Integral Equation to the Random Sequential Addition Model in Any Dimension

Integral-equation theories of the Random Sequential Addition (RSA) model have been proposed in our previous work. It has been extensively studied as a two-dimensional problem representing an irreversible adsorption of large particles on a surface. This RSA model is, however, flexible enough to be applied to situations in other dimensions. It was used to model the growth of a polymer chain or a car-parking problem in one dimension and model a random sequential packing in three dimensions. We used the Fourier transform to solve the Ornstein-Zernrke integral equation and its Percus-Yevick closure, both derived by utilizing the assumption of a binary mixture of quenched and annealed particles. In this work, we therefore applied the corresponding Fourier transform to one, two and three dimensions to compute the radial distribution functions, g(r), and found that they are in good agreement with the results from Monte Carlo simulations. This confirms the validity of the theory.