Predictive Interphase Engineering

• Predictive interphase engineering is the systematic design of interfacial regions that control chemical, structural, and functional properties across diverse materials.
• It integrates mechanistic models, phase-field simulations, and machine learning to map interfacial behavior from atomic to mesoscale, informing energy storage and multifunctional materials.
• Practical applications include optimizing battery CEI/SEI stability, enhancing dielectric and mechanical properties in nanocomposites, and tailoring composite stiffness through closed-form design rules.

Predictive interphase engineering is the systematic design and optimization of interfacial regions—comprising chemical, structural, and functional layers—that control key physical properties and device behaviors across diverse classes of materials. In contemporary applications, predictive interphase engineering couples mechanistic models, quantitative structure–property relationships, and closed-form or simulation-based design rules to program the formation, evolution, and function of interphases at atomic to mesoscale resolutions. This strategy is realized in batteries (CEI/SEI stabilization), nanocomposites (mechanical transfer, dielectric enhancement), eutectics (spacing regularity), topological heterostructures (functional orbital textures), and beyond, through the integration of first-principles, phase-field, machine learning, and continuum modeling methodologies.

1. Mechanistic Pathways and Universal Interphase Formation Models

Interphase engineering is governed by universal physicochemical mechanisms encompassing electron transfer, defect and radical formation, solvation chemistry, and cooperative phase behavior.

• Electrochemical SEI/CEI Growth: Interphase nucleation is initiated when electrode Fermi level $\phi_e$ approaches or crosses the electrolyte’s LUMO, activating electron injection and molecular reduction according to

$$j = F k_0 c_e\,\exp\left[-\alpha \frac{F(\phi_e-\phi_E)}{RT}\right]$$

Governing the initial kinetics in both batteries and supercapacitors, this equation encapsulates the electron-transfer limited regime (Hasan et al., 28 Nov 2025).

• Kinetic Growth Regimes: Once the interphase is established, growth typically transitions to migration- or tunneling-limited, or, in thick films, diffusion-limited self-passivation:

$$\frac{dL}{dt} = k_g\,e^{-E_a/RT} f(\Delta V) - k_{\text{diss}} L, \qquad L(t) \sim t^{1/2}$$

with $E_a$ as the activation barrier; $L$ is the thickness; $f$ reflects local potential or current magnitude (Hasan et al., 28 Nov 2025).

• Non-linear Overpotential Effects: In SEI films, transport across the interphase exhibits strong non-linearity. The overpotential through the SEI saturates at low currents:

$$j = j_{0,H}\,\sinh\left(\frac{F\,\eta_{\rm SEI}}{RT\,H}\right)$$

with $H$ and $j_{0,H}$ capturing the inner SEI’s ion-transport kinetics, directly measurable through EIS and GCD methods (Hess, 2017).

• Radical- and Defect-Driven Interphase Instability: In high-voltage or high-temperature systems, radical chain reactions (e.g., F$\cdot$ generation from anion decomposition) induce rapid chemical evolution and CEI reconstruction, prompting microcracking, compositional shifts, and capacity fade (Meng et al., 2024).

2. Quantitative Modeling, Simulation, and Machine-Learning Approaches

Predictive interphase engineering utilizes analytical, computational, and learning-based frameworks across scales:

• Bruggeman-Style Compact Group Models: For nanocomposites with explicit interphase shells, compact-group averaging yields Bruggeman-style, closed-form equations for effective conductivity and permittivity:

$$(1-\varphi)\frac{\sigma_0-\sigma}{2\sigma+\sigma_0} + c\frac{\sigma_1-\sigma}{2\sigma+\sigma_1} + (\varphi-c)\frac{\sigma_2-\sigma}{2\sigma+\sigma_2} = 0$$

where shell thickness $\delta$ directly modulates percolation thresholds and dielectric maxima (Sushko et al., 2013).

• Phase-Field Simulations: Evolution and stability of interphase boundary morphologies in ferroelectrics or grain microstructures are computed via gradient/elastic/electrostatic energy functionals and constrainted dynamic equations:

$$\frac{\partial P_i}{\partial t} = -L_{ij}\frac{\delta F}{\delta P_j}$$

with explicit consideration of electrical and mechanical compatibility factors $Q(\hat{n})$ and $B(\hat{n})$ for interface orientation (Zhang et al., 2022).

• Physics-Informed Neural Networks (PINNs): Multi-phase-field systems describing evolving complex interphases are efficiently and accurately solved by parallelized, composite-loss architectures employing mesh-free, interface-focusing sampling and transfer learning across spatiotemporal scales (Elfetni et al., 2024).
• Bayesian Data-Driven Interphase Mapping: In polymer nanocomposites, local AFM data is mapped onto exponentially decaying “single-body” and “multi-body” property gradients, with Bayesian inference employed to calibrate interphase spatial models ensuring macroscopic viscoelastic property targets (Li et al., 2018).

3. Structural, Chemical, and Property Characterization: Predictive Links

The robust design of interphases demands explicit control of structure–property relationships, encompassing thickness, composition, roughness, and defect density.

• Electrochemical Interfaces: High-temperature LHCEs reveal that CEI thickness ($\Delta t_{\rm CEI}$) and surface roughness ($R_q$) scale nearly linearly with capacity fade:

$$\%\text{Retention} \approx 100\% - 0.3\%\times\Delta t_{\rm CEI}[{\rm nm}] - 0.5\%\times R_q[{\rm \mu m}]$$

DODSi additives sustain sub-3 nm, low-roughness, crystalline CEIs correlating to $>$90% retention (Meng et al., 2024).

• Mechanical Nanocomposites: Nanoinclusion–interphase–matrix models rigorously relate interphase stiffness ($E_i$), thickness ($t_i$), and matrix modulus ($E_m$) via mean-field, Eshelby/Mori–Tanaka, and double-inclusion schemes, exposing the strong amplification or suppression of composite stiffness:
  • $E_i \gg E_m$ and moderate $t_i/r \to$ maximum stiffening, $E_i \ll E_m$ $\to$ decoupling and softening (Raoux et al., 2024).
• Atomistic/Quantum Descriptors: At Fe–Cu boundaries, the emergence of a single-layer mixed interphase with distinct magnetization ($\mu_B$/atom) and sharp composition profile is dictated by DFT-derived magnetic Friedel oscillations and oscillatory interfacial binding-energy kernels (Xie et al., 2024).
• Radiation Tolerance: Amorphous complexion thickness $d$ and normalized free volume $\phi = \sigma_v/\langle v\rangle_{\rm bulk}$ control sink efficiency. For maximum defect annihilation,

$$N_{\rm res}(d) = N_\infty + (N_0 - N_\infty)\exp[-d/d_0], \qquad \phi \gtrsim 10\%$$

ensures single-cascade tolerance ($N_{\rm res} \lesssim 1$ per event) (Aksoy et al., 2023).

4. Additive, Alloying, and Interface Control Strategies

Transferable predictive design rules across disciplines emerge from mechanistic, compositional, and structural control of interphases.

• Electrochemical Additives: Incorporating strong acid scavengers (e.g., DODSi) arrests radical cycles and suppresses microcracking in high-temperature battery operation; optimal concentration $\sim$0.5 wt% achieves saturation (Meng et al., 2024). Film-forming additives (e.g., FEC, VC) in batteries and supercapacitors yield targeted LiF-rich or polymeric interphases, with thickness and suppression scaling:

$$L_{\rm SEI} = L_0 + \kappa (c_{\rm add})^n,\quad \Delta I = I_{\rm neat}\exp[-\gamma c_{\rm add}]$$

(Hasan et al., 28 Nov 2025).

• Coatings and Functionalization: ALD/MLD coatings (Al$_2$O$_3$, TiO$_2$) as few as $2{-}10$ nm suppress leakage by orders of magnitude via electron tunneling limitation.

$I_t = I_0 \exp[-\beta d]$

(Hasan et al., 28 Nov 2025).

• Atomic-Scale Interphase Design: Doping in ferroelectrics (Gd, Zr in HfO$_2$) or alloying in steels are employed to control local misfit, eigenstrain, and oscillatory magnetic interactions, stabilizing preferred single-layer or coherent interphase structures and orientations (Grimley et al., 2017, Xie et al., 2024).
• Kinetic Protocols: Cycling protocols for T-SEI formation on Zn anodes optimize $J_{\rm crit}$ and $t_{\rm inc}$:

$$t_{\rm inc} = \frac{\pi D}{4}\left(\frac{nF(c_{\rm sat}-c_{\rm bulk})}{J}\right)^2, \quad J_{\rm crit} = \frac{nF D (c_{\rm sat}-c_{\rm bulk})}{\Delta}$$

to induce beneficial, periodically renewing interphases for smooth, epitaxial redeposition (Fuller et al., 2024).

5. Predictive Frameworks and Stepwise Engineering Recipes

Systematic predictive interphase engineering encompasses:

• Explicit Quantitative Criteria: For electrochemical interfaces, maintaining $$E_{\rm LUMO}(\text{anion}) - E_{\rm HOMO}(\text{solvent}) \gtrsim 5.5~{\rm eV}$$ prevents cross-reactions and ensures interphase robustness (Meng et al., 2024).
• Dimensionless Design: For radiation-robust amorphous interphases, ensure $d/R_c > 1.2$ and $\phi > 0.10$; for conductive percolation in composites, select $\delta$ and $\sigma_2$ to tune $c_c$ and $Re\,\epsilon$ (Sushko et al., 2013, Aksoy et al., 2023).
• Workflow Algorithms:

1. Input: device material specs, target properties, operational limits.
2. Screen: phase diagrams, electrolyte/additive options, coating candidates.
3. Calculate: interphase thicknesses, kinetic rates, conductivity.
4. Simulate: PINNs/phase-field or analytic models to validate emergent properties.
5. Iterate: adjust chemistry, structural motif, or cycling protocol to converge to target response (Hasan et al., 28 Nov 2025, Elfetni et al., 2024).

• Uncertainty Quantification: Employ Bayesian inference and surrogate optimization to map interphase property gradient spaces, propagate uncertainties, and select robust interphase architectures with minimal experimental trial.

6. Case Studies: Energy Storage, Topological Spintronics, and Multifunctional Materials

Predictive interphase engineering is operationalized across disparate systems, demonstrating unified principles:

System	Interphase Model/Function	Key Predictive Rule/Metric
Li-metal batteries	CEI/SEI radical-coupled, DODSi stabilized	Thickness $<$3 nm, $R_q$ $<$0.2 μm, $\Delta E_{\min}>5.5$ eV
Ferroelectrics (HfO$_2$)	Coherent O/M or O/O boundary	Interface misfit $\delta<2.2\%$ for flat, mobile boundaries
Polymer nanocomposites	Exponential modulus gradient	Single/multi-body $f(d)$, Bayesian-calibrated spatial assignment
Cu–Ta under radiation	Amorphous complexion, excess free-volume	Thickness $d>R_c$, $\phi>10\%$, $N_{\rm res}(d)<1$
vdW heterostructures	Magnetic topological interphase (Zeeman)	$g$-factor tunability via $E_{\rm FGT}$ (0–1.3 GV/m)

In all contexts, predictive interphase engineering critically depends on uniting mechanistic insight, rigorous computational or analytic modeling, and platform-specific structurally resolved property measurements, enabling rational, data-driven, and adaptive control of interfacial regions for next-generation materials and devices.