The micro/macroscale properties of micellar solutions and the nanoscale characteristics of aggregates are controlled by a complex combination of the properties of the surfactant, electrolyte solution, and thermodynamic conditions. The science and practice of micellar solutions have relied predominantly on various experimental characterization methods to determine their physicochemical properties among which the size of micelles is the most crucial factor as other properties of the solutions are mainly influenced by it. In contrast to the extensive experimental work, so far only very few theoretical studies have been devoted to the prediction of phase behavior and properties of surfactant solutions. Our thorough review of the literature reveals that the vast majority of the previous theoretical models have been based on molecular thermodynamic approaches with different conditions for achievement of an equilibrium state during the micellization process. The lack of general models capable of predicting the contribution of each aggregation step to the free energy of micellization under different conditions is a critical factor that severely limits the practical application of such models. The main purpose of the present study is to circumvent this challenge by approaching the problem from a different theoretical point of view. In addition, it is aimed at increasing our understanding and capability for accurate prediction of the behavior and properties of micellar solutions. To do so, novel models are proposed to quantify adsorption of ionic surfactant molecules onto the surface of normal micelles in aqueous media based on the concepts of the electrical double layer (EDL) and surface charging. These models are developed in cylindrical and spherical configurations that are the most commonly observed structures of surfactant aggregates and validated by comparison with available experimental data. Also, the cylindrical model is used to obtain a criterion of the necessary condition for the formation and evolution of less frequently seen worm-like micelles. The results of this study allow academic researchers and industrial practitioners to calculate the size of micelles formed in aqueous solutions by ionic surfactants using a few simple parameters whose exact or estimated values are readily available.

胶束溶液的微观/宏观特性和聚集体的纳米级特性由表面活性剂、电解质溶液和热力学条件的特性的复杂组合控制。胶束溶液的科学和实践主要依赖于各种实验表征方法来确定其理化性质，其中胶束的大小是最关键的因素，因为溶液的其他性质主要受其影响。与广泛的实验工作相比，迄今为止，只有很少的理论研究致力于预测表面活性剂溶液的相行为和性质。我们对文献的彻底审查表明，绝大多数先前的理论模型都基于分子热力学方法，在胶束化过程中实现平衡状态的条件不同。缺乏能够预测不同条件下每个聚集步骤对胶束化自由能的贡献的通用模型是严重限制此类模型实际应用的关键因素。本研究的主要目的是通过从不同的理论角度解决问题来规避这一挑战。此外，它旨在提高我们对胶束溶液行为和特性的准确预测的理解和能力。为此，基于双电层 (EDL) 和表面电荷的概念，提出了新的模型来量化离子表面活性剂分子在水性介质中正常胶束表面的吸附。这些模型是在圆柱形和球形构造中开发的，它们是表面活性剂聚集体最常见的观察结构，并通过与可用实验数据的比较进行验证。此外，圆柱模型用于获得较少见的蠕虫状胶束形成和进化的必要条件标准。这项研究的结果允许学术研究人员和工业从业者使用一些简单的参数来计算离子表面活性剂在水溶液中形成的胶束的大小，这些参数的精确或估计值很容易获得。