n Original Research Paper 127 Chemometrics and Intelligent Laboratory Systems, 10 (1991) 127-132 Elsevier Science Publishers B.V., Amsterdam zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Low dimensional reaction kinetics and self-organization zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR R. Kopelman *, L.W. Anacker, E. Clement, L. Li and L. Sander Departments of Chemistry and Physics, The University of Michigan, Ann Arbor, MI 48109 (U.S.A.) (Received 8 November 1989; accepted 23 February 1990) Abstract Kopelman, R., Anacker, L.W., Clement, E., Li, L. and Sander, L., 1991. Low dimensional reaction kinetics and self-organization. Chemometrics and Intelligent Laboratory Systems, 10: 127-132. Diffusion-limited reaction kinetics becomes anomalous not only for fractals, with their anomalous diffusion, but also for low-dimensional (one and two) and disperse media, where the random walk is compact. We focus on annihilation, recombination and trapping reactions under non-equilibrium steady state (steady source) or batch (big bang) conditions. The typical reactions are: A+A+Products, A+B+Products and A+C -D Products. We are interested in the global rate laws, and their relation to particle-particle distributions (e.g., pair-correlation and nearest-neighbor distribution functions) and in local rate laws (if definable). Anomalous reaction kinetics (more than classical kinetics) is particularly sensitive to initial conditions, source term structure, conservation laws (e.g., equal densities for A and B), excluded volume effects, and medium size, dimensionality and anisotropy. Analytical formalisms, scaling arguments, computer (and supercomputer) simulations and experiments (on chemical and physical reactions) all play an important role in the newly emerging picture. INTRODUCTION This work can be viewed as a natural extension of the activity dealing with relaxation phenomena and transient kinetics problems in disordered media [l-4]. Its domain of application spans vari- ous areas of the physics and chemistry of wn- densed matter. For example, reactions of the type A + A +O or A + T+T are models describing exciton kinetics in disordered molecular crystals or polymer blends. Reactions of the type A + B --, 0 are found in solid state physics in the case of electron-hole annihilation or defect fusion. A combination of experiments and Monte-Carlo simulations [5] has paved the way for a new theo- retical understanding of steady-state rate laws and the kinetic self-organization of atoms, defects and elementary excitations in low dimensional media. This theory is presented below. Diffusion limited trapping is of particular inter- est in studies of energy migration and lumines- cence [1,5]. We present below some new simula- tions and their relation to theory. This includes both rate laws and self-ordering. Of particular interest is the resulting anomalously high partial order of reactions as a function of trap wncentra- tion. ‘Big-bang’ reaction models are simpler than steady-source models, The pioneering work has been done by Ovchinnikov and Zeldovich [6] and 0169-7439/91/$03.50 0 1991 - Elsevier Science Publishers B.V.