ORDER-DISORDER PHENOMENA IN A DIFFUSION-REACTION MODEL OF INTERACTINGDIPOLES ON A SURFACE

We study the reaction efficiency of a surficial process in which a dif fusing, tumbling dipole A reacts (eventually and irreversibly) with a stationary target dipole B. In contrast to earlier studies of such irr eversible diffusion-reaction events (A+B-->C), we consider the situati on where at each and every site of the space accessible to the diffusi ng coreactant A, there is also embedded a fixed dipole. To quantify th e influence on the reaction efficiency of (angle-averaged, dipole-dipo le) potential interactions between the tumbling dipole A and the ensem ble of stationary dipoles, we design a lattice-statistical model to de scribe this problem and use both analytical methods and numerical tech niques rooted in the theory of finite Markov processes to work out its consequences. Specifically, we define the reaction space to be an nXn =N square-planar lattice with the target dipole occupying the centrosy mmetric site in that space and determine the mean number of steps requ ired before the irreversible event, A+B-->C, occurs. Our results revea l two qualitatively-distinct regimes of behavior for this diffusion-re action process, a low temperature (or strong coupling) regime dominate d by nearest-neighbor excursions only, and a high-temperature (or weak -coupling) regime dominated by non-nearest neighbor excursions of the tumbling dipole A, with the transition between these two regimes occur ring over a relatively narrow range of interparticle couplings. This b ehavior has the character of an ''order-disorder'' transition and is i nterpreted here in terms of an ''order parameter'' W related to a gene ralized Onsager length. The behavior uncovered is studied as a functio n of system size and of the boundary conditions imposed. (C) 1995 Amer ican Institute of Physics.