Scaling and Crossover to Tricriticality in Polymer Solutions

We propose a scaling description of phase separation of polymer solutions. The scaling incorporates three universal limiting regimes: the Ising limit asymptotically close to the critical point of phase separation, the "ideal-gas" limit for the pure-solvent phase, and the tricritical limit for the polymer-rich phase asymptotically close to the theta point. We have also developed a phenomenological crossover theory based on the near-tricritical-point Landau expansion renormalized by fluctuations. This theory validates the proposed scaled representation of experimental data and crossover to tricriticality.Comment: 4 pages, 3 figure

Competition of Mesoscales and Crossover to Tricriticality in Polymer Solutions

We show that the approach to asymptotic fluctuation-induced critical behavior in polymer solutions is governed by a competition between a correlation length diverging at the critical point and an additional mesoscopic length-scale, the radius of gyration. Accurate light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 200,000 up to 11.4 million clearly demonstrate a crossover between two universal regimes: a regime with Ising asymptotic critical behavior, where the correlation length prevails, and a regime with tricritical theta-point behavior determined by a mesoscopic polymer-chain length.Comment: 4 pages in RevTeX with 4 figure

Application of Minimal Subtraction Renormalization to Crossover Behavior near the 3^3He Liquid-Vapor Critical Point

Parametric expressions are used to calculate the isothermal susceptibility, specific heat, order parameter, and correlation length along the critical isochore and coexistence curve from the asymptotic region to crossover region. These expressions are based on the minimal-subtraction renormalization scheme within the $\phi^4$ model. Using two adjustable parameters in these expressions, we fit the theory globally to recently obtained experimental measurements of isothermal susceptibility and specific heat along the critical isochore and coexistence curve, and early measurements of coexistence curve and light scattering intensity along the critical isochore of $^3$He near its liquid-vapor critical point. The theory provides good agreement with these experimental measurements within the reduced temperature range $|t| \le 2\times 10^{-2}$