A Molecular Thermodynamic Model of Coacervation in Solutions of Polycations and Oppositely Charged Micelles

To guide the rational design of personal care formulations, we formulate a molecular thermodynamic model that predicts coacervation from cationic polymers and mixed micelles containing neutral and anionic surfactants and added salt. These coacervates, which form as a result of dilution of conditioning shampoos during use, deposit conditioning agents and other actives to the scalp or skin and also provide lubrication benefits. Our model accounts for mixing entropy, hydrophobic interactions of polycation with water, free energies of bindings of oppositely charged groups to micelles and polycations, and electrostatic interactions that capture connectivity of charged groups on the polycation chain and the micelle. The model outputs are the compositions of surfactants, polycation, salt, and water in the coacervate and in its coexisting dilute phase, along with the binding fractions and coacervate volume fraction. We study the effects of overall composition (of surfactant, polycation, and added salt), charge fractions on micelles and polycations, and binding free energies on the phase diagram of coacervates. Then, we perform coacervation experiments for three systems: sodium dodecyl sulfate (SDS)-JR30M, sodium methyl cocoyl taurate (Taurate)-JR30M, and sodium lauryl alaninate (Alaninate)-JR30M, where JR30M is a cationic derivative of hydroxyethylcellulose (cat-HEC), and rationalize their coacervation data using our model. For comparison with experiment, we also develop a parametrization scheme to obtain the requisite binding energies and Flory-Huggins χ parameter. We find that our model predictions agree reasonably well with the experimental data, and that the sulfate-free surfactants of Taurate and Alaninate display much larger 2-phase regions compared to SDS with JR30M.