Crystal Growth Kinetics of an Industrial Active Pharmaceutical Ingredient: Implications of Different Representations of Supersaturation and Simultaneous Growth Mechanisms

Abstract

The crystal growth kinetics of a proprietary active pharmaceutical ingredient (API) was investigated by isothermal seeded batch de-supersaturation experiments in solvent mixtures using the "true" thermodynamic representation of the supersaturation driving force, which considers the activities of the saturated and supersaturated states. Three approaches to approximate the experimentally inaccessible activity coefficients of the supersaturated state were assessed, as well as the most common approximation, which omits the activity coefficients altogether. Subsequently, the supersaturation data from the different expressions were fed into a population balance model to estimate kinetic parameters for the empirical, Burton− Cabrera−Frank, and birth-and-spread growth models. The results demonstrate that the approach used to compute the supersaturation alters the estimated kinetic parameters significantly, having potentially serious implications for their physical interpretation and for extracting the physical properties they represent in lumped form. Moreover, including the chemical activities in the supersaturation leads to kinetic parameters with a tighter joint confidence interval and weaker parameter correlation that can better explain the experimental observation of the API growing appreciably only under higher antisolvent amounts. Finally, the simultaneous occurrence of multiple crystal growth mechanisms is investigated, concluding that the additive contribution of B+S and BCF best explains the supersaturation decay observed in the experiments for this API.

Secondary Nucleation by Interparticle Energies. III. Nucleation Rate Model

“…Alternatively, eq 7 can be written in a form that reveals the physical mechanism of CNT 22 , 41 where B ( n ) is the frequency of monomer attachment to an n -sized cluster (i.e., a molecular cluster consisting of n monomers), z is the Zeldovich factor, C n is the equilibrium concentration of the n -sized clusters, and n * is the size of the critical clusters, i.e., the critical (nucleus) size. Considering that the rate of monomer attachment is often limited by the surface-integration step, 23 , 42 − 44 the monomer attachment frequency B ( n ) is given by 22 where k 0 is a lumped coefficient to be estimated from experimental data. This coefficient reflects the mass transport of solute molecules to the surface of an n -sized cluster, and its value is independent of mixing conditions.…”

Accounting for the Presence of Molecular Clusters in Modeling and Interpreting Nucleation and Growth

“…In this work, the surface-integration limited mechanism is considered as an example since this mechanism is frequently encountered in practice. 9 , 10 , 25 , 36 A corresponding expression for k n a is 1 where β is the sticking coefficient, k s is the surface shape factor, d 1 = ( V 1 / k v ) 1/3 is the molecular diameter defined with the volume shape factor k v and the molecular volume V 1 , and D is the diffusion coefficient of the solute molecules in the solution. According to the assumption on which eq 5 is based, the clusters grow through the mechanism of rough growth.…”

“…This supersaturation is often used, partly because it is easier to characterize experimentally. 9 The monomer-based supersaturation s is defined as 10 where C 1,e is the monomer solubility (i.e., the monomer concentration at equilibrium).…”

“…Note that crystallization kinetics described through these two supersaturations of reference can be closely comparable to each other; a similar discussion has also been presented elsewhere. 9 , 11 …”

“… 15 Likewise, several issues can negatively affect the experimental characterization of growth kinetics. Seeded batch de-supersaturation experiments, which is a standard method of characterizing growth kinetics for process design, 9 , 21 − 23 can be accompanied by secondary nucleation. 9 , 24 In addition, some intrinsic properties of a compound (e.g., crystal morphology) can make measured data nonrepresentative.…”