Effects of metastable phases on surface tension, nucleation, and the disappearance of polymorphs

In nature, we often find that multiple solid phases form from the same solution. Zeolites present the best-known example. The preferential formation of one solid form over the other, 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, although some estimates of thermodynamic functions (like enthalpy and entropy) are becoming available. Motivated by the observation that wetting of the interface between two stable phases by multiple metastable phases of intermediate order can reduce the surface tension significantly [T. R. Kirkpatrick, D. Thirumalai, and P. G. Wolynes, Phys. Rev. A 40(2), 1045 (1989)], we develop a statistical mechanical approach based on a Landau-Ginzburg type free energy landscape to calculate the surface tension under various free energy situations. We analyze the trapping of a metastable phase in the presence of a thermodynamically stable phase. The interplay between free energy differences and the surface tension is partly captured in classical nucleation theory. We provide an explanation of the quickly disappearing polymorphs (QDPMs) that often melt back to the liquid (or the sol) phase. To this aim, we have presented the failure of classical nucleation theory and the importance of considering a multidimensional nucleation theory. Simple model calculations are performed to show that 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. Even a change in the curvature of the free energy surfaces induced by the change in temperature (T) can play a role in determining the sequence of the formation of phases. Finally, we show that our model systems could describe some of the real polymorphic systems, like phosphates and zeolites.