Nonexponentiality of time dependent survival probability and the fractional viscosity dependence of the rate in diffusion controlled reactions in a polymer chain

Brownian dynamics (BD) simulations have been carried out for the time dependent survival probability [Sp(t)] of donor–acceptor pairs embedded at the two ends of an ideal polymer chain. Long distance fluorescence resonance energy transfer (FRET) between the donor and the acceptor is assumed to occur via the Forster mechanism, where the transfer rate k(R) is a function of the distance (R) between the donor and acceptor. For the Rouse chain simulated here, k(R) is assumed to be given by k = kF/[1 + (R/RF)6], where kF is the rate in the limit of zero separation and RF is the Forster radius. The survival probability displays a strong nonexponential decay for the short to intermediate times when RF is comparable to RM [distance at which the R2P(R) is maximum]. The nonexponentiality is also more prominent in the case of highly viscous polymer solutions. It is predicted that the FRET rate can exhibit a fractional viscosity dependence. This prediction can be tested against experiments. We have also compared the BD simulation results with the predictions of the well-known Wilemski–Fixman (WF) theory at the level of survival probability. It is found that the WF theory is satisfactory for the smaller RF values (where the rate is small). However, the agreement becomes progressively poorer as the Forster radius is increased. The latter happens even at intermediate strengths of kF. The present results suggest the need to go beyond the WF theory.