Description of Phase Behavior of Polymer Blends by Different Equation-of-State Theories. 1. Phase Diagrams and Thermodynamic Reasons for Mixing and Demixing

Abstract

A comparison has been made between the Sanchez-Lacombe equation-of-state theory and the theory of Patterson for describing the phase behavior of various polymer blends. Phase diagrams have been determined as well as PVT data, in order to determine the reduction parameters of the polymers used. With these data the phase diagrams were simulated applying these two theories. Furthermore, the cause of compatibility or incompatibility, Le., the influence of free volume and enthalpic effects were investigated. Both theories show surprisingly similar behavior with respect to the mentioned properties.

Lower and Upper Critical Ordering Temperatures in Compressible Diblock Copolymer Melts from a Perturbed Hard-Sphere-Chain Equation of State

“…Our theory predicts that for a PS/PBMA blend, LCST rises with increasing pressure at a rate about +200 °C/kbar that is 1 order of magnitude larger than the measured rates for mixtures of ethylene−vinyl acetate copolymer with a chlorinated polyethylene and for the blend of PSD and PVME that also exhibit LCST behavior. Similarly, the analysis by Rudolf and Cantow shows that the lattice-fluid theory and the equation-of-state theory by Patterson also predicts a very large pressure dependence of LCST in polymer blends. , …”

“…Similarly, the analysis by Rudolf and Cantow shows that the lattice-fluid theory and the equation-of-state theory by Patterson also predicts a very large pressure dependence of LCST in polymer blends. 53,54…”

Study on theχParameter for Compressible Diblock Copolymer Melts

“…In analyzing the phase behavior of the copolymer, a proper choice of the cross-interaction parameter ε 12 is essential. ε 12 is determined by adjusting it around the geometric mean (ε 11 ε 22 ) 1/2 of self-interaction parameters to predict a correct critical temperature using eq A4 in Appendix A for the corresponding low molecular weight PS/PI blends measured by Rudolf and Cantow . Each molecular parameter set for PI in Table demands its own ε 12 to predict the reported critical temperature.…”

Upper and Apparent Lower Critical Solution Temperature Branches in the Phase Diagram of Polymer:Small Molecule Semiconducting Systems

“…This selective, separate fit reproduces the data very well but cannot fit the phase behavior as a whole with a single functional form of χ. Modifications to the F–H theory have been proposed by various researchers that account for the relationship of the χ interaction parameter with polymer chain parameters such as molecular weight, shape, rigidity, etc. − One modified theory utilizing an equation of state of the constituent components to account for the compressibility has also been proposed that is capable of predicting not only LCST but also a concurrent UCST and LCST behavior. − With addition of a free volume term, eq can be modified to a more generalized functional form of where the third term ( C ln T term) accounts for the effect of the free volume change with temperature. , Different signs of C lead to various types of phase diagrams: a positive C gives a combined USCT and LCST or hourglass phase diagram if the UCST and LCST merge, while a negative C results in closed loop phase diagram. When C is zero, eq reduces to the F–H theory of eq .…”