Introduction to Fundamental Concepts

Common Principles of Molecular Electronics and Nanoscale Electrochemistry

“…Briefly, R ct is defined in electrochemistry as resistance to the transfer of electrons from one phase (metallic electrode, for instance) to another (for example, a molecular gate, as illustrated in Figure a). In ref , note that C μ̅ = G / k is the expected response of an ensemble of molecules assembled in an electrode, comprising a molecular film, as displayed in Figure a. , The response that confirms the interdependence of electrochemical capacitance, quantum of conductance and electron transfer through the definition of C μ̅ = G / k is shown in Figure for alkane molecular films . Also interesting is the correspondence of C μ̅ with the first-principles density functional theory that was recently postulated, , allowing electrochemical events to be rationalized within an approach of conceptual quantum chemistry and first principle quantum mechanics …”

“…This obviously corresponds to the time-scale of the electrochemical reaction conforming to a single electron transfer such as , where k is the well-known electron transfer rate constant. Equation is validated in ref and thus represents the quantum RC circuit model for electrochemistry at room temperature. The temperature obviously introduces broadening effects that can be explained using statistical thermodynamics.…”

“…(a) Molecules assembled on an electrode, forming a molecular film embedded in an electrolyte. This situation can be modeled by an ensemble of individual quantum point contacts (see more details in ref ). (b) This is the expected thermal broadening given by [see also eq ].…”

“…Equation thus connects the electron transfer rate and the quantum of conductance concepts in such a way that renders electron transfer and transport totally interchangeable through the microscopic accessing of C μ̅ . Figure shows (see ref for a demonstration) that an ensemble of individual quantum point contacts exemplified by ideally individual h /2 e 2 and C q,n components, associated in series, provides an average response that is a series association encompassing the individual elements to provide R q and C μ̅ as universal elements representing, for instance, the experimental response of electroactive molecular films. This is the response obtained experimentally by impedance spectroscopy measurements. − ,,, In other words, the quantum equivalent RC circuit of the ensemble is depicted as the series combination of R q and C μ̅ elements, which globally provides an electron transfer rate of k = ( R q C μ̅ ) −1 , as shown in Figure c.…”

“…(a) An individual quantum point contact structure comprising a molecular chemical capacitor, C μ , assembled on an electrode and electronically coupled through quantum channels; (b) the same as in part a but within the point contacts immersed in an electrolyte environment. In the inset, note how this pictorial approach couples with perturbation theory, C μ̅ (ω) = d q (ω)/d V (ω), as detailed in ref .…”