Impact of orientational distribution of adsorbing objects on dynamics of Random Sequential Ballistic Adsorption (RSBA) dynamics

Recently, by proposing a new variant of Random Sequential Adsorption (RSA) namely Random Sequential Ballistic Adsorption (RSBA) model [Pradip B. Shelke, A.G. Banpurkar, S.B. Ogale, A.V. Limaye, Surf. Sci. 601 (2007) 274], we addressed the issue of adsorption dynamics of extended objects where the objects, upon adsorption, protrude outside the substrate. This study brought out the role of the arriving trajectory in the adsorption dynamics. In the present work the possible role of the orientational distribution of the arriving objects in the RSBA dynamics is investigated. The dynamics of RSBA of needles (line segments) is studied analytically and by computer simulation for different types of θ distributions of arriving needles, θ being the angle made by the arriving needle with normal to the substrate. Three types of θ distributions, namely a uniform distribution over the range (0, π/2), a Gaussian distribution and a distribution uniform over the solid angle, are considered. Analytical treatment establishes that in all the three cases, the number n(t) of adsorbed objects at a late time t follows a power law n(t) ∼ tα, and the exponent α depends on the specifics of the θ distribution. In general, for distribution f(θ) ∝ θβ, for θ → 0, α is found to be 2/(β + 3). The simulation results are in excellent agreement with the analytical findings and together they reveal that the orientational distribution of arriving objects has significant consequences for the Random Sequential Ballistic Adsorption (RSBA) process.