Double-exponential relaxation near the critical point of an ionic micellar system.

Abstract

The system dodecylammonium chloride+water+KCl (0.30M) has been studied using dynamic light scattering near the liquid-liquid critical point. The correlation functions have been found to be single-exponential for temperatures well above the critical one, while a new decay process at longer times becomes evident at |T-${\mathit{T}}_{\mathit{c}}$|4 K. The correlation functions can be well fitted either with the sum of two exponentials or with a double-exponential distribution using Laplace inversion methods. The decay rate associated with the fast relaxation mode has a diffusive character over the whole temperature range, while the decay rate of the slow mode is diffusive in the long-wavelength limit; and at higher wave vectors q shows a crossover from a ${\mathit{q}}^{2}$ to a ${\mathit{q}}^{3}$ dependence. The relative weight of the amplitude of the slow relaxation mode decreases as the temperature and the angle of observation increase. The diffusion coefficient associated with concentration fluctuations has been calculated from both relaxation modes using the characteristics of the matrix equation that relates the transport coefficient matrix and the susceptibility matrix for asymmetric binary fluids. It has been analyzed in terms of the predictions of the mode-coupling theory, and good agreement is found when experimental shear viscosity data are used together with correlation lengths obtained from static light-scattering measurements. The apparent relaxation rate associated with the background contribution has a clear diffusive character, i.e., ${\mathit{q}}^{2}$ dependence. It shows a smooth temperature change and far from ${\mathit{T}}_{\mathit{c}}$ it agrees with the values expected for the micellar dynamic. \textcopyright{} 1996 The American Physical Society.