# Percolation of aligned rigid rods on two-dimensional square lattices.

@article{Longone2012PercolationOA, title={Percolation of aligned rigid rods on two-dimensional square lattices.}, author={Pablo Longone and P. M. Centres and Antonio Jos{\'e} Ramirez-Pastor}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2012}, volume={85 1 Pt 1}, pages={ 011108 } }

The percolation behavior of aligned rigid rods of length k (kmers) on two-dimensional square lattices has been studied by numerical simulations and finite-size scaling analysis. The kmers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The process was monitored by following the probability R(L,k)(p) that a lattice composed of L×L sites percolates at a concentration p of sites occupied by particles of size…

## 24 Citations

### Percolation of aligned rigid rods on two-dimensional triangular lattices.

- Materials SciencePhysical review. E
- 2019

An exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered.

### Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

- Materials Science
- 2012

Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length k (k-mers) on two-dimensional square lattices. The…

### Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice

- Mathematics
- 2017

Monte Carlo simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of linear k-mers (also known as rods or needles) on a two-dimensional…

### Inverse percolation by removing straight rigid rods from square lattices in the presence of impurities

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2019

Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse percolation by removing straight rigid rods from square lattices contaminated with…

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

- Materials SciencePhysical review. E
- 2017

The diffusion-driven self-assembly of rodlike particles was studied by means of Monte Carlo simulation and 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.

### Monte Carlo Simulation of Evaporation Driven Self-Assembly in Suspension of Colloidal Rods

- Physics
- 2018

The vertical drying of a colloidal film containing rod-like particles was studied by means of kinetic Monte Carlo (MC) simulation. The problem was approached using a two-dimensional square lattice…

### Jamming and percolation of k2-mers on simple cubic lattices

- PhysicsPhysical review. E
- 2019

A complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolations, regardless of the size k considered.

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

- Materials SciencePhysical review. E
- 2016

The vertical drying of a colloidal film containing rodlike particles was studied by means of kinetic Monte Carlo (MC) simulation and significant evaporation-driven self-assembly and orientation stratification of the k-mers oriented along the x and y directions were observed.

### Site trimer percolation on square lattices.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

Percolation of site trimers (k-mers with k=3) is investigated in a detailed way making use of an analytical model based on renormalization techniques in this problem to establish the tendency of p(c) to decrease as k increases.

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