Monte Carlo simulation of evaporation-driven self-assembly in suspensions of colloidal rods

Abstract

The vertical drying of a colloidal film containing rodlike particles was studied by means of kinetic Monte Carlo (MC) simulation. The problem was approached using a two-dimensional square lattice, and the rods were represented as linear k-mers (i.e., particles occupying k adjacent sites). The initial state before drying was produced using a model of random sequential adsorption (RSA) with isotropic orientations of the k-mers (orientation of the k-mers along horizontal x and vertical y directions are equiprobable). In the RSA model, overlapping of the k-mers is forbidden. During the evaporation, an upper interface falls with a linear velocity of u in the vertical direction and the k-mers undergo translation Brownian motion. The MC simulations were run at different initial concentrations, p_{i}, (p_{i}∈[0,p_{j}], where p_{j} is the jamming concentration), lengths of k-mers (k∈[1,12]), and solvent evaporation rates, u. For completely dried films, the spatial distributions of k-mers and their electrical conductivities in both x and y directions were examined. Significant evaporation-driven self-assembly and orientation stratification of the k-mers oriented along the x and y directions were observed. The extent of stratification increased with increasing value of k. The anisotropy of the electrical conductivity of the film can be finely regulated by changes in the values of p_{i}, k, and u.

Diffusion-driven self-assembly of rodlike particles: Monte Carlo simulation on a square lattice

“…In this state, no additional k-mer can be placed because the presented voids are too small or of inappropriate shape. The values of p j for different values of k have recently been calculated at the thermodynamic limit [49], while our estimations of p j for a particular lattice size L = 256 have also recently been presented in [45]. The total number of k-mers at the jamming state, N k , was equal to p j L 2 /k.…”

“…On a square lattice, in the course of diffusion, the horizontal and vertical stacks of k-mers separated from one another and a characteristic coarsening was observed [45]. Such self-assembly of k-mers can significantly affect the properties of the films.…”

“…The irreversible RSA process leads to a nonequilibrium state of the system, and further selforganization in the deposited film is possible owing to deposition-evaporation processes or the diffusion motion of the k-mers. Several problems related to such type of self-assembly of k-mers have previously been discussed [39][40][41][42][43][44][45]. Dynamic MC simulations using a deposition-evaporation algorithm for simulation of the dynamic equilibrium of k-mers on square lattices have been applied [39].…”

Anisotropy in electrical conductivity of two-dimensional films containing aligned nonintersecting rodlike particles: Continuous and lattice models

“…In our calculations, two conducting buses subjected to a potential difference were applied to the opposite borders of such a plane. Electrical conductivity was calculated in the direction along the alignment of the particles (longitudinal conductivity, ) and in the direction across the alignment (transversal conductivity, ⊥) (see [40,41] for details). Two algorithms were applied to calculate the electrical conductivity, viz., the Frank-Lobb algorithm [42] (continuous model) and the direct electrifying algorithm [43] (lattice model).…”

Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem

“…We put σ i = 1, and σ c = 10 6 in arbitrary units for the conductivities of insulating and conducting sites, respectively. In our calculations, the two conducting buses were applied to the opposite borders of the lattice, and electrical conductivity was calculated between these buses in the horizontal, σ x and vertical σ y directions (see [15,34] for the details).…”