Random sequential adsorption of polydisperse mixtures on lattices

Random sequential adsorption of linear and square particles with excluded volume interaction is studied numerically on planar lattices considering Gaussian distributions of lateral sizes of the incident particles, with several values of the average mu and of the width-to-average ratio omega. When the coverage. is plotted as function of the logarithm of time t, the maximum slope is attained at a time t(M) of the same order of the time tau of incidence of one monolayer, which is related to the molecular flux and/or sticking coefficients. For various mu and omega, we obtain 1.5 tau < t(M) < 5 tau for linear particles and 0.3 tau < t(M) < tau for square particles. At t(M), the coverages with linear and square particles are near 0.3 and 0.2, respectively. Extrapolations show that coverages may vary with mu up to 20% and 2% for linear and square particles, respectively, for mu >= 64, fixed time, and constant omega. All theta vs log t plots have approximately the same shape, but other quantities measured at times of order tM help to distinguish narrow and broad incident distributions. The adsorbed particle-size distributions are close to the incident ones up to long times for small omega, but appreciably change in time for larger w, acquiring a monotonically decreasing shape for omega = 1/2 at times of order 100 tau. At t(M), incident and adsorbed distributions are approximately the same for omega <= 1/8 and show significant differences for omega >= 1/2; this result may be used as a consistency test in applications of the model. The pair correlation function g(r, t) for omega <= 1/8 has a well defined oscillatory structure at 10t(M), with a minimum at r approximate to mu and maximum at r approximate to 1.5 mu, but this structure is not observed for w >= 1/4.