Orientational order in lipid monolayers: A one-dimensional model

Abstract

Lipid monolayers at low temperatures and large spreading pressure exhibit long-range translational order and the hydrophobic alkane chains of the lipid molecules are then stretched out in an all-trans configuration. The orientational order of the remaining rotational degree of freedom of these alkane chains is studied by means of Monte Carlo and molecular dynamics simulations as well as analytical calculations, but considering a one-dimensional rather than a two-dimensional model. Depending on the interactions among the chains, the ground state of the model is either a ‘‘uniformly tilted’’ state (all chains are tilted by an average angle +θ̄ or −θ̄ relative to the direction perpendicular to the lattice direction) or a ‘‘no-tilt’’ state (θ̄=0). At nonzero temperature, the uniform tilt state disorders by soliton-like kink–antikink excitations, in addition to phonon-like excitations, which exist also in the no-tilt state. In the continuum limit the treatment can be related to the Krumhansl–Schrieffer theory of the one-dimensional φ4 model. However, the quantitative predictions of the latter are in pronounced disagreement with the numerical results, in the temperature regime investigated. By our Monte Carlo techniques, we are able to study the orientational correlation function over the full temperature range, except extremely low temperatures. It is shown that for this model and temperature range the molecular dynamics technique requires much more computer time in order to obtain similarly reliable results than our discretized Monte Carlo approach.