Interfacial Structure Analysis Model for the Crystal Morphology Prediction of Centrosymmetric Growth Units

Abstract

Crystallization is used in various industries such as pharmaceutical, defense, food, electronics, and energy to obtain solid phase products. The quality of these products depends on their physical and chemical properties including polymorph, particle size, particle size distribution, morphology, and purity. Because these properties are determined by the crystallization process, predicting and controlling the crystal properties are essential parts of optimizing the process. Among those crystal properties, morphology has impacts on both the product efficacy and process efficiency such as the dissolution rate, bioavailability, reactivity, wettability, flowability and so on. Therefore, there have been continuous researches on developing models that can be used for predicting the crystal morphology. In these models, there are habit-controlling factors which are recognized as either internal or external. The internal factors include the crystal structure and interactions within the crystal, whereas external factors include the solvent, temperature, and supersaturation. Early models such as Bravais-Friedel-Donnay Harker model or Attachment Energy model considered only the internal factors, which is viable for crystal growth from vapor but not for growth from a solution. In order to predict the morphology of crystals grown from solution, mechanistic models such as two-dimensional nucleation growth model and spiral growth model were developed to account for the external habit controlling factors. Among spiral growth models, the Interfacial Structure Analysis (ISA) model suggested two collective external habit-controlling factors. The first external habit-controlling factor is the anisotropic local concentration of the growth units at the interface. The second external habit-controlling factor is the orientational and conformational free energy barrier for reorientation of the growth units. In this model, an adsorbed growth unit with the orientation and conformation identical to that of a growth unit in the crystal is defined as the F1-unit. All the other adsorbed growth units in the interfacial layer are defined as the F2-unit. The external factors are calculated from the concentration of the F2-units within one interplanar spacing from the surface and the free energy barriers between F2-units and F1-unit using molecular dynamics simulation of the solid-fluid interface. The relative growth rates of the faces are calculated by using these two external factors and spiral growth model based on the Burton-Cabrera-Frank theory. In this dissertation, a model is developed that generalizes the previous ISA model and Extended Interfacial Structure Analysis (EISA) model with regard to the orientation and conformation of the growth unit. In the original ISA model, one angle was used whereas in the EISA model, more than two angles were used to identify the F1-unit. These methods are limited to simple molecular structures since sampling of the angles for complex molecules such as those containing rings becomes difficult within a molecular dynamics simulation. To overcome this difficulty, order parameters that can distinguish the F1-unit and F2-unit are used to reduce the dimensionality of the free energy surface. Moreover, metadynamics is used to cross the free energy barriers and calculate their heights in this lower dimension. By using this analysis and polygonal spiral growth model, the morphology of crystal comprised of centrosymmetric growth unit can be predicted. Adipic acid crystal and β-HMX crystal are two representative crystals comprised of centrosymmetric growth units. For both crystals, the role of the anisotropic local concentration of the growth units at the interface as the habit controlling factor was found to be significant. As for the chain-like molecule of adipic acid, orientational free energy surface revealed that most of the molecules are adsorbed parallel to the surface with the azimuthal angle of π/2. This resulted in relative rate to be correlated with the azimuthal angle of the F1-unit, in that small azimuthal angle of the F1-unit require high free energy for ordering of the growth units. On the other hand, the orientational and conformational free energy surface of β-HMX obtained from metadynamics simulation with order parameters that identify F1-units showed that for all faces, the chair conformation of the crystal results in the instability of the F1-units at the interface. Therefore, all F2-units were assumed equivalent and only the local concentration of the growth units at the interface was used for the prediction of the morphology. For both crystals, polygonal spirals were assumed with appropriate rotation kinetics for different spiral geometries which showed more resemblance to the experimental morphologies than those obtained by using the original assumption of concentric circular spirals.