Random sequential adsorption: line segments on the square lattice

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We study kinetics of the rmgle-layer random sequenrisl adsorption of lint segments of ked kn5h on the square IatIjcc by a Monte Carlo srmulatton. The area covered b) the line segments grows with time and finally reacher a jamming limit when no more adsorption is possible. The jamming coverage depends on the segment length and 11s vanation IS studted At the late stage, approach of the coverage to the jamming limit IS arymptotieally exponential, with a rate found to be independent of the segment length. Based on our Monte Carlo data, an (act expression for the late-stage deposition kinettcs 15 conjectured. Random sequential adsorption (RSA), has been the subject of much recent experimental and theoretical investigation. Objects of fiGte size are randomly deposited (adsorbed) on an initially empty substrate so that no two objects overlap. The Quantity of interest is the fraction of the total area B(f) in time i, covered by the depositing particles. Due to the blocking of the area by the already randomly adsorbed particles, the limiting (3amming') coverage, ~(co), is less than the close packing. The emergence of this jammed state is iduenced by the infiuite memory effects. Consequently, its formation cannot he described by mean-field theory, except for very early times, when 6(t)af. Experimental studies 11-41 include, e.g., adhesion of colloidal particles 131 and proteins (2) on homogeneous substrates, with relaxation times much longer than the formation time of deposits. Theoretical studies (S-171 of RSA include series expansions IS, l@J, numerical Monte Carlo (Mc) simulations (9,14-16), and some analytical results 1171, mostly for one- dimensional systems. In such studies, it was shown that the precise form of the long-time behaviour of b'(r) depends on the shape and orientational freedom of the adsorbing particles. Earlier studies have focused on continuum deposition models for which a power-law behaviour of the late-stage deposition 1171