FIG. 5.

The time-dependent rate coefficient for the irreversible reaction, given the initial distribution ρ(r, t = 0|eq) = Θ(r − a). The figure shows the time dependence of the rate coefficient $k_{\text{rate}}^{\rho =\Theta }\left(t\right)$ for various values of the association constant κ_r = 1, 2, 5, 10, 20. The other parameters are D = 1, a = 2. The solid lines are obtained from the analytical expression for $k_{\text{rate}}^{\rho =\Theta }\left(t\right)$ (Eq. (A3)). The dashed lines refer to the approximate solutions for short (Eq. (79)) and long times (Eq. (85)).