Association and dissociation of Na<sup>+</sup> between bulk, cluster and micelle sites in aqueous sodium decanoate solutions elucidated by <sup>23</sup>Na NMR relaxation experiments and quadrupolar relaxation modelling.

Abstract

Counter-ion distribution in aqueous ionic surfactant solutions is a complex phenomenon, which is challenging to study experimentally. The degree of counter-ion binding to charged aggregates can significantly impact water activity. In atmospheric aerosols, which often include organic surfactants, such mechanisms may in turn strongly affect cloud droplet formation and earth's radiation balance. Here, we combine ²³Na nuclear magnetic resonance (NMR) relaxation and diffusion experiments with advanced relaxation modelling for determining counter-ion dynamics and distribution in aqueous sodium decanoate solutions. Relaxation modelling of a complex system may require too many parameters to determine. Here, we assume, based our previous ¹H NMR study, that below the critical micelle concentration (CMC), surfactants are monomers or form small clusters (about five decanoate ions), and above the CMC they form small clusters or larger micelles (about 48 decanoate ions). We propose two analytical relaxation models for the system. The number of adjustable parameters is reduced by molecular dynamics simulations. Our analysis indicates that below the CMC, the vast majority (about 97%) of Na⁺ counterions are unbound in the bulk, whereas above the CMC, a significant amount (36-58%) of Na⁺ ions are bound to micelles or clusters, greatly reducing the impact of both Na⁺ ions and surfactant aggregates on water activity. Also, Na⁺ ions associated with micelles undergo fast dynamics with sub nanosecond correlation times.