Reexamination of the static and dynamic critical phenomena in water-amphiphile micellar solutions.

Abstract

A source of the apparent deviation from three-dimensional (3D) Ising model behavior of the static critical phenomenon experimentally observed in several binary mixtures of water\char21{}nonionic-amphiphile systems has been identified. Analyses were made, in particular, on two ethylene glycol mono-n-dodecyl ether-water systems ${\mathrm{C}}_{12}$${\mathrm{E}}_{5}$-${\mathrm{H}}_{2}$O and ${\mathrm{C}}_{12}$${\mathrm{E}}_{8}$-${\mathrm{H}}_{2}$O (where E represents ether), for which a very extensive set of data has been published. Our analyses show that, in fact, all published experimental data are consistent with the 3D Ising exponents if several isochores, including the most critical one, are simultaneously analyzed using the linear model equations of state. Owing to the flatness of the coexistence curves it is experimentally rather hard to locate very precisely the critical concentration. With added difficulties of obtaining very pure amphiphile samples and correcting data for multiple-scattering contribution near the critical point in a conventional light-scattering experiment, the determination of the critical indices is always subject to large errors. All the sources of errors tend to lower the measured indices. For the dynamic critical phenomena, a combined use of the linear model equations of state and the full mode-coupling theory, including the background effect, allows us to fit all the dynamic light-scattering data along the ``critical'' and off-critical isochores by assuming a single value of the Debye cutoff wave number ${q}_{D}$ which is equal to the inverse of the average hydrodynamic diameter 2${R}_{H}$ of the micelles. We point out the strong influence of the background effect on the critical concentration fluctuation dynamics for systems formed from unusually large objects in solution.