An examination of the cloud curves of liquid-liquid immiscibility in aqueous solutions of alkyl polyoxyethylene surfactants using the SAFT-HS approach with transferable parameters

The phase equilibria of aqueous solutions of n-alkyl polyoxyethylene ethers (C(i)E(j)) are characterized by the presence of so-called cloud curves which represent the region of liquid-liquid immiscibility of two micellar solutions tone rich and one poor in surfactant). The systems exhibit a lower critical solution temperature (LCST), which denotes the lower Limit of immiscibility; in some cases a complete closed-loop region with an upper critical solution temperature (UCST) is seen corresponding to re-entrant miscibility. In this case the behavior can be explained in terms of the competition between the incompatibility of water with the alkyl chain and the hydrogen bonding between water and the head groups. We have used a simplified version of the statistical associating fluid theory (SAFT), which is based on the thermodynamic perturbation theory of Wertheim for associating fluids: the original SAFT-LJ equation of state treats the molecules as chains of Lennard-Jones segments while the simplified SAFT-HS equation treats molecules as chains of hard-sphere repulsive segments with van der Waals interactions. The water molecules are modeled as hard spheres with four associating sites to treat the hydrogen bonding; the dispersion forces are treated at the van der Waals mean-field level. The surfactant molecules are modeled as chains of hard-sphere segments with two or three bonding sites to treat the terminal hydroxyl group and an additional three sites per oxyethylene group; the dispersion forces are again treated at the mean-field level. For appropriate choices of the intermolecular parameters, the SAFT-HS approach predicts cloud curves with both a UCST and an LCST. The critical temperatures and the extent of immiscibility are in very good agreement with the experimental data. We have studied the transferability of the intermolecular potential parameters for different members of the C(i)E(j) homologous series. Although the general trends are reproduced, slightly different values of the unlike dispersion forces have to be used for the various systems in order to provide quantitative agreement with experiment. This is not altogether surprising for such complex aqueous micellar solutions. We have explored a relationship between the structure of the surfactant molecule and the value of the unlike intermolecular potential parameter which enables one to predict the phase behavior of aqueous solutions of any member of the C(i)E(j) homologous series.