Effect of particle size distribution and dynamics on the performance of two-dimensional packing

Extensive computer simulation is used to revisit and to generalize two classical problems: (i) the random car-parking dynamics of A. Rényi and (ii) the irreversible random sequential adsorption (RSA) of parallel squares of same size on a planar substrate of area L². In this paper, differently from the classical RSA, the squares obey the size distribution n(a)=n(1)a^−τ, where a=1,2,3,… is the area of the squares. Using this scaling distribution and three classes of packing dynamics we study the final packing fraction of particles, ?(τ,L), and in particular its thermodynamic limit L→∞. We show that the efficiency to attain a high/low packing density of particles on the substrate is strongly dependent on the value of the exponent τ and on the characteristics of the dynamics.