  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.
