  Isolated, atomically thin conducting membranes of graphite, called graphene,
have recently been the subject of intense research with the hope that practical
applications in fields ranging from electronics to energy science will emerge.
Here, we show that when immersed in ionic solution, a layer of graphene takes
on new electrochemical properties that make it a trans-electrode. The
trans-electrode's properties are the consequence of the atomic scale proximity
of its two opposing liquid-solid interfaces together with graphene's well known
in-plane conductivity. We show that several trans-electrode properties are
revealed by ionic conductivity measurements on a CVD grown graphene membrane
that separates two aqueous ionic solutions. Despite this membrane being only
one to two atomic layers thick, we find it is a remarkable ionic insulator with
a very small stable conductivity that depends on the ion species in solution.
Electrical measurements on graphene membranes in which a single nanopore has
been drilled show that the membrane's effective insulating thickness is less
than one nanometer. This small effective thickness makes graphene an ideal
substrate for very high-resolution, high throughput nanopore based single
molecule detectors. Sensors based on modulation of graphene's in-plane
electronic conductivity in response to trans-electrode environments and voltage
biases will provide new insights into atomic processes at the electrode
surfaces.
