Multi-Objective Path Planning for Single Crystal Size and Shape Modification

Abstract

The application of consecutive cycles of growth and dissolution during crystallization from solution is a possibility to systematically modify crystal size and shape. Under the assumption that crystal size and shape can be described by two independent dimensions, we propose a derivative-free path planning methodology to compute temperature profiles that induce a desired size and shape modification of a single crystal in a batch crystallization framework. The proposed methodology allows screening of a subset of the crystal size and shape space for possible size and shape changes, thereby quantifying the trade-off between the required path time and the allowed number of growth and dissolution stages. We compare this methodology with an alternative, gradient-based path planning approach and present case studies based on models of the compounds potassium dihydrogen phosphate and β l-glutamic acid. Analyzing the results of these case studies reveals that an explicit temperature dependence of the growth and dissolution rates of the independent crystal dimensions can have a significant impact on the trade-off between the path time and the number of stages.