Carbon Layer Sliding & Reorganization

• Carbon layer sliding and reorganization are structural transformations in low-dimensional carbon materials, governed by van der Waals forces, registry effects, and defect mediation.
• The interplay of interatomic forces, layer bending, and defect-induced energy fluctuations enables tuning of friction, electronic properties, and ion transport critical for energy devices.
• Advanced computational models and operando experiments reveal that manipulating stacking order and defect density can optimize thermal, mechanical, and electrochemical performance.

Carbon layer sliding and reorganization denote the coupled in-plane and interlayer structural transformations occurring in graphitic, graphenic, and other low-dimensional carbon-based materials under mechanical, electrochemical, or thermal stimuli. These processes govern the dynamic energetics, mesoscale architecture, defect evolution, and transport phenomena relevant to devices such as lithium-ion batteries, NEMS, solid lubricants, and composite systems. The mechanistic complexity arises from the interplay among interatomic forces, registry-dependent energy landscapes, stress release mechanisms, defect mediation, and charge/ion transfer at the atomic level.

1. Fundamental Mechanisms of Carbon Layer Sliding and Reorganization

The canonical energy landscape for interlayer motion in layered carbon materials arises from van der Waals (vdW) dispersion anchoring and registry-dependent electronic or ionic interactions. In graphite and graphene-derived systems, vdW forces fix the equilibrium interlayer distance (as captured by a –C₆/R⁶ pairwise expression), while the corrugation of the sliding landscape—i.e., the lateral oscillations in system energy as layers are translated in-plane—stems from short-range repulsion (Pauli), electrostatic, or orbital hybridization effects, depending on material polarity and defect concentration (Marom et al., 2010, Oz et al., 2015).

In practice, carbon layer sliding entails the following:

• Registry (Commensurability): Lateral alignment (e.g., AA, AB (Bernal), or twisted/misaligned) of lattices sets the magnitude and periodicity of the energy corrugation.
• Layer Bending and Deformation: Processes such as peeling or rolling induce in-plane bends and out-of-plane curvature, driving local layer sliding and the generation of complex stacking/kink morphologies (Korhonen et al., 2015).
• Defect Mediation: Stacking faults, vacancies, or layer-scale dislocations lower sliding energy barriers locally, serving as nucleation centers for sliding or pinning centers impeding motion (Wang et al., 8 Aug 2025, Siahlo et al., 2018).
• Ionic/Molecular Coupling: Intercalation/deintercalation of ions (e.g., Li⁺) or molecules dynamically modulates local interactions and can drive stage transitions—transitions in the periodicity of Li-stuffed carbon galleries—by facilitating or pinning lateral sliding (Wang et al., 8 Aug 2025).
• Thermal and Mechanical Activation: Thermal fluctuations (thermolubricity) and applied stress dynamically trigger early slips, layer relaxations, or aging phenomena modulated by local potential barriers (Sheehan et al., 2020, Wang et al., 2023).

The phenomenology spans from nearly free sliding ("structural superlubricity") in incommensurate or misaligned structures, with static friction approaching zero (Wang et al., 2023, Androulidakis et al., 2020), to pinning-dominated regimes where defect or commensuration effects nucleate domain boundaries, stick–slip motion, and require substantial threshold forces for displacement (Oz et al., 2015, Korhonen et al., 2015).

2. Energetics, Registry Index, and Corrugation Models

The energetic foundation for predicting carbon layer sliding comprises atomistic and geometric models:

• Pairwise Potential Approaches: Empirical 6–12 Lennard-Jones and registry-dependent Kolmogorov–Crespi potentials quantify interlayer forces for both flat and non-parallel interfaces (Popov et al., 2011, Oz et al., 2015). For layered nanotubes, the sliding barrier per atom, ΔU_z, approaches a radius-independent value for tubes with R₂ > 5 nm, simplifying asymptotic estimation of mechanical properties (Popov et al., 2011).
• Registry Index (RI) Models: The RI quantifies the commensurability between layers, mapping atomic overlays via normalized geometric overlaps or projected Gaussian functions. This approach maps sliding energy landscapes efficiently, capturing not only commensurate (high corrugation) but also superlubric (low corrugation) regimes (Oz et al., 2015). The RI is given as:

$$\mathrm{RI} = \frac{S_{\mathrm{tot}} - S_{\mathrm{opt}}}{S_{\mathrm{adv}} - S_{\mathrm{opt}}}$$

where S₍ₐ₎ are normalized total geometrical overlaps for real, optimal, or adverse stacking.

In heterostructures, such as C/BN nanotubes or BNNT/graphene, lattice mismatch substantially reduces corrugation, enabling superlubric trends (Oz et al., 2015). The same philosophy extends to curved architectures—nanoscrolls and rolled ribbons—where incommensurability caused by curvature serves as a kinetic facilitator for structural reorganization (Siahlo et al., 2018).

3. Coupling Between Sliding, Reorganization, and Material Function

Carbon layer sliding is not an isolated mechanical phenomenon but is coupled in various ways to electronic, ionic, optical, and transport properties:

• Electromechanical Coupling: In h-BN and boron nitride analogs, sliding along nearly free-sliding paths induces strong bandgap modulations (up to ~0.6 eV) and can change the gap character from direct to indirect, enabling electromechanical tuning for functional device applications (Marom et al., 2010).
• Ferroelectric Switching: Across-layer sliding in graphene-based heterostructures (e.g., graphene/BN) can break inversion symmetry and enable low-barrier electrically switchable vertical polarization, a phenomenon termed across-layer sliding ferroelectricity, suitable for ultra-high-density non-volatile memory (Yang et al., 2022).
• Ionic Transport and Battery Operation: During Li intercalation in graphite, local inhomogeneities in Li distribution and stress release drive spatially resolved sliding and layer reorganization, facilitating and regulating transitions between stage structures (Stage-2, -3, etc.), and impacting lithiation/delithiation kinetics and internal stress management in batteries (Wang et al., 8 Aug 2025).

The material's response to sliding is further modulated by:

• Defects: Stacking faults and atom-layer-scale disorders generally promote sliding and reorganization by lowering local energy barriers, whereas atomic vacancies or "trapping" defects locally pin layers and restrict both ionic transport and sliding (Wang et al., 8 Aug 2025, Siahlo et al., 2018).
• Environmental Factors: Humidity and adsorbed molecules affect lubricity and friction, primarily via formation of boundary lubricating layers (e.g., water anchored by surface –OH), as revealed by ab initio MD for Si-doped carbon coatings (Kajita et al., 2016).

4. Experimental Probes and Observational Signatures

Multiple classes of experiments and simulations capture layer sliding/reorganization phenomena:

• In situ Spectroscopy and Imaging: Raman microscopy detects reorganization in amorphous carbon films via band shifts/broadenings, capturing the timescales of aromatization and sp³→sp² transitions (Pardanaud et al., 2013). Optical and electrical probes on tribolayers reveal the phase separation between sp² and sp³ regions induced by friction-driven transformations (Mailian et al., 2016).
• Electrochemical/Tribological Cell Studies: In operational devices (e.g., polished HDD carbon overcoats), sliding speed, applied voltage, and polarity asymmetrically control wear and reorganization via tribo-electrochemical reactions, observed by in situ electrical, acoustic, and displacement techniques (Rajauria et al., 2016).
• Mechanical Manipulation (Peeling, AFM): MD and continuum models elucidate the registry shifts, kink evolution, and behavior under peeling and mechanical shearing, resolving how stacking order and sliding cause local electronic and mechanical transformation (Korhonen et al., 2015, Wang et al., 2023, Androulidakis et al., 2020).
• Computational Approaches: Deep learning potentials provide ab initio accuracy for dynamic simulations of Li intercalation, tracking both ion and carbon layer kinetics over relevant timescales (Wang et al., 8 Aug 2025).

5. Scaling Laws, Pinning, and Superlubricity

The nature and scaling of frictional and dynamic properties with contact area, geometry, and defectiveness underpin practical device performance:

• Kinetic and Static Friction: In defect-free, incommensurate (superlubric) interfaces, kinetic friction scales linearly with area (Fₖ ∝ A), while static friction, dominated by edge or domain wall pinning, exhibits sublinear growth (Fₛ ∝ A^α with α ≈ 1/4–1/2) (Wang et al., 2023, Popov et al., 2011). The Prandtl–Tomlinson (PT) model captures the kinetic-to-stick–slip crossover, with η = (2π² U₀)/(K_p a²) as the transition parameter.
• Effect of Geometry: In nanotubes and nanoribbons, size and wall number (single-wall vs. multi-wall, faceting) dictate whether rolling or sliding dominates, with rolling kinetic friction rising linearly with area and sliding friction in misaligned multi-walls exhibiting sublinear scaling due to superlubricity (Mandelli et al., 2020).
• Role of Boundary and Elasticity: Pinning is edge-dominated in finite flakes, with frictional oscillations as the moiré commensurate regions enter/exit boundary zones. Elasticity (parameterized by bending/Young modulus) governs the critical size at which stick–slip is suppressed and sliding becomes truly superlubric (Wang et al., 2023).

Superlubricity is enhanced in heterostructures with lattice mismatch (e.g., graphene/BN, CNTs/hBN), random stacking, induced wrinkles or strain, and sliding along achiral directions (Oz et al., 2015, Androulidakis et al., 2020).

6. Material Design and Technological Implications

Carbon layer sliding and reorganization provide a suite of tunable design variables for advanced device architectures:

• Energy Devices: Engineering stacking faults and controlling defect types in graphite anodes facilitates efficient Li transport, stage transitions, and internal stress management for high-rate and long-cycle batteries (Wang et al., 8 Aug 2025).
• Solid Lubricants and MEMS/NEMS: The direct correlation between commensurability, registry, and friction enables design of coatings and contacts with tailored lubricity and wear resistance; environmental adaptability is achieved via controlled functionalization (e.g., Si-doping for enhanced hydroxylation and water boundary films) (Kajita et al., 2016).
• Composites: Layer-by-layer assembly combined with polymeric matrices enables controlled reorganization and alignment, resulting in composites with anisotropic electrical, thermal, and EMI shielding properties (Zhan et al., 2020).
• Thermal Management: Interlayer sliding in vdW systems can modulate phonon-phonon interactions and dramatically tune thermal conductivities by shifting stacking configuration, as formulated by regulation ratio R = Kₛ/Kᵢ (K: thermal conductivity after/before sliding) (Yu et al., 2023).
• Nanoelectronics and Data Storage: ALSF in graphene-based heterostructures allows for low-barrier, reversible polarization switching—foundational for non-volatile memory and ultra-dense bit storage (potentially exceeding 10⁴ Tbit/inch²) (Yang et al., 2022).

These functionalities hinge on the ability to precisely manipulate and predict the sliding and reorganization landscape at atomic to mesoscopic scales, leveraging deep learning-based atomistic modeling, kinetic theory, and advanced characterization techniques.

7. Future Directions and Open Challenges

Advancing the control and exploitation of carbon layer sliding/reorganization requires:

• Multi-scale Integration: Bridging quantum-scale energetics (registry indices, charge redistribution, phonon renormalization) with microstructural dynamics (stage transformation, stress release, defect evolution) in realistic device architectures.
• Tailored Defect Engineering: Systematic optimization of stacking fault densities, atomic-scale vacancy concentrations, and controlled doping to tune the balance between sliding facilitation and pinning, for application-specific targets.
• Operando Monitoring: Developing spatially and temporally resolved probes (operando Raman, in situ imaging, local force spectroscopy) to directly correlate ionic, electronic, and structural evolution under real cycling and stress conditions.
• Coupled Multi-field Dynamics: Understanding and harnessing the interplay between electronic, thermal, mechanical, and ionic transport as modulated by dynamic sliding and reorganizing interfaces, particularly under nonequilibrium driving (mechanical load, electric/magnetic fields, thermal gradients).

Addressing these aspects will consolidate the foundational understanding of carbon layer sliding/reorganization and facilitate the rational design of advanced carbon-based devices with tailored functionality across energy storage, electronics, and tribological domains.