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Understanding excitation and charge transfer in disordered media is asignificant challenge in chemistry, biophysics and material science. We studytwo experimentally-relevant measures for carriers transfer in finite-sizechains, the trapping mean first-passage time (MFPT) and the steady statetransfer time (SSTT). We discuss the relationship between these measures, andderive analytic formulae for one-dimensional chains. We exemplify the behaviorof these timescales in different motifs: donor-bridge-acceptor systems, biasedchains, and alternating and stacked co-polymers. We find that the MFPT and theSSTT may administer different, complementary information on the system, jointlyreporting on molecular length and energetics. Under constraints such as fixeddonor-acceptor energy bias, we show that the MFPT and the SSTT are optimized(minimized) under fundamentally different internal potential profiles. Thisstudy brings insights on the behavior of the MFPT and the SSTT, and suggeststhat it is beneficial to perform both transient and steady state measurementson a conducing network so as to gather a more complete picture of itsproperties.

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