Light Scattering and Pseudospinodal Curves: The Isobutyric-Acid-Water System in the Critical Region

Abstract

Intensity and linewidth measurements of light scattered by the isobutyric acid in water system are reported for various equilibrium states in the critical neighborhood of the temperature-concentration diagram. By extrapolation of these data to zero scattering angle and then to (unrealized) states below the phase separation temperature one may determine a common "pseudospinodal curve" ${T}_{\mathrm{sp}}(X)$ described by ${T}_{\mathrm{c}}\ensuremath{-}{T}_{\mathrm{sp}}(X)\ensuremath{\sim}{|X\ensuremath{-}{X}_{\mathrm{c}}|}^{\frac{1}{{\ensuremath{\beta}}^{\ifmmode\dagger\else\textdagger\fi{}}}}$ where $X$ is the concentration, and we find ${\ensuremath{\beta}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\simeq}0.37\ifmmode\pm\else\textpm\fi{}0.04$. As expected on the grounds of the homogeneity hypotheses, the value of ${\ensuremath{\beta}}^{\ifmmode\dagger\else\textdagger\fi{}}$ is essentially the same as the previously observed value of the exponent $\ensuremath{\beta}$ for the coexistence curve. Empirical equations of the form $I_{C,0}^{}{}_{}{}^{\ensuremath{-}1}\ensuremath{\propto}{[T\ensuremath{-}{T}_{\mathrm{sp}}(X)]}^{\ensuremath{\gamma}}$ and $D\ensuremath{\propto}{[T\ensuremath{-}{T}_{\mathrm{sp}}(X)]}^{{\ensuremath{\gamma}}^{*}}$ are used to effect the extrapolations to determine ${T}_{\mathrm{sp}}(X)$. Here ${I}_{C,0}$ and $D$ are the extrapolated zero-angle scattering intensity and the diffusion coefficient, while $\ensuremath{\gamma}$ and ${\ensuremath{\gamma}}^{*}$ are corresponding critical exponents. We show theoretically, however, that a value ${\ensuremath{\beta}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\ne}\frac{1}{2}$ is inconsistent with the general validity of these empirical formulas, which should thus be discarded as over-all representations of the variations of $D$ and ${I}_{C,0}$. A tentative test is made of a more general scaling equation for ${I}_{C,0}$ by a convenient plot. Moderate success is obtained. The measurements confirm the exponent values $\ensuremath{\gamma}=1.24\ifmmode\pm\else\textpm\fi{}0.03$ and ${\ensuremath{\gamma}}^{*}=0.67\ifmmode\pm\else\textpm\fi{}0.03$. The distinction between pseudospinodal curves, determined by extrapolation from stable thermodynamics states, and a true spinodal curve which (if it exists) can only be observed by measurements on metastable states, is emphasized.