Applied Mathematics, University of Waterloo
Modeling the Interaction of Graphene with a Liquid Electrolyte
Graphene is a two dimensional sheet of hexagonally bonded carbon atoms with remarkable electronic properties. One of the applications of graphene is in an electrolytically gated field effect transistor, where the surface of graphene is in contact with a liquid electrolyte. These transistors can be used as biological and chemical sensors, with sensitivity to pH and ion concentration arising from the adsorption of ions to the graphene-electrolyte interface. There is a significant amount of experimental work measuring the capacitance and conductivity of these transistors, with very little theoretical background. This work first proposes a model for the capacitance, while taking into account the finite size of ions, dielectric saturation, and ionic polarization. This work next proposes a site-binding model, which will account for the bonding of protons (H+) and hydroxyl (OH-) groups, as well as salt ions, to the graphene interface. The site-binding model will give the sensitivity of the configuration to pH and ion concentration.