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
Growth of hard-rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, "standing-up" transition) is an entropic effect and is mainly governed by the equilibrium solution, rendering a continuous transition [Paper I, M. Oettel et al., J. Chem. Phys. 145, 074902 (2016)]. Strong non-equilibrium effects (e.g., a noticeable dependence on the ratio of rates for translational and rotational moves) are found for attractive substrate potentials favoring lying rods. Results from the lattice and the continuum models agree qualitatively if the relevant characteristic times for diffusion, relaxation of nematic order, and deposition are matched properly. Applicability of these monolayer results to multilayer growth is discussed for a continuum-model realization in three dimensions where spherocylinders are deposited continuously onto a substrate via diffusion. Published by AIP Publishing. [http://dx
We have studied the connectivity percolation transition in suspensions of attractive square-well spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. In the 1980s the percolation threshold of slender fibers has been predicted to scale as the fibers' inverse aspect ratio [Phys. Rev. B 30, 3933 (1984)]. The main finding of our study is that the attractive spherocylinder system reaches this inverse scaling regime at much lower aspect ratios than found in suspensions of hard spherocylinders. We explain this difference by showing that third virial corrections of the pair connectedness functions, which are responsible for the deviation from the scaling regime, are less important for attractive potentials than for hard particles.
By means of computer simulations and kinetic rate equations, we study the formation of a film of rod-like particles which are deposited on a substrate. The rod-rod interactions are hard with a short-range attraction of variable strength and width, and the rod-substrate interactions favor lying rods with a variable strength. For a rod aspect ratio of 5 and deposition of up to an equivalent of one monolayer of standing rods, we demonstrate a rich variety of growth modes upon variation of the three interaction parameters. We formulate rate equations for the time evolution of densities of islands composed of standing, lying, and mixed rods. Input parameters such as diffusion constants, island capture numbers, and rod reorientation free energies are extracted from simulations, while rod reorientation attempt frequencies remain as free parameters. Numerical solutions of the rate equations in a simple truncation show rough qualitative agreement with the simulations for the early stage of film growth but an extension to later stages requires to go significantly beyond this simple truncation.
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