Equilibrium properties of the lattice system with SALR interaction potential on a square lattice: quasi-chemical approximation versus Monte Carlo simulation

Groda Groda,Di Caprio Di Caprio,Vikhrenko Vikhrenko

doi:10.5488/cmp.21.43002

Abstract

The lattice system with competing interactions that models biological objects (colloids, ensembles of protein molecules, etc.) is considered. This system is the lattice fluid on a square lattice with attractive interaction between nearest neighbours and repulsive interaction between next-next-nearest neighbours. The geometric order parameter is introduced for describing the ordered phases in this system. The critical value of the order parameter is estimated and the phase diagram of the system is constructed. The simple quasi-chemical approximation (QChA) is proposed for the system under consideration. The data of Monte Carlo simulation of equilibrium properties of the model are compared with the results of QChA. It is shown that QChA provides reasonable semiquantitative results for the systems studied and can be used as the basis for next order approximations.

Highlights

At present, there is a great interest in studying the processes of self-organization and self-assembly in systems of a nanoscale range
Such an increase of the order parameter corresponds to the order-disorder phase transition, which is of the second order like in the system with the nearest neighbour repulsive interaction [10]
It is shown that the competing interactions lead to the order-disorder phase transitions

Summary

Introduction

There is a great interest in studying the processes of self-organization and self-assembly in systems of a nanoscale range. Despite their rather large dimensions, the interactions remain of the same order as the thermal energy This leads to a large variety of possibilities for various phase transitions in such systems at room temperature. One of the simplest methods for investigating the general properties of SALR systems is to consider their lattice models. In [8] the generalized quasi-chemical approximation (QChA) was proposed for lattice systems with SALR interaction potential on a triangular lattice. This approximation has demonstrated its applicability for estimating the equilibrium properties of the model in the disordered phase. We present the results for a similar model of the lattice fluid on a square lattice and propose a geometric order parameter, which makes it possible to investigate the ordered phases in the system

The model and its order parameter

The quasi-chemical approximation

Calculation and simulation results

Conclusion