Quantum Rate Theory for Graphene

Abstract

The quantum rate theory predicts the electron transfer rate between quantum states governed by the ratio between the quantum conductance and capacitance (Phys. Chem. Chem. Phys. 2020, 22, 26109−26112). This rate is important not only for describing the quantumness of the electron transfer of electrochemical reactions but also for understanding electron transport in molecular electronics (Phys. Chem. Chem. Phys. 2020, 22 (19), 10828−10832). Additionally, this quantum rate principle is applicable for describing conductive and capacitive V-shapes of graphene (Carbon 2021, 184 821−827). In the present work, we demonstrate the relationship between the quantum rate theory for a single-layer graphene and the relativistic quantum mechanical theory of electrons according to the Dirac equation. As the merger of quantum mechanics and relativity theory, quantum rate theory is the key to analyzing quantum electrodynamics in two-dimensional structures (e.g., honeycomb-like carbon such as graphene) using an inexpensive benchtop electrochemical setup. In this study, the quantum rate model for graphene is introduced along with its applicability to the diffusionless electrochemical transport of electrons, as exemplified for molecular films comprising redox switches. This didactic approach demonstrates that the best means of conducting electron transport in graphene is the AC mode of electric current modulation, in which electric displacement current is imperative. A maximum quantum rate of electron transport occurs at the Dirac point, where net carrier concentrations are at their minimum, in contrast to the traditional DC mode of modulating conductance. This analysis opens an avenue of possibilities for fabricating quantum devices with electronic semiconducting accuracy, for example, biological sensors in complex environments.

Reagentless Quantum-Rate-Based Electrochemical Signal of Graphene for Detecting SARS-CoV-2 Infection Using Nasal Swab Specimens

“…Accordingly, to obtain τ or k signals of the aforementioned interface, we use time-dependent spectroscopic approaches, from which G and C q can be measured via the ratio between the potential or current perturbation and the response current or potential response. The perturbations can coincide (or not) with the internal quantum frequency response of the states within graphene, but in one or another case, τ or k can be obtained according to the rules predicted by eq . Accordingly, there are different frequency possibilities (each must be verified independently for each designed interface); however, in the present study, we focus on two different frequency regimes, namely, the equilibrium f e and resonant f r .…”

“…This impressive improvement in sensitivity when using graphene-based structures and temporal quantum transducer methods is a consequence of the unique quantum properties of graphene allied to the high quality of the chemical modification of the interface with an appropriate number of graphene layers (see Figure S1 for further details) and the appropriate coupling of the chemical structure of the receptors to the resonance characteristic time of the graphene-based structures. The transducer signal mechanism involved is theoretically supported by quantum-rate theory applied to graphene, as described in more detail in a previous study …”

“…In the present study, we used concepts within quantum-rate theory as applied to graphene to demonstrate, as a proof of concept, a new transducer methodology that, as shown in Figure , in addition to being extremely sensitive for quantifying proteins in serum, can also be applied qualitatively for the diagnosis of SARS-CoV-2 in highly complex biological samples obtained from nasal swabs. In contrast to the traditional DC GFET mode of operation, the transducer mechanism of a quantum-rate GFET is based on the existence of an intrinsic displacement current within the channel which induces time perturbation.…”

Quantum rate as a spectroscopic methodology for measuring the electronic structure of quantum dots

“…with the relativistic electrodynamics of graphene. 21 Note that origin of g e was introduced in the previous section and does not requires further additional analysis. These energy and electric current degeneracies imply that the electric current is ambivalent, as is the case of redox reaction dynamics 11 and the quantum electrodynamics of organic semiconducting compounds and graphene.…”

“…It has been experimentally demonstrated 11,15,16 that E = e 2 / C q is a degenerated state of energy for experiments conducted in an electrolyte environmental medium, such as that effectively E is E = g s g e (e 2 /hC q ), where g s is the electron spin degeneracy and g e is the energy degeneracy state associated with the electric-field screening effect of the electrolyte over the quantum states contained in molecules, 11 graphene, 8,21 as well as quantum dots (as will be demonstrated here).…”