Simple formulas for prediction of the sizes of worm-like and globular micelles in symmetrical electrolyte solutions

Abstract

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.