THEORETICAL AND EXPERIMENTAL DETERMINATIONS OF THE CROSSOVER FROM DILUTE TO SEMIDILUTE REGIMES OF MICELLAR SOLUTIONS

A theoretical framework for predicting the crossover surfactant concentration, X*, marking the transition from dilute to semidilute solution regimes of micellar solutions is presented. In the dilute regime, the micellar solution consists of identifiable, rodlike micelles which are singly dispersed in the solvent, whereas in the semidilute regime it consists of a transient network of entangled rodlike micelles. The theoretical formulation incorporates the unique salient features of the micellar system, including the self assembling nature, polydispersity, and flexibility of the rodlike micelles present in solution. This general theoretical description is then utilized to examine the possible occurrence of a crossover from dilute to semidilute regimes in aqueous solutions of the nonionic surfactant n-dodecyl hexaethylene oxide (C12E6). We find that in the C12E6-H2O system the X* versus temperature crossover concentration curve intersects the coexistence curve, delineating the boundary between the one-phase and two-phase regions of the phase diagram, in the vicinity of the lower consolute (critical) point, thus bisecting the phase diagram into dilute and semidilute regimes. It is noteworthy that the X* values that we predict using the full micellar size distribution agree well with those predicted under the assumption of monodisperse micelles having an aggregation number n corresponding to <n>w, the weight-average micelle aggregation number. The paper also presents an attempt to experimentally estimate the C12E6 crossover concentration, X*, based on a comparison of the predicted dilute-solution viscosities, calculated in the context of a generalized Doi-Edwards theory applied to flexible, polydisperse rodlike micelles, with measured viscosities as a function of C12E6 concentration and temperature. The experimentally deduced X* values compare favorably with the theoretically predicted ones. As in the case of X*, it is noteworthy that predicted viscosities utilizing the full micellar size distribution are in close agreement with those predicted under the assumption of monodisperse micelles having an aggregation number, n = <n>w. We also find an interesting temperature dependence of the viscosity versus C12E6 concentration curves. At very low surfactant concentrations, the viscosity follows the conventional behavior, that is, it decreases with increasing temperature. However, beyond a certain surfactant concentration, the temperature dependence is reversed, that is, the viscosity increases with increasing temperature. An interpretation of this behavior in the context of micellar growth is suggested. A discussion of the implications of the new findings for modeling the phase behavior of aqueous micellar solutions containing nonionic surfactants of the alkyl polyethylene oxide (C(i)E(j)) type is also presented.