Pressure-area relations for Langmuir monolayers

Pressure-area relations are derived for quasi-static compression of a Langmuir monolayer in the regimes of expanded and partially compressed chains. A monolayer is treated as an ensemble of flexible chains anchored at a flat water-air interface. Formation of surface pressure is attributed to excluded-volume interactions between segments of hydrophobic tail-groups. Close-form expressions are derived for the energy of interactions. Based on this relations, strength of excluded-volume interactions is evaluated by fitting pressure-area isotherms on stearic, behenic and pentacosadiynoic acids. It is found that the dimensionless strength of excluded-volume interactions is weakly affected by chain length and its value is close to frac(1, 3).