Electron-electrolyte coupling in AC transport through nanofluidic channels

Abstract

The transport properties of nanofluidic channels are usually studied under constant (DC) voltage or pressure driving. However, the frequency response under sinusoidal (AC) drivings offers rich insights into the time-dependent transport mechanisms. Inspired by recent electrochemical approaches, we investigate the couplings between ionic and electronic transport under AC driving. We show that conduction electrons of the channel walls participate in ionic current via capacitive electrochemical coupling, defining a critical frequency and length scale where electron-dominated conductivity emerges. We further analyze how electron-ion coupling modifies electro-osmotic flows, and demonstrate that fluctuation-induced momentum transfer between the electrolyte and wall electrons produces distinct AC transport signatures depending on the charge carrier polarity. Altogether, we establish a frequency-dependent transport matrix that couples ionic, electronic and hydrodynamic flows. These findings establish AC nanofluidic transport as a powerful probe of interfacial phenomena under confinement, and suggest new directions for engineering nanofluidic functionalities through electron-electrolyte coupling.

Figures (5)

• Figure 1: Model(a) Schematic of the system: an AC ionic current and an AC hydrodynamic flow are driven through a nanochannel with electrically conducting walls by an AC ionic voltage drop and an AC pressure drop. (b) Schematic of the solid-liquid interface: Coulomb interactions couple ions in the electrolyte to electrons in the channel wall. (c) Sketch of the transport matrix of the system. The nanofluidic sector corresponds to the properties investigated in nanofluidic experiments in which we want to integrate the electronic degrees of freedom of the conducting wall. The electrochemical sector corresponds to the properties traditionally investigated in electrochemistry.
• Figure 2: Capacitive effects of the conducting wall on ionic transport.(a) Equivalent electronic circuit of the system: the ionic and electronic paths are connected by the continuous interfacial capacitor. (b) Typical result for the current in the ionic ($J(x)$) and electronic ($1-J(x)$) paths as a function of the normalized position $x/L$ along the channel. The current is exchanged between the two paths over a typical length scale $\ell$, which is indicated by the vertical lines. (c) Exchange length $\ell$ as a function of the frequency $\omega/2\pi$ for different confinements $h$. Here, $\mathcal{C}_{\rm EDL}=$ 20 $\mu$F/cm$^2$, $c_s=1$ M, $D_{\rm i}=5\cdot 10^{-9}$ m$^2$/s and the electronic resistivity is $R_\textnormal{e} W/L=$ 10 k$\Omega$. (d) Critical frequency for opening the electronic path, as a function of the nanochannel confinement $h$ and for different nanochannel lengths $L$. (e) Real and imaginary parts of the equivalent impedance $Z$ of the system as a function of frequency, assuming a nanochannel length $L=100$$\mu$m, confinement $h=$ 10 nm, interfacial capacity $\mathcal{C}_{\rm EDL}=$ 20 $\mu$F/cm$^2$, salt concentration $c_s=1$ M, ionic diffusivity $D_{\rm i}=5\cdot 10^{-9}$ m$^2$/s and electronic resistivity $R_\textnormal{e} W/L=$ 10 k$\Omega$. (f) Current amplification, defined as the ratio of the electric current in the presence and in the absence of the electronic path, as a function of the frequency, for varying interfacial capacities $\mathcal{C}_{\rm EDL}$. (g) Current amplification as a function of the confinement $h$, for varying frequencies as well as the high frequency limit.
• Figure 3: AC conduction through a clogged channel.(a) Schematic of a clogged channel, where direct ionic conduction between the two ionic electrodes is blocked. The main path taken by the AC current is represented. (b) Impedance of the system with the same parameters as in Fig. \ref{['fig2']}.
• Figure 4: Nanofluidic impedances with conducting walls. We consider a channel where transport is dominated by surface charge (Du $\gg 1$) and slippage ($b\gg h$), of height $h=10$ nm, width $W= 1 \mu$m and length $L=100 \mu$m, with interfacial capacity $\mathcal{C}_{\rm EDL}=$ 20 $\mu$F/cm$^2$, ionic diffusivity $D_{\rm i}=5\cdot 10^{-9}$ m$^2$/s, electronic friction $\xi_{\rm e}=10^{-13}$ kg/s, bare hydrodynamic friction coefficient $\lambda_{\rm h} = 10^{4}$ Pa.s/m, van der Waals friction coefficient $\lambda_{\rm he}=10^4$ Pa.s/m and a solid with a charge density $n_{\rm e}=-10^{14}e$/cm$^2$ and a bare electronic resistivity $R_\textnormal{e} W/L=$ 10 k$\Omega$Coquinot2024. (a)-(b) Ionic impedance $Z_\textnormal{i}$ normalized by its DC value $R_\textnormal{i}$ as a function of frequency for various surface charges. (c)(d) Hydrodynamic impedance $Z_\textnormal{h}$ normalized by its DC value $R_\textnormal{h}$ as a function of frequency for various surface charges. (e)-(f) Electro-osmotic impedance $Z_\textnormal{EO}$ normalized by its DC value $|R_\textnormal{EO}|$ as a function of frequency for various surface charges. We have set Coulomb drag cross-terms to zero ($R_\textnormal{ie}=R_\textnormal{he}=0$) in the first row and restored them in the second row of plots.
• Figure 5: Nanofluidic transport with conducting walls. Same system parameters than in Fig. \ref{['fig4']}. (a) Low and high frequency ionic conductance $G_{\rm i}$ of the channel as a function of the surface charge. In the absence of Coulomb drag ($R_\textnormal{ie}=R_\textnormal{he}=0$) the conductance is identical at low frequency and corresponds to the dashed green line at high frequency. (b) Low and high frequency permeance $\mathcal{L}_\textnormal{h}$ of the channel as a function of the surface charge. (c) Low and high frequency electro-osmotic mobility $\mu_{\rm EO}$ of the channel as a function of the surface charge. For (b)-(c) the transport coefficient is independent of frequency in the absence of Coulomb drag and corresponds to the low-frequency limit. The stars indicate the low surface charge limit obtained from the bulk transport resistances in Eq. \ref{['resistances-bulk']}, with $c_s= 1$ mM, and including the hydrodynamic Coulomb drag in (c).