Statistical thermodynamics of flexible-chain surfactants in monolayer films. I. Theory of fluid phases

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Abstract
A general statistical mechanical theory is developed to describe structural and thermodynamic properties of surfactant monolayer films at the interface between water and a hydrophobic solvent. It is assumed that the surfactants are comprised of a single head group and one or more flexible hydrocarbon tails, and that the head group serves only to constrain one end of the molecule to the aqueous interfacial plane. Each chain is characterized by the profile of volume it occupies perpendicular to the interfacial plane. Since the position of the maximum in the volume profile varies with conformation, the lateral excluded area of each conformation is approximated as an average over all pairs of conformations. By assuming ‘‘ideal’’ two-dimensional mixing of solvent with the chains, and of chains with each other, the entropy of the monolayer is then determined. For purposes of determining interaction energies, the surfactant chains are also characterized by the position and orientation of their surface area available for nearest-neighbor contact. The orientational distribution of chain surface may be highly anisotropic, particularly at high molecular surface densities when the chains are largely aligned, so the total area of intermolecular contact cannot be determined from the chain segment profile alone, as in regular solution theory. Interaction energies among chain, solvent, and water are reduced to two parameters, one related to the chain–solvent interfacial tension, and the other to the difference of chain–water and solvent–water interfacial tensions. The equilibrium chain probability distribution is obtained by minimizing the free energy with respect to the distribution, from which all structural and thermodynamic properties can be predicted. In the subsequent paper (part II), pressure-area isotherms are predicted using a modified cubic lattice model for the chains, and shown to be characterized by two first-order phase transitions.