On the relationship between the mean first-passage time and the steady state transfer rate in classical chains

TL;DR

This paper explores the relationship between mean first-passage time and steady state transfer rate in classical chains, providing analytic formulas and analyzing their behavior in various molecular systems to enhance understanding of charge transfer processes.

Contribution

It derives analytic formulas linking MFPT and SSTT in one-dimensional chains and compares their behavior across different molecular motifs, revealing their complementary insights.

Findings

MFPT and SSTT provide different, complementary information.

Optimal internal potential profiles differ for MFPT and SSTT under fixed bias.

Both transient and steady state measurements are beneficial for characterizing transfer networks.

Abstract

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 carriers transfer in finite-size chains, the trapping mean first-passage time (MFPT) and the steady state transfer time (SSTT). We discuss the relationship between these measures, and derive analytic formulae for one-dimensional chains. We exemplify the behavior of these timescales in different motifs: donor-bridge-acceptor systems, biased chains, and alternating and stacked co-polymers. 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 on 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.