(707c) Depiction and Prediction of Practical Pathways for Crystallization

For many systems in which phase transformation is driven by supersaturation, the limits of viable processing conditions are conventionally displayed on a metastable zone width (MSZW) diagram.  This type of diagram consists of a two-dimensional space defined by concentration and temperature axes, on which a metastable limit (line) and a solubility limit (line) are superimposed. The metastable limit corresponds to conditions for which nucleation is so rapid that it is seemingly instantaneous.  The solubility limit corresponds to an equilibrium in which no nucleation occurs: there is no driving force and hence the time for transformation approaches infinity.  The concentration difference between these limits at fixed temperature, or the temperature difference between these limits at fixed concentration, serves to define the MSZW.  The limits are typically obtained from experimental observation (i.e. the diagrams are descriptive rather than predictive).  Also, the MSZW is found to depend on the supersaturation rate.  Although MSZW diagrams are useful, the absence of a time axis is a significant constraint to their application in process design.  Kinetic data are intrinsically time-dependent, and this attribute is not conveyed in conventional MSZW diagrams.

We have recently [1] shown how the kinetics of supersaturation-driven phase transformations can be richly displayed on time-concentration-temperature-transformation (TCTT) diagrams, derived with reference to the time-temperature-transformation (TTT) diagrams that have long been used by metallurgists to summarize and develop processes used in steelmaking.  The value of such diagrams lies in their ability to clearly suggest time-efficient process pathways to a final product, straightforwardly promoting desired structures and properties while also suppressing undesired characteristics and properties.  Metallurgy and industrial pharmacology share a common goal in this regard, and transformation diagrams can avoid the trial-and-error aspects of the MSZW approach.

Another attractive aspect of TCTT diagrams is that (like TTT diagrams) they lend themselves to prediction, thus offering the possibility of adding further efficiency to process design.  We have combined (i) classical modeling (Kolmogorov-Johnson-Mehl-Avrami) of nucleation and growth and (ii) modeling (Flory-Warner and Maier-Saupe) of the isotropic-to-nematic liquid crystal phase transformation for rod like mesogens as a function of concentration and temperature, to illustrate how specific TCTT diagrams for liquid crystalline systems can be developed from first principles.  We propose that prediction of TCTT and similar diagrams can serve as a convenient guide for process design in polymer crystallization, pharmaceutical product crystallization, food processing, and many other phase transformation processes.

[1]  J. Komadina, S.W. Watt, I.J. McEwen and C. Viney, Rate of lyotropic nematic phase formation: derivation and application of time-concentration-temperature-transformation diagrams, DOI: 10.1021/cg501459m, (2015).