Percolation of functionalized colloids on patterned substrates

Abstract

We study the percolation properties for a system of functionalized colloids on patterned substrates via Monte Carlo simulations. The colloidal particles are modeled as hard disks with three equally-distributed attractive patches on their perimeter. We describe the patterns on the substrate as circular potential wells of radius Rp arranged in a regular square or hexagonal lattice. We find a nonmonotonic behavior of the percolation threshold (packing fraction) as a function of Rp. For attractive wells, the percolation threshold is higher than the one for clean (non-patterned) substrates if the circular wells are non-overlapping and can only be lower if the wells overlap. For repulsive wells we find the opposite behavior. In addition, at high packing fractions the formation of both structural and bond defects suppress percolation. As a result, the percolation diagram is reentrant with the non-percolated state occurring at very low and intermediate densities.

Shape control of soft patchy nanoparticles under confinement

“…Patchy particles, also referred to as "colloidal molecules", are entities of colloidal size, whose surface is decorated by attractive spots, giving rise to effective anisotropic interactions. [4][5][6] From a theoretical standpoint, patchy particles display remarkable thermodynamic properties in the bulk as well as close to surfaces; [7][8][9][10][11][12] their promising features triggered great efforts to synthesize patchy units at the micron scale. Unfortunately, limitations in the synthesis of patchy colloids have been for quite a long time the greatest bottleneck for their application in materials science.…”

Percolation thresholds of randomly rotating patchy particles on Archimedean lattices

“…Percolation is extensively studied in stochastic processes, phase transitions and critical phenomena, and widely applied in various problems such as exploring gelation in polymers, transport behaviors in porous media, the spread of epidemics, the fractal structure of landscapes etc. [11,12] There exist many studies on percolation of patchy particles in the continuum space, for which recent examples include different percolated states in mixtures of patchy colloids [13], reentrant percolation * Electronic address: huhao@ahu.edu.cn of inverse patchy colloids [14] and of patchy colloids on patterned substrates [15], effects of surface heterogeneity on percolation thresholds of random patchy spheres [16], the design of patchy particle gels with tunable percolation thresholds [17]. However, except a study on directed percolation of patchy disks on the square lattice [18], we find that the percolation behavior of patchy particles on lattices remains largely unexplored, possibly due to that patchy particles are made in the continuum space [1,2].…”

Analytical approximation of the inverse percolation thresholds for dimers on square, triangular and honeycomb lattices

“…Percolation theory has been attracting the wide attention of researchers for several decades [1][2][3][4], and the activity in this field is still growing [5][6][7][8][9][10][11][12]. It settles the basis to the understanding of the behavior of many systems such as transport and flow in porous media [1,2], network theory [13][14][15][16], transport in disordered media [17,18], spread of disease in populations [19], forest fire propagation [20], simulated spread fire in multi-compartmented structures [21], spread of the computer virus [22], etc.…”