Langmuir monolayers as disordered solids: Disorder and elastic fluctuations in mesophases

Ordering in Langmuir monolayer mesophases is examined using an approach bas ed on the elastic theory of crystals. Molecular tails are modeled as "defec ts" grafted onto a two-dimensional elastic medium and are characterized by elastic dipoles. It is assumed that disorder in the parent, LS, phase is du e to competition between local (within a domain) and global (hexagonal arra ngement of domains) structure. By treating the LS phase as a mixture of rec tangular and/or oblique domains (rectangular and/or oblique defects within the two-dimensional elastic medium), density fluctuations due to elastic in teractions between domains are analyzed. The correlation function for the e lastic dipoles is calculated and the elastic interactions' renormalization of the elastic properties of mesophases is analyzed. Results are shown to b e compatible with very recent experiments on microscopic and macroscopic el asticity of the monolayers as well as those on positional disorder in LS an d S phases. Kinetic aspects of the elastic response are considered, as is t he contribution of the elastic domains' reorientations to x-ray diffuse sca ttering. (C) 1999 American Institute of Physics. [S0021-9606(99)70446-0].