Diffusion-controlled $A+\overrightarrow{A}0$ 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 $A+\overrightarrow{A}0$ 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 $S\left(\zeta \right),$ $\zeta {=N}_0^{2}Dt,$ of A is transformed from Torney-McConnell’s form or its modified one into the Kohlrausch form $S\left(\zeta \right)=\exp \left[-\right(\zeta /{\zeta }_{1/e}{)}^{\beta }],$ so that $S\left(\zeta \right)$ becomes still more nonexponential, where $N_0,\hspace{0.5em}D,$ and t are the initial density, diffusion coefficient, and reaction time, respectively. The argument $\beta$ is reduced as if the fractal dimension of the lattice is reduced from unity. Concurrently, the parameter ${\zeta }_{1/e}$ increases, so that the $1/e$ decay time $\tau$ at a given temperature increases significantly. As long as, however, the mean height of the barriers remains unchanged, the temperature dependence of $\tau$ 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.