Two-exponential correlation functions near the critical point of a micellar system

The critical behavior of the dodecilammonium chloride plus water plus KCl system has been studied by static and dynamic light scattering. The line of critical points intercepts a surface corresponding to first-order phase transitions at low concentrations of KCl and low temperature, thus leading to the existence of a critical end point. The correlation length and osmotic susceptibility experimental data can be well described by simple scaling laws with three-dimensional Ising critical exponents for all the salt concentrations. This suggests that approaching the surface of first-order phase transitions does not affect the nature of the liquid-liquid critical point, in agreement with the predictions of Fisher and Barbosa [Phys. Rev. B 43, 11 177 (1991)]. Far from the critical temperature $T_c$ single-exponential correlation functions are found at all the salt concentrations studied. However, as $T_c$ is approached a new slower relaxation mode appears and becomes dominant near $T_c.$ This behavior is independent of [KCl] and thus of the proximity to the first-order transition surface. The two-exponential decay has been analyzed in terms of the asymmetric $H$ model of Hohenberg and Halperin [Rev. Mod. Phys. 49, 435 (1977)], which allows one to separate the background and critical contributions. The contribution of the critical concentration fluctuations can be very well described in terms of the mode-coupling theory. The analysis of the relative weight of the two contributions has allowed us to conclude that background and critical contributions are very weakly coupled.