Towards the control of crystal shape and morphology distributions in crystallizers

Meenesh R Singh, Purdue University

Abstract

Crystal morphology is a critical determinant of the physical properties of crystalline materials. The synthesis of crystals with desired morphologies requires a framework to guide the selection of environmental conditions. The framework developed here utilizes combinatorics to generate a graph of different morphologies connected by edges describing morphology transformations. These edges collectively form a polyhedral cone containing domains of different morphologies in a crystal-state space. The face-specific growth rates of crystals allow the identification of accessible regions within the polyhedral cone using a generalized single-crystal model. Here we introduce Morphology Domain as a fundamental property of crystals which can be used to screen crystallization conditions for the controlled synthesis of desired crystal morphologies that is both facile and readily usable. A user-friendly tool, MorphologyDomain, is presented that facilitates diverse applications. The evolution of morphology distributions due to crystal growth inside the Morphology Domain is described by a Morphological-Population Balance Model (M-PBM) which readily submits to solution by the Method of Characteristics. The methodology, illustrated in controlling crystal morphologies of Potassium Acid Phthalate using additives, paves the way for model-based control of shape control of crystallization processes. The modeling framework is extended to account for nuclei shape distribution and growth rate dispersion due to local fluctuations in supersaturation. A stochastic model is derived from the framework of density and temperature fluctuations. The resulting dispersions in size and shape of nuclei are obtained by multi-dimensional maximization of Gibbs free energy in Morphology Domain of Potassium Acid Phthalate. The model predictions are validated with the experimental measurements of growth rate dispersions in Potassium Acid Phthalate crystals. The stochastic model provides the first rational and quantitative basis for observed dispersions in crystallization processes. A new technique is developed for measurement of 3D crystal morphology and identification of its polymorph using tomographic images. Confocal Microscopy is used for the first time to obtain tomographic images of crystals that are coated with a suitable fluorescent dye. The image-analysis program developed here is also suitable for repeated measurements to produce morphology distributions. This work has also produced a method to experimentally determine polar plots of growth rates and dissolution rates from the dynamic images of crystals obtained from hot-stage microscopy. The method relies on the solution of the characteristics for crystal dissolution. The methodology is demonstrated to obtain polar plots of Succinic acid at different sub-saturations.

Degree

Ph.D.

Advisors

Ramkrishna, Purdue University.

Subject Area

Chemical engineering

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