Statistical thermodynamics of flexible-chain surfactants in monolayer films. II. Calculations for a modified cubic lattice model

Abstract

A modified cubic lattice model of chain conformations is incorporated within the general theory developed in the preceding article, and used to predict pressure-area isotherms for monolayers at the interface between water and a hydrophobic ‘‘solvent.’’ The statistical weight of each cubic lattice conformation is determined by enumerating all rotational isomeric states, and then performing a Boltzmann sum over the set of RIS conformers best described by that cubic lattice state. The isotherms are predicted to depend strongly on both chain length and on the energy of chain-solvent mixing, but only weakly on the energy difference between chain–water and solvent–water contact. In particular, with only a slight positive energy of chain–solvent mixing, two phase transitions are predicted. Both transitions are characterized by a critical point and involve only fluid phases. One extends to very low surface densities and resembles a liquid/gas transition. The other appears at high densities, and, by comparison with predictions of structural properties, is shown to result from the independence, in part, of conformational and translational degrees of freedom of the surfactant molecules.