Comments on the relation between osmotic stress and surface force measurements

Abstract

The thermodynamics of osmotic stress measurements for water(1) - amphiphile(2) lamellar liquid crystals and of corresponding, direct surface force experiments are treated in parallel. It is concluded that the well-known relationship commonly used to obtain the repulsive interaction pressure, π = ( kT V 1 )In( p 0 1 p 1 ), refers to a hypothetical situation where the liquid crystal is geometrically constrained and simultaneously exposed to the vapor pressure of pure water, p 0 1, instead of its own equilibrium vapour pressure, p 1. This relation is demonstrated to be generally valid within limits set by a conventional incompressibility approximation. In corresponding experiments carried out with adsorbed monolayers (or bilayers) in a surface force apparatus, the chemical potentials of water and amphiphile are ideally kept constant, eventually resulting in depletion of the interacting monolayers at strong repulsion. Conversely, in the osmotic stress case, it follows from the Gibbs-Duhem condition that the packing densities in the liquid crystal bilayers must increase upon reducing the water content. On this basis we find that osmotic stress measurements should generally yield higher interaction pressures than corresponding surface force measurements for one and the same thickness of the thin film repeat unit (that comprises a central water part and two adjacent amphiphile monolayers), as is in agreement with recent experimental findings.