Phase behavior and structure of a lattice model of microemulsions

DE VIRGILIIS, ANDRES

Buenos Aires

Conferencia; STATPHYS'27 - International Conference on Statistical Physics; 2019

IUPAP

The critical behaviour of a ternary mixture of hydrophilic, hydrophobic and amphiphilic (surfactant) molecules is investigated by means of extensive Monte Carlo simulations. The model formulated by Widom as a simple description of a microemulsion is adopted, taking advantage of its equivalence to a spin-1/2 Ising model on a simple cubic lattice with ferromagnetic nearest-neighbor interactions, antiferromagnetic next-nearest-neighbor interactions and half as strong antiferromagnetic interactions at two lattice steps. The respective interaction constants in the Ising model are related, through a table of translation, to the activities of the three species and the surfactant film curvature energy in the microemulsion model.We focus on the order-disorder phase transition between ferromagnetic (oil or water-rich) and paramagnetic (disordered, microemulsion-like) phases. A simulation strategy combining a standard Metropolis sampling and multiple histogram reweighting technique is employed, which allows for an accurate location of the phase boundary. The critical behavior we found is shown to be compatible with the 3D Ising universality class, as expected. In addition, a suitable finite size scaling analysis is performed to obtain the critical amplitudes for magnitudes as magnetization, susceptibility and interfacial tension. The critical amplitudes ratios extracted from our data are in reasonable agreement with the universal values coming from experiments and theoretical calculations on systems in the same universality class.In addition, the scattering function in the disordered state is calculated from the analysis of configurations generated at specific points in the phase diagram. It is shown that S(q), with q spherically averaged, is of the Teubner-Strey form adopted by microemulsions. From a fit of S(q) data we extract the period and the attenuation length of the corresponding pair correlation function. These two length scales, which describe the microemulsion state, are shown to be compatible after a suitable rescaling with values reported in several experiments.