Random sequential adsorption of polydisperse mixtures on a cubic lattice

Abstract The irreversible random sequential adsorption of polydisperse mixtures of ‘lattice animals’ on a three-dimensional cubic lattice is investigated using Monte Carlo simulations. A ‘lattice animal’ is defined as a 3D object composed of a group of points connected as nearest neighbors on a lattice. Polydisperse mixtures consist of n objects of varying sizes but sharing the same basic shape. This study analyzes the influence of polydispersity and the geometrical properties of the shapes on the jamming density <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>θ</mml:mi> <mml:mtext>J</mml:mtext> </mml:msub> </mml:mrow> </mml:math> and the temporal evolution of the density <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> . The approach of the coverage to the jamming limit <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>θ</mml:mi> <mml:mtext>J</mml:mtext> </mml:msub> </mml:mrow> </mml:math> is found to be exponential, expressed as <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:mtext>J</mml:mtext> </mml:msub> <mml:mo>−</mml:mo> <mml:mi>A</mml:mi> <mml:msup> <mml:mtext>e</mml:mtext> <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> , both for the mixtures and their individual components. The values of relaxation time σ are determined by the number of different orientations m that the lattice animals can take when placed on a cubic lattice. It is observed that the parameter σ increases linearly with the number of mixture components n of the same basic shape. Additionally, the partial jamming densities and corresponding relaxation times σ decrease as the size of the mixture components increases.