LCST phase behavior according to the Simha-Somcynsky theory: application to the n-hexane polyethylene system

Abstract

Expressions for the free energy of mixingδG, including equation of state contributions, have been previously derived by Jain and Simha. However, the chemical potentials and compositional derivatives required for the description of phase behavior were approximated by polynomial fits to the theoreticalδG for a particular case. Exact and general equations for a binary system are now derived. This opens the way for future analyses of phase equilibria, based on the Simha-Somcynsky (S-S) theory. The present application involves asimulation of the system n-hexane/polyethylene, previously treated by Jain and Simha. The analysis is extended now to a wide range of molar masses from 8 to 103 kg/mole and binodals as well as spinodals and critical conditions are computed over a wider range of pressures than previously. In the simulation the polymer samples are assumed to be monodispers. The phase boundaries differ significantly from the previous ones, as one should expect from the higher derivatives of polynomial fits. However, previous conclusions concerning an iso hole or free volume fraction difference between the constituents as a critical condition for the appearance of a lower critical solution temperature (LCST) stand. Moreover, and as an alternative, this condition can be expressed in terms of the excess free volume fraction hexc of the mixture. Master curves for binodals and spinodals can be generated for different pressures over a reasonable temperature distance from the critical point. Similarly, hexc at the binodal and spinodal condition can be represented by universal curves. Finally, we discuss the variation of the critical coordinates with chain length and conclude with an evaluation of the x-function for different compositions, temperature, and pressure.