SIZE DISPARITY AND LOWER CRITICAL SOLUTION TEMPERATURE - A CRITICAL INVESTIGATION OF FREE-VOLUME DISPARITY

By critically examining a simple model system of equilibrium polymeriz ation that is athermal in the traditional sense, we demonstrate that m any of the consequences of the free-volume disparity induced by size d isparity are inconsistent with its current understanding. Despite its traditional name, the model is not truly athermal because of the compr essibility. The resulting energetics endows the model system with a ve ry rich and complex behavior. The analytical results that are obtained in a mean-field approximation show how and when an upper critical sol ution 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 land not of the components) t hat 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 fi ee 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 t hat 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 includi ng hourglass emerges, despite the fact that the conventional mechanism for hourglass in not present. (C) 1998 American Institute of Physics. [S0021-9606(98)50944-0].