Hidden role of metastable phases on surface tension and in the selection of solid polymorphs from melt
The preferential formation of one solid over the other, as it precipitates out from the melt at specific temperatures, is often explained by invoking a competition between thermodynamic and kinetic control. A quantitative theory, however, could not be developed because of the lack of accurate values of relevant surface tension terms. Motivated by the observations that wetting of the interface between two stable phases by multiple metastable phases of intermediate order can reduce the surface tension significantly (Kirkpatrick-Thirumalai-Wolynes (KTW), Phys. Rev. A 1989, 40 (2), 1045; Santra et al., J. Phys. Chem. B, 2013, 117, 13154 ), we develop a statistical mechanical approach based on a Landau-Ginzburg type free energy functional to calculate the surface tension between two stable phases in the presence of N number of metastable phases. Simple model calculations are performed that show the surface tension between two coexisting stable phases (melt and the stable crystalline forms) depends significantly on the number, relative depths and arrangements of the free energy minima of the metastable phases, in addition to the size of the nucleus. We provide an explanation of the quickly disappearing polymorphs (QDPMs) that often melt back to the liquid (or, the sol) phase. It is shown that our model systems could describe some aspects of solid formation in real polymorphic systems, like phosphates and zeolites.