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

To guide the rational design of personal care formulations,weformulate a molecular thermodynamic model that predicts coacervationfrom cationic polymers and mixed micelles containing neutral and anionicsurfactants and added salt. These coacervates, which form as a resultof dilution of conditioning shampoos during use, deposit conditioningagents and other actives to the scalp or skin and also provide lubricationbenefits. Our model accounts for mixing entropy, hydrophobic interactionsof polycation with water, free energies of bindings of oppositelycharged groups to micelles and polycations, and electrostatic interactionsthat capture connectivity of charged groups on the polycation chainand the micelle. The model outputs are the compositions of surfactants,polycation, salt, and water in the coacervate and in its coexistingdilute phase, along with the binding fractions and coacervate volumefraction. 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 dodecylsulfate (SDS)-JR30M, sodium methyl cocoyl taurate (Taurate)-JR30M,and sodium lauryl alaninate (Alaninate)-JR30M, where JR30Mis a cationic derivative of hydroxyethylcellulose (cat-HEC), and rationalizetheir coacervation data using our model. For comparison with experiment,we also develop a parametrization scheme to obtain the requisite bindingenergies and Flory-Huggins & chi; parameter. We find thatour model predictions agree reasonably well with the experimentaldata, and that the sulfate-free surfactants of Taurate and Alaninatedisplay much larger 2-phase regions compared to SDS with JR30M.