Local Study on Hydrogen and Hydrogen Gas Bubble Formation on A

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Local Study on Hydrogen and Hydrogen Gas Bubble Formation on a Platinum Electrode Alberto Battistel, Christopher Raymond Dennison, Andreas Lesch, and Hubert H. Girault J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10920 • Publication Date (Web): 09 Apr 2019 Downloaded from http://pubs.acs.org on April 9, 2019

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The Journal of Physical Chemistry

Local Study on Hydrogen and Hydrogen Gas Bubble Formation on A Platinum Electrode Alberto Battistel,∗,† Christopher R. Dennison,† Andreas Lesch,‡,† and Hubert H. Girault† †École Polytechnique Fédérale de Lausanne (EPFL), Laboratoire d’Electrochimie Physique et Analytique (LEPA), Rue de l’Industrie 17, CH-1951 Sion, Switzerland ‡University of Bologna, Department of Industrial Chemistry "Toso Montanari", Viale del Risorgimento 4, I-40136 Bologna, Italy E-mail: [email protected]

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Abstract This work investigates the effect of current density on the hydrogen gas bubble formation during electrolysis on a platinum electrode. Local detection of bubble evolution was performed electrochemically by using an hydrogen collecting microelectrode placed in close proximity of a larger hydrogen generating platinum electrode. The microelectrode probe locally measured the concentration of dissolved molecular hydrogen produced during electrolysis. In acidic conditions, it was found that at low electrolysis currents the concentration of dissolved hydrogen could temporarily rise up to 50 times the saturation level, while once a large current was reached, the concentration dropped, increasing the concentration of hydrogen inside gas bubbles, and became independent of the current. Through laser reflectance, the onset of bubble formation was found (∼ −0.7 mA/cm2 ) which was lower than the first bubble observable by naked eye or detected by the microelectrode probe.

Introduction One of the most attractive methods for the storage of renewable energy storage is hydrogen production from water splitting 1 . However, the hydrogen evolution reaction (HER) remains a technical challenge. On the other hand, research on chlorine evolution showed great improvement, such that dimensionally stable anodes (DSA®) were considered as one of the greatest technological breakthroughs of the twentieth century 2 . Nevertheless, DSAs provide only minor improvement in the electrocatalytic performance compared to the graphite electrodes previously used. In fact, their great success came from the reduction of the bubble effect 2 . The so-called bubble effect is given by the adhesion of the gas phase to the electrode surface, thereby blocking the surface area by forming an insulating bubble curtain and thus reducing the contact area with the electrolyte. This curtain forced designers to allow a larger gap between the two electrodes of an electrochemical cell which in turn increased the total ohmic losses of the system due to the electrolyte resistance. 2


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The effect of insulating bodies lying on the electrode surface was studied by several authors who found a correlation between the size of the insulator and the variation of ohmic and activation overpotentials 3–5 . Noise analysis at microelectrodes showed that the main contribution of the gas bubbles was resistive in nature and given by blocking the electrode surface and cross-sectional area of the electrode 6 . During electrolysis, the proximity of the electrodes gets readily enriched with molecular gas which locally reaches supersaturation levels leading to a metastable condition where any local fluctuation can result in the nucleation of gas bubbles. Nucleation of this new phase is determined by geometrical irregularities at the electrode, and, on a cavity-free electrode surface, such an event requires a high level of supersaturation 7 . On the contrary, the presence of cavities with small pockets of gas favors the nucleation of a bubble with low or even zero activation energy 7,8 . Craig et al. showed the correlation between the composition of the electrolyte and bubble coalescence 9 . The coalescence was found to be the predominant step in the bubble growth at low current densities, while at higher current densities the bubbles are influenced by the distribution of gas cavities 10 . Shibata measured the supersaturation level during H2 evolution by measuring the charge required to oxidize the dissolved gas 11 . He found that the concentration of molecular hydrogen was a monotonic function of the current density of the cathode, which reached a limiting value of 116 mM at circa −300 mA/cm2 . More recently, Zeradjanin et al. employed scanning electrochemical microscopy (SECM) in the sample generation-tip collection mode to visualize the chlorine evolution at a DSA 12,13 . They found that the gas bubble evolution influenced the microelectrode current. SECM was often applied in various works addressing hydrogen and oxygen evolution 14–18 . However, the focus was either on material characterization or electrokinetics; the dynamically generated gas phase created at the electrode found little attention. One exception is the work of Chen et al. who studied oxygen evolution and found through noise analysis that only a few points of the electrode surface were the predominant spots for bubble formation 19 . Dukovic and Tobias cast a model to describe how the current distribution was influenced 3



by the presence of a bubble on the electrode 20 . They found that according to the electrocatalytic properties of the substrate and the current density, the reaction rate could be favored by the presence of a bubble. They called this phenomenon “enhancement effect” and concluded that this effect was larger at lower current density. The concentration of dissolved gas was low in proximity of the bubble and increased with the distance, in accordance with the prediction of Vogt 21 . The bubbles act as a sink for molecular hydrogen by collecting dissolved gas from the solution, which lowers locally the supersaturation and the concentration overpotential. Brussieux et al. showed the correlation between hydrophobicity of the electrode surface and the mechanism of bubble evolution 22 . Several authors discussed the effect of the convection induced by the bubbles 23–26 . This is divided in microconvection, when the mass transport is induced by single bubbles, and macroconvection, when it is given by collective stirring. Other authors focused on the concentration overpotential as well 4,21,27 . However, these studies were limited by the difficulty of measuring local quantities. In fact, there was no available way to detect the supersaturation level next to a gas bubble. In this work, the local effect of bubble evolution was studied on a platinum electrode in acidic conditions during electrolysis. Microelectrode investigations were performed to measure the actual concentration of dissolved hydrogen in the proximity of a platinum electrode during hydrogen evolution. Hydrogen bubbles quickly formed and reduced the saturation of dissolved gas measured locally by the microelectrode. However, electrochemical experiments are only indirectly sensitive to the formation of gas bubbles, which alter the concentration distribution of dissolved hydrogen by stirring and trapping. To have a complete image of the system, laser reflectance experiments were also performed during electrolysis. Since the laser beam is sensitive mostly to optical variation of the light path it provided information regarding the initial formation of bubbles.

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Experimental Solutions were prepared from H2 SO4 (Sigma Aldrich) and milli-Q®water and were 0.5 M. Electrochemical experiments For the electrochemical experiments, two potentiostats were used simultaneously to achieve a high-current, flexible bipotentiostat. A Sycopel Scientific Ministat was used to polarize the platinum cathode (W E1 ) using a Ag | AgCl 3 M KCl reference electrode (RE) with double junction and a platinum mesh as counter electrode (CE). W E1 was made of a platinum foil polished with 400 grit sand paper (see SI) and the cell was mounted on the top of it leaving an exposed surface area of 1.13 cm2 (1.2 cm diameter) facing upward to allow easily evacuation of the gas bubbles. Cell geometry was adapted from reference 28,29 in order to achieve homogeneous current density on the W E1 (see SI). The counter electrode had a cylindrical shape (inner diameter circa 2 cm and height circa 1.3 cm) to enclose all the current lines and the reference electrode was placed externally as described in reference 29 . A second potentiostat (CompactStat, Ivium Technologies) was used to control the microelectrode tip (W E2 ), which was a 25 µm diameter platinum disk electrode (ratio between tip radius and electrode radius ∼ 10). The tip was connected as working electrode and the counter and reference electrode leads were connected with the large platinum cathode in such a way that the microelectrode potential of +500 mV was controlled against the larger platinum cathode (W E1 ), which worked as a reversible hydrogen quasi-reference electrode. Referencing the microelectrode potential to the true reference electrode was not practical given the large ohmic drop occurring in the cell. The microelectrode tip was mounted on a SECM stage (CHI900, CH Instruments). It was placed in the middle of the W E1 which was working as substrate and far from the borders where large hydrogen bubbles often remained pinned. The tip-to-substrate distance was generally 10 µm. The tip acted as an amperometric sensor in the substrate generation - tip collection mode while W E1 was polarized in the region of hydrogen evolution. A schematic is reported in the Supporting Information. 5



The approach curves were performed waiting enough time to have a stable thickness of the diffusion layer (between 1 and 5 minutes) and at the rate of 1 µm/s. Data were recorded externally though an ADC (USB 6008, National Instruments) operating in differential mode to avoid ground loops. Ground loops, noise, and potentiostat connections were carefully checked with dummy cells and the best results were found when both potentiostats were operated in floating mode. To minimize the effect of noise and increase the resolution of the ADC, 2000 samples were averaged per second, de facto increasing the digital resolution of the ADC (oversampling). Optical experiments For the reflectance experiments, a laser diode (CPS184, Thorlabs) with a wavelength of 650 nm, a silicon photodiode (918D-UV-OD3, Newport), and an optical power meter (Model 1935-C, Newport) were used. Light intensity was recovered either directly or by lock-in amplifier (Model SR830 DSP, Stanford Research Systems) at 400 Hz with a time-constant of 300 ms which reduced noise slightly, but did not change the results. Platinum was used as the cathode and reticulated carbon as the anode. The cell had a cylindrical body with 2 cm diameter and 3 cm height and was placed in a goniometric system where the laser source and the light detector were placed on two opposite arms of the goniometer. The platinum cathode was at the fulcrum of the two arms. Two sides of the cell were made of two parallel microscope slides placed perpendicular to the cathode in such a way that once reflected from the cathode the light was collected by the detector. The width of the windows was 7 mm and their lower border was 4 mm away from the bottom of the cell. The total width of the optical path was 33 mm (from slide to slide). A schematic of the setup is reported in the Supporting Information. The goniometer was placed at an opening angle of 90 ◦ which was previously optimized to give the maximum light intensity at the detector. The experiment consisted in running a linear current ramp between the cathode and the anode and measure the variation of the light intensity as function of the current density. The ramp was performed at 10 µA/s.

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Results The local concentration of dissolved molecular hydrogen, c, at the microelectrode tip, neglecting any effect of convection, was calculated from:

itip = 4 n F D c rtip

(1)

where itip is the current at the microelectrode tip, n is the number of electrons involved in the reaction, F is the Faraday constant, D is the diffusion coefficient of hydrogen in water solution (5.11 · 10−5 cm2/s 30 ), and rtip is the radius of the microelectrode disk. The small size of the microelectrode guaranteed that only strong convection happening within one or two radii distance from the tip would sensibly alter the flux of electroactive species. Furthermore, feedback effects were also neglected given the large abundance of protons in solution. The microelectrode tip being an amperometric probe, can oxidize, and therefore detect, only the molecular hydrogen dissolved in solution and not that present inside the hydrogen bubbles, which are insulating. Figure 1 a) shows the concentration of dissolved hydrogen measured by the microelectrode tip during a cyclic voltammetry of the cathode. The potential of the cathode, i.e. the substrate, was swept at 100 mV/s between 0 V and −2.5 V vs. the reference electrode, with the microelectrode tip 10 µm distance from the substrate. Considering the large currents (> 400 mA/cm2 ), the system behavior was dominated by the ohmic drop in the cell. The jumps in the substrate current were given by the movements of large bubbles on the electrode surface which grew preferentially between the border of the cathode and the wall of the cell. These bubbles could grow as big as few millimeters and some remained pinned in the cell until the end of the experiment when no more current flowed. The concentration of dissolved molecular hydrogen measured by the tip increased remarkably at low substrate current densities directly after initialization of the current ramp and then dropped to a value nearly constant and independent of the current. Apart from the 7


c / mM

a)

0

Overshoot

20

Plateau

10

−200 −400

0 0

10

20

30

40

50 0 −200

20

−400

0 0

50

100 t/s c / mM

c) 40 20 0 50

150

j / mA cm−2

b) 40 c / mM

t/s

c / mM

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j / mA cm−2


200 d)

4 2 0

55

60

65

140

t/s

145

150

155

t/s

Figure 1: Concentration of dissolved hydrogen measured at the microelecrode tip (blue lines) during a cyclic voltammetry at the cathode (green lines). a) single cycle; b) multiple cycles. c) and d) details of part b). very beginning, the signal measured by the tip was very noisy probably because the diffusion profile was locally perturbed by the growth and release of bubbles. Interestingly, the high value of hydrogen concentration was not detected in the return scan of the cyclic voltammetry. Note that the saturation concentration for hydrogen in water at 25 ◦ C is 0.78 mM (calculated from reference 30 ). This behavior was consistent, repeatable, and independent of the scan rate as visible in Figure 1 b) which shows several cycles of the cyclic voltammetry and the simultaneous detection of dissolved hydrogen for several scans. The patterns were the same as for the first cycle, with an initial rapid increase in hydrogen followed by a plateau in concentration which lasted almost until the end of the voltammetry. Details of the concentration overshoot and of 8


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the end of scan are given in Figure 1 c) and d). The concentration overshoot was on average between 20 and 40 mM (between 25 and 50 times the saturation) and mostly broke down abruptly in a range between −50 and −150 mA/cm2 of the substrate current. In the middle of the plateau, the hydrogen concentration showed an even larger relative variation which was between 1 and 6 mM. In all the cases, the concentration of dissolved hydrogen was larger than its solubility at atmospheric pressure and it could reach supersaturation levels of over 60 times the concentration of the saturation concentration. Several other features were observed. The tip current was usually more noisy just after the overshoot and at the end of the plateau, just before returning to zero. In some experiments at the end of the return scan a small increase in current at the tip was observed. However, this was never as high as the initial overshoot and returned to the value of the plateau within a short time. A small decrease of the current at the microelectrode was observable in the very beginning of the cyclic voltammetry (see Supporting Information). Here, up to few nanoamperes of cathodic current were recorded. This was probably due to the adsorption of hydrogen on the platinum cathode which generates a pseudo-capacitance, a phenomenon which is usually investigated by Surface Interrogation Scanning Electrochemical Microscopy 15,31 . It is interesting to understand if the overshoot of the hydrogen concentration of Figure 1 was a transitory phenomenon simply connected with the rapid change of the potential (current) of the substrate or whether the drop in hydrogen concentration between the overshoot and the plateau was observable independently of the way the substrate current was controlled. In Figure 2, a step-wise increase of potential at the cathode was performed while recording the local concentration of hydrogen. In part (a), the concentration detected initially increased step-wise up to 33 mM following the increase of the current at the cathode until some −80 mA/cm2 (at circa 650 s). This corresponds to the current densities of the concentration overshoot (overshoot range). After this point, the concentration dropped to between 5 and 15 mM, and below 5 mM beyond −130 mA/cm2 . This is consistent with 9


0 40 −100 20 0 0

−200

Overshoot region 500 t/s

1000

b) 10

0 −200

5

−400 0 0

200

400 t/s

j / mA cm−2

c / mM

a)

c / mM

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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j / mA cm−2


600

Figure 2: Step-wise increase of current density at the cathode and local measurement of dissolved hydrogen. a) current density range where the concentration overshoot appears. b) current density range of the concentration plateau. what was observed in Figure 1 and represents the fact that at a particular current density, around −80 mA/cm2 in this case, the local concentration of hydrogen dropped dramatically. At circa −20 mA/cm2 , the signal at the microelectrode became noisy, probably because of the local disturbance of gas bubbles. However, the cathode current was affected by noise only from around −50 mA/cm2 . Beyond this value the current transient at the cathode was not flat within every step in potential, but showed a typical decrease given by the growth of large bubbles. Figure 2 b) shows the hydrogen concentration detected by the tip at substrate current densities from circa −130 mA/cm2 up to −350 mA/cm2 and then back to zero current. Despite the large variation in the substrate current (more than 200 mA/cm2 ), the concentration of dissolved hydrogen was between 1 and 9 mM. In order to understand what promoted the overshoot of hydrogen concentration, an experiment was conducted in which the upper vertex of the cyclic voltammetry was moved in the cathodic direction at each cycle (Figure 3). For the first five cycles, when the upper

10


30 15 0 0 15

2

100 6

3

4

5

200

6

300 t/s 8

7

10 7

8

11 12

9

400

0 −0.5 −1 −1.5 −2 500

600 10 0 −0.5 −1 −1.5 −2

9

10 5 0 300

350

E / V vs. SHE

c / mM

1

c / mM

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


400

E / V vs. SHE

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450

t/s Figure 3: a) dependence of the concentration overshoot on the vertex potential of the cyclic voltammetry. b) details of the region where the overshoot disappears. Upper vertex from 1 to 3 0.2 V, then 0.1 V vertex 4, 0 V (5 ), −0.1 V (6 ), −0.2 V (7 ), −0.3 V (8 ), −0.4 V (9 ), and vertex from 10 to 12 0.2 V. potential was anodic enough to completely suppress the current at the cathode, the overshoot appeared at the beginning of every cycle and the measured concentration of hydrogen dropped to zero at the end of every cycle. Instead, for the following scans with lower anodic vertex potential, the overshoot disappeared and the hydrogen concentration became independent on the cathodic current of the platinum electrode as show in details in Figure 3 b). Once the first upper vertex potential of the cyclic voltammetry was recovered, the overshoot returned as intense as in the beginning. The overshoot in hydrogen concentration was dependent on the current density of the substrate, but also on its history, typical of hysteretic behavior. In fact, the overshoot could only appear at low currents and only in the beginning of the electrolysis. This was probably given by a different mechanism in the bubble formation showing in the beginning a metastable system. This system switched to a stable mechanism, which, above a certain current density, could more efficiently remove molecular hydrogen from the solution. Once initiated this mechanism remained active at all the current densities. 11



i / µA

a) −5 mA cm−2 0.3 0.2 0.1 0 0

100

200 z / µm

300

400

i / µA

b) −75 mA cm−2 1 0.5 0 0

50 z / µm

100

c) −288 mA cm−2 i / µA

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0.2 0.1 0 0

Linear fit Exponential fit 50 z / µm

100

Figure 4: Typical concentration profile of dissolved hydrogen with linear and exponential interpolation for different current densities. a) low current density (−5.2 mA/cm2 ), b) current density corresponding to the overshoot of hydrogen concentration (−75 mA/cm2 ), and high current densities where the concentration of hydrogen is current-independent (−288 mA/cm2 ). The concentration profile of dissolved hydrogen above the substrate was investigated through approach curves at different current densities. During an approach curve, the microelectrode is vertically translated from the solution towards the cathode surface. A current is recorded as a function of the working distance, i.e. the distance z between microelectrode mA and substrate. Figure 4 a) shows the case of −5.2 cm 2 substrate current when very little

bubbles are visible to naked eye. The linear extrapolation gave a diffusion layer of 253 µm (391 µm for exponential fitting see SI for details). The signal measured at the microelectrode was noisy, proving that some microscopic bubbles were present in proximity of the substrate.

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Figure 4 b) and c) show the case when there was an overshoot in concentration of dissolved hydrogen (−75 mA/cm2 ) and during the concentration plateau (−288 mA/cm2 ), respectively. In both cases the results are noisy, confirming the presence of bubbles which were clearly visible at these regimes. The fact that all the approach curves had their usual shape, i.e. a clear monotonic decay, although with some noise, suggests that the microelectrode tip was not obstructed by gas bubbles. A complete discussion on the blockage or hindering of the microelectrode tip is reported in the Supporting Information. Neglecting the influence of convection of the gas bubbles, from linear extrapolation it was possible to estimate a length of the diffusion layer of 63 µm and 29 µm for the concentration overshoot and for the concentration plateaus, respectively (81 µm and 39 µm for exponential extrapolation). Approach curves at current densities lower than −5 mA/cm2 were difficult to perform since the diffusion layer took a long time to establish fully and was very unstable at large distances. It is noteworthy to mention that apart from the case of the overshoot, the interpolation, both linear and exponential, were faithful to the data only to about 50 − 80 % of the length of the diffusion profile. The value of the diffusion layer were between 20 and 50 % larger for the exponential fitting than for the linear one mainly because the linear fitting was restricted to a shorter range. Table 1 gives a summary of the results extracted from the approach curves. Table 1: Summary of the data recovered from the approach curves of Figure 4; the results from the exponential extrapolation are reported in parenthesis.

Low current density Concentration overshoot Concentration plateau

Substrate current density mA / cm 2

Flux at the substrate (from (3)) / µmol cm2 s

Flux calculated from the approach curves (from (2) with v = 0) / µmol cm2 s

−5.2

27 · 10−3

14 · 10−3 (9.3 · 10−3 )

253 (391)

−75

0.39

0.24 (0.22)

63 (81)

−288

1.5

0.14 (0.11)

29 (39)

13


Diffusion layer / µm


To determine the onset of bubble formation, the reflectance of a laser beam on the cathode was studied as function of the current density. This technique is more sensitive than the electrochemical measurements because the microelectrode can only indirectly determine the presence of gas bubbles. On the other hand, any bubbles would strongly scatter the light coming from a laser beam. As visible in Figure 5, the light intensity was flat at current densities lower than one milliampere and sharply decayed at higher currents. This is in agreement with the formation of gas bubbles which scatter the light of the laser, decreasing the total reflectance of the electrode. The onset of bubble formation was calculated either by linear or exponential extrapolation on the first part of the reflectance decay and gave a value of −0.68±0.27 mA/cm2 and −0.76 ± 0.22 mA/cm2 , respectively. The two values are within the same margin of error, however the exponential extrapolation extend to lower values of reflectance. Beyond circa −1.5 mA/cm2 , the reflectance was very noisy and scattered, and did not show a particular trend. At even larger current densities the solution assumed a foggy-opaque aspect because of the intense light scattering given by the large amount of gas bubbles in solution. The onset of bubble formation found herein is in agreement with the experiments of Figure 4, where some noise was already visible at −5 mA/cm2 . Nonetheless, to naked eye, the first bubbles do not appear before −2 mA/cm2 . This kind of experiments should not be confused with the electroreflectance measured for example by Bewick and Tuxford 32 who showed, contrary to our experiments an appreciable variation in the electrode reflectance at low currents.

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1

Pn

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.5

Lin. extrap. Exp. extrap.

−1.5

−1 −0.5 j / mA cm–2

0

Figure 5: Normalized reflected power, Pn , of the laser beam on the platinum cathode as function of the current density.

Discussion Not only the amount of hydrogen dissolved in solution plays a role in the industrial electrolysis, but also the convection generated by the bubble formation and their moving. The shape of the approach curves of Figure 4 can be used to quantify the flux of hydrogen produced at the substrate and link it with the rate of gas absorption by the gas bubbles and with the convection they produce. The flux, J, of molecular hydrogen produced at the cathode in the direction perpendicular to the cathode can be expressed as:

J = −D ∇c + c v

(2)

where D and c are the diffusion coefficient and the concentration of molecular hydrogen, respectively, and v is the velocity of the fluid which is zero at the cathode surface. The diffusion coefficient is taken as independent of the position, while concentration and velocity are position-depend. This equation is valid for small concentrations, with the assumption that the fluxes of species are independent of each other. The flux can be linked to the current density, j, measured at the substrate: 15



J =−

j nF

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(3)

where n is the number of electrons involved in the reaction which is equal to two. The flux, J, of hydrogen can be calculated from the current at the cathode through (3) and from the approach curves with (2) taking v equal to zero. The results are reported in Table 1. There is very good agreement between the results recovered from the linear and the exponential extrapolation of the approach curves (apart from the length of the diffusion profile at low currents). The fluxes recovered from the substrate and those extrapolated from the approach curves are within a factor of two at the low current and at the overshoot, while the largest discrepancy was at the current density corresponding to the concentration plateau. The discrepancies can be explained by the collection efficiency of the microelectrode which is lower than one and by the neglected convection effects which can produce large turbulence at large current densities. The material balance is controlled by: ∂ c = −∇ · J + R ∂t

(4)

where R is the reaction rate of trapping molecular hydrogen into the gas phase which is the bubble mechanism of formation and growth. Considering a first order reaction (the reaction is linearly dependent on the driving force) and depletion of the molecular hydrogen in solution, the rate equation is:

R=−

∂ c = −k c ∂t

(5)

where k is the rate constant. This treatment is usually reserved for chemical reactions. However, assuming that the driving force for bubble formation or expansion is connected with the level of supersaturation in the liquid and that the bubbles have a fit distribution, it can be applied also to this system. 16


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2

10

vlin vexp

0

vn

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

−2

10

−3

10

−2

−1

10

10

xn

0

10

Figure 6: Normalized fluid velocity vn calculated for different concentration profile as function of distance from the electrode. Substituting (2) into (4) gives: ∂2 ∂ ∂ ∂ c = −D 2 c + c v + v +R ∂t ∂x ∂x ∂x

(6)

Plugging (5) into (6) and assuming a steady-state condition (∂c/∂t = 0 ), we get a diffusionconvective-reaction differential equation:

−D

∂2 ∂ ∂ c+v c+c v−kc = 0 2 ∂x ∂x ∂x

(7)

The concentration profile is known in different conditions, while the velocity of the fluid is unknown. The concentration profiles of Figure 4 can be interpolated either linearly, as it is usually done in textbooks, or exponentially which simplified the calculations and at least in the case of the overshoot gave better results also at large distances. The normalized velocity velin for the linear approximation is:

velin (xn ) =

(xn − 2) xn 2 (xn − 1)

(8)

where xn = x/δ and δ is the length of the diffusion profile. The normalization factor is 17



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Table 2: Estimated values for the rate constant k. k/s

−1

Low current density ∼ 0.03

Concentration overshoot ∼ 0.8

Concentration plateau ∼3

−δ k, the slope of velocity at x → 0. Whilst the normalized velocity in the exponential case is (normalization factor −(δ2 k−D)/δ):

veexp (xn ) = exn − 1

(9)

The full derivation can be found in the Supporting Information. Both solutions are independent of the concentration of dissolved gas and, as visible in Figure 6, they coincide for xn 1 and go with an unitary slope to zero at xn = 0. In the case of the linear concentration profile, the velocity tends to infinity approaching xn → 1. In the exponential case, the velocity growth is first linear and then exponential. In both cases, the dimensional velocity is negative meaning that the fluid is moving toward the substrate as expected if the bubbles move upward on an electrode facing up. For D δ 2 k , representing the case in which diffusion is small compared to the trapping of molecular hydrogen into the bubbles in the diffusion layer, the two solutions coincide at xn → 0. Unfortunately, from these experiments it is not possible to recover a value for the velocity of the electrolyte and of the rate constant k of absorption of hydrogen by the gas phase. However, taking an estimated value for v in the order of 10 cm/s 26 it is possible to calculate a value of k which for the three approaches curves of Figure 4 is given in Table 2. The complete derivation can be found in the Supporting Information. The results found so far can be rationalized considering the four mechanisms of gas phase formation in liquids: homogeneous nucleation (mechanism I), heterogeneous nucleation (II), pseudo-classical nucleation (III), and non-classical nucleation (IV) 7,8 . The first two mechanisms are the classical ones in which the nucleation is associated with an activation energy. Of course, in the case of heterogeneous nucleation the activation energy is lower than in the 18


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homogeneous case since in a three-boundary system the surface tension of the solid lowers the total energy requirement. The pseudo-classical mechanism (III) also includes a threeboundary system in which the solid phase possesses a gas cavity which is any irregularity of the surface where a gas pocket can remain trapped. In this cavity the curvature radius of the gas pocket is lower than the critical curvature for nucleation, and the nucleation energy is further lowered. This is the typical case for any non-smooth surface. In case IV, instead, the gas pocket has a curvature larger than the critical radius and no activation energy is required to form a bubble (non-classical nucleation mechanism). Figures 1, 2, and 3 show that initially a large supersaturation of dissolved hydrogen was present in the nearside of the substrate. It was also observed that at the beginning, quite large bubbles formed (see Supporting Information) at some particular spots, as usually also seen for boiling 33 . However, this observation cannot be confirmed above a few tens of milliamperes per square centimeter since the solution is no longer transparent. Large supersaturation levels suggest either a mechanism II or a mechanism III with only low density of gas cavities. Well defined and stable active spots for gas evolution were already observed by Chen et al. during oxygen evolution 19 . As explained by Jones et al., large bubbles also have large nucleation time which would be inefficient in lowering the saturation level of dissolved gas 7,8 . The fact that there are some preferential spots for bubble evolution confirms that a mechanism III is involved. However, once the current density at the substrate went beyond −50 to −150 mA/cm2 , the supersaturation dropped to unitary levels sometimes showing a very noisy transition time. A low supersaturation suggests a pseudo-classical mechanism (III) for bubble nucleation, probably mixed with a non-classical mechanism (IV). Interestingly this mechanism, or mechanisms, once initiated were stable almost until the substrate ceased to produce hydrogen. Assuming that mechanism III was active throughout the electrolysis, the difference between the concentration overshoot and the concentration plateau can be explained in 19



terms of the activation of mechanism IV. One can imagine that small cavities are suitable at any current density to maintain a small gas pocket. This pocket would have a small curvature radius requiring a non-negligible activation energy to trigger the bubble growth. However, once the current increases, any irregularity of the surface can behave as a cavity and stable gas pockets of a size suitable to sustain a non-classical mechanism of nucleation appear. This can explain also the hysteretic behavior in the gas concentration with the current. In fact, once created these gas cavities would be relatively stable and could survive also when the current is lowered. However, if gas production goes too low, these gas pockets, having a large curvature radius and therefore a large surface area, would deflate and eventually disappear faster than the other pockets. However, without a simultaneous analysis of the bubble population, size, and distribution it is difficult to back up any theory.

Conclusion In this work, the bubble formation during electrolysis was studied locally on a platinum electrode. It was possible to monitor the amount of molecular hydrogen released in the solution through a microelectrode placed in close proximity to the cathode. The concentration of hydrogen was found to reach an overshoot of supersaturation (between 25 and 50 times the saturation level) at rather low current densities (between −50 and −150 mA/cm2 ) and then decrease abruptly to a plateau of a few saturation units for more extreme currents. This phenomenon was not observed once the current was decreased and large supersaturations were detected only when the current was almost completely zero. Approach curves were recorded at different current densities of the substrate to investigate the length of the diffusion profile of molecular hydrogen which passed from 250 µm at low current density to 60 µm during the concentration overshoot and to 30 µm during the concentration plateau. The change in supersaturation levels and its hysteretic behavior suggested that the system follows different mechanisms for gas bubble formation. A possible explanation is that a type III mechanism

20


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for bubble nucleation is always active which takes advantage of small gas pockets present on the surface, while a type IV mechanism takes over at larger current densities. The latter requires larger gas pockets which disappear once the electrolysis current reaches zero, explaining the hysteretic behavior observed in the concentration analysis. The first instance of gas bubble formation was also investigated by observing the change in reflectance of the electrode during gas evolution. A fast decay of the reflectance was found when bubbles started to evolve and it was possible to estimate the first gas phase formation which was happening already below −1 mA/cm2 . This result was not in agreement with what was observed by eye or indirectly through the noise in the current transients measured at the microelectrode. Assuming the system followed the diffusion-convective-reaction differential equation where the gas bubbles contribute to both stir the solution and trap the dissolved molecular hydrogen, it was possible to estimate the shape of the electrolyte velocity in the nearside of the electrode. It was found that the electrolyte velocity rises linearly in the first part of the diffusion layer, near the substrate. Although unexpected results were found by observing the concentration of dissolved hydrogen during gas evolution, no quantitative model can be drawn, and further experiments are necessary to unveil the nature of gas bubble formation at a cathodic electrode. In particular it is fundamental to combine information coming from different techniques to be able to quantify all the variables of the system.

Supporting Information Available The supporting information contains the details of the experimental session of the main article, some details not discussed in the main body, and the full derivation of the electrolyte velocity divided into eight sections: 1. Electrochemical setup 21



2. Laser reflectance setup 3. Visual appearance of the substrate during bubbling 4. Characterization of platinum substrate 5. Hydrogen adsorption pseudo-capacitance 6. Blockage and hindering of the microelectrode tip by gas bubbles 7. Full derivation for the differential equations 8. Estimation of the rate constant k

Acknowledgement The Gateway Fellowship from the Research School PLUS of the Ruhr Universität Bochum is gratefully acknowledged for the financial support of the project.

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TOC Graphic

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Local Study on Hydrogen and Hydrogen Gas Bubble Formation on A

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