Crystal Engineering for Process and Product Design

Michael F. Doherty

Department of Chemical Engineering University of California Santa Barbara

Pan American Study Institute on Emerging Trends in Process Systems Engineering1 Why Crystals?

• Crystalline organic solids ubiquitous in ¾ chemicals & specialty chemicals ¾ home & personal care ¾ food and pharma • Almost 100% of small MW drugs are isolated as crystalline materials • Over 90% of ALL pharmaceutical products are formulated in particulate, generally crystalline form • Pharma industry worldwide > $500 billion/year sales

2 Why Modeling?

“If you can’t model your process, you don’t understand it. If you don’t understand it, you can’t improve it. And, if you can’t improve it, you won’t be competitive in the 21st century.”

Jim Trainham, DuPont/PPG

3 Conceptual Design

You can’t understand the process if you don’t understand the chemistry

4 Role of Engineer in Industry

To make, evaluate and justify technical decisions in support of business

5 Why Crystal Shape?

• Crystal shape impacts: ¾ Downstream processing – filtering, washing, drying, etc (avoid needles and flakes) ¾ End use properties – bulk density, mechanical strength, flowability, dispersibility and stability of crystals in suspension, dissolution rate, bioavailability, catalytic properties ¾ Nano switches, …..

• The ability to predict and manipulate crystal shape enables optimized product & process design

6 Crystallization – Multiple Tasks

• Separation and purification task ¾ crude separation followed by recrystallization ¾ crystal purity ¾ enantiomer ¾ hydrate, solvate, co-crystal • Particle formation task ¾ mean particle size and particle size distribution ¾ particle shape • Structure formation task ¾ internal crystal structure or polymorph

7 Solid – Liquid Equilibrium

P = 1 atm T (°C) 188 (°C)

Solubility of Succinic Acid (Based on Qiu and Rasmuson 1990) 160.00

140.00

120.00

100.00

Solid solute in 80.00 equilibrium 0 (°C) 60.00 with liquid solution 40.00 Load of Succinic Acid (g/kg water)

20.00

0.00 15 20 25 30 35 40 Saturation Temperature (oC) 0 1 solvent xsolute solute (Water) (Succinic Acid) 8 Low Supersaturation: Succinic Acid

C

(g/L solution) Unstable { ~5 g/L solution (Qin & Rasmusm) Metastable

2.2 (°C){ Hofmann & Doherty Stable

24 (°C) 30 (°C) T (°C)

9 Slow growth for higher purity and well-formed morphology Solubility of Ibuprofen in Various Solvents

10 Crystals Form in Various Shapes

Zeolite Zeolite

Succinic acid PABA

11 12 Faujasite FCC Catalyst

Thanks to Michael Lovette – Albert Sacco group 13 Crystal Shape - Ibuprofen

Gordon & Amin US Patent 4,476,248 issued to The Upjohn Company • Objective of the invention: “an improved crystalline habit and crystal shape of ibuprofen” • Method of crystallization from solvents with δH>8, such as methanol, ethanol (instead of hexane or heptane). • Faster dissolution rate, larger particle size, lower bulk volume, reduced sublimation rates and improved flow properties.

Ibuprofen grown out Ibuprofen grown out of hexane of methanol

14 Klug & Van Mil Patent: DuPont Adipic Acid Shape Modification

15 Crystal Size

• Beta-carotene – food colorant. Color shade is determined by the narrow size distribution in the submicron range • New brilliant ink pigments in the nanoparticle size range • Tungsten carbide particles – narrow CSD 5-7 microns • Formulated drugs – CSD 30-70 microns • Inhalable drugs – CSD 1-5 microns (<10 microns) • Injectable drugs – CSD 200-500 nm

16 Key Issues for Process Development

• How to design for the desired material properties? ¾ crystal purity ¾ mean particle size and particle size distribution ¾ polymorph ¾ particle shape ¾ enantiomer • How to scale up? ¾ vessel design ¾ system design & process synthesis

17 Crystal Shape Evolution

• Crystals do not grow into their equilibrium shapes • What Gibbs thought • Crystals spontaneously form facets • The evolution model for faceted crystals • Steady-state shapes

18 Equilibrium Crystal Growth & Shape

• Idealized shape at infinitesimal supersaturation and looooooooooong times • Gibbs equilibrium condition for shape of facetted crystals (1877-78)

min∑γ iiA ,s . t . fixed V i • Wulff (1901) construction - solves the Gibbs minimization problem

C. Herring, “Some Theorems on the Free Energies of Crystal Surfaces,” Phys. Rev., 82, 87-93 (1951)

19 Wulff Construction

γ1

γ γ 2 6 d1 d6 d2 γ γ γ 12= ==" i d d5 3 dd12 di γ3 γ5 d4

γ4

20 What Gibbs Thought

Gibbs (Collected Works, pp. 325-326) “On the whole it seems not improbable that the form of very minute crystals in equilibrium with solvents is principally

determined by the condition that ( ∑ γ ii A ) shall be a minimum for the volume of the crystal, but as theyi grow larger (in a solvent no more supersaturated than is necessary to make them grow at all), the deposition of new matter on the different surfaces will be determined more by the orientation of the surfaces and less by their size and relations to the surrounding surfaces. As a final result, a large crystal, will generally be bounded by those surfaces alone on which the deposit of new matter takes place least readily. But the relative development of the

different kinds of sides will not be such as to make ( ∑ γ iiA ) a minimum”. i

21 Methodology for Calculating Shape

22 Perspectives

¾ Engineers believe that their models approximate nature

¾ Scientists believe that nature approximates their models

¾ Mathematicians don’t give a damn either way

23 Faceted Growth

Thomas, L. A., N. Wooster, and W.A. Wooster, Crystal Growth, Discussions of the Faraday Society, 343 (1949)

24 Spontaneous Faceting of TiN

SEM micrographs showing faceting process of spherical TiN seeds Liu et al., Crystal Growth & Design, 6, 2404 (2006)

25 Faceted Growth of Succinic Acid

100 μm

1 picture = 1 min. exp.

26 Growth Mechanisms

Growth modes for a crystal face as a function of supersaturation. The solid line is the growth rate. The short dashed lines are the growth rates if 2D nucleation or rough growth continued to be dominant below their applicable driving force ranges. The long dashed line is the rate if spiral growth was the persistent mechanism above its applicable range of driving force.

27 Crystal Shape and Growth Models

• Crystals grow by the flow of steps across the faces • Sources of steps ¾ 2-D nuclei - birth and spread model ¾ spirals growing from screw dislocations • Sources of edges – strong bond chains (PBC’s) • Sources of docking points for solute incorporation – kinks on edges (missing molecules along bond chains)

28 Spiral Growth of Organic Crystals

AFM images of spiral growth on hen egg white lysozyme surface (Durban, Carlson and Saros, J. Phys. D: Appl. Phys., 1993)

First electron micrographs of spirals: long chain paraffin AFM image of spiral growth on a 50μm canavalin n-hexatriacontane, C36H74 x 16000 (Dawson and protein surface (Land et al., Phys. Rev. Lett., 1996) Vand, Proc. Roy. Soc., 1951)

29 Step Formation

2-D Nucleation / Birth & Spread Spirals from a Screw Dislocation on a Parrafin Crystal (BCF) on Calcite

Ghkl Anderson & Dawson, Proc. Roy. Soc., 1953

y h Paloczi, Hansma, et al., Applied Physics Letters, step 73, 1658 (1998) v

30 BCF Growth Model

Rate of growth normal to face hkl Ghkl

ii yi Gvdy= (/) dhkl hkl hkl step vi i = edge i on face hkl

yi)( hkl depends on shape of spiral and step velocities

, ikink −1 i hkl av p +∝ exp(5.01[)( φ hkl RT )]/

d hkl kink, i −1 Gahkl ∝+p[1 0.5exp(φhkl / RT )] ()yi hkl

31 Distribution of Kinks

kink kink −φ+ −φ− e kT e kT p = p = poverall = pp+ + − + Q − Q

kink kink −0 −−φφ+− Qe=+kT ekT + e kT

v1 kink kink • Three microstates φ+ φ− • Boltzmann factors • Partition function (Q) • What is the probability of finding a kink at a site on the bond chain?

Bulk 32 Kinks on Steps of Ferritin Crystal

33 Solid State and Solvent Effects

Face velocities depend on: ¾ crystallography (unit cell, space group, etc) ¾ atom-atom pair potentials (including charge distribution) ¾ bond chains (we have a fast, automated new method for finding them) and kink energies ¾ growth unit ¾ solvent

d 5.0 W slAslls −+=−+= l γγγγγγγs )(2

34 Spiral Growth Model

N l ⎛⎞vh ⎛⎞h τα= ci,1− sin( ) G ==∞ ∑ ii,1− hkl ⎜⎟⎜⎟ i=1 vi ⎝⎠y hkl ⎝⎠τ hkl

• Unknown: lc, v, N, h

⎧ 0 if lstep< l c • Characteristic Spiral Time – τ vstep = ⎨ ¾ Time required for the formation of the ⎩vifl∞ step≥ l c first spiral turn. ¾ The time that occurs between consecutive step passes by the same • Each spiral side on each face can location. have different energetics. (Different • N = number of spiral relevant sides velocities and critical lengths)

35 Critical Length: Gibbs-Thomson

Δ=−ΔGNμsolute + Aγ moles of solute transferred to nucleus solution nucleus Δμμsolute=−> solute μ solute 0

First Term: Free energy decrease due to formation of the bulk solid phase Second Term: Free energy increase due to formation of surface

36 One Gibbs But Which Thomson?

William Thomson (Lord Kelvin) J. J. Thomson 1824-1907 1839-1903 1856-1940

1877-78 Mid 1870’s 1888 37 Shape Evolution Models

• Curved surfaces – Hamilton-Jacobi equation ¾ Most general case (PDE’s) ¾ Complete mathematical treatment by Lighthill & Whitham, “On Kinematic Waves I & 2,” Proc. Roy. Soc., 229, 281 & 317 (1955) ¾ Sir Charles Frank, Alexander Chernov, circa 1960

• Faceted surfaces – new model (ODE’s) ¾ Zhang, Sizemore and Doherty, “Shape Evolution of 3- Dimensional Faceted Crystals,” AIChEJ, 52, 1906 (2006) ¾ Snyder and Doherty, “Faceted Crystal Shape Evolution During Dissolution or Growth,” AIChEJ, 53, 1377 (2007)

38 G3 G 2 G Shape Evolution Model 4

H1 dH i dx i H = Gi =uxii− , ref dt dξ

Hi Gi xi = Ri = Href Gref Gi >0 Growth

dxi Gref =−()Rx Dissolution ii Gi < 0 dt Href

39 Shape Evolution Model

Growth: eigenvalues = -1 dx G G i ref Stable Steady State =−Rxii, ddξ = t dξ Href (Chernov Condition)

Dissolution: dx Gref eigenvalues = +1 i D ddtξ =− =−xiiR , Unstable Steady State dξ Href (Unrealizable)

Unique Steady State Rxii− =0 (different for growth & dissolution)

40 Steady-State Growth Shapes

v 1 Real growth shapes at low supersaturation

v6 v2

d1 Frank-Chernov Condition d6 d2

vv12 vi d ===" 5 d3 dd12 di d4

v3 v5

v4 A. A. Chernov, “The Kinetics of the Growth Forms of Crystals,” Soviet Physics-Crystallography, 7, 728-730 (1963)

41 General Principle

The faster the rate of growth of a face the smaller its size on the crystal particle

Fast faces grow out and do not appear on the final growth shape

42 Relative Growth & Dissolution Rates

• Experiment & correlations ¾ e.g., the beautiful measurements on paracetamol crystal faces by Shekunov and Grant, “In Situ Optical Interferometric Studies of the Growth and Dissolution of Paracetamol (Acetaminophen). I. Growth Kinetics,” J. Phys. Chem. B, 101, 3973 (1997) • Semi-Mechanistic models ¾ BFDH model ¾ AE model • Mechanistic models ¾ Spiral growth model (BCF, Chernov)

43 3-Dimensional Crystal Shape Evolution

● Shape Evolution Scenarios

– Continuous evolution: change in relative sizes of faces ODE

– Discrete events: face, edges and vertices appearance/disappearance Major Task

● Face Appearance/Disappearance

– Always associated with edge and vertex changes

● On a simple vertex

● On a compound vertex – Euler's rule must be obeyed

44 Identify List of Candidate Planes

• Growth shape is dominated by SLOW moving faces ¾ Include all low index planes in list • Dissolution shape is dominated by FAST moving faces ¾ Higher index planes move faster – how to identify the correct planes and cut off the list? • Selecting the candidate faces is different for growth and dissolution

45 The Model

¾ Crystallography defines the set of candidate faces

¾ Relative normal growth velocities known from first principles

¾ Known initial shape (links to nucleation)

46 Naphthalene

Calculate molecular interactions and slow growing planes

(001)

(110)

(201)

47 Naphthalene

(001)

(110)

(201)

48 Naphthalene

(001)

Calculate

lc, v, N, h (110)

Spiral Evolution (201)

49 Naphthalene

(001) Calculate Relative Growth Rates

(001) (110)

(201) (110)

(201)

50 Naphthalene

Solvent Prediction Experiment*

Ethanol:

Cyclohexane:

Solvent Effect

dis 0.5 γγγls=+− l sW γγ A =+− l γγ s2( l s )

2 2 γ cyclo = 25.3erg / cm γ ethanol = 22.8erg / cm

51

*Grimbergen, et. al. J. Phys. Chem B, 1998, 102, 2646-2653. Anthracene in 2-propanol

Prediction

Experiment

52 α-Glycine in Water

Experiment – Poornachary, Chow and Tan Cryst. Growth & Des., (2007)

(020)

Prediction based on a hydrogen bonded dimer growth unit

(110) (011)

53 3-D Shape Evolution: Adipic Acid

(-1 0 2) (-1 0 2) (0 0 2) (-1 1 1) (-1 1 1) (0 0 2)

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

(2 0 -2) (2 0 -2)

(-1 0 2) (0 0 2) (-1 0 2) (-1 1 1) (-1 1 1) (0 0 2) (0 1 1) (0 1 1) (1 0 0) (1 0 0)

(2 0 -2)

54 Experimental Shape

Davey et al., J. Chem. Soc. Faraday Trans., 88, 3461 (1992) 55 Shape Evolution from Equilibrium-Shaped Seed

Seed Shape:

Experiment:

• Evolution of a succinic acid crystal grown out of water from a seed (here chosen as the equilibrium shape) to its steady state shape.

56 Application - Ibuprofen

Storey & York (1997) Ibuprofen grown from methanol 002

100

a c

011 b

100 002

011 Storey & York (1997) Ibuprofen grown from hexane Predicted – ibuprofen grown from hexane (top) and methanol (bottom)

57 Population Balance Modeling

• Shape Factor:

kh(), G • Link: Shape Evolution Model ⎯ ⎯⎯⎯⎯v h kl h kl → PBM

• One Dimensional MSMPR Crystallizer

Population Balance:

Solute Mass Balance:

58 Size & Shape Evolution – Succinic Acid

200 160

150

140 100

50 120 0 0 500 1000 1500 )

-1 100 m ⋅μ 80 -1

60 n (liter

40

20

0 0 500 1000 1500 h (μm) 020

Initial and steady-state distribution Size distribution transient dynamics

59 General Guidelines for Pharma

“From Form to Function: Crystallization of Active Pharmaceutical Ingredients,” N. Variankaval, A. S. Cote and M. F. Doherty (Merck & UCSB), AIChEJ, 54, 1682 (2008)

• Drive down production costs • Internal survey at Merck revealed that dry milling (pin or jet milling) costs more than the entire drug product formulation process. Additional, problems ¾ serious industrial hygiene concerns due to dust ¾ crystal form/crystallinity difficult (or impossible) to preserve across the dry milling step ¾ product from dry milling is often rich in fines and/or highly electrostatic – downstream processing very difficult • Quality by Design – adopt a strategy that incorporates particle size and shape control into the final crystallization directly so that dry milling is eliminated from manufacturing processes

60 Adopt a New Approach

• Develop growth-dominated processes in which nucleation, agglomeration, and particle breakage are minimized ¾ provide ample seed surface area ¾ provide rapid micro-mixing in order to avoid locally high supersaturation at the feed point where antisolvent or reagent is introduced ¾ charge reagents to the system via a recycle loop set up to circulate locally around the crystallizer. Use mixing tees, static mixers, or other devices to achieve rapid micro-mixing in the loop, which removes this burden from the vessel agitator ¾ design and operate vessel agitator to provide low shear blending and solids suspension

61 Wet Milling by Sonication

Kim et al., Crystallization Process Development …, Org. Process R&D, 7, 997 (2003) 62 Opportunities: Other Materials

• Inorganic crystals ¾ zeolites, tungston carbide for lighting, ZnO nanocrystals, photovoltaics ….

• Proteins and colloids

• Metals and metal oxide catalysts

63 Opportunities

• Process models & process systems engineering • Improving the model ¾ Complex bond chains, growth units, kinks – pharma molecules ¾ Critical edge length – thermodynamic or kinetic? ¾ Supersaturation-dependent relative velocities ¾ Absolute growth rates – can this be done? • Co-solvents & anti-solvents • Co-crystals – hydrates, solvates, and genuine co-solids (inclusion compounds) • Polymorphic phase transformations • Additives & impurities • Nucleation and polymorph selection • Racemic mixtures, enantiomeric resolution • From single particles to suspensions • Experiments ¾ on surfaces for growth model validation ¾ for polymorph selection ¾ growth units & precursors ¾ nucleation of API molecules – size, structure and shape of nuclei?

64 Molecules to Products

65 Extra Slides

66 Dissolution at Crystal Edges – 1 PBC

(001) • Faces appear at certain (011) locations in dissolution ¾ Edges ¾ Vertices

(010)

67 Dissolution at Crystal Edges – 2 PBC’s

(012) (001) • Faces appear at certain locations in dissolution ¾ Edges (021) ¾ Vertices

(010)

68 Dissolution at Vertices – 0 PBC’s

• Faces appear at certain (001) locations in dissolution ¾ Edges ¾ Vertices

(100) (010)

(111)

69 Experimental Apparatus

•Peltier Cell •~2-3mL Batch Crystallizer

70