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Electrochemical measurements of the nucleation rate of individual H2 bubbles at the surface of Pt nanoelectrodes (radius = 7-41 nm) are used to determine the critical size and geometry of H2 nuclei leading to stable bubbles. Precise knowledge of the H2 concentration at the electrode surface,CH2surf, is obtained by controlled current reduction of H+ in a H2SO4 solution. Induction times of singlebubble nucleation events are measured by stepping the current, to control CH2surf, while monitoring the voltage. We find that gas nucleation follows a first-order rate process; a bubble spontaneously nucleates after a stochastic time delay, as indicated by a sudden voltage spike that results from impeded transport of H+ to the electrode. Hundreds of individual induction times, at different applied currents and using different Pt nanoelectrodes, are used to characterize the kinetics of phase nucleation. The rate of bubble nucleation increases by four orders of magnitude (0.3-2000 s-1) over a very small relative change in CH2surf (0.21-0.26 M, corresponding to a ~0.025 V increase in driving force). Classical nucleation theory yields thermodynamic radii of curvature for critical nuclei of 4.4 to 5.3 nm, corresponding to internal pressures of 330 to 270 atm, and activation energies for nuclei formation of 14 to 26 kT, respectively. The dependence of nucleation rate on H2 concentration indicates that nucleation occurs by a heterogeneous mechanism, where the nuclei have a contact angle of ~150° with the electrode surface and contain between 35 and 55 H2 molecules. [ABSTRACT FROM AUTHOR]

The Young-Laplace equation is central to the thermodynamic description of liquids with highly curved interfaces, e.g., nanoscale droplets and their inverse, nanoscale bubbles. The equation relates the pressure difference across an interface to its surface tension and radius of curvature, but the validity in using the macroscopic surface tension for describing curved interfaces with radii smaller than tens of nanometers has been questioned. Here we present electrochemical measurement of Laplace pressures within single H2 bubbles between 7 and 200 nm radius (corresponding, respectively, to between 200 and 7 atm). Our results demonstrate a linear relationship between a bubble's Laplace pressure and its reciprocal radius, verifying the classical thermodynamic description of H2 nanobubbles as small as ∼10 nm. [ABSTRACT FROM AUTHOR]

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 O 2 nanobubbles resulting from the electrooxidation of H 2 O 2 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 O 2 molecules contained in the nucleus (50 to 900 molecules).

Electrochemical measurements of the nucleation rate of individual H 2 bubbles at the surface of Pt nanoelectrodes (radius = 7-41 nm) are used to determine the critical size and geometry of H 2 nuclei leading to stable bubbles. Precise knowledge of the H 2 concentration at the electrode surface, C H 2 surf , is obtained by controlled current reduction of H + in a H 2 SO 4 solution. Induction times of single-bubble nucleation events are measured by stepping the current, to control C H 2 surf , while monitoring the voltage. We find that gas nucleation follows a first-order rate process; a bubble spontaneously nucleates after a stochastic time delay, as indicated by a sudden voltage spike that results from impeded transport of H + to the electrode. Hundreds of individual induction times, at different applied currents and using different Pt nanoelectrodes, are used to characterize the kinetics of phase nucleation. The rate of bubble nucleation increases by four orders of magnitude (0.3-2000 s -1 ) over a very small relative change in C H 2 surf (0.21-0.26 M, corresponding to a ∼0.025 V increase in driving force). Classical nucleation theory yields thermodynamic radii of curvature for critical nuclei of 4.4 to 5.3 nm, corresponding to internal pressures of 330 to 270 atm, and activation energies for nuclei formation of 14 to 26 kT, respectively. The dependence of nucleation rate on H 2 concentration indicates that nucleation occurs by a heterogeneous mechanism, where the nuclei have a contact angle of ∼150° with the electrode surface and contain between 35 and 55 H 2 molecules.

Herein, we use Pt nanodisk electrodes (apparent radii from 4 to 80 nm) to investigate the nucleation of individual O 2 nanobubbles generated by electrooxidation of hydrogen peroxide (H 2 O 2 ). A single bubble reproducibly nucleates when the dissolved O 2 concentration reaches ∼0.17 M at the Pt electrode surface. This nucleation concentration is ∼130 times higher than the equilibrium saturation concentration of O 2 and is independent of electrode size. Moreover, in acidic H 2 O 2 solutions (1 M HClO 4 ), in addition to producing an O 2 nanobubble through H 2 O 2 oxidation at positive potentials, individual H 2 nanobubbles can also be generated at negative potentials. Alternating generation of single O 2 and H 2 bubbles within the same experiment allows direct comparison of the critical concentrations for nucleation of each nanobubble without knowing the precise size/geometry of the electrode or the exact viscosity/temperature of the solution.

This article describes the dynamic steady state of individual H 2 nanobubbles generated by H + reduction at inlaid and recessed Pt nanodisk electrodes. Electrochemical measurements coupled with finite element simulations allow analysis of the nanobubble geometry at dynamic equilibrium. We demonstrate that a bubble is sustainable at Pt nanodisks due to the balance of nanobubble shrinkage due to H 2 dissolution and growth due to H 2 electrogeneration. Specifically, simulations are used to predict stable geometries of the H 2 /Pt/solution three-phase interface and the width of exposed Pt at the disk circumference required to sustain the nanobubble via steady-state H 2 electrogeneration. Experimentally measured currents, i ss , corresponding to the electrogeneration of H 2 , at or near the three-phase interface, needed to sustain the nanobubble are between 0.2 and 2.4 nA for Pt nanodisk electrodes with radii between 2.5 and 40 nm. However, simple theoretical analysis shows that the diffusion-limited currents required to sustain such a single nanobubble at an inlaid Pt nanodisk are 1-2 orders larger than the observed values. Finite element simulation of the dynamic steady state of a nanobubble at an inlaid disk also demonstrates that the expected steady-state currents are much larger than the experimental currents. Better agreement between the simulated and experimental values of i ss is obtained by considering recession of the Pt disk nanoelectrode below the plane of the insulating surface, which reduces the outward flux of H 2 from the nanobubble and results in smaller values of i ss .

The Young-Laplace equation is central to the thermodynamic description of liquids with highly curved interfaces, e.g., nanoscale droplets and their inverse, nanoscale bubbles. The equation relates the pressure difference across an interface to its surface tension and radius of curvature, but the validity in using the macroscopic surface tension for describing curved interfaces with radii smaller than tens of nanometers has been questioned. Here we present electrochemical measurement of Laplace pressures within single H 2 bubbles between 7 and 200 nm radius (corresponding, respectively, to between 200 and 7 atm). Our results demonstrate a linear relationship between a bubble's Laplace pressure and its reciprocal radius, verifying the classical thermodynamic description of H 2 nanobubbles as small as ∼10 nm.

Coulter counters measure the size of particles in solution by passing them through an orifice and measuring a resistive pulse, i.e., a drop in the ionic current flowing between two electrodes placed on either side of the orifice. The magnitude of the pulse gives information on the size of the particle; however, resolution is limited by variability in the path of the translocation, due to the Brownian motion of the particle. We present a simple yet powerful modified Coulter counter that uses programmable data acquisition hardware to switch the voltage after sensing the resistive pulse of a nanoparticle passing through the orifice of a nanopipet. Switching the voltage reverses the direction of the driving force on the particle and, when this detect-switch cycle is repeated, allows us to pass an individual nanoparticle through the orifice thousands of times. By measuring individual particles more than 100 times per second we rapidly determine the distribution of the resistive pulses for each particle, which allows us to accurately determine the mean pulse amplitude and deliver considerably improved size resolution over a conventional Coulter counter. We show that single polystyrene nanoparticles can be shuttled back and forth and monitored for minutes, leading to a precisely determined mean blocking current equating to sub-angstrom size resolution.

Exploring the nucleation of gas bubbles at interfaces is of fundamental interest. Herein, we report the nucleation of individual N2 nanobubbles at Pt nanodisk electrodes (6–90 nm) via the irreversible electrooxidation of hydrazine (N2H4 → N2 + 4H(+) + 4e(–)). The nucleation and growth of a stable N2 nanobubble at the Pt electrode is indicated by a sudden drop in voltammetric current, a consequence of restricted mass transport of N2H4 to the electrode surface following the liquid-to-gas phase transition. The critical surface concentration of dissolved N2 required for nanobubble nucleation, CN2,critical(s), obtained from the faradaic current at the moment just prior to bubble formation, is measured to be ∼0.11 M and is independent of the electrode radius and the bulk N2H4 concentration. Our results suggest that the size of stable gas bubble nuclei depends only on the local concentration of N2 near the electrode surface, consistent with previously reported studies of the electrogeneration of H2 nanobubbles. CN2,critical(s) is ∼160 times larger than the N2 saturation concentration at room temperature and atmospheric pressure. The residual current for N2H4 oxidation after formation of a stable N2 nanobubble at the electrode surface is proportional to the N2H4 concentration as well as the nanoelectrode radius, indicating that the dynamic equilibrium required for the existence of a stable N2 nanobubble is determined by N2H4 electrooxidation at the three phase contact line.

Resistive-pulse sensing has generated considerable interest as a technique for characterizing nanoparticle suspensions. The size, charge, and shape of individual particles can be estimated from features of the resistive pulse, but the technique suffers from an inherent variability due to the stochastic nature of particles translocating through a small orifice or channel. Here, we report a method, and associated automated instrumentation, that allows repeated pressure-driven translocation of individual particles back and forth across the orifice of a conical nanopore, greatly reducing uncertainty in particle size that results from streamline path distributions, particle diffusion, particle asphericity, and electronic noise. We demonstrate ∼0.3 nm resolution in measuring the size of nominally 30 and 60 nm radius Au nanoparticles of spherical geometry; Au nanoparticles in solution that differ by ∼1 nm in radius are readily distinguished. The repetitive translocation method also allows differentiating particles based on surface charge density, and provides insights into factors that determine the distribution of measured particle sizes.

Currently there is no widespread agreement on an explanation for the stability of surface nanobubbles. One means by which several explanations can be differentiated is through the predictions they make about the degree of permeability of the gas-solution interface. Here we test the hypothesis that the gas-solution interface of surface nanobubbles is permeable by experimental measurements of the exchange of carbon dioxide. We present measurements by attenuated total reflection Fourier transform infrared (ATR-FTIR) and atomic force microscopy (AFM), demonstrating that the gas inside surface nanobubbles is not sealed inside the bubbles, but rather exchanges with the dissolved gas in the liquid phase. Such gas transfer is measurable by using the infrared active gas CO2. We find that bubbles formed in air-saturated water that is then perfused with CO2-saturated water give rise to distinctive gaseous CO2 signals in ATR-FTIR measurements. Also the CO2 gas inside nanobubbles quickly dissolves into the surrounding air-saturated water. AFM images before and after fluid exchange show that CO2 bubbles shrink upon exposure to air-equilibrated liquid but remain stable for hours. Also air bubbles in contact with CO2-saturated water increase in size and Ostwald ripening occurs more rapidly due to the relatively high gas solubility of CO2 in water.