Phase separation in living micellar networks

We present a lattice model based on two n-->0 spin vectors, capable of trea ting the thermodynamics of living networks in micellar solutions at any sur factant concentration. We establish an isomorphism between the coupling con stants in the two spin vector Hamiltonian and the surfactant energies invol ved in the micellar situation. Solving this Hamiltonian in the mean-field a pproximation allows one to calculate osmotic pressure, aggregation number, free end and cross-link densities at any surfactant concentration. We deriv e a phase diagram, including changes in topology such as the transition bet ween spheres and rods and between saturated and unsaturated networks. A pha se separation can be found between a saturated network and a dilute solutio n composed of long flexible micelles or a saturated network and a solution of spherical micelles. (C) 1999 Elsevier Science B.V. All rights reserved.