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Crystal Engineering for Product and Process Design 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 y Gvdy= (/)ii d i hkl hkl hkl step vi i = edge i on face hkl ( ) depends yoni hkl shape of velocitiespiral and s step kink, i −1 ( )vi hkl [∝ 1 ap 0 + . 5φ hkl exp(/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 0 . 5 γ=ls γ + l γ s −W A = γ l γ +2 s (l − s γ ) γ 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.
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