Abstract
A one-dimensional model is used to study the tilt/no-tilt transition in the liquid condensed phase of a lipid monolayer at the air/water interface. The head groups are modelled by hard rods of length b and the alkane chains by rigid tails of length a(a>>b). The interaction between these model lipid molecules is purely repulsive with a soft, short range, repulsion allowed between the tilting tails. The model is aimed at highlighting the excluded volume role in the tilt/no-tilt transition. The model is solved analytically and, in the limit of the temperature T to 0, the equation of state exhibits-at most-three distinct phases; isotropic, 'tilting' and 'nontilting'. At finite temperatures the transition from one phase to the other is continuous but, at low temperatures, still sharp.