Mass–count plots for crystal size control

Abstract

We present measurements from batch crystallization as a trajectory in the phase space mapped out by the crystal mass and the total chord count. This new perspective yields a framework for monitoring and controlling crystallization that has two beneficial attributes: first, crystallization is seen as movement—we find that this fosters an intuitive understanding of crystallization kinetics; and, second, the problem of controlling the average crystal size is cast as a trajectory-endpoint control problem—we find that this promotes the development of spatially-oriented control schemes.The utility of the proposed framework is demonstrated by application. In particular, we apply the framework to: 1) elucidate the effects of simple temperature manipulations on the crystallization kinetics; 2) interpret the actions applied by supersaturation control (SSC) and direct nucleation control (DNC) to produce large crystals; and 3) develop a control scheme—termed spatially-guided action trajectory endpoint control (sGATEC)—that can be applied to produce crystals of pre-selected average size.