Competitive random sequential adsorption of point and fixed-sized particles: analytical results

We study the kinetics of competitive random sequential adsorption (RSA) of particles of binary mixture of points and fixed-sized particles within the mean-field approach. The present work is a generalization of the random car parking problem in the sense that it considers the case when either a car of fixed size is parked with probability q or the parking space is partitioned into two smaller spaces with probability (1-q) at each time event. This allows an interesting interplay between the classical RSA problem at one extreme (q=1), and the kinetics of fragmentation processes at the other extreme (q=0). We present exact analytical results for coverage for a whole range of q values, and physical explanations are given for different aspects of the problem. In addition, a comprehensive account of the scaling theory, emphasizing on dimensional analysis, is presented, and the exact expression for the scaling function and exponents are obtained.