Electrochemical Shot Noise of a Redox Monolayer

Redox monolayers are the base for a wide variety of devices including high-frequency molecular diodes or biomolecular sensors. We introduce a formalism to describe the electrochemical shot noise of such a monolayer, confirmed experimentally at room temperature in liquid. The proposed method, carried out at equilibrium, avoids parasitic capacitance, increases the sensitivity, and allows us to obtain quantitative information such as the electronic coupling (or standard electron transfer rates), its dispersion, and the number of molecules. Unlike in solid-state physics, the homogeneity in energy levels and transfer rates in the monolayer yields a Lorentzian spectrum. This first step for shot noise studies in molecular electrochemical systems opens perspectives for quantum transport studies in a liquid environment at room temperature as well as highly sensitive measurements for bioelectrochemical sensors.

Figure 1

Illustration of current and noise versus time and voltage, considering a slow scan rate compared to the electron transfer rates ($k_{\mathrm{sum}}\gg 1/t_{\mathrm{step}}$). (a) $I$ vs $E$, with the evolution of $I$ as the time after voltage step is increased. (b) Voltnoisograms (PSD vs $E$) taken at low frequency [Eq. (8)] corresponding to the same conditions as in (a). (c) Sampled staircase voltammetry example, with the raw current data (black dots), a double exponential decay fit of the current (red), and the voltage steps (yellow). In this example, each voltage step is of 2.25 mV, starting at 195 mV. (d) Raw currents subtracted with exponential fits (blue). (e) PSD spectrum of one current time trace in (d).

Figure 2

Example of current CVs obtained at different $\nu$ (electrode area $\approx 45{\mathrm{mm}}^2$, $E$ vs Ag/AgCl (3 M NaCl), electrolyte: $[{\text{NaClO}}_4]=0.5\mathrm{M}$).

Figure 3

(a) PSD of the current versus $E$ obtained at different $\nu$, at $f\approx 20\mathrm{Hz}$. (b) PSD at $f\approx 20\mathrm{Hz}$ and $E=0.35\mathrm{V}$ versus $\nu$.

Figure 4

(a) CV of a ${\mathrm{FcC}}_{11}\mathrm{SH}$ SAM on gold. (b) PSD measured at $0.014\mathrm{mV}/\mathrm{s}$ at $E<E^0$, $E\approx E^0$, and $E>E^0$. (c) PSD versus potential at 10 Hz. The dashed line is fitted using Eq. (7) considering a lognormal distribution of $H$ with $\sigma =3.97\%$ of the mean value of $H$.