Elastocapillary cleaning of twisted bilayer graphene interfaces

Two-dimensional materials such as graphene exhibit unique properties that can be tailored by assembling layers into van der Waals (vdW) heterostructures. Twisted bilayer graphene (tBLG) in particular shows emergent physics (moiré bands, correlated states, superconductivity). However, device fabrication often introduces interfacial contamination (e.g., water, hydrocarbons). vdW forces can corral these contaminants into nanoscale pockets (“self-cleaning”), leaving surrounding regions atomically clean. Prior observations indicate that such pockets can coarsen and merge spontaneously over time or with annealing, aiding removal of contaminants. The common explanation has been an Ostwald ripening mechanism driven by capillarity and mass transport between bubbles. Yet this view neglects the mechanics of the encapsulating thin graphene sheets, which can bulge and wrinkle and thereby mediate long-range interactions without direct mass exchange. The research question is to determine what drives the rapid, spontaneous aggregation and coalescence of interfacial nanopockets in tBLG and how elastic deformation and capillarity combine to control pocket morphology and interactions. The study investigates pocket geometry and merging under controlled mechanical stretch, demonstrating self-renewal of tBLG interfaces and proposing an elastocapillary cleaning mechanism.

Self-cleaning at vdW interfaces has been reported, where contaminants aggregate into bubbles or pockets, leaving interfaces clean (Haigh et al.; Khestanova et al.; Sanchez et al.). Related macroscopic phenomena include liquid blisters/lenses under thin solids, but nanoconfined liquids in vdW materials are notable for mobility. Coarsening and merging of interfacial pockets have been observed over time or with annealing and attributed to Ostwald ripening (capillarity-driven diffusion). Studies have also probed nanobubble growth and transport in graphene liquid cells and unusual collective behaviors of confined water. The role of thin sheet mechanics (tension, wrinkling) is established in elastocapillarity and capillary wrinkling of membranes, but prior nanopocket ripening explanations have not incorporated the elasticity of 2D materials. Superlubricity at twisted graphene interfaces enables low friction, simplifying interfacial force balance considerations. Recent works on droplets capped by elastic films show pretension can dominate shape, suggesting analogous control for nanopockets in vdW materials.

Experimental platform: A suspended micro–nano bubble device was used. Monolayer graphene was prepared by mechanical exfoliation and stacked into twisted bilayers on microhole-patterned SiO2/Si substrates using a water droplet-assisted transfer method. The twist angle was controlled during stacking and quantified by moiré periodicity (for small angles) or Raman spectroscopy (for larger angles). Suspended tBLG was fabricated on substrates with circular holes of radii 1.5 and 2.5 µm. Interfacial contaminants (water or ethanol) were trapped between graphene layers forming nanopockets tens to hundreds of nanometers in radius. AFM and Raman: AFM (Asylum Research Cypher) characterized nanopocket morphology and applied mechanical stimuli. The tip had a normal spring constant ~0.08 N/m and torsional constant ~16.0 N/m; scan frequency 6 Hz; contact-mode scans induced pocket motion. AFM lateral force and deflection images provided moiré visibility and height profiles to extract pocket radius a and height h. Raman (Renishaw, 514 nm) with <0.5 mW laser, 1.0 cm−1 spectral and 500 nm spatial resolution assessed twist angle for large-angle samples. Pressurization and pretension control: Suspended tBLG drumheads were placed in a high-pressure autoclave filled with N2 for several days to stabilize pressure. Pressurization produced a bulged drumhead of height H over hole radius A, imparting a nearly equibiaxial pretension T_pre ~ E_2D H^2/A^2 near the center pockets. Aspect ratios h/a of nanopockets were measured across varying H/A to study pretension effects and wrinkling suppression. Ethanol nanopockets: An ethanol droplet replaced water in the transfer process to encapsulate ethanol at the interface. The same suspension and characterization protocols were used to compare water and ethanol pocket behaviors under pretension. Molecular dynamics (MD): LAMMPS simulations modeled two water-filled nanopockets intercalated in a graphene bilayer. Each droplet contained ~4300 water molecules; the simulation cell was 100 × 80 nm^2, periodic in-plane and open out-of-plane. Graphene interactions used AIREBO with adjusted cutoff 0.2 nm; water used rigid SPC/E with SHAKE; long-range Coulomb via PPPM (accuracy 10−4). Water–graphene interaction employed 12–6 Lennard-Jones between O–C with ε = 4.063 meV, σ = 0.319 nm. Simulations were equilibrated at 300 K (Berendsen thermostat). Pretension was introduced by stretching the box by 1% or 2%. Coalescence energetics were probed via constrained energy minimization: droplet center-of-mass positions were tethered with springs of stiffness k (1600 N/m for minimal fluctuation enabling spontaneous merging at d ≤ 2.5a; 0.16 N/m for larger fluctuations). After ~10 ns equilibration, potential energy landscapes versus inter-droplet distance d were obtained after simulated annealing to 0 K at 3 × 10−15 K/s. The nominal droplet radius was a = 4 nm.

1. Self-cleaning and mobility: AFM showed that interfacial nanopockets (water or ethanol) in tBLG are highly mobile and can be actuated by tip scanning at room temperature, leaving behind recovered, contamination-free moiré patterns. Nanopockets spontaneously coalesce when neighboring pockets are present.
2. Volume conservation suggests liquid content: Across 18 samples, the ratio of total nanopocket volume before and after coalescence mostly ranged from ~0.90 to ~1.05, consistent with predominantly incompressible liquid (water) contents and minimal gas contribution.
3. Pocket geometry and size/twist insensitivity: Nanopocket profiles are well approximated by spherical caps characterized by height h and radius a. The aspect ratio h/a is insensitive to pocket size and host tBLG twist angle over the measured range, indicating an effective constant contact angle modified by membrane tension. A horizontal force balance at the contact line yields cos β_o ≈ (N_r′ + γ_gg/2)/(N_r + γ_gl), with superlubricity allowing N_r ≈ N_r′.
4. Elastocapillary parameter controls shape: Recasting the relation in terms of sheet stiffness E_2D and interfacial energies gives an aspect ratio governed by an elastocapillary parameter Δγ/E_2D (Δγ = 2γ_g − γ_gg). Systems with larger Δγ produce higher h/a. Fitted values give (Δγ)^{1/4} ≈ −0.122 (θ ≈ 7.3°) and ≈ 0.107 (θ ≈ 10°–13°) for pretension-free conditions.
5. Pretension flattens nanopockets and suppresses wrinkling: Increasing drumhead pretension (via H/A) reduces h/a in good agreement with the theoretical prediction for unwrinkled membranes. A geometric criterion predicts onset/suppression of hoop-compression-induced wrinkling; experiments align with this criterion, showing wrinkle suppression at higher pretension. Ethanol pockets behave similarly to water pockets under pretension.
6. Long-range pocket–pocket interactions are elasticity-mediated and enhanced by wrinkles: Outside each pocket, tensile and compressive stresses induce wrinkling that distorts moiré patterns. Without pretension, two neighboring pockets exhibit apparent attraction and spontaneous merging upon mechanical actuation; under ~1% pretension, pocket–pocket attraction is diminished, and pockets follow the stimulus direction instead of merging directly. Theory indicates interaction tension decays as r−2 without wrinkles, slowing to r−1 when wrinkles form, extending the interaction range and biasing coalescence.
7. Elastocapillary driving forces: Asymmetric pretension around a pocket near a neighbor flattens the side facing higher tension, decreasing the effective contact angle locally and producing a net capillary force toward coalescence, in addition to elastic forces from stress gradients.
8. MD confirmation and energetics: Simulations reveal two stages: a long-range attraction stage for d > 2.5a driven by elastic restoration and wrinkling-mediated interactions (including formation of a unidirectional wrinkle bridging droplets), followed by spontaneous coalescence for d < 2.5a upon initial contact. Pretension (1–2%) reduces aspect ratios (from ~0.15 to ~0.13), suppresses wrinkles and lowers the energy gradient driving attraction. The merged state is the reference energy minimum; relative potential energy decreases with decreasing d, with the reduction gradient weakening as pretension increases.

The study addresses the fundamental question of what drives the spontaneous aggregation and coalescence of interfacial nanopockets in twisted bilayer graphene beyond classical Ostwald ripening. Observations of rapid, room-temperature coalescence under mechanical stimuli and the recovery of moiré patterns, combined with pocket mobility and volume conservation, suggest that mass diffusion between pockets is not required. Instead, the elasticity of graphene sheets plays a crucial role: bulging pockets generate stress fields and hoop compression that induce wrinkling, which in turn mediates long-range, slowly decaying interactions between pockets. These interactions create asymmetric pretension around neighboring pockets, modifying their local effective contact angles and producing net capillary forces that, together with elastic forces, bias motion toward coalescence. Applying uniform pretension flattens pockets and suppresses wrinkling, thereby reducing the long-range attraction and controlling whether pockets coalesce or follow the direction of external stimuli. MD simulations corroborate the elastocapillary picture by showing a wrinkle-mediated attraction stage and a separate spontaneous coalescence stage upon contact, distinct from diffusion-driven Ostwald ripening. Overall, the findings demonstrate an elastocapillary mechanism where deformable boundaries and membrane tension govern nanopocket morphology, interaction range, and coalescence dynamics, enabling deterministic control of interface cleaning.

Twisted bilayer graphene interfaces exhibit self-cleaning through the formation, mobility, and coalescence of interfacial liquid nanopockets, with surrounding moiré patterns recovering after pocket motion. The geometry of nanopockets is size- and twist-insensitive under low pretension, consistent with an effective contact-angle framework modified by membrane tension and governed by an elastocapillary parameter. Pretension flattens nanopockets and suppresses wrinkling, which reduces long-range, elasticity-mediated attractions and enables control over coalescence. An elastocapillary mechanism, combining elastic stress fields and capillary forces due to tension-modified contact angles, explains rapid coalescence without mass diffusion. MD simulations validate a two-stage process of attraction and spontaneous merging and the suppressive effect of pretension on wrinkles and driving forces. These insights suggest practical routes to fabricate cleaner vdW devices via mechanical treatments (e.g., controlled stretching or stamping) and inform design of graphene liquid cells where confinement pressures and dynamics depend on both capillarity and elasticity. Future work could quantify elastocapillary parameters across materials and contaminants, refine models to include initial pretension and curvature effects, explore anisotropic mechanics and large-scale pocket shapes, and develop real-time control strategies for interface cleaning.

Experimental datasets of aspect ratio versus pretension are relatively sparse in H/A, and pre-existing pretension from transfer may slightly shift the wrinkling instability domain, leading to modest discrepancies with the theoretical criterion. The tension-field-based model for wrinkled pockets tends to overestimate aspect ratios, likely underestimating elastic energies due to simplifying assumptions (neglecting initial pretension, non-uniform wrinkling, and drumhead curvature). In experiments, the spontaneous coalescence stage after initial contact is difficult to resolve temporally. MD simulations are constrained by system size, droplet size, and potential models; large-scale anisotropic effects (e.g., ellipticity due to graphene’s directional bending resistance) are not captured. Simulated wrinkle bridges do not form fluid channels, highlighting that the mechanism differs from diffusion-driven ripening; direct measurement of interfacial mass transport was not performed.