Coexistence curve and diameter of polystyrene in cyclohexane

Abstract

We have measured the coexistence curve of a high-molecular-weight (${M}_{w}=1.56\ifmmode\times\else\texttimes\fi{}{10}^{6}$) polystyrene in cyclohexane over a temperature range of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}<\frac{({T}_{c}\ensuremath{-}T)}{{T}_{c}}<4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$. The concentration difference ${X}^{+}\ensuremath{-}{X}^{\ensuremath{-}}$, in volume fraction of polystyrene, was well represented by the expression ${X}^{+}\ensuremath{-}{X}^{\ensuremath{-}}=B{\ensuremath{\epsilon}}^{\ensuremath{\beta}}+{B}_{1}{\ensuremath{\epsilon}}^{\ensuremath{\beta}+\ensuremath{\Delta}}+{B}_{2}{\ensuremath{\epsilon}}^{\ensuremath{\beta}+2\ensuremath{\Delta}}$ based on the Wegner expansion, where $\ensuremath{\beta}=0.327\ifmmode\pm\else\textpm\fi{}0.004$ and $\ensuremath{\Delta}$ is fixed at 0.50. The concentration difference could also be well represented by the expression ${X}^{+}\ensuremath{-}{X}^{\ensuremath{-}}=B{\ensuremath{\epsilon}}^{\ensuremath{\beta}}+{B}^{\ensuremath{'}}{\ensuremath{\epsilon}}^{{\ensuremath{\beta}}^{\ensuremath{'}}}$, where a somewhat higher value of $\ensuremath{\beta}$ was required. The diameter in the temperature range $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}<\frac{({T}_{c}\ensuremath{-}T)}{{T}_{c}}<{10}^{\ensuremath{-}2}$ was represented by $\frac{({X}^{+}+{X}^{\ensuremath{-}})}{2}\ensuremath{-}{X}_{c}=A{\ensuremath{\epsilon}}^{\ensuremath{\mu}}$, where $\ensuremath{\mu}=0.860\ifmmode\pm\else\textpm\fi{}0.006$. We have established, for the first time, the value of the asymptotic critical exponent $\ensuremath{\beta}$ of even a polymer system to be like that presently calculated for the Ising model. The observed exponent $\ensuremath{\mu}(=1\ensuremath{-}\ensuremath{\alpha})$ is consistent with results of specific-heat measurements.