Theory of hexagonal and stripe phases in monolayers

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Abstract
Epifluorescence microscopy can be used to visualize the shapes of solid lipid domains in two-phase regions of monolayers at the air—water interface. The shapes of certain lipid domains result from a competition between a one-dimensional line tension and long-range intermolecular electrostatic repulsion. Under specified conditions, a finite two-dimensional domain with one shape can undergo a sharp transition to a second shape, as the area of the domain is changed. Two-dimensional infinite arrays of domains can also have transitions involving changes in the shapes and patterns of domains, such as the stripe to hexagonal phase transition [Andelman, D., Brochard, F. & Joanny, J. F. (1987) J. Chem. Phys. 86, 3673-3681]. The present paper treats the hexagonal and stripe phases with the same approximations and methods of calculation as used previously for the isolated, finite domains. It is shown that one effect of electrostatic repulsion between domains is to cause these domains to increase in size as they approach one another on monolayer compression. It is also shown that there can be two distinct conditions where the hexagonal and stripe phases coexist.