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

Abstract

The diffusion-driven self-assembly of rod-like particles was studied by means of Monte Carlo simulation. The rods were represented as linear $k$-mers (i.e., particles occupying $k$ adjacent sites). In the initial state, they were deposited onto a two-dimensional square lattice of size $L\times L$ up to the jamming concentration using a random sequential adsorption algorithm. The size of the lattice, $L$, was varied from $128$ to $2048$, and periodic boundary conditions were applied along both $x$ and $y$ axes, while the length of the $k$-mers (determining the aspect ratio) was varied from $2$ to $12$. The $k$-mers oriented along the $x$ and $y$ directions ($k_x$-mers and $k_y$-mers, respectively) were deposited equiprobably. In the course of the simulation, the numbers of intraspecific and interspecific contacts between the same sort and between different sorts of $k$-mers, respectively, were calculated. Both the shift ratio of the actual number of shifts along the longitudinal or transverse axes of the $k$-mers and the electrical conductivity of the system were also examined. For the initial random configuration, quite different self-organization behavior was observed for short and long $k$-mers. For long $k$-mers ($k\ge 6$), three main stages of diffusion-driven spatial segregation (self-assembly) were identified: the initial stage, reflecting destruction of the jamming state, the intermediate stage, reflecting continuous cluster coarsening and labyrinth pattern formation and the final stage, reflecting the formation of diagonal stripe domains. Additional examination of two artificially constructed initial configurations showed that this pattern of diagonal stripe domains is an attractor, i.e., any spatial distribution of $k$-mers tends to transform into diagonal stripes. Nevertheless, the time for relaxation to the steady state essentially increases as the lattice size growth.

arXiv comment12 pages, 14 figs, 3 videos, 53 refs. Submitted to Phys. Rev. E

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• Aging in two dimensional suspensions of rods as driven by Brownian diffusion
• Pattern formation in a two-dimensional two-species diffusion model with anisotropic nonlinear diffusivities: a lattice approach
• Diffusion dynamics and steady states of systems of hard rods on the square lattice
• Characterisation of diffusion-driven self-organisation of rodlike particles by means of entropy of generalised two-dimensional words
• Jammed systems of oriented dimers always percolate on hypercubic lattices
• Monte Carlo simulation of entropy-driven pattern formation in two-dimensional system of rectangular particles
• Impact of packing fraction on diffusion-driven pattern formation in a two-dimensional system of rod-like particles