Modelling of the Polymorph Nucleation Based on Classical Nucleation Theory

Abstract

To elucidate the relative nucleation rates of different polymorphs, a competitive kinetic model is developed based on classical nucleation theory to describe the time evolution of two different polymorphic cluster size distributions controlled by the association and dissociation of the solute molecules during polymorph nucleation. Although there is only one type of the solute molecules, the agglomerated solute clusters are divided into two types-A form and B form, which resemble the structures and morphologies of the different mature polymorphs and eventually lead to the formation of two polymorphic crystals. A dissociation kernel is incorporated into the proposed model to account for gradual dissolution of the solute clusters smaller than a critical nucleus size due to the thermodynamic instability. By fitting the experimental induction period data and the final measured weight fractions of eflucimibe polymorphs with the proposed model, the association and dissociation rate constants for two polymorphs are determined. The developed model is satisfactory to explain the competitive mechanism of polymorph nucleation for eflucimibe that B form dominates at higher supersaturation while A form dominates at lower supersaturation. The results also indicate that A form is more stable than B form with a transition energy of 3.1 kJ/mole at 35 • C.

Influence of Taylor Vortex Flow on the Crystallization ofl-Glutamic Acid as an Organic Model Compound

“…The σ and ν m are interfacial tension of the solid contact with the solution and molecular volume, respectively; k and T ( 0 K) are the Boltzmann constant and the solution temperature; S is the supersaturation defined with C and C eq as the solute concentration and the solubility of the polymorphs. The supersaturation is known as a critical factor for polymorph selection. , The induction time τ ind is inversely proportional to nucleation rate J because of the relation τ ind ∝ J –1 . − Thus, eq can be rewritten as From Figures b and S2, we can extract the values ln τ ind and 1/[ T 3 (ln S ) 2 ] at different Taylor numbers. Thereby, we can estimate the kinetic and thermodynamic parameters in eq of both polymorphs via the linear correlation between ln τ ind and 1/[ T 3 (ln S ) 2 ], as shown in Figure c.…”

“…The supersaturation is known as a critical factor for polymorph selection. 56,57 The induction time τ ind is inversely proportional to nucleation rate J because of the relation τ ind ∝ J −1 . 1−3 Thus, eq 4 can be rewritten as…”

Thermodynamic vs. Kinetic Basis for Polymorph Selection

“…Polymorphs pairs Eflucimibe [12], d-Mannitol [28] and Famotidine [30], o-Aminobenzoic acid, Stavudine [31], L-Histidine [32], BPT Propyl Ester [33], Florfenicol [34] and L-Glutamic acid [35] each of which show a preference for the stable polymorph at low supersaturations and a preference for the metastable polymorph at higher supersaturations. Shiau used a competitive kinetic model that predicted this behaviour for eflucimibe based on the model derived association and dissociation rate constant for the two polymorphs [36]. More specifically, metastable Form II of o-aminobenzoic acid was the first observed crystalline form when the supersaturation was 2 and above; the stable Form I was the first to crystallise for supersaturations less than 1.5.…”

2D Monte Carlo Simulation of Patchy Particles Association and Protein Crystal Polymorph Selection

“…Similar to BSM are the 'sticky patch' models that are becoming increasingly popular. Computer simulations (including the Monte Carlo method) are very well suited to studying protein crystal nucleation and polymorphism [16][17][18][19][20][21]. Other different approaches to crystal polymorphism were reported recently [22][23][24][25].…”