Scaling, tricriticality, and crossover in polymer solutions

Abstract

Generalizing a scaled universal description of phase separation in polymer solutions proposed by Benjamin Widom, we have developed a scaled representation of coexistence curves, osmotic susceptibilities and correlation lengths that accounts for a crossover between a regime with Ising (fluctuation-induced) asymptotic critical behaviour, where the correlation length of the critical fluctuations prevails, and a mean-field tricritical regime with theta-point behaviour controlled by the mesoscopic polymer chain. This theoretical description is compared with experimental data on liquid–liquid phase-equilibria and light-scattering measurements of susceptibilities and correlation lengths. In addition, we demonstrate the validity of de Gennes' prediction for the molecular-weight scaling of the critical amplitudes.

Acknowledgments

We acknowledge a long-time friendship and fruitful discussions with Benjamin Widom. It was Widom who encouraged us to address the challenging issue of crossover between Ising criticality and tricritical theta-point behaviour. We have benefited from research collaborations with V.A. Agayan, E.E. Gorodetskii, J. Hager and A.F. Kostko. The research was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, Department of Energy under Grant DE-FG02-95ER-14509.