Monte Carlo methods used in inverted hexagonal lipid phase and in simulations of thermally fluctuating lipid vesicles

Two different uses of Monte Carlo methods in soft matter physics are presented in the following work. Firstly, the Monte Carlo simulated annealing is used to minimize the elastistic energy of the inverted hexagonal phase (HII) optimal geometry. We will do a brief overview on the mechanics of the HII lipid phase. In our model the expression for the lipid monolayer free energy consists of two energy contributions: the bending energy which involves also a deviatoric term, and the interstitial energy which describes the deformation energy due to stretching of the phospholipid molecule chains. On the basis of the derived expression for the lipid monolayer free energy, we will theoretically predict optimal geometry and physical conditions for the stability of the inverted hexagonal phase. Using the Monte Carlo simulated annealing method, we will theoretically describe first steps in the LαHII phase transition. Another interesting subject investigated by means of Monte Carlo simulations are the thermal fluctuations of nearly spherical vesicles. The theoretical basis of this analysis was done by Milner and Safran (Phys Rev A 36(9):4371–4379, 1987. doi:10.1103/PhysRevA.36.4371) that uses the mean field approximation. In this work we will show the application of the Monte Carlo simulations and show the correlation between the time mean simulated thermal fluctuations decomposed into spherical harmonics and the bending stiffness in 2-dimensional and 3-dimensional space.