In an industrial crystallization process, crystal shape strongly influences end-product quality and functionality as well as downstream processing. Additionally, nucleation events, solvent effects and polymorph selection play critical roles in both the design and operation of a crystallization plant and the patentability of the product and process. Therefore, investigation of these issues with respect to a priori prediction is and will continue to be an important avenue of research.In this review, we discuss the state-of-the-art in modeling crystallization processes over a range of length scales relevant to nucleation through process design. We also identify opportunities for continued research and specific areas where significant advancements are needed.

Several molecular organic crystals are known to exhibit significant changes to their steady-state growth shapes when grown in solutions with different supersaturations. In this article, we describe a first-principles model for the prediction of supersaturation-dependent growth shapes that is capable of capturing this phenomenon. The model begins with the prediction of the growth shape at an arbitrarily low supersaturation, for which all faces present on the steady-state shape grow by spirals. The dominant growth mechanisms (spiral or two-dimensional nucleation) are then determined over a specified range of supersaturations, based on the surface energies of edges present on the faces of the low-supersaturation (spiral growth) shape. These energies are estimated from the set of strong intermolecular interactions contained within each face and solubility parameter data. Steady-state growth shapes are then predicted as a function of supersaturation. A case-study performed on naphthalene grown in ethanol is presented in order to demonstrate the implementation of this model. The predictions from this case study are in remarkable agreement with the results of prior experiments performed for this system.

Needle-shaped crystals, typified by aspect ratios of (1:1:100−1000) are often the steady-state growth shapes in the crystallization of active pharmaceutical ingredients from solution. Crystals with such high aspect ratio shapes are troublesome in the subsequent processing steps required in the formation of a drug product. Therefore, the ability to design crystallizations that directly avoid the formation of needles is of significant interest. In this article, a causality for the formation of needles and guidance for solvent selection based on this causality are provided. The causality presented in this article was formed based on a spiral growth model and requires the presence of a single strongest periodic bond chain within the lattice that is parallel to the direction of elongation of the crystal. The article provides a method for predicting the formation of a needle for a given solute−solvent system based on this causality. Furthermore, three case studies are provided that demonstrate good agreement between experimentally obtained and predicted shapes. As a result, generalized guidance for solvent selection based on the objective of avoiding needles is provided.

Crystallization is the primary process used to purify synthetic drug substances and intermediates as well as to control bulk properties, including particle size, surface area, and flowability. Accordingly, new or improved tools to aid crystallization design are of central importance to drug development. In this Perspective, we provide a brief review of the state of the art, identify current challenges, and highlight key opportunities within different aspects of crystallization process development for synthetic pharmaceutical compounds.

The impact of particle shape on end‐use efficacy and downstream processing efficiency has driven industrial and academic efforts to control/manipulate the shapes obtained by crystallization. Strategies for controlling crystal shape have focused primarily on chemical routes; with shapes optimized through either solvent selection or the use of growth inhibiting additives. However, the chemical design space for crystallization may be limited, and/or the additional separation and purification steps required to remove additives or engineered solvents may be uneconomical. The application of cycles of dissolution and growth as a means for attaining desired crystal shapes is examined. A dynamic model for determining the shapes that can be attained by cycling is developed, and the results of proof of concept experiments performed using adipic acid and paracetamol are presented. The predictions obtained using the dynamic model were shown to be in good agreement with the results from the paracetamol experiments. © 2011 American Institute of Chemical Engineers AIChE J, 2012

Recently, a general mechanistic spiral growth model, including a kink rate expression that enables crystal morphology prediction for all kinds of organic molecules (both centric and noncentric), was developed. However, we have discovered that the kink rate model for the step velocity in solution growth is inconsistent with the attachment and detachment rate expressions for noncentric growth units at kink sites, so these expressions are revisited to make them selfconsistent. Here, we derive a new expression for the kink rate for noncentrosymmetric organic molecules, which correctly accounts for the effect of solvent molecules on growth kinetics. We also generalize the kink rate model to consider other species such as additives. Using the spiral growth model with the improved kink rate expression, we have studied the steady state morphology of paracetamol crystals at low supersaturation to understand the morphology transition induced by the solvent effect and compared our predictions with experimental measurements. The model is able to capture the variation in the shape of paracetamol crystals grown from different solvents with reasonable accuracy.

Kink sites play a critical role in crystal growth. The incorporation of a growth unit into a kink site (1) maintains the free energy of the edge constant and (2) creates another site with the same properties. These properties allow growth through successive incorporation events to proceed in a self-sustaining manner such that the equilibrium spacing between kinks is maintained on average. Traditionally the distributions of kink sites have been determined using a single-site model whereby the probabilities of encountering a kink site adjacent to an edge and encountering a disturbance along an edge are assumed equivalent. In this paper, we develop multisite models that determine the probabilities of encountering kink sites; with the requirement that they obey both properties necessary for growth through successive self-sustaining incorporation events. The probabilities determined using the multisite models diverge significantly from the single-site model for edges with intermolecular interactions ≲6k(b)T between successive molecules. The implications of these findings for the development of predictive crystal shape models and experimental analysis are discussed.

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