Coupled concentration-charge dynamics in asymmetric 1:1 electrolytes, local transient response and fluctuations

TL;DR

This work investigates the coupled evolution of concentration and charge in asymmetric 1:1 electrolytes under diffusion asymmetry and external electric fields. By combining Brownian dynamics simulations with a linearized stochastic density functional theory, the authors derive closed-form expressions for the intermediate scattering matrix and predict two relaxation modes—a fast charge-relaxation mode and a slow ambipolar-diffusion mode—whose properties are tuned by the diffusion asymmetry $\gamma$ and the field strength. The study reveals field-induced modifications to screening, cross-correlations, and a bifurcation in relaxation behavior, with excellent quantitative agreement between SDFT and BD across a wide range of wave vectors and both equilibrium and non-equilibrium steady states. The results illuminate how diffusion asymmetry and external driving can tune electrolyte transport, offering a framework applicable to nanofluidics, energy harvesting, and iontronic circuits, and point to extensions including explicit solvent and hydrodynamics for more concentrated systems.

Abstract

We investigate the coupled dynamics of concentration and charge in asymmetric 1:1 electrolytes, focusing on the interplay between diffusion asymmetry and external electric fields. Using Brownian dynamics simulations and linearized stochastic density functional theory (SDFT), we analyze the transient response of charge and number currents to inhomogeneous electric fields, as well as the steady-state spatio-temporal fluctuations under uniform fields. Our results reveal that asymmetry in ionic diffusion coefficients introduces a non-trivial coupling between charge and number transport, which modifies the two relaxation modes already present in symmetric electrolytes -- a fast one associated with charge relaxation and a slow one linked to ambipolar diffusion. The dynamics are further modulated by the applied field, which enhances diffusion, alters screening lengths, and induces oscillatory behavior in the relaxation modes. The SDFT framework provides closed-form expressions for the intermediate scattering matrix, capturing the dynamics of density fluctuations and cross-correlations between number and charge. These predictions are validated by simulations, demonstrating excellent agreement across a wide range of wave vectors, both at equilibrium and under a finite electric field. Our findings highlight the critical role of diffusion asymmetry and external fields in tuning the transport properties of electrolytes, with implications for nanofluidic devices, energy harvesting, and iontronic circuits. This work bridges theoretical insights with practical applications, offering a robust framework for understanding and controlling electrolyte dynamics in asymmetric systems.

Figures (10)

• Figure 1: Overview of the present study of number and charge current fluctuations in electrolytes.
• Figure 2: (a) Charge current, $J_{Z}^{K_{E}}$, and (b) number current, $J_{N}^{K_{E}}$, normalized by the ideal Nernst-Einstein current $J^{\rm NE}$ (see Eq. \ref{['eq:JNE']}) and as a function of time normalized by the Debye relaxation time $\tau_\mathrm{D}$ (see Eq. \ref{['eq:taud']}), in response to the inhomogeneous electric field given by Eq. \ref{['eq:Ert_complex']}. Colored lines indicate the BD simulation results for reduced wave vectors $K_{E}=k_{E}/\kappa \in \left\{0.12, \, 0.5, \, 1, \, 2, \, 4\right\}$ (from dark red to dark blue), with shaded areas corresponding to 95% confidence intervals. Analytical SDFT predictions are also indicated as black lines, for electrolytes with symmetric ($\gamma=0$, solid lines) and asymmetric ($\gamma=0.5$, dashed lines) diffusion coefficients.
• Figure 3: Relative weights of the steady-state ($S_{ZZ}$), slow ($A_s$) and fast ($A_f$) contributions to the charge current, as a function of the reduced wave vector $k_{E}/\kappa$. Open (resp. filled) symbols indicate the weights obtained by fitting the BD results for the current to Eq. \ref{['eq:res_current']} for $\gamma=0$ (resp. $\gamma=0.5$). Solid (resp. dashed) lines indicate the predictions of SDFT for $\gamma=0$ (resp. $\gamma=0.5$). The errorbars correspond to one standard deviation of the fitted parameters, calculated from the covariance matrix of the regression fit.
• Figure 4: Elements of the static structure matrix $\hat{\boldsymbol{F}}(K,t=0)$ quantifying the static number-number ($F_{NN}$, blue), number-charge ($F_{NZ}$, green), charge-number ($F_{ZN}$, red) and charge-charge ($F_{ZZ}$, orange) correlations (see Eq. \ref{['eq:def_hat_F']}), as a function of the reduced wave vector $K=k/\kappa$. Open and filled symbols are results from BD simulations at equilibrium ($\mathcal{E}=0$) and at NESS under a constant uniform electric field with reduced magnitude $\mathcal{E}=1$, respectively. The corresponding SDFT predictions Eqs. \ref{['F_cc0']}-\ref{['F_zc0']} are shown as dashed (resp. solid) lines for $\mathcal{E}=0$ (resp. $\mathcal{E}=1$).
• Figure 5: Parametric plot in the complex plane (as a function of the reduced wave number $K=k/\kappa$) of the frequencies $\Omega_{s,f}(K)$ (defined in Eqs. \ref{['eq:Omega1']} and \ref{['eq:Omega2']}) characterizing the two modes of the coupled number and charge fluctuations. Arrows indicate decreasing wave vector $K\rightarrow0$, with filled and empty heads corresponding to $\Omega_s(K)$ (slow mode, closer to the origin of the complex plane) and $\Omega_f(K)$ (fast mode), respectively. The black filled and empty circles mark the "hydrodynamic" limits $\Omega_s(K\to0) = 0$ and $\Omega_f(K\to0) = i$ corresponding to salt diffusion and charge relaxation, respectively. The black lines correspond to equilibrium ($\mathcal{E} = 0$); the parametric plots for different values of asymmetry $\gamma$ overlap at equilibrium. The other curves correspond to NESS ($\mathcal{E} = 1$), with orange, blue, green and red for $\gamma = 0$, $0.02$, $0.1$, and $0.5$, respectively. The orange cross at $(0,\frac{1}{2}+\frac{1}{4\mathcal{E}^2})$ indicates the bifurcation point at wave vector $K^*=1/2\mathcal{E}$ (see Eq. \ref{['eq:k_crit']}) in the symmetric ($\gamma=0$) non-equilibrium case.