Regression Analysis for the Two-Step Growth Kinetics of Crystals in Pure Solutions

The overall growth kinetics of ammonium pentaborate, borax decahydrate, and boric acid crystals in pure solution, were analyzed using a two-step mass transfer model. Four different linear expressions of the two-step mass transfer model (TSM), which include the widely used expressions of Sobczak and Karpinski, were discussed. The influence of linearization for an assumed second-order reaction kinetics on the mass transfer and reaction steps was studied for various crystallization systems with overall growth kinetic order ranging from 1 to >= 2. The overall growth kinetics of ammonium pentaborate and borax decahydrate were used to study the effect of linearization as a function of temperature and seed size. The complexities in using the linearized TSM expression to predict the mechanism of the crystal growth process in pure solutions were discussed. A Type 3 expression of Karpinski that successfully represents the overall crystal growth kinetics was determined to be successful in representing two-step growth of borax decahydrate and ammonium pentaborate crystals. Type 1 and Type 4 expressions were determined to be inappropriate for the studied crystallization systems, because they either poorly fit the growth kinetics or produce kinetic parameters without physical meaning. The Sobczak expression well-represents the overall crystal growth kinetics of second order or more, and the Karpinski expression was determined to be successful in representing the overall crystal growth kinetics of order near or equal to unity.