Equations of state for Langmuir monolayers with two-dimensional phase transitions

A generalized Volmer's equation is derived for a multicomponent Langmuir monolayer. This general equation is then used to derive the equations of state for the monolayer of a single amphiphile considering the two-dimensional (2D) main phase transition. A theory developed recently (J. Phys. Chem. 1996, 100, 15478) is extended to incorporate the important case that the area per one amphiphile molecule within the aggregate differs from that characteristic for the nonaggregated amphiphile. The general equation derived involves four parameters, two of which refer to the state of the gaseous monolayer whereas the other two parameters express the 2D aggregation constant and the difference between the area per one amphiphile molecule within the aggregate and the area per one nonaggregated molecule. The experimental Pi-A isotherms for Langmuir monolayers of various amphiphiles, either measured by the authors or referred to elsewhere, agree well with the proposed model for physically reliable values of model parameters.