Langmuir monolayers as disordered solids: Strain-state calculations applied to stearic acid

Abstract

This paper presents a calculational procedure to determine the equilibrium phase for a given surface pressure . The monolayer is treated as orientationally free tails grafted to a two-dimensional net formed by the head groups of the amphiphilic molecules. The head groups form a subsystem with translational degrees of freedom characterized by strain variables in the plane of the surface, and the tail groups compose a subsystem characterized by rotational degrees of freedom. The order in the monolayer derives indirectly from the crystalline head groups through translational-rotational coupling. A stress-strain relation is derived which shows the energetically most favorable path for reorientation of the molecules due to a two-dimensional strain. This set of strain states for a given symmetry ͑phase͒ allows a contribution to the strain-state partition function to be computed. It is then straightforward to calculate the strain-state contribution to the free energy for a given phase and estimate the transition temperature between phases.

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

“…6 In recent elegant studies of the shear elasticity of monolayers, 7,8 it has been confirmed that these phases are more crystalline in nature, rather than hexatic. These findings strongly support our previously introduced model of Langmuir monolayers as disordered solids, 3,9 as do other studies 10,11 that demonstrate mesophases can be treated as two-dimensional ͑2D͒ solids.…”

“…The results of this study further support the generality, efficacy, and usefulness of our model that treats mesophases of Langmuir monolayers as disordered solids. In this, as well as earlier treatments, 3,10,11 we have endeavored to show how the elastic solid theory of Langmuir monolayers is a natural, easily extended approach that offers a completely consistent and unifying structure for understanding a wide variety of experimental findings for Langmuir monolayers. …”

“…10,11 The potential energy landscape for a system with vertical molecules exhibits minima corresponding to elastic domains with small energy barriers for a reorientation. 10 Moreover, the calculated energy minima for a two-molecule unit cell, thought to always contain amphiphiles in a herring-bone arrangement, is essentially identical to that found for a onemolecule unit cell, thereby making discrimination between these structures impossible. Results of the monolayer architecture minimization, in particular Figs.…”

“…7 and 8 of Ref. 10, can be taken as the optimum local structures for rectangular and/or oblique domains. When these structures are grafted onto a global, hexagonal net, as in Fig.…”

Langmuir monolayers as disordered solids: Strain-tilt-backbone coupling and natural order parameters for the swiveling transitions

“…We shall, following our previous suggestions 3 and other work, advocate the concept of Langmuir monolayers as disordered solids. 6 Theoretical attempts to describe the symmetries of the phases in the generic (-T) phase diagram attack the problem from two opposite viewpoints: liquid-crystalline or solid state. But it is always the hexagonal, high-pressure ͑LS͒ phase which serves as the highest symmetry, parent phase.…”