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

## TL;DR

This study uses NMR to track sodium ions in surfactant solutions, showing how their binding changes with concentration and affects water activity.

## Contribution

A novel combination of 23Na NMR relaxation and quadrupolar relaxation modelling to quantify Na+ ion dynamics in sodium decanoate solutions.

## Key findings

- Below the CMC, 97% of Na+ ions remain unbound in bulk water.
- Above the CMC, 36–58% of Na+ ions bind to micelles or clusters.
- Bound Na+ ions exhibit fast dynamics with sub-nanosecond correlation times.

## 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.

This study uses 23Na NMR and quadrupolar relaxation modelling to quantify Na+ partitioning between bulk water, aggregates, and micelles in decanoate solutions, revealing weak binding below the CMC and stronger association at higher concentration.