Exactly solvable models of irreversible adsorption with particle spreading

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Abstract
We introduce several models of irreversible adsorption in which nonrigid particles are deposited sequentially at random positions onto a line. Once adsorbed, a particle can immediately undergo an irreversible transition in which its size changes from 1 to σ>1. In the first model, the center of mass of a particle remains unchanged during the spreading so that the transition occurs if there is enough room on both sides of the particle. In the second model, a particle grows if the total available space on both sides of the particle is larger than σ, irrespective of how it is distributed on the two sides; if the particle encounters its closest neighbor during the transition, it continues to spread on the unbounded side until it reaches a size σ. In the last model, the spreading transition is equivalent to a conformational change resulting from a tilting process; once adsorbed, the particle grows either to the right or to the left, provided that there is space available. We obtain expressions for the kinetics of these three models by introducing a gap density function. A comparison of results from each of these models allows us to determine the influence of the detailed mechanism of the spreading transition on the overall adsorption process.

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