Coexistence curve and diameter of polystyrene in cyclohexane

Abstract

We have measured the coexistence curve of a high-molecular-weight ($M_w=1.56\mathrm{}\times {10}^6$) polystyrene in cyclohexane over a temperature range of $4\times {10}^{-5\mathrm{}}<\frac{(T_c-T)}{T_c}<4\mathrm{}\times {10}^{-2\mathrm{}}$. The concentration difference $X^{+}-X^{-}$, in volume fraction of polystyrene, was well represented by the expression $X^{+}-X^{-}=B{\epsilon }^{\beta }+B_1{\epsilon }^{\beta +\Delta }+B_2{\epsilon }^{\beta +2\mathrm{}\Delta }$ based on the Wegner expansion, where $\beta =0.327\mathrm{}\pm 0.004$ and $\Delta$ is fixed at 0.50. The concentration difference could also be well represented by the expression $X^{+}-X^{-}=B{\epsilon }^{\beta }+B^{\prime }{\epsilon }^{{\beta }^{\prime }}$, where a somewhat higher value of $\beta$ was required. The diameter in the temperature range $4\times {10}^{-5\mathrm{}}<\frac{(T_c-T)}{T_c}<{10}^{-2\mathrm{}}$ was represented by $\frac{(X^{+}+X^{-})}{2}-X_c=A{\epsilon }^{\mu }$, where $\mu =0.860\mathrm{}\pm 0.006$. We have established, for the first time, the value of the asymptotic critical exponent $\beta$ of even a polymer system to be like that presently calculated for the Ising model. The observed exponent $\mu (=1-\alpha )$ is consistent with results of specific-heat measurements.