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We study approach to the large-time jammed state of the deposited particlesin the model of random sequential adsorption. The convergence laws are usuallyderived from the argument of Pomeau which includes the assumption of thedominance, at large enough times, of small landing regions into each of whichonly a single particle can be deposited without overlapping earlier depositedparticles and which, after a certain time are no longer created by depositionsin larger gaps. The second assumption has been that the size distribution ofgaps open for particle-center landing in this large-time small-gaps regime isfinite in the limit of zero gap size. We report numerical Monte Carlo studiesof a recently introduced model of random sequential adsorption on patternedone-dimensional substrates that suggest that the second assumption must begeneralized. We argue that a region exists in the parameter space of thestudied model in which the gap-size distribution in the Pomeau large-timeregime actually linearly vanishes at zero gap sizes. In another region, thedistribution develops a threshold property, i.e., there are no small gaps belowa certain gap size. We discuss the implications of these findings for newasymptotic power-law and exponential-modified-by-a-power-law convergences tojamming in irreversible one-dimensional deposition.

Nonstandard Convergence to Jamming in Random Sequential Adsorption: The Case of Patterned One-Dimensional Substrates