Measuring Quantum Capacitance in Energetically Addressable Molecular Layers

Abstract

The Fermi level or electrochemical signature of a molecular film containing accessible orbital states is ultimately governed by two measurable series energetic components, an energy loss term related to the charging of appropriately addressable molecular orbitals (resonant or charge transfer resistance), and an energy storage or electrochemical capacitance component. The latter conservative term is further divisible into two series contributions, one being a classic electrostatic term and the other arising from the involvement and charging of quantized molecular orbital states. These can be tuned in and out of resonance with underlying electrode states with an efficiency that governs electron transfer kinetics and an energetic spread dependent on solution dielectric. These features are experimentally resolved by an impedance derived capacitance analysis, a methodology which ultimately enables a convenient spectroscopic mapping of electron transfer efficacy, and of density of states within molecular films.

Capacitance spectroscopy and density functional theory

“…We have previously shown that this enables a quantification of an electron chemical (redox) capacitance and its associated quantum components within energetically addressable molecular films, 2,3 and that these charging characteristics, in the past loosely ascribed to ''pseudo capacitance'' (or faradaic capacitance), 4 represent a specific manifestation of the general mesoscopic capacitance 5,6 principles introduced by Marcus Buttiker. We have previously shown that this enables a quantification of an electron chemical (redox) capacitance and its associated quantum components within energetically addressable molecular films, 2,3 and that these charging characteristics, in the past loosely ascribed to ''pseudo capacitance'' (or faradaic capacitance), 4 represent a specific manifestation of the general mesoscopic capacitance 5,6 principles introduced by Marcus Buttiker.…”

“…We have previously shown that this enables a quantification of an electron chemical (redox) capacitance and its associated quantum components within energetically addressable molecular films, 2,3 and that these charging characteristics, in the past loosely ascribed to ''pseudo capacitance'' (or faradaic capacitance), 4 represent a specific manifestation of the general mesoscopic capacitance 5,6 principles introduced by Marcus Buttiker. 2,3,5,6 We note that this resembles concepts introduced by Serge Luryi 1 is his consideration of quantum capacitance in devices comprising an interphase boundary between a metal and a two-dimensional electron gas i.e., not a redox/electroactive configuration 5,6 in which quantum capacitance was not theoretically associated with any electron chemical potential variation. 2,3,5,6 We note that this resembles concepts introduced by Serge Luryi 1 is his consideration of quantum capacitance in devices comprising an interphase boundary between a metal and a two-dimensional electron gas i.e., not a redox/electroactive configuration 5,6 in which quantum capacitance was not theoretically associated with any electron chemical potential variation.…”

“…7 This electron chemical capacitance is redox (faradaic) capacitance (C r ) where energetic donor-acceptor states are associated with reduced and oxidized chemical states in the molecular film, arising specifically from the coupling of a supporting electrode density of states [g m (E)] to the redox site molecular density of states [g r (E)]. 5, 6 We have shown that C r is comprised of two distinct series contributions thus 1/C r = 1/C e + 1/C q (see Fig. It is also resolved free of nonfaradaic capacitive components, i.e.…”

“…It is also resolved free of nonfaradaic capacitive components, i.e. 5,6 In contrast with molecular electronic (conductance) measurements, where, in general, molecules of interest must bridge between two biased electrodes, CS constitutes a frequency-dependent single probe measurement. 5, 6 We have shown that C r is comprised of two distinct series contributions thus 1/C r = 1/C e + 1/C q (see Fig.…”

“…those not associated with redox state occupancy. 2,5,6 In this approach, since the electronic density of states in the metal is much higher than that associated with the addressable redox states of the molecule, it follows that variations in voltage impact the latter to a much greater extent such that C r p e 2 g r (E). 3a), where C e is the electrostatic or geometrical capacitance arising from charge separation in the normal (classical) sense and C q the quantum capacitance, arising very specifically from the chemical potential changes associated when charging a nanoscale (atomic/molecular scale) entity.…”