  In this work we present and discuss theoretical models of redox molecular
junctions that account for recent observations of nonlinear charge transport
phenomena, such as hysteresis and hysteretic negative differential resistance
(NDR). A defining feature in such models is the involvement of at least two
conduction channels - a slow channel that determines transitions between charge
states of the bridge and a fast channel that dominates its conduction. Using
Marcus theory of heterogeneous electron transfer (ET) at metal-molecule
interfaces we identify and describe different regimes of nonlinear conduction
through redox molecular bridges, where the transferring charge can be highly
localized around the redox moiety. This localization and its stabilization by
polarization of the surrounding medium and/or conformational changes can lead
to decoupling of the current response dynamics from the timescale of the
voltage sweep (that is, the current does not adiabatically follow the voltage),
hence to the appearance of memory (thermodynamic irreversibility) in this
response that is manifested by hysteresis in current-voltage cycles. In
standard voltammetry such irreversibility leads to relative shift of the
current peaks along the forward and backward voltage sweeps. The common origin
of these behaviors is pointed out and expressions of the threshold voltage
sweep rates are provided. In addition, the theory is extended (a) to analyze
the different ways by which such phenomena are manifested in single sweep
cycles and in ensemble averages of such cycles, and (b) to examine quantum
effects in the fast transport channel.
