A Predictive Theory of Electrochemical Ostwald Ripening for Electrodeposited Lithium Metal

TL;DR

The work presents a predictive theory for electrochemical Ostwald ripening during non-dendritic Li metal electrodeposition by embedding SEI and electrolyte resistances into a Barton-type overpotential framework. A unified, dimensionless growth law $v_{\rho}=\frac{d\rho}{d\tau}=\frac{1}{\Re+\omega\rho}\left(\frac{1}{\rho_s}-\frac{1}{\rho}\right)$, together with a continuity equation and mass-balance constraint, reveals a transition between 2D SEI-limited and 3D electrolyte-limited growth and yields analytical expressions for nucleus size, density, and distribution. The model quantitatively links plating conditions (including $R_{SEI}$, wettability $\theta$, and current density $i$) to deposit morphology and Coulombic efficiency, with two asymptotic regimes: a 2D ripening scenario where distributions broaden and $N$ scales as $\sim i/\sqrt{\tau}$, and a 3D ripening regime where the distribution collapses to a delta function while $\rho$ grows as $\sim (j\tau/\nu)^{1/3}$. Validation against experimental datasets (including Arrhenius fits for $R_{SEI}$ with $E_A=32$ kJ/mol) demonstrates strong agreement for nucleus sizes, distributions, and their relation to Coulombic efficiency, supporting broad applicability to metal electrodeposition beyond Li. The framework provides actionable insights for optimizing plating protocols to enhance battery lifetime by controlling SEI resistance, current density, and wettability.

Abstract

Electrode morphology critically determines the stability and efficiency of lithium metal anodes, yet no predictive framework has explained how measurable parameters control deposition. Here we introduce the first theoretical model of electrochemical Ostwald ripening, capturing the competition between electroplating and surface-energy-driven redistribution and identifying it as the governing process behind morphology evolution in the non-dendritic regime. The framework explicitly incorporates SEI resistance, electrolyte conductivity, electrode wettability, and current density revealing the transition from 2D SEI-limited to 3D electrolyte-limited growth. The model yields analytical expressions for nucleus size, density and distribution that quantitatively reproduce independent experimental results and establishes a direct link between plating conditions, morphology, and Coulombic efficiency. By providing experimentally accessible relationships between key parameters and deposition outcomes, the framework enables predictive understanding of lithium plating and provides a broadly applicable basis for controlling electrodeposition morphology across diverse electrochemical systems.

Figures (7)

• Figure 1: Ostwald ripening framework mediating the influence of key factors on lithium morphology. The central sequence illustrates the evolution from an initially broad distribution of small nuclei to a final morphology dominated by larger ones, highlighting the growth of larger nuclei at the expense of smaller ones.
• Figure 2: Comparison of 2D and 3D behavior in constant-current electrochemical Ostwald ripening. (a) Phase diagram showing the 2D/3D and no ripening regimes. The left and right dotted line mark approximate nuclei sizes at nucleation and at full coverage. (b) Time evolution of average nucleus size ($\langle r \rangle$, top), and nucleation density ($N$, bottom) in both 2D and 3D regimes. (c) Shape parameter ($v/s$) as a function of contact angle ($\theta$). Inset: Comparison of $\langle r \rangle$ (in units of ${V_m}/{F} \sqrt{{\sigma R_{SEI}S_{tot}}}$ from Eq. \ref{['eq_r_2D']}) for two different contact angles. (d) Time evolution of the nucleus size distribution: initially following the $f^\infty_{2D}$ profile, the system gradually transitions to a 3D regime with a narrowing distribution. Different time steps are color-coded; insets illustrate the evolving surface coverage.
• Figure 3: Comparison of model predictions (Eqs.\ref{['eq_n_2D']}-\ref{['eq_r_cov']}) with experimental data. (a) Nucleus radii ($r$) at different temperatures ($T$) Wang2019 are shown as red squares. Temperature-dependent variations in $R_{\mathrm{SEI}}$ were obtained via Arrhenius fit of measured values (see Section \ref{['sec_exp_fit']}). Blue squares represent nucleus radii at different current densities ($i$) and deposited charges Pei2017. (b) Experimental nucleus size distribution extracted from a large-area SEM image (Fig.S6(a)Pei2017) is shown as a bar plot; the red line depicts the theoretical 2D distribution $f^\infty_{2D}$ (Tab.\ref{['tab_1']}). (c) Experimentally measured coulombic inefficiency (1-CE) Wang2019 vs. calculated $1/r_{cov}$ (Eq. \ref{['eq_r_cov']}).
• Figure S1: Flow diagram of the rescaled nucleus size $z$ as governed by Eq. \ref{['seq_of_motion_z_2D']}. Arrows indicate the direction of $v(z, \gamma)$ for different values of $\gamma$. The orange line denotes the unstable (repelling) fixed point $z_-$, while the blue line marks the stable (attracting) fixed point $z_+$.
• Figure S2: Upper bounds of the function $v(z)$ for the case $\gamma < 2$. For $z < z^*$, $v(z) \leq v_{\mathrm{max}}$, whereas for $z > z^*$, $v(z) \leq \gamma - \tfrac{1}{2}z$.