(300f) Collision Theory Re-Interpretation of Kinetic Data for the Growth of Organic Crystal Surfaces; Implications for the Precipitation of Pharmaceuticals in Trans-Critical Environments?

We expect that the challenge of interrelating kinetic data on the growth of organic crystal faces  across a wide variety of environmental conditions (from liquids, to gas-expanded liquids, to moderate- and low- density gases) will be simplified by uniformly adopting a molecular “collision-theory” viewpoint-----ie., interpreting/reporting single crystal face {klm}  growth rate data in terms of dimensionless effective overall  “incorporation probabilities”, e, bounded by 1/ Z, where Z (often 1, 2 or 4) is the number of growth molecules per unit cell of the relevant crystal structure. In effect, this is equivalent to the generally accepted notion that, at any given departure from interfacial equilibrium and surface temperature, “only a fraction of the total (surface) sites are available for attachment” and incorporation. Remarkably, however, this valuable perspective is rarely mentioned for CG from melts¹, or from liquid solutions², and is now even uncommon for the physical vapor growth of low molecular weight organics³ ((eg., “surrogates” for active (pharmaceutical) ingredients (APIs)). Motivated, in part, by the sparsity of reliable published growth rate information on actual APIs, especially under “compressed gas-expanded liquid” processing conditions of current pharmaceutical interest^4,5, we therefore illustrate here a tractable method to re-interpret (in terms of abovementioned dimensionless overall “incorporation probabilities”) available growth rate data for a selection of organic compounds [with the stoichiometry: CaHbOcNd ranging from succinic acid (with a=4) to rubrene (a=42), including acetaminophen (a=8), and the 28-atom stereo isomer: ethylene diamine d-tartrate(a=6)]. For instructive quantitative  illustrations we consider only interface-controlled, face-specific experimental rate data obtained on single crystals immersed in dilute otherwise single component carrier fluids at supersaturations much smaller than the threshold for homogeneous nucleation, and for crystals large enough to be outside the domain of interface curvature-shifted equilibrium solute composition. We close with a brief discussion of implications of such overall e(S,T; {klm})-estimates for: a) readily identifying the particle size range at which fluid-phase diffusional limitations will inevitably set in, and, more ambitiously: b) estimating the growth rate of structurally similar API-surrogates in, say, expanded liquid (gas-anti-solvent) or dense-carrier vapor precipitation conditions------ of current interest for the production of “micronized” drugs.

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Prepared for presentation at AIChE 2013 Annual Mtg., San Francisco,CA; Nov.4-8, 2013                                                      May 10, 2013  

^* LW Jones Jr.   Professor of Chemical Engineering, Director:  Sol Reaction Engineering Group

daniel.rosner@yale.edu

References: 

1. Rosner, DE, “Collision Theory Re-Interpretation of Kinetic Data for the Growth  of Organic Crystal Surfaces; Part  I. Melt Growth; Implications for the Precipitation of Pharmaceuticals in Trans-critical Environments?"; Crystal Growth & Design(ACS)(to be submitted); March   2013

2.  Rosner, DE, “Collision Theory Re-Interpretation of Kinetic Data for the  Growth  of Organic Crystal Surfaces; Part  III. Solution–Growth”. Crystal Growth & Design (ACS) (to be submitted); May 2013

3.. Rosner, DE, “Collision Theory Re-Interpretation of Kinetic Data for the  Growth  of Organic Crystal Surfaces; Part  II. .Physical Vapor–Growth”. Crystal Growth & Design(ACS) (to be submitted), June 2013

4.  Martin, A. and Cocero, MJ, “Micronization Processes With Supercritical Fluids: Fundamentals and Mechanisms”, Advanced Drug Delivery Reviews (Elsevier),vol 60, pp 339-350(2008)

5 Rosner, DE and Arias-Zugasti, M, “Theory of Pharmaceutical Powder ‘Micronization’ Using Compressed Gas Anti-solvent (Re-) Precipitation”; Paper # WG10S1O1, European  Aerosol Conference; Granada, Spain ,  September 6, 2012; J Supercritical Fluids(to be submitted) August, 2013