Osmotic compressibility and correlation range of a macromolecular solution near its critical mixing point

Abstract

From the angular distribution of the scattered-light intensity for polystyrene in cyclohexane near its critical mixing point, we have measured $\frac{I_{c,0\mathrm{}}}{T}$ ($I_{c,0\mathrm{}}$ being the extrapolated zero-angle scattering intensity), which is directly proportional to the osmotic isothermal compressibility ${\chi }_T$, and the long-range correlation length $\xi$. We find ${\left(\frac{I_{c,0\mathrm{}}}{T}\right)}^{-1\mathrm{}}=B{(\frac{T}{T_{\mathrm{sp}}}-1)}^{1.24\pm 0.01}$ and $\xi =(5.83\mathrm{}\pm 0.20){(\frac{T}{T_{\mathrm{sp}}}-1)}^{-0.62\mathrm{}\pm 0.02}$ Å along the isochore very near the critical concentration, and ${\left(\frac{I_{c,0\mathrm{}}}{T}\right)}^{-1\mathrm{}}=(2.3\mathrm{}\pm 0.1)B{(1-\frac{T}{T_c})}^{1.21\pm 0.02}$ and $\xi =(2.40\mathrm{}\pm 0.12){(1-\frac{T}{T_c})}^{0.65\pm 0.03}$ Å along the concentrated phase and ${\left(\frac{I_{c,0}}{T}\right)}^{-1\mathrm{}}=(5.9\mathrm{}\pm 0.3)B{(1-\frac{T}{T_c})}^{1.25\pm 0.03}$ along the dilute phase of the coexistence curve. In addition, we have determined the value of the critical exponent ($\delta \simeq 4.4$) which describes the concentration dependence of the chemical potential $\mu$ along the critical isotherm.