Random-sequential adsorption of disks of different sizes

The random-sequential adsorption of disks with two or more sizes onto a planar substrate has been investigated using computer simulations. For a binary mixture of large and small disks, we find that the large-disk coverage reaches its asymptotic value exponentially, while the small disk reaches its asymptotic value algebraically according to Feder’s law. For a uniform distribution of disk radii, the total coverage approaches its asymptotic value algebraically [ρ(∞)-ρ(t)∼${\mathit{t}}^{\mathrm{-}\mathit{p}}$, where ρ(t) is the coverage at time t], but the characteristic exponent p has an effective value smaller than 1/2. If the distribution of disk radii from which the disks are selected for attempted addition is Gaussian, then the exponent p has a very small effective value, and the distribution of adsorbed disks becomes very non-Gaussian if the initial Gaussian distribution is broad. Many of our simulation results can be understood in terms of the theoretical work of Talbot, Tarjus, and Schaff [Phys. Rev. A 40, 4808 (1980)], but other aspects of this work are beyond current theoretical approaches.