Thermodynamics Of Phase Behaviors For Polymer Fluids

The phase separation of polymer-containing system has increasingly become the focus of attention in physics, chemistry and materials science. Many theoretical and experimental efforts have been made to elucidate the fundamental physical picture of this phenomenon. The first description of statistical thermodynamics of the phase equilibrium of polymer solutions and mixtures was given by Flory and Huggins. To explain the lower critical solution temperature (LCST), Flory, Orwoll and Vrij (FOV) extended the c parameter theory established by Prigogine. The free volume introduced in the FOV theory accounts for the compressibility of polymer systems. Sanchez and Lacombe (SL) established a lattice fluid theory in the mid 70's. The distinct difference between FOV and SL theories is that the distribution of free volume is uniform around the hard-core in the former and is random in the latter. The first part of our work iscalculating the phase diagram, Flory-Huggins parameter and enthalpy of mixing of the system PES/Phenoxy by means of SL theory. From our calculation, the calculated phase diagrams are almost coincide with the experimental cloud points.As we know, synthesizing polymers from gaseous monomers, producing polymer blends in an extruder or forming articles from a blend by injection molding are always carried out at high pressure, thus the effects of pressure on the miscibility of polymers or of polymer and solvent have been the focus of research in recent years. Although FOV theory and SL theory are successful in calculating the phase diagrams of polymer solutions and polymer mixtures near or at atmosphere pressure for some systems containing polymers, it is often failed to use them to predict the pressure dependence of equilibrium phase separation behavior at high pressures without modification of the theories. An et al. suggested a method to calculate the effects of pressure on the miscibility of polymer solutions and polymer mixtures by considering the interaction energy parameter as a linear function of pressure and obtained the phase diagrams in accordance with experimental data at high pressures. However, it is difficult to conduct further research on this subject due to the scarcity of experimental information on phase diagrams at different pressures. The system polystyrene (PS)/cyclohexane (CH), as a typical polymer solution, has been extensively studied in the past decades and the phase diagrams atdifferent pressures and at different molecular weights of PS were measured by different researches. Thus we chose the PS/CH solutions as the model systems for this work. From the references cited, we know that the pressure dependence of the UCST is quite different for PS with low (37kg mol"1) and high molecular weights (670kg mol"1). Another part of our work is introducing a Gibbs interaction energy, g'n , to expound the interactions between unlike mers and its variation with pressure using SLLFT. The spinodals and binodals of the systems CH/PS were calculated for different molecular weights PS at different pressure and the pressure of optimum miscibility at fixed concentration (near critical point) was predicted theoretically. The results of these computations agree with experiments. According to the calculated results, we can give a reasonable explanation of the phenomenon reported by Saeki et al. Furthermore, from our calculation, the Flory-Huggins interaction parameters almost linearly depend on the reciprocal of temperature, on pressure, on concentration and on the reciprocal of the square root of the molecular weights of PS if the other three variables are held constant.The shear influence on phase behavior is very substantial for some polymer solutions and polymer mixtures. Different researchers have made a lot of interesting work about the shear dependence of phase-separation behavior because this phenomenon is of great importance to the practical process. Owing to the difficulty ofexperiment, there have been only a few reports directly showing the shift of cloud point at a fixed shear rate. Thermodynamically, Horst and Wolf have dealt with the effects of shear rate on phase diagrams on the basis of Flory -Huggins theory and calculated some phase diagrams for the model systems of polymer solutions and polymer mixtures. However, it is still difficult to understand the occurrence of lower critical solution temperatures (LCST) on the basis of the original FH theory because of the ignorance of free volume effects unless a particular dependence of the Flory-Huggins interaction parameter on temperature and composition is considered. In addition, the used combining rules for the zero-shear viscosity and the steady state shear compliance failed to describe the PVME/PS system in the above calculation. According to the reasons mentioned above, the shear influence on phase separation behavior is introduced into the Sanchez-Lacombe lattice fluid model (SLLF model) in this work because it is normally used to predict the equilibrium phase behaviors of polymer systems with LCST. Meanwhile, a valid combining rule is used to calculate the zero-shear viscosity of PVME/PS mixtures. A partly quantitative comparison between the theoretical calculations and Higgins' experimental data is made. Also the shear rate influence on cloud point temperature and the combining effects of pressure and shear on Spinodals are discussed at a certain composition. The shear influence on the Gibbs energy and equation of state is embodied only by ^-parameter. With the increase of the concentration of PS, there areextrema, and the concentrations and temperatures of those extrema are corresponding to those of shear-induced miscibility gap of the Spinodals exactly, which is similar to the effect of Flory-Huggins interaction parameters. Furthermore, the three points of the three-phase equilibrium at about T=376.24K are found on stable Binodal. The shear-induced mixing becomes inconspicuous and the shear-induced demixing becomes conspicuous with the increase of pressure.