Monolayers of hard rods on planar substrates. I. Equilibrium

Abstract

The equilibrium properties of hard rod monolayers are investigated in a lattice model (where position and orientation of a rod are restricted to discrete values) as well as in an off-lattice model featuring spherocylinders with continuous positional and orientational degrees of freedom. Both models are treated using density functional theory and Monte Carlo simulations. Upon increasing the density of rods in the monolayer, there is a continuous ordering of the rods along the monolayer normal ("standing up" transition). The continuous transition also persists in the case of an external potential which favors flat-lying rods in the monolayer. This behavior is found in both the lattice and the continuum models. For the lattice model, we find very good agreement between the results from the specific DFT used (lattice fundamental measure theory) and simulations. The properties of lattice fundamental measure theory are further illustrated by the phase diagrams of bulk hard rods in two and three dimensions. Published by AIP Publishing. [http://dx

Monolayers of hard rods on planar substrates. II. Growth

“…2(b) with α = 3. This is likely a combination of effects: the density functional is less precise for longer rods, 18 and the packing fraction η(= L ρ 12 + ρ 3 ) is particularly sensitive to resulting errors in the number density ρ 12 = ρ 1 + ρ 2 ; so, the error in η scales with L. Apart from this, isotropic deposition with its random insertion of rod species i = 1, 2 appears to emphasize errors in the calculation of ρ 12 . Fig.…”

“…25,26 In Ref. 18, we provide the basic definitions and examples for the functionals and their equilibrium properties for mono-component rods in two and three dimensions and in the monolayer case. In the present work, we only need the free energy functional for the homogeneous case for the monolayer.…”

“…(2) and (3) does not feature biaxiality for L ≤ 12. 18 We, therefore, make the assumption that ρ 1 = ρ 2 also holds for the non-equilibrium setting of the rod-lengths studied in the simulations (with L = 5 and 9 investigated below). We consider two different modes of particle deposition: (i) perpendicular deposition and (ii) isotropic deposition.…”

“…Nevertheless, restricted-orientation models of hard rods already show a rich phase diagram, 16 which compares qualitatively well with that of unrestricted-orientation models. 17 In a previous paper, 18 we have investigated the equilibrium properties of lattice rods by classical density functionals from fundamental measure theory (FMT) and simulation. For the case of monolayers, a continuous λ-σ-transition ("standing-up transition") has been found, which also persists in the case of finite substrate potentials.…”

Hard rectangles near curved hard walls: Tuning the sign of the Tolman length

“…These particles show more complex structuring near walls as both translational and orientational degrees of freedom are coupled. Although one of the simplest of such systems, namely orientable hard rectangles in two spatial dimensions near a wall, has been intensely studied by means of experiments [43][44][45][46], simulations [47][48][49][50], DFT calculations [46,[50][51][52][53], and other theories [54], the curvature dependence of the interfacial tension in this system has not yet been explored. Here we close this gap.…”