A molecular model for tilting phase transitions between condensed phases of Langmuir monolayers

Abstract

A model of interacting rigid rods is proposed to describe tilting phase transitions in monolayers of freely rotating long-chain molecules with hexatic in-plane order. The model takes into account steric repulsion and van der Waals attraction between neighboring rods as well as the orientational entropy of individual rods, all within a mean field approximation limited to the unit cell. Two variants of the model are proposed, with different constraints on the polar molecular headgroups. In the first, the headgroups are grafted to a hexagonal close-packed (hcp) lattice, and in the second, the headgroup lattice deforms to accommodate to the tilt. For the monolayer on a solid substrate, tilt has two opposing actions on the internal energy. The decrease in the distance between rods acts to reduce the interaction energy, while the decrease in the overlapping length of the rods acts to increase it. As the area per molecule increases, the competition between these two effects drives the first-order phase transition U(untilted molecules)→NNN (collective tilt of the molecules in the direction of the next-nearest neighbor). This transition is present for both the fixed and the deformable lattices. For the monolayer on the water surface, the molecular tilt is accompanied by an increasing contact of the polar heads with the water. In this case, the effective interaction potential appears to be temperature dependent and under some circumstances can result in the first-order phase transition being replaced by a second-order one (U→NN) with the collective tilt in the direction of the nearest neighbor. The results obtained with the help of this model are compared with computer simulations and with experiment.

Model calculations of Langmuir monolayers: Pressure effects on tilting behavior of idealized amphiphiles

“…A NNN tilt for smaller values of d 0 on an unconstrained lattice agrees with results from rigid rod calculations. 6 Also in agreement is the lattice expansion in the direction of the tilt and contraction in the perpendicular direction. The vertical phase agrees with the report 9͑b͒ of a global vertical minimum for strings with d 0 ϭ1/3 and 15 beads in length.…”

“…For example, spherocylinders grafted to a hard two-dimensional lattice have recently been studied. 6 A first-order phase transition from an untilted phase to a next nearest neighbor ͑NNN͒ tilted phase was found as the lattice spacing was increased. The expanded lattice had a lower energy than that giving the untilted phase.…”

“…Instead, tilting is determined by the lattice spacing and the finite length of the cylinders, with the tilt magnitude being inversely proportional to the length. 6 More chemically relevant ''coarse-grained'' models that consist of a linear molecule composed of Lennard-Jones centers, or united atoms, have also been studied. 9 To aid the visualization of these systems, they will be referred to as beaded strings ͑Fig.…”

“…4 However, the very complexity that leads to numerical accuracy frequently hinders conceptual clarity. At the other extreme, simple models based on planar figures, 5 rigid rods, [6][7][8] and linear molecules composed of Lennard-Jones centers, 9 have been studied. While these do not reproduce experimental data quantitatively, they do give a clear qualitative picture of the mechanisms governing the complicated behavior of these systems.…”

Nonlinear elasticity and friction of liquid-crystalline polymer monolayers

“…Brushes with LC ordering have been investigated far less than isotropic brushes. [4][5][6][7][8] Recent experiments using Scanning Force Microscopy ͑SFM͒ and Surface Force Apparatus ͑SFA͒ technique revealed a strong correlation between the monolayer structure and their tribology. [9][10][11][12][13] In particularly, the friction force strongly depends not only on the interactions in the monolayer, which in most cases depends on the chemical nature of the chains, but also on the chain length.…”