phase. et al. (1989). Moreover, applying pressure or grinding of the dry crystals of The solubility of orthorhombic MHBA in ACN, HAc, acetone the metastable form did not result in phase conversion, as and EtAc is presented in Fig. 4 and listed in Table 2. recorded by FTIR. The purity of the crystallized polymorphs was established 3.1.4. Crystal morphology based on the difference between the two polymorphs, as The crystal morphology of the two polymorphs differed. Small observed through the different methods of analysis. In partic- and highly agglomerated crystals were typically obtained of ular FTIR-ATR contributed with important information, as the the stable monoclinic polymorph. The orthorhombic form two polymorphs exhibited very different absorption peaks at crystallized in the form of rods, albeit with some variation in 1683 and 1727 cm−1. DSC also provided with some knowledge crystal size and degree of agglomeration. Both polymorphs are as analysis of the metastable form resulted in an exother- displayed in Fig. 5. mic transformation peak. In addition, investigation by photo microscopy facilitated in estimating the purity since the two 3.1.5. Stability and purity polymorphs differed in crystal morphology. Finally, the solu- The orthorhombic polymorph of MHBA appeared relatively bility study indicated whether mixtures existed through the stable in both solution and when ﬁltered and dried in air. The evolution of solution concentration over time. The pseudo- driving force for phase conversion in solution, i.e. the solubility equilibrium of the metastable polymorph could be established ratio (mole fraction-based) between the orthorhombic and the as the concentration remained constant over time, whereas a monoclinic polymorph, corresponded to approximately 1.2 in polymorphic transformation resulted in a rapid concentration the investigated temperature range, as shown above. In terms decrease down to the solubility level of the stable polymorph. of supercooling this corresponds to more than 13 ◦C in ace- Of the solvents used, only water yielded phase transformation tone. The orthorhombic phase converted normally into the from the metastable to the stable polymorph almost directly stable monoclinic polymorph after a couple of hours in the after nucleation and thus crystal samples comprising poly- 10–50 ◦C region. Water emerged as an exception to this behav- morphic mixtures.

Table 2 – Solubility of orthorhombic MHBA with associated standard deviations Temperature (◦C) Solubility (standard deviation) [number of samples] (g MHBA/kg solvent)

ACN HAc Acetone EtAc

10 30.39 [1] 68.91 [1] 320.49 [1] 85.50 (0.30) [2] 15 35.01 (0.05) [2] 73.87 (0.31) [2] 336.51 (0.53) [3] 91.19 (0.02) [2] 20 40.63 (0.02) [2] 81.22 (0.46) [2] 354.66 (0.33) [4] 98.45 (0.17) [2] 25 47.35 (0.08) [2] 89.62 (0.06) [2] 377.20 (1.00) [4] 107.63 (0.34) [3] 30 55.15 (0.02) [2] 99.59 (0.12) [2] 401.95 (1.54) [3] 116.72 (0.45) [2] 35 64.91 (0.17) [2] 110.73 (0.08) [2] 428.64 (0.07) [2] 127.56 (0.04) [2] 40 75.46 (0.16) [2] 123.91 (0.54) [2] 455.55 (1.33) [2] 138.90 (0.20) [4] 45 88.09 (0.13) [2] 136.64 (0.02) [2] 487.82 (2.74) [2] 152.25 (0.35) [2] 50 101.82 (0.75) [3] 150.51 (0.42) [2] 527.20 [1] 166.09 (0.43) [2] european journal of pharmaceutical sciences 28 (2006) 377–384 381

Fig. 5 – Crystals of the orthorhombic MHBA (left, magniﬁed 40 times) and monoclinic MHBA (right, magniﬁed 90 times), obtained through evaporation crystallization from ACN and MeOH, respectively, at 20 ◦C.

3.2. Thermodynamics Table 3 – Regression curve coefﬁcients of monoclinic MHBA in six solvents between 10 and 50 ◦C 3.2.1. The temperature dependence of solubility Solvent ABC The temperature dependence of the solubility is often × 5 − × 3 described in a so-called van’t Hoff plot, by plotting ln(xeq) ver- Methanol 4.0847 10 3.7193 10 5.5720 5 3 sus the reciprocal of the absolute temperature. Fig. 6 displays Acetonitrile 2.4787 × 10 −4.3765 × 10 7.4073 × 5 − × 3 the van’t Hoff plot of both polymorphs of MHBA in all solvents Acetic acid 5.3662 10 5.4935 10 8.8903 Acetone 2.9953 × 105 −2.9522 × 103 4.3921 between 10 and 50 ◦C. Water 1.4880 × 106 −1.3813 × 104 22.663 The van’t Hoff curves in the present work are well corre- Ethyl acetate 4.6804 × 105 −4.6404 × 103 7.3219 lated by a 2nd order polynomial for each solvent: Temperature, T, refers to absolute temperature and xeq to mole frac- 2 tions. x = A 1 + B 1 + C ln eq T T (1) HvH mate Soln from solubility data by The regression curve coefﬁcients, A, B and C of monoclinic and orthorhombic MHBA are listed in Tables 3 and 4, respec- 1 HvH =−R 2A + B (3) tively. In all cases R2 > 0.999. Soln T The slope of the van’t Hoff curve is given by The van’t Hoff enthalpy of solution differs from the calorimet- HvH dlnxeq ric enthalpy of solution. However, in a previous contribution = Soln (2) dT RT2 (Nordstrom and Rasmuson, 2006) the relation was mapped in detail by a thermodynamic analysis, and it was shown that HvH where Soln is the so-called van’t Hoff enthalpy of solution. Tm By derivation of Eq. (1) and insertion into Eq. (2) we may esti- HvH = CS T + Hf T Soln p d ( m) T T ∂ x L ln + Cp dT + RT ln (4) ∂ ln a T Tm

S L where Cp and Cp denotes the heat capacity of the solid and the f supercooled melt, respectively, and H (Tm) is the enthalpy of fusion at the melting point. The heat capacities are often

Table 4 – Regression curve coefﬁcients of orthorhombic MHBA in four solvents between 10 and 50 ◦C Solvent ABC

Acetonitrile 9.0490 × 105 −8.7379 × 103 14.853 Acetic acid 9.3087 × 105 −7.9226 × 103 12.821 Acetone 6.3220 × 105 −5.1567 × 103 8.1947 Fig. 6 – van’t Hoff plot of monoclinic (full curves) and Ethyl acetate 7.4970 × 105 −6.3951 × 103 10.268 orthorhombic (dashed curves) MHBA between 10 and 50 ◦C in methanol (×), acetonitrile (♦), acetic acid (), acetone (), Temperature, T, refers to absolute temperature and xeq to mole frac- water () and ethyl acetate (+). tions. 382 european journal of pharmaceutical sciences 28 (2006) 377–384

regarded constant with temperature, thus simplifying the expression to ∂ x vH f ln H = [H (Tm) + Cp(T − Tm) + RT ln ] (5) Soln ∂ ln a T and if we apply the deﬁnition of the activity coefﬁcient, in the solution

xeq = a (6) Fig. 7 – Illustration of the nature of van’t Hoff curves of a solid phase in four solvents. we may write

solvents. This is in accordance with Fig. 7. Since the solid-state 1 properties remain unchanged at constant temperature, this HvH = Hf T + Cp T − T + RT Soln [ ( m) ( m) ln ] ∂ (7) + ln correlation directly reflects the influence of the solvent on the 1 ∂ ln x T relation between the solubility and the van’t Hoff enthalpy of where C denotes the heat capacity difference between the HvH p solution. The relation between the Soln and the molar sol- supercooled liquid and the solid, which regularly is positive. ubility in different solvents at constant temperature can be The heat capacity difference at temperature T is an experi- correlated by mentally inaccessible parameter, which commonly is simpli- HvH = ˛ x 2 + ˇ x fied by other expressions or entirely neglected (Gracin and Soln (ln( eq)) ln( eq) (8) Rasmuson, 2002). HvH ˛ ˇ Using Eq. (4) for Soln and the Raoult’s law definition where and denote regression coefficients specific for each underlying Eq. (6) we may rationalize the behavior of solubil- HvH solid phase, and are given in Table 5 ( Soln in kJ/mol). In ity for a given substance in different solvents and at different all cases R2 > 0.99. The data in water deviate from the gen- temperatures. eral behavior, in that the significantly lower solubility is not At the fusion temperature the free energy difference HvH accompanied by a correspondingly higher Soln. between the solid and the melt is zero and it follows that The second correlation corresponds to the increase in solu- ln(x )=0and = 1. Hence HvH eq bility with increasing temperature. In Fig. 8, Soln and ln(xeq) in each solvent increase as the temperature increases. This 1. for the same solid in different solvents all curves in a van’t is also in accordance with the behavior illustrated in Fig. 7. Hoff plot intersect at the fusion temperature. HvH The ln(xeq) and Soln predominantly increase with temperature because the Hf(T) increases with increasing temper- HvH f From Eq. (4) we may infer that Soln equals H (Tm) when ature, due to the decreasing magnitude of the heat capacity T = Tm and it follows that: term. Two solid-state properties may be estimated from this trend. Firstly, since ln(xeq) = 0 for the pure melt we expect 2. for the same solid in different solvents all van’t Hoff curves each solubility curve to approach ln(xeq) = 0 as the tempera- approach the same slope upon approaching the fusion tem- ture increases towards the melting point. Thus, extrapolation

perature. of the increase in solubility with temperature to ln(xeq) = 0 pro-

For most compounds the solubility increases with temperature and we expect:

≤ HvH ≥ 3. the slope of a van’t Hoff curve 0, i.e. Soln 0.

As a result, we expect that for each solid phase the van’t Hoff curves in different solvents will in principle behave as illustrated in Fig. 7.

3.2.2. Estimation of melting temperature and enthalpy In our previous paper on p-hydroxybenzoic acid, it was shown and discussed that the thermodynamic properties of a system can be explored in detail by examining the relation between HvH Soln, ln(xeq) and T. Here this approach is applied to MHBA. HvH Fig. 8 – The effect of solubility and temperature on HvH In Fig. 8, Soln, is plotted versus ln(xeq) for both monoclinic Soln HvH for monoclinic (open symbols) and orthorhombic (symbols and orthorhombic MHBA in the different solvents. The Soln ◦ is calculated from Eq. (3) and Tables 3 and 4. with black background) MHBA in 10 C increments between ◦ Two different correlations can be deduced from the curves 10 and 50 C in methanol (×), acetonitrile (♦), acetic acid (), in Fig. 8. At constant temperature, a lower solubility is asso- acetone (), water () and ethyl acetate (+). The dashed line HvH represents the Hf(T ) of the monoclinic MHBA. ciated with a higher Soln, for each polymorph in different m european journal of pharmaceutical sciences 28 (2006) 377–384 383

Table 5 – Regression curve coefﬁcient of Eq. (8) for monoclinic and orthorhombic MHBA T (◦C)

10 15 20 25 30 35 40 45 50

Monoclinic ˛ 0.5792 0.5822 0.5951 0.6080 0.6398 0.6695 0.6912 0.6834 0.7098 ˇ −1.533 −1.801 −2.055 −2.311 −2.541 −2.774 –3.061 −3.422 −3.705

Orthorhombic ˛ 0.6031 0.6194 0.6389 0.6581 0.6850 0.7280 0.7697 0.8200 0.8586 ˇ −1.238 −1.568 −1.921 −2.303 −2.680 −3.042 –3.429 −3.821 −4.271 vides an estimate of the melting temperature. Fig. 9 depicts this behavior for both polymorphs and all solvents. Using simple linear extrapolation the average of the melting temperature of the monoclinic MHBA in Fig. 9 gives a value of 202 ◦C (standard deviation of 24 ◦C, six solvents), as compared to 202.8 ◦C obtained in the DSC measurement. The corresponding linearly extrapolated average fusion temperature of the orthorhombic MHBA amounts to 193 ◦C (standard ◦ deviation of 19 C) as estimated from four solvents. Unfortu- Fig. 10 – Illustration of the anticipated monotropic stability nately, this value cannot be compared with a value determined relation between the stable monoclinic MHBA and the by DSC since the orthorhombic polymorph undergoes phase metastable orthorhombic MHBA in a van’t Hoff plot. conversion prior to fusion. The average melting points of the two polymorphs, determined by extrapolation are not differ- ◦ ent with sufficient statistical confidence. However, for each bic polymorph at 10 C for all solvents whereas the opposite ◦ HvH individual solvent the melting point determined by extrapo- holds at 50 C for all solvents. The transition in Soln between lation is always higher for the monoclinic form. the polymorphs occurs for ACN and acetone at approximately ◦ ◦ The second solid-state property that can be investi- 30 C and for HAc and EtAc at approximately 50 C. These f f gated from the trends in Fig. 8 is H (Tm). As the tem- results suggest that H (Tm) for the orthorhombic form is perature increases towards the melting temperature, ln(xeq) higher than for the monoclinic polymorph. HvH f approaches zero and Soln approaches H (Tm). Unfortu- nately, the heat of fusion value for the monoclinic form 3.2.3. The polymorphic nature of MHBA obtained by simple linear extrapolation is not close to the In the DSC thermogram of the orthorhombic form, the tran- value obtained in the DSC measurement. However, from sition in the region: 160–170 ◦C is exothermic. Accordingly, HvH f Fig. 8 it is seen that Soln for the orthorhombic polymorph H (Tm) seems to be higher for the orthorhombic form than HvH increases more rapidly with temperature than Soln for the for the monoclinic form, and this agrees with the result of the HvH HvH monoclinic form for all solvents. In addition, the Soln of extrapolation of Soln for each polymorph with increasing the monoclinic polymorph exceeds that of the orthorhom- temperature. However, at the same time Fig. 9 suggests that the melting temperature of the monoclinic MHBA is above that of the orthorhombic polymorph. According to the rules by Burger and Ramberger (1979), the combination of a higher f melting temperature and a lower H (Tm) for one of the polymorphs points to an enantiotropic polymorphism. On the other hand, the solubility data clearly shows that the monoclinic form is the stable form at room temperature, and the DSC thermogram of the orthorhombic form shows that the same relation holds in the region 160–170 ◦C. In our data, we find no tendency for a transition in stability. The intersection of the curves of the two polymorphs in Fig. 8 directly implies that at a certain solubility (and temperature) the solubility curves have the same slope. Above and below this value the solubility curves diverge. Since, the solubility is higher for the orthorhombic form in the same temperature range the Fig. 9 – The increase in solubility with temperature for molar solubility difference between the two polymorphs has monoclinic (empty symbols) and orthorhombic (filled a minimum in this temperature region. Hence, we believe that symbols) MHBA in 5 ◦C increments from 10 to 50 ◦Cin the system is monotropic and that the phase diagram can be methanol (×), acetonitrile (♦), acetic acid (), acetone (), illustrated as shown in Fig. 10. water () and ethyl acetate (+). The dashed line represents The parameter causing the greater curvature of the van’t the Tm of the monoclinic MHBA. Hoff curve of the metastable form in Fig. 10 should be the heat 384 european journal of pharmaceutical sciences 28 (2006) 377–384

S capacity term, Cp(T − Tm), which increases with decreasing Cp heat capacity of solid (J/(mol K)) temperature. A difference in magnitude of the Cp between Cp heat capacity difference between supercooled liquid the polymorphs results in different temperature dependences and solid (J/(mol K)) HvH f f of Soln and H (T) and hence different curvatures in a van’t H (T) enthalpy of fusion at temperature T (J/mol) f Hoff plot. The greater curvature in Fig. 10 points towards a H (Tm) enthalpy of fusion at the melting point (J/mol) greater magnitude of the term C (T − T ) for the orthorhom- HvH p m Soln van’t Hoff enthalpy of solution (J/mol) bic form in comparison to the monoclinic form. Since also a R gas constant (8.314 J/(mol K)) lower fusion temperature of the orthorhombic polymorph was T temperature (K) suggested there are strong indications of a lower Cp(s)ofthe Tm fusion temperature (K) orthorhombic form in comparison to the monoclinic form. The x concentration (mol/mol total) anticipated exception to the polymorph rules by Burger and xeq solubility (mol/mol total) xid Ramberger (1979) can thus be explained. eq ideal solubility (mol/mol total)

Greek letters 4. Conclusions ˛ regression curve coefficient ˇ regression curve coefficient The presence of two polymorphs of MHBA is corroborated activity coefficient through studies by FTIR, DSC, photo microscopy, single-crystal X-ray diffractometry and solubility measurements in six solvents. Monoclinic MHBA is shown to be the stable phase and Acknowledgements orthorhombic MHBA the metastable phase between 10 and 50 ◦C. The molar solubility of the metastable polymorph is The authors acknowledge the Swedish Research Council for about 1.2 times higher than that of the stable polymorph. A financial support, Andreas Fischer, Inorganic chemistry, Royal comprehensive thermodynamic analysis conducted within a Institute of Technology for much appreciated help with single van’t Hoff enthalpy of solution framework is used to ratio- crystal X-ray diffractometry analysis. nalize the solubility data. By plotting molar solubility versus references the van’t Hoff enthalpy of solution, two marked trends are revealed. In different solvents and at constant temperature, a higher solubility leads to a lower van’t Hoff enthalpy of solu- Bacon, G.E., Jude, R.J., 1973. Zeitschrift fur¨ Kristallographie, Bd. tion. In each solvent, increasing temperature leads to increas- 138, 19. ing solubility and increasing van’t Hoff enthalpy of solution. Burger, A., Ramberger, R., 1979. MikroChim. Acta (Wien) II, By extrapolation of solubility data the fusion temperature can 259–271, 273–316. be estimated. The results suggest that the orthorhombic form Cochran, W., 1953. Acta Crystallogr. 6, 260. has a higher enthalpy of fusion but a lower melting temper- Gracin, S., Rasmuson, A., 2002. J. Chem. Eng. Data 47, ature. However, solubility data and DSC measurements point 1379–1383. Gridunova, G.V., Furmunova, N.G., Struchkov, Y.T., Ezhkova, Z.I., towards a monotropic system. Hence, the polymorphic system Grigoreva, L.P., Chayanov, B.A., 1982. Kristallografiya 27 (2), of MHBA seems to be an exception to the polymorph rules by 267. Burger and Ramberger, and a difference in heat capacity of the Heath, E.A., Singh, P., Ebisuzaki, Y., 1960. Acta Crystallogr., C48. solid forms can explain this behavior. Kirk-Othmer, 1997. Encyclopedia of Chemical Technology, vol. 21, 4th ed. Wiley, New York, p. 619. Nakai, Y., Yamamoto, K., Terada, K., Oguchi, T., Saito, H., 5. Nomenclature Watanabe, D., 1989. Chem. Pharm. Bull. 37 (4), 1055–1058. Nordstrom, F., Rasmuson, A., 2006. J. Pharm. Sci. 95 (4), a activity (mol/mol total) 748–760. A regression curve coefficient Sabbah, R., Le, T.H.D., 1993. Can. J. Chem. 71, 1378–1383. B regression curve coefficient Skoog, Holler, Nieman, 1992. Principles of Instrumental Analysis, 5th ed. Saunders College publishing, USA. C regression curve coefficient Sundaralingam, M., Jensen, L.H., 1965. Acta Crystallogr. 18, CL p heat capacity of liquid (J/(mol K)) 1053. 1668 J. Chem. Eng. Data 2006, 51, 1668-1671

Solubility and Melting Properties of Salicylic Acid

Fredrik L. Nordstro1m† and Åke C. Rasmuson* Department of Chemical Engineering and Technology, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

The solubility of salicylic acid has been investigated in methanol, acetonitrile, acetic acid, acetone, water, and ethyl acetate from (10 to 50) °C. No new polymorphs or solvates of salicylic acid were found. The melting properties of salicylic acid were determined by differential scanning calorimetry. A correlation was observed between the solubility and the van’t Hoff enthalpy of solution. A higher solubility was related to a lower van’t Hoff enthalpy of solution. Water differed from the organic solvents in terms of solubility and its correlation to the van’t Hoff enthalpy of solution. In addition, the morphology of salicylic acid crystals recrystallized from water differed from the other solvents.

Introduction Salicylic acid, also known as ortho-hydroxybenzoic acid or 2-hydroxybenzoic acid, was used as early as 400 B.C. as an analgesic and is naturally prevalent in willow leaves, as well as in poplar and birch trees, through its glucosides.1 The main Figure 1. Salicylic acid. part of the production of salicylic acid is currently used in the (HiperSolv, >99.8 %). The water was distilled, deionized, and manufacture of aspirin.2 The molecular structure of salicylic filtered at 0.2 µm. acid is given in Figure 1. Equipment and Procedures. Saturated solutions were pre- As opposed to its isomers, p- and m-hydroxybenzoic acid, pared in test tubes and in 250 mL bottles. Solubilities were no polymorphism of salicylic acid has been discovered, nor have measured at temperatures ranging from (10 to 50) °Cin5°C solvated modifications been encountered. The crystal structure increments. The temperature was controlled by thermostat baths, salicylic acid is monoclinic and has been resolved by Cochran,3 and the true temperature was validated by a calibration mercury Sundaralingam and Jensen,4 and most recently by Bacon and thermometer (Thermo-Schneider, Wertheim, Germany, uncer- Jude.5 The basic synthon of the crystal structure of salicylic tainty of ( 0.01 °C). acid is centrosymmetric carboxylic acid dimers. The hydroxyl Syringes (10 mL) and needles were used to sample (3 to 6) group is hydrogen bonded intramolecularly to the carbonyl mL of solution into preweighed glass vials. Syringes and needles oxygen. This leads to a less flexible molecule and dimer and a were preheated when necessary to prevent nucleation inside the reduced intermolecular hydrogen bonding capacity, which likely syringes during sampling. Filters (PTFE, 0.2 µm) were utilized explains why the overall tendency for polymorphism and when the sedimentation rate was slow or when instant sampling solvation is reduced. was necessary. The filters were also preheated to exceed the Limited data is available on the solubility and temperature solution temperature. Suspensions of water and salicylic acid dependence of the solubility of salicylic acid. The aim of this were always filtered (nitrocellulose, 0.2 µm). The mass of the paper is to explore the melting properties and solubility of saturated (filtered) clear solution was recorded. Drying of salicylic acid in six solvents, that is, methanol, acetonitrile, acetic samples was conducted primarily in ventilated laboratory hoods acid, acetone, water, and ethyl acetate in the temperature range at room temperature. The mass of the samples was recorded (10 to 50) °C. repeatedly throughout the drying process to establish the point Experimental Section at which no solvent remained. The samples were weighed a final time when all the solvent was evaporated. Complete drying The solubility of salicylic acid in six different pure solvents was determined as occurring when the mass of the sample has been determined gravimetrically in the temperature range remained constant over time. ° (10 to 50) C, and the melting temperature and enthalpy of Fourier transform infrared spectroscopy with attenuated total fusion at the melting temperature have been determined by reflectance module, FTIR-ATR (Perkin-Elmer Instruments, differential scanning calorimetry. Spectrum One), having a ZnSe window, was used for identifica- Materials. Salicylic acid (CAS Registry Number 69-72-7) tion of the solid phase. A wavelength range of (4000 to 650) > was purchased from Sigma-Aldrich, purity 99 %, and was cm-1 and a scanning frequency of eight per sample was used used as obtained. The five organic solvents were purchased from for each analysis. Visual identification and imaging was carried > VWR/Merck: methanol (HiperSolv, 99.8 %), acetonitrile out with a photo microscope, Olympus, SZX12, and at elevated > (LiChroSolv, Gradient grade, 99.8 %), acetic acid (Pro temperatures with a hot stage microscope, Olympus BH-2. > Analysi, 96 %), acetone (HiperSolv, 99.8 %), and ethyl acetate Differential scanning calorimetry (DSC), TA Instruments, DSC 2920, provided information of melting temperature and enthalpy * Corresponding author. E-mail: [email protected]. Fax: +46 8 105228. of fusion at the melting temperature. The calorimeter was † E-mail: [email protected]. calibrated against the melting temperature and enthalpy of fusion

Table 1. Mole Fraction Solubility of Salicylic Acid (1) in Six Solvents between (10 and 50) °C 3 10 x1 (standard deviation) [number of samples] t/°C methanol acetonitrile acetic acid acetone water ethyl acetate 10 99.35 (0.40) [8] 19.17 (0.22) [6] 37.77 (0.31) [5] 146.25 (0.08) [4] 0.156 (0.010) [12] 109.08 (0.57) [3] 15 107.81 (0.12) [4] 22.29 (0.22) [8] 42.93 (0.22) [6] 156.85 (0.05) [4] 0.178 (0.010) [12] 116.47 (1.05) [9] 20 117.72 (0.18) [9] 25.49 (0.20) [7] 48.38 (0.84) [7] 168.04 (0.09) [4] 0.208 (0.012) [8] 125.14 (0.38) [8] 25 128.02 (0.26) [11] 29.44 (0.31) [5] 54.93 (0.60) [8] 179.24 (0.11) [4] 0.247 (0.020) [14] 135.71 (0.74) [10] 30 139.37 (0.43) [8] 34.43 (0.19) [5] 62.54 (0.69) [10] 191.85 (0.24) [6] 0.304 (0.025) [15] 145.17 (1.12) [10] 35 150.53 (0.25) [6] 38.96 (0.38) [4] 71.11 (0.05) [5] 202.38 (0.19) [5] 0.368 (0.018) [10] 156.56 (1.02) [12] 40 163.59 (0.46) [8] 45.30 (0.05) [2] 80.54 (0.66) [7] 215.04 (0.38) [4] 0.452 (0.018) [15] 167.52 (1.50) [10] 45 176.81 (0.36) [7] 52.42 (0.34) [6] 091.82 (0.45) [6] 228.01 (0.32) [6] 0.553 (0.015) [10] 179.88 (1.69) [9] 50 191.68 (0.35) [5] 59.37 (0.89) [11] 104.24 (0.36) [6] 241.28 (0.24) [4] 0.682 (0.018) [8] 192.15 (1.90) [9] of indium. Samples, (1 to 10) mg, were heated at (1, 2, or 5) salicylic acid, x, in ethyl acetate at 25 °C in the present study K/min from (10 to 180) °C in hermetic Al pans while being is lower than the solubility given by De Fina et al.7 (x ) 0.1357 purged with nitrogen at a rate of 50 mL/min. The crystal vs x ) 0.1425). structure was determined using a Bruker-Nonius KappaCCD Salicylic acid crystallized from water differed from the single-crystal X-ray diffractometer. organic solvents by a significantly lower solubility and altered Equilibrium was established by dissolution to saturation of crystal morphology. The solubility of salicylic acid in water is solid material as well as by crystallization to saturation in a listed in Table 1 and depicted in Figure 3 together with data of solution originally brought into a supersaturated state. The Apelblat and Manzurola.8 attainment of equilibrium was confirmed by repeated measurements over time and from different mother liquors. In all Salicylic acid crystallizes as needles in all solvent but form dissolution experiments, an excess amount of commercial peculiar hollow tubes with square cross-sectional areas from salicylic acid was partly dissolved either in glass bottles or in water, as illustrated in Figure 4. In addition, these crystals glass test tubes. The bottles/tubes were placed in a water bath exhibited the unusual quality of being able to adsorb water either and magnetic stirring was used at 300 rpm and 600 rpm, inside the tubes or on the surface of the crystals (due to this respectively. In the crystallization experiments, supersaturation property of the crystals, the gravimetrically conducted solubility was generated by cooling at 1 K/min until the solution nucleated analysis suffered from difficulties). Thus, the primary source spontaneously. In some experiments, the concentration of the of error of the solubility study in water stems from water solution was recorded for up to 2 weeks to evaluate the time adsorbed on salicylic acid crystals. required for establishment of equilibrium. This also allowed for evaluation of solid-phase stability and possible chemical degradation. The solid phase in equilibrium with the solution was analyzed by sampling suspensions of crystals and solution. The suspension samples were collected in conjunction to extracting the first and last solubility samples of the experiment. The filtered crystals were analyzed with FTIR-ATR at room temperature. IR spectra from (4000 to 650) cm-1 were then collected throughout the drying of the crystals until no solvent remained. Complete dryness was determined as when the obtained IR pattern remained constant over time. The filtered and dried crystals obtained from the suspension were also examined by DSC at a heating rate of 2 K/min, ranging from (10 to 180) °C. × Results Figure 2. Mole fraction solubility, x, of salicylic acid in methanol, ; acetonitrile, ]; acetic acid, 4; acetone, O; and ethyl acetate, +, between The solubility of salicylic acid with associated standard (10 and 50) °C. deviation is listed in Table 1. In all experiments, salicylic acid emerged only in its unsolvated monoclinic modification, as determined through FTIR-ATR, DSC, and photomicroscopy. The monoclinic structure as characterized by Cochran,3 Sunda- ralingam and Jensen,4 and Bacon and Jude5 was confirmed identical to the phase in this study by single-crystal X-ray diffraction crystallography. The solubilities of salicylic acid in the solvents methanol, acetonitrile (ACN), acetic acid, acetone, and ethyl acetate are presented in Figure 2. The solubility of salicylic acid was found to be very sensitive to trace amounts of water in some organic solvents. Small quantities of water gave rise to considerable solubility increases in the solvents acetonitrile, acetone, and ethyl acetate. Experi- mental variations observed between experiments are thus likely due to the effect of water contamination. The changing solubility Figure 3. Mole fraction solubility, x, of salicylic acid in water at (10 to of the binary solvent system of water and ACN has been 50) °C with 95 % confidence limits. Solubility data of Apelblat et al.8 is investigated by Gomaa et al.6 The mole fraction solubility of included, 0. 1670 Journal of Chemical and Engineering Data, Vol. 51, No. 5, 2006

Figure 5. van’t Hoff plot of salicylic acid in methanol, ×; acetonitrile, ]; acetic acid, 4; acetone, O; water, 0; and ethyl acetate, +, from (10 to 50) °C. Figure 4. Microscope photo of salicylic acid (32 times magnification) recrystallized from water through evaporation crystallization at room temperature.

Table 2. Enthalpy of Fusion at the Melting Temperature and the (peak and onset) Melting Temperature of Salicylic Acid as Determined by DSC at (1, 2, and 5) K/min

average ∆fusH average peak tm average onset tm kJ‚mol-1 °C °C 27.09 159.5 158.2 standard deviation 0.22 0.3 0.6 scans 9 14 14

Table 3. Regression Curves of Salicylic Acid in Six Solvents between (10 and 50) °C ) 2 + + regression curve ln x A(K/T) B(K/T) C Figure 6. Mole fraction solubility and van’t Hoff enthalpy of solution of solvent 10-5A 10-3BCsalicylic acid at 30 °C, in methanol, ×; acetonitrile, ]; acetic acid, 4; acetone, O; water, 0; and ethyl acetate, +. methanol 2.8005 -3.3598 6.0623 acetonitrile 6.1837 -6.6941 11.975 acetic acid 8.1088 -7.6933 13.781 Table 4. Regression Curves Coefficients of eq 2 of Salicylic Acid acetone -0.16214 -1.0345 1.9335 between (10 and 50) °C water 27.341 -21.529 33.157 ° R ethyl acetate 2.9967 -3.2949 5.6791 t/ C â 10 0.0651 -4.67 - The enthalpy of fusion at the melting temperature, ∆fusH, and 15 0.136 4.82 20 0.195 -5.03 the melting temperature, tm, have been determined by DSC at 25 0.270 -5.24 (1, 2, and 5) K/min. The outcome of the study is summarized 30 0.383 -5.40 in Table 2. The ∆fusH value has also been determined by Pinto 35 0.466 -5.66 et al.9 to 26.1 kJ/mol with a melting temperature of 159.3 °C 40 0.617 -5.83 and 158.7 °C (onset), respectively, Sabbah and Le10 to 18.2 45 0.787 -6.04 - kJ/mol (at the triple point), and by Mayer et al.11 to 14.2 kJ/mol. 50 0.912 6.38

Discussion vH A marked correlation between solubility and ∆solnH was Figure 5 depicts the solubility of salicylic acid as obtained found between all solvents except water. It has been shown in in a van’t Hoff plot. The curves displayed in Figure 5 are previous work with p-hydroxybenzoic acid12 and m-hydroxy- nonlinear and well correlated with 2nd degree polynomials for benzoic acid13 that these correlations (excluding water) at each their respective solvent. The regression curve coefficients are temperature can be well fitted with 2nd degree polynomial listed in Table 3. Fits of R2 exceeding 0.9997 were obtained in regression curves (dot-dashed curve in Figure 6) all solvents. vH )R 2 + The slope of a van’t Hoff curve corresponds to the so-called ∆solnH ln x â ln x (2) van’t Hoff enthalpy of solution (sometimes referred to as the R vH where and â denote regression curve coefficients. The apparent enthalpy of solution), ∆solnH, through regression curve coefficients and associated fits are listed in Table 4. vH )- ‚ ∆solnH R slope (1) Overall, fits are obtained where R2 exceeds 0.906. Fits of higher R2 are obtained at lower temperatures. The trend is vH The ∆solnH value reflects the temperature dependence of attributed to solution properties solely as solid-state properties solubility and is different from the (calorimetric) enthalpy of are constant at constant temperature. 12 vH solution. The relation between solubility and ∆solnH of sali- The behavior of salicylic acid in water deviates from the cylic acid at 30 °C is given in Figure 6. organic solvents in Figure 6. The lower solubility is not Journal of Chemical and Engineering Data, Vol. 51, No. 5, 2006 1671 compensated sufficiently by a higher van’t Hoff enthalpy of the organic solvents in terms of solubility, van’t Hoff enthalpy solution to allow salicylic acid to follow the observed trend. A of solution, and through the crystal morphology. behavior consistent with the observed correlation between the organic solvents implies a 60 times higher solubility in water Acknowledgment at 30 °C. However, the data of the salicylic acid-water system The authors acknowledge Andreas Fischer, Inorganic Chemistry, is outside the range of the observed correlation. Royal Institute of Technology for much appreciated help with single The lowest solubility of salicylic acid at 30 °C was obtained crystal X-ray diffractometry analysis and John Pertoft for micro- in water giving x ) 3 × 10-4, whereas the highest solubility at scope photos. 30 °C amounted to x ) 0.19 in acetone. Thus, the ratio between Literature Cited the highest and lowest solubility exceeds 630. The molar solubility decreases in the order of acetone, ethyl acetate, (1) Ullmann. Encyclopedia of Industrial Chemistry; VCH: Weinheim, Germany, 1993; Vol. A23, pp 477-483. methanol, acetic acid, acetonitrile, and water. The high solubility (2) Kirk-Othmer. Encyclopedia of Chemical Technology, 4th ed.; Wiley: in acetone, ethyl acetate, and methanol may relate to a fairly New York, 1997; Vol. 21, pp 601-626. low cohesive energy of the solvent itself. Methanol is also (3) Cochran, W. The Crystal and Molecular Structure of Salicylic Acid. Acta Crystallogr. 1953, 6, 260-268. capable of hydrogen bond donation and acceptance simulta- (4) Sundaralingam, M.; Jensen, L. H. Refinement of the Structure of neously, as well as being able to accommodate the aromatic Salicylic Acid. Acta Crystallogr. 1965, 18, 1053-58. ring of the solute. Acetic acid appears as the most ideal solvent (5) Bacon, G. E.; Jude, R. J. Neutron-diffraction Studies of Salicylic Acid R - as suggested by the predominant carboxylic acid groups of both and -Resorcinol. Z. Kristallogr. Board 1973, 138,19 40. (6) Gomaa, E. A.; El-Khouly, A. A.; Mousa, M. A. Association of Salicylic salicylic acid and acetic acid. In acetonitrile, the affinity for Acid in Acetonitrile-Water Media. Ind. J. Chem., Sect. A: Inorg., Bio- salicylic acid is reduced. Acetonitrile cannot provide hydrogen inorg., Phys., Theor. Anal. Chem. 1984, 23, 1033-4. bond donation but is only capable of hydrogen bond acceptance. (7) De Fina, K. M.; Sharp, T. L.; Lindsay, E. R.; Acree, W. E., Jr. - Solubility of 2-Hydroxybenzoic Acid in Select Organic Solvents at Consequently, the solute solvent affinity is not fully developed. 298.15 K. J. Chem. Eng. Data 1999, 44, 1262-64. Salicylic acid exhibits a very low solubility in water as (8) Apelblat, A.; Manzurola, E. Solubility of 2-Furancarboxylic, Glutaric, compared with the organic solvents. The aromatic ring of the Pimelic, Salicylic, and o-Phthalic Acids in Water from 279.15 to 342.15 K, and Apparent Molar Volumes of Ascorbic, Glutaric and solute induces an increased structuring of the surrounding water, Pimelic Acids in Water at 298.15 K. J. Chem. Thermodyn. 1989, 21, which leads to an unfavorable decrease of entropy. Moreover, 1005-8. the cohesive energy of water itself is high as substantiated (9) Pinto, S. S.; Diogo, H. P.; Minas da Piedade, M. E. Enthalpy of through the high boiling point and density. In addition, salicylic Formation of Monoclinic 2-Hydroxybenzoic Acid. J. Chem. Thermo- dyn. 2003, 35, 177-188. acid in water deviated from the organic solvents in terms of (10) Sabbah, R.; Le, T. H. D. Thermodynamic Study of Three Isomers of the correlation between solubility and the temperature depen- Hydroxybenzoic Acid. Can. J. Chem. 1993, 71, 1378-83. dence of solubility (i.e., the van’t Hoff enthalpy of solution). (11) Mayer, M. M.; Howell, W. J.; Tomasko, D. L. Solid-Liquid Equilibria in the Systems Thianthrene + Phenanthrene, Salicylic Acid + Phenanthrene, and 3-Hydroxybenzoic Acid + Phenanthrene. J. Chem. Conclusions Eng. Data 1990, 35, 446-49. No new polymorphs or solvates were found of salicylic acid (12) Nordstro¨m, F.; Rasmuson, A. Phase Equilibria and Thermodynamics of p-Hydroxybenzoic Acid. J. Pharm. Sci. 2006, 95, 748-760. as investigated in six solvents between 10 °C and 50 °C. The (13) Nordstro¨m, F.; Rasmuson, A. Polymorphism and Thermodynamics solubility of salicylic acid varied considerably with solvent, of m-Hydroxybenzoic Acid. Eur. J. Pharm. Sci. (in press). indicative of nonideal behavior. A correlation between different solvents at constant temperature was observed by plotting the Received for review March 23, 2006. Accepted June 12, 2006. The van’t Hoff enthalpy of solution vs ln x. Higher solubility was authors acknowledge the Swedish Research Council for financial related to a lower van’t Hoff enthalpy of solution at all support. temperatures. Salicylic acid in water differed significantly from JE060134D J. Chem. Eng. Data 2006, 51, 1775-1777 1775

Solubility and Melting Properties of Salicylamide

Fredrik L. Nordstro1m and Åke C. Rasmuson*

Department of Chemical Engineering and Technology, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

The solubility of salicylamide in methanol, acetonitrile, acetic acid, acetone, water, and ethyl acetate has been determined between (10 to 50) °C. The onset melting temperature and enthalpy of fusion has been determined by differential scanning calorimetry to 138.7 °C and 29.0 kJ‚mol-1, respectively. Only the monoclinic structure of salicylamide was observed at crystallization.

Introduction The solubility of solids in solution is a vital process parameter and of interest for numerous applications. In this work, the solubility of salicylamide has been investigated in five organic solvents and water from (10 to 50) °C. The melting temperature and enthalpy of fusion of salicylamide have also been deter- Figure 1. Salicylamide. mined. Salicylamide or 2-hydroxybenzamide is a mild analgesic with the point at which no solvent remained. The samples were anti-inflammatory and antipyretic properties.1 It has been used weighed a final time when all the solvent was evaporated. The in protections against fungus in, for example, oils, soaps, and balance used during the experimental work had an accuracy of lotions.2 ( 0.0001 g. 3-5 The crystal structure of salicylamide has been resolved The melting temperature, tm, and enthalpy of fusion at the and only been found as a monoclinic form in which carboxy melting temperature, ∆fusH, was determined by differential group dimerization is a key structural element, resembling the scanning calorimetry (TA Instruments, DSC 2920) at a heating crystal structure of salicylic acid. The existence of polymorphic rate of 2 K‚min-1 from (10 to 170) °C. Samples were pre- or solvated modifications of salicylamide has hitherto not been pared in hermetic aluminum pans and purged with nitrogen at encountered. Limited solubility data of salicylamide are available a rate of 50 mL‚min-1. The calorimeter was calibrated against in the literature. The molecular structure of salicylamide is the melting temperature and enthalpy of fusion of indium. presented in Figure 1. The experimental procedure conducted for salicylamide is similar to the procedure described in previous contributions for Experimental Section p-hydroxybenzoic acid,6 m-hydroxybenzoic acid,7 and salicylic acid.8 Salicylamide was purchased from Sigma-Aldrich (purity > 99 %) and used as obtained. The solubility of salicylamide (CAS Results and Discussion Registry No. 65-45-2) was determined gravimetrically in The monoclinic phase of salicylamide was obtained from all methanol, acetonitrile, acetic acid, acetone, water, and ethyl ° solvents in the given temperature interval. Crystallization experi- acetate between (10 and 50) C. The solubility of salicylamide ments with primary nucleation yielded no other modifications. was determined through (2 to 9) measurements at each tem- The solubility of salicylamide with associated uncertainty is perature for all solvents. The temperature was controlled by listed in Table 1 and presented in Figure 2. thermostat baths, and the true temperature was validated by a The solubility data were fitted with a second order poly- calibration mercury thermometer (Thermo-Schneider, Wertheim, nomial: Germany, uncertainty of ( 0.01 °C). Saturation was established from an undersaturated solution (dissolution) as well as from a ) 2 + + supersaturated solution (crystallization through primary nucle- ln x A(K/T) B(K/T) C (1) ation at a cooling rate of 1 K‚min-1). The solution concentration was recorded over time at constant temperature to evaluate the where A, B, and C are solvent-specific constants. Table 2 lists time needed for equilibrium to be established. Preheated syringes the regression curve coefficients of salicylamide between (10 ° 2 (10 mL) and needles were used to sample (3 to 6) mL of solution and 50) C where R exceeds 0.998 for all solvents. into preweighed glass vials. The mass of the saturated solution Reproducible solubility data were obtained through dissolu- was recorded. The samples were dried in ventilated laboratory tion and crystallization experiments from all solvents. The hoods at room temperature. The mass of the samples was solubility data of salicylamide in water are similar to the data 9 ) ) recorded repeatedly throughout the drying process to establish reported by Edwards et al. (x 0.000404 vs x 0.000391 of the present work at 30 °C). * Corresponding author. Fax: +46 8 105228. E-mail: Rasmuson@ The ∆fusH, tm, and entropy of fusion, ∆fusS, of salicylamide ket.kth.se. have been determined by DSC and are given in Table 3. The

Figure 2. Mole fraction solubility, x, of monoclinic salicylamide in methanol; ×, acetonitrile; ], acetic acid; 4, acetone; O, water; 0, ethyl acetate; +, between (10 and 50) °C.

Figure 3. Left: Crystal morphology of salicylamide at 90× magnification, obtained through evaporation crystallization from ACN at room temperature. Right: Crystal morphology of salicylamide at 40× magnification, as obtained from water through evaporation crystallization at room temperature.

Table 1. Mole Fraction Solubility, x, of Salicylamide (1) in Six Solvents between (10 and 50) °C with 95 % Confidence Limits 3 t 10 (x1 ( 95 % confidence limits) °C methanol acetonitrile acetic acid acetone water ethyl acetate 10 26.72 ( 0.23 20.10 ( 0.10 58.54 ( 0.08 99.30 ( 0.41 0.160 ( 0.003 55.28 ( 0.39 15 30.69 ( 0.09 24.04 ( 0.13 65.25 ( 0.12 107.85 ( 0.23 0.205 ( 0.005 60.70 ( 0.18 20 35.12 ( 0.16 28.18 ( 0.12 72.95 ( 0.22 117.83 ( 0.24 0.261 ( 0.002 67.03 ( 0.45 25 40.60 ( 0.19 33.28 ( 0.16 82.39 ( 0.27 129.43 ( 0.31 0.317 ( 0.006 75.49 ( 1.04 30 46.66 ( 0.28 39.58 ( 0.22 92.78 ( 0.39 140.62 ( 0.33 0.391 ( 0.010 83.45 ( 0.41 35 53.58 ( 0.37 47.64 ( 0.46 103.59 ( 0.29 153.52 ( 0.38 0.485 ( 0.041 92.81 ( 0.61 40 62.51 ( 0.26 55.79 ( 0.47 117.15 ( 0.39 168.19 ( 0.43 0.594 ( 0.003 102.76 ( 0.38 45 71.91 ( 0.18 65.15 ( 0.72 131.38 ( 0.37 181.61 ( 0.48 0.757 ( 0.027 114.32 ( 0.48 50 83.59 ( 0.17 77.32 ( 0.94 145.16 ( 0.19 198.42 ( 0.74 0.974 ( 0.008 127.16 ( 0.53

Table 2. Solubility Regression Curve Coefficients of Equation 1 Table 3. Melting Properties of Salicylamide as Determined by 13 DSC Scans at 2 K/min with 95 % Confidence Limits solvent 10-5A 10-3BC t (peak)/°C 140.0 ( 0.4 methanol 10.612 -9.6331 17.165 m t (onset)/°C 138.7 ( 0.5 acetonitrile 7.7728 -8.2299 15.464 m ∆ H/kJ‚mol-1 29.0 ( 0.3 acetic acid 5.8647 -5.9911 11.001 fus ∆ S/J‚mol-1‚K-1 70.4 ( 0.7 acetone 3.8895 -4.1667 7.5517 fus water 12.693 -12.437 19.3719 ethyl acetate 6.6841 -6.3453 11.173 Conclusions The highest molar solubility of salicylamide was obtained in -1 ∆fusH determined in the present work to 29.0 kJ‚mol is higher acetone, followed by acetic acid, ethyl acetate, methanol, than the value of 26.7 kJ‚mol-1 previously reported.10 The acetonitrile, and finally water. The onset melting temperature melting temperature of salicylamide has previously been and enthalpy of fusion were determined to be 138.7 °C and reported to be in the range of (138 to 142) °C.11 29.0 kJ‚mol-1, respectively. Only the monoclinic structure was Salicylamide crystallizes in the form of hexagonal plates. The encountered in this study. crystal morphology of SA, as typically obtained from all solvents but water, is displayed in Figure 3 (left). The crystals obtained Literature Cited from water were found in the form of needles, as depicted in (1) Ullmann, F. Encyclopedia of Industrial Chemistry, Vol. A23; VCH: Figure 3 (right). Weinheim, Germany, 1993; pp 477-483. Journal of Chemical and Engineering Data, Vol. 51, No. 5, 2006 1777

(2) Kirk, R. E.; Othmer, D, F. Kirk-Othmer Encyclopedia of Chemical (9) Edwards, L. J. Salicylamide: thermodynamic dissociation constant. Technology, 4th ed., Vol. 21; Wiley: New York, 1997; pp 601-626. Solubility and quantitative estimation by U.-V. absorption spectro- (3) Penfold, B. R.; White, J. C. B. The crystal and molecular structure of photometry. Trans. Faraday Soc. 1953, 49, 234-236. benzamide. Acta Crystallogr. 1959, 12, 130-135. (10) Landolt-Bo¨rnstein, Group IV/8. Thermodynamic Properties of Organic (4) Sasada, Y.; Takano, T.; Kakudo, M. Crystal structure of salicylamide. Compounds and their Mixtures. SubVolume A. Enthalpies of Fusion Bull. Chem. Soc. Jpn. 1964, 37, 940-946. and Transition of Organic Compounds; Springer: New York, 1995; (5) Pertlik, F. Crystal structure and hydrogen bonding schemes in four p 168. benzamide derivates (2-hydroxy-benzamide, 2-hydroxy-thiobenzamide, (11) Hernandez-Gutierrez, F.; Pulido-Cuchi, F. Identification and deter- 2-hydroxy-N,N-dimethyl-benzamide, and 2-hydroxy-N,N-dimethyl- mination of salicylamide. Anal. Chim. Acta 1951, 5, 450-458. thiobenzamide). Monatsh. Chem. 1990, 121, 129-139. (6) Nordstrom, F.; Rasmuson, A. Phase equilibria and thermodynamics of p-hydroxybenzoic acid. J. Pharm. Sci. 2006, 95, 748-760. Received for review April 27, 2006. Accepted July 11, 2006. The (7) Nordstrom, F.; Rasmuson, A. Polymorphism and thermodynamics of authors appreciate an acknowledge the Swedish Research Council for m-hydroxybenzoic acid. Eur. J. Pharm. Sci. 2006, 28, 377-384. financial support. (8) Nordstrom, F.; Rasmuson, A. Solubility and melting properties of salicylic acid. J. Chem. Eng. Data 2006, 51, 1668-1671. JE060178M Determination of the Activity of the Solid Phase of

Molecular Compounds

Fredrik L. Nordström and Åke C. Rasmuson*

Dept. of Chemical Engineering and Technology, Royal Institute of Technology, 100 44

Stockholm, Sweden

* Phone: +46 (0) 8 790 8227, fax: +46 (0) 8 105 228, email: [email protected]

1 Abstract

The activity of the solid phase of an organic molecular compound is often defined using the melt at the same temperature as the thermodynamic reference. However, far below the melting temperature, the properties of this reference state cannot be determined experimentally, and different simplifications and approximations are normally adopted. In the present work, a novel method is presented to determine the activity of the solid phase (= ideal solubility) and the heat capacity difference between the supercooled melt and solid. The approach is based on rigorous thermodynamics, using standard experimental thermodynamic data at the melting temperature of the pure compound and solubility measurements in different solvents at various temperatures.

The method is illustrated using data for ortho-, meta-, and para-hydroxybenzoic acid, salicylamide and paracetamol. The results show that complete neglect of the heat capacity terms may lead to estimations of the activity that are incorrect by a factor of 12. Other commonly used simplifications may lead to estimations that are only one third of the correct value.

Keywords: Solid-state activity; ideal solubility; heat of fusion; heat capacity; supercooled liquid heat capacity

2 1. Introduction

The solubility of organic compounds in various solvents is of significant importance to the industry in the design of manufacturing processes and for the application of the compound and prediction of its behavior. The solubility depends on solute and solvent properties as often described by the relation

a xeq = (1) γ eq where xeq is the molar solubility concentration, γeq is the activity coefficient at equilibrium, and a is the activity of the solid phase. Usually, the reference state of the activity is the pure melt at the same temperature, by which the activity coefficient is defined within a Raoult’s law framework.

Current and former research efforts in predicting solubility have primarily focused on resolving the influence of the solvent on solubility by prediction of the activity coefficient, e.g. via solubility parameter methods [1,2] and group contribution methods, e.g. UNIFAC [3]. However, the accuracy in the prediction of solubility is, equally dependent on the estimation of the solid- state activity, and this has received much less attention.

The activity of the solid depends on the enthalpy of fusion at the temperature of interest.

However, far away from the melting temperature the reference state of a supercooled melt is in practice experimentally inaccessible. Hence, simplifications and approximations are used. A standard simplification often encountered in the engineering literature is to assume that the enthalpy of fusion is independent of temperature:

f Δ TH m )( ⎛ 11 ⎞ ln a = ⎜ − ⎟ (2) ⎝ m TTR ⎠

An alternative approach has been suggested [1]:

3 f Δ TH m )( ⎛ T ⎞ ln a = ln⎜ ⎟ (3) RTm ⎝ Tm ⎠ and a less simplified approach leads to:

f Δ TH m )( ⎡ 11 ⎤ Δ TC mp )( ⎡ ⎛ Tm ⎞ Tm ⎤ ln a = ⎢ − ⎥ − ⎢ln⎜ ⎟ +− 1⎥ (4) ⎣ m TTR ⎦ R ⎣ ⎝ T ⎠ T ⎦ where ΔCp(Tm) is the difference in heat capacity between the melt and the solid at the melting temperature. The simplifications behind equation (2) - (4), inevitably result in, more or less, poor estimations of the activity of the solid, and accordingly to that the activity coefficients at equilibrium, calculated from experimental data by equation (1), are of questionable quality.

In the present paper is presented a novel approach to determine the activity of the solid phase that avoids the assumptions behind equation (2), (3) and (4). In this approach, the activity of the solid phase is determined from the solubility and temperature dependence of solubility of the compound in different solvents and at different temperatures. Together with data on melting temperature and enthalpy of melting, these solubility data are used within a rigorous thermodynamic framework to determine the activity of the solid phase. For illustration, the method is applied to five organic compounds, viz. para-, meta- and ortho-hydroxybenzoic acid, salicylamide and paracetamol.

2. Experimental

Most of the experimental data required for the present work have been published previously [4-

8]. However, most of the heat capacity data of interest for comparison and for evaluation of the heat capacity of the supercooled melt has been determined here.

Heat capacity measurements were performed using Differential Scanning Calorimetry, TA

Instruments, DSC2920, from 10 oC, in 5 oC increments, to approximately 30 oC above the

4 melting temperature of o-hydroxybenzoic acid, m-hydroxybenzoic acid, p-hydroxybenzoic acid and salicylamide. All heat capacity measurements were conducted by modulated isothermal DSC.

The modulation amplitude was ± 0.5 oC and the modulation period was 80 s. The isothermal period was 20 min. For each measurement a sample of 10 to 15 mg was placed in a hermetic Al pan while being purged with nitrogen at a flow rate of 50 ml/min. The calorimeter was calibrated against the melting temperature and enthalpy of fusion of Indium, and the heat capacity of sapphire.

o-hydroxybenzoic acid (CAS registry number 69-72-7), m-hydroxybenzoic acid (CAS registry number 99-06-9), p-hydroxybenzoic acid (CAS registry number 99-96-7) and salicylamide (CAS registry number 65-45-2) were purchased from Sigma-Aldrich and used as obtained (purity >

99%). Only that solid form of the compound that is thermodynamically stable at the temperatures in question is considered.

Experimental data of melting properties and solubility of the investigated compounds are given in table 1.

5 TABLE 1

Melting property data and solvents used in solubility study of the investigated compounds

(acronyms in parenthesis)

o-hydroxy m-hydroxy p-hydroxy Salicylamide Paracetamol benzoic acid benzoic acid benzoic acid (SA) [7] (PA) [8] (OHBA) [4] (MHBA) [5] (PHBA) [6]

Onset Tm/K 431.35 474.75 487.65 411.85 443.6 f ΔH (Tm) 27.09 35.92 30.85 29.00 27.1 /kJ·mol-1 f ΔS (Tm) 62.80 75.66 63.26 70.41 61.1 /J·mol-1·K-1 Solvents used methanol, methanol, methanol, methanol, methanol, in solubility acetonitrile, acetonitrile, acetonitrile, acetonitrile, ethanol, 1- study1 acetic acid, acetic acid, acetic acid, acetic acid, propanol, 2- acetone, ethyl acetone, ethyl ethyl acetate acetone, ethyl propanol, 1- acetate acetate acetate butanol, acetone, ethyl acetate 1 The solubility of hydroxybenzoic acid isomers and salicylamide was measured between 10 and 50 oC in 5 oC increments, the solubility of paracetamol between -5 and 25 oC in 5 oC increments.

The temperature dependence of the heat capacity of the solid form of the hydroxybenzoic acid isomers and salicylamide is very well described by a linear function

p += kTkC 21 (5)

where T is given as absolute temperature and R2 exceeded 0.999 for all the investigated compounds. The regression coefficients of equation (5) are presented in table 2 together with solid and melt heat capacity of paracetamol [9].

6 TABLE 2

Heat capacity regression curve coefficients of equation (5)

Compound k1 k2 Measured temperature interval [K] OHBA (solid) 0.4023 14.88 280-405 MHBA (solid) 0.4603 5.37 280-460 PHBA (solid) 0.4401 15.92 280-460 SA (solid) 0.4942 -15.10 280-395 PA (solid) [9] 0.6688 -29.34 370-420 PA (melt) [9] 0.2099 273.2 470-510

Considerable sublimation prior to fusion unfortunately limited the upper range of the measurements and significant evaporation upon fusion prevented heat capacity data of the melt to be determined for the investigated compounds.

No heat capacity data of salicylamide is available in the literature. Heat capacity data for the isomers of hydroxybenzoic acid between 94 and 288 K have been reported [10]. These heat capacity data exceeds the heat capacity data measured in this study by approximately 10 to 30

J·mol-1·K-1 at 280 K.

3. Theory

In the usual definition of the activity of the solid phase, a, of a molecular compound, the hypothetical supercooled melt is used as the thermodynamic reference state, and

f T T Δ TH m )( ⎡ ⎤ 111 1 ΔC p ln a = ⎢ − ⎥ p dTC +Δ− dT (6) RTTTR R ∫∫ T ⎣ m ⎦ Tm Tm

f where ΔH (Tm) is the enthalpy of fusion at the melting temperature, and ΔCp is given by

pp −=Δ p sClCC )()( (7)

7 Occasionally, equation (6) is derived from the equilibrium condition at the triple-point based on the assumption that the Poynting pressure correction and gas non-ideality are neglected [11,12].

However, equation (6) is actually perfectly rigorous when the supercooled liquid is used as the reference and do not require assumptions. At constant pressure, the definition of the activity of the solid phase is:

− μμ ls Δ f TG Δ f TS Δ f TH )()()()()( ln a = −= = − (8) RT RT R RT where µ(s) and µ(l) denote the chemical potential of the solid and the supercooled melt, respectively, and Δ f (TG ) is the free energy of fusion. Since

T ΔC f ( f TSTS )() +Δ=Δ p dT (9) m ∫ T Tm

T f ( f )() Δ+Δ=Δ dTCTHTH (10) m ∫ p Tm we can through equation (8)-(10) easily derive at equation (6) without assumptions.

According to equation (6), ΔCp has to be integrated from the melting temperature down to the temperature of interest, T, which however is problematic since the properties of the supercooled melt far below the melting temperature cannot be properly characterized. Hence, different approximations are commonly adopted. In the engineering literature, a standard simplification is to completely neglect the heat capacity terms, leading to equation (2). However, there are results in the literature that suggest that this approximation is invalid at the temperatures of normal processing of organic fine chemicals and pharmaceuticals [13-15]. An alternative approach [1] is to assume that ΔCp is constant and is approximated by the entropy of fusion at the melting temperature, leading to equation (3). With modern instruments, the isobaric heat capacity of the solid, Cp(s) can be determined below the melting temperature and the isobaric heat capacity of

8 the melt, Cp(l), can be determined above the melting temperature, as long as the compound does not decompose. If ΔCp is assumed constant and equal to the value at the melting temperature

(curve a in figure 1) we derive at equation (4). Alternatively, with sufficient experimental heat capacity data above the melting temperature, extrapolation of Cp(l) can be carried out to the temperature of interest (curve b in figure 1) and an integration of the ΔCp terms in equation (6) can be performed.

CP(l) b ΔCP(Tm) a ΔCP(T) Heat capacity CP(s)

T T m Temperature

FIGURE 1. Illustration of the heat capacity of the solid and liquid form of a compound at different temperatures. Solid curves correspond to experimental heat capacities and dashed curves (a and b) to approximated heat capacity of the supercooled liquid.

In the approach of the present work, all previous assumptions and the requirements for experimental determination of ΔCp are replaced by determination of the solubility and temperature dependence of solubility of the compound in different solvents and at different temperatures. Together with data on melting temperature and enthalpy of melting, these solubility data are used within a rigorous thermodynamic framework to determine ΔCp(T) and the activity

9 of the solid phase in accordance with equation (6) as is developed below. For the application of the method we need to establish the thermodynamic relation between the solubility and the temperature dependence of the solubility, as well as the influence of solution non-ideality.

By combination of equation (1) and (6) we arrive at the general solubility equation:

f T T Δ TH m )( ⎡ ⎤ 111 1 ΔC p xeq γ eq )ln()ln( +−= ⎢ − ⎥ p dTC +Δ− dT (11) RTTTR R ∫∫ T ⎣ m ⎦ Tm Tm

The temperature dependence of the experimental solubility data is often referred to as the apparent enthalpy of solution or as denoted in the present work, the van’t Hoff enthalpy of

vH solution, ΔH So ln :

vH ⎛ ∂ ln x ⎞ ΔH So ln ⎜ ⎟ = 2 (12) ⎝ ∂T ⎠eq RT

vH ΔH So ln is determined from the change in molar solubility with temperature in a van’t Hoff plot, as depicted schematically in figure 2.

1/Tm 1/T

Solvent A

ln(xeq) Ideal solution vH Slope Δ−= So ln / RH Slope Δ−= f /)( RTH Solvent B Slope Δ−= vH / RH So ln

FIGURE 2. van’t Hoff plot illustrating the solubility of an arbitrary organic compound in different solvents.

A thermodynamic interpretation of the empirical van’t Hoff enthalpy of solution at constant pressure can be obtained if equation (8) is inserted into the Gibbs-Helmholtz equation leading to

⎛ ∂ ln a ⎞ Δ f TH )( ⎜ ⎟ = (13) ⎝ ∂T ⎠ RT 2 which combined with equation (1) gives:

⎛ ∂ ln x ⎞ ⎛ ∂ lnγ ⎞ Δ f TH )( ⎜ ⎟ + ⎜ ⎟ = 2 (14) ⎝ ∂T ⎠eq ⎝ ∂T ⎠eq RT

If equation (12) and (14) are combined with equation (10) we obtain:

T ⎛ ∂ lnγ ⎞ vH f )( −Δ+Δ=Δ RTdTCTHH 2 ⎜ ⎟ (15) So ln m ∫ p ∂T Tm ⎝ ⎠eq

vH Previous contributions [4-6] have shown experimentally that ΔH So ln correlates strongly to ln(xeq) for the same solid phase in different solvents at constant temperature and pressure:

vH So ln =Δ ( xfH eqI )ln( ) constant T (16)

As envisaged by the curves in figure 2, a lower molar solubility is linked to a steeper slope, and

vH thus to a higher ΔH So ln . The underlying reason is that the solubility curves in a van’t Hoff plot all converge to the same point at the melting temperature.

In the present work, equation (16) is used to describe how the van’t Hoff enthalpy of solution and the solubility depend on the solvent, at constant temperature. In a series of solvents, the

vH correlation between ΔH So ln and ln(xeq) is determined experimentally. Along that correlation, the

f solid-state properties, i.e. the ΔH (Tm) and the integral terms of ΔCp in equation (11) and (15), remain constant, but the conditions in the solution change, i.e. the ln(γeq) in equation (11) and

11 vH (∂lnγ/∂T)eq in equation (15) depend on the solvent. The experimental correlation between ΔH So ln and ln(xeq) is depicted in figure 3 as a solid curve.

f vH =Δ II afTH )(ln)( ΔH Soln

ΔC = 0 p f ΔH (Tm) vH Soln =Δ xfH eqI )(ln

f ΔCp = ΔS (Tm)

ΔC = ΔCp p ΔHf(T)

id 0 ln(xeq) = xa eq )ln()ln( 0

FIGURE 3. Schematic presentation of the experimental correlation between molar solubility and the van't Hoff enthalpy of solution (solid curve), and the relation between the activity of the solid and enthalpy of fusion as a function of ΔCp (dashed line) at constant temperature. The intersection between the curves represents the activity of the solid phase (ideal solubility) and the enthalpy of fusion at temperature T. The commonly used approximations of ΔCp (i.e. ΔCp = 0,

f and ΔCp = ΔS (Tm)) are also inserted.

In a wide range of solvents, equation (16) cover from negative to positive deviation from

Raoult’s law, i.e. the activity coefficient may change value from below unity to above unity. At a

12 certain point the solution is ideal. For an ideal solution, the activity coefficient is unity, γeq = 1,

id and the solubility, xeq , equals the activity of the solid phase.

f T T id Δ TH m )( ⎡ ⎤ 111 1 ΔC p ln( eq ln) ax == ⎢ − ⎥ p dTC +Δ− dT (17) RTTTR R ∫∫ T ⎣ m ⎦ Tm Tm

⎛ ∂ lnγ ⎞ In addition, for an ideal solution, ⎜ ⎟ = 0 and the van’t Hoff enthalpy of solution ⎝ ∂T ⎠eq

vH f Δ So ln idealH )( equals the enthalpy of fusion of the pure solid at temperature T, i.e. ΔH (T):

T Δ vH f f )()()( Δ+Δ=Δ= dTCTHTHidealH (18) So ln m ∫ p Tm

On one hand, equation (17) and (18) describe the ideal solution on the experimental correlation

vH between ΔH So ln and ln(xeq), on the other hand, these equations also describe the properties of the pure solid state. When the melting temperature and the melting enthalpy of the pure solid have

id vH f been determined, the values of eq = ax )ln()ln( (equation (17)) and Δ So ln Δ= THidealH )()(

(equation (18)) only depend on the integral terms of ΔCp, which are unknown. Inserting different values of ΔCp into equation (17) and equation (18) lead to a functional relationship between

id vH f xeq )ln( and ΔH So ln (ideal) , i.e. between ln(a) and ΔH (T), at constant temperature:

vH id Δ So ln = II xfidealH eq ))(ln()(

≡ constant T (19)

f =Δ II afTH ))(ln()(

13 In the present work, equation (19), representing the relation between equation (17) and (18), are used to describe how the activity of the solid phase and the enthalpy of fusion at temperature T

vH depend on the unknown function Δ p (TC ) . In a plot over ΔH So ln versus ln(xeq) equation (19) appears as a line (dashed line in figure 3), denoted as the solid-state activity line. The commonly

f used approximations, given by equation (2) (ΔCp = 0) and equation (3) (ΔCp = ΔS (Tm)), are also shown on this line (figure 3).

The very basis for our method to determine the activity of the solid phase is to find the point of intersection between equation (16) and equation (19). Along the correlation of equation (16)

vH between ΔH So ln versus ln(xeq) the point of intersection corresponds to the ideal solution since equation (11), (15), (17) and (18) all apply, i.e. the solubility (equation (11)) equals the activity of the solid phase (equation (17)) and the van’t Hoff enthalpy of solution (equation (15)) equals the enthalpy of fusion of the solid phase (equation (18)). Along the relation of equation (19) between

vH id ΔH So ln (ideal) versus xeq )ln( , the point of intersection corresponds to the point where the

function Δ p (TC ) has its correct form and value giving the actual activity of the solid phase at that particular temperature.

The correlation given by equation (16) is determined by solubility experiments in a series of solvents, with the ambition to cover from negative to positive deviation from Raoult’s law. To

vH determine ΔH So ln of course different temperatures have to be included even though the correlation holds for a specific temperature. The basis for the solid-state activity line, given by equation (19) (i.e. equation (17) and (18)) is established by experimental determination of the

melting temperature and melting enthalpy. Then a functional form of Δ p TC )( is inserted and the

14 task is to determine the specific values of the parameters of the Δ p (TC ) function that correspond to the point of intersection with equation (16).

In the simplest case, ΔCp is constant independent of temperature. Then the integrations in equation (17) and (18) are easily performed:

f id Δ TH m )( ⎡ 11 ⎤ q ⎡ ⎛ Tm ⎞ Tm ⎤ eq ax )ln()ln( == ⎢ − ⎥ − ⎢ln⎜ ⎟ +− 1⎥ (20) ⎣ m TTR ⎦ R ⎣ ⎝ T ⎠ T ⎦

vH f f Δ So ln m −+Δ=Δ= TTqTHTHidealH m )()()()( (21)

in which p =Δ qC . By assigning different values to q, we can establish a constant temperature

vH id relation - equation (19) - between Δ So ln (idealH ) (equation (20)) and ln xeq (equation (21)). This

vH relation intersects the experimental correlation between ΔH So ln and ln(xeq), revealing the location on the correlation - equation (16) - where the solution is ideal and the location on the solid-state activity line (equation (19)) where the correct value of q (= ΔCp) is found. For each temperature

vH we have three equations (equation (16), (20) and (21)) and three unknowns ( Δ So ln (idealH ) ,

id f ln xeq and q) giving only one solution of q, as long as Tm and ΔH (Tm) are known. When ΔCp is constant, the activity of the solid phase can be obtained algebraically as shown below. When ΔCp depends on temperature, then additional solubility data at different temperatures are required for determination of the activity, i.e. we need experimental relations of equation (16) at different temperatures. If ΔCp is linearly dependent on temperature:

p m −+=Δ TTrqC )( (22) the equations for the solid state becomes:

15 f 2 id Δ TH m )( ⎡ 11 ⎤ q ⎡ ⎛ Tm ⎞ Tm ⎤ r ⎡ ⎛ Tm ⎞ Tm T ⎤ eq ax )ln()ln( == ⎢ − ⎥ − ⎢ln⎜ ⎟ +− 1⎥ − ⎢Tm ln⎜ ⎟ +− ⎥ (23) ⎣ m TTR ⎦ R ⎣ ⎝ T ⎠ T ⎦ R ⎣ ⎝ T ⎠ T 22 ⎦

r Δ vH f f TTqTHTHidealH )()()()( −−−+Δ=Δ= TT )( 2 (24) So ln m m 2 m

We now have two unknowns, q and r, to determine at the point of intersection where ln(xeq)

id vH vH equals ln xeq (equation (23)) and ΔH So ln equals Δ So ln (idealH ) (equation (24)). Hence we need to determine the experimental correlation, equation (16), at two different temperatures as a minimum. In that case we have six equations, i.e. (16), (23), and (24) at two different

vH id temperatures, and we have six unknowns, i.e. Δ So ln (idealH ) and ln xeq at two different temperatures and q and r.

If a second order equation of ΔCp is required we would need at least experimental correlations, equation (16), at three different temperatures. In that case we have three different equations at

vH id three different temperatures, and we have nine unknowns, i.e. Δ So ln idealH )( and ln xeq at three different temperatures and the three parameters of the second order Cp(T) relation. In the present work as is shown below, we have found no ground to go beyond the linear dependence of ΔCp

(equation (22)) and the parameters q and r are determined by optimization using data from 7 different temperatures for paracetamol and 9 different temperatures for hydroxybenzoic acid isomers and salicylamide. In this case we have information enough to establish whether the assumed order of temperature dependence of ΔCp is sufficient and correct, and we have actually released all the limiting assumptions that are behind equation (2), (3) and (4), besides the assumption that the solid phase is pure.

16 4. Results and discussion

4.1. Evaluation

vH The experimental correlations between ΔH So ln and ln(xeq), equation (16), for the investigated compounds are shown in figure 4 at 15 oC (left) and 35 oC (right).

30 30 R2 = 0.983 R2 = 0.951 20 20 10 10 OHBA OHBA 0 0 -6 -4 -2 0 -6 -4 -2 0 30 30 R2 = 0.998 R2 = 0.997 20 20 10 10 MHBA MHBA 0 0

-6 -4 -2 0 -6 -4 -2 0 30 30 R2 = 0.999 R2 = 0.999 20 20 [kJ/mol] 10 10 PHBA PHBA 0 0 -6 -4 -2 0 -6 -4 -2 0 30 30 R2 = 0.912 R2 = 0.941 20 20 10 10 SA SA 0 0 -6 -4 -2 0 -6 -4 -2 0 30

R2 = 0.916 20

10 PA 0 -6 -4 -2 0

ln(xeq) [mol/mol] FIGURE 4. Correlation between van’t Hoff enthalpy of solution and molar solubility at 15 oC

(left) and 35 oC (right) for five organic compounds in various solvents.

The diagrams in figure 4 are representative for the compounds at all investigated temperatures.

The data are well correlated by a second order relation of the type:

vH 2 H So ln =Δ α()xeq + β xeq )ln()ln( (25) which automatically satisfies the condition that the van't Hoff enthalpy of solution approaches zero when xeq approaches unity. The result is presented as solid curves in figure 4. α and β are compound-specific regression function coefficients at constant temperature. The coefficients α and β of the different hydroxybenzoic acid isomers are given in previous work [4-6], while the coefficients for salicylamide and paracetamol are listed in table 3.

TABLE 3

Regression curve coefficients of equation (25) for salicylamide and paracetamol.

Temperature/oC Salicylamide Paracetamol α β R2 α β R2 -5 162.9 -2528.2 0.953 0 168.1 -2781.7 0.952 5 174.4 -3059.6 0.943 10 399.2 -3985.3 0.901 177.1 -3372.1 0.932 15 493.2 -4157.5 0.912 190.5 -3667.9 0.916 20 574.6 -4422.9 0.923 191.4 -4044.6 0.899 25 666.3 -4753.6 0.936 194.1 -4430.8 0.872 30 813.1 -4993.7 0.940 35 1019.4 -5188.6 0.941 40 1222.3 -5515.1 0.946 45 1507 -5746.1 0.950 50 1973.1 -5771.5 0.954

Based on the equation of the activity of the solid (equation 17) and the enthalpy of fusion

(equation (18)) it can be shown that the constant temperature solid-state activity line (equation

(19) is a straight line if ΔCp is treated as being constant with temperature from Tm to T:

18 vH id Δ So ln eq )ln()( +⋅= ixsidealH (26) with

− TTR )( s = m (27) ⎛ T ⎞ T ln⎜ m ⎟ m +− 1 ⎝ T ⎠ T as the slope and

⎛ T ⎞ T ln⎜ m ⎟ −+ 1 f ⎝ T ⎠ T Δ= THi )( m (28) m ⎛ T ⎞ T ln⎜ m ⎟ m +− 1 ⎝ T ⎠ T as the intercept. Then the activity of the solid phase can be determined algebraically by combining equation (25) and (26):

2 +−+− 4)( iss αββ xa id )ln(ln == (29) eq 2α

The corresponding van’t Hoff enthalpy of solution in the ideal solution (i.e. ΔHf(T)) can be calculated using equation (25) and (29), and the ΔCp can be calculated by combining e.g. equation (21) and (26):

f Δ−+⋅ THias m )()ln( Cq p =Δ= (30) − TT m where lna is given by equation (29).

The approach is illustrated in figure 5 for m-hydroxybenzoic acid at 30 oC. The two curves

vH intersect at approximately ln(xeq) = -3.66 and ΔH So ln = 17.87 kJ/mol. In figure 5, on the solid-

f state activity line is also marked the activity for ΔCp = 0 (equation (2)) and ΔCp = ΔS (Tm)

(equation (3)), respectively.

35 30 25

20 [kJ/mol]

15 10

0 -6 -5 -4 -3 -2 -1 0

ln(xeq) [mol/mol]

FIGURE 5. Determination of the activity of the solid phase and the enthalpy of fusion at temperature T of m-hydroxybenzoic acid at 30 oC from the intersection (circle) between the solubility - van't Hoff enthalpy of solution regression curve (solid), equation (16), and the solid- state activity line (dashed), equation (19), based on constant ΔCp with temperature. The symbol □ represents experimental data, and the symbols Δ and ◊ correspond to the approximations of the activity of the solid phase using equation (2) and (3), respectively.

For each temperature where we have experimental solubility data in several solvents, the activity of the solid phase and ΔCp can be estimated. In the present work, it is found that the value of ΔCp clearly depends on the temperature for all the compounds except perhaps paracetamol.

Accordingly, the assumption of constant ΔCp used in the evaluation above is not fulfilled. In table

4 a temperature averaged value for each compound is presented.

20 When ΔCp is assumed to be linearly dependent on temperature (equation (22)) the parameters q and r are determined from equation (23) and (24), by optimization using data from 9 different temperatures, i.e. 9 correlations (equation (16)), for ortho-, meta- and para-hydroxybenzoic acid and salicylamide (10 to 50 oC in 5 oC increments), and from 7 different temperatures, i.e. 7 different correlations (equation (16)), for paracetamol (-5 to 25 oC in 5 oC increments). In the optimization we use the objective function:

2 n ∧ ⎛ f f ⎞ ∑⎜ Δ−Δ THTH )()( ⎟ F = n=1 ⎝ ⎠ (31) n where n is the number of different temperatures. For a selected value of q, the r value for each

vH temperature is determined from the intersection of the experimental correlation of ΔH So ln versus ln(xeq) (equation (16)) and the solid state activity curve for each temperature (equation (19)).

These values of q and r give the values of ΔHf(T). The average of the r-values over the different temperatures is inserted into equation (24) together with the current q-value to calculate the

Δ ˆ f TH )( -values, and the value of F can be calculated. A residual is illustrated in figure 6. Then a new q-value is inserted and the calculations are repeated to provide for a new value of F. This stepwise operation is continued until the q-value giving the minimum F-value has been found.

For each compound, the resulting optimum value of q and the corresponding average value of r, are listed in table 4.

vH T3 ΔH Soln T2

T1 ˆ f Δ TH 2 )( f Δ TH 2 )(

ln(aˆ ) a )ln( xeq )ln( T 2 T 2

FIGURE 6. Schematic presentation of the residual in the optimization at three different temperatures.

TABLE 4

-1 -1 Determined constants of ΔCp (J·mol ·K ) when assumed constant, and when assumed linearly dependent on temperature.

ΔCp = f(T) ΔCp = q ΔCp = q + r(Tm – T) Compound q q r o-Hydroxybenzoic acid 93.3 143.3 -0.6201 m-Hydroxybenzoic acid 105.9 165.7 -0.5037 p-Hydroxybenzoic acid 102.7 140.8 -0.2970 Salicylamide 126.9 192.3 -0.9322 Paracetamol 104.4 95.4 0.0951

A plot of the residuals in terms of activity of the solid phase at the optimum is presented in figure 7, and is compared with the corresponding residuals for ΔCp = q.

22 0.008 OHBA 0.004 0

-0.004

-0.008 0 204060 0.008 MHBA 0.004 0 -0.004

-0.008 0 204060 0.008 PHBA 0.004

-0.004

-0.008 0 204060 0.008 SA 0.004 0 -0.004

-0.008 0 204060 0.008 Residuals of the activity of the solid phase [mol/mol] phase ofsolid the activity of the Residuals PA 0.004

-0.004

-0.008 -10 0 10 20 30 o Temperature [ C]

FIGURE 7. Residual plot of the regression analysis of the activity of the solid phase for o- hydroxybenzoic acid, ◊, m-hydroxybenzoic acid, □, p-hydroxybenzoic acid, Δ, salicylamide, o, and paracetamol, +. The symbols with white and grey background depict the approximations ΔCp

= q and ΔCp = q + r(Tm - T), respectively.

23 For ΔCp = q, the residuals are up to 17 % of the activity of the solid phase, and there is a clear systematic deviation with temperature for all compounds with the possible exception of

paracetamol. For p ( m −+=Δ TTrqC ) , the residuals are overall much smaller. The average residual in the activity of the solid phase is: OHBA: 0.13 %, MHBA: 0.32 %, PHBA: 0.13 %,

SA: 0.35 % and PA: 0.21 % and the systematic deviations with temperature are quite weak. Thus, expressing ΔCp as being linearly dependent on temperature appears to be a good representation of the true dependence of ΔCp on temperature for these compounds. Employing a higher order polynomial function to represent the temperature dependence of ΔCp is for these compounds redundant. Even though a small increase in the fit of the regression is obtained, it also leads to a less realistic temperature dependence of ΔCp outside the range of data.

4.2. Activity and activity coefficients

Based on equation (23) and the data in table 4 using the linear temperature dependence representation of ΔCp, the activity of the solid phase of the investigated compounds, is presented in figure 8.

24 0.20

0.15

0.10

0.05

Activity of the solid phase solid the of Activity 0.00

-10 0 10 20 30 40 50 60 Temperature [oC]

FIGURE 8. Activity of the solid phase of o-hydroxybenzoic acid, ◊, m-hydroxybenzoic acid, □, p-hydroxybenzoic acid, Δ, salicylamide, o, and paracetamol, +.

Obviously, m-hydroxybenzoic acid has the lowest activity, p-hydroxybenzoic acid has somewhat higher activity, followed by paracetamol, o-hydroxybenzoic acid and finally salicylamide. With a properly determined activity of the solid phase, the activity coefficients can be calculated from the experimental solubility. In figure 9 it is shown how the activity coefficient at equilibrium of o-hydroxybenzoic acid depends on the solvent and on the temperature. The activity coefficients appear to converge towards unity with increasing temperature, as can be expected.

0 Activity coefficientActivity at equilibrium 275 325 375 425 Temperature [K] FIGURE 9. Activity coefficients at equilibrium of o-hydroxybenzoic acid in methanol, ◊, acetonitrile, □, acetic acid, Δ, acetone, o, and ethyl acetate, +, between 283 and 323 K. The melting temperature of o-hydroxybenzoic is depicted as a grey circle.

Three different approximations of ΔCp have been addressed in this report, viz. i) ΔCp = 0

f (equation (2)), ii) ΔCp = ΔS (Tm) (equation (3)) and iii) ΔCp = q (equation (20)). Equation (4), which is based on the assumption that ΔCp is constant and equal to ΔCp(Tm), has not been evaluated since the heat capacity of the melt could not be determined for any of the investigated compounds but paracetamol. It has been shown that ΔCp = q + r(Tm – T) (equation (23)) provides an accurate representation of ΔCp of the substances in this work. Thus by using the solid-state activity determined through equation (23) as the reference, we may estimate the error in the activity of the solid phase for the three approximations. Table 5 lists the average error over the different temperatures of the solid-state activity for the different approximations.

26 TABLE 5

Comparison of the average error in the estimation of activity of the solid phase using three different approximations of ΔCp.

Approximation o-Hydroxy m-Hydroxy p-Hydroxy Salicyl- Paracetamol benzoic acid benzoic acid benzoic acid amide ΔCp = 0 62 % 85 % 85 % 62 % 76 % (equation (2)) f ΔCp = ΔS (Tm) 36 % 57 % 60 % 42 % 43 % (equation (3)) ΔCp = q 17 % 33 % 25 % 17 % 5 % (equation (20))

Table 5 (and figure 5) reveals a significant inaccuracy in the estimation of the activity of the solid phase upon approximating ΔCp as zero. By this assumption the estimated value of the activity may become as low as 1/12 of the correct value. The other two approximations (equation

(3) and (20)) systematically result in that the activity of the solid phase becomes lower than the

f real value. Although approximating ΔCp with ΔS (Tm) instead of neglecting ΔCp all together increases the accuracy in determining the activity, a considerable error is still present. By this approximation the estimated value of the activity may become as low as 1/3 of the correct value.

vH By estimating the activity of the solid phase from the intersection between the ln(xeq) - ΔH So ln regression curve and the solid-state activity line, it is possible to significantly increase the accuracy. However, assuming a constant ΔCp from the melting temperature to the experimental temperature (as also is done in equation (4)) is overly simplified for these compounds. Only paracetamol exhibits a more or less constant ΔCp with temperature. A comparably better result, however, is obtained by acknowledging that ΔCp depends linearly on the temperature. A linear dependence on temperature is also commonly used in regression of experimental heat capacity data of solids and liquids.

27 By analyzing the terms of equation (24) it is found that for the compounds of the present work and in the range of temperatures considered, the contribution from the melting enthalpy to the

ΔHf(T) amount to less than 50 %. The heat capacity terms tend to dominate the value of ΔHf(T) and consequently also profoundly affect the value of the activity of the solid phase. An estimation of the solid-state activity by the commonly used equation (2) is thus fraught with serious error.

4.3. Heat capacity of the supercooled melt

Determination of ΔCp and Cp(s) enables the determination of the experimentally inaccessible

Cp(l) through equation (7). The heat capacities of the solid and melted phases of the investigated compounds are presented in figure 10.

28 400

300

200 OHBA 100 250 350 450 550 400

300

200 MHBA

] 100 -1 250 350 450 550 ·K 400 -1 300

200 PHBA 100 250 350 450 550 400

300

200 SA Heat capacity [J·mol 100 250 350 450 550 400

300

200 PA 100 250 350 450 550 Temperature [K] FIGURE 10. Experimental solid heat capacity (grey background) and determined supercooled liquid heat capacity (white background) of five organic compounds. The liquid heat capacity above the melting temperature is included for paracetamol [9].

Figure 10 and the fact that r is negative shows that ΔCp decreases with decreasing temperature for all compounds except paracetamol. The slope of the melt heat capacity with temperature of paracetamol, however, is lower in the range 268 to 298 K than when above the melting temperature. For the hydroxybenzoic acid isomers, the heat capacity of both the solid and the supercooled melt decreases in the order para-, meta- and ortho-isomer.

4.4. Uncertainty of the estimation of the activity of the solid Phase

The uncertainty of the approach presented herein to estimate the activity of the solid phase is

vH primarily drawn from experimental scatter around the ΔH So ln - ln(xeq) correlation (equation (16)).

The relation between the molar solubility and the van’t Hoff enthalpy of solution for real solvents is given by equation (11) and (15), and our second order polynomial (equation (25)) is just an

vH empirical correlation of experimental data. A better fit between the real solubility and the ΔH So ln yields a higher confidence in the estimation of the intersection with the solid-state activity line.

Of the investigated compounds, the hydroxybenzoic acid isomers exhibit the best fit (i.e. R2) followed by salicylamide and paracetamol. Difficulties may appear in accurately determining the

vH ΔH So ln as it is calculated from the temperature dependence of solubility. It is therefore expected that using a larger number of solvents at a higher number of experimental temperatures and over

vH a wider temperature range would generally increase the confidence of the ΔH So ln - ln(xeq) correlation. Furthermore, a greater difference in slope between the solid-state activity line and the

vH ΔH So ln - ln(xeq) relationship increases the accuracy in the estimation of the activity of the solid phase. A greater difference in slope between the two curves is normally obtained for compounds of lower melting temperature, alternatively, at higher experimental temperature. The functional

30 form of the relationship between ΔCp and temperature is initially an assumption in the calculations, but the assumption can be verified during the evaluation of the solubility data at different temperatures.

A direct validation of the method presented herein requires the actual value of ΔCp over the investigated temperature interval, which is essentially experimentally inaccessible. We may, however, use the solid heat capacity below the melting temperature and the melt heat capacity above the melting temperature to estimate the ΔCp at the melting temperature for paracetamol.

The experimental ΔCp of paracetamol at the melting temperature amounts to 99.8 (± 2.8) [9]

-1 -1 -1 -1 J·mol ·K , which can be compared to the value of 104.4 J·mol ·K obtained when ΔCp = q, and

-1 -1 the value 95.4 J·mol ·K obtained when ΔCp = q + r(Tm – T), respectively. In addition, a decreasing ΔCp with decreasing temperature emerges for all compounds with the possible exception of paracetamol. This behavior is consistent with the understanding of Cp approaching zero as the temperature approaches 0 K, as stated by the third law of thermodynamics.

31 5. Conclusions

The activity of the solid phase of a molecular compound against its hypothetical supercooled melt can be determined by combining, within a rigorous thermodynamic framework, standard thermodynamic experimental data at the melting temperature with measurements over solubility in different solvents at different temperatures. This allows for accurate determination of the activity coefficients from experimental solubility data, and for determination of the heat capacity of the supercooled melt at room temperature and atmospheric pressure.

Acknowledgements

The authors acknowledge the Swedish Research Council and the Industrial Association for

Crystallization Research and Technology for financial support.

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the melting point, Pharm. Res. 7 (1990) 1157-1162.

[14] H. Hojjati, S. Rohani, Measurements and prediction of solubility of paracetamol in water-

isopropanol solution: Part 2. Prediction, Org. Proc. Res. Dev. 10 (2006) 1110-1118.

[15] G.D. Pappa, E.C. Vuotsas, K. Magoulas, D.P. Tassios, Estimation of the differential molar

heat capacities of organic compounds at their melting points, Ind. Eng. Chem. Res. 44

(2005) 3799-3806.

Prediction of Solubility Curves and Melting Properties of Organic and Pharmaceutical Compounds

Nordström, Fredrik L. and Rasmuson, Åke C.

Dept. of Chemical Engineering and Technology, Royal Institute of Technology,

SE-100 44 Stockholm, Sweden

Phone: +46 8 790 8227, Fax: +46 8 105 228

Email: [email protected]

ABSTRACT

The relationships between solubility, temperature dependence of solubility, melting temperature and melting enthalpy are investigated for the purpose of finding relations that can significantly reduce the need for experimental work in the selection of the solvent for processing of organic fine chemicals and pharmaceuticals. The relationships are investigated theoretically and by evaluation of experimental data for 41 organic and pharmaceutical compounds comprising a total of 115 solubility curves in organic and aqueous solvents. The work considers selection of the equation for correlation of solubility data based on thermodynamic considerations and ability to predict melting properties of the solute from solubility data, prediction of the temperature dependence of solubility, and prediction of solubility curves in new solvents. While it is a simple task to find an equation to obtain a descent fit of experimental solubility data, it is more challenging to find relations that are sufficiently sound thermodynamically to allow for extrapolation to the melting temperature. However, with a proper choice of equation it is shown that the melting temperature of the solute can readily be predicted from solubility data in organic solvents (average accuracy of -5 K, standard deviation of 26 K). Relationships are identified by which the entire solubility curve can be predicted of the compound in a new solvent using only the melting properties and a single solubility data point in that solvent.

Key words: Prediction of solubility, Prediction of melting properties, temperature dependence of solubility, van't Hoff enthalpy of solution.

2 1. INTRODUCTION

Development and processing of pharmaceuticals rely on accurate determination of solubility data and melting properties of the Active Pharmaceutical Ingredient (API). The collection of solubility data for pharmaceutical and organic compounds is however a costly, tedious and labor intensive undertaking, and usually requires a considerable amount of the API. Regression of solubility data is typically employed to allow for interpolation and extrapolation with temperature. One application pertinent in the pharmaceutical industry is estimation of enantiotropic polymorphic transition temperatures from solubility data. Melting properties of the API are occasionally inaccessible due to the occurrence of polymorphic and/or solvated modifications causing phase conversion at elevated temperatures. Other common problems that may appear are decomposition and/or sublimation prior to fusion, which reduces or prevents direct measurement of the melting properties. Thus, the understanding of the relations between different properties of the compound, the influence of different solvents and the relation between different solutes in the same solvent are of great importance as is the development of predictive tools in order to determine these fundamental parameters.

A variety of approaches are available in the literature for prediction of melting temperature

(Katrizky et al., 2001), and they are typically employed for different classes of compounds.

Among these are classical Quantitative Activity-Property Relationship (QAPR) by e.g.

Abramowitz et al. (1990), Dearden (1991) and Charton et al. (1994), group contribution methods by e.g. Simamora et al. (1993), and correlations between similar type of compounds (e.g. Chickos et al., 2001, Gavezzotti, 1995). However, among fundamental physical properties, the melting temperature is one of the most difficult to predict (Martin et al., 1979, Katrizky et al., 2001,

Simamora et al., 1993) and standard deviations are typically obtained in the range of 17 to 35 oC

3 (lower for narrow test sets). On the other hand, for stable, unsolvated crystalline solutes the melting temperature is usually rather easy to determine experimentally, while metastable, solvated or temperature-sensitive compounds often are subjected to experimental problems.

Unfortunately, also the prediction of melting enthalpy is fraught with difficulties. The melting enthalpy can readily be calculated from the melting temperature and the melting entropy. The melting entropy exhibits a dependence with melting enthalpy (Gilbert, 1999), which can be ordered into different groups depending on the molecular geometry (Martin et al., 1979). Thus, prediction of melting enthalpy from melting temperature and melting entropy is possible and often performed (e.g. Chickos et al., 1990), but requires information on the structural symmetry of the compound, unless using more simple empirical relationships such as e.g. Walden's rule.

Fewer studies have been aimed at using solubility data to predict melting properties of the solute.

Lohmann et al. (1997) achieved satisfactory predictions of melting properties from solubility data of selected compounds near the melting temperature by assuming ideal behavior and neglecting the heat capacity difference between the supercooled melt and solid. Recently, Chickos et al.

(2002) developed a method by using solubility data of nonaqueous solvents together with the so- called theory of mobile order and disorder to predict melting properties. This approach also utilizes group additivity to estimate the total entropy phase change and requires several interaction parameters of the solute and solvent, respectively.

The relation between solubility, temperature dependence of solubility and melting properties of a solute can be explored through the laws of thermodynamics. It is often suggested that the ideal solubility is directly inferred from the melting properties of the solute and that the corresponding temperature dependence of solubility can be obtained from the enthalpy of fusion at temperature

T. However, for non-ideal solutions the situation is more complex. The thermodynamic relationship between solubility and melting properties has been used extensively but nearly

4 always by introduction of approximations that are too crude to be justified at the normal temperatures of processing quite far away from the melting temperature. The temperature dependence of solubility has attracted little attention. The temperature dependence of the molar solubility can be described by an enthalpic term, which in the present contribution is referred to as the van’t Hoff enthalpy of solution (sometimes reported as the apparent enthalpy of solution, enthalpy of dissolution or heat of solution). This enthalpic term is not equal to the calorimetric enthalpy of solution but comprises several thermodynamic parameters, as analyzed by

Hollenbeck (1980). The van’t Hoff enthalpy of solution is an experimentally accessible thermodynamic quantity that correlates well to other physical properties. Nordstrom and

Rasmuson, 2006a-c examined the van’t Hoff enthalpy of solution and found a strong correlation to the molar solubility in organic solvents at constant temperature. In addition, the temperature dependence of the van’t Hoff enthalpy of solution was investigated and used to predict the melting temperature and melting enthalpy of p-hydroxybenzoic acid (Nordstrom and Rasmuson,

2006a).

In the present paper, the thermodynamic relations for real, non-ideal systems are explored and exploited. In the evaluation we use a test set of 41 different organic and pharmaceutical compounds comprising a total of 115 solubility curves. The work investigates the relationship between solid-liquid solubility, the temperature dependence of solubility and the melting properties of the pure solute, for non-ideal systems, through thermodynamic theory and experimental data. The analysis is used for (i) prediction of solubility curves in new solvents, (ii) selection of regression equation of solubility, and (iii) prediction of melting properties of the solute.

5 2. THEORY

2.1. Thermodynamic Basis

The molar solubility of a compound, xeq, expresses the concentration of the solute in the solution at solid-liquid equilibrium with the pure solid phase of the solute. Accordingly, the solubility depends on the thermodynamic stability of the solid phase, as well as, on the conditions in the solution. At equilibrium, the activity of the solute in the solution, as, equals the activity of the solid phase, a, if the same reference state is used. For molecular compounds the reference state is often chosen as the pure compound as a liquid/melt (Raoult's law reference) and in this case we may write:

== xaa γ eqeqs (1)

where γeq is the activity coefficient of the solute in the saturated solution. For the given reference state the activity of the solid is directly related to the Gibbs free energy change upon fusion,

ΔGf(T):

f −=Δ ln)( aRTTG (2)

where

Δ f TH )( ⎛ ⎞ 111 T ΔC 1 T ln a = m ⎜ − ⎟ + p dT Δ− dTC (3) ⎜ ⎟ RTTR ∫∫T RT p ⎝ m ⎠ TmmT

(Nordstrom and Rasmuson, 2008), which with Eq. 1 yields the general solubility equation

Δ f TH )( ⎛ ⎞ 111 T ΔC 1 T ln x = m ⎜ − ⎟ + p dT dTC −Δ− lnγ (4) eq ⎜ ⎟ RTTR ∫∫T RT p eq ⎝ m ⎠ TmmT

f where ΔH (Tm) is the enthalpy change upon melting and ΔCp is the heat capacity difference between the supercooled melt and solid form. Often in the literature we may find an empirical equation that relates the molar solubility to the temperature dependence of solubility:

vH ⎛ ∂ ln x ⎞ ΔH So ln ⎜ ⎟ = 2 (5) ⎝ dT ⎠eq RT

The enthalpy term is referred to as the van't Hoff enthalpy of solution, and can be obtained from

vH the slope of the solubility curve in a so-called van't Hoff plot (slope = Δ− So ln RH ) where lnxeq is plotted versus 1/T. The van’t Hoff enthalpy of solution differs from the calorimetric enthalpy of solution and can be expressed as (Nordstrom and Rasmuson., 2006a):

⎡ T ⎛ ∂ lnγ ⎞ ⎤ 1 vH f )( −Δ+Δ=Δ RTdTCTHH 2 (6) So ln ⎢ m ∫ p ⎜ ⎟ ⎥ ⎝ ∂T ⎠ x ⎛ ⎛ ∂ lnγ ⎞ ⎞ ⎣⎢ Tm ⎦⎥ ⎜1+ ⎜ ⎟ ⎟ ⎝ ⎝ ∂ ln x ⎠T ⎠

Thus, the van’t Hoff enthalpy of solution depends on the solid-state properties: melting enthalpy, melting temperature and the temperature dependence of the heat capacity difference between the

7 supercooled melt and the solid, and on the solution properties: change in the activity coefficient of the solute with temperature at constant concentration, and change in the activity coefficient of the solute with concentration at constant temperature.

2.2. Approximations

The molar solubility, Eq. 4, and the temperature dependence of the molar solubility, Eq. 6, are thermodynamically rigorous and combined describe solubility curves of solutes in non-ideal solutions. In the development of a general semi-empirical model for solubility curves we assume that the melting temperature and melting enthalpy are readily available by experimental determination. However, the ΔCp versus T function, and the concentration and temperature dependences of the activity coefficient are more difficult to estimate and require further analysis.

2.2.1. Approximation of ΔCp

The heat capacity of the supercooled melt is normally experimentally inaccessible at temperatures significantly below the melting temperature. A frequently used simplification is to assume that ΔCp is negligible. In several studies however, it has been shown that this is likely to be a poor assumption at temperatures of most processes (Neau and Flynn, 1990, Neau et al.,

1997, Pappa et al., 2005, Nordstrom and Rasmuson, 2008). Following the work of Hildebrand et al., 1970, Neau et al., 1997, showed that a better approximation is made if the ΔCp is assumed

f equal to the entropy of fusion at the melting temperature, ΔS (Tm). In the present work we insert an empirical coefficient, σ:

f p σ Δ⋅≈Δ TSC m )( (7)

and allow σ to be a general regression coefficient equal for all compounds. The entropy of fusion at the melting temperature is given by

f f Δ TH m )( TS m )( =Δ (8) Tm

By inserting Eq. 1, 7 and 8 in Eq. 4 we obtain:

Δ f TH )( ⎡ − 11 − σσσ ⎛ T ⎞⎤ m ⎜ ⎟ xa eq lnlnln γ eq =+= ⎢ − + ln⎜ ⎟⎥ (9) ⎣ m TTTR m ⎝ Tm ⎠⎦

2.2.2. Approximations of the activity coefficient derivatives

The change of the activity coefficient with temperature at constant concentration, (∂lnγ/∂T)x, present in Eq. 6, can for a regular solution be shown to follow:

⎛ ∂ lnγ ⎞ lnγ eq ⎜ ⎟ −= (10) ⎝ ∂T ⎠ x T

For simplicity we also introduce the notation, PD:

1 PD = (11) ⎛ ∂ lnγ ⎞ 1+ ⎜ ⎟ ⎝ ∂ ln x ⎠T

9 If Eq. 9 -11 are inserted into Eq. 6 we derive at

⎡ T ⎛ ⎛ T ⎞⎞ ⎤ vH ⎢ f THH ⎜ +⋅Δ=Δ σ ln1)( ⎜ ⎟⎟ − ln ⎥ ⋅ PDxRT (12) So ln m T ⎜ ⎜ T ⎟⎟ eq ⎣⎢ m ⎝ ⎝ m ⎠⎠ ⎦⎥

A schematic representation of lnγ versus lnx at constant temperature is given in Figure 1 to analyze how PD depends on the solubility. Solid curves represent a solid dissolved in a solvent at increasing concentration, disregarding any solubility limitation.

10 Henry’s law region lnγ

E BC 1: lnγ = -lnx lna

γ > 1

Raoult’s law, γ=1 C (0,0) lnx

γ < 1

BC 2: lnγeq = lna

Figure 1. Schematic representation of the relation between the activity coefficient and concentration at constant temperature for an arbitrary non-electrolytic compound in several solvents (solid curves) exhibiting positive and negative deviations from Raoult's law. The boundary at which Henry's law applies is depicted as a dashed line. The boundary condition, BC

1, is given as a dot-dot-dashed line, and the activity of the solid phase is presented as a dot- dashed line.

In a particular solvent at constant temperature, the activity coefficient of the solute depends on the concentration. If we move from left to right in Figure 1: at low concentration we expect to find a Henry’s law behavior where the activity coefficient is constant (γ>1 for positive deviations

11 from Raoult's law and γ<1 for negative deviations from Raoult's law) and hence (∂lnγ/∂lnx)T is zero. At intermediate concentration the activity coefficient in the normal case gradually approach unity either from positive or negative deviation from Raoult's law. In this region (∂lnγ/∂lnx)T is negative or positive, respectively. When x is approaching unity (far right in Figure 1) the activity coefficient approaches unity in accordance with the Raoult's law definition, and (∂lnγ/∂lnx)T again approaches zero. In addition, we may state that since x∈[0,1]: lnγ ≥ lnas, and since as∈[0,1], lnγ ≤ -lnx (boundary condition 1).

Inserted in Figure 1 is also a dot-dashed line having a slope of -1 that represents saturated solutions of a particular solute in different solvents. At constant temperature, the activity of the solid is constant and hence also the activity of the solute in the solution regardless of the solvent.

Along this line is marked five points (denoted as A to E) covering solvents at which the solubility is very high (γeq<<1) to solvents at which the solubility is very low (γeq>>1). The derivative

(∂lnγ/∂lnx)T in Eq. 11 and 12 thus represents the slope of the solid curves at the cross section with

vH the dot-dashed line in Figure 1. Since the ΔH So ln can only exhibit a finite (and normally positive) value, we may also note that (∂lnγ/∂lnx)T > -1 (see Eq. 6). At xeq = 1 it follows that lnγeq = lnas

(boundary condition 2) and (∂lnγ/∂lnx)T is infinite. At point A (∂lnγ/∂lnx)T exhibits a positive finite value. As the solubility decreases (from point A to point B), the γeq increases and

(∂lnγ/∂lnx)T decreases. However, as long as γeq is less than unity, (∂lnγ/∂lnx)T will be positive (an exception to this rule may occur in case of very low activity, discussed below). In an ideal solution γeq equals unity and (∂lnγ/∂lnx)T equals zero (point C). In a solvent where γeq>1,

(∂lnγ/∂lnx)T is negative (point D). As the solubility decreases further the concentration level finally reaches the region in which Henry’s law applies, i.e. the γeq is constant with concentration

(point E). At this point (∂lnγ/∂lnx)T = 0.

12 For an arbitrary organic molecular compound at constant temperature in different solvents, we may summarize:

• when γeq < 1 (negative deviation from Raoult’s law) ⇒ (∂lnγ/∂lnx)T ≥ 0 and PD ≤ 1

• when γeq = 1 (ideal solution, xeq = a) ⇒ (∂lnγ/∂lnx)T = 0 and PD = 1.

• when γeq > 1 (positive deviation from Raoult’s law) ⇒ (∂lnγ/∂lnx)T ≤ 0 and PD ≥ 1.

• when xeq → 1 ⇒ γeq → as and (∂lnγ/∂lnx)T → ∞ and PD → 0.

• when xeq → 0: ⇒ (∂lnγ/∂lnx)T → 0 and PD → 1

In Figure 2 is given a schematic representation of how PD is expected to vary with the solubility of a compound in different solvents at constant temperature, i.e. along the dot-dashed line in

Figure 1 from point A to E.

Raoult’s law, γeq = 1 PD D

1 C E

Henry’s law region B

A 0

0 1 lnxeq/lna

Figure 2. Expected behavior of PD in solvents with decreasing solubility at constant temperature. The solubility is normalized with respect to the solid-state activity.

By normalizing lnxeq on lna, different compounds are expected to fall on the same curve.

However, the height of the peak in Figure 2 also depends on the activity of the solid: a lower activity leads to a lower peak height of PD and the peak disappears completely when the activity of the solid is such that γeq ≤ 1 in Henry’s law region. This event however requires an exceptionally low activity of the solid of the compound and is therefore not frequently encountered for organic compounds.

For the development of a general semi-empirical model for the van’t Hoff enthalpy of solution, we introduce for PD a mathematical description of the schematic behavior depicted in Figure 2.

For negative deviations from Raoult’s law (i.e. γeq < 1 or eq ax < 1lnln ), we assume:

ln x PD ≈ eq (13) ln a

so that PD is unity when γeq is unity. For positive deviations from Raoult’s law we assign PD the empirical expression:

2 ⎛ ln x ⎞ ⎡ ⎛ ln x ⎞ ⎤ PD ε⎜ eq −≈ ⎟ exp1 ⎢ ϕ⎜ eq −−⋅ ⎟ ⎥ +11 (14) ⎜ ln a ⎟ ⎜ ln a ⎟ ⎝ ⎠ ⎣⎢ ⎝ ⎠ ⎦⎥

This equation starts with PD = 1 when γeq = 1 (Raoult’s law) and ends at PD = 1 when lnxeq/lna approaches infinity (Henry’s law region). The coefficients ε and φ describe the height and width of the peak of PD, respectively. The coefficient φ, however, increases with increasing solid-state activity. To compensate for this, we introduce a normalized coefficient φ*, given by:

ϕ ϕ ⋅−= ln* a (15)

Hence, for the general case

2 ⎛ ln x ⎞ ⎡ ⎛ ln x ⎞ ⎤ PD ε⎜ eq −≈ ⎟ ⎢ϕ ⋅⋅ ln*exp1 a⎜ eq − ⎟ ⎥ +11 (16) ⎜ ln a ⎟ ⎜ ln a ⎟ ⎝ ⎠ ⎣⎢ ⎝ ⎠ ⎦⎥

2.3. Semi-empirical Solubility Model

We summarize for the van't Hoff enthalpy of solution that for negative deviations from Raoult’s law:

⎡ T ⎛ ⎛ T ⎞⎞ ⎤ ln xeq vH ⎢ f THH ⎜ +⋅Δ=Δ σ ln1)( ⎜ ⎟⎟ − ln xRT ⎥ (17) So ln m T ⎜ ⎜ T ⎟⎟ eq ln a ⎣⎢ m ⎝ ⎝ m ⎠⎠ ⎦⎥

and for positive deviations from Raoult’s law:

2 ⎡ T ⎛ ⎛ T ⎞⎞ ⎤ ⎡ ⎛ ln x ⎞ ⎡ ⎛ ln x ⎞ ⎤ ⎤ vH f ⎜ ⎜ ⎟⎟ ⎢ ⎜ eq ⎟ ⎢ ⎜ eq ⎟ ⎥ ⎥ So ln ⎢ THH m +⋅Δ=Δ σ ln1)( ⎜ ⎟ − ln xRT eq ⎥ ε⎜ −⋅ ⎟ ϕ ⋅⋅ ln*exp1 a⎜ − ⎟ +11 T ⎜ T ⎟ ⎢ ln a ⎢ ln a ⎥ ⎥ ⎣⎢ m ⎝ ⎝ m ⎠⎠ ⎦⎥ ⎣ ⎝ ⎠ ⎣ ⎝ ⎠ ⎦ ⎦ (18) where lna is determined from Eq. 9. In the present work, Eq. 17 and 18 are used to correlate

vH experimental ΔH So ln of different compounds in different solvents at constant temperature.

15 Previous contributions (Nordstrom and Rasmusona-c) have shown that there is a strong correlation at constant temperature, between the molar solubility and the van’t Hoff enthalpy of solution for the same compound in different solvents. This relation can be explored within the semi-empirical model. At constant temperature the activity of the solid is invariant as long as the crystal structure is unchanged. Hence, a change in the van’t Hoff enthalpy of solution can only be exerted via a change in solubility and in the PD term. From Eq. 17 we can at constant temperature derive that

vH 2 H So ln =Δ α xeq + β ln)(ln xeq (19)

where α and β are solid-state property constants. This equation has been successfully used to correlate the experimental relationship between the molar solubility and the temperature dependence of solubility for five organic compounds, where R2 > 0.9 (Nordstrom and Rasmuson,

2008). We may also at constant temperature derive from Eq. 12 that in the Henry's law region, where PD is unity:

vH H So ln α −=Δ ln xRT eq (20)

The only assumption underlying Eq. 20 is the approximation of a regular solution. From Eq. 19 and 20 and the expected change in PD with molar solubility we arrive at a general relationship at constant temperature between the molar solubility and the temperature dependence of solubility

(as given by the van't Hoff enthalpy of solution), shown in Figure 3.

Henry’s law 30

10 Raoult’s law

0 -20 -15 -10 -5 0

lnxeq [mol/mol] Figure 3. Relationship between the molar solubility and the temperature dependence of solubility

(given as the van't Hoff enthalpy of solution) for a solid phase in different solvents at constant temperature.

2.4. Extrapolation to the Melting Temperature

At changing temperature both the solid and solution properties change in Eq. 4 and 6. The solid-

vH state parameter responsible for the change in solubility and in ΔH So ln is the integral term of ΔCp, the value of which decreases with increasing temperature. The conditions in the solution, characterized by γeq, (∂lnγ/∂lT)x and (∂lnγ/∂lnx)T (and accordingly also PD) also depend on temperature. However, at the melting temperature of the solid if can be deduced from the thermodynamically rigorous Eq. 4 and 6 that:

17 vH f So ln Δ=Δ THH m )( (21)

s xa eq == 0lnln (22)

Thus, for the same compound all solubility curves are expected to converge towards the melting temperature where they exhibit the same slope in a van't Hoff plot (Nordstrom and Rasmuson,

b 2006 ). Ergo, the solution properties γeq and PD will approach unity upon approaching the melting temperature. The γeq and PD in solvents displaying negative deviations from Raoult's law are therefore expected to continuously increase with increasing temperature while the γeq and PD in solvents displaying positive deviations from Raoult's law are expected to continuously decrease with increasing temperature. The resulting generalized behavior of solubility curves at different temperatures is pictured in a van't Hoff plot in Figure 4 for an arbitrary compound in different solvents.

1/Tm 1/T 0

γeq < 1 vH Δ⋅−= HRSlope Soln

Rao ult’ Slo s law pe= , γ -R· eq = ΔHf 1 (T)

γ > 1 eq vH Δ⋅−= HRSlope Soln

ln(xeq) Henry’s law region

Figure 4. Illustration of a generalized van’t Hoff plot of an arbitrary compound in several solvents.

19 3. EVALUATION AND DISCUSSION

The solutes explored in the present study involve a total of 41 organic and pharmaceutical compounds, comprising a total of 81 solubility curves in organic solvents and 34 solubility curves in water. The solubility and melting properties of the investigated solutes are listed in Table 1.

For all solutes, melting temperature and melting enthalpy are found in the literature, and in case of several different solid forms, only the most stable known polymorph is included. The onset melting temperature of the solute is preferred over the peak melting temperature. Average melting temperature is used when several values are found. More recent data are given priority over older data. To assure that melting properties and solubility data concern the same solid phase, data where a solid-solid transition occurs in the thermogram, and solubility curves having a discontinuity in the slope are left out of this study. All solubility data used have been determined at atmospheric pressure and around room temperature. In all cases, the temperature does not exceed the boiling point of the solvent and there are at least data at five different temperatures spanning over a minimum of 20 K.

Table 1. Solutes and solvent investigated in this study.

f Solute Tm ΔH (Tm) Solvent Temperature

[K] [kJ/mol] interval of

solubility data

[K]

Acenaphtene 366.6* 1 21.48* 1 Chloroform 289.25-324.051

1,1 Dichloro ethane 288.65-323.751

20 1,2 Dichloro ethane 288.15-323.251

Tetrachloro ethylene 288.15-322.151

Tetrachloro methane 291.15-327.151

Trichloro ethylene 289.15-322.851 o-Acetylsalicylic acid 4142 29.802 Water 278.15-345.153

Adipic acid 424.654 33.995 Acetone 273.15-313.155

1-butanol 273.15-333.155

1,4-Dioxane 283.15-333.155

Ethanol 273.15-333.155

Methanol 273.15-313.155

1-Propanol 273.15-333.155

2-propanol 273.15-333.155

Water 278.15-338.156

Allobarbital 446.157 32.37 Water 293.15-318.158 o-Aminophenol 449.23* 9 25.4* 9 Water 273.15-353.158 m-Aminophenol 394.83* 9 19.6* 9 Water 283.15-333.158 p-Aminophenol 462.50* 9 26.0* 9 Water 286.15-353.1510

Anthracene 48911 29.3711 N,N-Dimethyl 303.0-322.812

formamide

1,4-Dioxane 303.0-322.812

Water 273.45-323.1511

Benzocaine 362.857 22.37 Water 288.15-323.158

Benzoic acid 395.6513 17.9813 Water 281.15-337.1514

21 Caffeine 509.457 22.07 Water 273.15-363.158

2,6-Dimethyl 384.1515 25.0615 Methanol 251.15-335.5515

-naphtalene

Ethanol 247.15-336.1515

1-propanol 248.75-333.1515

1-Butanol 247.55-336.3515

1-Pentanol 252.65-338.6515

1-Hexanol 246.15-335.1515

16α, 17α- 478.5516 26.4416 Acetic acid 293.60-326.0517

Epoxyprogesterone

Acetone 285.35-327.4517

1,4-Dioxane 288.45-332.5517

Ethanol 286.10-328.4517

Ethyl acetate 285.45-328.4517

Methanol 282.50-327.6017

Erythritol 390.918 39.418 Acetone 286.35-328.3519

Ethanol 287.55-339.1519

Methanol 287.35-327.3519

Water 288.85-354.2519

2-Furan 402.520 22.620 Water 279.15-341.1521 carboxylic acid

Glutaric acid 370.654 17.964 Water 279.15-342.1521

Hydroquinone 443.722 27.222 Acetic acid 289.45-341.2523

22 Butyl acetate 279.55-344.7023

Ethanol 276.65-342.1523

Ethyl acetate 278.70-345.1023

Methanol 281.65-343.4023

Water 280.50-342.1023 m-Hydroxy 474.8**24 35.9224 Acetic acid 283.15-323.1524 benzoic acid

Acetone 283.15-323.1524

Acetonitrile 283.15-323.1524

Ethyl acetate 283.15-323.1524

Methanol 283.15-323.1524

Water 283.15-323.1524 p-Hydroxy 487.7**25 30.8525 Acetic acid 283.15-323.1525 benzoic acid

Acetone 283.15-323.1525

Acetonitrile 283.15-323.1525

Ethyl acetate 283.15-323.1525

Methanol 283.15-323.1525

Ibuprofen 347.226 25.526 Acetone 283.15-308.1526

Ethanol 283.15-308.1526

Ethyl acetate 283.15-308.1526

Methanol 283.15-308.1526

4-methyl-2-pentanone 283.15-308.1526

23 2-propanol 283.15-308.1526

Toluene 283.15-308.1526

Isophthalic acid 617.4127 43.227 Water 300.15-368.1528

DL-Malic acid 40229 33.5229 Water 278.15-338.156

2-Methyl anthracene 47911 24.0611 Water 273.45-323.1511

Nalidixic acid 501.930 35.9330 1,4-Dioxane 283-31330

Water 283-31330

Naphtalene 353.3*1 18.24*1 Chloroform 288.85-322.951

1,1 Dichloro ethane 288.35-323.751

1,2 Dichloro ethane 288.35-321.851

Tetrachloro ethylene 288.45-323.951

Tetrachloro methane 288.45-321.851

Trichloro ethylene 288.35-323.251

Nicotinic acid 510.457 27.97 Water 274.15-361.158

3-Nitrobenzoic acid 41431 21.432 Water 278.15-343.1533

Paracetamol 443.634 27.134 Acetone 268.15-298.1534

Acetonitrile 268.15-298.1534

1-Butanol 268.15-298.1534

Ethanol 268.15-298.1534

Ethyl acetate 268.15-298.1534

Methanol 268.15-298.1534

1-Propanol 268.15-298.1534

2-Propanol 268.15-298.1534

24 Water 273.15-298.1534

Phenacetin 407.235 31.2535 1,4-Dioxane 293-31336

Water 293-31336

Phthalic acid 463.4527 36.527 Water 298.15-368.1528

Salicylamide 411.9**37 29.0037 Acetic acid 283.15-323.1537

Acetone 283.15-323.1537

Acetonitrile 283.15-323.1537

Ethyl acetate 283.15-323.1537

Methanol 283.15-323.1537

Water 283.15-323.1537

Salicylic acid 431.4**38 27.0938 Acetic acid 283.15-323.1538

Acetone 283.15-323.1538

Acetonitrile 283.15-323.1538

Ethyl acetate 283.15-323.1538

Methanol 283.15-323.1538

Water 283.15-323.1538

Silybin 42439 44.8739 Water 293.15-313.1539

Succinic acid 4584 31.464 Water 278.15-338.156

Tartaric acid 43540 34.3240 Water 278.15-338.156

Terephthalic acid 698.1528 53.5728 Water 301.45-368.1528

Thiourea 452.241 16.042 1-Butanol 294.66-328.2541

Ethanol 293.66-337.1641

Methtanol 298.66-334.7241

25 o-Toluic acid 38043 20.144 Water 278.15-338.1545 m-Toluic acid 38543 16.043 Water 278.15-348.1545 p-Toluic acid 45543 23.643 Water 278.15-343.153

Urea 40546 14.142 Water 273.15-343.1547

* At triple point, ** Onset melting temperature, (1) Kotula and Marciniak, 2001, (2) Kirklin, 2000, (3) Apelblat and

Manzurola, 1999, (4) Khetarpal et al., 1980, (5) Gaivoronskii and Granzhan, 2005, (6) Apelblat and Manzurola,

1987, (7) Sangster, 1999, (8) Yalkowsky and He, 2003, (9) Sabbah and Gouali, 1995, (10) Zhao et al., 2005, (11)

Dohanyosova et al., 2003, (12) Cepeda and Gomez, 1989, (13) Lin and Nash, 1993, (14) Apelblat et al., 2006, (15)

Kim and Cheon, 2004, (16) Nie et al., 2006, (17) Nie and Wang, 2005, (18) Barone et al., 1990, (19) Hao et al.,

2005, (20) Roux et al., 2004, (21) Apelblat and Manzurola, 1989, (22) Verevkin, 1999, (23) Li et al., 2006, (24)

Nordstrom and Rasmuson, 2006b, (25) Nordstrom and Rasmuson, 2006a, (26) Gracin and Rasmuson, 2002, (27)

Sabbah and Perez, 1999, (28) Han et al., 1999, (29) Ceolin et al., 1990, (30) Bustamante et al., 1999, (31) Chacko et al., 2005, (32) Rai and Mandal, 1990, (33) Manzurola and Apelblat, 2002, (34) Granberg and Rasmuson, 1999, (35)

Ruelle and Kesselring, 1998, (36) Bustamante and Bustamante, 1996, (37) Nordstrom and Rasmuson, 2006d, (38)

Nordstrom and Rasmuson, 2006c, (39) Zhang et al., 2005, (40) Li et al., 1991, (41) Kim and Lee, 1994, (42) Stradella and Argentero, 1993, (43) Martin et al., 1979, (44) Holdiness, 1983, (45) Strong et al., 1989, (46) Saito et al., 1966,

(47) Pinck and Kelly, 1925.

3.1. Model Analysis of Solubility and its Temperature Dependence

Each set of experimental solubility data of the 115 solubility curves have been fitted to the regression equation:

-1 lnxeq = AT + B + CT (23)

26 where A, B and C are regression coefficients and T is given as absolute temperature. The

vH associated experimental ΔH So ln has been determined through Eq. 5 and 23.

vH 2 So ln ( +−=Δ CTARH ) (24)

The solubility model, as given by eq 9, 17 and 18, applied to the investigated solutes (in Table 1) results in three unknown coefficients, viz. σ, ε and φ*. The three coefficients are determined from

vH o o 115 values of ΔH So ln for each temperature between 10 and 30 C in 5 C steps by non-linear regression. The objective function to be minimized is:

N vH vH 2 ∑()ΔH So ln (experimental i Δ− H So ln predicted)() i RMS = i (25) N

In Table 2 is presented the resulting coefficients obtained by the optimization.

27 Table 2. Coefficients, RMS and standard deviation for prediction of the van’t Hoff enthalpy of solution.

Temperature σ ε φ* RMS (std dev) RMS (std dev)

[oC] [mol·mol-1] [kJ·mol-1] [kJ·mol-1]

Organic solvents Water

γeq<1 γeq>1

10 1.958 1.632 0.276 2.57 (2.68) 5.12 (5.15) 8.16 (8.28)

15 1.940 1.624 0.294 2.32 (2.42) 4.53 (4.57) 6.87 (6.98)

20 1.922 1.619 0.311 2.07 (2.15) 4.19 (4.22) 6.09 (6.19)

25 1.897 1.622 0.333 1.83 (1.91) 4.20 (4.23) 6.04 (6.13)

30 1.868 1.620 0.355 1.63 (1.70) 4.75 (4.78) 6.76 (6.86)

In Figure 5 is shown the fit of the equations by using the values of the coefficients: σ, ε and φ* determined in the regression analysis given in Table 2, plotted versus the experimental values of

vH o ΔH So ln between 10 and 30 C.

50000

40000

30000

20000

10000

[J/mol] Predicted

0 0 10000 20000 30000 40000 50000

Experimental vH [J/mol] ΔH Soln Figure 5. Plot of predicted versus experimental van’t Hoff enthalpy of solution between 10 and

30 oC. The symbols with white and dark background depict solubility data in water and organic solvents, respectively.

Based on this test set of 41 compounds and 115 solubility curves, it is seen that better predictions were generally obtained for solubility data in organic solvents than in water. In particular accurate predictions were obtained for organic solvents displaying negative deviation from

Raoult’s law and at higher temperatures. In Table 2 we may observe that ε is not changing much with temperature and not in a regular way. However, σ and ϕ* expose a clear systematic dependence on temperature.

The deviations shown in Figure 5 are perhaps to some extent due to uncertainty in the determination of the van’t Hoff enthalpy of solution from the slope of the experimental solubility data. However, errors are also introduced in the approximations used in the determination of the

29 predicted van’t Hoff enthalpy of solution, particularly relevant for cases of low solubility in water. Approximating ΔCp as constant over the temperature range T to Tm, is considered to be a clear simplification, even though the actual value is adjusted by the regression coefficient σ. The value of the coefficient σ in Table 2 decreases with increasing temperature, which suggests a general temperature dependence of ΔCp. The parameter σ corresponds to k·Tm in the work of Yu

(1995). For a collection of compounds Yu (1995) found k at the melting temperature to range from 0.001 and 0.007 with an average of approximately 0.003. In the current work, the average value of k for the 115 solubility curves becomes 0.0046 at 20 oC, but decreases with increasing temperature.

Another important approximation is the regular solution assumption used in Eq.10 to simplify the temperature derivative of the activity coefficient. Systems in which the molecular volume differs between the solute and the solvent may give rise to deviations. Concerning the approximation of the behavior of PD versus concentration, as described by Figure 2 and Eq. 17 and 18: aqueous solubility data generally exhibits a greater deviation in comparison to data in organic solvents except at very low solubility concentrations (i.e. in the Henry's law region where PD = 1). This suggests that the activity coefficient - concentration relationships in water differ to some extent from organic solvents.

vH Overall, the parameters affecting the prediction of ΔH So ln the greatest are solubility, melting temperature and PD. The melting enthalpy on the other hand was seen to have a small influence

vH on the magnitude of the ΔH So ln . Thus, assigning values to the melting enthalpy that may deviate considerably from the actual value (± 50 %) will not result in a significantly altered predicted value of the van’t Hoff enthalpy of solution.

30 3.2. Prediction of Solubility Curves

The generalized behavior of solubility curves, as explored through the above model, shows that the temperature dependence of solubility (i.e. the van't Hoff enthalpy of solution) is linked to the melting properties of the solute and the solubility at one temperature for organic compounds.

Thus, this relationship can be used for prediction of entire solubility curves in new solvents. For a solute for which the melting temperature and melting enthalpy have been determined, we need only one single solubility value in that solvent (xeq,exp, at temperature Texp), to predict the van’t

Hoff enthalpy of solution, i.e. the temperature dependence of the solubility, using the values of the determined regression coefficients: σ, ε and φ* in Table 2.

The relationships can then be used to determine the three coefficients in Eq. 23. Applying Eq. 23 at the melting temperature gives through Eq. 22:

−1 0 m ++= CTBAT m (26)

Hence, the solubility curve is described by three equations, viz. Eq. 23, 24 and 26. Since Eq. 23 also contains three coefficients we may solve for A, B and C:

vH 2 ΔH So ln Tm mTT exp A = − xeq exp, )ln( 2 (27) R exp − TT m m − TT exp )(

vH 22 22 ΔH So ln m − TT exp )( m + TT exp )( B = 2 + xeq exp, )ln( 2 (28) RTexp m − TT exp )( m − TT exp )(

31 vH ΔH So ln Tm C = − xeq exp, )ln( 2 (29) expexp − TTRT m )( m − TT exp )(

Thus, a solubility curve can be established by determining the coefficients A, B and C in Eq. 27 through 29. The method is illustrated in Figure 6 for phenacetin in 1,4-dioxane based on the experimental solubility value at 25 oC (from Bustamante et al., 1996). The uncertainty in the prediction of the solubility curve is mainly due to the uncertainties in the relationships of the van’t Hoff enthalpy of solution, i.e. Eq. 17 and 18. By using the standard deviation in the regression of the van't Hoff enthalpy of solution (in Table 2) of the 115 solubility curves, we may establish limits of confidence of the predicted solubility curve. In Figure 6 are inserted 68 % and

95 % confidence limits corresponding to one and two standard deviations. The experimental solubility at other temperatures (Bustamante et al., 1996) is also included for comparison.

32 0.05

0.04

0.03

0.02

Solubility [mol/mol] Solubility 0.01

0.00 285 290 295 300 305 310 315 Temperature [K]

Figure 6. Predicted solubility curve of phenacetin in 1,4-dioxane (full curve) based on the experimental solubility at 25 oC (white circle) and the associated melting properties (Table 1).

The dotted and dashed curves correspond to 68 and 95 % confidence limits, respectively, drawn from the prediction of the van’t Hoff enthalpy of solution. The grey circles depict the experimental solubility between 20 and 40 oC (Bustamante et al., 1996).

Thus, it is possible to estimate the entire solubility curve with limits of confidence using only a single solubility measurement in that solvent*. An experimental solubility curve that appears outside the established 95 % confidence limits of the predicted solubility curve may appear for statistical reasons (i.e. the 5 %), indicate that equilibrium is not achieved in the solubility measurements, or actually signal that the solid phase at Texp differs from the solid phase at Tm, i.e. another polymorph or solvate.

* A simple program for prediction of solubility curves can be retained from the authors upon request

33 3.3. Regression of Solubility Data and Extrapolation to the Melting

Temperature

A regression equation of solubility, RES, is usually fitted to experimentally determined solubility data at different temperatures. In the literature, many different equations have been proposed and used, and some additional are included in Table 3. The RES are divided into four categories depending on the number of RES coefficients and its mathematical form. These equations are normally used in the sole purpose of fitting solubility data at different temperatures to enable interpolation and extrapolation. We have explored the thermodynamics and goodness of fit of these RES, and their capability of extrapolation to the melting temperature, and for that purpose

vH Table 3 also includes the corresponding representation of ΔH So ln , derived through Eq. 5.

34 Table 3. Investigated RES. A, B, C and D are RES coefficients and T is given in K.

Category RES lnx vH eq Δ So ln / RH

A A1 AT-1 + B -A

A2 A + BT BT2

A3 A + Bln(T) BT

B B1 AT-2 + BT-1 + C -2AT-1 - B

B2 AT-1 + B + CT -A + CT2

B3 A + BT + CT2 BT2 + 2CT3

B4 AT-2 + B + CT2 -2AT-1 + 2CT3

C C1 AT-2 + BT-1 + Cln(T) -2AT-1 – B + CT

C2 AT-1 + B + Cln(T) -A + CT

C3 A + BT + Cln(T) BT2 + CT

C4 AT + BT2 + Cln(T) AT2 + 2BT3 + CT

D D1 AT-2 + BT-1 + C + DT -2AT-1 – B + DT2

D2 AT-1 + B + CT + DT2 -A + CT2 + 2DT3

D3 AT-2 + BT-1 + C + Dln(T) -2AT-1 – B + DT

D4 AT-1 + B + CT + Dln(T) -A + CT2 + DT

3.3.1. Thermodynamic evaluation of RES

By Eq. 4 and 6 we may investigate how the different equations in Table 3 agree with the laws of thermodynamics. Quite frequently, linear regression of solubility data is employed in a van't Hoff

vH plot (i.e. RES A1), which implies that ΔH So ln is constant with temperature. This behavior is

35 obtained if the solution is ideal and the ΔCp term is negligible, which in practice is never the case for real solutions.

When PD is unity, from Eq. 5 and 12 we can derive at:

ln eq += lnTBAx (30)

i.e. RES A3, a relation proposed by Hildebrand (1952). This equation thus applies for solubility data in the Henry’s law region (when PD is unity) under the assumption of a regular solution and that ΔCp can be considered constant with temperature. Should the molar solubility relate to the van't Hoff enthalpy of solution according to Eq. 17, then the following RES is obtained:

++ lnTCTBTA ln x = (31) eq + DRT

where A, B and C are coefficients that depend on the solid-state properties of the solute and D relates to the properties of the solution. When the solvent specific constant D is zero Eq. 31 simplifies into the relation proposed by Grant et al. (1984), i.e. RES C2. This RES is frequently encountered in the literature today when fitting solubility data. Within the present analysis RES

C2 can be derived from rigorous thermodynamic theory by assuming that PD is linearly related to lnxeq/lna, and using the assumption of an ideal solution, as well as, a ΔCp that is constant with temperature.

36 3.3.2. Goodness of fit of RES to solubility data

The different RES of Table 3 have been correlated to the 115 different experimental solubility curves. The coefficients, A, B, ….., were determined by a non-weighted least-square minimization of χ2

2 1 2 χ BA ,...),( = ∑∑[]− 21 iijijeq BATTfx ,...),,...;,()(ln (32) N f ij

using the computer software Origin, version 6.1 (OriginLab). (lnxeq)ij is the measured values of the dependent variable (lnxeq)j for the values of the independent variables T1 = T1i, T2 = T2i,…, and Nf is the number of degrees of freedom (= number of data points minus the number of RES coefficients). The RES coefficients were determined to a minimum of six significant digits. The goodness of fit of each of the RES in Table 3, as given by χ2, is given in Table 4.

37 Table 4. Goodness of fit (104·χ2) of 15 RES to 115 solubility curves.

Category RES Negative deviations from Positive deviations from

Raoult's law (γeq < 1) Raoult's law (γeq > 1)

Organic solvents Water Organic solvents Water

(38 solubility (6 solubility (43 solubility (28 solubility

curves) curves) curves) curves)

A A1 22.1 12.3 12.8 121

A2 12.5 11.6 27.9 69.0

A3 16.4 10.1 14.4 92.6

B B1 10.2 1.92 9.75 17.6

B2 9.43 1.97 10.0 18.1

B3 8.94 1.98 9.38 18.6

B4 9.27 1.95 10.4 18.4

C C1 10.2 1.93 9.92 17.6

C2 9.71 1.93 9.98 17.8

C3 9.28 1.97 9.78 18.2

C4 8.93 1.98 9.28 18.5

D D1 4.73 1.97 4.67 16.2

D2 4.37 2.03 4.86 16.5

D3 4.82 1.97 4.63 16.1

D4 4.55 2.00 4.76 16.4

38 The goodness of fit, as described by χ2, differed to some extent between water and organic solvents and between RES belonging to different categories. In organic solvents, the goodness of fit increases by approximately a factor of two for each added coefficient to the RES. Within each category, only small differences in χ2 are found among the individual RES with the exception of category A, and hence the number of adjustable RES coefficients is more important than the actual equation. In water, no significant improvement in the goodness of fit was obtained by adding a fourth coefficient to the RES. It appears that solubility data in water is adequately described by RES comprising only three coefficients, as also noted by Grant et al. (1984).

3.3.3. Extrapolation of the RES to the melting temperature

At increasing temperature solubility data should approach the conditions at the melting

vH f temperature where lnxeq = 0 and So ln Δ=Δ (THH m ) . Hence, the different RES can be evaluated for thermodynamic consistency in this respect. Tm can be found by inserting lnxeq = 0 into the

f equations of Table 3 and ΔH (Tm) is obtained by differentiation according to Eq. 5. In Table 5 is given the corresponding equations for melting temperature and melting enthalpy.

39 f Table 5. Predictions of melting properties from RES coefficients. Tm in [K] and ΔH (Tm) in

[J/mol]

f Category RES Tm ΔH (Tm)/R

A A1 -A/B -A

2 A2 -A/B BTm

A3 exp(-A/B) BTm

2 0.5 -1 B B1 2A/(-B + (B – 4AC) ) -2ATm - B

2 0.5 2 B2 (-B + (B – 4AC) )/(2C) -A+CTm

2 0.5 2 3 B3 (-B + (B – 4AC) )/(2C) BTm + 2CTm

2 0.5 0.5 -1 3 B4 [(-B + (B – 4AC) )/(2C)] -2ATm + 2CTm )

-1 C C1 Numeric or -2ATm - B + CTm

C2 graphic approach -A + CTm

2 C3 BTm + CTm

2 3 C4 ATm + 2BTm + CTm

-1 2 D D1 -2ATm - B + DTm

2 3 D2 -A + CTm + 2DTm

-1 D3 -2ATm - B + DTm

2 D4 -A + CTm + DTm

The melting temperature and melting enthalpy have been predicted for each RES through Table 5 using the test set of 115 solubility curves for the 41 different compounds. The results are summarized in Table 6 as the average difference between the predicted and experimental melting temperature, Tm,pred - Tm, exp, for solubility data in organic solvents and water, respectively. In

40 some cases, the prediction of Tm failed entirely in that e.g. a negative temperature is obtained.

The frequency as to how often the predictions do not fail in this way has been characterized and denoted Frequency of Consistent Predictions, FCP.

41 Table 6. Prediction of melting temperature from extrapolation of solubility data.

Category RES Organic solvents Water

(81 solubility curves) (34 solubility curves)

Tm,pred-Tm,exp std. dev. FCP Tm,pred-Tm,exp std. dev. FCP

[K] [K] [%] [K] [K] [%]

A A1 127.5 204.0 100 500.8 673.1 85.3

A2 -5.0 26.0 100 73.2 128.7 100

A3 25.2 53.0 100 160.9 168.6 97.1

B B1 18.2 54.0 92.6 70.5 113.0 88.2

B2 0.2 37.0 90.1 24.3 71.5 85.3

B3 -5.0 29.3 80.2 14.7 82.2 73.5

B4 -6.5 31.8 91.4 69.1 332.5 91.2

C C1 16.8 52.2 92.6 65.4 107.6 88.2

C2 4.6 38.1 90.1 36.1 78.0 88.2

C3 -2.4 29.6 87.7 21.2 75.7 79.4

C4 -6.1 27.1 76.5 11.8 81.8 70.6

D D1 -16.0 39.4 60.5 43.1 198.8 61.8

D2 -25.3 35.3 53.1 -3.1 78.7 55.9

D3 -13.1 42.3 61.7 77.7 322.5 64.7

D4 -17.6 39.5 59.3 5.9 104.4 55.9

From the data in Table 6, we can draw a few general conclusions: (i) solubility data in organic solvents allows for a better estimation of the melting temperature of the solute, (ii) two

42 coefficients in the RES (category A) provide for high robustness (high FCP) but in the case of

RES A1 and A3 poor precision and accuracy (iii) four coefficients (category D) generally leads to poor robustness and accuracy, (iv) there is no significant difference between RES having three coefficient (category B and C), i.e. a logarithmic term is not required, (v) with respect to the data of the present study RES A2, B2 and C3 are superior in organic solvents. The accuracy and precision of the prediction of the enthalpy of melting is rather poor with standard deviations typically exceeding 10 kJ/mol. In Figure 7 is shown the prediction of the melting temperature of the solutes using RES A2 and B2.

550

500 [K]

m 450

400

T Predicted 350

300 300 350 400 450 500 550

Experimental Tm [K] Figure 7. Prediction of melting temperature by extrapolation of solubility data through RES A2

(circles) and RES B2 (crosses).

From the test set used in the present study it is seen that solubility data in organic solvents can be utilized in a relatively simple way to predict the melting temperature of organic compounds.

43 Overall, the accuracy and precision in the predictions of the melting temperature can be improved using a few experimental features. Better predictions were normally obtained when the distance to the melting temperature is shorter, i.e. in highly soluble solvents and for solutes of lower melting temperature. In addition, using solubility data of the same solute in several solvents of course increases the accuracy in the predictions.

44 5. CONCLUSIONS

The relationship between solubility, temperature dependence of solubility (i.e. van’t Hoff enthalpy of solution), melting temperature and melting enthalpy has been investigated theoretically, as well as, with experimental data for 41 organic and pharmaceutical compounds comprising a total of 81 organic and 34 aqueous solubility curves. The link between solubility, temperature dependence of solubility (i.e. van’t Hoff enthalpy of solution) and melting temperature could be experimentally verified, whereas the relation to melting enthalpy was more difficult to establish.

Within the semi-empirical model a correlation of solubility and melting data is proposed that leads to a generalized function for prediction of the temperature dependence of solubility. This allows for entire solubility curves to be established from the melting properties of the solute and a single solubility data at one temperature. Limits of confidence can be constructed in which the solubility curve is likely located. Thus, the collection of solubility data for e.g. a pharmaceutical compound can be significantly reduced.

Since solubility curves of organic solutes approach the melting temperature of the solute it is possible to predict the melting temperature of the solute based on solubility data in organic solvents. Two regression equations of solubility are identified that in the prediction of the melting temperature gives an average absolute error of 19.8 (A2) and 21.7 K (B2), respectively.

ACKNOWLEDGEMENTS

The Swedish Research Council is acknowledged for financial support.

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55 Metastable Zone Width of Salicylamide

Fredrik L. Nordström and Åke C. Rasmuson

Dept. of Chemical Engineering and Technology, Royal Institute of Technology, Stockholm, Sweden

Fredrik L. Nordström, KTH, Kemiteknik/TS, 100 44 Stockholm, Sweden, phone +46 8 790 6402, fax +46 8 105228, email [email protected]

Åke Rasmuson, KTH, Kemiteknik/TS, 100 44 Stockholm, Sweden, phone +46 8 790 8227, fax +46 8 105228, email [email protected]

ABSTRACT The metastable zone width of salicylamide has been determined at constant cooling rates (polythermal method) by measuring the onset of nucleation. This study has investigated the influence of saturation temperature (30 to 50 oC), solvent (methanol, acetonitrile, acetic acid and ethyl acetate), cooling rate (5, 10 and 20 oC/h), solution volume (15, 150 and 500 ml) and solvent evaporation. Experiments were repeated up to approximately 200 times at each set of experimental conditions (a total of 2911 recorded nucleations) to establish both the average and the distribution in the onset of nucleation. The cooling rate and solvent exerted the greatest influence on the metastable zone width of salicylamide, whereas the influence of saturation temperature and solution volume was negligible. A correlation was observed between the supersaturation at the average onset of nucleation and the ratio between the viscosity of the solvent and concentration of the solute. It was also found that solvent evaporation during cooling crystallization may have a considerable impact on the metastable zone width. A significant variation in the onset of nucleation was obtained at all experimental conditions, which was normally Gaussian distributed with supersaturation ratio.

Key words: Salicylamide, metastable zone width, supersaturation, primary nucleation, nucleation kinetics

2 1. INTRODUCTION The metastable zone width, MZW, refers to the supersaturated concentration at which nucleation first spontaneously commences. The MZW of pharmaceutical and organic compounds conveys information of the nucleation behavior in different solvent system. Primary nucleation can be induced at supersaturation above the MZW and seeding crystallization can be performed at supersaturation below the MZW. Thus, the MZW constitutes an important experimental factor in the design of the crystallization process. However, many factors may significantly influence the width of the metastable zone. Among these are operating and hydrodynamic conditions such as rate of agitation, cooling rate, temperature, solution volume, reactor and impeller characteristics, as well as, external conditions such as solvent impurities, presence of foreign particles, solution history and ultrasound.

Primary nucleation is generally considered as a stochastic phenomenon inherent in the random motion of solute molecules forming into sub-critical clusters and subsequent crystals. Yet, few studies report of the variance of the MZW determined under reproducible experimental conditions. As the stochastic nature of primary nucleation can only be captured by a great number of experiments it is imperative that the nucleation events are repeated (Izmailov, 1999).

In the present paper, the influence of saturation temperature, solvent, cooling rate, solution volume and solvent evaporation on the MZW of salicylamide has been investigated. No data of the MZW of salicylamide has been reported previously. The experiments have been repeated during identical experimental conditions, comprising a total of 2911 recorded nucleation events. The ortho-isomeric compound salicylamide has only been found to crystallize as a monoclinic structure (Sasada et al., 1964; Pertlik, 1990). No polymorphs or solvates have been encountered in the investigated solvents (Nordström and Rasmuson, 2006).

3 2. EXPERIMENTAL Salicylamide (CAS registry number: 65-45-2) was purchased from Sigma-Aldrich (purity 99 %) and used as obtained. The solvents methanol (HiperSolv, purity > 99.8 %), acetonitrile (LiChrosolv, gradient grade, purity > 99.8%), acetic acid (Pro Analysi, purity 96 %), acetone (HiperSolv, purity > 99.8 %) and ethyl acetate (HiperSolv, purity > 99.8 %) were purchased from VWR/Merck and used as obtained.

Saturated solutions were prepared by partially dissolving salicylamide in respective solvent in 250 ml bottles. The bottles were sealed and the solutions equilibrated for a minimum of four hours at constant temperature. The saturated solutions were filtered at 0.2 µm (PTFE) and inserted into 20 ml test tubes (solution volume of 15 ml), 250 ml bottles (solution volume of 150 ml) and 500 ml bottles (solution volume of 500 ml). Teflon magnetic stirrers with pivot rings were added to the test tubes (stirrer bar dimension: 15x8 mm) and bottles (stirrer bar dimension: 35x8 mm). The test tubes and bottles were sealed to prevent solvent evaporation and contamination. (i) The test tubes and bottles were placed in water baths at 10 oC above the saturation temperature of the solutions. The acetone solutions were placed in water baths at 5 oC above the saturation temperature when the saturation temperature was 50 oC (as the boiling point of acetone is 56 oC) and 10 oC above the saturation temperature when the saturation temperature was 35, 40 or 45 oC. The solutions in the test tubes and bottles were agitated at 300 rpm (magnetic stirring plate by Variomag) for a minimum of three hours. (ii) The test tubes and bottles were then transferred to a cryostat (Julabo, FP 45) and agitated at 400 rpm. The water temperature in the cryostat corresponded to the saturation temperature of the solutions. A total of 14 test tubes or 4 bottles were placed simultaneously in the cryostat. (iii) After 15 min, the solutions were cooled simultaneously at a constant cooling rate of 5, 10 or 20 oC/h until nucleation was observed in all the solutions. The onset of nucleation and the temperature of the cooling water, shown by the cryostat display, were recorded by a video camera. The experimental setup of the determination of the MZW is illustrated in Figure 1. (iv) After the solutions crystallized, the test tubes or bottles were transferred back to the water bath where the water temperature exceeded the saturation temperature. The crystals in the solutions were dissolved completely. The procedure given by the steps (i) - (iv) were repeated for a maximum of 10 times. A total of at least 50 nucleation temperatures were recorded for each experimental condition.

After the last cooling crystallization sequence, the crystals in the solutions were dissolved completely and the concentration of the solutions determined gravimetrically. The experimental procedure of the gravimetric concentration measurements and the solubility of salicylamide in afore mentioned solvents have been reported previously (Nordström and Rasmuson, 2006). The temperature of the water bath and cryostat was controlled by a calibration mercury thermometer (Thermo-Schneider, Wertheim, Germany, accuracy of 0.01 oC).

D ___oC C

A E

Figure 1. Experimental setup of the determination of the MZW for a solution volume of 150 and 500 ml. The bottles (A) were placed on stirring plates (B) in the cryostat (C) and cooled at constant cooling rate from saturation temperature until all the solutions crystallized. The sequence was filmed by a video camera (D) and recorded by a VCR (E), which was connected to a TV monitor (F). The onset of nucleation, as given by the nucleation temperature, was determined using the recorded video tapes.

The MZW of salicylamide was also determined in jacketed glass crystallizers (SWAB, 250 ml), that were connected to a cryostat. A saturated solution of 150 ml was filtered at 0.2 µm and inserted into the crystallizer. The crystallizer was placed on top of a magnetic stirrer plate and the solution was agitated at 400 rpm using a teflon spin bar (stirrer bar dimension: 35x8 mm). The same procedure as previously outlined was employed in the glass crystallizer, except in these experiments the crystallizer solution was in half the experiments left without the crystallizer lid leaving the solution exposed to the surrounding air.

5 3. THEORY

Nucleation of the solid phase occurs when the solution is supersaturated. The window from the solubility curve to the onset of nucleation is denoted metastable zone width, MZW. The MZW is illustrated in Figure 2 for a cooling crystallization performed at constant concentration starting at the solubility curve, point 1 (T1, x1, γ1), until nucleation commences at point 2 (T3, x1, γ2).

ΔT Solubility

T ,x ,γ 3 1 2 T1,x1,γ1 2 1

Δµ

Concentration, x T3,x3,γ3 3

Temperature, T

Figure 2. Illustration of the metastable zone width during cooling crystallization.

During nucleation invoked by cooling crystallization, the MZW can be expressed in terms of degree of undercooling, ΔT:

−=Δ TTT 31 (1) or in terms of supersaturation ratio at the onset of nucleation, s:

x s = 1 (2) x3

The thermodynamic driving force at the onset of nucleation, Δµ, can be written:

⎡ x γ 21 ⎤ =Δ RTµ 3 ln⎢ ⎥ (3) ⎣ x γ 33 ⎦

6 and is often simplified to:

≈Δ 3 ln sRTµ (4) which assumes that γ2 ≈ γ3. This approximation can only be thermodynamically justified when the influence of temperature on γ is negligible, when the solution is ideal (i.e. γ is unity) or when x1 ≈ x3.

According to the classical nucleation theory, CNT, the energy barrier, ΔGcrit, in the formation of a thermodynamically stable (spherical) nucleus is related to the driving force of nucleation and the interfacial energy, γsl.

16πγ V 23 G =Δ msl (5) crit 3Δµ2 where Vm is the molecular volume of the solute. The nucleation rate, J, is within the classical nucleation theory given by an Arrhenius type of relation.

0 ⎡ Δ− Gcrit ⎤ = JJ exp⎢ ⎥ (6) ⎣ kT ⎦ where J0 is the pre-exponential factor. Several experimental factors are known to affect the MZW. Amongst the most predominant are e.g. hydrodynamic conditions (rotation speed, vessel and agitator geometry), cooling rate, solution volume, temperature and solution history. Some of these factors are introduced into the CNT through the pre-exponential factor, Jo, by different models (e.g. Zettlemoyer, 1969, Myerson and Izmailov, 1993, Mersmann, 1996, Kashchiev and Rosmalen, 2003).

7 4. RESULTS

The influence of five experimental variables on the MZW of salicylamide has been investigated in this work, viz. saturation temperature, Teq, solvent, cooling rate, -dT/dt, solution volume, Vsoln, and finally the importance of having crystallizers that are sealed (not allowing evaporation to the outside air) or open to the surrounding air (no lid on the crystallizer). The results are summarized per solvent in Table 1 through 5. The MZW is listed as the average supersaturation, savg, and average undercooling, ΔTavg. The standard deviation and the observed minimum and maximum values are given in brackets.

Table 1. MZW of salicylamide in methanol (884 nucleations). Den. Vessel type Exp. parameters MZW Teq -dT/dt Vsoln savg (std.dev.) ΔTavg (std.dev.) No of exp. {smin-smax} {ΔTmin-ΔTmax} [oC] [oC/h] [ml] [oC] A1 Sealed 50 5 15 1.42 (0.31) 11.2 (7.0) 128 test tube {1.06-2.48} {2.0-31.5} A2 Sealed 45 5 15 1.32 (0.16) 9.3 (4.5) 56 test tube {1.07-1.87} {2.4-21.7} A3 Sealed 40 5 15 1.57 (0.35) 15.1 (7.6) 56 test tube {1.13-2.50} {4.3-32.7} A4 Sealed 35 5 15 1.41 (0.26) 11.6 (6.1) 53 test tube {1.09-2.26} {3.2-29.4} A5 Sealed 30 5 15 1.38 (0.18) 11.3 (4.5) 56 test tube {1.15-2.04} {5.0-25.9} A6 Sealed 50 10 15 1.75 (0.33) 18.5 (7.0) 136 test tube {1.05-2.72} {1.5-34.9} A7 Sealed 50 20 15 1.90 (0.39) 21.4 (7.6) 126 test tube {1.12-2.79} {3.9-35.8} A8 Sealed 50 20 150 1.87 (0.33) 21.1 (6.2) 128 250 ml bottle {1.22-2.66} {6.8-34.1} A9 Sealed 50 20 500 1.96 (0.32) 22.7 (5.7) 125 500 ml bottle {1.30-2.83} {8.9-36.2} A10 Open 50 20 150 1.05 (0.01) 1.5 (0.4) 10 crystallizer {1.02-1.07} {0.7-2.1} A11 Sealed 50 20 150 1.43 (0.23) 11.9 (5.4) 10 crystallizer {1.14-1.86} {4.4-21.3}

8 Table 2. MZW of salicylamide in acetonitrile (717 nucleations). Den. Vessel type Exp. parameters MZW Teq -dT/dt Vsoln savg (std.dev.) ΔTavg (std.dev.) No of exp. {smin-smax} {ΔTmin-ΔTmax} [oC] [oC/h] [ml] [oC] B1 Sealed 50 5 15 1.42 (0.28) 9.9 (5.8) 133 test tube {1.04-2.16} {1.3-23.1} B2 Sealed 45 5 15 1.32 (0.19) 8.1 (4.0) 54 test tube {1.09-2.03} {2.6-21.1} B3 Sealed 40 5 15 1.41 (0.27) 9.7 (5.1) 55 test tube {1.11-2.26} {3.2-24.2} B4 Sealed 35 5 15 1.37 (0.26) 8.9 (5.2) 56 test tube {1.07-2.15} {1.9-22.6} B5 Sealed 30 5 15 1.28 (0.17) 7.0 (3.6) 56 test tube {1.11-1.84} {2.9-18.0} B6 Sealed 50 10 15 1.67 (0.37) 14.5 (6.9) 205 test tube {1.07-2.45} {2.0-26.8} B7 Sealed 50 20 15 1.64 (0.38) 14.2 (6.8) 138 test tube {1.10-2.49} {2.9-27.2} B8 Open 50 20 150 1.08 (0.02) 2.4 (0.5) 10 crystallizer {1.06-1.12} {1.8-3.6} B9 Sealed 50 20 150 1.36 (0.15) 9.1 (3.2) 10 crystallizer {1.19-1.60} {5.2-14.2}

Table 3. MZW of salicylamide in acetic acid (396 nucleations). Den. Vessel type Exp. parameters MZW Teq -dT/dt Vsoln savg (std.dev.) ΔTavg (std.dev.) No of exp. {smin-smax} {ΔTmin-ΔTmax} [oC] [oC/h] [ml] [oC] C1 Sealed 50 5 15 1.76 (0.43) 23.4 (10.7) 110 test tube {1.08-2.97} {3.4-47.4} C2 Sealed 45 5 15 1.79 (0.38) 24.4 (9.3) 84 test tube {1.17-2.62} {6.9-41.7} C3 Sealed 50 10 15 2.23 (0.43) 34.0 (8.6) 70 test tube {1.25-3.13} {9.7-49.6} C4 Sealed 50 20 15 2.32 (0.41) 35.9 (8.1) 112 test tube {1.29-3.12} {11.1-49.5} C5 Open 50 20 150 1.38 (0.18) 13.7 (5.4) 10 crystallizer {1.17-1.70} {7.1-23.1} C6 Sealed 50 20 150 1.62 (0.22) 20.8 (5.2) 10 crystallizer {1.41-2.18} {14.9-34.0}

9 Table 4. MZW of salicylamide in acetone (423 nucleations). Den. Vessel type Exp. parameters MZW Teq -dT/dt Vsoln savg (std.dev.) ΔTavg (std.dev.) No of exp. {smin-smax} {ΔTmin-ΔTmax} [oC] [oC/h] [ml] [oC] D1 Sealed 50 5 15 1.24 (0.13) 12.4 (5.9) 70 test tube {1.06-1.67} {3.6-29.7} D2 Sealed 45 5 15 1.32 (0.15) 15.7 (6.5) 70 test tube {1.06-1.74} {3.7-31.9} D3 Sealed 40 5 15 1.42 (0.16) 20.0 (6.7) 51 test tube {1.10-1.72} {5.6-31.0} D4 Sealed 35 5 15 1.38 (0.23) 17.7 (9.1) 54 test tube {1.07-1.81} {3.8-33.9} D5 Sealed 50 10 15 1.40 (0.22) 18.9 (8.9) 71 test tube {1.08-1.83} {4.7-34.9} D6 Sealed 50 20 15 1.43 (0.17) 20.6 (7.0) 87 test tube {1.12-1.73} {6.7-31.7} D7 Open 50 20 150 1.15 (0.05) 8.0 (2.3) 10 crystallizer {1.08-1.24} {4.6-12.4} D8 Sealed 50 20 150 1.19 (0.04) 10.4 (2.0) 10 crystallizer {1.14-1.27} {7.9-14.1}

Table 5. MZW of salicylamide in ethyl acetate (491 nucleations). Den. Vessel type Exp. parameters MZW Teq -dT/dt Vsoln savg (std.dev.) ΔTavg (std.dev.) No of exp. {smin-smax} {ΔTmin-ΔTmax} [oC] [oC/h] [ml] [oC] E1 Sealed 50 5 15 1.47 (0.21) 17.6 (6.7) 126 test tube {1.09-2.03} {3.8-33.6} E2 Sealed 45 5 15 1.60 (0.29) 21.5 (8.5) 65 test tube {1.17-2.41} {7.2-42.3} E3 Sealed 50 10 15 1.75 (0.28) 25.8 (7.6) 140 test tube {1.18-2.44} {7.7-42.7} E4 Sealed 50 20 15 1.67 (0.30) 23.5 (8.5) 140 test tube {1.13-2.57} {5.7-45.1} E5 Open 50 20 150 1.40 (0.19) 15.6 (6.2) 10 crystallizer {1.18-1.72} {7.9-25.6} E6 Sealed 50 20 150 1.48 (0.19) 18.0 (6.4) 10 crystallizer {1.13-1.78} {5.9-27.2}

The MZW of salicylamide was determined under reproducible experimental conditions. For the same experimental parameters, saturated solutions were prepared in vessels having identical geometry. The dimensions of the magnetic stirring bars were unchanged and the solutions were agitated with a constant rotation speed throughout all experiments. No systematic deviations were observed between different mother liquors or between solutions in different test tubes, bottles or crystallizers. The onset of nucleation of salicylamide was observed as a rapid transformation

10 from a transparent solution into a white suspension and the temperature at which crystals first appeared in the solutions was determined with an estimated accuracy of ± 0.1 oC. The only factor that resulted in systematic deviations in the MZW of salicylamide under identical experimental conditions was solution history. Solutions kept undersaturated for e.g. only 15 min yielded a systematic reduction in the undercooling temperature, ΔT, at the onset of nucleation during consecutive cooling crystallizations. This effect disappeared if the solutions were kept in an undersaturated state for at least one hour. In this study, undersaturated solutions were stored for at least three hours.

No polymorphs or solvates of salicylamide are known other than a monoclinic unsolvated structure, reported by Sasada et al., 1964, and Pertlik, 1990. Previous cooling crystallization experiments with a cooling rate up to 60 oC/h revealed no new crystalline phases, as observed by Differential Scanning Calorimetry, DSC, Fourier Transform Infrared with an Attenuated Total Reflectance, FTIR-ATR, Hot Stage and Photo Microscopy and an extensive solubility study (Nordström and Rasmuson, 2006).

11 5. EVALUATION AND DISCUSSION

5.1. MZW and saturation temperature

The influence of the saturation temperature, Teq, on the MZW of salicylamide was small for all solvents. Similar savg was observed for measurements of the MZW at saturation temperatures between 30 to 50 oC for the same solvent. The range in the MZW region from minimum to maximum observed onset of nucleation was also seen to be essentially unaffected by different saturation temperatures. The MZW of salicylamide in acetone is presented in Figure 3 at four different saturation temperatures.

0.22

0.2

0.18

0.16

0.14

0.12

Concentration [mol/mol]

0.1 0 1020304050 Temperature [oC]

o o Figure 3. MZW of salicylamide in acetone between 35 to 50 C (Vsoln = 15ml, -dT/dt = 5 C/h). The dashed curve depicts the solubility of salicylamide in acetone and the triangles represent the averaged values.

The only plausible effect of the saturation temperature on the MZW that can be interpreted from these results is found in the distribution of the data. At very low supersaturation (s < 1.1) nucleation occurred more frequently at higher saturation temperatures, rather than the opposite, for all solvents. This effect can possibly be explained with the CNT, which states that the critical free energy of a nucleus decreases with higher temperature (see Eq. 5).

12 5.2. MZW and cooling rate In the literature, it is often found that log(ΔT) is linearly related to log(-dT/dt) (Nyvlt, 1983, Mullin, 2001, Kubota, 2008), from which the apparent nucleation order can be calculated from the method proposed by e.g. Nyvlt, 1968. In Figure 4 is shown the relation between log(ΔTavg) and log(-dT/dt) for the MZW of salicylamide in five solvents.

1.6

1.5

1.4

)

avg 1.3

T Δ 1.2

log( 1.1

1.0

0.9 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 log(-dT/dt)

Figure 4. Relationship between undercooling at the average onset of nucleation (ΔTavg) and cooling rate (-dT/dt), in methanol; ◊, acetonitrile; □, acetic acid; Δ, acetone; O, and ethyl o acetate; X (Vsoln = 15 ml, Teq = 50 C).

As seen in Figure 4, a higher cooling rate typically increases the degree of undercooling at the average onset of nucleation, as can be expected. This effect is particularly dominant between a cooling rate of 5 and 10 oC/h but is reduced between 10 and 20 oC/h. The relation between log(ΔTavg) and log(-dT/dt) is however rather weak in all solvents. An equally poor correlation is obtained when using the value of undercooling at the maximum observed onset of nucleation irrespective of solvents. As a result, it is difficult to acquire any reliable information concerning the apparent nucleation order of salicylamide. The influence of the cooling rate on the MZW is instead seen to be secondary to the significant variation in the MZW.

5.3. MZW and the role of the solvent The solvent exerts a comparably strong effect on the MZW of salicylamide, which was observed in the average onset of nucleation and in the variation in the onset of nucleation. The supersaturation ratio at the average onset of nucleation ranged from 1.24 in solutions of acetone o o up to 1.76 in solutions of acetic acid (Vsoln = 15 ml, Teq = 50 C and -dT/dt = of 5 C/h). This difference in supersaturation ratio corresponds to a driving force of 0.54 and 1.32 kJ/mol in

13 solutions of acetonitrile and acetic acid, respectively. Although errors are introduced in the equation of Δµ by not accounting for the ratio of the activity coefficient (Eq. 3 and 4), it appears that the driving force at the average onset of nucleation of salicylamide is not independent of the solvent. Experiments repeated during identical experimental conditions resulted in a greater distribution in the MZW in solvents where the supersaturation ratio at the average onset of nucleation was greater. The MZW in different solvents is presented in Figure 5 as cumulated distributions.

100%

50%

Cumulated MZW distribution 0%

11.522.53

Supersaturation ratio

o o Figure 5. Cumulated MZW of salicylamide (Vsoln = 15 ml, Teq = 50 C and -dT/dt = of 5 C/h), in solutions of methanol (A1); ◊, acetonitrile (B1); □, acetic acid (C1); Δ, acetone (D1); O, and ethyl acetate (E1); X.

Within series of experiments performed in the same solvent and during identical experimental conditions, the onset of nucleation ranged from a supersaturation ratio of 1.08 to 2.97 in solutions o of acetic acid and from 1.06 and 1.67 in solutions of acetone (Vsoln = 15 ml, Teq = 50 C and - dT/dt = 5 oC/h). These differences in supersaturation ratio at the onset of nucleation correspond to a driving force between 0.20 and 2.50 kJ/mol in acetic acid and between 0.16 and 1.25 kJ/mol in acetone. The dominating factors responsible for differences in nucleation kinetics in different solvents are according to the CNT the driving force and the interfacial energy between the crystal and the solution (Eq. 5). The observed variation in the onset of nucleation of salicylamide between repeated experiments in solutions of acetic acid thus implies that the critical free energy varies by a factor of approximately 150, if the interfacial energy can be assumed constant with temperature.

Due to difficulties in experimentally quantifying the interfacial energy, the influence of the solvent on nucleation is often related to other more experimentally accessible parameters. The

14 interfacial energy between the crystal surface and the solution has in the literature been related to the solubility and enthalpy of solution (Nielsen and Söhnel, 1971; Mersmann, 1990; Bennema and Söhnel, 1990). Furthermore, bond energies at the surface of crystals have been related to bond energies in the bulk, often within the context of the so-called equivalent wetting condition (Liu and Bennema, 1993). Another property to which nucleation kinetics has been related is viscosity. In nucleation from melts a decrease in nucleation rate has been observed above a certain degree of supercooling, which was believed to originate from an increase in viscosity (Mullin, 2001). In these cases an optimum supersaturation ratio is present at which the nucleation rate is at a maximum, and excessive supercooling beyond this point reduces the rate of nucleation. This behavior has not only been confined to melts as it also has been observed in viscous supersaturated solutions of citric acid (Mullin, 2001) and in protein crystallization of lysozyme (Pan et al., 2005).

In the present study, no clear correlation could be established between the supersaturation ratio or driving force at the average onset of nucleation and the solubility or enthalpy of solution. Nor did a clear relation appear to physicochemical properties of the solvent such as boiling point, polarity, viscosity, density, molecular weight or pH. However, a comparably stronger correlation emerges when the viscosity of the solvent is divided by the solubility of the solute (in terms of moles solute per unit volume), as depicted in Figure 6.

2.4

2.2

2.0

1.8

1.6

1.4

Supersaturation ratio 1.2

1.0 0.00.10.20.30.40.50.60.7 η/C [Pa·s·m3·mol-1] m Figure 6. Relationship between the supersaturation ratio at the average onset of nucleation and 3 solvent viscosity divided by the solubility (moles salicylamide per m ) in five solvent (Vsoln = 15 o o o o ml, Teq = 50 C), at a cooling rate of 5 C/h (white diamonds), 10 C /h (grey squares) and 20 C /h (black triangles). The error bars represent 95 % confidence limits of the supersaturation ratio at the average onset of nucleation. Solvent viscosity from Xiang et al., 2006, Nikam et al., 1998, Narayan et al., 1988, Moreno et al., 2001, Hazra and Venkateswarlum, 1978, and Bleazard et al., 1996.

As shown in Figure 6, a linear relationship emerges at all cooling rates between the supersaturation ratio and the ratio between the solvent viscosity, η, and concentration, Cm (given as moles solute per unit volume). The reciprocal of viscosity is proportional to the diffusivity via the Stokes-Einstein equation and hence to the molecular mobility in the solution. The trends shown in Figure 6 therefore indicate that the onset of nucleation of salicylamide is facilitated by a greater molecular mobility (lower viscosity) and a higher concentration of solute molecules in the solution. It can be expected that a greater number of solute molecules per unit volume capable of migrating more rapidly in the solution corresponds to a greater collision frequency of the solute molecules.

5.4. MZW and the influence of the solution volume The effect of the solution volume on the MZW of salicylamide was investigated in methanol (A7- A9 in Table 1) at three different solution volumes, viz. 15, 150 and 500 ml. The average onset of nucleation was essentially unaffected by the solution volume. Although the variation in the MZW decreased slightly with increasing solution volume, the decrease is not statistically significant. The lack of influence of solution volume on the average onset of nucleation of salicylamide

16 agrees with the expected nucleation mechanism stemming from a collision frequency of solute molecules per unit volume, which is an intensive parameter. In Figure 7 is depicted the influence of solution volume on the MZW of salicylamide in methanol solutions at a cooling rate of 20 oC/h.

20%

15%

10% Frequency [%] Frequency 5%

0% 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 Supersaturation

o Figure 7. MZW distribution histogram of salicylamide in methanol (Teq = 50 C, -dT/dt = 20 oC/h) at 15 ml; black (A7), 150 ml; grey (A8) and 500 ml; white (A9).

5.5. MZW and the design of the crystallizer and importance of solvent evaporation Crystallizers and impellers of different type and dimension may, sometimes considerably, influence the crystallization kinetics (Mullin, 2001). To explore the importance of the vessel on the MZW of salicylamide, additional nucleation experiments were conducted in 250 ml jacketed crystallizers. The nucleation experiments in methanol at 150 ml show that the MZW of salicylamide is indeed affected by replacing the 250 ml bottles with 250 ml crystallizers. The MZW of salicylamide in methanol in the 250 ml crystallizers amounted to savg = 1.43 ± 0.14 (A11), compared to savg = 1.87 ± 0.06 (A8) in 250 ml bottles. Although only 10 experiments were repeated in the crystallizers, the difference is sufficiently significant not be disregarded as merely a statistical artifact. As the cooling crystallizations were performed using identical experimental conditions, i.e. constant cooling rate, saturation temperature, solution volume, stirring rate, the difference in MZW can only be attributed to the design of the vessel.

17 Measurements of the MZW were also conducted in crystallizers where the solution was exposed to the surrounding air (using no crystallizer lid), as opposed to the standard procedure in this work where evaporation of the solution to the outside air was prevented by using airtight lids. The results reveal a sometimes dramatic change in the average MZW, as well as, in the distribution. The influence on the MZW differs for different solvents. The savg decreases from 1.43 (A11) to 1.05 (A10) in methanol, and from 1.36 (B9) to 1.08 (B8) in acetonitrile upon removing the lid to the crystallizer. The associated variation in the MZW also decreases from a standard deviation in savg from 0.23 to 0.01 in methanol, and from 0.15 down to 0.02 in acetonitrile. Thus, a significantly increased repeatability is obtained in the observed onset of nucleation in these solutions. The corresponding behavior in acetic acid, acetone and ethyl acetate is not as notable. Although savg decreases to some extent in experiments when the crystallizer lid is removed, the difference in the variation of MZW is not significant. The results from the nucleation experiments in 250 ml jacketed crystallizers (open and closed) are shown in Figure 8.

2.4

2.2 o 2.0 rati n

o 1.8

1.6

persaturati 1.4

Su Supersaturation ratio 1.2

1.0

Acetone Acetone Methanol Methanol Acetic acid Acetic Acetic acid Acetic Acetonitrile Acetonitrile Ethyl acetateEthyl acetateEthyl Figure 8. MZW of salicylamide in open (O) and closed (X) crystallizers at a cooling rate of 20 oC/h in methanol (A10, A11), acetonitrile (B8, B9), acetic acid (C5, C6), acetone (D7, D8) and ethyl acetate (E5, E6).

The significant difference in the onset of nucleation of salicylamide in solutions of methanol and acetonitrile between crystallizers having a lid or no lid suggests that evaporation of the solution may influence the nucleation kinetics. With a continuous evaporation of the solvent from the surface of the solution follows an increasing concentration in the bulk, as well as, the emergence

18 of a concentration gradient in the solution, which is particularly predominant at the surface of the solution. The presence of local regions of increased supersaturation facilitates the onset of nucleation and may explain both the observed decrease in the MZW in solutions of methanol and acetonitrile and the substantial reduction in the variation of MZW. However, the absence of a significant difference in the MZW between open and closed crystallizers in acetic acid, acetone and ethyl acetate contradicts the role of evaporation as the sole catalyst for an expedited nucleation process. The nucleation process of salicylamide in acetone, which exhibits the lowest boiling point and highest volatility of the investigated solvents, should in that case be substantially facilitated by evaporation to the surrounding air, which was not observed. The reduction in the MZW in solutions of methanol and acetonitrile in open crystallizers is likely an effect of a different nucleation mechanism. The onset of nucleation in methanol and acetonitrile in open crystallizers was always preceded by a thin layer of crystals formed at the glass wall adjacent to the solution surface, where the crystal layer was in contact with the solution. This process was never observed for sealed crystallizers or in the other solvents.

5.6. Distribution in the MZW The onset of nucleation of salicylamide is more or less confined to a certain supersaturation region (smin to smax), which is related to the solvent and the experimental conditions. Within that region, a Gaussian distribution with supersaturation was normally obtained in all solvents (as e.g. seen in Figure 7), and hence the supersaturation ratio at the average onset of nucleation corresponds approximately to the supersaturation ratio having the most frequent nucleation events. An analysis of the variation in the MZW of salicylamide shows that the variation is related to the associated average value in the MZW, where the slope of the trend line corresponds to the coefficient of variation (given as 100·std.dev./(savg-1)), and equals 43.8. In Figure 9 is plotted the standard deviation in savg versus savg for all data in Table 1 through 5.

0.7

avg 0.6

0.5

0.4

0.3

0.2

0.1

in s Standard deviation 0.0 1.01.21.41.61.82.02.22.4 savg

Figure 9. Relation between the standard deviation and supersaturation at the average onset of nucleation in solutions of methanol; ◊, acetonitrile; □, acetic acid; Δ, acetone; O, and ethyl acetate; X. Data from all experimental conditions (Table 1-5).

By selecting experimental conditions that increases the width of the metastable zone, e.g. using a substantially higher cooling rate, we may also expect a greater spread in the onset of nucleation. As seen in Figure 9, all the data appear more or less on the same trend line, regardless of solvent and experimental condition. Should the variation in the MZW of salicylamide be representative for organic compounds in general, then it is of utmost importance that studies of the kinetics of nucleation are reproduced. Failure to repeat nucleation experiments may give rise to substantial errors and unexpected, as well as, unwanted crystallization behaviors.

20 6. CONCLUSIONS The metastable zone width of salicylamide at constant cooling rate is weakly related to saturation temperature and solution volume, while cooling rate and solvent exert a stronger influence on the width of the metastable zone. The influence of the solvent on the onset of nucleation of salicylamide appears to be linked to the ratio between the viscosity of the solvent and the concentration of the solute. The trends suggest that a greater molecular mobility and a greater concentration of solute molecules in the solution reduce the metastable zone width of salicylamide. The metastable zone width decreased, sometimes dramatically, in crystallizers where the solvent was allowed to evaporate during the cooling crystallization as opposed to when the crystallizer was sealed. The onset of nucleation of salicylamide varied significantly between reproducibly conducted experiments. The variation in the metastable zone width was for the most part Gaussian distributed with supersaturation and proportional to the supersaturation corresponding to the average onset of nucleation (coefficient of variation = 43.8). It is shown that measurement of the metastable zone width must be repeated to ensure that data of nucleation kinetics are properly captured.

21 REFERENCES

Izmailov, A.F.; Myerson, A.S.; Arnold, S., 1999, A statistical understanding of nucleation, J. Cryst. Growth, 196, 234-242.

Sasada, Y.; Takano, T.; Kakudo, M., 1964, Crystal structure of salicylamide, Bull. Chem. Soc. Jpn. 37, 940-946.

Pertlik, F., 1990, Crystal structure and hydrogen bonding schemes in four benzamide derivatives (-hydroxy-benzamide, 2-hydroxy-thiobenzamide, 2-hydroxy-N,N-dimethyl-benzamide and 2- hydroxy-N,N-dimethyl-thiobenzamide), Monatsh. Chem. 121, 129-139.

Nordström, F.L.; Rasmuson, Å.C., 2006, Solubility and melting properties of salicylamide, J. Chem. Eng. Data 51, 1775-1777.

Zettlemoyer, A.C., 1969, Nucleation, Marcel Dekker, New York, p 225-327.

Myerson, A.S.; Izmailov, A.F., 1993, The structure of supersaturated solutions, in Handbook of crystal growth, vol. 1a (editor: Hurle, D.T.J.), North-Holland, Amsterdam, p 249-306.

Mersmann, A., 1996, Supersaturation and nucleation, Trans IChemE, 74(A7), 812-820.

Kashchiev, D.; Rosmalen, G.M., 2003, Review: Nucleation in solutions revisited, Cryst. Res. Techn. 38, 7-8, 555-574.

Nyvlt, J., 1983, Induction period of nucleation and metastable zone width, Collections of the Czechoslovak Chem. Comm., 48, 1977-1983.

Kubota, N., 2008, A new interpretation of metastable zone widths measured for unseeded solutions, J. Cryst. Growth, 310, 629-634.

Nyvlt, J., 1968, Kinetics of crystallization in solution, J. Cryst. Growth, 3-4, 377-383.

Nielsen, A.E.; Sohnel, O., 1971, Interfacial tensions, electrolyte crystal-aqueous solution, from nucleation data, J. Cryst. growth, 11, 233-242.

Mersmann, A., 1990, Calculations of interfacial tensions, J. Cryst. Growth 102, 841-847.

Bennema, P.; Söhnel, O., 1990, Interfacial surface tension for crystallization and precipitation from aqueous solutions, J. Cryst. Growth 102, 547-556.

Liu, W-Y.; Bennema, P., 1993, The relation between macroscopic quantities and the solid-fluid interfacial structure, J. Chem. Phys., 98(7), 5863-5872.

Mullin, J.W., 2001, Crystallization, 4th ed., Butterworth-Heinemann, Oxford.

Pan, W.; Kolomeisky, A. B.; Vekilov, P. G., 2005, Nucleation of ordered solid phases of proteins via a disordered high-density state: Phenomenological approach, J. Chem. Phys., 122, 174905.

Xiang, H.W.; Laesecke, A.; Huber, M.L., 2006, A new reference correlation for the viscosity of methanol, J. Phys. Chem. Ref. Data 35(4), 1597-1620.

Nikam, P.D.; Mahale, T.R.; Hasan, M., 1998, Densities and viscosities for ethyl acetate+pentan- 1-ol, +hexan-1-ol, +3,5,5-tromethylhexan-1-ol, +heptan-1-ol, +octan-1-ol, and +decan-1-ol at (298.15, 303.15 and 308.15) K, J. Chem. Eng. Data 43, 436-440.

Narayan, J.; Wanchoo, R.K.; Raina, G.K.; Wani, G.A., 1988, Viscosity and surface tension of p- xylene-ethyl acetate liquid mixtures, Can. J. Chem. Eng. 66, 1021-1026.

Moreno, R.; Camacho, A.; Olea, P.; Canzonieri, S.; Postigo, M., 2001, Estudio volumetrico y viscoso del sistima acetato de etilo +n-propanol en funcion de la temperatura, Rev. Bol. Quim. 18(1), 79-84.

Hazra, S.K.; Venkateswarlu, C., 1978, The viscosity of binary mixture acetone(1)-water(2) system, Chem. Petro-Chem. J. 9(3), 29-34.

Bleazard, J.G.; Sun, T.F.; Teja, A.S., 1996, The thermal conductivity and viscosity of acetic acid- water mixtures, Int. J. Thermophys. 17(1), 111-125.

23 (2/1) p-Aminobenzoic Acid-Acetone Solvate Crystal data: C17H20N2O5, Mr=332.36, Crystal dimensions 3 Baroz Aziz,a Fredrik Nordstroma* and Andreas 0.3×0.3×0.3 mm . space group P1bar, a=5.0400(8)Å, b b=8.2978(12)Å, c=20.447(5)Å, α=88.67(2)º, β=83.165(14) º, Fischer 3 -3 – γ=84.50(2) º, V=845.1(3) Å , Z=2, ρcalc.=1.306 Mg⋅m , μ=0.10 mm 1 a . Dept. of Chemical Engineering and technology, Royal Data collection: Bruker-Nonius KappaCCD diffactometer, Institute of technology, Stockholm, Sweden, and bInorganic MoKα radiation, graphite monochromator, φ & ω scans, 11345 Chemistry, Royal Institute of technology, Stockholm, Sweden. reflections, 2923 unique reflections, R =0.13, 1464 reflections with E-mail: [email protected] int I>2σ(I).

A solvate of p-aminobenzoic acid has been obtained from acetone. The crystal structure of the acetone solvate has been Refinement: A structure model could be obtained using direct methods (SHELXS-97). The structure was refined on F2 with determined using single-crystal x-ray diffraction at 150 K. The anisotropic displacement parameters for all non-H atoms (SHELXL- solvate crystallizes in the triclinic crystal system with one acetone 97). 221 L.S. parameters. R =0.054, wR =0.133, S=0.97, residual molecule and two p-aminobenzoic acid molecules in the asymmetric 1 2 electron density (peak/hole): 0.23/–0.23. unit (C H N O , Z=2, space group P1bar, a=5.0400 (8)Å, 17 20 2 5 Crystallographic data (excluding structure factors) for the b=8.2978 (12)Å, c=20.447 (5)Å, α=88.67 (2)°, β=83.165 structure(s) reported in this paper have been deposited with the (14) °, γ=84.50 (2) °). The structure features N–H···N, N–H···O Cambridge Crystallographic Data Centre as supplementary and O–H···O hydrogen bonding. The solubility of the solvated publication no. CCDC 634098. Copies of the data can be obtained structure has been determined in acetone between 5 and 50 oC. DSC free of charge on application to CCDC, 12 Union Road, Cambridge and microscopy studies suggest transformation/desolvation into the CB2 1EZ, UK (fax: (44) 1223 336-033; e-mail: α-polymorph at elevated temperatures and once brought from [email protected]). solution.

2.3. Solubility Keywords: p-aminobenzoic acid; solvate; adducts; complex; solubility The solubility of p-aminobenzoic acid was determined gravimetrically between 5 and 50 oC in 5 oC increments. The 1. Introduction temperature was controlled by a thermostat and the true temperature was validated by a calibration mercury thermometer (Thermo- p-aminobenzoic acid is a known enantiotropic polymorphic Schneider, Wertheim, Germany, accuracy of 0.01ºC). Saturated compound. Two crystal structures have previously been reported, solutions were prepared in 250 ml bottles and cooled at 1 K/min named the α- and β-modification. The crystal structure of the α- until crystallization. The time to reach equilibration was determined polymorph has been resolved by Killean et al. (1965) and Lai & by concentration measurements conducted from 30 min up to 24 Marsh (1967), while the crystal structure of the β-polymorph has hours. Based on the concentration-time study, the suspensions were been determined by Alleaume & Salas-Ciminago (1966) and equilibrated under agitation by a magnetic teflon stirrer for at least recently refined by Gracin & Fischer (2005). p-aminobenzoic acid one hour before retrieving samples. The suspensions were left has previously been reported by Kuhnert-Brandstaetter & Grimm without agitation until complete sedimentation of crystals. Preheated (1969) to form a solvate in acetone. However, the crystal structure of syringes and needles were used to sample 3-6 ml of the (clear) this expected solvate was never resolved. solution into pre-weighed glass vials. The weight of the empty vials, In the present paper, the crystal structure of the p-aminobenzoic the saturated clear solution and the final dry desolvated residue after acid acetone solvate is reported with solubility data in acetone, evaporation of the acetone was recorded. The weight of the residue crystal morphology and Differential Scanning Calorimetry (DSC) was recorded continuously until complete dryness and complete analysis. desolvation was achieved.

2. Experimental 2.4. Differential Scanning Calorimetry (DSC)

2.1. Material Crystal samples of p-aminobenzoic acid-acetone solvate were analyzed using a DSC-2920, TA Instruments. The calorimeter was p-aminobenzoic acid (CAS 150-13-0) was purchased from calibrated against the melting temperature and melting enthalpy of Sigma-Aldrich (purity > 99 %) and used as obtained. The Indium at a nitrogen flow of 50 ml/min. Samples (5-10 mg) were commercially available p-aminobenzoic acid corresponds to the α- heated at 5 K/min from 20 oC to 200 oC in hermetic Al-pans while polymorph. Acetone was purchased from VWR (Pro Analysi) being purged with nitrogen. having a purity of > 99.8 %. 2.5. Photo Microscopy

2.2. Crystal Structure Determination Microscopy studies were performed using an Olympus SZX12 photo microscope. Crystals were obtained from supersaturated Saturated solutions of p-aminobenzoic acid and acetone were solutions in acetone through evaporation crystallization at ambient prepared at room temperature and filtered (0.2µm, PTFE) into glass temperature (approximately 20 oC). Crystals were placed in an open containers. Crystals were obtained through evaporation container and let to desolvate over time. o crystallization at ambient temperature (20 C). The formed crystals were kept in a saturated solution and in a sealed vessel to prevent desolvation. A selected crystal was transferred immediately to the cold N2 flow (150 K) of the diffractometer. 3. Results and Discussion dimers and the acetone molecules are stacked in layers down the crystallographic a-axis. This continuous repetition forms channels of Two p-aminobenzoicacid molecules are incorporated in the acetone molecules in the crystallographic a-direction. The rapid crystal lattice for each acetone molecule. There are two molecules of desolvation process, observed in Fig. 4, may thus be expected to p-aminobenzoic acid and one acetone molecule in the asymmetric originate from the appearance of these channels in conjunction with unit. Each of the p-aminobenzoic acid molecules forms a a comparably weak bonding between the acetone oxygen and the p- centrosymmetric dimer about an inversion center (Fig. 1 and 2). The aminobenzoic acid amino group. bonding between the two molecules in each dimer is achieved by O– H···O bonding between the two carboxy group, which leads to closed loops. The acceptor-O atoms of molecule 1 are involved in an N– 4. Conclusions H···O bond with molecule 2 as donor. The acetone molecule is The solvate crystallizes in the triclinic crystal system in which attached to molecule 1 via an N–H···O bond. Even the N2 atom in two p-aminobenzoic acid molecules are present in the crystal molecule 2 acts as both hydrogen bond donor (N–H···N and N– structure for each acetone molecule. The two molecules in the H···O) and acceptor towards adjacent molecules. Details about the asymmetric unit each form a centrosymmetric dimer about an H-bond geometry can be found in Table 1. inversion center. The stability of the solvate exceeds the stability of The solubility of the solvate between 5 to 50 oC is presented in the unsolvated α- and β-polymorphs between 5 to 50 oC. The p- Table 2. The solubility of the unsolvated polymorphic structures of aminobenzoic acid-acetone solvate likely transforms into the α- p-aminobenzoic acid could not be estimated in acetone as the solvate modification at elevated temperatures. exhibits a lower solubility than the unsolvated polymorphic structures and causes rapid phase conversions into the solvate upon contact with acetone over the entire investigated temperature interval. Thus, the stability of the solvated structure exceeds the stability of the corresponding unsolvated polymorphs (α and β) in the investigated temperature interval. The structurally similar compound p-hydroxybenzoic acid has also been reported by Heath et al. (1992) to form a (2/1) solvate in acetone. This solvated structure displays a similar stability relationship between the solvate and ansolvate according to Nordstrom & Rasmuson (2006), albeit with a conjectured stability transition located at approximately 50 oC. Similar to the structure of p-aminobenzoic acid-acetone solvate, the p-hydroxybenzoic acid- acetone solvate forms dimers between the p-hydroxybenzoic acid molecules through O-H···O H bonds. Moreover, both the p- aminobenzoic acid and p-hydroxybenzoic acid molecules link to the acetone molecule via hydrogen bonding through the para-substituted amino and hydroxy group, respectively. DSC analyses of the p-aminobenzoic acid-acetone solvate revealed an endothermic transition or desolvation typically located between 70 to 80 oC at a heating rate of 5 oC/min. The transformation enthalpy amounts to approximately 90 J/g solvate. The melting temperature was approximately 187 oC, which by Gracin & Rasmuson (2004) corresponds to the melting temperature of the α-polymorph. A DSC thermogram of the p-aminobenzoic acid-acetone solvate is given in Fig. 3. The similar melting Figure 1 temperature signifies a desolvation or transformation of the p- aminobenzoic acid-solvate at elevated temperature into the α- The hydrogen bonding pattern of molecule 1. Molecules in the asymmetric unit with transparent atoms. polymorph. The transformation into the expected α-form is likely inherent in the structural similarity between the solvate and the α- polymorph, as well as, in the higher stability of the α-form over the β-format elevated temperature. Both the solvate and α-modification are based on dimers in which the carboxy groups of p-aminobenzoic acid molecules are linked together via hydrogen bonds. The β- polymorph on the other hand, links the carboxy group to the amino group, thus exemplifying a distinctly different structure. Crystals of p-aminobenzoic acid-acetone solvate were obtained in the shape of tetragonal prisms, often elongated into needles. The crystals desolvated rapidly after being brought from solution. This process took place within a few minutes when the crystals were exposed to the atmosphere. The desolvation process of a p- aminobenzoic acid-acetone solvate crystal is depicted in Fig. 4. The acetone molecule is incorporated into the crystal lattice via one hydrogen bond from the oxygen to the amino group of the p- aminobenzoic acid molecule. Pairs of p-aminobenzoic acid molecules are linked together in dimers, through 2 O-H···O H bonds arranged about a center of symmetry. The p-aminobenzoic acid

Figure 4

Desolvation process of p-aminobenzoic acid-acetone solvate crystal, magnified 90 times. The images were captured with approximately 20 s Figure 2 intervals starting where all the free acetone just evaporated from the surface The hydrogen bonding pattern of molecule 2. Molecules in the asymmetric of the crystal. unit with transparent atoms.

Table 1 H bond geometry.

D—H···A D—H H···A D···A D—H···A N1—H11N···O5 0.93 2.19 3.068 (3) 156 N1—H12N···N2 0.88 2.45 3.221 (3) 144 i N2—H21N···O1 0.91 2.15 3.069 (3) 171 ii N2—H22N···N1 0.96 2.36 3.310 (4) 165 iii O2—H2O···O1 0.84 1.80 2.643 (3) 177 iv O4—H4O···O3 0.84 1.79 2.636 (3) 174 Symmetry codes: (i) x-1, y-1, z; (ii) x-1, y, z; (iii) -x+3, -y+2, -z; (iv) -x+1, -y, -z+1.

Table 2

Solubility of p-aminobenzoic acid-acetone solvate in acetone (in moles unsolvated p-aminobenzoic acid per moles total), based on four solubility Figure 3 measurements at each temperature.

DSC thermogram of p-aminobenzoic acid-acetone solvate at a heating rate of Temperature Mole fraction solubility 103·Standard deviation 5 oC/min. [oC] [mol·mol-1] [mol/mol] 5 0.0446 0.703 10 0.0515 0.735 15 0.0575 0.176 20 0.0644 0.122 25 0.0722 0.112 30 0.0811 0.169 35 0.0918 0.216 40 0.0960 0.215 45 0.1166 0.207 50 0.1314 0.279

The authors acknowledge the Swedish Research Council for financial support.

References Alleaume, M. & Salas-Ciminago, G. (1966) Decap, J, Compt. Rend. Ser. C. 262(5), 416-417. Gracin, S. & Fischer, A. (2005) Acta Cryst. E61, 1242-1244. Gracin, S. & Rasmuson, A. C. (2004) Cryst. Growth Des. 4(5), 1013-1023. Heath, E. A., Singh, P. & Ebisuzaki, Y. (1992) Acta Cryst. C48, 1960-1965. Killean, R. C. G., Tollin, P., Watson, D. G. & Young, D. W. (1965) Acta Cryst. 19, 482-483. Kuhnert-Brandstaetter, M. & Grimm, H. (1969) Mikrochim. Acta 57(6), 1208-1209. Lai, T. F. & Marsh, R. E. (1967) Acta Cryst. 22(6), 885-893. Nordstrom, F. L. & Rasmuson, A. C. (2006) J. Pharm. Sci. 95(4), 748-760.

(2/1) p-Hydroxybenzoic acid-1,4-Dioxane Solvate

Andreas Fischera and Fredrik Nordströmb

aDepartment of Inorganic Chemistry, Royal Institute of Technology, 100 44 Stockholm, Sweden. bDepartment of Chemical Engineering and Technology, Royal Institute of Technology, 100 44 Stockholm, Sweden

Correspondence e-mail: [email protected]

Abstract A 2/1 solvate of p-hydroxybenzoic acid has been obtained from 1,4-dioxane, C7H6O3.0.5(C4H8O2). The compound crystallizes in the monoclinic crystal system (space group P21/n) with one p-hydroxybenzoic acid molecule and one 1,4-dioxane molecule in the asymmetric unit. The structure displays O-H···O hydrogen bonding between the carboxyl groups of p-hydroxybenzoic acid molecules, and O-H···O hydrogen bonding between the hydroxy groups of the p-hydroxybenzoic acid molecules and the O-atoms of the 1,4-dioxane molecules.

Experimental p-Hydroxybenzoic acid (CAS 99-96-7) was purchased from Sigma-Aldrich and used as obtained (purity > 99 %). 1,4-Dioxane was purchased from Merck/VWR (CAS 123-91-1) having a purity of > 99.5 %.

Crystals of p-hydroxybenzoic acid-1,4-dioxane solvate were obtained through slow evaporation crystallization from supersaturated solutions of 1,4-dioxane at ambient temperature (approximately 20 oC). The crystals were kept in the solution to avoid desolvation. A single crystal was then transferred directly to the diffractometer and cooled down to approximately 170 K using the cold N2 flow.

Crystal data:

C7H6H O3·0.5(C4H8H O2), Mr=182.18, Crystal dimensions 0.33 × 0.18 × 0.14 mm, monoclinic, space group P21/n, a=7.3127 (6) Å, b=5.7623 (3) Å, c=20.316 (2) Å, β = 3 -3 –1 93.359 (7)°, V=854.60 (11) Å , Z=4, ρcalc.=1.416 Mg⋅m , μ=0.11 mm .

Data collection: Bruker-Nonius KappaCCD diffactometer, MoKα radiation, graphite monochromator, φ & ω scans, 21766 reflections, 1964 unique reflections, Rint=0.075, 1320 reflections with I>2σ(I).

Refinement: A structure model could be obtained using direct methods (SHELXS-97). The structure was refined on F2 with anisotropic displacement parameters for all non-H atoms (SHELXL-97). 120 L.S. parameters. R1=0.051, wR2=0.131, S=1.03, residual electron density (peak/hole): 0.47/–0.28.

Comment The crystal lattice comprises two molecules of p-hydroxybenzoic acid for 1,4-dioxane molecule. There are one molecule of p-hydroxybenzoic acid and one molecule of 1,4- dioxane in the asymmetric unit. The oxygen atoms in 1,4-dioxane are connected to the hydroxy group in the p-hydroxybenzoic acid molecules via hydrogen bonds. The carboxylic groups in the p-hydroxybenzoic acid molecules are linked intermolecularly around an inversion center. The 1,4-dioxane molecules form channels down the crystallographic b-axis in the crystal lattice. Details about the hydrogen bond geometry are given in Table 1.

Table 1. Hydrogen bond geometry D—H···A D—H H···A D···A D—H···A O1—H1···O2i 0.84 1.80 2.6416 (19) 175 O3— 0.84 1.86 2.6867 (19) 166 H3O···O4ii Symmetry codes: (i) −x+1, −y+2, −z; (ii) −x+3/2, y+1/2, −z+1/2.