Angular distribution of light scattered from critically quenched liquid mixtures

Abstract

Light scattering was used to determine the structure factor $S(k,\ensuremath{\tau})$ of two binary mixtures which were quenched through the critical point. The experiments, which were carried out in isobutyric acid-water and 2,6-lutidine-water, show that the normalized structure factor has the scaling form $\overline{S}(k,\ensuremath{\tau})={K}^{\ensuremath{-}3}F(\frac{k}{K})$ where ${K}^{\ensuremath{-}1}$ is the size of a growing domain and $F(x)$ is time independent. Our findings are in approximate agreement with those of Marro et al., who obtained $\overline{S}(k,\ensuremath{\tau})$ from a computer simulation of a quenched $A\ensuremath{-}B$ Ising lattice. The computer experiments yield an initial time dependence in $F(x)$, whereas the light-scattering measurements reveal no evidence of this transient effect over the (dimensionless) time interval $6\ensuremath{\lesssim}\ensuremath{\tau}\ensuremath{\lesssim}1000$. The experiments spanned the temperature range $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\ensuremath{\le}\ensuremath{\epsilon}\ensuremath{\le}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, where $\ensuremath{\epsilon}\ensuremath{\equiv}|\frac{{T}_{f}}{{T}_{c}}\ensuremath{-}1|$. In this interval the integrated scattering cross section at every instant of time is proportional to ${\ensuremath{\epsilon}}^{2\ensuremath{\lambda}}$ with $0.22\ensuremath{\le}\ensuremath{\lambda}\ensuremath{\le}0.33$.