Examining the effect of chain length polydispersity on the phase behavior of polymer solutions with the statistical associating fluid theory (Wertheim TPT1) using discrete and continuous distributions

Abstract

Polymers are naturally polydisperse. Polydispersity may have a large effect on the phase behavior of polymer solutions, in particular, on the liquid-liquid phase equilibria. In this paper, we determine the cloud and shadow curves bounded by lower critical solution temperatures for a number of polymer+solvent systems where the polymer is polydisperse in terms of molecular weight (chain length). The moment method [P. Sollich, P. B. Warren, and M. E. Cates, Adv. Chem. Phys. 116, 265 (2001)] is applied with the SAFT approach to determine cloud and shadow curves with continuous Schulz-Flory distributions. It is seen that chain length polydispersity always enhances the extent of liquid-liquid phase equilibria. The predicted cloud curves obtained for continuous distributions are very similar to those obtained for simple ternary mixtures with the same polydispersity index, while the corresponding shadow curves can be very different depending on the composition of the parent distribution. The ternary phase behavior can be used to provide an understanding of the shape of the cloud and shadow curves. Regions of phase equilibria between three liquid phases are found for ternary systems when the chain length distribution is very asymmetrical; such regions are not observed for Schulz-Flory distributions even in the case of a large degree of polydispersity.

The Influence of Synthesis Method on Characteristics of Buffer and Organic Solutions of Thermo- and pH-Responsive Poly(N-[3-(diethylamino)propyl]methacrylamide)s

“…This method also allows polymers of various architectures to be obtained [20,21]. It is important to note that the decrease in the molar mass polydispersity index provided by RAFT polymerization can significantly improve the stimuli-responsive properties of polymers in solution and gels [22][23][24][25][26].…”

Continuous Thermodynamics of Polydisperse Polymer/Solvent Systems: Polystyrene/Cyclohexane and Polystyrene/Methyl Acetate Mixtures

“…17−19 Similar works for polydisperse polymer solutions were also reported by Choi and Bae 20 and Enders and co-workers. 21,22 In addition, applications of continuous thermodynamics to equations of state, including statistical associating fluid theory 23,24 and lattice fluid theory, 25 have been reported by several researchers. As noted by Hu et al, 15 the primary advantage of the continuous thermodynamic approach is its convenience, which arises from replacing the summation over all components with integration.…”

A duality-based optimisation approach for the reliable solution of (P, T) phase equilibrium in volume-composition space

“…The mixture exhibits LLE at some conditions, and also a very small region of LLLE. To illustrate the complexity of the phase behaviour being studied, we refer to the cloud and shadow curves presented in [88]. These are phase diagrams at a fixed weight ratio of the two polymer molecules, and allow the polymer phase behaviour to be represented over a range of temperatures.…”

“…The last ternary mixture for which we show results has been studied in [88]. The model is representative of a polydisperse solvent-polymer mixture.…”