EXACTLY SOLVABLE MODELS OF IRREVERSIBLE ADSORPTION WITH PARTICLE SPREADING

We introduce several models of irreversible adsorption in which nonrig id particles are deposited sequentially at random positions onto a lin e. Once adsorbed, a particle can immediately undergo an irreversible t ransition in which its size changes from 1 to sigma > 1. In the first model, the center of mass of a particle remains unchanged during the s preading 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 t otal available space on both sides of the particle is larger than sigm a, irrespective of how it is distributed on the two sides; if the part icle encounters its closest neighbor during the transition, it continu es to spread on the unbounded side until it reaches a size sigma. In t he last model, the spreading transition is equivalent to a conformatio nal change resulting from a tilting process; once adsorbed, the partic le grows either to the right or to the left, provided that there is sp ace available. We obtain expressions for the kinetics of these three m odels by introducing a gap density function. A comparison of results f rom each of these models allows us to determine the influence of the d etailed mechanism of the spreading transition on the overall adsorptio n process.