Mean First-Passage Time and Steady-State Transfer Rate in Classical Chains

Understanding excitation and charge transfer in disordered media is a significant challenge in chemistry, biophysics, and material science. We study two experimentally relevant measures for carrier transfer in finite-size chains, a mean first-passage time (MFPT) and the steady-state transfer time (SSTT). We discuss the relationship between these measures and derive analytic formulas for 1D chains. We exemplify the behavior of these time scales in different motifs: donor-bridge-acceptor systems, biased chains, and alternating and stacked copolymers. We find that the MFPT and the SSTT may administer different, complementary information on the system, jointly reporting on molecular length and energetics. Under constraints such as fixed donor-acceptor energy bias, we show that the MFPT and the SSTT are optimized (minimized) under fundamentally different internal potential profiles. This study brings insights into the behavior of the MFPT and the SSTT and suggests that it is beneficial to perform both transient and steady-state measurements on a conducing network so as to gather a more complete picture of its properties.