Abstract The Aggregation Surface Equation (ASE) is attained by coupling the Gibbs adsorption equation and surface aggregation isotherm. The resulting equation can be used to study fluid-fluid interfaces in connection with the micelle formation process. This new equation contains two boundary conditions in the vicinity of the saturation region: (i) the critical micelle concentration (CMC), which corresponds to the onset of micelle formation; and (ii) the critical spherical micelle concentration (CSC) (i.e. the completion of spherical micellar aggregates). These boundary conditions, which appear within a narrow surfactant concentration range, provide the basis to calculate the average aggregation number under the assumption of constant average aggregation number and spherical micelles geometry. The resulting Surface Equation (SE) contains the maximum surface concentration of the surface monolayer, the critical micelle concentration and the micelle average aggregation number. The mass action law allows extending the ASE as a function of the free monomer, as opposed to the total or nominal surfactant concentration, which was recently performed in the STAND model (Langmuir, 32, (16), (2016), 3917-3925). This paper presents a simple and direct method to calculate the micellar average aggregation number from surface tension data and the proposed surface equation.

中文翻译：

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从表面方程估计胶束聚集数的平衡模型

摘要 聚集表面方程（ASE）是通过耦合吉布斯吸附方程和表面聚集等温线得到的。所得方程可用于研究与胶束形成过程相关的流体-流体界面。这个新方程包含饱和区附近的两个边界条件：(i) 临界胶束浓度 (CMC)，对应于胶束形成的开始；(ii) 临界球形胶束浓度 (CSC)（即球形胶束聚集体的完成）。这些边界条件出现在一个狭窄的表面活性剂浓度范围内，为在恒定平均聚集数和球形胶束几何形状的假设下计算平均聚集数提供了基础。所得表面方程 (SE) 包含表面单层的最大表面浓度、临界胶束浓度和胶束平均聚集数。质量作用定律允许将 ASE 扩展为游离单体的函数，这与最近在 STAND 模型中执行的总或标称表面活性剂浓度相反 (Langmuir, 32, (16), (2016), 3917-3925) ）。本文提出了一种简单而直接的方法，可以根据表面张力数据和所提出的表面方程计算胶束平均聚集数。这是最近在 STAND 模型中执行的 (Langmuir, 32, (16), (2016), 3917-3925)。本文提出了一种简单而直接的方法，可以根据表面张力数据和所提出的表面方程计算胶束平均聚集数。这是最近在 STAND 模型中执行的 (Langmuir, 32, (16), (2016), 3917-3925)。本文提出了一种简单而直接的方法，可以根据表面张力数据和所提出的表面方程计算胶束平均聚集数。