Diffusion-controlled A+A⃗0 reaction of nonequilibrium states on a disordered linear-chain lattice

To investigate the kinetics of photoexcited states in MX chain compounds the diffusion-controlled irreversible reaction of A+A⃗0 on a disordered linear lattice is examined by numerical simulation, where A and 0 denote the photoexcited state and its annihilation, respectively. The lattice disorder is introduced by irregular energy barriers of which the height obeys a Gaussian distribution around a given value. As the irregularity evolves the survival probability S(ζ), ζ=N₀²Dt, of A is transformed from Torney-McConnell’s form or its modified one into the Kohlrausch form S(ζ)=exp[-(ζ/ζ_1/e)^β], so that S(ζ) becomes still more nonexponential, where N₀, D, and t are the initial density, diffusion coefficient, and reaction time, respectively. The argument β is reduced as if the fractal dimension of the lattice is reduced from unity. Concurrently, the parameter ζ_1/e increases, so that the 1/e decay time τ at a given temperature increases significantly. As long as, however, the mean height of the barriers remains unchanged, the temperature dependence of τ is not altered by the irregularity. The present results are consistent in various respects with the decay properties of long-lived solitons observed in degenerated MX chain compounds.