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Critical Nuclei Size, Rate, and Activation Energy of H2 Gas Nucleation Sean R. German, Martin A. Edwards, Hang Ren, and Henry S. White J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b13457 • Publication Date (Web): 23 Feb 2018 Downloaded from http://pubs.acs.org on February 23, 2018
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Critical Nuclei Size, Rate, and Activation Energy of H2 Gas Nucleation Sean R. German1, Martin A. Edwards1, Hang Ren1, Henry S. White1* 1. Department of Chemistry, University of Utah, 315 S 1400 E, Salt Lake City, Utah 84112
Abstract 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, , is obtained by controlled current reduction of H+ in a H2SO4
solution. Induction times of single-bubble nucleation events are measured by stepping the current to control 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 4 orders of magnitude (0.3 – 2000 s-1) over a very small relative change
in (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 1 ACS Paragon Plus Environment
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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.
Introduction Phase formation begins with nucleation – the stochastic appearance of nanoscale domains or clusters, which, if sufficiently large, grow into the new phase. The driving force for phase transformation and subsequent growth is a supersaturation; i.e., a concentration of molecular constituents that exceeds the equilibrium concentration. As the formation of small clusters is energetically unfavorable at moderate supersaturation, a relatively improbable fluctuation in local composition is necessary to form a nucleus of a critical size whose growth is subsequently favored. Classical nucleation theory1 based on Arrhenius rate laws and how it relates to bubble formation specifically2 has been thoroughly described. However, to our knowledge, direct measurement of the kinetics of nucleation of individual critical gas nuclei and the subsequent determination of their geometry, has never previously been reported. The formation of gaseous bubbles in a liquid phase is a phase change phenomenon that has recently been attributed to both valuable and deleterious impacts on energy generation systems.3,4 For instance, bubbles have been implicated in the deactivation of electrocatalytic nanoparticles and the enhancement of gas transport in fuel cells.5,6 In addition to their technological relevance, gas bubbles also represent an important model system for fundamental studies of nucleation. Electrochemical generation of a supersaturation, by controlling the potential or current at an electrode, is a useful means for investigating and controlling nucleation; e.g., 2 ACS Paragon Plus Environment
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electrodeposition of nanoparticles,7-10 films,11,12 and electrogeneration of gas bubbles.13-16 Nucleation at large electrodes occurs stochastically at numerous sites, complicating experimental interpretation. However, employing electrodes of nanometer dimensions can reduce the number of potential nucleation events to unity, reducing complexity; this approach has been applied to study nucleation of single nanoparticles.7 Recently, in non-electrochemical systems, it was also demonstrated that nucleation energetics can be determined from the distributions of induction times at various supersaturations for single crystal nucleation events.17 We recently reported using voltammetry at Pt nanoelectrodes to induce the formation of single nanobubbles using several gas evolving electrochemical systems (H2, N2, and O2 bubbles were generated from proton reduction,14,18,19 hydrazine oxidation,20 and hydrogen peroxide oxidation,21 respectively). Using voltammetric techniques, we have measured the radii of curvature of critical nuclei,22 lifetimes of nanobubbles,23 their stable geometries,24 and their internal pressures.25 However, on the timescale of the voltammetric measurements at moderate scan rates (e.g., 1 V/s), bubble nucleation appears instantaneous once a critical concentration is reached at the electrode surface.
Scheme 1 depicts the process of
electrochemical generation of dissolved gas (H2 in this case), spontaneous formation of a critical bubble nucleus, and subsequent rapid growth of a nanobubble to cover the electrode. In this work, we precisely control the supersaturation of dissolved H2 at a Pt nanoelectrode using controlled current methods to determine the rate of bubble nucleation as a function of H2 supersaturation. These measurements allow for the determination of the activation energy for gas nucleation, as well as the size and geometry of the critical nuclei. 3 ACS Paragon Plus Environment
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Scheme 1. Illustration of critical nucleus formation and subsequent growth of an H2 nanobubble induced by electroreduction of H+ to H2. Experimental Section Sulfuric acid (96.2% Mallinckrodt) and potassium chloride (Mallinckrodt, ACS grade) were used as received. Aqueous solutions were prepared from ultrapure water (18.2 MΩ·cm , Barnstead Smart2Pure). Pt nanodisk electrodes were fabricated as previously described.26 Their apparent radii,
a, were measured from the voltammetric diffusion-limited current, , for the oxidation of 5 mM
ferrocene dissolved
in
acetonitrile containing 100
mM tetrabutylammonium
hexafluorophosphate (TBAPF6) using27
4
(1)
where (2.4 x 10-5 cm2 s-1)28 and are the diffusion coefficient and bulk concentration of
ferrocene, respectively, =96485 C/mol is Faraday’s constant, and is the number of electrons
transferred per molecule (= 1 for Fc oxidation).
A HEKA EPC 10 patch clamp amplifier was used to collect current-voltage (i-E), currenttime (i-t), and voltage-time (E-t) data, which were filtered with a 4-pole Bessel filter at 10 kHz and sampled at 50 kHz. For applied current-step experiments, a LabVIEW program employing an FPGA card (National Instruments, PCIe-7852) was developed to control the current while monitoring voltage and automatically stepping the current back to 0 nA within 80 μs upon 4 ACS Paragon Plus Environment
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detecting nucleation (E > -0.8 V). A Ag/AgCl electrode in 3 M NaCl (BASi) was used as a counter/reference electrode in a two electrode configuration. Results and Discussion Figure 1A shows cyclic voltammograms for the generation of individual H2 bubbles, similar to the voltammetric response that we previously reported.14,18 The 41 nm radius Pt electrode was immersed in an aqueous solution of 0.5 M H2SO4 with 50 mM KCl and the voltage swept at 10, 100, and 1000 mV/s. As the potential is swept negative of ~-0.25 V vs Ag/AgCl, a current corresponding to H2 generation (H+ reduction) increases exponentially. At a peak
current, , the current precipitously drops as a bubble nucleates and quickly grows to cover
the electrode, hindering transport of H+ to the Pt surface, with an initial rate that is faster than
the amplifier bandwidth permits us to measure (
