Coexistence curve of polystyrene in methylcyclohexane. VI. Two-phase behavior of ternary system near the tricritical point

Abstract

Tricritical two-phase behavior of bimodal polystyrene (PS) in methylcyclohexane (MCH) was studied by using the Flory–Huggins theory combined with an empirically determined interaction parameter. In the ternary system PSI+PSII+MCH with the molecular weight M1=1.73×104 for PSI, the tricritical system was obtained for PSII with M2=2.24×105, which yielded a coincidence of the upper and lower critical end points. For the tricritical mixture the two-phase coexistence curve was calculated in the temperature range 0.01<Tt−T<6 K with Tt being the tricritical temperature. In a diagram of temperature, total PS volume fraction, the dilute and concentrated branches of the coexistence curve showed very different behavior. The log–log plots to estimate the exponent β for the dilute branch, concentrated branch, and the difference between them were curved, and the slopes of the plots, which decreased with decreasing temperature, were much larger than the exponent expected for the nonsymmetric tricritical point. This observation suggested that the asymptotic range is limited very near the tricritical point (TCP). According to analytical arguments with the original Flory–Huggins theory, the critical line of the tricritical system was conjectured to be tangent to the dilute branch of the coexistence curve at the TCP.