Ideal Polarized Interfaces with Limited Amount of Free Electric Charge Carriers

Many modern electrochemical applications use electrode-electrolyte interfaces for selective detection and quantification of chemicals or biological species. Electrodes can be fabricated from various materials such as metals, semimetals, semiconductors or doped dielectrics. Extremely thin (atomic) layers of metals or graphene as well as semiconductor materials contain a limited amount of electric charge carriers (electrons, holes). It will be shown that electrodes made of these substrates can exhibit unusual behavior that affects electrochemical characteristics of electrode-electrolyte interface. An exact expression for the differential capacitance of the electrode phase was derived. The suggested model expect a finite amount of electric carries in the matter, however, it describes classical metal-electrolyte interfaces as well. The electrolyte phase is described by the both classical Poisson-Boltzmann equation and distribution valid for compact ionic layers that are formed in concentrated electrolytes and/or under higher applied potentials. If both sides of the interface are treated together, one can determine the potential drops in the electrolyte and electrode phases. If the dynamics of electrode-electrolyte interface is not limited by the transport in an electrolyte, then various electrochemical characteristics of the interface can also be calculated. Recently, we proved that the theory is agreement with classical thermodynamic equations for the electrode-electrolyte interface. We believe that the presented work can be useful in trendy applications such as supercapacitor development, photocatalysis or electrochemical sensing of biological molecules.

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