Random sequential adsorption and percolation on discrete substrates

Abstract Random sequential adsorption (RSA) is a broadly used model for irreversible deposition on substrates. Over the last decades, a huge number of works have been published concerning this topic. Here we give a brief review of the results for irreversible deposition on two-dimensional discrete substrates. Depositing objects are randomly and sequentially adsorbed onto the substrate, and they are not allowed to overlap, so the jamming coverage <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>θ</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>j</mml:mi> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> is less than in close packing. The kinetics of the process is described by the time-dependence of the coverage fraction <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , and for the discrete substrates, this dependence was found to be of the form: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>θ</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>j</mml:mi> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo> <mml:mi>A</mml:mi> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>t</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . Another topic of interest is the percolation of the deposit that can occur at a certain coverage. The coverage of the surface is increased through the RSA process up to the percolation threshold when a cluster that extends through the whole system appears. A percolating cluster arises in the system when the opposite edges are connected via some path of nearest neighbor sites occupied by the particles. Studying percolation is of great interest due to its relevance to conductivity in composite materials, flow through porous media, polymerization, the properties of nanomaterials, etc.