Kinetics and Spatial Organization of Competitive Reactions

In this chapter, we review some kinetic and geometric properties of two-species annihilation in which an encounter between two distinct species A and B leads to the formation of an inert product I, A + B → I [7.1]. Examples of this reaction include electron-hole recombination in irradiated semiconductors [7.2], catalytic reactions on surfaces [7.3], exciton dynamics [7.4], and annihilation of primordial monopoles in the early universe [7.5]. At a more abstract level, two-species annihilation is a realization of an interacting Brownian particle system, a connection which has been helpful in establishing rigorous results [7.6]. For detailed discussion of Brownian motion see Chap. 5. For other types of reactions see Chap. 8.

[1]  Sander,et al.  Steady-state diffusion-controlled A+B-->0 reactions in two and three dimensions: Rate laws and particle distributions. , 1989, Physical review. A, General physics.

[2]  J. Preskill.  Cosmological Production of Superheavy Magnetic Monopoles , 1979 .

[3]  S. Redner,et al.  Saturation transition in a monomer-monomer model of heterogeneous catalysis , 1990 .

[4]  Leyvraz,et al.  Spatial organization in the two-species annihilation reaction A+B-->0. , 1991, Physical review letters.

[5]  Sidney Redner,et al.  Nearest-neighbour distances of diffusing particles from a single trap , 1990 .

[6]  J. Spouge,et al.  Exact solutions for a diffusion-reaction process in one dimension. , 1988, Physical review letters.

[7]  V V Slezov,et al.  Diffusive decomposition of solid solutions , 1987 .

[8]  Eugene A. Kotomin,et al.  Kinetics of bimolecular reactions in condensed media: critical phenomena and microscopic self-organisation , 1988 .

[9]  G. Bond,et al.  Heterogeneous Catalysis: Principles and Applications , 1974 .

[10]  E. Ben-Naim,et al.  Partial absorption and “virtual” traps , 1993 .

[11]  D. Lévesque,et al.  Electrical properties of polarizable ionic solutions. II. Computer simulation results , 1989 .

[12]  F. Leyvraz.  Two-species annihilation in three dimensions : a numerical study , 1992 .

[13]  Ottino,et al.  Evolution of a lamellar system with diffusion and reaction: A scaling approach. , 1989, Physical review letters.

[14]  A. Mikhailov.  Selected topics in fluctuational kinetics of reactions , 1989 .

[15]  ben-Avraham,et al.  Interparticle distribution functions and rate equations for diffusion-limited reactions. , 1988, Physical review. A, General physics.

[16]  P. Meakin,et al.  Simple models for heterogeneous catalysis: Phase transition‐like behavior in nonequilibrium systems , 1987 .

[17]  G. Weiss.  First passage time problems for one-dimensional random walks , 1981 .

[18]  M. Scheucher,et al.  A soluble kinetic model for spinodal decomposition , 1988 .

[19]  Steady-state chemical kinetics on fractals: Segregation of reactants. , 1987, Physical review letters.

[20]  Zhang,et al.  Dynamic scaling of growing interfaces. , 1986, Physical review letters.

[21]  Rácz,et al.  Properties of the reaction front in an A+B-->C type reaction-diffusion process. , 1988, Physical review. A, General physics.

[22]  E. Weinberg,et al.  Density fluctuations and particle-antiparticle annihilation , 1984 .

[23]  J. E. Kiefer,et al.  Some properties of the a+b → C reaction-diffusion system with initially separated components , 1991 .

[24]  A. A. Ovchinnikov,et al.  Kinetics of diffusion controlled chemical processes , 1989 .

[25]  R. Kopelman,et al.  Steady-state chemical kinetics on fractals: Geminate and nongeminate generation of reactants , 1987 .

[26]  Goldberg,et al.  Experimental determination of the long-time behavior in reversible binary chemical reactions. , 1992, Physical review letters.

[27]  S. Redner,et al.  Inhomogeneous two-species annihilation in the steady state , 1992 .

[28]  T. Ohtsuki.  Diffusion-controlled recombination of charged particles , 1984 .

[29]  R. Kopelman,et al.  Space-and time-resolved diffusion-limited binary reaction kinetics in capillaries: experimental observation of segregation, anomalous exponents, and depletion zone , 1991 .

[30]  STATISTICAL PROPERTIES OF THE DISTANCE BETWEEN A TRAPPING CENTER AND A UNIFORM DENSITY OF DIFFUSING PARTICLES IN TWO DIMENSIONS , 1990 .

[31]  Ottino,et al.  Diffusion and reaction in a lamellar system: Self-similarity with finite rates of reaction. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[32]  Blumen,et al.  Scaling properties of diffusion-limited reactions: Simulation results. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[33]  J. Klafter,et al.  Concentration fluctuations in reaction kinetics , 1985 .

[34]  Charles R. Doering,et al.  Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics , 1991 .

[35]  F. Wilczek,et al.  Particle–antiparticle annihilation in diffusive motion , 1983 .

[36]  Maury Bramson,et al.  Asymptotic behavior of densities for two-particle annihilating random walks , 1991 .

[37]  Stanley,et al.  Reaction kinetics of diffusing particles injected into a d-dimensional reactive substrate. , 1993, Physical review letters.

[38]  Raoul Kopelman,et al.  Fractal Reaction Kinetics , 1988, Science.

[39]  S. Havlin,et al.  Fractals and Disordered Systems , 1991 .

[40]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[41]  Lebowitz,et al.  Asymptotic behavior of densities in diffusion-dominated annihilation reactions. , 1988, Physical review letters.

[42]  Maury Bramson,et al.  Asymptotics for interacting particle systems onZd , 1980 .

[43]  Dynamics and spatial organization in two-species competition , 1992 .

[44]  Maury Bramson,et al.  Spatial structure in diffusion-limited two-particle reactions , 1991 .

[45]  A. Messiah.  Quantum Mechanics , 1961 .

[46]  J. Klafter,et al.  Transient A+B→0 reaction on fractals: stochastic and deterministic aspects , 1991 .

[47]  Exact results for a chemical reaction model. , 1991, Physical review letters.

[48]  Michael E. Fisher,et al.  The reunions of three dissimilar vicious walkers , 1988 .

[49]  D. Torney,et al.  Diffusion-limited reaction rate theory for two-dimensional systems , 1983, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[50]  A. Jaffe,et al.  Statistical Physics and Dynamical Systems: Rigorous Results , 1985 .

[51]  Scaling properties of diffusion-limited reactions on fractal and euclidean geometries , 1991 .

[52]  Sander,et al.  Source-term and excluded-volume effects on the diffusion-controlled A+B-->0 reaction in one dimension: Rate laws and particle distributions. , 1989, Physical review. A, General physics.

[53]  Redner,et al.  Fluctuation-dominated kinetics in diffusion-controlled reactions. , 1985, Physical review. A, General physics.

[54]  West,et al.  Steady-state segregation in diffusion-limited reactions. , 1988, Physical review letters.

[55]  S. Redner,et al.  Universal behaviour of N-body decay processes , 1984 .

[56]  Reaction limited catalytic reaction in one dimension , 1992 .

[57]  Daniel ben-Avraham,et al.  Computer simulation methods for diffusion‐controlled reactions , 1988 .

[58]  J. T. Cox,et al.  Diffusive Clustering in the Two Dimensional Voter Model , 1986 .

[59]  Segregation in annihilation reactions without diffusion: Analysis of correlations. , 1989, Physical review letters.

[60]  R. Glauber.  Time‐Dependent Statistics of the Ising Model , 1963 .

[61]  Stanley,et al.  Scaling anomalies in reaction front dynamics of confined systems. , 1993, Physical review letters.

[62]  H. Larralde,et al.  Diffusion-controlled reaction, A+B→C, with initially separated reactants , 1992 .

[63]  Kopelman,et al.  Density of nearest-neighbor distances in diffusion-controlled reactions at a single trap. , 1989, Physical review. A, General physics.

[64]  H. Stanley,et al.  Novel dimension-independent behaviour for diffusive annihilation on percolation fractals , 1984 .

[65]  Finite-size 'poisoning' in heterogeneous catalysis , 1990 .

[66]  R. Kopelman,et al.  Reaction front dynamics in diffusion-controlled particle-antiparticle annihilation : experiments and simulations , 1990 .

[67]  Jiang,et al.  Simulation study of reaction fronts. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[68]  Krapivsky.  Kinetics of monomer-monomer surface catalytic reactions. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[69]  Taitelbaum.  Nearest-neighbor distances at an imperfect trap in two dimensions. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[70]  Kopelman,et al.  Exotic behavior of the reaction front in the A+B-->C reaction-diffusion system. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[71]  J. Bishop,et al.  Electron-hole recombination, disordered spins and the nearest-available-neighbour distribution , 1986 .

[72]  R. Ziff,et al.  Noise-induced bistability in a Monte Carlo surface-reaction model. , 1989, Physical review letters.

[73]  Stanley,et al.  "Random-force-dominated" reaction kinetics: Reactants moving under random forces. , 1992, Physical review letters.

[74]  P. ZhangYi-Cheng.  Equilibrium states of diffusion-limited reactions , 1987 .

[75]  Cornell,et al.  Role of fluctuations for inhomogeneous reaction-diffusion phenomena. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[76]  Leyvraz,et al.  Spatial structure in diffusion-limited two-species annihilation. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[77]  William M. Yen,et al.  Laser Spectroscopy of Solids , 1981 .

[78]  J. Tauc,et al.  Optical studies of excess carrier recombination in a-Si: H: evidence for dispersive diffusion , 1980 .

[79]  B. Chopard,et al.  Some properties of the diffusion-limited reaction nA + mB → C with homogeneous and inhomogeneous initial conditions , 1992 .

[80]  N. Agmon,et al.  Theory of reversible diffusion‐influenced reactions , 1990 .

[81]  Cornell,et al.  Steady-state reaction-diffusion front scaling for mA+nB--> , 1993, Physical review letters.

[82]  D. ben-Avraham,et al.  Statics and dynamics of a diffusion-limited reaction: Anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition , 1990 .

[83]  K. A. Pronin,et al.  Metastable states in diffusion-controlled processes , 1989 .

[84]  Kinetics of a monomer-monomer model of heterogeneous catalysis , 1992 .

[85]  A. A. Ovchinnikov,et al.  Role of density fluctuations in bimolecular reaction kinetics , 1978 .

[86]  Fractal clustering of reactants on a catalyst surface. , 1986, Physical review. B, Condensed matter.

[87]  Stanley,et al.  Reaction front for A+B-->C diffusion-reaction systems with initially separated reactants. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[88]  Kinetics of n-species annihilation: Mean-field and diffusion-controlled limits. , 1986, Physical review. A, General physics.

[89]  I. Campbell.  Catalysis at surfaces , 1988, Focus on Catalysts.

[90]  Sidney Redner,et al.  Scaling approach for the kinetics of recombination processes , 1984 .

[91]  Kopelman,et al.  Statistical properties of nearest-neighbor distances at an imperfect trap. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[92]  Sokolov,et al.  Diffusion-controlled reactions in lamellar systems. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[93]  ben-Avraham,et al.  Equilibrium of two-species annihilation with input. , 1988, Physical review. A, General physics.