Electronic origin of reorganization energy in interfacial electron transfer

Abstract

Electron transfer (ET) reactions underpin energy conversion and chemical transformations in both biological and abiological systems. The efficiency of any ET process relies on achieving a desired ET rate within an optimal driving force range. Marcus theory provides a microscopic framework for understanding the activation free energy, and thus the rate, of ET in terms of a key parameter: the reorganization energy. For electrified solid-liquid interfaces, it has long been conventionally understood that only factors in the electrolyte phase are responsible for determining the reorganization energy and the electronic density of states (DOS) of the electrode serves only to dictate the number of thermally accessible channels for ET. Here we show instead that the electrode DOS plays a central role in governing the reorganization energy, far outweighing its conventionally assumed role. Using atomically layered heterostructures, we tune the DOS of graphene and measure outer-sphere ET kinetics. We find the ensuing variation in ET rate arises from strong modulation in a reorganization energy associated with image potential localization in the electrode. This work redefines the traditional paradigm of heterogeneous ET kinetics, revealing a deeper role of the electrode electronic structure in interfacial reactivity.

Figures (3)

• Figure 1: Electrochemistry of MLG-hBN-crystalline donor/acceptor heterostructures.(a) Schematic illustrations of electrochemical measurement at MLG surfaces using SECCM (b) Optical micrograph of a device fabricated from an exfoliated monolayer graphene flake on hBN and RuCl$_3$. (c) Representative steady-state voltammograms of 2 mM Ru(NH$_3$)$_6^{3+}$, depicting the mean current from the forward and backward sweeps, in 0.1 M KCl solution obtained at gold, graphite and MLG-hBN heterostructures (with and without $\alpha$-RuCl$_3$). Scan rate: 100 mV s$^{-1}$. (d) 2D displacement hexagon legend for the displacement field maps in c and dDependence of the interfacial ET rate constant, $k^0$, on the thickness of hBN spacer between MLG and RuCl$_3$ (crystalline acceptor) or WSe$_2$ (crystalline donor). Each data point represents the mean of multiple measurements for samples with a given hBN thickness; error bars indicate the standard deviation for each $k^0$ where n varies from $3-6$.
• Figure 2: RuCl$_3$ induced doping in MLG and quenching of hBN fluorescence(a) Top: Raman G-peak spectra of MLG/hBN, MLG/WSe$_2$, and MLG/$\alpha$-RuCl$_3$ heterostructures. Bottom: G-peak spectra of MLG/hBN/$\alpha$-RuCl$_3$ heterostructures with varying hBN thickness. Solid lines indicate Voigt fits from which peak positions are obtained. (b) Hall resistance, R$_{xy}$, as a function of magnetic field at 1.8 K for three hBN thicknesses in MLG/hBN/$\alpha$-RuCl$_3$ heterostructure devices, compared to undoped MLG. (c) Absolute carrier density in MLG, $\vert n \vert$, as a function of hBN spacer thickness in MLG/$\alpha$-RuCl$_3$, derived from Raman G-peak shifts (circles) and Hall measurements (squares), compared to $\vert n \vert$ predicted first-principles calculations (dashed black line, Bokdam2013). A polynomial fit (solid red line) phenomenologically models the sub-20 nm regime where enhanced doping deviates from classical screening, due to defect-mediated charge transfer. Error bars indicate the standard deviation for each $|n|$ where the number of data points for each $|n|$ varies from $6-10$. (d) Schematic illustration of band alignment and interfacial charge transfer between graphene and $\alpha$-RuCl$_3$, depicting ${E_{\mathrm{F}}}$ shifts and corresponding DOS modifications. $W_\mathrm{Redox}$ denotes redox molecule probability distributions ($W_\mathrm{Ox}$: oxidized; $W_\mathrm{Red}$: reduced). (e) Illustration of the experimental setup for liquid-induced fluorescence measurements in hBN/$\alpha$-RuCl$_3$ heterostructures. (f) hBN emitter density vs. illumination time in regions with (violet) and without (teal) $\alpha$-RuCl$_3$. Inset: Wide-field fluorescence image (561 nm laser, $\sim$5 kW cm$^{-2}$, 6 ms exposure). Scale bar: 5 $\mu m$.
• Figure 3: DOS-dependent electrode polarization and charge-transfer kinetics.(a) Standard charge-transfer rate constants ($k^0$) as a function of $\mu$, normalized to the standard rate constant at undoped graphene ($k^{0\prime}$). Experimental data (symbols) compared to model using fixed $\lambda$ (red dotted line) and $\lambda(\mu)$ derived from $\ell_\mathrm{TF}$ (red solid line). Error bars indicate the standard deviation for each $k^0$ where n varies from $3-6$. (b) Simulated polarization response of the electrode upon switching the charge state of a redox ion. The redox ion is positioned at a fixed distance of 5 Å above the electrode surface in the z-direction. Polarization magnitude is visualized using an exponential color scale. (c) Reorganization energy ($\lambda$) as a function of DOS and chemical potential ($\mu$). Left Inset: Free energy surfaces of electron transfer for [Ru(NH$_3$)$_6$]$^{3+/2+}$ redox couple for $\mu$ = 0 eV (solid gray), 0.05 eV (dotted magenta), and 0.5 eV (dashed blue). Right Inset: $\ell_\mathrm{TF}$ vs. $\mu$, calculated from DOS.