Kuni Fedor M, Shchekin Alexander K, Rusanov Anatoly I, Grinin Alexander P
Research Institute of Physics by V. A. Fock, St. Petersburg State University, Petrodvoretz, St. Petersburg, 198504, Russia.
Langmuir. 2006 Feb 14;22(4):1534-43. doi: 10.1021/la052136m.
Equilibrium and nonequilibrium distributions of molecular aggregates in a solution of a nonionic surfactant are investigated at the total surfactant concentration above the second critical micelle concentration (CMC2). The investigation is not limited by the choice of a specific micellar model. Expressions for the direct and reverse fluxes of molecular aggregates over the potential humps of the aggregation work are derived. These aggregation work humps set up activation barriers for the formation of spherical and cylindrical micelles. With the aid of the expressions for molecular aggregate fluxes, a set of two kinetic equations of micellization is derived. This set, along with the material balance equation, describes the molecular mechanism of the slow relaxation of micellar solution above the CMC2. A realistic situation has been analyzed when the CMC2 exceeds the first critical micelle concentration, CMC1, by an order of magnitude, and the total surfactant concentration varies within the range lying markedly above the CMC2 but not by more than 2 orders of magnitude. For such conditions, an equation relating the parameters of the aggregation work of a cylindrical micelle to the observable ratio of the total surfactant concentration and the monomer concentration is found for an equilibrium solution. For the same conditions, but in the nonequilibrium state of materially isolated surfactant solution, a closed set of linearized relaxation equations for total concentrations of spherical and cylindrical micelles is derived. These equations determine the time development of two modes of slow relaxation in micellar solutions markedly above the CMC2. Solving the set of equations yields two rates and two times of slow relaxation.
在非离子表面活性剂溶液中，当表面活性剂总浓度高于第二临界胶束浓度（CMC2）时，研究了分子聚集体的平衡和非平衡分布。该研究不受特定胶束模型选择的限制。推导了分子聚集体在聚集功的势垒上的正向和反向通量表达式。这些聚集功势垒为球形和圆柱形胶束的形成设置了活化能垒。借助分子聚集体通量的表达式，推导了一组两个胶束化动力学方程。这组方程与物料平衡方程一起，描述了CMC2以上胶束溶液缓慢弛豫的分子机制。分析了一种实际情况，即CMC2比第一临界胶束浓度CMC1高出一个数量级，且表面活性剂总浓度在明显高于CMC2但不超过两个数量级的范围内变化。对于这种情况，在平衡溶液中找到了一个将圆柱形胶束聚集功参数与表面活性剂总浓度和单体浓度的可观测比值相关联的方程。对于相同条件，但在物质隔离的表面活性剂溶液的非平衡状态下，推导了一组关于球形和圆柱形胶束总浓度的线性化弛豫方程。这些方程确定了明显高于CMC2的胶束溶液中两种缓慢弛豫模式的时间发展。求解这组方程得到两个弛豫速率和两个弛豫时间。
