FIG. 9.
Probability of two particles having associated between times 0 and t, given they were separated by a distance r0 initially. Results for the exact propagator are shown as black dashed lines (Eq. (27)). The binding radius is σ = 1 nm. The probabilities of association were gathered from 106 simulation trajectories with Δt = 0.1 μs. Set of D values considered was 0.05, 0.5, 5 nm2 μs−1. (a) Results are shown for ka = 1 nm2 μs−1 and three r0 (σ, (σ + Rmax)/2, Rmax) choices. (b) Results are shown for the absorbing boundary condition (ka = ∞) and three r0 ((σ + Rmax)/3, (σ + Rmax)/2, Rmax) choices. Large insets show the differences between results of Eq. (27) and simulations. Trajectory overlap issues can result in simulated association values slightly lower than exact, for reactions where D becomes very slow and ka is large. Small insets compare the maximum error made for the same respective parameters used in 2D and 3D simulations within 20 μs.