Crystallization of Parabens: Thermodynamics, Nucleation and Processing

School of Chemical Science and Engineering

Department of Chemical Engineering and Technology

Division of Transport Phenomena

Huaiyu Yang

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 2013, kl. 10:00 i sal K1, Teknikringen 56, Stockholm. Avhandlingen försvaras på engelska. Cover: Microscope images of butyl paraben crystals.

Crystallization of Parabens: Thermodynamics, Nucleation and Processing

Doctoral Thesis in Chemical Engineering

TRITA-CHE Report 2013:20

ISSN 1654-1081

ISBN 978-91-7501-723-5

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

Abstract

In this work, the solubility of butyl paraben in 7 pure solvents and in 5 different ethanol-water mixtures has been determined from 1 ˚C to 50 ˚C. The solubility of ethyl paraben and propyl paraben in various solvents has been determined at 10 ˚C. The molar solubility of butyl paraben in pure solvents and its thermodynamic properties, measured by Differential Scanning Calorimetry, have been used to estimate the activity of the pure solid phase, and solution activity coefficients.

More than 5000 nucleation experiments of ethyl paraben, propyl paraben and butyl paraben in ethyl acetate, acetone, methanol, ethanol, propanol and 70%, 90% ethanol aqueous solution have been performed. The induction time of each paraben has been determined at three different supersaturation levels in various solvents. The wide variation in induction time reveals the stochastic nature of nucleation. The solid-liquid interfacial energy, free energy of nucleation, nuclei critical radius and pre-exponential factor of parabens in these solvents have been determined according to the classical nucleation theory, and different methods of evaluation are compared. The interfacial energy of parabens in these solvents tends to increase with decreasing mole fraction solubility but the correlation is not very strong. The influence of solvent on nucleation of each paraben and nucleation behavior of parabens in each solvent is discussed. There is a trend in the data that the higher the boiling point of the solvent and the higher the melting point of the solute, the more difficult is the nucleation. This observation is paralleled by the fact that a metastable polymorph has a lower interfacial energy than the stable form, and that a solid compound with a higher melting point appears to have a higher solid-melt and solid-aqueous solution interfacial energy.

It has been found that when a paraben is added to aqueous solutions with a certain proportion of ethanol, the solution separates into two immiscible liquid phases in equilibrium. The top layer is water-rich and the bottom layer is paraben-rich. The area in the ternary phase diagram of the liquid-liquid-phase separation region increases with increasing temperature. The area of the liquid-liquid-phase separation region decreases from butyl paraben, propyl paraben to ethyl paraben at the constant temperature.

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Cooling crystallization of solutions of different proportions of butyl paraben, water and ethanol have been carried out and recorded using the Focused Beam Reflectance Method, Particle Vision and Measurement, and in-situ Infrared Spectroscopy. The FBRM and IR curves and the PVM photos track the appearance of liquid-liquid phase separation and crystallization. The results suggest that the liquid-liquid phase separation has a negative influence on the crystal size distribution. The work illustrates how Process Analytical Technology (PAT) can be used to increase the understanding of complex crystallizations.

By cooling crystallization of butyl paraben under conditions of liquid-liquid-phase separation, crystals consisting of a porous layer in between two solid layers have been produced. The outer layers are transparent and compact while the middle layer is full of pores. The thickness of the porous layer can reach more than half of the whole crystal. These sandwich crystals contain only one polymorph as determined by Confocal Raman Microscopy and single crystal X-Ray Diffraction. However, the middle layer material melts at lower temperature than outer layer material.

Key words:

Nucleation, Induction time, Interfacial energy, Ethyl paraben, Propyl paraben, Butyl paraben, Methanol, Ethanol, Propanol, Acetone, Ethyl acetate, Solubility, Thermodynamics, Activity, Activity coefficient, Liquid-liquid phase separation, Ternary phase diagram, Melting point, Boiling point, Polarity, Cooling crystallization, Sandwich crystal, Porous, Particle Vision and Measurement, Focused Beam Reflectance Method, Infrared Spectroscopy, Confocal Raman Microscopy, X-Ray Diffraction, Differential Scanning Calorimetry.

Abstrakt

I detta projekt har lösligheten av butylparaben i 7 rena lösningsmedel och i 5 olika blandningar av etanol och vatten bestämts från 1 °C till 50 °C. Lösligheten av etylparaben och propylparaben i olika lösningsmedel har bestämts vid 10 °C. Den molära lösligheten av butylparaben i rena lösningsmedel och dess termodynamiska egenskaper, uppmätta med DSC, har använts för att uppskatta aktiviteten hos den rena fasta fasen samt aktivitetskoefficienter i lösning.

Över 5000 kärnbildningsexperiment har genomförts med etylparaben, propylparaben och butylparaben löst i etylacetat, aceton, metanol, etanol, propanol och 70% och 90% etanol blandat med vatten. Induktionstiden har bestämts för varje paraben vid tre olika övermättnadsnivåer i olika lösningsmedel. Den stora variationen i induktionstid visar på att kärnbildningen är stokastisk. Ytenergin mellan fast fas och vätska, den fria kärnbildningsenergin, kärnornas kritiska radie samt den preexponentiella faktorn har bestämts för parabenerna i dessa lösningsmedel utifrån den klassiska kärnbildningsteorin, och olika metoder för utvärdering har jämförts. Ytenergin för parabenerna i dessa lösningsmedel tenderar att öka med minskande molfraktion vid jämvikt men korrelationen är inte så stark. Effekten av lösningsmedlet på kärnbildningen av respektive paraben, och parabenernas kärnbildningsbeteende i respektive lösningsmedel diskuteras. En trend i data är att ju högre lösningsmedlets kokpunkt och ju högre det fasta materialets smältpunkt desto svårare kärnbildning. Denna observation stämmer överens med det faktum att en metastabil polymorf har lägre ytenergi än den stabila formen, och även att en fast förening med högre smältpunkt förefaller att ha en högre ytenergi mellan fast fas och smälta samt mellan fast fas och en vattenlösning.

Det har påvisats att när en paraben tillsätts en vattenlösing med en viss proportion etanol, så separerar lösningen vid jämvikt i två icke-blandbara vätskefaser. Den övre fasen är vattenrik och den undre rik på paraben. Storleken av tvåfas-vätskeområdet i ett ternärt fasdiagram ökar med ökande temperatur, och minskar vid konstant temperatur från butylparaben till propylparaben och därefter etylparaben.

Kylkristallisation av lösningar med olika proportioner butylparaben, vatten och etanol har utförts och analyserats med FBRM, PVM och in-situ IR spektroskopi. FBRM och IR kurvorna och PVM fotografierna visar hur vätske-vätskefasseparation och kristallisation inträffar. Resultaten indikerar att vätske-vätskefasseparation har en negativt påverkan på kristallstorleksfördelningen. Arbetet illustrerar hur processanalytisk teknologi (PAT) kan användas för att öka förståelsen av komplexa kristallisationsprocesser.

Genom kylkristallisation av butylparaben under tvåfas-vätskeförhållanden har kristaller bestående av ett poröst lager mellan två solida lager framställts. De yttre lagren är genomskinliga och kompakta medan det mellersta lagret är fullt av porer. Det porösa lagrets tjocklek kan uppgå till över hälften av hela kristallens tjocklek. Dessa sandwich-kristaller består endast av en polymorf, vilket har visats med Ramanspektroskopi och enkristallröntgendiffraktion. Smältpunkten för materialet i mittenlagret är dock lägre än för det i de yttre lagren.

List of Papers

I. Yang, H.; Rasmuson, Å. C., (2013) Nucleation of butyl paraben in different solvents (submitted to Crystal Growth & Design)

II. Yang, H.; Thati, J.; Rasmuson, Å. C., (2012) Thermodynamics of molecular solids in organic solvents. The Journal of Chemical Thermodynamics 48, (0), 150-159.

III. Yang, H.; Rasmuson, Å. C., (2012) Investigation of Batch Cooling Crystallization in a Liquid–Liquid Separating System by PAT. Organic Process Research & Development 16, (6), 1212-1224.

IV. Yang, H.; Michael Svärd; Rasmuson, Å. C., (2013) Influence of Solvent and Solid State Structure on Nucleation of Parabens (to be submitted)

V. Yang, H.; Rasmuson, Å. C., (2013) Sandwich crystals of butyl paraben (submitted)

VI. Yang, H., Rasmuson Å. C., (2010) Solubility of Butyl Paraben in Methanol, Ethanol, Propanol, Ethyl Acetate, Acetone, and Acetonitrile. Journal of Chemical & Engineering Data: p. 25-38

VII. Yang, H.; Rasmuson, Å. C., Ternary diagrams of ethyl paraben and propyl paraben (to be submitted)

Crystal structure determination

VIII. Yang, H.; Svärd, M,; Chen, H,; (2013) X-ray Crystallography of Butyl paraben (submitted to CCDC)

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Conference contribution (not included)

IX. Yang, H., Svärd, M., Rasmuson Å. C, (2012) Interaction of parabens and solvents molecules in crystallization, 10th International Workshop on Crystal Growth of Organic Materials, University of Limerick, Limerick, Ireland

X. Yang, H., Rasmuson Å. C, (2011) Crystallization of butyl paraben in mixtures of water and ethanol, 18th International Symposium on Industry Crystallization, ETH, Zurich, Switzerland

XI. Yang, H., Rasmuson Å. C, (2011) Nucleation of butyl paraben, propyl paraben and ethyl paraben in ethanol, ethyl acetate and acetone, 44th British Association for Crystal Growth, University College London, London, UK

XII. Yang, H., Rasmuson Å. C, (2010) Nucleation and crystallization of butyl paraben in liquid-liquid phases, 9th International Workshop on Crystal Growth of Organic Materials, Nanyang Technological University, Singapore

Related work (not included)

XIII. Yang, H, (2010) Investigations into the crystallization of butyl paraben, Licentiate Thesis in Chemical Engineering, Royal Institute of Technology (KTH), TRITA-CHE Report 2011:43, ISSN 1654-1081

XIV. Yang, H.; Rasmuson, Å. C., Crystallization in droplets of butyl paraben (manuscript)

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Notations

Activity of solid phase, actual solute activity ［mol•L-1/ mol•L-1］

Equilibrium solute activity ［mol•L-1/ mol•L-1］ 2 Surface area ［m ］ Activity of solid phase at temperature T ［mol•L-1/ mol•L-1］ -1 -1 Activity of solid phase at melting temperature ［mol•L / mol•L ］ -1 -1 Activity of the solute in the saturated solution ［mol•L / mol•L ］

Regression curve coefficient in estimating molar fraction solubility Pre-exponential factor ［m-3•L-1］ -3 -1 Estimated pre-exponential factor ［m •L ］ Slope of correlation line in estimating induction time -1 Actual solute concentration ［mol•L ］ Equilibrium solute concneetration ［mol•L-1］ -1 Each of the available M molecules at stage 1 in nucleation process ［mol•L ］ -1 Concentration of one molecule cluster ［mol•L ］ -1 Concentration of n molecules cluster ［mol•L ］ -1 Concentration of n molecules cluster at time t ［mol•L ］ -1 Concentration of n-1 molecules cluster ［mol•L ］ -1 Concentration of n+1 molecules cluster ［mol•L ］ -1 -1 Heat capacity of the solute as a pure melt ［J•g •K ］ -1 -1 Heat capacity of the solid form ［J•g •K ］ Monomer diffusion coefficient ［m2•L-1］ Natural logarithm, 2.7183

-1 Frequency of molecule attachment to n-1 molecules cluster ［s ］ -1 Frequency of molecule attachment to n molecules cluster ［s ］ -1 Frequency of molecule attachment to n molecules cluster at time t ［s ］ Frequency of the attachment of molecules to critical nucleus ［s-1］

Force of buoyancy ［N］

Force of evaporation dynamic ［N］

Force of intermolecular force ［N］ -1 Frequency of molecule detachment to n molecules cluster ［s ］ -1 Frequency of molecule detachment to n molecules cluster at time t ［s ］ -1 Frequency of molecule detachment to n+1 molecules cluster ［s ］

Gibbs free energy at stage 1 in nucleation process ［kJ/mol］

Cluster excess free energy ［kJ/mol］

Rate of homogeneous nucleation ［m-3］ Rate of homogeneous nucleation at time t ［m-3•L-1］ -3 -1 Steady-state nucleation rate ［m •L ］ Boltzmann constant, 1.38×10−23 ［J•K-1］ −8 Number constant, 7.4×10 Number of all nucleation experiments

Solute molecular weight ［g］

Solvent molecular weight ［g］ Number of molecules in cluster

Number of molecules in the critical nucleus Average number of nucleus appearing in nucleation experiments -1 Avogadro constant, 6.022×1023 ［mol ］ Pressure ［N•m-2］

Probability of appearing m cases in N random and independent cases

Probability of no nucleation appearing in m experiments

Probability of nucleation in one experiment, proportion of nucleated experiments in all nucleation experiments Regression curve coefficient in estimating heat capacity Numerical constant in two step nucleation equation

Radius of cluster ［nm］

Critical nuclei radius ［nm］ Gas constant, 8.3145 ［J• mol-1•K-1］ Supersaturation

Induction time of nucleation at ［s］ Median induction time of nucleation ［s］

Average induction time of nucleation ［s］

Induction time of nucleation ［s］

Time for a nucleus to grow to detectable size ［s］

Time for formation of a stable nucleus ［s］

Relaxation time ［s］ Temperature ［K］

Melting temperature ［K］

Extrapolated melting temperature at mole solubility equal to unit ［K］ Frequency factor 3 Volume of a solvent molecule ［m ］ 3 Volume of a solute molecule ［m ］ Volume of solution ［m3］ Actual solute molar fraction solubility ［mol/mol total］ Equilibrium solute molar fraction solubility ［mol/mol total］ x

Molar fraction solubility ［mol/mol total］ Extrapolated mole solubility at melting temperature ［mol/mol total］

Molar fraction solubility in ideal solution ［mol/mol total］

Work for homogenous formation of one molecule cluster ［kJ/mol］

Work for homogenous formation of n molecules cluster ［kJ/mol］ Work for homogenous formation of n molecules critical nucleus ［kJ/mol］

Regression curve coefficient in estimating van’t Hoff enthalpy of solution at constant temperature

Activity coefficient in the solution at equilibrium -2 Surface tension of liquid phase ［mJ•m ］ -2 Surface tension of solid phase ［mJ•m ］ -2 Interfacial surface tension ［mJ•m ］ Numerical factor Number change of all nucleus at time t ［m-3］ Density of solid material ［g•cm-3］ Mean free path of particles in the solution ［m］ Viscosity of solvent ［kg•s-1•m-1］

Chemical potential of one molecule at stage 1 in nucleation ［kJ/mol］ process

Chemical potential of one molecule at stage 2 in nucleation ［kJ/mol］ process

Chemical potential of the solid phase ［kJ/mol］

Thermodynamic state of chemical potential of the solid ［kJ/mol］

Thermodynamic reference state of chemical potential of the solid ［kJ/mol］ phase Solid-liquid interfacial energy ［mJ•m-2］ -2 Surface tension of pure solvent ［mJ•m ］ -2 Experimental interfacial energy ［mJ•m ］ -2 Estimated interfacial energy by Mersmann equation ［mJ•m ］ -2 Estimated interfacial energy by Neumann equation ［mJ•m ］ -2 Surface tension of liquid phase ［mJ•m ］ -2 Surface tension of solid phase ［mJ•m ］ -2 Estimated interfacial energy by Turnbull equation ［mJ•m ］ Time lag ［s］ -1 -1 Heat capacity difference between the solute as a pure melt and the ［J•mol •K ］ solid form Gibbs free energy ［kJ•mol-1］

-1 Critical free energy ［kJ•mol ］ -1 Gibbs free energy of fusion ［kJ•mol ］ -1 Volume excess energy ［kJ•mol ］

Dissolution enthalpy ［kJ•mol-1］ Enthalpy of fusion ［kJ•mol-1］ Enthalpy of fusion at temperature T ［kJ•mol-1］ -1 Enthalpy of fusion at melting temperature ［kJ•mol ］ Extrapolated van’t Hoff enthalpy of solution at melting ［kJ•mol-1］

temperature -1 van’t Hoff enthalpy of solution ［kJ•mol ］ -1 van’t Hoff enthalpy of ideal solution ［kJ•mol ］ -1 van’t Hoff enthalpy of solution at temperature ［kJ•mol ］ van’t Hoff enthalpy of ideal solution at temperature ［kJ•mol-1］

-1 Entropy of mixing ［kJ•mol ］ Energy of desolvation ［kJ•mol-1］ Different chemical potential of one molecule between the new ［kJ•mol-1］ phase (stage 2) and the old phase (stage 1)

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Abbreviations and Acronyms

AC Acetone ACE Acetonitrile App Appendix BP Butyl paraben CRM Confocal Raman Microscopy DSC Differential Scanning Calorimetry E Ethanol EA Ethyl Acetate EP Ethyl Paraben Equ. Equation Exp. Experiment FBRM Focused Beam Reflectance Method IR Infrared LLPS Liquid-liquid Phase Separation MP Methanol Paraben MS Material Studio Objective Function PP Propyl Paraben PVM Particle Vision and Measurement XRD X-Ray Diffractomer SEM Scanning Electron Microscopy

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Contents

Abstract ...... iii

List of Papers ...... vii

Notations ...... ix

Abbreviations and Acronyms ...... xiii

1. Introduction ...... 1 1.1 Scope of the research work ...... 2 1.2 Objectives ...... 2 2. Theory ...... 3 2.1 Thermodynamics of solid-liquid equilibrium ...... 3 2.1.1 Solubility equations ...... 4 2.1.2 Thermodynamic proprieties of pure solid ...... 4 2.1.3 Relation between solubility and solid-state thermodynamic properties...... 6 2.2 Theory of homogenous nucleation ...... 7 2.2.1 Cluster and nucleation work ...... 7 2.2.2 Nucleation rate ...... 10 2.2.3 Induction time and interfacial energy determination ...... 11 2.2.4 Estimation of interfacial energy ...... 13 2.2.5 Empirical estimation of pre-exponential factor ...... 14 3. Materials and experimental work ...... 15 3.1 Materials ...... 15 3.1.1 Molecular and crystal structure of parabens ...... 15 3.1.2 Polymorphism and particle morphologies of parabens ...... 16 3.2 Phase equilibrium...... 17 3.2.1 Solubility ...... 17 3.2.2 Liquid-liquid phase separation and ternary phase diagrams ...... 18 3.3 Thermodynamic properties of pure solid at melting ...... 18 3.4 Nucleation experiments ...... 19 3.5 Cooling crystallization and sandwich crystals ...... 19

4. Results...... 21 4.1 Solubility ...... 21 4.2 Liquid-liquid phase separation and ternary phase diagram...... 22 4.3 Thermodynamic properties of pure solid ...... 24 4.4 Relation between solid-state thermodynamic properties and solubility ...... 25 4.5 Nucleation experiments ...... 28 4.5.1 Random nature of nucleation ...... 28 4.5.2 Statistical analysis of induction time ...... 28 4.5.3 Determination of interfacial energy of parabens in various solvents ...... 29 4.5.4 Determination of interfacial energy by other methods ...... 32 4.5.5 Influence of solute and solvent on nucleation process ...... 35 4.6 Correlation of interfacial energy with solvent and solute properties ...... 37 4.6.1 Interfacial energy and solvent boiling point ...... 37 4.6.2 Interfacial energy and solute melting point ...... 39 4.6.3 Interfacial energy, boiling point and melting point ...... 41 4.7 Cooling crystallization and sandwich crystals ...... 41 5. Discussion ...... 47 5.1 Liquid-liquid phase separation ...... 47 5.2 Thermal history on nucleation ...... 48 5.3 Bonding in nucleation ...... 48 6. Conclusion ...... 51

7. Reference ...... 53

Acknowledgement ...... 59

Appendix 1 Solubility and solubility equations ...... 61 Appendix 2 Relation between solubility and solid-state thermodynamic properties ...... 65 Appendix 3 Unit cell parameters of parabens crystals ...... 67

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1. Introduction

Crystallization is a very old technology and information regarding the crystallization of both salt and sugar goes back to the beginning of civilization. Now, crystallization is a separation and purification technique employed to produce a wide variety of materials from bulk commodity chemicals to specialty chemicals. Crystallization can be defined as a phase change in which a crystalline product is obtained from a solution [1]. Crystallization is a key component of almost all processes in the manufacturing of small molecule pharmaceuticals [2]. Crystallization is essential in processing and development for purification of intermediates, formation of the product, and prevention of crystallization in amorphous products [3]. A deep understanding of the crystallization process and the phase diagrams is essential to control kinetics and thermodynamics of the process.

Crystallization process consists two major events: nucleation and crystal growth. Nucleation [1] includes primary nucleation and secondary nucleation. Primary nucleation includes homogeneous and heterogeneous nucleation. Secondary nucleation includes initial breeding, polycrystalline breeding, macroabrasion, dendritic, fluid shears and contact nucleation. In this work, we mainly focus on homogenous nucleation of organic compounds in different solvents. Supersaturation is the driving force of nucleation, and nucleation rate increases with increasing supersaturation. Once crystallization starts, the supersaturation can be relieved by a combination of nucleation and crystal growth.

Nucleation is the process of forming new phase and is the widely spread phenomenon in both nature and technology [4]. In nature, nucleation is reported involving in different phenomena as, e.g. electron condensation in solids [5], volcano eruption [6], rupture of foam [7], membrane and emulsion bilayers [8, 9], formation of shells and bone structures [3, 10]. Nucleation in solution happens in a supersaturated solution which is not at equilibrium, and it is required for crystallization to occur. In order to relieve the supersaturation and move towards equilibrium, the solution nucleates and crystallizes. Nucleation in condensation and evaporation, all crystallization and many other processes plays a prominent role. In technology, nucleation is one of the key mechanisms of crystallization processes, which are of significant importance to our society in industrial production of metallurgic and polymeric materials, and of inorganic and organic compounds.

Crystal nucleation has a governing influence on the product properties. At the same time, nucleation is the mechanism of crystallization that is the least understood which leads to significant problems in the design, operation and control of industrial processes. Nucleation behavior is known to be unreliable and case sensitive. Because of this, industrial processes are developed by trial and error, and they often lack sufficient robustness. Sometimes lack of reproducibility requires rework or even disposal of the batch. Furthermore, the nucleation work done is often of a rather applied nature, and sometimes without sufficient control over important conditions. Plenty of nucleation researches so far have been done on studying the influence of the solution, solution equilibrium and supersaturation [11, 12]. Most experimental work has been done with poor experimental efficiency and insufficient appreciation for the inherent stochastic nature of the process. The influence of the solvent and solute has been explored in some studies [13-15] , but often the actual driving force is not properly characterized. Relatively little is known about the molecular processes in solution that precedes

1 the appearance of a solid crystalline material and how these processes are influenced by the process conditions and the molecular properties of the crystallizing compound.

1.1 Scope of the research work

This work is focused on interaction between organic and ethanol aqueous solvents and drug-like organic solutes: i) Thermodynamics: properties of solid solute in saturated solution and relation between solute and solvents in phase equilibrium. Solubility of parabens in different solvents and ternary phase diagrams of butyl paraben, water and ethanol have been determined. Thermodynamic properties of pure solid have been determined by DSC. Relationship between thermodynamic properties of pure solid and solubility of butyl paraben has been investigated. Ternary diagram of parabens, water and ethanol and liquid-liquid phase separation have been determined. ii) Nucleation: solid (solute) - liquid (solvent) interfacial energy and relation between solvent and solutes at a constant supersaturation. Thousands of nucleation experiments of paraben in various solvents have been investigated. Induction time has been determined at different supersaturation levels. Solid-liquid interfacial energy, free energy of nucleation and critical nuclei radius have been determined by 5 different methods and compared. Influence of solvents on nucleation is discussed by correlating interfacial energy with physical and chemical properties of solvent. The relation of interfacial energy and melting point of solute and boiling point of solvent is derived. iii) Crystallization processing: in-site and off line observation and relation between solute and solvents at varied driving force. Cooling crystallization experiments of butyl paraben in several ethanol aqueous solutions have been observed by FBRM, PVM in-situ IR. A novel kind of sandwich crystals of butyl paraben was obtained in LLPS crystallization and has been investigated to determine the chemical and physical properties.

1.2 Objectives

The overall goal of this work is to investigate nucleation and crystallization of drug-like organic molecules in a few different solvents, for the purpose of advancing the control and efficiency of crystallization of modern and future pharmaceutical compounds.

2. Theory

Solubility and crystallization in solution focus on the transitions between solid [16] and liquid phase [17]. The dissolution of a solid into a solvent can be considered following two steps, fusion of the solid and mixing with the solvent (T1 part in Figure 2. 1), to reach equilibrium. The crystallization of a solute from the solution is more complicated. First solution forms supersaturation usually by cooling (or evaporating, adding anti-solvent, etc.), size of clusters grows to critical radius, then nucleates and crystals grow, (T2 part in Figure 2. 1), finally solution reaches equilibrium again[18].

Figure 2. 1 Change if free energy in crystallization, dissolving and mixing process at constant temperature T1 > T2, respectively.

2.1 Thermodynamics of solid-liquid equilibrium

Solubility reflects a thermodynamic equilibrium in which the chemical potential of the solute is equal to the chemical potential of the solid phase [18]. The solubility of a substance fundamentally depends on the used solvent as well as on temperature and pressure. Solubility occurs under dynamic equilibrium, which means that solubility results from the simultaneous and opposing processes of dissolution and precipitation of solids. The solubility equilibrium clarifies when the two processes proceed at an equal rate. When the solute and the solvent are in equilibrium, the chemical potential of the solute in solution is equal to the chemical potential of the solid. Hence, the activity of the solid is equal to the activity of the solute in the solution. The solubility depends on solute and solvent properties as is often described by the relation:

(1) where is the activity of the solute in the saturated solution. R is gas constant. stands for: , i.e. represents the difference in chemical potential of the solid phase, , and the thermodynamic reference state, . is the activity coefficient in the solution at equilibrium (detailed in thermodynamic properties section) and is the molar solubility concentration (detailed in solubility equations section).

2.1.1 Solubility equations Many research works about solubility and correlation of solubility data have been reported, where the equations used to correlate the solubility data contain one or more of the parameters, T, T2, T3, T-1, T-2, lnT and constant, etc. Nordström and Rasmuson [19] explored the capability of 15 different solubility equations, among which some equations give very small standard deviation for correlating the solubility data, but one of the equations is a little better for estimating melting point and enthalpy of melting point:

(2) where , and are regression coefficients. For a particular solute, 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 solution, :

(3)

The associated experimental can be determined through Equ. 3,

(4)

2.1.2 Thermodynamic proprieties of pure solid At equilibrium the chemical potentials for the solute in solution and pure solid are identical:

(5) or

(6) where T is the temperature. Rearranging Equ. 6 gives:

(7) Since the free energy of fusion is the difference in chemical potential between the pure melt (solute) and the pure solid, with combining Equ. 7,

(8) The Gibbs-Helmholtz equation gives:

(9)

From Equ. 8 and Equ. 9, we arrive:

(10)

4 or:

(11) with integrating Equ. 11, the final formula gives:

∫ ∫ (12)

Considering a thermodynamic cycle, the solid is heated up to the melting point, melts and then cooled down to temperature T as a supercooled liquid, the enthalpy of the cycle gives

∫ ∫ (13)

is given by (shown in Figure 2. 2)

(14) where is the heat capacity of the solute as a pure melt, and is the heat capacity of the solid form.

Figure 2. 2 Example of determining by using heat capacity of the solute as a pure melt and the solid form from DSC measurement The heat capacity plays an important role in calculating enthalpy of fusion at temperature T. In the DSC measurement, the heat capacity curves of the solute as a pure melt and of the solid form can be obtained. Nordström and Rasmuson [19] assumed the curves of heat capacity are linearly dependent on the temperature ( ), (15)

However, the heat capacity curves of some materials had been proved to be not linear [20, 21] and, accordingly, second order or third order equations were also used to describe the heat capacity. In the present work, the second order equation of heat capacity is investigated, with a reference of melting temperature, as Equ. (15) and . For an ideal solution the (i) activity coefficient equals unity, (ii) the mole fraction solubility equals the activity of the solid phase (Equ. 1) and (iii) the van’t Hoff enthalpy of solution equals the enthalpy of fusion (with Equ. 13):

∫ (16)

Combining Equ. 12 with Equ. 16, we arrive at:

( ) ∫ ∫ (17)

The Equ. 16 and 17 for the solid state substitute Cp with Equ. 15, respectively:

( ) ( ) ( )

(18)

(19)

Equ. 18 and Equ. 19 both depend on 5 thermal parameters, , , , and . Both equations contain four terms, and these four terms for each equation (except T and Tm) both contains , , and , respectively. Sometimes in order to estimate the heat capacity, simplified equations, e.g. neglect of one or more of , and , are used.

2.1.3 Relation between solubility and solid-state thermodynamic properties For a particular solute, the saturated solution in a range of different solvents can change from exhibiting negative to positive deviations from Raoult’s law, i.e. the activity coefficient range from values below unity to values above unity. Among these solvents there should be accordingly one in which the activity coefficient is unity. In addition, as the solute concentration increases with increasing temperature we expect that the activity coefficient gradually approaches unity, and that the mole fraction solubility becomes unity at the melting point. This then suggests that if solubility data versus temperature are extrapolated, the melting temperature and the enthalpy of melting should be obtained by Equ. (2) at , regardless of the solvent. The extrapolated melting point and enthalpy should be same as the results from

DSC experiments. For an ideal solution, the equals to , however, for a particular solute, the difference between and in saturated solution in a range of different solvents can also changes from exhibiting negative to positive deviation. Nordström and Rasmuson [22] developed a semi-empirical method to identify the ideal solubility, which makes use of solubility data in different solvents and at different temperatures. For each temperature the relation between molar fraction solubility with enthalpy of fusion is established. The of the solid solute in all these different solvents at each temperature are correlated with , and they are well fitted by a second-order relation of the type:

(20) In theory, every point on this curve represents one solvent, and this curve should go across the ideal solvent when equals to lna and equals to at the certain temperature. At each same time, there are several curves at different temperatures and every curve should go across the point which represents the ideal solvent at different temperatures. It is assumed that among these solvents there is accordingly one in which the activity coefficient is unity.

2.2 Theory of homogenous nucleation

Nucleation can be divided into primary nucleation and secondary nucleation [23]. Primary nucleation occurs in the absence of crystalline surfaces, whereas secondary nucleation involves the active participation of these surfaces. Primary nucleation can be divided into homogeneous nucleation and heterogeneous nucleation [24]. Homogeneous nucleation occurs when the clusters of new phase are only in contact with the old phase, which rarely occurs in practice[1]; however, it forms the basis of several nucleation theories. Heterogeneous nucleation is usually induced by the presence of other phase or molecular species in the old phase [4], e.g. foreign molecules, microscopic particles, bubbles, etc. Nucleation theory was pioneered by Gibbs [25], and Becker and Döring [26] and Zeldovich [27] initiated the development of the theory today known as classical nucleation theory (CNT). Numerous modifications of the classical theory which extended this theoretical concept considerably have been presented by Lothe and Pound [28] and Binder and Stauffer [29]. Nucleation mechanism has been studied for about 90 years [30], but the theory is developing slowly. The theory assumes that nuclei are formed by monomers in solution aggregating into clusters having the structure of the bulk crystalline material. The cluster will become thermodynamically stable and able to grow into a larger crystal if its size exceeds a critical size where the free energy gain of forming the bulk of the crystalline material overcomes the free energy cost of creating the phase boundary. Turnbull [31] is perhaps the first to address the stochastic nature of the nucleation process and gave a simple equation. Toschev [32] further developed this aspect of the nucleation theory, as well as the difference between steady state and non-steady state nucleation. The non-steady state nucleation results in a time lag [33, 34], before establishment of steady state nucleation [35]. Little is known about this time lag, but theoretical studies have been made [36, 37]. Unfortunately, even with modern technologies it is very difficult to experimentally observe clusters and the process where a cluster turns into a crystal, however various simulation techniques are helpful [38]. Recently, Jiang and ter Horst [39] applied the steady-state stochastic formulation of the nucleation theory to crystallization of m-aminobenzoic acid and L-histidine, expecting the induction time follow the lognormal distribution. However, more experiments shows different distributions, e.g. ‘S’ shape, indicating a more complicated nucleation procedure. Although the CNT is not perfect [40-43], the CNT is still the most widely used as basic theory in nucleation research [44-47].

2.2.1 Cluster and nucleation work In the classical nucleation theory [4], nucleation in a system of M molecules is the result of the addition of molecules to a cluster (n molecules). A cluster reaches a critical size for forming a nucleus when it contains a critical number of molecules ( ). Following the theory of homogeneous nucleation, the Fisher-Turnbull equation [48] associates the rate of formation of nucleus of critical number of molecules with the free energy, , to develop a stable nucleus ( molecules). If the cluster is always sphere-shape, with increasing radius, r, the cluster with critical number of molecules (nucleus) has a critical radius, . Figure 2. 3 depicts schematically the process from system of M molecules (or atoms) in its initial stage 1 when it is of uniform density and has Gibbs free energy at constant temperature, T, and under constant pressure, P,

(21) where is the chemical potential of one molecule in stage 1. At stage 2, when the system contains a cluster of n (integer) molecules (n = 1, 2, 3….), the system has Gibbs free energy G2.

(22)

7 where is the chemical potential of one molecule in system of stage 2 inside the dashed circle, and and together account the energy change of the system for forming the n molecules cluster.

molecules molecules molecules molecules System Cluster Nucleus Nucleus

Stage 1 Stage 2 Stage 2 Stage 3

Figure 2. 3 Schema of forming nucleus

Therefore, the work, , for homogenous formation of n molecules cluster can be determined by

(23) where the is the different chemical potential of one molecule between the new phase, , and the old phase ,

(24)

The , also known as the cluster excess energy, , is usually considered as energy change for forming the boundary between old phase and new phase. In nucleation research, it is often assumed that the cluster has only one shape during the nucleation process and the specified shape is the statistically most probable one, also called equilibrium shape [49-51]. The spherical shape of cluster with radius, , is most often used in nucleation study, show as Equ. (25)

(25)

The is the interfacial energy (interfacial tense) of a cluster, which also indicates that it is unfavorable when a molecule move from inside of the cluster to the surface [52], therefore, the is positive. The is volume excess energy, also written as , which is negative,

(26)

where the is volume of one solid molecule, is the Avogadro constant, is molecular weight, is the density of the solid phase,

(27) combining Equ. (23), (24), (25) and (26), we get

(28)

Since the is negative and proportional to third order of r, and is positive and proportional to second order of , the work for forming a cluster has a maximum value at the point , when a nucleus forms with critical radius, ,

(29) the critical maximum work for forming a critical nucleus can be calculated,

(30) and also the critical number of molecules for forming a critical nucleus can be determined,

(31) since , with Equ. (28) and (30) we arrive,

(32)

where is the critical free energy, is the critical cluster excess energy. Combining Equ. (23), (28), (30), (31) and (32), we can find the relationship between , , with r and n by Equ. (33) and (34), and the curve, free energy vs r, is shown in Figure 2. 4.

( ( ) ( ) ) (33)

( ( ) ( ) ) (34)

Figure 2. 4 Schema of nucleation process

2.2.2 Nucleation rate In nucleation process, size of clusters will increase or decrease by attaching other molecules or detaching some molecules, respectively. For mathematic convenience, it is assumed that the n molecules cluster can change size only by nearest-size transition,

(35)

(36)

where and represent concentration of one molecule clusters and n molecules clusters in M molecules system, respectively. and are the frequencies of molecule attachment to and detachment from an n molecule cluster (n=2, 3, 4, …. , M-3, M-2, M-1) , respectively.

(1.37)

Nucleation rate is the frequency of appearance at time t of all supernuclei (n > n*, n* is the number of molecules the critical cluster contains) per unit volume,

(38) where (number / m3) is given by

∑ (39) The rate of homogeneous nucleation can be expressed in the form of the Arrhenius reaction rate equation:

( ) (40) and

(41) where is a numerical factor, sometimes it can be given by [49, 53],

( ) (42)

is frequency of the attachment of molecules to the critical nucleus. k is Boltzmann constant. In the solution, the is given by,

( ) (43) where is a frequency factor, is mean free path of particles in the solution which is approximately equal to the atomic diameter, is the energy of desolvation. For homogenous nucleation, can be considered as each of the available M molecules in the system of stage 1, also as the role of an active center for nucleation,

(44)

The equilibrium cluster size distribution is of form,

(45)

(46)

Therefore, combine Equ. (41), (42) and (43) we arrive[24],

( ) ( ) ( ) (47)

The nucleation driving force : (48) where S is the supersaturation, given by

(49) a is the actual solute activity, which is dependent both on temperature and concentration, the and is equilibrium solute activity i.e. the activity at which the solute and the condensate are in phase equilibrium. The supersaturation, S, is also usually approximated by,

(50)

(51) where and are actual and equilibrium solute concentration, respectively; and are actual and equilibrium solute molar fraction solubility, respectively.

Compared with the parameter, ( ), the parameter is not obviously influenced by

supersaturation, and, therefore, usually is considered to be a constant number parameter, , at different supersaturation conditions. Combine Equ. (29), (33), (40), (48) and (51), we arrive

( ) (52)

2.2.3 Induction time and interfacial energy determination The induction time, , is the time period [54] from the establishment of the supersaturated state to the first observation of crystals in the solution and is assumed to contain three parts [55]:

(53) where is relaxation time or transient period, is the time required for formation of a stable nucleus, and is the time for a nucleus to grow to detectable size. Usually it is assumed that and are negligible compared to , and that the induction time is inversely proportional to the nucleation rate:

(54)

(55)

Induction time experiments are usually evaluated by plotting the versus , for determination of the interfacial free energy from the slope, . Knowing the interfacial energy allows for calculation of the critical free energy, , of nucleation and the radius, , of the critical nucleus. If the nucleation is assumed to be a random and independent process, the probability of finding m nuclei within a certain time frame, , is given by a Poisson distribution [32]:

(56) where N is the average number of nuclei formed within the same time frame. The probability of finding no nuclei is obtained at and the probability of finding any number of nuclei ≥1 at time, t, is given by:

(57)

Toschev [56] suggested that N is proportional to the steady-state nucleation rate, , and Jiang and ter Horst [39] used:

(58) In one experiment, the probability of nucleation will increase with time, since average number of nuclei increase with time. In a set of parallel experiments at equal conditions the number of experiments that have nucleated will increase with time, i.e. represents the proportion of the nucleated experiments in the total experiments. will increase with time because N will increase with time. Combining the Equ. (57) and Equ. (58), which also introduced by Jiang and ter Horst [39],

(59) A similar equation was presentated by Turnbull [31], and for the two-step model, Knezic[57] derived at: , where and are constants. Equ. (59) can be rearranged into:

(60) where the left hand side equals . Accordingly, plotting the number of experiments nucleated versus time, a straight line should be obtained, from which the nucleation rate can be determined [32]. An alternative evaluation of the nucleation rate from the same treatment[4] is to use the fact that

(61)

where is the time when 63.2 % of all experiments have nucleated, i.e. can be directly read from a plot over cumulative fractional number of parallel experiments that have nucleated versus time at . Both these methods rely on that the cumulative distribution of nucleated tubes can be described by Equ. (60). Behind the treatment leading to Equ. (60), is the assumption that the nucleation occurs at steady-state conditions with respect of the cluster distribution. Clusters constantly form and redissolve in each size class but the distribution maintains a steady-state in the solution. In case of non-steady state conditions the nucleation distribution will show a curvature at short induction times as shown by Toschev[32], and there is a time lag for the diffusional process to reach steady state conditions [58, 59]. The nucleation rate of a non-steady nucleation process is dependent on the time [35], and the average number of nuclei formed is given by,

[ ∑ ] (62) where the is the time lag. When Equ. (62) transforms into the simple linear relationship [36] of Equ. (58), but at shorter time the number of nuclei increases non-linearily with time asymptotically approaching the straight line [55]. In melt crystallization and nucleation of liquids or solids from vapor phase the lag time [37, 60] is about s, and is therefore neglected. However, Kantrowitz [61] suggested that can be of importance and Andres and Boudart [33] reported several experimental cases in which the time lag cannot be neglected. Courtney[62] showed that the transient period is dependent on the size of cluster (number of molecule in one cluster) and temperature, and it is also dependent on the supersaturation [59]. The time lag can be hours or one day in viscous liquids [63].

In the case where and cannot be neglected Equ. (60) should be replaced by,

(63)

Jiang and ter Horst [39], assumed that the time of the first nucleation in a set of parallel experiments could be interpreted as and corrected Equ. (60) for that. Equ. (63) illustrates that the time lag and the growth time will not change the slope of the plot of Equ. (60) but only induce a lateral translation of the curve. Hence the nucleation rate can be established from the straight line that should appear after an initial time period when plotting vs. , which is same as vs. t.

2.2.4 Estimation of interfacial energy Mersmann [64] developed proposition of Nielsen and Sohnel [65] and estimated a linear correlation between interfacial energy and solubility from data of many inorganic compounds, and this proposition combining with several corrections [18, 54] is given:

(64) where c is solubility with unit of mol/L, and this equation describes that the interfacial energy increase with decreasing solubility. Turnbull proposed an empirical relationship that solid-liquid interfacial is proportional to its melting enthalpy for more than a dozen of metals [48, 66]. For solution, the solid-liquid interfacial is proportional to its dissolution enthalpy [64, 67, 68] with a proportional constant of 0.32,

(65) where the can be determined [48] by

∫ (66) in a dilute solution,

[ ] (67)

The Neumann equation [69, 70] relates the interfacial energy, , to the surface tension of the liquid, , and the surface energy of the solid, :

[ √ ] (68)

It has been suggested [71, 72] that, for a liquid mixture can be estimated by a linear interpolation:

(69) where the and are mole fractions of solvent A and solid solute in solution, respectively, and is surface tension of the pure solvent. Equ. (68) and (69), have been fitted to the experimental interfacial energy and the liquid surface energy by minimizing the objective function

∑ ( ) (70) to assess the solid surface energy of solute. Based on Equ. (68), the optimum value of combined with is able to estimate interfacial energy of solute in these solvents.

2.2.5 Empirical estimation of pre-exponential factor The properties of the pre-exponential factor have been analyzed [4, 54] showing that:

√ (71)

√ D is the monomer diffusion coefficient, C is the concentration of solute in the supersaturated solution, and is the volume of a solvent molecule in the solution. Wilke and Chang showed a correlation of diffusion coefficient in various dilute solutions [73],

(72)

where is a number constant, is solvent molecular weight and is viscosity of solvent. Many experimental results indicate the parameter decreases in high concentration solution

[74-76], however, to simplify this equation is assume to be identical to , reported by Wilke and Chang [73]. Combining Equ. (71) and (72), it gives:

(73)

3. Materials and experimental work

In this work, solubility of parabens, benzocaine and butamben in methanol, ethanol, propanol, ethyl acetate, acetone, acetonitrile or mixture of water and ethanol, and the ternary diagram of parabens, water and ethanol have been determined. Thermodynamic properties of solid parabens have been determined by DSC and the relationship between solubility and thermodynamic properties has been studied. Induction time of parabens in different solvents has been investigated. In addition, cooling crystallization of butyl paraben in ethanol aqueous solvents have been investigated. Properties of a novel kind of sandwich crystals obtained in cooling crystallization have been determined.

3.1 Materials

Ethyl paraben (EP, CAS reg. no. 120-47-8, purity > 99.0%), propyl paraben (PP, CAS reg. no. 94-13-3, purity >99.0%) and butyl paraben (BP, reg. no. 94-26-8, purity > 99.0 %) were purchased from Aldrich and was used without further purification. Ethanol of 99.7% purity was purchased from Solveco chemicals. Methanol (≥ 99.9 %), propanol (≥ 99.8 %), ethyl acetate (99.8 %), acetone (99.9 %) and acetonitrile (≥ 99.8 %) were purchased from VWR. Water was distilled, deionized and filtered at 0.2 µm. Parabens, alkyl esters of p-hydroxybenzoic acid, are the most common preservatives in use nowadays. Owing to their relatively low toxicity, parabens (or their salts) are found in thousands of cosmetic, toiletries, food and pharmaceutical products[77-81]. These compounds and their salts are used primarily for their bactericidal and fungicidal properties [82, 83]. Owing to the above mentioned factors, methyl- ethyl-, propyl- or butyl-paraben are all usually used as food preservative [84].

3.1.1 Molecular and crystal structure of parabens All parabens (Figure 3. 1) have both –OH and -O=C-O- functional groups connected to a aromatic ring, and a carbon chain of different length (C2, C3, C4) connected to functional group -O=C-O-, respectively. The crystal structures of three parabens are shown in Figure 3. 2, and the crystal structure are all similar to each other.

Figure 3. 1 Molecular structure of ethyl paraben (a), propyl paraben (b) and butyl paraben (c) The crystal structures of EP [85] and PP [86] are available in the Cambridge structural database, whereas the structure of BP is not, although its unit cell parameters and basic features are reported [87, 88]. The crystal structure of BP was solved by single-crystal XRD on a crystal grown by slow solvent evaporation from ethanol solution (Paper VIII). EP, PP and BP all show slip-planes in their crystal structures (Figure 3. 2). It is reported [89] that the slip planes in crystal structure leads to greater plasticity, greater compressibility and

15 greater tablet-ability. Hydrogen bonds exist only inside the slip plane and accordingly serve as intraplanar strengthening for all parabens with the bond length of 2.681 Å, 2.730 Å and 2.758 Å for EP, PP and BP, respectively. The mobility of slip plane in its lattice in the order EP < PP < BP revealed by simulation of attachment energy [89], maybe resulting from the longer alkyl chain. Two molecules in the asymmetric unit exist in EP and PP crystals, and the angle between two aromatic ring planes is 7.78 ° and 5.08 °, respectively. However, the angle between two aromatic ring planes of BP is 0 ° (parallel), because of only one molecule of BP in the asymmetric unit. Moreover, the van der Waals nonbonded interaction [87] of aromatic ring ··· aromatic ring decreases from EP, PP to BP, however, the interactions of alkyl chain ··· alkyl chain and alkyl chain -- aromatic ring increase. The interaction of the alkyl chain ··· alkyl chain is much smaller than other two kinds of interactions in each paraben, respectively.

EP PP BP

(1 0 0) (0 1 0) (1 0 0) (0 1 0) (1 0 0) (0 1 0)

(7 2 11) (7 1 4) (-2 0 5)

Figure 3. 2 Crystal unit cell of ethyl paraben, propyl paraben and butyl paraben with three planes in crystal structure. (1 0 0) planes and (0 1 0) planes for all parabens and aromatic ring planes, (7 2 11), (7 1 4) and (-2 0 5) plane for ethyl paraben, propyl paraben and butyl paraben, respectively.

3.1.2 Polymorphism and particle morphologies of parabens Only one polymorph of butyl paraben, propyl paraben and ethyl paraben has been found and reported until now [87, 88]. The PXRD spectra of three parabens are shown in Figure 3. 3 and the peaks of propyl paraben are very close to peaks of ethyl paraben. The single crystals of three paraben obtained by slow evaporation in ethanol are shown in Figure 3. 4. There is no obvious difference between these crystals, and the single crystals of parabens obtained in different solvents, respectively, are also similar under SEM (paper IV).

14000 ethyl paraben 12000 propyl paraben butyl paraben 10000

8000

6000 Intersity

4000

2000

0 0 10 20 30 40 50 60 2

Figure 3. 3 PXRD spectra of ethyl paraben[85], propyl paraben[86] and butyl paraben (paper VIII) determined from single crystal structure

EP PP BP Figure 3. 4 Single crystals of ethyl paraben, propyl paraben and butyl paraben by slow evaporation in ethanol

3.2 Phase equilibrium

3.2.1 Solubility Solubility of butyl paraben from 10.0 to 50.0 ˚C was determined by the gravimetric method in pure ethyl acetate, propanol, acetone, methanol, acetonitrile, ethanol and mixture of water and ethanol. The solubility of ethyl paraben and propyl paraben in ethanol, acetone, ethyl acetate and acetonitrile and the solubility of benzocaine and butamben in acetone, ethanol, ethyl acetate and mixture of ethanol and water at 10.0 ˚C have been determined. The temperature was controlled by thermostat baths with stability of ± 0.02 ˚C. The temperature measurement was calibrated by a mercury thermometer (Pricision, Arno amavell, 6983 kreuzwerthelm with uncertainty of ± 0.01 ˚C). A bottle of 200 ml with solvent about 50 ml and an amount of paraben was kept initially in water bath at constant temperature. Saturation was reached by dissolution from a surplus of solid paraben added to the solution, assuring there was solid phase in the solution at equilibrium. The solutions were kept under agitation 400 rpm for more than 12 hours to reach the equilibrium. A 10 ml syringe in its unbroken plastic bag was put into the water bath for several minutes in order to reach the same temperature as the solution. Then the syringe with needle was used to sample (2 to 4 ml) the solution in the bottles. A filter (PTFE 0.2 µm) was attached to the syringe through which the sample of solution was transferred into two small pre-weighed plastic bottles (1-2 ml solution per bottle). Each bottle was quickly covered to prevent

17 evaporation and weighed with its content. Then the cover was removed and the samples were dried in ventilated laboratory hoods at room temperature (about 25 ˚C). The solid sample mass was recorded repeatedly throughout the drying process to establish the point where the weight remained constant which took more than one month. The weight of the final dry sample was used for calculation of the solubility of course with appropriate correction for the weight of the covers. The balance (Mettler AE 240) used during the experiment work had a resolution of 0.00001 g. These steps were repeated for different parabens in different solvents at certain temperature, respectively.

3.2.2 Liquid-liquid phase separation and ternary phase diagrams Liquid-liquid phase separation and ternary phase diagram of each paraben, water and ethanol were determined at 1.0 ˚C, 10.0 ˚C, 20.0 ˚C, 30.0 ˚C, 40.0 ˚C, or 50.0 ˚C. A 300 ml glass bottle with plastic cover put in the thermostat baths whose temperature was controlled with stability of ± 0.02 ˚C. The balance (Tamro HF-300G, A&D Company) used during the experiment work had a resolution of ± 0.001 g. Homogenous solution is clear, but liquid-liquid phase separation solution was cloudy when stirred, resulting from the discontinues phase dispersing in the continues phase. Different regions were explored by adding of paraben, water or ethanol step by step. Firstly, a starting point in the ternary phase diagram was chosen, mixture of paraben, water and ethanol with the certain proportion was prepared in a glass bottle under 300 rmp agitation, kept in water bath at constant temperature. Then one of these materials, butyl paraben, water or ethanol, was added into this solution step by step until a different phase form (for example clear solution changed cloudy or the solution starts to contain undissolved solid butyl paraben, etc.). After phase changed, other two materials were added by smaller step to clarify the location of this phase boundary more exactly. This procedure was repeated from different starting points and more points beside the phase boundary were obtained. Finally, the boundary of ternary phase diagram at certain temperature was optimized through these points. The same method was used for measuring ternary phase diagrams at other temperatures with uncertainty below 1%.

3.3 Thermodynamic properties of pure solid at melting

Melting points, enthalpy of fusion at the fusion temperature of paraben and specific heat capacity of butyl paraben were determined by using differential scanning calorimetry (DSC), TA Instruments, DSC 2920. The calorimeter was calibrated against the melting properties of indium. Samples (2 to 3 mg) of paraben were heated from 293 K, in 5 K increments per minutes, to approximately 40 K above the melting temperature of each paraben, respectively, then cooled down to 293 K, and repeated 2 times for each sample (totally 5 samples). All heat capacity measurements were conducted by modulated isothermal DSC 2920. The modulation amplitude was ± 0.5 K and the modulation period was 80 s. The isothermal period was 30 min. For each measurement one sample of 2 to 6mg was placed in a hermetic Al pan while being purged with nitrogen at a flow rate of 50 ml/min. Pans were selected so that the difference in weight between sample pan and reference pan to ± 0.10 mg. The calorimeter was calibrated against the melting temperature and enthalpy of fusion of Indium, and the heat capacity of sapphire. The heat capacity signal was calibrated with 3 runs of a sapphire sample in the relevant temperature interval.

3.4 Nucleation experiments

The induction time data of parabens has been determined in pure methanol, ethanol, propanol, acetone, ethyl acetate, and in mixtures of ethanol and water having 70% or 90% ethanol by weight. 100mL homogenous solutions of paraben in a solvent were prepared in 300ml glass bottles in a water bath at constant temperature above the saturation temperature, stirred by magnetic stirrers for 30 min to assure that all of the paraben was dissolved in the solutions. By using a 10 mL syringe, solution was quickly distributed into 10 tubes (about 5 ml per tube) respectively, each equipped with small magnetic stir bar, and then the tubes were sealed by parafilm to prevent evaporation.

30.0

30.01  s F  1 2 3 4   water bath for dissolving 5 6 7 8 9 0 T G

Recirculatingrefrigerated tube frame multiple magnetic stirrer circulator at coolerdissolving 1 (20temperature degree C)

water bath for nucleating

10.0

9.99  s F  1 2 3 4   5 6 7 8 9 0 T G tubes

refrigerated circulator at nucleating teimperature

light

Figure 3. 5 Method of determining induction time After keeping these 30 tubes in water bath (dissolving water bath in Figure 3. 5) at dissolving temperature for 30 minutes under 500 rpm agitation, they were transferred to another water bath (nucleating water bath in Figure 3. 5) kept at a constant nucleating temperature which is below saturation temperature. These tubes, fixed with plastic and transparent frame, were put on a big magnetic plate with stirring rate 200 rpm, and a SONY camera (DCR-SR72) was set at a declining angle to observe the solution inside each tube. The solution was initially perfectly clear but became turbid as nucleation starts. After all the tubes had nucleated, they were transferred to the dissolving water bath and hold 30 minutes before transferred to nucleating water bath again. The experiments were repeated at the same temperature several times, and then repeated at two other nucleation temperatures several times. All the recorded videos were played on a computer. The induction time was determined (detailed in paper I) from putting tubes into the water bath at supersaturated temperature to the time turbid appeared in the tubes. The threshold for determination of nucleation was a reduced sharpness in the visibility the white stirrer in each tube or black lines on the magnetic plate (Figure 3. 5). For each condition more than 100 induction time data was determined.

3.5 Cooling crystallization and sandwich crystals

Five cooling crystallization experiments with different concentration of butyl paraben, water and ethanol, and from Exp. 1 to Exp. 5, the proportion of water increased and the proportion of

19 butyl paraben decreased. The solutions were heated to 45 ˚C and equilibrated 30 minutes, after which the solutions were cooled down to 5 ˚C at the rate - 0.1 ˚C per minute. The solutions of each experiment were prepared in a 1 L glass cylindrical crystallizer (Mettler Toledo LabmaxTM) with a double glass jacket to circulate the thermostatic water and were agitated with a stirring rate of 200 rpm. The temperature and agitation in crystallizer were controlled and observed by iControl Labmax version 4.0. To visualize the processes occurring in situ, cooling crystallization was monitored using IR, FBRM and PVM. IR probe (React IRTM diamond ATR composite) with a measurement range from 2000 - 650 cm-1 was operated with measurement duration 2 s, which was controlled by icIR version 4.0 The FBRM probe (D600L version) has a measurement range of 0.25 - 2000 μm, controlled by icFbrm version 4.0. Five population ranges used were 0-5 μm, 5-40 μm, 40-120 μm, 120-500 μm, 0-1000 μm, 0-500 μm, with measurement per 2 s. PVM probe (Model 700) was operated with an image update rate of 6 images per minute, and in-situ 600 μm × 800 μm photos are obtained. The equipments of cooling crystallization are shown as Figure 3. 6.

PVM FBRM

Online particle size measurement system

Cooling jacket

Temperature Temperature 20

0 0h 2h 4h 6h 8h 10h Time (h) 02:31:3403:31:3404:31:3405:31:3406:31:3407:31:3408:31:3409:31:3410:31:3411:31:34 -- In-process particle vision Thermal controller system

On-line IR measurement system

Figure 3. 6 The equipment for the cooling crystallization experiments in ternary phase diagram The crystals obtained in Exp. 4 of cooling crystallization were observed under optical microscope (Olympus SZX 12) and SEM (Hitachi S-4800). The layers of the sandwich crystals were examined by Confocal Raman Microscopy, using a WITec alpha300 system (WITec GmbH, Germany) with a 532 nm laser for excitation, and an objective with 100× magnification and numerical aperture NA = 0.9. The optical parameters give a lateral resolution of 500 nm. Three different areas about 0.2 μm2 on each layer of the sandwich crystal were examined. Each Raman spectrum was recorded with an integration time of 0.5 s, from 10 accumulation spectra. The data was evaluated using the software program WITec project 2.06 (Ulm, Germany). A sandwich crystal was mounted to collect the single crystal X-ray diffraction data in full sphere strategy on an Oxford Diffraction Xcalibur CCD diffractometer with Mo Kα radiation (λ = 0.71073Å). Data integration and faces index were carried out by the CrysAlis software package from Oxford Diffraction.

4. Results

4.1 Solubility

The Figure 4. 1 shows the solubility of paraben in ethyl acetate, propanol, acetone, methanol, acetonitrile, ethanol and in ethanol aqueous solvents from 10.0 ˚C to 50.0 ˚C. It is obvious that solubility in these solvents all increase with the increasing temperature, the temperature dependence varies. In pure solvents, the solubility in acetonitrile is more sensitive to temperature. The solubility of butyl paraben in water and 10 % and 30 % ethanol is much lower than in other solvents. The solubility in methanol is highest at 10.0 ˚C, but solubility is highest in 70 % ethanol at 50.0 ˚C. The solubility curves of butyl paraben in ethyl acetate, propanol, methanol, and ethanol are nearly parallel (detailed in paper VI).

water methanol 10 10% ethanol ethanol 30% ethanol acetone 50% ethanol 8 propanol 70% ethanol acetonitrile 90% ethanol 6 ethyl acetate

4 Solubility (g/g)

0 10 20 30 40 50

Temperate/ C Figure 4. 1 Solubility of butyl paraben in pure solvents and ethanol aqueous solvents from 1.0˚C to 50.0˚C There is only one data of solubility in 50 % ethanol, and no solubility data is presented here in water above 50.0 ˚C, in 10 % ethanol above 40.0 ˚C, in 30% ethanol above 20.0 ˚C, since the liquid-liquid phase separation occurs in these solutions. LLPS and ternary diagrams will be discussed in Section 4.2. Figure 4. 2 shows that the solubility of parabens in mixture of ethanol and water correlated by a third order polynomial equation [90] (Appednix. 1). At 10.0 ˚C, solubility of butyl paraben is higher than propyl paraben and solubility of ethyl paraben is lowest in pure ethanol and mixture solvents with high proportion of ethanol. However, in water and 10% ethanol-water the solubility of ethyl paraben is highest, and the solubility of butyl paraben is lowest, which is consistent with the literature that the solvation process induces a higher solubility of ethyl paraben than propyl paraben and butyl paraben [87] in water.

12 EP 50°C PP 50°C 10 PP 40°C BP 50°C BP 40°C 8 BP 30°C BP 20°C BP 10°C 6 BP 1°C

g g / paraben g solvent 2

0.0 0.2 0.4 0.6 0.8 1.0 g ethanol / g solvent

Figure 4. 2 Solubility of ethyl paraben, propyl paraben, butyl paraben (Paper VII) in ethanol aqueous solvents and the third order polynomial correlated curves.

4.2 Liquid-liquid phase separation and ternary phase diagram

Figure 4. 3 shows the ternary phase diagrams of each paraben in water and ethanol mixture in temperature range from 1.0 ˚C to 50.0 ˚C and lines are the best attempt to identify phase boundaries. There are five regions in the diagram, for ethyl paraben at 50.0 ˚C, for propyl paraben at 40.0 ˚C and 50.0 ˚C and for butyl paraben from 10.0 ˚C to 40.0 ˚C. Region 1 (liquid phase) is an undersaturated (with respect to paraben) homogeneous solution. In Region 2 (liquid-liquid phase), two liquid phases are in equilibrium however they are undersaturated with respect to butyl paraben. In Region 3 (solid-liquid phase), a water rich homogeneous liquid is saturated with butyl paraben. In Region 4 (solid-liquid-liquid phase) solid paraben and two liquid phases are in equilibrium. In Region 5 (solid-liquid phase), solid butyl paraben is in equilibrium with an ethanol rich solution and the solution appears a bit yellow, resulting from the high concentration of butyl paraben. For butyl paraben at 1.0 ˚C, all regions but 1 and 3 are absent, and the diagram only presents a simple solid-liquid phase equilibrium. Already at 10.0 ˚C the diagram is much more complex exposing all five regions, and the solid-liquid solubility line cuts through the liquid-liquid phase separation region (region 2 and 4). At increasing temperature the liquid-liquid phase separation region expands gradually into the ethanol lean part of the diagram and the solubility curve of butyl paraben moves along with that, meaning that primarily the region of an unsaturated system (with respect to butyl paraben) of two liquids expands. From 30 ˚C and upwards region 4 decreases until we reach 50 ˚C where region 3 and 4 have essentially disappeared. Along with these changes also Region 5, bound by the solubility curve of butyl paraben in ethanol rich solution and the liquid-liquid phase separation boundary, gradually decreases in size with increasing temperature. One reason is that the concentration of butyl paraben in the ethanol rich solution steadily increases with increasing temperature.

BP BP BP 50.0 ˚C 40.0 ˚C 30.0 ˚C Region 1 (Liquid Phase) Region 2 (Liquid-liquid Phase) Region 3 (Solid-liquid Phase) Region 4 (Solid-liquid-liquid Phase) Region 5 (Solid-liquid Phase 2)

W E W E W E BP BP BP 20.0 ˚C 10.0 ˚C 1.0 ˚C

W E W E W E BP-PP-EP PP EP 50.0 ˚C 50.0 ˚C 50.0 ˚C

W E W E W E

Figure 4. 3 Ternary phase diagrams of butyl paraben, water and ethanol at 1.0 ˚C, 10.0 ˚C, 20.0 ˚C, 30 ˚C, 40.0 ˚C and 50.0 ˚C, and composing points of solution for five cooling experiment, Exp. 1 to Exp. 5, in these ternary diagrams. Ternary diagrams of propyl paraben, water and ethanol, ethyl paraben, water and ethanol at 50.0 ˚C For all parabens, the boundary lines between region 3 and region 4 and between region 4 and region 5 are straight, indicating at considerable concentration of butyl paraben liquid-liquid phase separation is only dependent on the solvent but independent on the solute. The straight boundary line between 2 and 4, which is also solubility curve of parabens in liquid-liquid phase solution, indicates that the saturation of liquid-liquid phase separation solution is nearly independent on proportion of ethanol. In this ternary system, the area of liquid-liquid phase separation region increases with increasing temperature, compared with many ternary system in literature, where the area of liquid-liquid phase separation region decreases with increasing temperature [91, 92]. The LLPS solution for all parabens has two layers: top layer is paraben-lean and water-rich layer and bottom layer is paraben-rich and water-lean layer, and the concentrations of ethanol in these two layers are both closed to the concentration of ethanol in the whole LLPS solution.

4.3 Thermodynamic properties of pure solid

Figure 4. 4 shows heat flow of one sample of 2-3 mg paraben in DSC measurement, which curve is the average of 5 samples repeated 2 times. The melting temperature of all parabens (Table 4. 1), with standard deviation below 0.6 K, are in good consistence with literature value [87, 93]. The enthalpy of melting of ethyl paraben and propyl paraben are little lower than literature values. of butyl paraben is 25.535 kJ/mol, with standard deviation 1.934 kJ/mol, is in the range of literature values (24.1 - 27.4 kJ/mol). The melting point increases in the order: BP < PP < EP, which is the opposite order of the molecular weight. However, the enthalpy of melting and molecular volume of PP is highest. In addition, the enthalpy of melting of BP is lowest and the molecular volume of EP is lowest.

80 EP 60 PP BP

20 Cool

0 Heat flow (mW) -20 Heat

-40

0 30 60 90 120 150 Temperature (C)

Figure 4. 4 Heat flow of parabens in DSC measurement (circulations of heating and cooling)

Table 4. 1 Physical properties of parabens Melting Enthalpy of Density Molecular volume Molecular weight temperature (˚ ) melting (kJ/mol) (g/cm3) (10-28m3) (g/mol) EP 115.49 25.761 1.168 2.362 166.2 PP 96.38 26.507 1.134 2.638 180.2 BP 67.34 25.535 1.231 2.620 194.2 The average heat capacity curve of the solid form, from about 304 K to 315 K, and average heat capacity curve of the solute as a pure melt of butyl paraben, from about 356 K to 369 K are shown in Figure 4. 5. The red and green lines in Figure 4. 5 show the correlation by first order equations and second order equations, respectively, for both heat capacity of the solid form and the solute as pure melt. Then the can be determined by Equ. (14) and (15) with first order (w=0) and second order correlation with unit J/g/K:

(74)

(75)

experiment curves first order equation second order equation

3.6 (J/g/K)

p 2.8 C

2.7

2.6 -40 -30 10 20 30 T-T (K) m Figure 4. 5 Heat capacity curves (black), first order correlation (red) and second order correlation (green)

4.4 Relation between solid-state thermodynamic properties and solubility

The solubility data of butyl paraben can be well correlated by the non linear equation (Equ. 2) and of butyl paraben are obtained (paper VI). By using the Equ. 4 with , the

of butyl paraben in different solvents at different temperature are obtained (App. 2).

50 curves

)

-1

mol 

30 340.49K kJ

( 313.15K

293.15K 303.15K 323.15K /

283.15K

Solv 20 H curves 10 Expetimental, and w=0 Expetimental Optimal T,H,q,r, and w=0 Optimal w,r 0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 lnx eq

Figure 4. 6 Correlation between of solution and molar fraction solubility at 283.15 K to 323.15 K for butyl paraben in 6 solvents (Equ. 4 vs. Equ. 2), and the correlation between

and (Equ. 19 vs. Equ. 18). Dotted curves: the second-order relation of the versus (Equ. 20). Green solid line: thermodynamic properties from experimental value and w=0. Blue solid line: thermodynamic properties from optimization and w=0.

Figure 4. 6 presents solubility data (open plots) as van’t Hoff enthalpy of solution versus the logarithm of the solubility mole fraction, as given by Equ. 2 and 4 for each solvent. The corresponding dashed curves (below called solubility-van’t Hoff enthalpy, , curve) are the second order correlations corresponding to Equ. 20, and 6 open dots of each curve represents solubility data in 6 pure solvents, in acetonitrile, in methanol, in ethanol, in ethyl acetate, in propanol and acetone from up to down, respectively. The values for acetonitrile, methanol, ethyl acetate, propanol and acetone are well correlated by the second order equation, Equ. 20, including some considerable deviations for the ethanol values. The green more horizontal solid line (Figure 4. 6) with solid dots is describing the properties of an ideal saturated solution, i.e. the activity and the enthalpy of fusion of the pure solid phase, as a function of temperature. The solid dots on the solid curve (below called activity-fusion enthalpy, , curve) are the ideal solubility and the enthalpy of fusion for each experimental temperature according to Equ. 18, and Equ. 19, respectively. The green solid curve has been calculated by insertion of experimentally determined data for melting enthalpy, melting temperature, and the heat capacity is correlated by first order equation, Equ. 74, i.e. q and r according to the data in the first row of Table 4. 2. Ideally the dots on the green curve should fall on the intersection between the green curve and the curves. Even though the agreement is reasonably good it is not perfect. In order to reach a better agreement, the entire pure solid phase curve, the individual dots or both might have to be shifted.

Considering the uncertainty of the heat capacity of the melt, , especially the extrapolation far below the melting point, the first order equation may not be the optimum representation. The second order Equ. 75 of has been investigated (red solid curve in Figure 4. 6), which make the dots on the curve better fitting to the curves. In addition, the optimal Equ. 76 has been investigated to determine the optimal thermodynamic properties of pure solid, , , q, r and w,

∑ [ ] (76) In order to find the minimum sum of difference between the enthalpy values from curves with that from curve which have equal , billions of attempts within large range of 5 parameters have been calculated by program on computer, and the optimal value can be determined after the whole optimization process. We can find the optimization of all the five parameters, , , q, r and w, or fix one or more to find the optimizations of other parameters. Table 4. 2 Experimental and optimal values of 4 parameters in Equ. 18 and Equ. 19

q r w OF curve Color 2 3 (kJ/mol) (J/mol/K) (J/mol/K ) (J/mol/K ) (Equ.76) Experimental w=0 Green 340.38 25.535 115.264 0.301 0 9.564 Optimal values w=0 Blue 344.00 20.800 149.800 -1.200 0 0.934 Experimental values Red 340.49 25.535 122.215 -2.107 -0.0147 6.644 Optimal values Black 340.49 25.535 122.215 -1.350 -0.0099 5.336 Blue curve represents the hypothetical solvent whose activity coefficient is unity. The dots are almost both on the curves and on the curve, which is in much better agreement than the curves with green curve. The optimal parameters of and are 344.0K and 20.80KJ/mol, respectively, which are similar as the extrapolated values from the correlated solubility equations in ethyl acetate, propanol, acetone, methanol and ethanol (paper II). Table 4. 2 shows the optimal values of 4 parameters, the optimal melting temperature is a little higher than the experimental value; the optimal enthalpy is smaller than the experimental value; w equals to 0 and the optimal values of q and r are much different from

26 the experimental value. By using the optimal values the curves can fit the curve very well, however, the enthalpy of fusion is not consistent with DSC measurements. Similar as green curve, the red curve has been calculated by insertion of experimentally determined data, and, however, the heat capacity is correlated by a second order equation, Equ. 75. The melting enthalpy, melting temperature, q, r and w are shown in third row of Table 4. 2. While the black curve uses the optimal values of r and w. Figure 4. 6 illustrates these two curves are closed to each other. Table 4. 2 shows the w and r values from experiment and from optimization are also closed, which suggests that second order correlation for heat capacity introduce a better fitting between curve and

curves.

ln  Acetonitrile Methanol Ethyl Acetate -0.5 3

Ethanol coefficient Activity

Propanpl = 340.49K

Acetone m T

-1.0 2 lna

-1.5 1

0 280 290 300 310 320 330 340 Temperature (K)

Figure 4. 7 of butyl paraben from Equ. 18 and corresponding of butyl paraben in 6 solvents at temperature 274.15 K - 323.15 K

Figure 4. 7 suggests when temperature increases to melting point, 340.49 K, the of butyl paraben in methanol, ethanol, propanol, ethyl acetate, acetone and acetonitrile all tend to one point that equal to unit (App. 2). The curves in Figure 4. 7 show that the activity coefficients in 6 solvents are also dependent on the temperature and the activity coefficients in these solvents increase or decrease toward unity. The black curve was used to determine the activity, and from 274.15 K to 323.15 K, there is no case of changing in sigh for the activity curves of butyl paraben in all solvents, however, at about 330 K, there is a slight transition from to for the activity curve of butyl paraben in ethyl acetate, which is better than activity determined by other three curves. Moreover, the dots from curve from optimization 2 is better consistent with curves than the dots from other three curves (Table 4. 2), and the activity value from optimization 2 would be most reasonable (values of thermodynamic properties of solid-state butyl paraben are shown in App. 2)

4.5 Nucleation experiments

4.5.1 Random nature of nucleation Figure 4. 8(a) shows the induction time from 20 tubes in 6 batches. The solutions in these 20 tubes are equal (100mL solution was equally separated into 20 tubes), the supersaturation is same (nucleated at 283.15K), dissolving time and stirring rate are all in equal conditions. The random distribution was revealed by the random color in whole range of Figure 4. 8(a). However, the induction time results show wide variation both for each tube in all 6 parallel batches and for 20 tubes in the each batch. In Figure 4. 8(b), ‘–’ represents average induction time of each tube in 6 batches, and bar shows spread range of induction time in 6 batches. a) b) 6 Batch 1st 499.0

400.0 Batch 2nd 5 320.0 600 Batch 3rd 280.0 Batch 4th 230.0 Batch 5th 4 180.0 450 Batch 6th 130.0

80.00 Average induction time

40.00 Range per tube

3 300 Batch No.

2 Induction Time(s) 150

1 0 2 4 6 8 10 12 14 16 18 20 5 10 15 20 Tube No. Tube No. Figure 4. 8 Induction time for 20 tubes from 1st to 6th batch under equal experimental conditions. a) Contour schema for induction time data. b) The range and average of induction time per tube. In 6 parallel batches, the longest induction time for one tube can reach nearly 10 times longer than the shortest induction time. Among all experimental data, the longest induction time is nearly 30 times longer than the shortest value. All these variations indicate the random nature of nucleation. However, the variation of average induction time for each tube and variation of average induction time for each batch is narrow, indicating the consistency of these data.

4.5.2 Statistical analysis of induction time For each solvent, more than 300 induction time data for each paraben at different supersaturation levels was determined. For butyl paraben in 70% ethanol, 90% ethanol, propanol, ethanol, methanol, ethyl acetate and acetone and for propyl and ethyl paraben in ethanol, ethyl acetate and acetone at three different supersaturation levels, totally more than 5000 induction time data was determined. The induction time data shows wider variation at lower supersaturation (paper I). Figure 4. 9 shows the induction time of parabens in different solvents at supersaturation from 1.06 to 1.48, and the cumulative distributions are dependent on the supersaturation as well as kind of solvent. These induction time results have been fitted by different mathematical functions in software Easyfit [94], which exposed that the induction time data is better fitted by Burr distribution (Figure 4. 10) than other distributions, e.g. lognormal distribution and normal distribution. In some solvents at lower supersaturation, several very long induction time data was recorded in the nucleation experiments, and the average value of induction time is highly influenced by these data. The mode of induction is always difficult to capture at the lower supersaturation, e.g. more than 2 equal induction times can hardly be found. The median value of induction time is not influenced by the very long induction time data neither influenced by the very short induction time data.

0.9

0.6

S= 1.29 BP-70% E

S= 1.26 BP-90% E S= 1.19 BP-PR S= 1.13 BP-E S= 1.15 BP-EA 0.3 S= 1.11 BP-ME S= 1.06 BP-AC

Cumulative distribution S= 1.26 PP-EA S= 1.25 PP-AC S= 1.48 PP-E S= 1.18 EP-EA S= 1.16 EP-AC S= 1.30 EP-E 200 400 600 800 t / s ind Figure 4. 9 Cumulative distribution of induction time of butyl paraben in 70% ethanol, 90% ethanol, propanol, ethanol, methanol, ethyl acetate and acetone and of induction time of propyl and ethyl paraben in ethanol, ethyl acetate and acetone at certain supersaturation, respectively. Each curve includes 100 - 150 experimental data.

Figure 4. 10 Schematic of induction time cumulative distribution shape

4.5.3 Determination of interfacial energy of parabens in various solvents In Figure 4. 11, the dots show the ln value of the median induction time of parabens in different solvents at 3 different supersaturation levels, respectively. According to Equ. (55), the interfacial energy is proportional to the slopes of the correlation lines. Therefore, the higher the slope in Figure 4. 11 the higher is the activation energy for nucleation and at equal driving force the longer induction time becomes. The data show that nucleation of butyl paraben is much easier in acetone than in the other solvents and that nucleation is most difficult in propanol and in water-ethanol mixtures. In EP and PP experiments, nucleation in ethanol is also most difficult, followed by ethyl acetate, then by acetone, which is same as for butyl paraben in these solvents.

9 70% E 90% E PR 8 E ME EA 7 AC

Lnt PP-E 6 6 PP-EA PP-AC EP-E EP-EA 5 EP-AC 4 0 10 20 4

0 50 100 150 200 250 300

-3 -2  T lnS 

Figure 4. 11 of butyl paraben in 70% ethanol, 90% ethanol, propanol, methanol, and butyl, propyl and ethyl paraben in ethanol, ethyl acetate and acetone versus with first order correlation lines, respectively. Bars indicate the 95% confidence interval of . Table 4. 3 shows the median induction time results of butyl paraben in 70% ethanol, 90% ethanol, propanol, ethanol, ethyl acetate, methanol and acetone in the top 21 rows, and propyl and ethyl paraben in ethanol, ethyl acetate and acetone in the bottom 6 rows. The slope B can be determined from butyl parabens in different solvents at three supersaturations in Figure 4. 11. The interfacial energy of parabens in these solvents, nucleation free energy per mol cluster, critical radius of nucleus and critical number of molecules for forming one nucleus can also be determined under each experiment condition, respectively, shown in Table 4. 3. Table 4. 3 shows when the driving forces (RTlnS) of nucleation increase for parabens in different solvents, the induction time, the critical free energy, the critical radius and critical number molecules all decrease. In some cases, the size of the critical nuclei is up to a few nanometers, and the number of molecules to make up a critical nucleus range down to a single molecule. Even though very low number of molecules in the critical nucleus has been reported before [95-97], this as well as the corresponding very low activation energies does not appear to be realistic since in this work the induction time much larger than zero are always recorded. However, in two cases, the critical radii are above 2 nm, and critical number of molecules are more than 200 (PP and EP in AC). The solid-liquid interfacial energy of parabens in acetone is smaller than 0.9 mJ·m-2, while, interfacial energy of butyl paraben in almost all other solvents is higher than 1 mJ·m-2. The interfacial energy of butyl paraben in pure alcohols is in the order: propanol > ethanol > methanol, and the interfacial energy of butyl paraben in ethanol aqueous solvents is in order that 70% E > 90% E > pure E. The interfacial energy of ethyl paraben and propyl paraben in pure solvents is in the order: ethanol > ethyl acetate > acetone, which is same as butyl paraben. In acetone and ethanol, interfacial energy of butyl paraben is higher than propyl paraben, and interfacial energy of ethyl paraben is lowest. In ethyl acetate, interfacial energy of three parabens is more or less equal.

Table 4. 3 Nucleation properties of parabens in different solvents Solute- RTlnS IT r c No.c lnA solvent (kJ/mol) (s) (kJ/mol) (mJ/m2) (nm) 0.487 854 5.50 1.1 23 BP-70%E 0.606 329 3.55 1.73 0.9 12 7.81 1.022 144 1.25 0.5 2 0.479 170 4.84 1.1 20 BP-90%E 0.531 113 3.94 1.64 1.0 15 9.17 0.563 99 3.50 0.9 12 0.317 3172 10.3 1.6 64 BP-PR 0.415 444 6.24 1.62 1.2 30 8.53 0.580 181 3.30 0.9 12 0.227 1360 7.10 1.6 63 BP-E 0.284 532 4.52 1.13* 1.3 32 7.92 0.471 141 1.65 0.8 7 0.250 587 5.72 1.4 46 BP-EA 0.333 178 3.24 1.13** 1.1 19 8.27 0.468 111 1.63 0.8 7 0.171 6861 10.51 2.0 123 BP-ME 0.244 624 5.14 1.07 1.4 42 7.83 0.486 148 1.29 0.7 5 0.094 65 0.74 1.0 16 BP-AC 0.139 55 0.34 0.30 0.7 5 8.35 0.224 50 0.13 0.4 1 0.283 8502 12.6 1.8 99 PP-E 0.330 4682 8.65 1.54 1.5 56 8.11 0.612 139 2.57 0.8 9 0.212 620 6.43 1.6 68 PP-EA 0.235 316 4.50 1.01 1.3 40 8.46 0.377 87 1.77 0.8 10 0.094 5449 9.56 2.3 202 PP-AC 0.118 2840 5.80 0.72 1.8 96 7.33 0.353 145 0.82 0.7 5 0.471 3058 12.33 1.4 55 EP-E 0.730 153 5.26 2.39 0.9 15 9.42 0.918 65 3.27 0.7 8 0.141 7813 9.60 2.0 144 EP-EA 0.235 1828 3.84 0.98 1.2 36 7.06 0.565 139 0.59 0.5 2 0.094 9450 11.74 2.4 253 EP-AC 0.165 1559 4.80 0.82 1.5 66 7.72 0.518 64 0.41 0.5 2

Uncertainty UT = 0.01K, UTime=1s, *=1.134,**=1.125

4.5.4 Determination of interfacial energy by other methods The interfacial energy and pre-exponential of butyl paraben in different solvents determined from induction time and from nucleation rate are compared. The median values of induction time (t in Figure 4. 12) in each experiment were used in section 4.4.4 to determine interfacial energy, , and pre-exponential factor, (results shown in Figure 4. 15). In this work the average values of induction time ( in Figure 4. 12) in each experiment have also been investigated to determine the interfacial energy and pre-exponential factor (shown in Figure 4. 15). At the same time other methods (discussed below) can be compared in Figure 4. 12.

1.0 t t tA Median: t A A

Average: tA 0.8 Equ 61: tE61

0.6 Median value Equ. 61 P =0.5 P =0.632 t t

t t t S=1.23 0.4 S=1.26 Initial part S=1.28 Initial part Equ. 60 Initial part 0.2

Equ. 60 Equ. 63 Cumulative distribution Equ. 60 Equ. 63 t Equ. 63 0.0 E61 tE61 tE61 0 100 200 300 400 Induction time (s)

Figure 4. 12 Median induction time, t. Average induction time, . Nucleation rate determined using by Equ. (61). Solid curves correlated by Equ. (60) with both solid and open dots. Dashed curves correlated by Equ. (63) with only open dots. The experimental cumulative distributions of induction time are shown in Figure 4. 9. The probability in cumulative distribution approaches 100% more quickly, indicating a higher nucleation rate of butyl paraben at this supersaturation level. The Equ. (60) was investigated to determine the nucleation, though the distribution not perfectly fits the lognormal distribution. Figure 4. 13 shows the induction time data of butyl paraben in ethanol under three different supersaturation. The slope of –lnP(0)/v vs. t was determined by fitting data with first order equation, the higher value of slope indicates the higher nucleation rate. Then, the nucleation rate obtained from Figure 4. 13 and Equ. (60) were used to determine the interfacial energy and pre-exponential factor (results shown in Figure 4. 15) by first order fitting lnJ vs. at three different supersaturation levels (red dots in Figure 4. 14). The induction time data (all dots in Figure 4. 12) can also be directly fitted by Equ. (59), and the fitting results are shown as dashed curve in Figure 4. 12, and the dashed correlation curves illustrate inconsistency with experimental data.

8.0x10

6.0x10 -3

/ m / S=1.23

-1 S=1.26 V

 4.0x10

N S=1.28 initial part 5 initial part 2.0x10 initial part Equation 60 Equation 63 0.0 0 100 200 300 400 t / s ind Figure 4. 13 Nucleation rate determined by first order correlation –lnP(0)/v vs. t. Solid line by Equ. (60) with both solid and open dots, and dashed line by Equ. (63) with only open dots. The solid curves in Figure 4. 13 represent the first order correlation by Equ. (63), and are drawn somewhat subjectively to capture the slope of the curve after the time lag and growth times, i.e. the initial part (y value below about ) of the data is not included. By plotting the nucleation rate for each supersaturation vs. the driving force function (blue dots in Figure 4. 14), the interfacial energy and the pre-exponential factor can be determined (results shown in Figure 4. 15). The corresponding plots for the other solvents look essentially the same, but the scatter around the straight line varies. The induction time data (only open dots) is also directly correlated by Equ. (59) without the initial part of experimental data, and the fitting results are shown as solid curves in Figure 4. 12, performing much better consistency with experimental data than the dashed curves.

9.5

9.0 Equation 60 Equation 61 Equation 63 8.5

8.0 ln ln J

7.5

7.0

-11 -10 -9 -8 T-3lnS-2

Figure 4. 14 Determination of nucleation parameters from the nucleation rate by Equ. (60), (61) and (63)

The experimentally found value, , from distribution curve in curve in Figure 4. 12 has been used to determine nucleation rate by Equ. (61). Then the interfacial energy and pre-exponential factor (results shown in Figure 4. 15) can be determined by first order fitting (black dots in Figure 4. 14) by Equ. (54). Considering the appearance of the data in Figure 4. 12 and Figure 4. 13, it is obvious that induction time data is not consistent with the dashed curves depicted by Equ. (60). The S-shape induction time distribution is not uncommon [2, 32, 98-100]. One explanation might be that the assumption of steady state nucleation on which Equ. (60) and Equ. (61) are based, are not fulfilled, i.e. the induction time distribution is not natural logarithm function distribution (Figure 4. 10). In fact, the shape of the data in Figure 4. 12 and Figure 4. 13 agrees reasonably with the shape expected for nucleation under non-steady state conditions, which is better fitted by burr distribution (Figure 4. 10). In the experiments, the tubes are moved from a water bath keeping the solutions undersaturated to a water bath having the desired nucleation temperature kept constant. However, more than 60 seconds are needed for the solution in the tubes to reach the temperature of the nucleation batch. In the non-steady state nucleation theory, nucleation might occur before cluster distribution has adjusted to the supersaturation conditions in the solution. Usually in steady state nucleation the time constant for cluster orderly arrangement is assumed to be negligible, but the actual situation for organic molecules in organic solvents hasn’t really been clarified. The non-steady state nucleation turns to steady state nucleation after a period for clusters to be orderly arranged, which might be revealed by the solid dots in Figure 4. 12 and Figure 4. 13. In relation to recent work on history of solution effects [101], this orderly arrangement time might be much longer than anticipated which might contribute to the curvature. All these five methods are based on the classical nucleation theory, induction time distribution and the slope of T3lnS-2 vs. lnt or -T3lnS-2 vs. lnJ was used to calculate the solid-liquid interfacial energy, free energy of nucleation, critical radius of cluster and critical number in one cluster. There is no big difference between the interfacial energy and pre-exponential factor obtained by these 5 methods. The order of interfacial energy for butyl paraben in these solvents are almost same (expect one case by Equ. (61) and by Equ. (63)).

12 70% E PR EA AC 70% E PR EA AC 2.4

90% E E ME 90% E E ME 2 9 1.8

1.2 Ln A

0.6 3 Interfacial energy mJ/m

0.0 0 Median Average Equ. 60 Equ. 61 Equ. 63 Median Average Equ. 60 Equ. 61 Equ. 63 value value Nucleation Nucleation Nucleation value value Nucleation Nucleation Nucleation induction induction rate rate rate induction induction rate rate rate time time time time Figure 4. 15 Interfacial energy, , pre-exponential factor, , of butyl paraben in different solvents by 5 methods In Figure 4. 16 the goodness of linear correlation (R2 – value) is compared. Method by using the median value directly from the cumulative distribution provides fairly better fit to a straight line

34 than other 4 methods. Concerning the three methods based on nucleation rate, the R2 – value is somewhat highest for the method based on Equ. (61) and is overall lowest for the method by Equ. (63). The median value is always used in statistical analysis which is not normal distribution [102] (Figure 4. 10) in medicine, social research or other fields. In addition, the median value of induction time in this work is less influenced by initial part and the extreme long induction time data, accordingly median induction time should be the more reliable approach for describing the nucleation experiments.

70% E PR EA AC 90% E E ME

1.0

0.8

0.6 Determination coefficient

Median Average Equ. 60 Equ. 61 Equ. 63 value value Nucleation Nucleation Nucleation induction induction rate rate rate time time

Figure 4. 16 Goodness of fit to a straight line in determination of interfacial energy and pre-exponential factor

4.5.5 Influence of solute and solvent on nucleation process All the solvent parameters listed in Table 4. 4 have been investigated to correlate with interfacial energy of parabens in these solvents. Figure 4. 17(i) shows that interfacial energy of butyl paraben increase with decreasing dipole moment of the solvents. However, there is no obvious relation found between the density and polarity [103], ( ), with interfacial energy. The inversely proportional correlation between pre-exponential factor and viscosity of solvent predicted by Equ. (73) is not consistent with butyl paraben cases, and the values estimated from Equ. (73) are always 1026 to 1027 higher than the experimental values. Table 4. 4 Solvents properties and nucleation properties Solvent Dipole Surface Boiling Viscosity lnA density moment tension (mJ/m2) T K (mPa∙s) (g / m3) (D) (mN∙m) >90%E >90%E 70%E 1.73 11.03 80.1 - 25.5 2.04 <1 <1 > 0.8 > 0.65 90%E 1.64 12.39 78.7 - 23.2 1.42 < 70%E <70%E PR 1.62 11.75 0.80 0.62 97.1 1.5 23.7 1.72 E 1.13 11.14 0.79 0.65 78.4 1.7 22.3 1.08 EA 1.13 11.49 0.90 0.23 77.2 1.6 24.0 0.46 ME 1.07 11.05 0.79 0.76 66.0 1.9 22.6 0.60 AC 0.30 11.57 0.79 0.36 56.1 3.0 23.3 0.33

Solubility at 10.0 ℃, [104, 105] at 20.0 ℃, [103], [105], Viscosity [105] at 25.0 ℃

Figure 4. 17(ii) shows the relation between interfacial energy and molar fraction solubility (paper VI) of butyl paraben in different solvents at 283.15K (paper II). The red dotted guiding line shows the tendency that the interfacial energy decreases with increasing solubility. However, the estimated value based on Mersmann equation[106] i.e. Equ. (64), (organic dots in Figure 4. 18) are always 3-4 time higher than the experimental results without a good correlation.

BP-E EP-E i) ii) BP-EA EP-EA BP-AC PR EP-AC 4 BP-ME mJ/m energy Interfacial PP-E

2 1.5 BP-PR PP-EA BP-90% E PP-AC BP-70% E 3 ME EA E

1.0 2

1 0.5

AC 2

Interfacial energy mJ/m 0

0.4 0.6 0.10 0.15 0.20 0.25 0.30

Dipole moment 1/D Mole fraction solubility

Figure 4. 17 Interfacial energy of parabens in different solvents vs. dipole moment and viscosity of solvents. The dotted line is a guiding line. The estimated interfacial energy values of butyl paraben from Turnbull equation, i.e. Equ. (65) Equ. (66) and Equ. (67) are somehow independent on the solvents (green dots in Figure 4. 18), and the interfacial energy of EP and PP cannot extrapolated by Turnbull equation, resulting from the lack of heat capacity data and solution enthalpy values.

12 Mersmann Neumann Turnbull equation equation equation EP EP BP

2 PP 9 PP BP BP

6 Slope of guiding line

3 =1 Estimated value mJ/m

0 1 2 3 Experimental valuemJ/m2

Figure 4. 18 Estimated interfacial energy values from Mersmann equation, Neumann equation and Turnbull equation. The dashed line is isoline of estimated value and experimental value.

The estimated values from Neumann equation, i.e. Equ. (68), Equ. (69) and Equ. (70), shows much better consistency with experimental values (blue dots in Figure 4. 18) compared with Mersmann equation and Turnbull equation, however, more than 70 % variation is found between estimated value with experimental values in some cases. In Figure 4. 19, the interfacial energy for each solute-solvent combination is plotted together with the mole fraction solubility at 283.15K. It can be seen that for each compound, the interfacial energy decreases and the solubility increases in the order: ethanol < ethyl acetate < acetone. The mole fraction solubility of the three parabens in each solvent increases in the order EP < PP < BP. In acetone, the interfacial energy is lowest for BP, followed by PP and then EP, and the order is same for parabens in ethanol, but in ethyl acetate interfacial energy of parabens clarifies only small differences. There appears to be no simple correlation to solvent polarity, as given by comparing dielectric constants, Reichardt’s polarity parameter [103] , however, weaker dependence of interfacial energy on paraben carbon tail length was observed with reduced solvent polarity.

0.35

2.5

) 0.30 2

2.0 0.25

1.5 0.20

1.0

0.15 Molefraction solubility

0.5 0.10 Interfacial energy(mJ/m

0.0 0.05 BP PP EP BP- PP EP BP- PP EP - - - - E -E E EA EA EA AC -AC -AC

Figure 4. 19 Mole fraction solubility and interfacial energy of ethyl, propyl and butyl paraben in ethanol, acetone and ethyl acetate

4.6 Correlation of interfacial energy with solvent and solute properties

4.6.1 Interfacial energy and solvent boiling point In Figure 4. 20, the interfacial energy as determined by the experiments (Table 4. 3) is plotted against the boiling point of the solvent (Table 4. 4). Obviously, there is a reasonably clear increase in interfacial energy of butyl paraben as the boiling points of the solvents (solvent mixture) increases, and interfacial energy of PP and EP shows fairly same tendency. This correlation is also in good agreement of several reported experimental studies for single organic compound in different solvents. Very few studies for determining solid-liquid interfacial energy of organic compound in different solvents are reported. Paracetamol had higher interfacial energy in solvent of higher boiling point [107, 108], the same tendency was reported for polymorph A famotidine in different solvents [109], and both of these two compounds are shown in Figure 4. 21,

E PP 1.5

2 BP 2

70%E 1.0

90%E mJ/m AC EA  PR 0.5

ME 2 1 E

EA EP E

mJ/m 

2 2

mJ/m  AC 1 AC EA 0

60 70 80 90 100 60 70 80 Boiling point C Boiling point CBoiling point ˚C

Figure 4. 20 Solid-liquid interfacial energy of parabens in different boiling point solvents 25 Famotidine polymorph A 20

Acetonitrile

15 Water ) 2 10 ME Water

3 (mJ/m

 AC 20%AC 2 ME 25%AC PR 35%AC 30%AC 1 Paracetamol

60 70 80 90 100 110 Boiling point C

Figure 4. 21 Solid-liquid interfacial energy of paracetamol and famotidine polymorph A in different boiling point solvents Metastable zone width experiments also revealed the tendency that the metastable zone becomes wider as the increasing solvent boiling point. It is reported that average RTlnS of m-aminobenzoic acid metastable zone was higher in higher boiling point solvent [110], shown in Figure 4. 22. The average supersaturation of vanillin metastable zone was larger in the higher boiling point solvent [111], also shown in Figure 4. 22 The experimental results revealed that at 290 K the racemic mandelic acid nucleated at larger supersaturation level in higher boiling temperature solvent [112], the order of the supersaturation is: in acetic acid (119 ˚ ) > in isobutyl acetate (118 ˚ ) > in toluene-methyl isobutyl ketone (111-117 ˚ ), and the boiling temperature, shown in brackets, of these solvents follow the same order.

Vanillin 16 Ethylvanillin 12 W 95%ethylene glycol 20%PR

40%PR  40%ethylene glycol 95%E 8 8 95%E 95%PR 20%ethylene glycol 40%PR

95%PR  40%PR 20%PR 20%E W 95%PR 4 0 80 90 100 80 90 100 0 Aminobenzoic acid Racemic mandelic acid 60 2.4 acetic acid

Supersaturation ACE 40 1.8

isobutyl acetate

W 

toluene-methyl isobutyl ketone 20 1.2 ME

60 80 100 112 114 116 118 Bolting point C Boiling point ˚C Bolting point C

Figure 4. 22 Metastable stable zone width of vanillin, ethyl vanillin, aminobenzoic acid and racemic mandelic acid vs. boiling point of the solvents.

4.6.2 Interfacial energy and solute melting point The interfacial energy can be correlated with the melting point of solute, and Figure 4. 23 indicates an increasing tendency with increasing melting point. For EP, PP and BP in ethanol or acetone, the interfacial energy increase with increasing melting point and interfacial energy of parabens in ethyl acetate is fairly equal. This would be in line with the expectation that the solid-melt interfacial energy would be proportional to the melting enthalpy of the solid [48, 66], and that the solid–solution interfacial energy would be proportional to the enthalpy of dissolution [106]. The blue dots in Figure 4. 24 shows the solid-melt interfacial energy of organic compounds plotted versus the melting point of the solid [113]. 13 experimentalinterfacial energy values (light blue dots) [66, 114-120] and 15 calculated interfacial energy values (dark blue dots) [68, 121] are included. Where experimental values are available the calculated values [68] are somewhat lower, but the order between compounds is essentially preserved. The diagram shows an overall trend that an increasing melting point is associated with an increasing solid-melt interfacial energy even though stearic acid and myristic acid appears to be clear exceptions. The black dots in Figure 4. 24 presents the solid-melt interfacial energy of 17 metals versus their melting points [122-129]. The blue and green dots in Figure 4. 24 shows that the solid-solution interfacial energy, primarily determined by precipitation, of 40 inorganic solid salts in aqueous solution [64, 65, 106, 130, 131] increases with increasing melting point of the solute [132], with MgF2 being a clear exception. These interfacial energy has been determined by methods, e.g. shape of the

39 grain-boundary-grooves, wedge-equilibrium method, Capillary Cone Method [133, 134], depression of melting points of small crystals, droplet homogenous nucleation, dihedral angles, maximum supercooling, and dihedral angles [135, 136].

2.5 2 2.0 PP 1.5 BP E EA 1.0

0.5 AC Interfacial energy mJ /m 0.0

70 80 90 100 110

 Melting point C Figure 4. 23 Melting point of parabens in solvents

400 Metal Inorganic compounds in aqueous solvent 300 2 Organic compounds Organic compounds by simulation

200

100

Interfacial energy mJ/m

0 500 1000 1500 2000

Melting point C

Figure 4. 24 Interfacial energy vs. melting points of metals, inorganic compounds, organic compound.

Table 4. 5 Interfacial energy for metastable polymorph and stable polymorph in literature Metastable Compound Solvent Stable polymorph reference polymorph Eflucimibe Ethanol 4.23 mJ/m2 5.17mJ/m2 [137] Indomethacin Ethanol 17 mJ/m2 27 mJ/m2 [138] D-mannitol Ethanol aqueous 4.59 mJ/m2 5.04 mJ/m2 [139] 1,4-truns-polyisoprene - 59.0 mJ/m2 91.5 mJ/m2 [140]

This correlation is paralleled by the fact that in polymorphicParabens systems the interfacial energy is always lower for a metastable polymorph (Table 4. 5) than for the stable form, and the nucleation of the metastable polymorph tends to be favored.2.5 The metastable form has a higher 2.600

Gibbs free energy than the stable form. Accordingly,2 in general we would expect the stable 2.300

2.000 form to have a lower enthalpy and a higher melting point,2.0 reflecting a stronger intermolecular 1.700 force in the solid phase. 1.400 1.100 1.5 0.8000 4.6.3 Interfacial energy, boiling point and melting point 0.5000

0.2000 From the analysis and comparison in Section 4.5.1 and1.0 4.5.2, we can infer that the interfacial

energy between solute and solvent increase with increasingmJ/m energy Interfacial melting point of solute and boiling 0.5 370 point of solvent and Figure 4. 25 shows this tendency is consistent with results both in parabens360 350 experiments and in many experiments reported in literature380 for more than 100 compounds. It is 340 well known that the melting point and boiling point areBoiling both point dependent370 of solvent K on the bonding energy 360 330 (intermolecular force). Therefore, it is proposed that the nucleation is highly350 correlated to the intermolecular force between solute, solvent and each other. Melting point of parabens K

Parabens Metal, inorganic, organic compounds

2.5 350.0

2.600 280.0 2 2.300 300 240.0

2.000 2 200.0 2.0 1.700 160.0

1.400 120.0

1.100 80.00 1.5 200 0.8000 40.00

0.5000 0

0.2000 1.0

100 Interfacial energy mJ/m energy Interfacial 0.5 370 4000 360 mJ/m energy Interfacial 3000 350 0 380 2000 2000 Boiling point of solvent K 340 370 Boiling point of solvent K 1000 360 330 1000 350 0 Melting point of solute K Melting point of parabens K

Figure 4. 25 Relation of interfacial energy and melting points of solute (left: parabens, right: moreMetal, than inorganic, 100 compounds organic incompounds literature) and boiling points of various solvents

350.0 4.7 Cooling crystallization and sandwich280.0 crystals 300 240.0

2 200.0

160.0 The solution of Exp. 1 started in region 1120.0 of the ternary phase diagram (Figure 4. 3), as an 200 80.00 undersaturated paraben-ethanol solution. The40.00 solution nucleated when the solution by cooling passed the solubility curve and “crossed 0 over” to region 5, where the crystals finally grew (Figure100 4. 26) The process was an ordinary cooling crystallization in a homogenous solvent, and the product size distribution was 4000 as expected from this type of process (Figure 4. 27). Interfacial energy mJ/m energy Interfacial 3000 During0 the cooling process ahead of nucleation, all the FBRM curves are close to zero. When 2000 2000 Boiling point of solvent K temperature reached1000 about 15 ˚C1000, nucleation took place and the jump of FBRM curves revealed crystals formed in all range of size (Figure 4. 26). After that the crystals grew in the 0 supersaturated solution and it appearedMelting point as of solute if K there was a contribution of secondary nucleation towards the end. During the whole process, the liquid remained non-turbid, meaning there was no liquid-liquid phase separation. The solution of Exp. 2 started close to the liquid-liquid phase separation boundary between region 1 and region 2 (Figure 4. 3), in a mixture of water and ethanol having a paraben concentration somewhat less than in Exp. 1. At cooling, the solution passed into the LLPS

41 region 2, and the formation of droplets was observed by the PVM (Figure 4. 26). At continued cooling, crystal nucleation occurred, the crystals grew in LLPS region 4, and the process ended in region 3. The size distribution (Figure 4. 27) is wide with a tendency of bimodality, but is still reasonably well formed. The FBRM results (Figure 4. 26) show that the liquid-liquid phase separation occurred quite early, which is also revealed by PVM that the droplets formed in region 2 and visually the solution became quite turbid. Then with decreasing temperature the white turbidity became more intense, like milk. At about 18 ˚C, nucleation took place as was observed in the FBRM signals. After crystal nucleation the solution remained milk-white. More crystals were formed at decreasing temperature and the process ended with a high concentration of crystals in region 3, which had no liquid-liquid phase separation.

Figure 4. 26 FBRM curves of Exp .1 to Exp. 5 with in-situ PVM photos in cooling crystallization process and off line microscope images of product crystals

The solution of Exp. 3 started more clearly inside region 1, and with a somewhat lower butyl paraben concentration than in Exp. 2. Liquid-liquid phase separation occurred when the solution entered into the LLPS region 2 at about 35 ˚C, as was observed both by the PVM response as the solution becoming milk-white, and by the FBRM data shown in Figure 4. 26. With decreasing temperature of solution, the FBRM curves increased slightly. When the solution was further cooled into region 4 butyl paraben nucleated at about 10 ˚C as shown by the rapid increase in the FBRM curves. Crystals formed but the solution remained milk-white, which were also shown in the PVM photos at various times, suggesting the formation of crystals in the LLPS solution. The crystals grew into the final product crystal size distribution in the liquid-liquid phase separation region, and towards the end the solution contained a lot of small crystals but remained non-transparent because of the liquid-liquid phase separation. Obviously, the poor crystal size distribution in Figure 4. 27 is related to that crystal formation took place and ended in a liquid-liquid phase separated mixture. Exp. 4 started inside region 2, and the FBRM curves indicated LLPS in the solution. When the temperature cooled down to about 20 ˚C, the solution entered into the region 4 and the number of particles rapidly increased since nucleation occurred. Interestingly, the number of particles in the range: 5 - 40 μm, show an immediate decrease at the crystal nucleation. This is interpreted as a change in droplet size distribution. After a short period, the FBRM curve of the 5 - 40 μm increased again as a result of crystal growth. The PVM photos at 4h50m show the crystal growth in region 4. The FBRM particle size distribution in Figure 4. 27 (in-situ) is not very smooth. The crystals are comparatively small which is likely due to a stronger nucleation because of a lower solubility at the ending point. The solution of Exp. 5 started in the LLPS region 2, having a butyl paraben concentration much less than in other experiments and having the highest water concentration of all. At cooling, the solution nucleated when passing into region 4, and by further cooling ended up in region 3. The FBRM curves (Figure 4. 26) show that there was a liquid-liquid phase separation from the beginning. Crystal nucleation occurred at about 15 ˚C, surprisingly revealed by that the number of recordings in the 0 - 5, 5 - 40, 40 - 120 intervals all suddenly decreasing quickly while the curve representing particles above 120 μm increased somewhat. The explanation for this is assumed to be the fact that butyl paraben is the component forcing a LLPS into a mixture of ethanol and water. When butyl paraben crystallizes out, the concentration of butyl paraben in the solution decreases leading to a redissolution of the droplets and an increase in the miscibility of the liquid phases. The PVM photo at 5h50m reveals that at the end of the experiment the liquid phase is homogeneous, showing that the process had moved into region 3. The product crystal sieve size distribution is essentially bimodal while the FBRM particle distribution is very irregular. The upper peak in the solid particle sieve size distribution (Figure 4. 27) is attributed to agglomeration. In Figure 4. 27, product size distributions of each experiment are shown. Figure 4. 27 (in-situ) shows the particle size distribution in each of the five experiments at the end of each experiment as recorded by the FBRM. The particles of Exp. 1 shows a well formed log-normal or gamma shaped distribution. For all other experiments, however, the product size distributions are more complex and irregular. The product particle size distribution from Exp. 2 is well shaped comparable to that of Exp. 1, but the distribution is much wider and has a tendency to bimodality at about 200 and 400 μm. From Exp. 3, the particles overall are fairly small - mainly below 400 μm with a tendency for the distribution to be bimodal. Nearly all the product particles of Exp. 4 are also below 400 μm, but compared to Exp. 3 the amount of crystals is much higher and there is not a strong bimodality. The distribution of Exp. 5 is very wide without any particular symmetry. Figure 4. 27 (off line) presentes the corresponding product particle size distribution as determined by sieving after filtration and drying. Differences

43 between two distributions (in-situ and off line) in Figure 4. 27 are due to that: i) the FBRM distributions are number distributions while the sieve distributions are mass distributions, ii) the FBRM instrument measures the cord length distribution while the sieving is normally assumed to separate the particles according to the second largest dimension, iii) the FBRM curves actually record liquid droplets in the suspension, if the process ends in a liquid-liquid phase separated region. This explains the large difference in the overall shape of the size distributions for Exp. 3, an experiment that terminates in the LLPS region 4. The particle size distribution of Exp. 3 from FBRM shows a substantial amount of particles below 100 μm which cannot be found in Figure 4. 27 (off line). For the other four experiments the size distributions are fairly similar from the two methods.

Figure 4. 27 Product properties of the five cooling crystallization experiments. In-situ: FBRM curves. Off line: weight of sieve fractions. The crystals obtained from each experiment are mainly rhombic in shape with various degree of the agglomeration. The material from Exp. 5 is strongly agglomerated but from Exp. 2 and 4 only weakly. In case of significant agglomeration the crystals tends to be less well-shaped. Overall, the liquid-liquid phase separation makes crystals smaller and more agglomerated and the wider particle size distribution. From our data it appears as if the LLPS has a detrimental effect on the crystallization of butyl paraben [141-143].

0.1 mm

(-1-11) (100)

(-111)

Figure 4. 28 Microscope and SEM images of sandwich crystals

In off line images of Figure 4. 26, it is noticed that the crystals obtained in Exp.4 have 3 layers. The crystals have a characteristic layer in the middle of each crystal, parallel to the basal planes (Figure 4. 28). The top and bottom layers are transparent and compact. The middle layer is multiporous and not transparent, which thickness can reach more than half of the whole crystals (Paper V). Figure 4. 26 also shows that the pores in the middle layer of sandwich crystals are randomly shaped with the radii in a range of several μm to dozens of nm. The Confocal Raman Spectrum has been investigated to determine the crystal in three different layers of the sandwich crystal, respectively, and the spectra are essentially identical, shown in Figure 4. 29. The IR spectra (paper V) and Confocal Raman spectra both indicate the same polymorph for the crystals from three layers of sandwich crystal as well as normal crystals.

9000 Top layer

6000 Middle layer Intensity 3000 Bottom layer

0 3000 2000 1000 -1 Wave number (cm ) Figure 4. 29 Confocal Raman spectra of three layers The outer plane parallel to the sandwich layer can be indexed as (100) face shown in Figure 4. 30 and in Figure 4. 28. The molecule stacking in (100) face, (-111) face and (-1-11) face is shown in Figure 4. 30. The single XRD reveals that the reflections along a* direction have irregular shape or missing position in some unwarp layers, indicating the disorder layer along a* direction. The flexible carbon tail in crystal structure also elongated along a* direction, and accordingly, the flexibility chain tail may induces more defects during the growth of the sandwich crystal. Figure 4. 31 shows DSC for the sandwich crystals and for the normal crystals. On the heating curve from the first cycle of the sandwich crystal, there is an endothermic broad peak before the appearance of the melting peak. In the repeated heating of the same sample that small peak has essentially disappeared. The endothermic peak might indicate that the lattice of the sandwich crystal is more disordered than that of the normal crystals. However, since the previous melting should have destroyed all features related to the sandwich structure, it is surprising to find that the tiny peak has not disappeared entirely in the second heating cycle. In the second heating, the peak value of the melting peak is the same as for the normal crystals. However, in the first heating the onset melting point in particular but also the peak value determined for the sandwich crystals is somewhat lower than for normal crystals about 1.0 ˚ . The explanation can be that in the heating process from the first cycle, the porous structure increases the specific surface area of the crystals, and, therefore, the melting temperature

45 decreases, corresponding to reports in the literature that the melting point decreases with decreasing particle size [144-146].

(100)

100

-111 -1-11 (-111) (-1-11)

Figure 4. 30 Molecule stacking in (100) plane, (-111) plane and (-1-11) plane and morphology of sandwich crystal.

First cycle of sandwich crystal -30 Second cycle of -12 sandwich crystal Cycle of Heat flow normal crystal -10

40 50 60

-20 T C Heat flow

-10

0 20 40 60 80 100 120 T C

Figure 4. 31 DSC curves of the sandwich crystals and normal crystals We expect the process of forming sandwich crystals starts from forming middle layer and ends with formation of outer layer. The nucleation happened in emulsion solution, and crystals grew in emulsion solution could form opaque crystals, and, however, the opaque crystal continued to grow in homogenous liquid solution may be the reason to form transplant crystal layers, and the thickness of the middle layer or top and bottom layer might be dependent on the crystal growth time in emulsion solution or in homogenous liquid solution, respectively. This may be an effective method to make porous crystals that are crystalline but have higher specific surface area for easily dissolving, lower melting point and higher solubility (paper V). However, the process of forming sandwich crystals must be very complicated and interesting.

5. Discussion

The crystal structure and molecule structure of three parabens are both very similar, and the single crystals of three parabens obtained by slow evaporation in ethanol, acetone and ethyl acetate, respectively, have very similar morphology. Though the butyl paraben contains longer carbon tail which may hinder aggregating and contacting between each other, the nucleation of butyl paraben is surprisingly often easier than propyl paraben and ethyl paraben, indicating that steric effect plays limited role in nucleation occurring in solution and larger molecule is not principally more difficult to nucleate. The correlation between interfacial energy with melting point and boiling point needs to be further clarified, and to be further investigated with the aid of quantum chemistry simulation. A database of interfacial energy of drug-like organic compounds in various solvents and other nucleation parameters is expected to be built. The melting points of parabens do not increase with their molecular weights, which might indicate the dominating molecular force in paraben crystals is not Van der Waals' force. The crystallization in liquid-liquid phase separation solution is very complicated and little has been understood until now, but the ternary phase diagram and liquid-liquid phase separation are used to obtain crystals with specific properties, e.g. agglomeration, porous structure. In addition, the influence of properties of different regions or different parts in ternary diagram on crystallization need to be further studied, and the results can help to control and design crystallization process for special products.

5.1 Liquid-liquid phase separation

All three parabens has the aromatic ring, ester functional group and hydrocarbon chain tail, resulting in very low solubility in water (less than 0.0002 g paraben in 1 g water below 40 ˚C), but these groups as well as –OH lead to high solubility in ethanol (more than 1.4 g paraben in 1 g ethanol at 50 ˚C). In the ethanol aqueous solvent, when the concentration of ethanol is low, the solution is dominated by water with very little paraben dissolved. With the increasing concentration of ethanol, more paraben is dissolved in the solution. When concentration of paraben is somehow in preponderance, the hydrophobicity of butyl paraben forces the solution into liquid-liquid phase separation with paraben lean and water rich layer (top layer) and paraben rich and water lean layer (bottom layer). The proportion of ethanol in the two layers is similar as the proportion of ethanol in the whole solution (paper VII). With increasing concentration of ethanol in the whole solution, the water-rich layer decreases, and the paraben-rich layer increases, until the solution is dominated by ethanol, leading to homogenous solution. Regardless of the proportion of ethyl paraben, propyl paraben and butyl paraben, when the ethanol proportion is more than 45 %, 60 % or 70 % in solvent, respectively, the water-rich layer liquid phase disappears, and accordingly, the liquid-liquid phase separation disappears. The liquid-liquid phase separation occurs at 84.5 ˚C, 75.6 ˚C and 49.4 ˚C for ethyl paraben, propyl paraben and butyl paraben in pure water, respectively. The temperature for liquid-liquid phase separation occurring in pure water is correlated to melting point of parabens, and the process of LLPS in pure water can be considered as melting liquid paraben is supercooled below the melting point of paraben and is mixed with pure water.

5.2 Thermal history on nucleation

The effect of solution memory have been found in early 20 century [147] focused on melting, and the influence of thermal history on polymorphs of crystals has been report [148, 149]. Recently, the influence of thermal history has been investigated in metastable zoo and nucleation [111, 150]. The thermal history of solution on nucleation also has been observed. 60 tubes with 5 mL solution (butyl paraben in propanol) has been investigated and repeated in equal experimental conditions (dissolving at 30.0 ˚C water bath with 500 rpm stirring rate, nucleating at 15.0 ˚C water bath, 200 rpm stirring rate, at supersaturation of 1.25), however, with different dissolving time, from 10 minutes to 2 days. Figure 5. 1 shows the average of induction time and 95 % confidence interval of 60 experimental results per batch with different dissolving time. There is a tendency that average induction time and the interval of induction time both increase with increasing dissolving time. Figure 5. 1 indicates that the influence of thermal history can be neglected compare with the wide distribution of induction time. The thermal history could also prolong the period of cluster redistribution. The Figure 5. 1 also indicates that the longer dissolving time could induce wider distribution of induction time results at equal experimental conditions.

500 2d 3h 450

400

350 20min

300 2h 10min 250

Time(s) 200

150 Induction time time (s) Induction 100

0 1 2 3 4 5 ExperimentBatch No. No. Figure 5. 1 Thermal history of solution in induction time experiments with 95 % confidence interval. Dashed line is guiding line.

5.3 Bonding in nucleation

The nucleation process can be considered as that the intermolecular force between solvent molecules and solute molecules breaks, and the intermolecular force between solute molecules and intermolecular force between solvent molecules form. In pure solid A and pure liquid B, bonding is in type of and , respectively. In a solution, solute and solvent molecules interact with each other, shown as stage 1 in Figure 5. 2. The solid horizontal lines exhibit the relative stability of the whole system during the nucleation. However, in supersaturated solution, the bonding is not thermodynamic favorable. To become thermodynamic favorable, the system needs to go over the energy barrier of the nucleation, resulting from the interfacial energy. Therefore, at stage 2 in Figure 5. 2, firstly i) the unstable bonding breaks, and then ii) new boning forms inside the clusters while new bonding forms near the surface of the cluster. However, since the specific surface of cluster is large, the new forming cluster is not stable, i.e. the ratio, number of

48 molecules on the surface of the cluster / number of molecules inside the cluster, is relatively high. In stage 3 shown in Figure 5. 2, more bonding forms inside with increasing size of the cluster and correspondingly specific surface area of the cluster decreases and the cluster also becomes more stable. After nucleation the bond also exist in the solution. Since in general the bonding energy of solid should be higher than the liquid, the intermolecular force is higher than . At final state the system is relatively more stable than the former two stages.

Stage 1 Stage 2 Stage 3

Cluster surface

Transition state

Solid surface Stability

Initial Final state state Nucleation process

A A A B A A B A B B B A A B A B A B A B A B A B B B B B A A B A A B B A B A B B B A B B B B B A A B A B A B A B B A A B A A B A A B B A A A A B B A B B A B B A A A A B B B A A A B B A A A A B A B A B A B A B A A A B B B A A A B B A A A A B B A B A B A A B B A B A B A B B B A B A A A A B B A B A A B A B A B A B A B A B A B A B B B B B B B B A A A B A B A B A B A B A B A B A B A B A

Stage 1 Stage 2 Stage 2 Stage 3

Figure 5. 2 Scheme of bonding and intermolecular force change in nucleation process The interfacial energy represents the free energy difference between solute molecules at the surface of the crystalline material and in the bulk crystalline solid. This free energy difference is essentially enthalpic and describes that the molecules at the surface of the solid phase lack part of the solid phase bonding, while compared to the molecules that have lost essentially the same amount of entropy as the molecules inside the solid crystalline phase. Hence, we expect that a more strongly bonded solid phase has a higher interfacial energy. However, the interface region

49 includes both the solid surface of the crystal and the solvent molecules nearby. In order to establish the interface region there will be a free energy change related to rearrangement of the solvent molecules and the bonding of these to the solid surface, and this is included in the interfacial free energy term. The missing solid phase bonding of the solute molecules at the solid surface is partly replaced by the bonding to solvent molecules. The stronger this bonding is the lower we expect the interfacial energy to be. Conversely, the stronger the bonding between solvent molecules among themselves, the weaker the bonding to the surface and hence the higher the interfacial energy becomes. This could explain the relation between the interfacial energy and the solvent boiling point. In addition, it is well known that the intermolecular force between solute and solvent will influence the nucleation process in stage 2. It is usually expected that the stronger bonding hinder the i) step in stage 2, i.e. the bonding between solute and solvent molecules breaks in the solution. However, in the ii) step of stage 2 the stronger bonding between the solvent molecules and the solute molecules on the cluster surface helps to stabilize the thermodynamic unfavorable surface of the cluster, which can promote the nucleation process. Therefore, we would argue that the nucleation and the interplay between solvent and solute molecules are both very complicated. It is not easy to simply draw a conclusion of the influence of intermolecular force in the solution on the nucleation process, and the relation between them needs to be further investigated.

6. Conclusion

Solubility of butyl parabens is high in acetone, ethanol, ethyl acetate, methanol, propanol and high percent ethanol aqueous solvents, from about 1 g/g solvent to about 11 g/g solvent. However, the solubility of butyl paraben in 10 % ethanol aqueous solvent and pure water is quite low, below 0.0007g/g solvent. The solubility of butyl paraben increases with increasing temperature in all solvents. Ternary phase diagram of ethyl paraben, propyl paraben and butyl paraben in ethanol aqueous solvents shows liquid-liquid phase separation at 50 ˚C, 40 ˚C and 10 ˚C, respectively, at which temperature 2 regions in ternary diagram separate to 5 regions. In liquid-liquid separation region, bottom layer is butyl paraben rich layer while top layer is butyl paraben lean layer. LLPS does not form in more than 45 %, 60 % or 70 % ethanol aqueous solvent for ethyl paraben, propyl paraben and butyl paraben, respectively, and at 84.5 ˚C, 75.7 ˚C and 49.4 ˚C LLPS occurs when ethyl paraben, propyl paraben or butyl paraben is dissolved in pure water, respectively.

The strong relation between solid-liquid solubility data and thermodynamic data of the pure solute was revealed by fitting solubility and van’t Hoff enthalpy with activity and fusion enthalpy fusion of solution, which can be exploited for prediction of solid-state activity. The work further shows that a more accurate characterization of the pure solid free energy can be obtained by combining differential scanning calorimeter results with data over solubility in various solvents. For butyl paraben, the best result appears to be obtained if DSC measurements over melting enthalpy, melting temperature and heat capacity difference at the melting point between the melt and the solid, are combined with a determination of the heat capacity difference versus temperature relation by correlation to solubility data.

More than 5000 induction values show wide variation, indicating the random nature of the nucleation. The cumulative distribution curves are better fitted by the Burr distribution than others. The interfacial energy and pre-exponential factor have been determined by 5 methods, Overall, the data obtained from the different methods of evaluation are fairly consistent. However, using the median value of induction time distributions appears to provide for the best treatment of the data, under the assumption that the nucleation occurs under steady-state conditions. Furthermore, it remains to

51 be clarified that the nucleation can be treated as occurring under steady-state conditions or non-steady-state conditions. The interfacial energy of butyl paraben determined using median induction time increases in the order: acetone < methanol < ethyl acetate < ethanol < propanol < 90% ethanol < 70% ethanol, and interfacial energy of propyl paraben and ethyl paraben increase in the same order: acetone ethyl < acetate < ethanol. Good correlations between interfacial energy with melting point of parabens and boiling point of solvents are found, which is in good agreement with the literature of polymorphic compounds nucleation and metastable zone width experiment and the tendency is in good consistence with relation between interfacial energy of more than 100 compounds with their melting points. Therefore, it is proposed that lower interfacial energy is related to lower intermolecular force between solute molecules or between solvent molecules, which enhance nucleus surface molecules enthalpic stability and according makes nucleation easier.

Cooling crystallization experiments reveal that the product crystal size distribution significantly depends on the composition at the starting point in ternary diagram. A liquid−liquid phase separation creates a solution having a higher concentration of butyl paraben and a solution having a lower concentration of butyl paraben. This leads to altered conditions for the nucleation and crystal growth in cooling process. In the results of the present study a process not traversing the liquid−liquid separation region generates the largest crystals with the least agglomeration and the best shaped size distribution. In all experiments where the solution is a mixture of water and ethanol and the process trajectory involves liquid−liquid phase separation, the individual crystals are smaller and more agglomerated, and the size distribution is less well shaped. LLPS strongly influences and always negatively influences the product distribution.

A novel kind of sandwich crystal was obtained in cooling crystallization in LLPS solution. The outer layers are transparent and compact while the middle layer is full of pores with radius from several μm to dozens of nm. The thickness of the porous layer can reach more than half of the whole crystal. The crystals contain only one polymorph. The crystal in middle layer has lower melting point than outer layer crystals resulting from the larger specific surface area.

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Acknowledgement

I would like to express my deep and sincere gratitude to my supervisor Professor Åke C. Rasmuson for plenty of discussions and suggestions, and for friendly chatting and arguing. Professor Åke Rasmuson helps me start the scientific investigations (a random distribution of clusters / many unknowns), go over the barrier (the increasing size of clusters / more questions and hypothesizes) and clarify the results (one nucleus / prove one hypothesis).

My great gratitude to Professor Hongyuan Wei (Tianjin University) and Dr. Ziyun Yu for introducing me into the science of crystallization in chemical engineering and for lots of helps during my study and research.

My great gratitude to Dr. Andreas Fischer (Inorganic Chemistry), Hong Chen (Stockholm University) Dr. Bo Yin (Polymer Technology) and Fan Zhang (Surface and Corrosion Science) for performing analyses of single XRD, SEM or CRM.

My great gratitude to Dr. Denise Croker (University of Limerick) and other colleagues in SSPC for guiding and helping in my crystallization experiments and research in University of Limerick.

My great gratitude to Dr. Mårten Behm (Applied Electro Chemistry), Adjunct Professor Per H. Svensson (Inorganic Chemistry) for my licentiatseminarium.

My great gratitude to Professor Kieran Hodnett (University of Limerick) and Assistant Professor Matthäus Bäbler (Energy Process) for several informal discussions.

My great gratitude to Dr. Michael Svärd for many Swedish translations as well as Swedish abstract and discussions about the lab and simulation work, as well as solid good chatting in traveling and spare time.

My great gratitude to all the colleagues in crystallization group, Jan Appelqvist, Dr. Jyothi Thati, Dr. Kerstin Forsberg, Shuo Zhang, Jin Liu for all the kindly help in the lab and in office or research discussions.

My great gratitude to Associate Professor Longcheng Liu, Apolinar Picado, Dr. Zhao Wang, Professor Luis R Moreno, Professor Ivars Neretnieks, Associate Professor Joaquin Martínez, Dr. Jan Sedzik, Raúl Rodríguez Gomez, Batoul Mahmoudzadeh, Helen Winberg, Maria Kanellopoulou, Maryam Mohammadi, Soheila Ghafarnejad Parto, Pirouz Shahkarami,Guomin Yang, for informal discussions in group seminars, in lunch and in fika, and sharing.

My great gratitude to my friends for discussions about the nature or social scientific topics and my friends all over the world for communication, attention, encouragement and consideration.

Then, my great gratitude to my parents, Yudong Yang and YueZhen Wang, and all my family members for their supports, without these supports my research achievements could not come out.

Finally, my great thanks to my beautiful, apprehensive, and intelligent wife, Fan Zhang. I am indebted to you for lots of late nights and for a lot of early mornings in the weekends. I owe my deepest gratitude to you for endless love, support, and understanding. Wherever I go you are my only Fan and whenever I am always your loyal fans.

Appendix 1 Solubility and solubility equations

al.

(g/g)

in Acetonitrile Acetonitrile in

0.3787 (0.0021) 0.3787 (0.0060) 0.8141 (0.0022) 1.5640 (0.0453) 3.0451 (0.0694) 5.9884

(g/g)

in Ethyl acetate Ethyl acetate in

0.7366 (0.0060) 0.7366 (0.0248) 1.0038 (0.0380) 1.4443 (0.0014) 2.2101 (0.0230) 3.5981

Confidence Interval) Confidence

(g/g)

in Propanol Propanol in

1.2962 (0.0044) 1.2962 (0.0006) 1.7299 (0.0018) 2.4017 (0.0307) 3.4888 (0.1126) 5.6489

(g/g)

in Acetone Acetone in

1.9961 (0.0012) 1.9961 (0.0001) 2.7013 (0.1012) 3.8653 (0.0810) 6.1756

1.5020 (0.0036) 1.5020

Average solubility of butyl paraben (95% (95% paraben ofbutyl solubility Average

(g/g)

in Ethanol in

1.4780 (0.0007) 1.4780 (0.0306) 2.0517 (0.0677) 3.0896 (0.0251) 4.6883 (0.0250) 8.3645

(g/g)

in Methanol Methanol in

1.7584 (0.0052) 1.7584 (0.0017) 2.6149 (0.0887) 3.7881 (0.0525) 5.8415

10.3143 (0.0435) 10.3143

Solubility of butyl paraben in methanol, ethanol, acetone, propanol, ethyl acetate and acetonitrile and 95% confidence interv confidence 95% and acetonitrile and acetate ethyl propanol, acetone, ethanol, methanol, in paraben ofbutyl Solubility

1 1

)

˚C

9.9

(

19.9 29.9 39.9 49.9

Temperature Temperature TableA1

Table A1-2. The values of parameters for BP in pure solvents in lnx = A (T/K)-1 + B + C (T/K). Methanol Ethanol Acetone Propanol Ethyl acetate Acetonitrile

A -1145.19 -1430.23 339.8378 187.9712 -698.157 -13800.4

B -1.0869 1.3469 -8.6206 -8.1433 -3.24275 74.6545

C 0.01289 0.00826 0.02208 0.0220 0.01525 -0.1007

Table A1-3 Constant numeral variables in polynomial solubility equation,

, of parabens in mixture of water and ethanol

EP 40 °C 0.2210 -0.579 7.794 -5.815 0.9966 PP 50 °C 0.00106 -1.039 13.980 -10.800 0.9987 PP 40 °C 0.000350 -7.726 8.270 -5.885 1.0000 BP 50 °C 0 26.470 -8.880 -9.220 1.0000 BP 40 °C 0.000588 26.440 -33.240 11.490 1.0000 BP 30 °C 0.000386 -1.157 19.020 -14.870 0.9959 BP 20 °C 0.000348 -0.339 7.805 -5.476 0.9948 BP 10 °C 0.000291 -0.486 4.456 -2.482 0.9997 BP 1 °C 0.000240 -0.554 3.360 -1.731 0.9910 BZC 10°C 0.00359 -0.18475 0.69379 -0.35765 0.96035 BTN 10°C 0.00386 -0.30649 1.20266 -0.56657 0.97901

) ) ) )

) )

2 2 2 2

3 4

- - - -

- -

10 10 1 10

10 10

× × × ×

× ×

0384

(g/g)

06 77 51 50

27 76

1 1.4780 2.0517 3.0896 4.6883 8.3645

. . . .

. .

in Ethanol in

(3 (6 (2 (2

( (7

) ) ) ) ) )

4 4 3 2 1 2

------

10 10 10 10 10 10

× × × × × ×

0315 3826 9095 3481 2472 9040

......

(g/g)

1 41 1 39 1 77 3 57 5 09 9 67

......

(1 (3 (1 (1 (1 (2

in 90% Ethanol 90% Ethanol in

) ) ) ) ) )

3 3 2 3 2 2

------

10 10 10 10 10 10

623

0118 × × × × × ×

6254 9809 7751 5127

. . .1

(g/g)

85 59 46 56 21 42

0. 0. 1 3 6

......

( (5 (3 (8 (2 (3

in 70% Ethanol 70% Ethanol in

)

------

(g/g)

0.1580

in 50% Ethanol 50% Ethanol in

100% ethanol aqueous solution and stand deviation deviation stand and solution aqueous ethanol 100%

) )

3 3

- -

5 4

- -

10 10

presents LLPS) presents

× ×

------

× ×

7 6

(g/g)

(

080 . 782 .1

. .

3 6

(7 (

in 30% Ethanol 30% Ethanol in

Average solubility of butyl paraben (stand deviation) (stand paraben ofbutyl solubility Average

weight percent 0% percent weight

) ) ) )

5 4 4 4

- - - -

6 5 6 6

- - - -

10 10 10 10

× × × ×

-- --

× × × ×

3 0

(g/g)

53 3 20

. .

086 750 009 516

. .

2. 2. 5 6

(4 (2. (4 (5.3

in 10% Ethanol 10% Ethanol in

) ) ) ) )

4 4 4 4 4

- - - - -

6 5 5 5 5

- - - - -

10 10 10 10 10

× × × × ×

(g/g)

78 42 10

399 . 908 478 808 .05

in water in

2. 1

2. 2. 3 3. 5.884

(7 (2. ( ( (1.4

4 Solubility of butyl paraben in in paraben ofbutyl 4Solubility

)

˚ ˚

Table A1 Table

0 9.9

19.9 29.9 39.9 49.9 Temperature ( Temperature

Appendix 2 Relation between solubility and solid-state thermodynamic properties

Table A2-1 Temperature versus lnx of butyl paraben from Equ. 2

Temperature/K AC PR E EA ME ACE -1.328 -1.426 -1.606 -1.609 -1.73 -3.283 274.15 -1.168 -1.25 -1.365 -1.39 -1.482 -2.589 283.15 -1.079 -1.152 -1.236 -1.271 -1.347 -2.247 288.15 -0.989 -1.053 -1.111 -1.154 -1.215 -1.933 293.15 -0.898 -0.954 -0.987 -1.038 -1.085 -1.647 298.15 -0.806 -0.854 -0.867 -0.923 -0.957 -1.387 303.15 -0.714 -0.754 -0.749 -0.809 -0.831 -1.152 308.15 -0.621 -0.654 -0.634 -0.697 -0.707 -0.94 313.15 -0.528 -0.553 -0.521 -0.585 -0.586 -0.751 318.15 -0.434 -0.452 -0.41 -0.475 -0.465 -0.583 323.15

Table A2-2 of solution versus molar solubility at 283.15 K to 323.15 K for butyl paraben in 6 solvents Temperature/K 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 -1.17 -1.08 -0.99 -0.9 -0.81 -0.71 -0.62 -0.53 -0.43 acetone 11.89 12.42 12.95 13.49 14.04 14.61 15.18 15.76 16.34 -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 propanol 13.1 13.62 14.16 14.7 15.25 15.81 16.37 16.95 17.54 -1.37 -1.24 -1.11 -0.99 -0.87 -0.75 -0.63 -0.52 -0.41 ethyl acetate 17.4 17.59 17.79 18 18.2 18.41 18.63 18.84 19.06 -1.39 -1.27 -1.15 -1.04 -0.92 -0.81 -0.7 -0.59 -0.48 ethanol 15.97 16.33 16.7 17.08 17.46 17.84 18.24 18.64 19.04 -1.48 -1.35 -1.22 -1.09 -0.96 -0.83 -0.71 -0.59 -0.47 methanol 18.11 18.42 18.73 19.05 19.37 19.7 20.03 20.37 20.71 -2.59 -2.25 -1.93 -1.65 -1.39 -1.15 -0.94 -0.75 -0.58 acetonitrile 47.63 45.24 42.81 40.34 37.82 35.26 32.66 30.02 27.33

Table A2-3 Solution curves (Equ. 20) of butyl paraben in 6 solvents at each temperature Temperature/K 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

a1 5.55 7.12 9.25 12.15 16.15 21.59 28.6 35.58 32.82

1 -4.06 -4.17 -4.28 -4.48 -4.85 -5.7 -7.73 -12.95 -26.93 Standard Deviation 0.999 0.999 0.998 0.998 0.998 0.997 0.996 0.994 0.992

Table A2-4 Solubility-enthalpy curves (Equ. 19 versus Equ. 18). Green solid line: thermodynamic properties from experimental value and w=0. Blue solid line: thermodynamic properties from optimization and w=0. Red solid line: thermodynamic properties from experimental value using second order equations. Black solid line: thermodynamic properties from optimization r and w. Temperatu Green solid line Blue solid line Red solid line Black solid line

re/K 283.15 -1.56 18.43 -1.21 12.94 -1.64 20.63 -1.63 21.37 288.15 -1.42 19.09 -1.11 13.37 -1.49 21.05 -1.47 21.46 293.15 -1.29 19.74 -1.01 13.84 -1.33 21.48 -1.32 21.61 298.15 -1.15 20.38 -0.92 14.34 -1.19 21.9 -1.17 21.82 303.15 -1.01 21.02 -0.82 14.88 -1.04 22.33 -1.02 22.08 308.15 -0.87 21.65 -0.72 15.45 -0.89 22.76 -0.88 22.4 313.15 -0.74 22.27 -0.62 16.05 -0.75 23.19 -0.74 22.77 318.15 -0.6 22.88 -0.52 16.68 -0.61 23.61 -0.6 23.18 323.15 -0.46 23.49 -0.43 17.35 -0.47 24.04 -0.46 23.64

Table A2-5 a values of butyl paraben from experimental first order correlation and second order correlation of heat capacity, two optimization (1st: optimal T,H,q,r and w=0, 2nd: optimal r,w) activity Temperature K Experiment (w=0) Optimal (w=0) Experiment Optimal w,r 283.15 0.21 0.188 0.284 0.188 288.15 0.241 0.223 0.315 0.223 293.15 0.276 0.262 0.349 0.262 298.15 0.317 0.306 0.387 0.306 303.15 0.364 0.356 0.429 0.356 308.15 0.418 0.412 0.475 0.412 313.15 0.479 0.475 0.527 0.475 318.15 0.549 0.547 0.584 0.547 323.15 0.628 0.628 0.647 0.628

Table A2-6 activity coefficient of butyl paraben in 6 solvents at temperature 274.15 K-323.15 K Activity coefficient Temperature K ACE ME EA E PR AC 274.15 0.637 283.15 2.346 0.773 0.694 0.67 0.607 0.561 293.15 1.667 0.812 0.782 0.747 0.702 0.654 303.15 1.363 0.88 0.855 0.801 0.794 0.758 313.15 1.178 0.94 0.922 0.876 0.889 0.861 323.15 1.109 0.984 0.999 0.932 0.974 0.955

Appendix 3 Unit cell parameters of parabens crystals

Table 3-1 Crystal unit cell parameters Compound Ethyl paraben Propyl paraben Butyl apraben System monoclinic monoclinic monoclinic

Space group P21/c P21/c C2/c a Å 11.765 12.0435 8.2182 b Å 13.182 13.8292 14.7136 c Å 11.579 11.7847 2073.4 V Å3 1710.2 1860.0 20.0870 α ˚ 90 90 90 β ˚ 107.76 108.63 121.39 γ ˚ 90 90 90 Z 8 8 8 CAS No. 120-47-8 94-13-3 94-26-8