Scaling of demixing curves and crossover from critical to tricritical behavior in polymer solutions

In this paper we show that the virial expansion up to third order for the osmotic pressure of a dilute polymer solution, including first-order perturbative corrections to the virial coefficients, allows for a scaling description of phase-separation data for polymer solutions in reduced variables. This scaling description provides a method to estimate the Theta-temperature, where demixing occurs in the limit of vanishing polymer volume fraction $\phi$ and infinite chain-length $N$, without explicit assumptions concerning the chain-length dependence of the critical parameters $T_c$ and $\phi_c$. The scaling incorporates three limiting regimes: the Ising limit asymptotically close to the critical point of phase separation, the pure solvent limit and, the tricritical limit for the polymer-rich phase asymptotically close to the Theta point. We incorporate the effects of critical and tricritical fluctuations on the coexistence curve scaling by using renormalization-group methods. We present a detailed comparison with experimental and simulation data for coexistence curves and compare our estimates for the Theta-temperatures of several systems with those obtained from different extrapolation schemes.