Fluctuation of the number of particles deposited on a flat surface by a random sequential adsorption mechanism

The problem of the fluctuations of the number n of particles adsorbed on surfaces through a random sequential adsorption process is discussed. Attention is paid, in particular, to the effect of the size of the adsorbing surfaces upon the variance sigma2(n) of this number. On the basis of computer simulations, it is shown that sigma2(n) is not proportional to the area a of the surface but can be written as a sum of three contributions, which are proportional to a, a1/2, and a0. A theoretical estimate based on the relation between the radial distribution function g(r) and the fluctuation is presented and provides a basis for these findings. This analysis is of general validity and can, in particular, also be applied to the equilibrium case (in the absence of a phase transition) and to the ballistic deposition process.