Simple thermodynamic arguments are evoked to show that the pressure dependence of the Flory interaction parameter of miscible polymer blends, as derived from small-angle neutron scattering experiments, is directly related to the volume changes on mixing for these systems. This approach is validated by comparison to available experimental data. We make contact with existing theoretical approaches and show that it is thermodynamically inconsistent to model a blend with nonzero as having no volume change on mixing. Since the entropic contributions that arise from these volume changes on mixing account for more than 50% of the pressure dependence of , the use of regular solution theory, where the pressure dependence is purely enthalpic in origin, gives an imperfect understanding of these situations. We finally show that, since the volume change on mixing is directly proportional to the parameter under ambient pressures, the critical temperature for any polymer blend will vary in an apparently "universal" fashion on pressurization. This conclusion is in agreement with experimental data for a large number of polymer blends.
IntroductionThe role of pressure on the thermodynamics of polymer mixtures has been intensely studied in the past few years since it has direct applications to processing and to novel synthesis schemes involving environmentally benign supercritical fluids. Pressure effects are also of interest from a fundamental standpoint since the thermodynamics of typical polymer blends are understood in the framework of the incompressible random phase approximation. 1-6 A rigorously incompressible system should be unaffected by pressure. However, since experimental results show that the critical temperature for polymer-polymer demixing, T c , is strongly affected by pressure, typically dT c /dP ≈ 25-50 K/kbar, it is clear that polymer blends show significant departures from this ideal limit. 5,7 Most successful approaches in this area incorporate free volume effects, either into the free energy of the system or into an equation of state. The pressure dependence of T c and , the Flory-Huggins interaction parameter, is then numerically derived. 7-14 While these methods have been quite successful at explaining the measured dT c /dP, they provide little physical insight into the effect of pressure.A line of thinking that helps build a picture at the molecular level for the effect of pressure on polymer blend thermodynamics is presented by Rabeony et al. 6 Here it is postulated that the central quantity is the interaction energy density, X ≡ ( /v 0 )RT. is the Flory interaction parameter, 15 v 0 is an arbitrary reference volume, R is the gas constant, and T is the temperature. The X values obtained from some of the blends considered appear to be unique functions of system density, and data from several pressures and temperatures for each of these systems can be collapsed onto a master curve. Since this approach explicitly assumes that volume changes on mixing are negligible, it suggests that the only role of pressu...