Growth Dynamics and Gas Transport Mechanism of Nanobubbles in Graphene Liquid Cells

Formation, evolution, and vanishing of bubbles are common phenomena in our nature, which can be easily observed in boiling or falling waters, carbonated drinks, gas-forming electrochemical reactions, etc. However, the morphology and the growth dynamics of the bubbles at nanoscale have not been fully investigated owing to the lack of proper imaging tools that can visualize nanoscale objects in liquid phase. Here we demonstrate, for the first time, that the nanobubbles in water encapsulated by graphene membrane can be visualized by in situ ultrahigh vacuum transmission electron microscopy (UHV-TEM), showing the critical radius of nanobubbles determining its unusual long-term stability as well as two distinct growth mechanisms of merging nanobubbles (Ostwald ripening and coalescing) depending on their relative sizes. Interestingly, the gas transport through ultrathin water membranes at nanobubble interface is free from dissolution, which is clearly different from conventional gas transport that includes condensation, transmission and evaporation. Our finding is expected to provide a deeper insight to understand unusual chemical, biological and environmental phenomena where nanoscale gas-state is involved.

There have been intensive efforts to characterize the nanobubbles in liquid phase, which includes ion conductance measurement through a solid-state nanopore 15 , topographic imaging by atomic force microscopy (AFM) 16 and direct visualization by optical methods 17,18 . None of these, however, was capable of imaging the liquid phase nanobubbles in real time with sub-10 nm resolution. In this regard, in-situ TEM would be the best method to observe the behaviours of nanobubbles, but the resolution is still limited by the thickness and the robustness of liquid cell membranes. Recently, it was reported that graphene can be utilized as a perfect liquid cell membrane for in-situ TEM imaging of nanocrystal growth thanks to its atomic thickness, flexibility, extraordinary mechanical strength and high conductivity 11 . Thus, we tried to investigate the evolution of nanobubbles by encapsulating them in a graphene liquid cell membrane for in-situ TEM imaging in ultra-high vacuum.
The graphene liquid cell was fabricated by the sequential wet transfer of monolayer graphene synthesized by chemical vapour deposition (Fig. S1) [19][20][21] . The water islands are naturally captured during the wet transfer process of graphene to a graphene-supported TEM grid (Fig. S2). As shown in Fig. 1, the top and side views of nanobubbles show the plano-convex morphology whose diameter ranges from 5 to 15 nm. It should be noted that the high mechanical flexibility and strength of graphene allows the cross-sectional imaging of nanobubbles in a folded liquid cell ( Fig. 1e to g).
We found that the contact angles of nanobubbles are ~71.2±1.2 regardless of their sizes (Fig. S3). These values were used to calculate the internal pressure of nanobubbles using Young-Laplace equation, , where is the pressure difference across the nanobubble interface, is the surface tension of water, and is the curvature radius of nanobubbles (Fig. 1h). According to this equation, Young-Laplace pressure inside a 10 nm-diameter nanobubble is calculated to be 27 MPa, which is 270 times higher than ambient pressure.
According to classical diffusion theory, the lifetime of a nanobubble was predicted to be ~1 s 22 . In fact, however, nanobubbles are very stable even for several hours as revealed by liquid-phase AFM 23 . Many explanations on this superstability of nanobubbles were proposed, including stabilization by three-phase contact line pinning 24 and dynamic equilibrium at water-vapour interface 25,26 . In addition, the critical radius of stable nanobubbles was predicted to be ~1.7 nm by molecular dynamic (MD) simulation 27 and ~85 nm by dynamic equilibrium theory 26 , but there has been no experimental confirmation so far. Here we show, for the first time, that the critical radius of stable nanobubbles is 4~6 nm as shown in Fig. 2a and b. For the nanobubble radius below the critical range, the radius keeps decreasing until it completely collapses, while the nanobubble lager than ~6 nm persists for more than 10 min. Surprisingly, the model calculation based on the structural parameters from the TEM observation gives the stable radius of 6.10 nm, which fits the critical radius range in Fig. 3a and b (please see Supplementary Information for more details).
Nanobubbles are growing by merging with adjacent nanobubbles, which shows clearly different two pathways depending on their relative sizes. In case that the sizes are distinctively different (R>R′), the smaller bubble tends to disappear near the surface of the growing larger bubble (Fig. 2c), which is similar to Ostwald ripening that is known as a solid state phenomenon that small crystals are dissolved and redeposited on to the surface of larger crystals. It seems that gas diffuses from one bubble to another across the persisting boundary. On the other hand, two similar-sized nanobubbles (R~R′) show a coalescing process after breaking their interface, followed by reshaping into dumbbell-like and spherical morphology (Fig. 2d). nanobubbles. The nanobubbles whose radii larger than 6 nm persist more than 10 min, while smaller bubbles tend to disappear in 1 min. In the Ostwald ripening-like process, the radius of the smaller nanobubble show a change in slope with respect to time, while the radius of the larger bubble steadily increases (Fig. 3c). Here, we suppose that a new pathway of gas diffusion is created when the thickness of the interface is smaller than  Usually, conventional gas transport between remote nanobubbles includes condensation, transmission and evaporation steps 14 . However, in case that two Ostwald ripening nanobubbles come into contact each other, the gaseous particles seem to diffuse as a discrete packet from one to another through the ultrathin water membrane without hydration, which needs to be importantly considered for the assembly and function of biomolecules and other systems where nanoscale gas state is involved. The instantaneous breakjunction of the ultrathin water membrane appears dominantly as the thickness decrease below ~2 nm as shown in Fig. 4b.
In summary, the liquid phase nanobubbles encapsulated by graphene membrane were visualized by in-situ UHV-TEM, showing the critical radius of nanobubbles determining its long-term stability as well as two different growth processes of merging nanobubbles depending on their relative sizes. It is remarkable that the instantaneous rupture of the ultrathin water membrane between nanobubbles allows direct unhydrated gas transport that has not been observed so far. We believed that this phenomenon needs to be importantly considered in various biological and environmental systems where nanoscale gas state is involved.

Methods
Preparation of monolayer graphene. Graphene was synthesized by the chemical vapour deposition method on a high purity copper foil (Alfa Aesar, 99.999%) with flowing 70 mTorr H 2 and 650 mTorr CH 4 gas. As grown graphene on Cu was spincoated with PMMA (poly methyl methacrylate) and back-side graphene was etched using oxygen plasma. Then, the PMMA layer on graphene was removed by acetone.
Remaining copper was etched in 1.8wt% ammonium persulfate (APS) solution. Finally, the monolayer graphene was rinsed with distilled water several times. that of an EM with a field-emission gun (FEG) filament falls, its current density is lower by about 100-1000 times than that of the FEG filament. Moreover, the current density of ~1 A cm −2 at most brings a temperature increase of a few degrees of celsius 28 , which perhaps hardly influences the sample in a recoding time, usually 2 to 5 minutes. In fact, while observing the magnified images, no changes in image detail arising from electron beam irradiations were detected. Therefore, we believed that these advantages as well as unique capabilities of graphene liquid cell as a perfect membrane for EM imaging 11,29 has enabled the characterization of nanobubbles without contamination in this study.    nanobubble and inter-bubble distance measured in Fig. 2c. d, Calculated internal pressure of Ostwald ripening nanobubbles in Fig. 2c. The inset shows the calculation result representing the liquid water density with respect to their relative size and distance between two adjacent nanobubbles, indicating that the water density decreases at the interface region as two bubbles get closer, which is a driving force to put two remote bubbles together.

A. Calculation on the stable radius of plano-convex shaped nanobubbles
The stable radius of nanobubbles was calculated considering the structural parameters from TEM observation and the molecular dynamics simulation results by Matsumoto et al. (Ref. 27). The setting temperature of water is 300K, and the system volume was fixed at V = 30 x 30 x 7.5 (nm) 3 . The liquid pressure of system P sys can be estimated from the density of liquid The surrounding liquid pressure of nanobubble, P liq is given by P liq = P vap -ΔP, where P vap is the gas pressure inside the nanobubble and ΔP is Young-Laplace pressure. At 300K, the vapor density inside nanobubble is very low, so it can be set as P vap = 0 in our calculation.
Thus, P liq simply can be expressed as ~ -ΔP. Now the radius of stable nanobubble can be derived from the equilibrium equation between liquid and system pressure, P liq = P sys as following: The   * Supplementary movies available on request: byunghee@snu.ac.kr