Dissociative Adsorption: A Solvable Model

A model of “hot”-dimer deposition in one dimension, introduced by Pereyra and Albano, is modified to have an unbounded dissociation range. The resulting dynamical equations are solved exactly. A related k-mer dissociation model is also introduced and its solution obtained as a quadrature. PACS numbers: 68.10.Jy and 82.65.-i Recent experimental studies [1] reported deposition processes in which prior to adhesion the arriving diatomic molecules break up into single-atom fragments which dissipate the excess energy by “flying apart” a large distance. A simplified one-dimensional (1D) model of these processes was introduced in [2]. The restriction to 1D was motivated by the possibility of extensive numerical Monte Carlo studies, and in fact, more realistic two-dimensional-substrate Monte Carlo modeling was alluded to in [2]. It is usually instructive to obtain solvable variants of 1D models. Indeed, exact calculations provide insight into more realistic higher-dimensional systems and yield test models for approximation schemes, in various reaction and adsorption processes reviewed, e.g., in [3-6]. In this work, we introduce a model with infinite dissociation range and with random initial conditions, which can be solved exactly for dimers as well as generalized to k-mer deposition with dissociation. The latter generalization allows discussion of the approach to the continuum limit [7-8]. In the deposition of “hot” dimers [2], one assumes that each successful deposition attempt in followed up by the dissociation of the dimer. The two monomer fragments move apart up to a certain maximal distance: they either stop on their own or run into existing clusters. In order to eliminate the upper bound on the allowed dissociation distance while still have the resulting model not sensitive to the finite-size end-effects, one has to consider initial states in which obstacles to the motion of the fragments after deposition are present with reasonable density. Thus we assume that initially the lattice is randomly covered with some finite monomer density ρ, measured per lattice site. Each dimer deposition event will be followed by instantaneous fragmentation and attachment of one monomer fragment at each end of the empty gap in which the deposition attempt has succeeded. Thus the gap size will be decreased by 2. For k-mer