Estimation of Nanoparticle’s Surface Electrostatic Potential in Solution Using Acid–Base Molecular Probes I: In Silico Implementation for Surfactant Micelles

Surface electrostatic potential Ψ is a key characteristic of colloid particles. Since the surface of the particles adsorbs various compounds and facilitates chemical reactions between them, Ψ largely affects the properties of adsorbed reactants and governs the flow of chemical reactions occurring between them. One of the most popular methods for estimating Ψ in hydrophilic colloids, such as micellar surfactant solutions and related systems, is the application of molecular probes, predominantly acid–base indicator dyes. The Ψ value is calculated from the difference of the probe’s indices of the apparent acidity constant between the examined colloid solution and, usually, some other colloid solution with noncharged particles. Here, we show how to implement this method in silico using alchemical free energy calculations within the framework of molecular dynamics simulations. The proposed implementation is tested on surfactant micelles and is shown to predict experimental Ψ values with quantitative accuracy depending on the kind of surfactant. The sources of errors in the method are discussed, and recommendations for its application are given.