Bipolar electrodes provide a powerful
and versatile means of coupling
two or more spatially separated electrochemical reactions. While normally
described in terms of macroscopic rate equations, the ongoing drive
toward the miniaturization of bipolar electrodes means that new regimes
are becoming accessible where stochasticity and the discreteness of
the electronic charge become relevant or even dominant. Here we explore
using both numerical simulations and analytical theory the behavior
of bipolar electrodes with nanoscale dimensions. We focus in particular
on the possibility of achieving single-molecule-level synchronization
between the two poles of a bipolar electrode, which would dramatically
extend the range of applicability of single-molecule electrochemistry.
We conclude that, while possible, fundamental limits on the potential
dependence of electron-transfer rates dictate that this will only
be achieved in the smallest (less than 10 nm) bipolar nanoelectrodes.
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