Heterochirality in Langmuir monolayers and antiferromagnetic Blume-Emery-Griffiths model

Chirality is quite a common property in organic molecules. Chiral molecules exist in two forms (called enantiomers) which cannot be superimposed by rotations and translations and may have very different biochemical properties. Experiments on Langmuir monolayers made up of chiral amphiphiles have shown that, in most cases, heterochiral interactions dominate, implying the formation of a racemic compound. It has been shown that a monolayer mixture of two enantiomers can be simply described by a two-dimensional (2-D) spin-1 lattice gas [Blume-Emery-Griffiths (BEG) model], where the heterochiral preference is represented by an effective antiferromagnetic coupling. By now just mean field calculations have been performed on this model. Here we present a revisitation of the tripod amphiphile model, proposed by Andelman and de Gennes [D. Andelman and P.-G. de Gennes, Compt. Rend. Acad. Sei. (Paris) 307, 233 (1988)], together with a rigorous proof of the heterochiral preference shown by the model in the hypothesis of van der Waals interactions. Moreover, a cluster variation analysis of the antiferromagnetic BEG model on a triangular lattice is performed and possible interpretations in terms of surface pressure-concentration phase diagrams for monolayer mixtures of enantiomers are discussed. The choice of a triangular lattice has been suggested by the triangularlike structure of condensed phases of Langmuir monolayers, shown by x-ray diffraction experiments.