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The partition equilibria of solutes between micelles and an aqueous phase is a key factor in many applications. Depending on the task, many micelle-solute combinations are possible. Therefore, theoretical methods to predict the partition behavior in micellar systems are needed. Here, two predictive methods are evaluated and compared. First, it is shown how molecular dynamics simulations (MD) with the umbrella sampling method can be used to calculate free energy profiles in micellar systems. The second applied method is an extension of the COSMO-RS theory to anisotropic systems termed COSMOmic. Both methods are compared by means of free energy profiles and experimental micelle/water partition coefficients. A particular focus is on the partitioning of ionized solutes. As experimental data for partitioning in micelles especially for charged solutes is rare, partition coefficients were also determined experimentally. To get a general understanding of micelles examples of all micelle classes (classified by headgroup charge) are studied: nonionic Triton X-114 (TX114), zwitterionic miltefosine (HePC), anionic sodium dodecyl sulfate (SDS), and cationic cetyltrimethylammonium bromid (CTAB). The free energy profiles of neutral solutes obtained from MD simulations and COSMOmic are in an overall good agreement, and partition coefficients from both methods are in good agreement with experimental data. Depending on the system, the results for charged solutes show some deviations between the methods and experimental data.

In this work, we studied the liquid–liquid equilibrium of ternary systems containing nonionic surfactant Triton X-114, inorganic salts, and water. The salt impact of five different sodium salts (NaCl, NaBr, NaI, Na2SO4, and Na2HPO4) and four different chlorides (NaCl, KCl, LiCl, NH4Cl) was investigated. The influence of the inorganic additives was studied at 30 °C because at this temperature all prepared mixtures faced a separation above the cloud point temperature (CPT) in micellar (surfactant-rich) and aqueous (surfactant-lean) phase. The salting-out ability of the cations follows the series Na+ > K+ > NH4 + > Li+. We observed a more pronounced effect among the anions, where the salting-out effect decreased in the order HPO4 2– ≈ SO4 2– > Cl– > Br– > I–. All salts, except NaI, lead to an increase in the Triton X-114 concentration in the micellar phase and to a decrease of the surfactant fraction in the aqueous phase. Inorganic salts also distributed unevenly between both phases and, thus, accumulated in the aqueous phase. In the case of stronger salting-out kosmotropic anions (HPO4 2–, SO4 2–), the salt load of water in the aqueous phase was higher compared to the weaker agents Br– and I–.

In practical applications, surfactant solutions are mostly used in mixtures of nonionic and ionic surfactants because they have improved characteristics compared to those of single surfactant solutions. By adjusting the composition of the micelles and the pH value, the solubilization of solutes can be enhanced. Nevertheless, the partitioning of solutes between nonionic/ionic mixed micelles and the aqueous phase is studied to a much lesser extent than for single surfactant solutions. Theoretical methods to predict partition equilibria in mixed micelles are of interest for screening studies. For those, the composition of the mixed micelle has to be known. Here we investigate mixtures of TX-114 (Triton X-114), Brij35 (C12E23), SDS (sodium dodecyl sulfate), and CTAB (cetyltrimethylammonium bromide). First, to investigate the surfactant compositions in the micelles, molecular dynamics (MD) self-assembly simulations were applied. Thereafter, the predictive COSMO-RS model, which applies the pseudophase approach, and its extension to anisotropic systems termed COSMOmic were compared for the prediction of partition equilibria in mixed micelles, where various molar ratios of the surfactants were considered. It could be demonstrated that both methods are applicable and lead to reasonable predictions for neutral molecules. However, taking into account the three-dimensional structure of the micelle is beneficial because the calculations with COSMOmic are in better agreement with experimental results. Because the partitioning behavior of ionizable molecules in mixed micelles is of particular interest, the partitioning of ionized isovanillin in mixed Brij35/CTAB micelles at different micelle compositions was calculated with COSMOmic. Using a thermodynamic cycle, the position-dependent pK of isovanillin within the micelle is calculated on the basis of COSMOmic free energy profiles. As a result, the protolytic equilibrium of isovanillin within the micelles can be taken into account, which is crucial for the reliable prediction of partition coefficients.

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