Evans, Huw
(1987)
Theories of cloud curve phase separation in nonionic micellar systems.
*University of Southampton, Doctoral Thesis*.

## Abstract

The calculation of phase equilibria using statistical mechanical techniques, both simulation and theoretical, is discussed. A thermodynamic perturbation theory is used to calculate the vapour-liquid coexistence curves of the atomic Lennard-Jones fluid and a series of linear triatomic Lennard-Jones molecular fluids. The results of the theory are in reasonable agreement with those of simulation. The treatment is extended to nonionic micellar systems. In these systems a phase separation is often observed on heating, where a concentrated isotropic micellar solution coexists with a more dilute isotropic micellar solution (the cloud curve). In the present theory this phase separation is treated as a simple liquid-gas transition in an equivalent one component micellar fluid. The lower critical temperature is given by a temperature dependent intermicellar interaction that becomes more attractive as the temperature is raised. The position of the critical point is used to predict the size of the micelles and the intermicellar interactions close to the cloud curve. In addition osmotic pressures and structure factors from neutron scattering experiments are calculated and comparison with experimental values provides further information about the micelles at temperatures below the cloud curve. The results for five systems, namely C_{8}E_{4}, C_{10}E_{4}, C_{12}E_{4}, C_{12}E_{6} and C_{12}E_{8} predict that C_{8}E_{4} micelles are spherical close to the cloud curve while the remaining four systems have nonspherical micelles. A minimum axial ratio of 5:1 is required to reproduce the critical volume fraction (φ_{c}) of 3.5% for C_{12}E_{8} if the micelles are assumed to be rigid rods at the critical temperature (T_{c}). It is shown that micellar growth with increasing temperature can induce a phase separation. It is likely that such growth plays a small part in the cloud curve mechanism but an increase in micelle size can lower both the critical volume fraction and temperature of the cloud curve. Percentage changes in T_{c} and φ_{c} with micelle growth indicate that φ_{c} is more sensitive to micelle size than T_{c}.

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