Size disparity and lower critical solution temperature: A critical investigation of free-volume disparity

Abstract

By critically examining a simple model system of equilibrium polymerization that is athermal in the traditional sense, we demonstrate that many of the consequences of the free-volume disparity induced by size disparity are inconsistent with its current understanding. Despite its traditional name, the model is not truly athermal because of the compressibility. The resulting energetics endows the model system with a very rich and complex behavior. The analytical results that are obtained in a mean-field approximation show how and when an upper critical solution temperature, a lower critical solution temperature (LCST) and an immiscibility loop may occur. We suggest that it is the difference in the thermal volume-expansion coefficients rather than the difference in free volumes of the coexisting phases (and not of the components) that plays a central role in determining the phenomenon of LCST and may be used to provide for its quantitative characterization. Too much or too little of free volume disfavors LCST; hence, it occurs only in a finite range of the pressure. Moreover, for the phenomenon of LCST to occur, the size disparity should be larger than some critical value that also depends on the pressure. A line of theta points is found in a four-parameter phase space characterizing the simple model. The model also enables us to understand how a variety of phase diagrams including hourglass emerges, despite the fact that the conventional mechanism for hourglass in not present.