Stability of Surface Nanobubbles: A Molecular Dynamics Study

Ionic adsorption on bulk nanobubble interfaces and its uncertain role in diffusive stability

HYPOTHESIS

Bulk nanobubbles have been proposed to improve gas exchange in a variety of applications, such as in water treatment, theragnostics, and microfluidic surface cleaning. However, there is currently no consensus regarding the mechanism responsible for their reportedly long lifetimes, which contradicts classical understanding of diffusive bubble dynamics. Recently, there has been increasing support for an electrostatic stability mechanism, following from experiments that observe negatively charged zeta potentials around nanobubbles.

SIMULATIONS

We use high-fidelity Molecular Dynamics simulations to model bulk nanobubbles under mechanical equilibrium in a sodium iodide electrolyte solution, to investigate ionic adsorption on the liquid-gas interface, and resulting zeta potential. We critically examine the hypothesised electrostatic stress underpinning this previously suggested stability mechanism, which is theorised to stabilise the nanobubbles against dissolution by counteracting the otherwise dominant effects of surface tension, however, has been too difficult to directly measure in experiments.

FINDINGS

Ions adsorb onto the liquid-gas interface, confirming an Electric Double Layer (EDL) distribution around the nanobubble with an estimated zeta potential, in accordance with experiments. However, we find no significant electrostatic stress exerted on the nanobubble surface, as any ion charge density in the EDL is completely neutralised by the rearrangement of the water molecules. As a result, the internal gas pressure is still well predicted by the standard Laplace pressure equation (with a fitted Tolman length correction ), challenging an essential assumption underlying the previously proposed theories, and we instead speculate on alternative mechanisms for electrostatic-based stability.

Mechanism of Charged Graphene Substrate Effects on the Stability of Interfacial Nanobubbles: Molecular Dynamics Simulations

Charged solid substrates play a crucial role in influencing the behavior of interfacial nanobubbles, although the underlying mechanisms are not yet fully understood. To explore this process in greater depth, we employed molecular dynamics (MD) simulations to systematically examine the effects of charged graphene on the morphological evolution, solid interface structure, and stability of interfacial nanobubbles, thereby revealing the intrinsic mechanisms. Our findings indicate that as surface charge density increases, the gas-solid interactions gradually diminish while the liquid-solid interactions significantly intensify. This results in a progressive reduction in both the contact angle and radius of the nanobubbles, eventually causing their detachment from the substrate and transformation to bulk-phase nanobubbles. Moreover, the enhanced gas accumulation effect at the solid interface leads to a reduction in the internal pressure of the bubbles, thus improving the stability of the interfacial nanobubbles. Additionally, the increase in the surface charge density elevates the water molecule density at the solid interface, which in turn strengthens the hydrogen bond network of interfacial water molecules, further stabilizing the liquid-solid interface structure. In summary, this study highlights the critical role of surface charge in regulating interfacial nanobubble behavior, providing new theoretical guidance for optimizing electrode materials and controlling bubble behavior in electrochemical systems.

Theoretical model of dynamics and stability of nanobubbles on heterogeneous surfaces

Surface nanobubbles have revealed a new mechanism of gas-liquid-solid interaction at the nanoscale; however, the nanobubble evolution on real substrates is still veiled, because the experimental observation of contact line motions at the nanoscale is too difficult.

HYPOTHESIS

This study proposes a theoretical model to describe the dynamics and stability of nanobubbles on heterogeneous substrates. It simultaneously considers the diffusive equilibrium of the liquid-gas interface and the mechanical equilibrium at the contact line, and introduces a surface energy function to express the substrate's heterogeneity.

VALIDATION

The present model unifies the nanoscale stability and the microscale instability of surface bubbles. The theoretical predictions are highly consistent to the nanobubble morphology on heterogeneous surfaces observed in experiments. As the nanobubbles grow, a lower Laplace pressure leads to weaker gas adsorption, and the mechanical equilibrium can eventually revert to the classical Young-Laplace equation above microscale.

FINDINGS

The analysis results indicate that both the decrease in substrate surface energy and the increase in gas oversaturation are more conducive to the nucleation and growth of surface nanobubbles, leading to larger stable sizes. The larger surface energy barriers result in the stronger pinning, which is beneficial for achieving stability of the pinned bubbles. The present model is able to reproduce the continual behaviors of the three-phase contact line during the nanobubble evolution, e.g., "pinning, depinning, slipping and jumping" induced by the nanoscale defects.

Removal of Nanoparticles by Surface Nanobubbles Generated via Solvent-Water Exchange: A Critical Perspective

The swift progression of technology in electronic fabrication is adhering to a trend of miniaturization, descending to the nanoscale. Surface contaminants, such as nanoparticles, can influence the performance of silicon wafers, thereby necessitating the evolution of novel cleaning methodologies. Surface nanobubbles (SNs) are phenomena that have attracted considerable attention over the past decade. A salient feature of SNs is their capacity to eliminate nanoparticles from silicon wafers. In this Perspective, our objective is to scrutinize whether this capability can be unequivocally ascribed to SNs. Initially, we offer a succinct elucidation of the nature of SNs; subsequently, we evaluate the claims regarding the cleaning efficacy of SNs; finally, we present our interpretation of the operative forces and propose potential scenarios of the interaction between SNs and nanoparticles. Consequently, the aim of this Perspective is to emphasize the significance of comprehending the interaction between SNs and nanoparticles with the intent to delineate new research trajectories bearing both fundamental and industrial ramifications.

The Behaviors of Interfacial Nanobubbles on Flat or Rough Electrode Surfaces in Electrochemistry

The existence of interfacial nanobubbles on electrode surfaces is thought to block the active area, leading to a considerable decrease in the energy conversion efficiency. Gaining insight into how bubbles form on electrodes will be beneficial for designing effective electrochemical cells and enhancing the electrolytic efficiency. In this article, molecular dynamics (MD) simulations are employed to make a systematic comparison of behaviors of interfacial nanobubbles on both flat and rough electrode surfaces in electrochemistry. On a flat electrode surface, bubble nucleation can be categorized into single-site and multisite nucleation, influenced by the electrode sizes and electrolytic rates. The various rates of gas production result in three different scenarios for single-site nucleation: "growth-growth," "growth-shrinking," and "growth-stabilization" behaviors. On a rough one, bubbles are pinned at an early stage. Either through cooperative release or self-release, the bubbles continue to grow until the influx and outflux gas of the bubble reach an equilibrium. In addition, the evolutionary mechanism of interface nanobubbles was discussed on a rough nanoelectrode surface. Based on the dynamic equilibrium mechanism, a theoretical relationship between contact angle and base diameter of equilibrium interfacial nanobubbles was developed. The theoretical model can qualitatively describe the simulation observation of how bubble's shape depends on the electrode surface morphology.

Diffusiophoretically Mediated Nanopatterning by Solvent Nanodroplets on Polystyrene Surfaces

Dissolution is a ubiquitous process in nature and industry. However, due to technical difficulties, the detailed dissolution process at the nanoscale has seldom been captured experimentally. In this study, we investigated the dissolution dynamics in the confinement of toluene surface nanodroplets on polystyrene (PS) thin films in oversaturated toluene/water mixture solutions. This was achieved by adjusting the immersion durations from several minutes to 9 h. Dissolution takes place upon the deposition of nanodroplets on the PS surfaces, leading to the formation of surface nanostructures. Interestingly, we found that the induced nanostructures underwent complex morphological changes, from complex nanocraters with central bulges and/or multiple rims to simple nanocraters. We speculate that diffusiophoresis plays a key role in the formation of the complex nanocraters, as it facilitates the transportation of dissolved PS molecules inside the nanodroplets. We believe this finding not only enhances our understanding of dissolution dynamics at the nanoscale but also holds promise for applications in dissolution-based nanopatterning.

Molecular Dynamics Study of the Microscopic Mechanical Balance at the Three-Phase Contact Line of Interfacial Nanobubble

This study reveals the microscopic mechanical balance at the three-phase contact line (TPCL) of an interfacial nanobubble on a substrate with a wettability pattern using molecular dynamics simulations. The apparent contact angle was compared to that evaluated using Young's equation, in which the interfacial tensions were computed using a mechanical route. The comparison was conducted by changing the wettability of the substrate from hydrophilic to neutral while maintaining a hydrophobic region in the center of the substrate. When the wettability pattern pins the TPCL at the wettability boundary, the contact angle computed by Young's equation is larger than the apparent contact angle because a pinning force exists in the inward direction of the nanobubble. Conversely, on the surfaces where the wettability pattern does not pin the TPCL, the contact angle computed by Young's equation agrees with the apparent contact angle because the pinning force disappears. The distribution of principal stresses around the TPCL, which was visualized for the first time in this study, indicates that large compressive principal stresses exist between the liquid phase and the solid substrate interface, which pin the TPCL at the surface wettability boundary, and that the maximum principal stress occurs in the inward direction of the nanobubbles at the TPCL. The normalized pinning force estimated from the maximum principal stress is equivalent to that measured experimentally.

Molecular Mechanisms of the Generation and Accumulation of Gas at the Interface

Gas-evolving reactions are widespread in chemical and energy fields. However, the generated gas will accumulate at the interface, which reduces the rate of gas generation. Understanding the microscopic processes of the generation and accumulation of gas at the interface is crucial for improving the efficiency of gas generation. Here, we develop an algorithm to reproduce the process of catalytic gas generation at the molecular scale based on the all-atom molecular dynamics simulations and obtain the quantitative evolution of the gas generation, which agrees well with the experimental results. In addition, we demonstrate that under an external electric field, the generated gas molecules do not accumulate at the electrode surface, which implies that the electric field can significantly increase the rate of the gas generation. The results suggest that the external electric field changes the structure of the water molecules near the electrode surface, making it difficult for gas molecules to accumulate on the electrode surface. Furthermore, it is found that gas desorption from the electrode surface is an entropy-driven process, and its accumulation at the electrode surface depends mainly on the competition between the entropy and the enthalpy of the water molecules under the influence of the electric field. These results provide deep insight into gas generation and inhibition of gas accumulation.

Contact angle and stability of interfacial nanobubble supported by gas monolayer

Since solid-liquid interfacial nanobubbles (INBs) were first imaged, their long-term stability and large contact angle have been perplexing scientists. This study aimed to investigate the influence of internal gas density and external gas monolayers on the contact angle and stability of INB using molecular dynamics simulations. First, the contact angle of a water droplet was simulated at different nitrogen densities. The results showed that the contact angle increased sharply with an increase in nitrogen density, which was mainly caused by the decrease in solid-gas interfacial tension. However, when the nitrogen density reached 2.57 nm-3, an intervening gas monolayer (GML) was formed between the solid and water. After the formation of GML, the contact angle slightly increased with increasing gas density. The contact angle increased to 180° when the nitrogen density reached 11.38 nm-3, indicating that INBs transformed into a gas layer when they were too small. For substrates with different hydrophobicities, the contact angle after the formation of GML was always larger than 140° and it was weakly correlated with substrate hydrophobicity. The increase in contact angle with gas density represents the evolution of contact angle from macro- to nano-bubble, while the formation of GML may correspond to stable INBs. The potential of mean force curves demonstrated that the substrate with GML could attract gas molecules from a longer distance without the existence of a potential barrier compared with the bare substrate, indicating the potential of GML to act as a gas-collecting panel. Further research indicated that GML can function as a channel to transport gas molecules to INBs, which favors stability of INBs. This research may shed new light on the mechanisms underlying abnormal contact angle and long-term stability of INBs.

Ultrasound-Responsive Biomimetic Superhydrophobic Drug-Loaded Mesoporous Silica Nanoparticles for Treating Prostate Tumor

Interfacial nanobubbles on a superhydrophobic surface can serve as ultrasound cavitation nuclei for continuously promoting sonodynamic therapy, but their poor dispersibility in blood has limited their biomedical application. In this study, we proposed ultrasound-responsive biomimetic superhydrophobic mesoporous silica nanoparticles, modified with red blood cell membrane and loaded with doxorubicin (DOX) (F-MSN-DOX@RBC), for RM-1 tumor sonodynamic therapy. Their mean size and zeta potentials were 232 ± 78.8 nm and −35.57 ± 0.74 mV, respectively. The F-MSN-DOX@RBC accumulation in a tumor was significantly higher than in the control group, and the spleen uptake of F-MSN-DOX@RBC was significantly reduced in comparison to that of the F-MSN-DOX group. Moreover, the cavitation caused by a single dose of F-MSN-DOX@RBC combined with multiple ultrasounds provided continuous sonodynamic therapy. The tumor inhibition rates in the experimental group were 71.5 8 ± 9.54%, which is significantly better than the control group. DHE and CD31 fluorescence staining was used to assess the reactive oxygen species (ROS) generated and the broken tumor vascular system induced by ultrasound. Finally, we can conclude that the combination of anti-vascular therapy, sonodynamic therapy by ROS, and chemotherapy promoted tumor treatment efficacy. The use of red blood cell membrane-modified superhydrophobic silica nanoparticles is a promising strategy in designing ultrasound-responsive nanoparticles to promote drug-release.

Confined Electrochemical Behaviors of Single Platinum Nanoparticles Revealing Ultrahigh Density of Gas Molecules inside a Nanobubble

Understanding the basic physicochemical properties of gas molecules confined within nanobubbles is of fundamental importance for chemical and biological processes. Here, we successfully monitored the nanobubble-confined electrochemical behaviors of single platinum nanoparticles (PtNPs) at a carbon fiber ultramicroelectrode in HClO₄ and H₂O₂ solution. Due to the catalytic decomposition of H₂O₂, a single oxygen nanobubble was formed on individual PtNPs to block the active surface of particles for proton reduction and to suppress their stochastic motion, resulting in significantly distinguished current traces. Furthermore, the combination of theoretical calculations and high-resolution electrochemical measurements allowed the nanobubble size and the oxygen gas density inside a single nanobubble to be quantified. Moreover, the ultrahigh oxygen density inside (1046 kg/m³) was revealed, indicating that gas molecules in a nanosized space existed with a high state of aggregation. Our approach sheds light on the gas aggregation behaviors of nanoscale bubbles using single-entity electrochemical measurements.

How sodium chloride extends lifetime of bulk nanobubbles in water

We present a molecular dynamics simulation study on the effects of sodium chloride addition on stability of a nitrogen bulk nanobubble in water. We find that the lifetime of the bulk nanobubble is extended in the presence of NaCl and reveal the underlying mechanisms. We do not observe spontaneous accumulation or specific arrangement of ions/charges around the nanobubble. Importantly, we quantitatively show that the N₂ molecule selectively diffuses through water molecules rather than pass by any ions after it leaves the nanobubble due to the much weaker water-water interactions than ion-water interactions. The strong ion-water interactions cause hydration effects and disrupt hydrogen bond networks in water, which leave fewer favorable paths for the diffusion of N₂ molecules, and by that reduce the degree of freedom in the dissolution of the nanobubble and prolong its lifetime. These results demonstrate that the hydration of ions plays an important role in stability of the bulk nanobubble by affecting the dynamics of hydrogen bonds and the diffusion properties of the system, which further confirm and interpret the selective diffusion path of N₂ molecules and the extension of lifetime of the nanobubble. The new atomistic insights obtained from the present research could potentially benefit the practical application of bulk nanobubbles.

The fate of bulk nanobubbles under gas dissolution

Artificially added or undesired organic and inorganic contaminants in solution that are interfacially active always tend to be adsorbed at the gas-liquid interface of micro- and nano-bubbles, affecting the stability of the tiny bubbles. In this work, by using molecular dynamics simulations we study how the adsorbed surfactant-like molecules, with their amphiphilic character, affect the dissolution of the existing bulk nanobubbles under low gas supersaturation environments. We find that, depending on the concentration of the dissolved gas and the molecular structure of surfactants, two fates of bulk nanobubbles whose interfaces are saturated by surfactants are found: either remaining stable or being completely dissolved. With gas dissolution, the bubble shrinks and the insoluble surfactants form a monolayer with an increasing areal density until an extremely low (close to 0) surface tension is reached. In the limit of vanishing surface tension, the chemical structure of surfactants crucially affects the bubble stability by changing the monolayer elastic energy. Two basic conditions for stable nanobubbles at low gas saturation are identified: vanishing surface tension due to bubble dissolution and positive spontaneous curvature of the surfactant monolayer. Based on this observation, we discuss the similarity in the stability mechanism of bulk nanobubbles and that of microemulsions.

Quantifying interfacial tensions of surface nanobubbles: How far can Young's equation explain?

Nanobubbles at solid-liquid interfaces play a key role in various physicochemical phenomena and it is crucial to understand their unique properties. However, little is known about their interfacial tensions due to the lack of reliable calculation methods. Based on mechanical and thermodynamic insights, we quantified for the first time the liquid-gas, solid-liquid, and solid-gas interfacial tensions of submicron-sized nitrogen bubbles at graphite-water interfaces using molecular dynamics (MD) analysis. It was revealed that Young's equation holds even for nanobubbles with different radii. We found that the liquid-gas and solid-liquid interfacial tensions were not largely affected by the gas density inside the nanobubbles. In contrast, the size effect on the solid-gas interfacial tension was observed, namely, the value dramatically decreased upon an increase in the gas density due to gas adsorption on the solid surface. However, our quantitative evaluation also revealed that the gas density effect on the contact angles is negligible when the footprint radius is larger than 50 nm, which is a typical range observed in experiments, and thus the flat shape and stabilization of submicron-sized surface bubbles observed in experiments cannot be explained only by the changes in interfacial tensions due to the van der Waals interaction-induced gas adsorption, namely by Young's equation without introducing the pinning effect. Based on our analysis, it was clarified that additional factors such as the differences in the studied systems are needed to explain the unresolved open issues - a satisfactory explanation for the nanobubbles in MD simulations being ultradense, non-flat, and stable without pinning.

Ion adsorption stabilizes bulk nanobubbles

The mechanism leading to the extraordinary stability of bulk nanobubbles in aqueous solutions remains an outstanding problem in soft matter, modern surface science, and physical chemistry science. In this work, the stability of bulk nanobubbles in electrolyte solutions under different pH levels and ionic strengths is studied. Nanobubbles are generated via the technique of ultrasonic cavitation, and characterized for size, number concentration and zeta potential under ambient conditions. Experimental results show that nanobubbles can survive in both acidic and basic solutions with pH values far away from the isoelectric point. We attribute the enhanced stability with increasing acidity or alkalinity of the aqueous solutions to the effective accumulation of net charges, regardless of their sign. The kinetic stability of the nanobubbles in various aqueous solutions is evaluated within the classic DLVO framework. Further, by combining a modified Poisson-Boltzmann equation with a modified Langmuir adsorption model, we describe a simple model that captures the influence of ion species and bulk concentration and reproduce the dependence of the nanobubble's surface potential on pH. We also discuss the apparent contradiction between quantitative calculation by ion stabilization model and experimental results. This essentially requires insight into the structure and dynamics of interfacial water on the atomic-scale.

Molecular simulations on the stability and dynamics of bulk nanobubbles in aqueous environments

Nanobubbles have attracted significant attention due to their unexpectedly long lifetimes and stabilities in liquid solutions. However, explanations for the unique properties of nanobubbles at the molecular scale are somewhat controversial. Of special interest is the validity of the Young-Laplace equation in predicting the inner pressure of such bubbles. In this work, large-scale molecular dynamics simulations were performed to study the stability and diffusion of nanobubbles of methane in water. Two types of force field, atomistic and coarse-grained, were used to compare the calculated results. In accordance with predictions from the Young-Laplace equation, it was found that the inner pressure of the nanobubbles increased with decreasing nanobubble size. Consequently, a large pressure difference between the nanobubble and its surroundings resulted in the high solubility of methane molecules in water. The solubility was considered to enable nanobubble stability at exceptionally high pressures. Smaller bubbles were observed to be more mobile via Brownian motion. The calculated diffusion coefficient also showed a strong dependence on the nanobubble size. However, this active mobility of small nanobubbles also triggered a mutable nanobubble shape over time. Nanobubbles were also found to coalesce when they were sufficiently close. A critical distance between two nanobubbles was thus identified to avoid coalescence. These results provide insight into the behavior of nanobubbles in solution and the mechanism of their unique stability while withstanding high inner pressures.

Cassie State Stability and Gas Restoration Capability of Superhydrophobic Surfaces with Truncated Cone-Shaped Pillars

The gas layer stability on superhydrophobic surfaces and gas restoration on the immersed superhydrophobic surfaces have been great challenges for their practical applications in recent years. Inspired by the naturally existing mushroom-like super-repellent superhydrophobic patterns, we choose superhydrophobic surfaces with truncated cone-shaped pillars as our research objects to tackle such challenges by tuning their geometrical parameters. We perform molecular dynamics simulations to investigate the Cassie-Wenzel transition under external pressure and the Wenzel-Cassie transition due to underwater spreading of compressed bubbles. Theories based on the Young-Laplace equation and total free-energy variation are developed to explore the influence of geometrical parameters of pillars on the pressure resistance and underwater gas restoration, which is in good agreement with simulation results. These simulation results and theoretical analysis suggest that cork-shaped pillars, analogous to the surface structures of natural organisms like springtails and Salvinia leaves, can be super-repellent to the liquid and favorable for the gas spreading process. Our study provides theoretical guidance for the design of superhydrophobic surfaces with both Cassie state stability and gas restoration capability.

Electrocatalytic generation and tuning of ultra-stable and ultra-dense nanometre bubbles: an in situ molecular dynamics study

Electrocatalytic generation of nanometre gas bubbles (nanobubbles) and their tuning are important for many energy and chemical processes. Studies have sought to use indirect or ex situ methods to investigate the dynamics and properties of nanobubbles, which are of fundamental interest. Alternatively, we present a molecular dynamics simulation method, which features in situ and high spatial resolution, to directly address these fundamentals. Particularly, our simulations can quantitatively reproduce the generation of ultra-stable and ultra-dense nanobubbles observed in electrochemical experiments. More importantly, our results demonstrate that the classical nucleation theory is still valid even for the scale down to several nanometres, to predict the dynamics and properties of nanobubbles. This provides general guidelines to design efficient nanocatalysts and nanoelectrodes. In our specific case, nanoelectrodes with wetting angles below 71° can suppress the generation of surface nanobubbles.

Dynamic Equilibrium Model for Surface Nanobubbles in Electrochemistry

Gas bubbles are ubiquitous in electrochemical processes, particularly in water electrolysis. Due to the development of gas-evolving electrocatalysis and energy conversion technology, a deep understanding of gas bubble behaviors at the electrode surface is highly desirable. In this work, by combining theoretical analysis and molecular simulations, we study the behaviors of a single nanobubble electrogenerated at a nanoelectrode. With the dynamic equilibrium model, the stability criteria for stationary surface nanobubbles are established. We show theoretically that a slight change in either the gas solubility or solute concentration results in various nanobubble dynamic states at a nanoelectrode: contact line pinning in aqueous and ethylene glycol solutions, oscillation of pinning states in dimethyl sulfoxide, and mobile nanobubbles in methanol. The above complex nanobubble behavior at the electrode/electrolyte interface is explained by the competition between gas influx into the nanobubble and outflux from the nanobubble.

Cavitation Mean Expectation Time in a Stretched Lennard-Jones Fluid under Confinement

We investigate the nucleation of cavitation bubbles in a confined Lennard-Jones fluid subjected to negative pressures in a cubic enclosure. We perform molecular dynamics (MD) simulations with tunable interatomic potentials that enable us to control the wettability of solid walls by the liquid, that is, its contact angle. For a given temperature and pressure, as the solid is taken more hydrophobic, we put in evidence, an increase in nucleation probability. A Voronoi tessellation method is used to accurately detect the bubble appearance and its nucleation rate as a function of the contact angle. We adapt classical nucleation theory (CNT) proposed for the heterogeneous case on a flat surface to our situation where bubbles may appear on flat walls, edges, or corners of the confined box. We finally calculate a theoretical mean expectation time in these three cases. The ratio of these calculated values over the homogeneous case is computed and compared successfully against MD simulations. Beyond the infinite liquid case, this work explores the heterogeneous nucleation of cavitation bubbles, not only in the flat surface case but for more complex confining geometries.

The interplay among gas, liquid and solid interactions determines the stability of surface nanobubbles

Surface nanobubbles are gaseous domains found at immersed substrates, whose remarkable persistence is still not fully understood. Recently, it has been observed that the formation of nanobubbles is often associated with a local high gas oversaturation at the liquid-solid interface. Tan, An and Ohl have postulated the existence of an effective potential attracting the dissolved gas to the substrate and producing a local oversaturation within 1 nm from it that can stabilize nanobubbles by preventing outgassing in the region where gas flow would be maximum. It is this effective solid-gas potential - which is not the intrinsic, mechanical interaction between solid and gas atoms - its dependence on chemical and physical characteristics of the substrate, gas and liquid, that controls the stability and the other characteristics of surface nanobubbles. Here, we perform free energy atomistic calculations to determine, for the first time, the effective solid-gas interaction that allows us to identify the molecular origin of the stability and other properties of surface nanobubbles. By combining the Tan-An-Ohl model and the present results, we provide a comprehensive theoretical framework allowing, among others, the interpretation of recent unexplained experimental results, such as the stability of surface nanobubbles in degassed liquids, the very high gas concentration in the liquid surrounding nanobubbles, and nanobubble instability in organic solvents with high gas solubility.

Forced oscillation dynamics of surface nanobubbles

Surface nanobubbles have potential applications in the manipulation of nanoscale and biological materials, waste-water treatment, and surface cleaning. These spherically capped bubbles of gas can exist in stable diffusive equilibrium on chemically patterned or rough hydrophobic surfaces, under supersaturated conditions. Previous studies have investigated their long-term response to pressure variations, which is governed by the surrounding liquid's local supersaturation; however, not much is known about their short-term response to rapid pressure changes, i.e., their cavitation dynamics. Here, we present molecular dynamics simulations of a surface nanobubble subjected to an external oscillating pressure field. The surface nanobubble is found to oscillate with a pinned contact line, while still retaining a mostly spherical cap shape. The amplitude-frequency response is typical of an underdamped system, with a peak amplitude near the estimated natural frequency, despite the strong viscous effects at the nanoscale. This peak is enhanced by the surface nanobubble's high internal gas pressure, a result of the Laplace pressure. We find that accurately capturing the gas pressure, bubble volume, and pinned growth mode is important for estimating the natural frequency, and we propose a simple model for the surface nanobubble frequency response, with comparisons made to other common models for a spherical bubble, a constant contact angle surface bubble, and a bubble entrapped within a cylindrical micropore. This work reveals the initial stages of growth of cavitation nanobubbles on surfaces, common in heterogeneous nucleation, where classical models based on spherical bubble growth break down.

Universal Gas Adsorption Mechanism for Flat Nanobubble Morphologies

The adsorption of gas molecules at the substrate beneath interfacial nanobubbles modifies the energy of the solid-gas interface, and therefore affects their morphology. In this work, we describe a simple thermodynamic model that captures the influence of gas adsorption and gives flat bubble shapes with reduced gas-side contact angles relative to the zero-adsorption case, in agreement with experimental studies. We show that this effect is general to both hydrophilic and hydrophobic substrates and has a stabilizing influence that extends nanobubble lifetimes.

Electrochemically Generated Nanobubbles: Invariance of the Current with Respect to Electrode Size and Potential

Gas-producing electrochemical reactions are key to energy conversion and generation technologies. Bubble formation dramatically decreases gas-production rates on nanoelectrodes, by confining the reaction to the electrode boundary. This results in the collapse of the current to a stationary value independent of the potential. Startlingly, these residual currents also appear to be insensitive to the nanoelectrode diameter in the 5 to 500 nm range. These results are counterintuitive, as it may be expected that the current be proportional to the circumference of the electrode, i.e., the length of the three-phase line where the reaction occurs. Here, we use molecular simulations and a kinetic model to elucidate the origin of current insensitivity with respect to the potential and establish its relationship to the size of nanoelectrodes. We provide critical insights for the design and operation of nanoscale electrochemical devices and demonstrate that nanoelectrode arrays maximize conversion rates compared to macroscopic electrodes with same total area.

Stability of pinned surface nanobubbles against expansion: Insights from theory and simulation

While growth and dissolution of surface nanobubbles have been widely studied in recent years, their stability under pressure changes or a temperature increase has not received the same level of scrutiny. Here, we present theoretical predictions based on classical theory for pressure and temperature thresholds (p_c and T_c) at which unstable growth occurs for the case of air nanobubbles on a solid surface in water. We show that bubbles subjected to pinning have much lower p_c and higher T_c compared to both unpinned and bulk bubbles of similar size, indicating that pinned bubbles can withstand a larger tensile stress (negative pressure) and higher temperatures. The values of p_c and T_c obtained from many-body dissipative particle dynamics simulations of quasi-two-dimensional (quasi-2D) surface nanobubbles are consistent with the theoretical predictions, provided that the lateral expansion during growth is taken into account. This suggests that the modified classical thermodynamic description is valid for pinned bubbles as small as several nanometers. While some discrepancies still exist between our theoretical results and previous experiments, further experimental data are needed before a comprehensive understanding of the stability of surface nanobubbles can be achieved.

Nanobubble-Assisted Nanopatterning Reveals the Existence of Liquid Quasi-Two-Dimensional Foams Pinned to a Water-Immersed Surface

This paper reports on our observation of a quasi-two-dimensional (quasi-2D) liquid nanofoam spontaneously appearing on a submersed solid surface. Unlike common liquid foams existing on top of the liquid, the quasi-2D liquid nanofoam is pinned to a water-immersed solid surface. The foam imaging was performed by a nanobubble imprint technique, which allows recording the positions of the surface nanobubbles by their imprints in a polystyrene film, as described in our previous papers [Tarábková et al. Langmuir 2014, 30, 14522; Tarábková et al., Langmuir 2016, 32, 11221]. Nanobubble imprints are then examined by ex situ atomic force microscopy. Besides randomly distributed nanoprotrusions corresponding to solitary nanobubbles, quasi-periodic arrangements of a tight cellular structure and more spaced round-shaped patterns, corresponding to "dry" and "wet" quasi-2D micro- and nanofoams, respectively, are identified. Although randomly spread solitary nanobubbles can occupy up to 30% of an immersed solid surface, their self-organization in a quasi-2D nanofoam leads to surface gas coverage reaching up to 80%, which implies significantly lowered surface wetting. Existence of a submersed quasi-2D nanofoam thus opens the novel question on the impact of dense surface nanobubble assemblies on heterogeneous processes at the solid-liquid interface.

Nucleation and Growth of a Nanobubble on Rough Surfaces

We study the nucleation and growth of a nanobubble on rough surfaces using molecular dynamics simulations. A nanobubble nucleates and grows by virtue of a heterogeneous surface reaction which results in the production of gas molecules near the surface. We study the role of surface roughness in the nucleation and growth behavior of a nanobubble. We perform simulations at various reaction rates and surface morphology and quantified the growth dynamics of a nanobubble. Our simulations show that after the onset of nucleation, the nanobubble grows rapidly with radius following t^1/3 behavior followed by a diffusive growth regime which is marked by t^1/2 growth behavior. This growth behavior remains independent of surface roughness and reaction rates over the range considered in this study. We also quantified the oversaturation of gas required for nucleation of a nanobubble and demonstrated its dependence on the surface morphology.

Probing the "Gas Tunnel" between Neighboring Nanobubbles

Surface nanobubbles are the main gaseous domains forming at solid-liquid interfaces, and their abnormally long lifetime (stability) is still an open question. A hypothesis "gas tunnel" was presented in a recent simulation study [ACS Nano 2018, 12 (3), 2603-2609], which was thought to connect two neighboring nanobubbles and make the nanobubbles remain stable. Herein, we aim to experimentally investigate the existence of gas tunnel and its role in governing nanobubble dynamics. By using an atomic force microscope, mutual effects between different gaseous domains including nanobubbles, nanopancakes, and nanobubble-pancake composite on a PS substrate undergoing violent tip perturbation and their effects on the undisturbed neighbors were investigated. The pancake between two nanobubbles can behave as a visible gas tunnel under the tip-bubble interaction. Based on statistical analysis of volume change in the different gas domains, the concept of a generalized gas tunnel is presented and experimentally verified. Nanobubbles are surrounded by a water depletion layer which will act as a channel along solid/liquid surfaces for adjacent nanobubbles to communicate with each other. Moreover, the change in contact angle of nanobubbles with the concentration of local gas oversaturation was studied, and the equilibrium contact angle of nanobubbles is further verified experimentally.

Surface nanobubbles: Theory, simulation, and experiment. A review

Surface nanobubbles (NBs) are stable gaseous phases in liquids that form at the interface with solid substrates. They have been particularly intriguing for their high stability that contradicts theoretical expectations and their potential relevance for many technological applications. Here, we present the current state of the art in this research area by discussing and contrasting main results obtained from theory, simulation and experiment, and presenting their limitations. We also provide future perspectives anticipating that this review will stimulate further studies in the research area of surface NBs.

Mechanical Stability of Surface Nanobubbles

Bubble cavitation is important in technologies such as noninvasive cancer treatment and diagnosis, surface cleaning, and waste-water treatment. The cavitation threshold is the critical external tensile pressure that induces unstable growth of the bubble. Surface nanobubbles have been previously shown experimentally to be stable down to -6 MPa, in disagreement with the Blake threshold, which is the classical cavitation model that predicts bulk bubbles with radii ∼100 nm should be unstable below -0.6 MPa. Here, we use molecular dynamics to simulate quasi-two-dimensional (2D) and three-dimensional (3D) nitrogen surface nanobubbles immersed in water, subject to a range of pressure drops until unstable growth is observed. We propose and assess new cavitation threshold models, derived from mechanical equilibrium analyses for both the quasi-2D and 3D cavitating bubbles. The discrepancies from the Blake threshold are attributed to the pinned contact line, within which the surface nanobubbles grow with constant lateral contact diameter, and consequently a reduced radius of curvature. We conclude with a critical discussion of previous experimental results on the cavitation of relatively large surface nanobubbles.

Pinning-Depinning Mechanism of the Contact Line during Evaporation of Nanodroplets on Heated Heterogeneous Surfaces: A Molecular Dynamics Simulation

Droplet evaporation on heterogeneous or patterned surfaces has numerous potential applications, for example, inkjet printing. The effect of surface heterogeneities on the evaporation of a nanometer-sized cylindrical droplet on a solid surface is studied using molecular dynamics simulations of Lennard-Jones particles. Different heterogeneities of the surface were achieved through alternating stripes of equal width but two chemical types, which lead to different contact angles. The evaporation induced by the heated substrate instead of the isothermal evaporation is investigated. It is found that the whole evaporation process is generally dominated by the nonuniform evaporation effect. However, at the initial moment, the volume expansion and local evaporation effects play important roles. From the nanoscale point of view, the slow movement of the contact line during the pinning process is observed, which is different from the macroscopic stationary pinning. Particularly, we found that the speed of the contact line may be not only affected by the intrinsic energy barrier between the two adjacent stripes ( ũ) but also relevant to the evaporation rate. Generally speaking, the larger the intrinsic energy barrier, the slower the movement of the contact line. At the specified temperature, when ũ is less than a critical energy barrier ( ũ*), the speed of the contact line would increase with the evaporate rate. When ũ > ũ*, the speed of the contact line is determined only by ũ and no longer affected by the evaporation rate at different stages (the first stick and the second stick).

Force Spectroscopy Revealed a High-Gas-Density State near the Graphite Substrate inside Surface Nanobubbles

The absorption of gas molecules at hydrophobic surfaces may have a special state and play an important role in many processes in interfacial physics, which has been rarely considered in previous theory. In this paper, force spectroscopic experiments were performed by a nanosized AFM probe penetrated into individual surface nanobubbles and contacted with a highly ordered pyrolytic graphite (HOPG) substrate. The results showed that the adhesion force at the gas/solid interface was much smaller than that in air measured with the same AFM probe. The adhesion data were further analyzed by the van der Waals force theory, and the result implied that the gas density near the substrate inside the surface nanobubbles was about 3 orders of magnitude higher than that under the standard pressure and temperature (STP). Our MD simulation indicated that the gas layers near the substrate exhibited a high-density state inside the surface nanobubbles. This high-density state may provide new insight into the understanding of the abnormal stability and contact angle of nanobubbles on hydrophobic surfaces, and have significant impact on their applications.

Long-Term Stability of Surface Nanobubbles in Undersaturated Aqueous Solution

Surface nanobubbles should not be stable for more than a few milliseconds; however they have been shown to persist for days. Pinning of the three-phase contact line of surface nanobubbles has been proposed to explain the discrepancy between the theoretical and experimental results. According to this model, two factors stabilize surface nanobubbles, namely solution oversaturation and surface pinning. Hereby, we investigate experimentally the impact of the solution saturation on the stability of nanobubbles. For this purpose, surface nanobubbles have been nucleated on hydrophobic surfaces by two methods, and then characterized by Atomic Force Microscopy (AFM). Thereafter, the surrounding liquid has been exchanged multiple times with partially degassed water. Two degassing techniques are presented. Both sets of experiments lead to the conclusion that surface nanobubbles are stable in undersaturated conditions for hours. We compare the measured lifetime of nanobubbles to calculations for pinned nanobubbles in undersaturated conditions. The stability of surface nanobubbles in undersaturated solutions observed here is incommensurate with the pinning mechanism as the origin of the long-term stability of surface nanobubbles.

Investigating Interfacial Effects on Surface Nanobubbles without Pinning Using Molecular Dynamics Simulation

We investigated how the stability of aqueous argon surface nanobubbles on hydrophobic surfaces depends on gas adsorption, solid-gas interaction energy, and the bulk gas concentration using molecular dynamics simulation with the SPC/E water solvent. We observed stable surface nanobubbles without surface pinning sites for longer than 160 ns, contrary to previous findings using monoatomic Lennard-Jones solvent. In addition, the hydrophobicity of a substrate has an effect to reduce the requirement degree of oversaturation on water bulk. We found that the gas enrichment layer, gas adsorption monolayer on the hydrophobic substrate, and water hydrogen bonding near the interface are likely necessary conditions for nanobubble stability. We concluded that gas nanobubble stability does not necessarily require three-phase pinning sites.

Attachment, Coalescence, and Spreading of Carbon Dioxide Nanobubbles at Pyrite Surfaces

Recently, it was reported that using CO₂ as a flotation gas increases the flotation of auriferous pyrite from high carbonate gold ores of the Carlin Trend. In this regard, the influence of CO₂ on bubble attachment at fresh pyrite surfaces was measured in the absence of collector using an induction timer, and it was found that nitrogen bubble attachment time was significantly reduced from 30 ms to less than 10 ms in CO₂ saturated solutions. Details of CO₂ bubble attachment at a fresh pyrite surface have been examined by atomic force microscopy (AFM) measurements and molecular dynamics (MD) simulations, and the results used to describe the subsequent attachment of a N₂ bubble. As found from MD simulations, unlike the attached N₂ bubble, which is stable and has a contact angle of about 90°, the CO₂ bubble attaches, and spreads, wetting the fresh pyrite surface and forming a multilayer of CO₂ molecules, corresponding to a contact angle of almost 180°. These MDS results are complemented by in situ AFM images, which show that, after attachment, CO₂ nano-/microbubbles spread to form pancake bubbles at the fresh pyrite surface. In summary, it seems that CO₂ bubbles have a propensity to spread, and whether CO₂ exists as layers of CO₂ molecules (gas pancakes) or as nano-/microbubbles, their presence at the fresh pyrite surface subsequently facilitates film rupture and attachment of millimeter N₂ bubbles and, in this way, improves the flotation of pyrite.

Do the contact angle and line tension of surface-attached droplets depend on the radius of curvature?

Results from Monte Carlo simulations of wall-attached droplets in the three-dimensional Ising lattice gas model and in a symmetric binary Lennard-Jones fluid, confined by antisymmetric walls, are analyzed, with the aim to estimate the dependence of the contact angle [Formula: see text] on the droplet radius [Formula: see text] of curvature. Sphere-cap shape of the wall-attached droplets is assumed throughout. An approach, based purely on 'thermodynamic' observables, e.g. chemical potential, excess density due to the droplet, etc, is used, to avoid ambiguities in the decision which particles belong (or do not belong, respectively) to the droplet. It is found that the results are compatible with a variation [Formula: see text], [Formula: see text] being the contact angle in the thermodynamic limit ([Formula: see text]). The possibility to use such results to estimate the excess free energy related to the contact line of the droplet, namely the line tension, at the wall, is discussed. Various problems that hamper this approach and were not fully recognized in previous attempts to extract the line tension are identified. It is also found that the dependence of wall tensions on the difference of chemical potential of the droplet from that at the bulk coexistence provides effectively a change of the contact angle of similar magnitude. The simulation approach yields precise estimates for the excess density due to wall-attached droplets and the corresponding free energy excess, relative to a system without a droplet at the same chemical potential. It is shown that this information suffices to estimate nucleation barriers, not affected by ambiguities on droplet shape, contact angle and line tension.

The Nucleation Rate of Single O2 Nanobubbles at Pt Nanoelectrodes

Nanobubble nucleation is a problem that affects efficiency in electrocatalytic reactions since those bubbles can block the surface of the catalytic sites. In this article, we focus on the nucleation rate of O₂ nanobubbles resulting from the electrooxidation of H₂O₂ at Pt disk nanoelectrodes. Bubbles form almost instantaneously when a critical peak current, i_nb^p, is applied, but for lower currents, bubble nucleation is a stochastic process in which the nucleation (induction) time, t_ind, dramatically decreases as the applied current approaches i_nb^p, a consequence of the local supersaturation level, ζ, increasing at high currents. Here, by applying different currents below i_nb^p, nanobubbles take some time to nucleate and block the surface of the Pt electrode at which the reaction occurs, providing a means to measure the stochastic t_ind. We study in detail the different conditions in which nanobubbles appear, concluding that the electrode surface needs to be preconditioned to achieve reproducible results. We also measure the activation energy for bubble nucleation, E_a, which varies in the range from (6 to 30) kT, and assuming a spherically cap-shaped nanobubble nucleus, we determine the footprint diameter L = 8-15 nm, the contact angle to the electrode surface θ = 135-155°, and the number of O₂ molecules contained in the nucleus (50 to 900 molecules).

Leakiness of Pinned Neighboring Surface Nanobubbles Induced by Strong Gas-Surface Interaction

The stability of two neighboring surface nanobubbles on a chemically heterogeneous surface is studied by molecular dynamics (MD) simulations of binary mixtures consisting of Lennard-Jones (LJ) particles. A diffusion equation-based stability analysis suggests that two nanobubbles sitting next to each other remain stable, provided the contact line is pinned, and that their radii of curvature are equal. However, many experimental observations seem to suggest some long-term kind of ripening or shrinking of the surface nanobubbles. In our MD simulations we find that the growth/dissolution of the nanobubbles can occur due to the transfer of gas particles from one nanobubble to another along the solid substrate. That is, if the interaction between the gas and the solid is strong enough, the solid-liquid interface can allow for the existence of a "tunnel" which connects the liquid-gas interfaces of the two nanobubbles to destabilize the system. The crucial role of the gas-solid interaction energy is a nanoscopic element that hitherto has not been considered in any macroscopic theory of surface nanobubbles and may help to explain experimental observations of the long-term ripening.

Diffusive interaction of multiple surface nanobubbles: shrinkage, growth, and coarsening

Surface nanobubbles are nanoscopic spherical-cap shaped gaseous domains on immersed substrates which are stable, even for days. After the stability of a single surface nanobubble has been theoretically explained, i.e. contact line pinning and gas oversaturation are required to stabilize it against diffusive dissolution [Lohse and Zhang, Phys. Rev. E, 2015, 91, 031003(R)], here we focus on the collective diffusive interaction of multiple nanobubbles. For that purpose we develop a finite difference scheme for the diffusion equation with the appropriate boundary conditions and with the immersed boundary method used to represent the growing or shrinking bubbles. After validation of the scheme against the exact results of Epstein and Plesset for a bulk bubble [J. Chem. Phys., 1950, 18, 1505] and of Lohse and Zhang for a surface bubble, the framework of these simulations is used to describe the coarsening process of competitively growing nanobubbles. The coarsening process for such diffusively interacting nanobubbles slows down with advancing time and increasing bubble distance. The present results for surface nanobubbles are also applicable for immersed surface nanodroplets, for which better controlled experimental results of the coarsening process exist.

Theory of nanobubble formation and induced force in nanochannels

This paper presents a fundamental theory of nanobubble formation and induced force in confined nanochannels. It is shown that nanobubble formation between hydrophobic plates can be predicted from their surface tension and geometry, with estimated values for the surface free energy and the force acting on the plates in good agreement with the results of molecular dynamics simulation and experimentation. When a bubble is formed between two plates, vertical attractive force and horizontal retract force due to the shifted plates are applied to the plates. The net force exerted on the plates is not dependent on the distance between them. The short-range force between hydrophobic surfaces due to hydrophobic interaction appears to correspond to the force estimated by our theory. We compared between experimental and theoretical values for the binding energy of a molecular motor system to validate our theory. The tendency that the binding energy increases as the size of the protein increases is consistent with the theory.

Solvent Exchange Leading to Nanobubble Nucleation: A Molecular Dynamics Study

The solvent exchange procedure has become the most-used protocol to produce surface nanobubbles, while the molecular mechanisms behind the solvent exchange are far from being fully understood. In this paper, we build a simple model and use molecular dynamics simulations to investigate the dynamic characteristics of solvent exchange for producing nanobubbles. We find that at the first stage of solvent exchange, there exists an interface between interchanging solvents of different gas solubility. This interface moves toward the substrate gradually as the exchange process proceeds. Our simulations reveal directed diffusion of gas molecules against the gas concentration gradient, driven by the solubility gradient of the liquid composition across the moving solvent-solvent interface. It is this directed diffusion that causes gas retention and produces a local gas oversaturation much higher near the substrate than far from it. At the second stage of solvent exchange, the high local gas oversaturation leads to bubble nucleation either on the solid surface or in the bulk solution, which is found to depend on the substrate hydrophobicity and the degree of local gas oversaturation. Our findings suggest that solvent exchange could be developed into a standard procedure to produce oversaturation and used to a variety of nucleation applications other than generating nanobubbles.