Elastocapillarity-driven 2D nano-switches enable zeptoliter-scale liquid encapsulation

The study addresses how to realize a programmable, reversible nanoscale switch that changes state in response to liquid-mediated capillary forces. Inspired by biological structures that adapt to stimuli, the authors aim to leverage elastocapillarity in engineered 2D material nanochannels to achieve controlled, reversible shape-switching at approximately 10-nm scales. Existing programmable structures typically operate above 10 micrometers due to mechanical limits of thin films and elastomers. The authors propose and demonstrate nanoscale switches using atomically flat, mechanically robust van der Waals layered materials (graphene, hBN, WS2). They establish a theoretical framework that links geometry, material stiffness, adhesion and wetting to predict switching and reversibility, enabling rational design of switchable nanofluidic elements and nanocapsules that can encapsulate zeptoliter volumes. This capability advances nanofluidics toward active elements for on-chip chemistry and biochemistry and adaptable materials.

Capillarity governs liquid-gas interfaces and wetting in porous media and drives fluid transport in plants. In nanoscale pores, capillary pressures can reach hundreds of bars, sufficient to deform confining media (elastocapillarity). At micro/nanoscale in semiconductor processing, wetting/drying can cause elastocapillary damage and stiction, limiting miniaturization. Prior work on van der Waals nanochannels with sub-nanometer height showed angstrom-scale sagging attributed to van der Waals interactions with sidewalls, used to detect water and capillary condensation. This mechanism differs from the elastocapillary caving-in employed here. Similar capillarity-induced collapse has been observed at larger scales in micromachined channels and nanopillar arrays. Mechanical properties of 2D materials have been characterized via blister tests, showing bending stiffness scaling roughly with thickness cubed for multilayer van der Waals materials. The present work builds on these insights to design channels in a regime where top walls can cave under capillary pressure yet reopen upon rewetting.

Device design and fabrication: Two-dimensional nanochannels were assembled by stacking layered crystals on SiO2/Si. The bottom wall was either a 2D crystal or the SiO2 substrate; a patterned 2D crystal (graphite) formed spacers/sidewalls; a top 2D crystal (graphene, hBN, or WS2) with controlled thickness acted as the flexible actuator. Graphite spacers of height h ~10–20 nm were defined by electron beam lithography and reactive ion etching; channel width w = 400–1000 nm; top wall thickness t = 10–40 nm; pitch p = 1–2 μm. Alternative devices used photolithography-defined SiO2 steps. Materials included hBN top walls for optical transparency and WS2 to study thickness dependence. Fabrication used polymer masks (PMMA or S1805) and deep reactive ion etching with O2/SF6/CHF3 for graphite/SiO2 patterning. Wetting/drying protocol: Channels were filled with various liquids (including isopropanol (IPA), water, and IPA-water mixtures) and dried either by nitrogen blow-drying or under an optical microscope. Supercritical CO2 drying (critical point) was used to eliminate the liquid-gas interface. The fraction of closed channels was quantified optically; partial collapse was counted proportionally to collapsed length. Liquids of different surface tensions (IPA ~21 mN/m; water ~72 mN/m; mixtures to interpolate 21–72 mN/m) provided varied capillary pressures. Imaging and metrology: Optical microscopy (bright-field; color channel chosen for maximum thin-film interference contrast) and dark-field high-speed imaging captured switching dynamics. AFM in tapping mode (Bruker FastScan) provided height maps and profiles to correlate optical contrast with topography and to quantify bending profiles and suspended lengths near adhered regions. Theoretical modeling: The caving-in criterion balances capillary pressure (set by surface tension and contact angles with top/substrate) and bending stiffness D of the top wall. Bending stiffness scales as ~t^3, with D taken from literature for given thicknesses (10–20 nm range). Capillary pressure was treated with a continuum Young-Laplace framework; wetting surface energy parameterized by contact angles (typical values used: theta_s ~65 degrees on 2D material-water; theta_t ~0 degrees for organic solvents and SiO2-water). An instability criterion yields a threshold relation (via a prefactor phi = 1/96) predicting whether channels cave under drying for given w, h, D, and liquid properties. Adhesion-stiffness analysis of closed channels: A model of the top crystal as an elastic plate of stiffness D adhering to a step-shaped substrate with adhesion energy Γ yields a polynomial bending profile H(x) = h A(x/l) with A(X) = 2X^3 - 3X^2 + 1 over a suspended length l. The peeling curvature C at the contact line relates to D and Γ and defines a geometry-independent measure of the curvature needed to peel the crystal. AFM profiles from WS2 on SiO2 (t = 6–48 nm) validated the model and extracted the scaling of C with thickness. Rewetting and reversibility: Upon rewetting a dry, closed channel, liquid invades side-capillaries and increases the suspended base length from l_c (dry) to l_wet by contributing wetting energy. Minimizing total energy (elastic + adhesion + wetting) yields a reversibility criterion for full reopening when l_wet > w/2. Phase diagram construction: Dimensionless parameters were defined: alpha = w^2/(C_c h) capturing geometry-dependent flexibility (with C_c related to peeling curvature) and g = Γ/G capturing wettability/adhesion ratio. The combined caving-in and reversibility criteria delimit regions in alpha–g space: stiff (no collapse), irreversible collapse, and switchable (reversible). Experimental data across different materials, geometries, and liquids were mapped to this phase diagram. Regeneration/contamination control: Acetone was avoided due to residue; devices contaminated by acetone were regenerated by hot acetone baths followed by IPA rinsing. Closed (dry) channels remained closed for months but reopened upon rewetting; switching was repeatable over many cycles.

• Demonstration of elastocapillarity-driven, programmable, reversible nanoswitches in 2D material nanochannels operating at ~10 nm scales. Channels switch from open (stiff) to closed (caved-in) states upon drying, controlled by liquid surface tension and channel geometry, and reopen upon rewetting.
• Surface-tension-tunable switching: Critical point drying with CO2 (no capillary interface) leaves channels open; IPA drying (gamma ~21 mN/m) partially collapses channels; water drying (gamma ~72 mN/m) collapses all channels in device D2. A switch-stimulus curve was established by counting closed channels versus surface tension (21–72 mN/m).
• Geometry dependence and threshold prediction: For h = 17 nm and t = 22 nm hBN top, channels with w = 420 nm remained open while w = 520 nm collapsed upon water drying (device D3). Using D = 1e-13 J for 22 nm hBN, the model predicted a caving-in width threshold w_th ~485 nm, consistent with observations (w_on < w_th < w_off).
• Bending/adhesion characterization: AFM profiles of closed channels matched a simple polynomial bending shape. Peeling curvature C scaled with thickness as C ~ t^{-Q/2} with Q = 2.88 ± 0.08, implying D ~ t^3, consistent with multilayer van der Waals plate theory and independent blister-test results. From thickness dependence, WS2–SiO2 adhesion energy was estimated as ~82 mJ/m^2.
• Reversibility criterion and phase diagram: A rewetting energy balance yielded inequalities combining caving-in and reversibility conditions, enabling a universal alpha–g phase diagram. Experimental points across multiple devices/liquids/materials aligned well with predicted stiff, irreversible, and switchable regions, enabling rational design.
• Robustness and cycling: Dry, closed channels remained closed for months but reopened upon rewetting. Reversible switching was repeatable over many cycles (noted in supplementary data).
• Zeptoliter nanocapsule: A functional nanocapsule was designed with switchable gates (w = 2 μm) and a stiff container (w_c = 600 nm), h = 37 nm, hBN top/graphene bottom. After IPA removal, gates closed, sealing ~100 zL of liquid; trapping time ~10 s was demonstrated. Phase-diagram parameters placed gates in the switchable region (alpha ~23) and the container in the stiff region (alpha ~4).

The findings validate the hypothesis that elastocapillary forces can be harnessed in 2D material nanochannels to realize programmable, reversible nanofluidic switches. By quantitatively linking channel geometry, material stiffness, adhesion, and liquid wettability, the work provides a predictive framework for designing nanoswitches. The agreement between model predictions (e.g., width thresholds, stiffness scaling, phase boundaries) and experiments demonstrates that nanofluidic elements can be deliberately engineered to switch based on capillary stimuli and recover upon rewetting. This enables active control in integrated nanofluidic circuits and affords new capabilities such as zeptoliter-scale liquid encapsulation in nanocapsules. The use of atomically smooth van der Waals materials minimizes roughness and enables reproducible interfacial properties, supporting both fundamental studies of nanoconfined fluids and potential applications in on-device chemistry/biochemistry. The phase diagram further suggests that some nanoslits used for transport studies may tolerate dry-state collapse yet remain suitable upon rewetting, potentially easing geometrical constraints for device design.

The study demonstrates elastocapillarity-driven, reversible nanoswitching in 2D material nanochannels and introduces a universal, predictive phase diagram based on two dimensionless parameters that capture geometry-dependent flexibility and wettability/adhesion. The approach enables rational design of switchable nanofluidic elements, including nanocapsules that can encapsulate zeptoliter volumes (~100 zL) using switchable gates while maintaining a stiff container. Main contributions include: (1) experimental realization and optical/AFM visualization of nanoswitching; (2) derivation and validation of caving-in and reversibility criteria; (3) quantitative adhesion/stiffness characterization via AFM bending profiles and peeling curvature scaling; and (4) demonstration of a functional nanocapsule. Future work could optimize gate geometry to increase trapping time and reduce leakage, refine surface chemistries to stabilize adhesion/wetting properties, extend to other 2D materials and liquids (including electrolytes), and integrate nanoswitches into more complex programmable nanofluidic circuits for studies of nanoconfined chemistry and biochemistry.

• Surface contamination and residue can affect adhesion energy and reversibility; acetone leaves residues that alter interfacial properties, though regeneration via hot acetone baths followed by IPA rinsing is possible.
• Near phase boundaries, device-to-device and channel-to-channel variability (geometry, adhesion) leads to probabilistic outcomes rather than deterministic switching.
• Dry, closed channels can remain closed for long periods; while beneficial for storage, this relies on stable dry conditions and consistent interfacial properties.
• The demonstrated nanocapsule exhibited a limited trapping time (~10 s), indicating leakage pathways; improvements require optimizing gate length and minimizing wall leakage.
• In solutions with electrolytes or solutes, drying may locally change concentrations, surface tension, and potentially lead to precipitation, complicating control of encapsulated environments; careful monitoring and design (short switch sections) are needed.
• Assumptions of continuum mechanics and Young-Laplace validity are applied down to few-nanometer confinement; while supported by literature, extreme confinement may introduce deviations.