Phase transitions in a monolayer of interconverting squares

The two successive fluid-fluid phase transitions in surfactant Langmuir monolayers are described using a highly simplified molecular model: a 'reactive' mixture of inter-converting squares of two different sizes. The model is solved by a mean-field lattice approach and by Monte Carlo simulations. The mean-field scheme involves a re-division of the original lattice into 'cells' which can contain either one large square representing the (projection on the lattice of) an amphiphilic molecule in a conformationally disordered ('expanded') state, or clusters consisting of 1-4 small squares, each representing an ordered ('stretched') molecule. This procedure circumvents some of the difficulties associated with the size disparity of the adsorbed particles. In spite of its simplicity, the model can explain some major, as well as some subtle, characteristics of experimental monolayer phase diagrams. These include the conditions under which the monolayer exhibits one phase transition, two or none; the decrease of the triple point temperature with increasing chain length, and the gradual decrease with temperature of the liquid-condensed phase density.