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

摘要

In this paper we show that the virial expansion up to third order for theosmotic pressure of a dilute polymer solution, including first-orderperturbative corrections to the virial coefficients, allows for a scalingdescription of phase-separation data for polymer solutions in reducedvariables. This scaling description provides a method to estimate theTheta-temperature, where demixing occurs in the limit of vanishing polymervolume fraction $\phi$ and infinite chain-length $N$, without explicitassumptions concerning the chain-length dependence of the critical parameters$T_c$ and $\phi_c$. The scaling incorporates three limiting regimes: the Isinglimit asymptotically close to the critical point of phase separation, the puresolvent limit and, the tricritical limit for the polymer-rich phaseasymptotically close to the Theta point. We incorporate the effects of criticaland tricritical fluctuations on the coexistence curve scaling by usingrenormalization-group methods. We present a detailed comparison withexperimental and simulation data for coexistence curves and compare ourestimates for the Theta-temperatures of several systems with those obtainedfrom different extrapolation schemes.