Thermodynamic effects of solid electrolyte interphase formation from solvation and ionic association in water-in-salt electrolytes

1. Problem Statement

Water-in-Salt Electrolytes (WiSEs), particularly those with high concentrations (e.g., 21 m LiTFSI), have emerged as promising next-generation electrolytes for lithium-ion batteries due to their expanded electrochemical stability window (ESW) and improved safety compared to dilute aqueous electrolytes. However, understanding the fundamental mechanisms behind this stability and the formation of the Solid Electrolyte Interphase (SEI) remains challenging.

Key challenges include:

• Complexity of the Interface: SEI formation occurs at the solid-liquid interface where electron transfer and reactions happen. Conventional atomistic modeling (like DFT) is computationally expensive for these large, complex systems, especially near the interface.
• Lack of Predictive Theory: Existing theories often fail to consistently link the coordination environments (solvation and ionic associations) of ions in the bulk and at the Electric Double Layer (EDL) to thermodynamic stability and reaction kinetics.
• Gap in High-Concentration Modeling: While theories exist for lower concentrations, the specific thermodynamic and structural properties of the 21 m LiTFSI WiSE (a gel-phase system) at electrified interfaces had not been rigorously validated against atomistic simulations using a unified analytical framework.

2. Methodology

The authors developed and applied a thermodynamic theory of hydration and ionic associations within the EDL, validated against Molecular Dynamics (MD) simulations.

• Theoretical Framework:

  • Model: The system is treated as an incompressible lattice gas comprising cations ($+$), anions ($-$), and water ($0$).
  • Associations: The theory accounts for thermoreversible associations between cation-anion and cation-water (ignoring weaker anion-water/water-water associations). It utilizes a Cayley tree cluster assumption to describe polydisperse aggregates.
  • Free Energy Functional: A free energy functional ($F$) is constructed including electrostatic contributions, ideal entropy of clusters, binding energies, configurational entropy, and gel-phase contributions.
  • Sticky-Cation Approximation: To handle the singularity where the cation solvation shell is full ($p_{+0} + p_{+-} \approx 1$), a "sticky-cation" approximation is employed, simplifying the mass action laws.
  • EDL Equations: The theory derives a modified Poisson-Boltzmann equation coupled with Boltzmann closure relations to establish equilibrium between the bulk and the EDL. A charge rescaling parameter ($\alpha$) is introduced to account for correlations beyond mean-field theory.

• Simulation & Validation:

  • MD Simulations: The authors utilized constant-charge MD simulations of 21 m LiTFSI WiSE (from previous work) to generate ground-truth data for the EDL structure at both negative (anode) and positive (cathode) electrodes.
  • Parameterization: The theory was parameterized using bulk MD data (association probabilities, volume fractions, and association constants).
  • Comparison: Theoretical predictions for volume fractions, cluster distributions, and association probabilities were compared against MD simulation results.

3. Key Contributions

1. Unified Theory for WiSEs: Extended the thermodynamic theory of ionic associations to the 21 m LiTFSI WiSE regime (gel phase), successfully solving the complex system of equations using Boltzmann closure relations.
2. Validation at the Interface: Provided the first rigorous qualitative validation of this analytical theory against atomistic MD simulations for the EDL of a high-concentration WiSE, capturing trends in species distribution and coordination environments.
3. Linking Structure to Reactivity: Established a direct formalism linking solvation/ionic aggregation to thermodynamic activity and reaction kinetics. This bridges the gap between microscopic coordination and macroscopic electrochemical stability.
4. Generalizability: Demonstrated that the formalism can be generalized to other electrolyte systems (e.g., ionic liquids, solvent-in-salt, Na-ion) by adjusting association constants and functionalities.

4. Key Results

A. EDL Structure and Composition

• Negative Electrode (Anode):
  • Simulation: Shows oscillations in species distribution, with anions depleted in the Helmholtz region and two distinct layers of $Li^+$ separated by a water layer.
  • Theory: Qualitatively captures the monotonic decay of anions and accumulation of cations/water in the diffuse layer. It correctly predicts the formation of a percolating ionic network (gel) in the bulk that breaks down near the interface.
  • Discrepancy: The theory (a local density approximation) cannot capture the sharp oscillations and specific layering in the Helmholtz region, where surface blocking effects dominate.
• Positive Electrode (Cathode):
  • Simulation: Shows a dip in anion concentration in the diffuse layer, a substantial water layer at the interface, and non-monotonic behavior in aggregate volume fractions.
  • Theory: Captures the qualitative trends: suppression of cations, enrichment of anions near the bulk, and the eventual depletion of the gel phase near the interface.

B. Thermodynamic Stability and Activity

• Bulk Activity:
  • As salt concentration increases from 0.5 m to 21 m:
    • $Li^+$ Activity: Increases monotonically.
    • Water Activity: Decreases significantly.
    • Anion Activity: Non-monotonic (increases then decreases).
• Redox Potential Shifts (Nernst Equation):
  • SEI Formation (LiF): The increased activity of $Li^+$ and anions leads to a positive shift (~0.35 eV) in the reduction potential for Li-salt formation (e.g., LiF). This thermodynamically favors the formation of an inorganic SEI.
  • Water Reduction: The decreased water activity causes a negative shift (~-10 mV) in the water reduction potential, making hydrogen evolution slightly less favorable thermodynamically.
  • Water Oxidation: The shift is minimal (-5 mV), suggesting that the improved oxidative stability of WiSEs is primarily kinetic (due to water depletion at the interface) rather than thermodynamic.

C. Reaction Kinetics

• SEI Formation: The theory predicts a high concentration of hydrated $Li^+$ and $Li^+$-TFSI clusters at the negative interface. This high local concentration of reactants facilitates the kinetics of Li-salt formation, promoting a passivating SEI.
• Water Oxidation: At positive potentials, the interface is dominated by free water. However, at lower surface charges, water depletion is predicted, which would kinetically suppress the Oxygen Evolution Reaction (OER).

5. Significance and Implications

• Mechanistic Insight: The paper provides a clear physical explanation for the expanded ESW in WiSEs: it is a combination of thermodynamic shifts (favoring SEI formation and suppressing water reduction) and kinetic barriers (reactant depletion at the interface).
• Design Principles: The formalism offers a tool for electrolyte design. By manipulating association probabilities (via chemistry or additives), one can tune the activity of specific species to stabilize the electrolyte or control SEI composition.
• Computational Efficiency: The analytical theory, once parameterized by a single bulk MD simulation, can predict EDL structures and thermodynamic properties across various concentrations and electrode potentials without the need for expensive interface-specific simulations.
• Future Directions: The authors note that while the theory explains why reactions are favored, it cannot predict which specific chemical species will form the SEI. Future work requires coupling this thermodynamic framework with atomistic reaction network models or Machine Learning Interatomic Potentials (MLIPs) to achieve chemically accurate predictions of interphase composition.

In summary, this work successfully bridges the gap between microscopic ionic associations and macroscopic battery performance, offering a robust, validated theoretical framework for understanding and designing next-generation electrolytes.