Sterol-induced raft-like domains in a model lipid monolayer

A two-dimensional system consisting a mixture of highly coarse-grained saturated (S-type), unsaturated (U-type) lipid molecules, and cholesterol (C-type) molecules is considered to form a model lipid monolayer. All the S-, U- and C-type particles are spherical in shape, with distinct interaction strengths. The phase behavior of the system is studied for various compositions ($x$) of the C-type particles, ranging from $x = 0.1$ to $0.9$. The results show that a structurally ordered complex is formed with the S- and C-types in the fluid-like environment of U-type particles, for $x \in \lbrace 0.5 - 0.6\rbrace$. The time-averaged hexatic order parameter $\left\langle \Psi_{6} \right\rangle$ indicates that the dynamical segregation of S- and C-types exhibits a positional order, that is found to be maximum for $x$ in the range of 0.5 - 0.6. The mean change in the free energy ($\Delta G(x)$) obtained from the mean change in enthalpy ($\Delta H$) and entropy ($\Delta S$) calculations suggests that $\Delta G$ is minimum for $x \sim 0.6$. A phenomenological expression for the Gibbs free energy is formulated by explicitly accounting for the individual free energies of S-,U- and C-type particles and the mutual interactions between them. Minimizing this phenomenological $G$ with respect to the C-type composition results in the optimal value, $x^* = 0.564 \pm 0.001$ for stable coexistence of phases; consistent with the simulation results and also the previous experimental observations \cite{raghavendra_effect_2023}. All these observations signify the optimal C-type composition, $x \sim 0.5 - 0.6$.