Mathematical Institute, University of Oxford, OX1 3LB, UK.
J Colloid Interface Sci. 2011 Aug 15;360(2):662-71. doi: 10.1016/j.jcis.2011.04.074. Epub 2011 Apr 27.
We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker-Döring system of equations, using realistic expressions for the reaction constants fit to results from Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated timescales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker-Döring theory for re-equilibration of surfactant solutions.
我们研究了在一级稀释后表面活性剂溶液中胶束聚集体的破裂。我们基于 Becker-Döring 方程组建立了一个数学模型，使用适合分子动力学模拟结果的实际反应常数表达式。我们利用典型聚集数的大小推导出一个连续统模型，用一个包含时间和聚集尺寸两个独立变量的常微分方程组代替偏微分方程。数值解表明，再平衡发生在两个截然不同的时间尺度上的两个阶段，这与实验和以前的理论一致。最后，我们指出 Becker-Döring 理论在表面活性剂溶液再平衡方面的一个局限性。
