Theories of cloud-curve phase separation in non-ionic alkyl polyoxyethylene micellar solutions

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Abstract
Two contrasting theories have been used to investigate the low critical volume fractions observed for the cloud curves of a range of alkyl polyoxyethylene surfactant solutions. These are a thermodynamic perturbation theory and Flory–Huggins solution theory. The former theory uses a model based on spherical micelles with a surrounding water solvation shell, and the mechanism of phase separation is considered to be the reduction of this solvation shell with temperature. The latter theory utilises the idea that micellar growth is largely responsible for cloud-curve behaviour and assumes the micelles are elongated. Both theories meet with limited success when compared with recent experimental data. Although it is possible to fit the cloud curves with both models the physical assumptions in the model are often unreasonable. The model of solvated spherical micelles can account for the cloud-curve behaviour of C8E4 with a critical volume fraction of 7% with acceptable parameters; however, fitting the lower critical volume fractions observed for C12E4, C12E6, C12E8 or C10E4 results in extensive solvation shells. Flory–Huggins theory on the other hand predicts substantial elongation of the micelles of all the above five systems, with aggregation numbers far in excess of those given by experiment. We conclude that micellar growth alone cannot account for the low critical volume fractions observed for many of these systems. A combination of the two effects is likely for those surfactant solutions with low critical volume fractions: a solvation shell combined with a degree of elongation of the micelle.

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