Critical behaviour of microemulsions: Monte Carlo simulations of Widom model

EDGAR A. BEA; ANDRÉS DE VIRGILIIS; MARTA L. TROBO

Los Polvorines

Workshop; First Workshop at UNGS on Transport Phenomena and Non-Equilibrium Processes; 2018

Universidad Nacional de General Sarmiento

As it is well known, water and oil are immiscible mainly due to itslarge interfacial tension being energetically unfeasible to createinterfaces by thermal fluctuations. However, if amphiphilic molecules(surfactant) are introduced, they can facilitate the formation ofinvisibly small droplets or more complex fluid phases(microemulsions). It is because the presence of the surfactant has anatural trend to organize the other two components promoting thecreation of interfaces that significantly reduce the interfacialtension. So a microemulsion is a phase where both a hydrophilicsubstance (polar, water) and other hydrophobic one (non-polar, oil)are uniformly mixed due to the self-assembly of a large interfacialsurface.Most models for microemulsions are phenomenological type or based onlattice models. As regards the latter, the simplest one is thatproposed by Widom, which is isomorphic to a three-dimensional spin-1/2Ising model. It has been extensively studied using mean field theory,which allowed to reveal qualitatively the phase diagram. Mean-fieldpredictions are limited due to competing ferromagnetic andantiferromagnetic interactions metastabilize the dynamics inconfigurations that are not of lower energy. Even though thesimplicity of Widom model, it is noticeable that it has not been soexplored by means of computer simulations.In this work we investigate the critical behavior of theorder-disorder phase transition of this model based on Monte Carlosimulations. We use a simulation strategy that combines a simpleMetropolis algorithm with sophisticated histogram extrapolationtechniques. This strategy allows us to explore very close to thecritical point by simulating in regions further away fromit, improving the determination of those quantities that are affectedby the finite size of the system. We extrapolate to the thermodynamiclimit by means of standard finite size scaling methods. The resultingcritical exponents are compatible with the 3D Ising universalityclass, suggesting the consistency of our data. Likewise, criticalamplitudes ratios give a reasonable agreement compared to those onesobtained from different systems, highlighting the difficulties in thecalculation of critical amplitudes in general.