Orientational ordering in lipid monolayers: A two‐dimensional model of rigid rods grafted onto a lattice

A simple model for lipid monolayers on water surfaces at high spreading pressure is investigated in this work. In this model, the hydrophilic head group of the lipid molecules form a rigid regular triangular lattice, and the hydrophobic alkane chains (assumed to be in an all‐trans state) are represented by rigid rods with two angular degrees of freedom (θ, φ). The rods consist of ‘‘effective monomers,’’ and between the effective monomers on neighboring rods a Lennard‐Jones interaction is assumed. The model is studied by exact ground‐state calculations, mean‐field theory, and Monte Carlo simulations. Basic parameters are rod length a and lattice constant b. The ground‐state phase diagram shows the following phases: for small b, the rods are oriented perpendicularly to the monolayer plane (no‐tilt phase, 〈θ〉=0); for somewhat larger b, a sixfold degenerate uniform‐tilt state occurs with all rods tilted towards one of their next‐nearest neighbors. For still larger b, the rods are tilted nonuniformly and form a ‘‘striped’’ structure. These unexpected phases do not occur if we allow a rectangular distortion of the lattice. For T>0, the simplest mean‐field theory predicts a gradual disordering of the uniform‐tilt state via a second‐order phase transition. For the transition region, the Monte Carlo results disagree with this picture. Instead they show a strong asymmetric first‐order phase transition with pronounced hysteresis. The transition temperature increases with increasing rod length a, qualitatively similar to experiment.