2022 Volume 90 Issue 12 Pages 127003
A stream of electron conductor powder (graphite, silver, and tin) was introduced to the measurement of Volta potential difference. The stream of the conductive powder was placed at the center of a vertical glass tube, while an aqueous electrolyte solution of KCl was run along the inner wall of the tube. The potential difference between the terminals of the streaming conductive powder electrode and the Ag/AgCl electrode inserted in the KCl solution was measured. From the experimental result, the real potential of the solvation of Cl− ion was determined. The values obtained by the present method were compared with the reported values based on the Kenrick method with mercury jet electrode.
The measurement of Volta potential difference, or contact potential difference, is a potentiometry with a voltaic electrochemical cell, in which an insulating (normally air) gap is included between two conducting phases.1 The cell potential is called “compensation potential,” which is corresponding to the difference of the work functions of the two conducting phases. When an ion conductor (electrolyte solution) is used instead of an electron conductor (metal), the “ionic work function” is responsible for the compensation potential. The negative value of the “ionic work function” is the so-called real potential of the solvation of ion, which corresponds to the work done to take an ion from a point at an infinite distance to a point inside an uncharged solution phase.2–4
Currently, the most widely used method for the measurement of Volta potential difference is the Kelvin probe method,5–14 in which the capacitance at the air gap is continuously modulated by periodical vibration of a probe electrode. The compensation potential is obtained from the ac output detected by a lock-in amplifier, etc. This method is so sensitive to the surface contamination, and thus special care must be taken to obtain reproducibility, especially when an electrolyte solution is included.13 As an alternative to the Kelvin probe method, the Kenrick method is known.15–24 Here, a jet of mercury probe electrode is directed down the middle of a vertical tube, and the inner surface of the tube is covered by a stream of the electrolyte solution. In this manner, the surfaces of the metal electrode and the electrolyte solution are continuously renewed. When the air gap is sufficiently small, the compensation potential can be measured by a high-input-impedance voltmeter. The Kenrick method has an advantage of small sensitivity to the surface contamination of the electrode,19 and thus the experimental results have been considered reliable and chosen for the determination of real potentials of ions.24,25 Nevertheless, very few reports have appeared on this method so far,16–23 probably because of its relatively complicated experimental setup.
We recently reported a Kenrick-type measurement of Volta potential difference with a dropping carbon fluid electrode.26 A carbon fluid prepared by mixing graphite powder and low-viscosity liquid paraffin was adopted in the place of mercury jet electrode. However, although it was possible to measure the compensation potential, the cell potential was unstable and it required long period (∼10 min) to obtain a result, which was mainly due to the instability of the composition of the two-component electrode. In the present study, we examined graphite, silver, and tin powders as the probe electrode of the Kenrick method. A stream of the conductive powder allowed the continuous renewal of the electrode surface. The thus obtained real potential of Cl− ion was compared with reported values.
Spherical graphite powder ICB-15020 with average diameter of 170 µm was purchased from Nippon Carbon (Tokyo, Japan). Atomized silver powder of 45–125 µm was obtained from Alfa Aesar. Atomized tin powder of 45–150 µm was from Hikari Material Industry (Nagano, Japan). All the powders were washed with distilled water, dried at 90 °C for 12 h, then washed by acetone, dried at 40 °C for 12 h, and stored in a desiccator with a relative humidity 25 %.
A hopper for the flow of the conductive powder was prepared by connecting a stainless-steel funnel (87 mm and 11 mm for upper and lower openings, respectively) and a stainless-steel decorating tip (Wilton, #2, round opening of 2 mm) with a masking tape. The outer surface of the hopper was coated by an insulating spray Hayacoat Mark2 AY-302G (Sunhayato, Tokyo, Japan) for insulation.
Measurement apparatus is shown in Fig. 1. A cylindrical water-jacketed glass cell (25 mm internal diameter, 60 mm length) was held in upright position, and the bottom opening was closed by a silicone rubber stopper. The upper surface of the silicone rubber stopper was covered with a thin PTFE sheet to prevent the test solution directly contacting with the silicone rubber. A glass tube (4 mm internal diameter, 105 mm length) was inserted through the stopper, and the upper end of the glass tube was held at 45 mm height from the surface of the PTFE sheet. A 1000-mL separating funnel was connected to the stopper through a high-density polyethylene tube. Reagent grade KCl from Nacalai (Kyoto, Japan) was used without further purification. A KCl aqueous solution was prepared with deionized distilled water and delivered from the separating funnel into the glass cell at the flow rate of about 130 µL s−1. After the glass cell was filled with the KCl solution, the solution overflowed along the inner wall of the glass tube. The hopper was carefully held at the center of the upper opening of the glass tube by using an XYZ positioner, not to make a direct contact with the KCl solution. The distance between the lower tip of the hopper and the KCl solution, or the thickness of the air gap, was about 1 mm. The assemblies of the glass cell, capillary, and electrodes were placed in a Faraday cage (30 cm × 30 cm × 40 cm, Hokuto Denko, Tokyo, Japan). Temperature of the KCl solution in the cell was kept at 25.0 ± 0.5 °C by circulating thermostated water. An Ag/AgCl reference electrode was immersed into the KCl solution. The Ag/AgCl electrode was prepared by the electrolytic oxidation of a silver wire (0.5 mm diameter) in a KCl solution at a constant current of 1 mA, and checked by potentiometry with 0.001–0.1 M (M ≡ mol dm−3) KCl solutions and a saturated calomel electrode, if it gave the conventional standard electrode potential (0.222 V vs. SHE at 25 °C).27
Measurement apparatus. (a) Conductive powder, (b) hopper, (c) water-jacketed glass cell, (d) silicone rubber stopper covered with a PTFE sheet, (e) glass tube, (f) Ag/AgCl electrode, (g) inlet of electrolyte solution, (h) drain, (i) inlet of thermostated water, (j) outlet of thermostated water, (k) Faraday cage, (l) voltmeter with high input impedance, (m) PC for data acquisition.
The compensation potential (Ec) for the cell (1) was measured by a high-input-impedance electrometer (8252, ADC Corp., Saitama, Japan, 200 TΩ input impedance).
| \begin{equation} \text{Cu $|$ Ag $|$ AgCl $|$ 0.002–0.020 M KCl (aq) $|$ air $|$ cp $|$ stnls $|$ Cu$'$} \end{equation} | (1) |
Electron work functions of conductive powders were determined by an ultraviolet photoelectron yield spectrometer in air (AC-3, Riken Keiki, Tokyo, Japan). This can measure work functions between 4.0–7.0 eV at ambient temperature and pressure.28,29
As a brief preliminary survey, the conductivity of various powders was examined by a digital multimeter. Graphite, silver, and tin powders gave sufficiently high conductivity, whereas copper, stainless steel, and aluminum powders did not show enough conductivity, probably due to the presence of insulating oxide films on the surface. In the following experiments, only graphite, silver, and tin powders were used.
The electrochemical cell for Volta potential difference includes air gap and thus the cell resistance is very high. Even when the voltmeter with high input impedance is applied, too high cell resistance can make the measurement impossible. Figure 2A shows a time course of the cell resistance (Rcell) of the cell (1) with a streaming carbon powder electrode, which was taken by a voltmeter with high input impedance. At t = 0, the stopper for the streaming powder was taken off and the graphite powder started to flow. Immediately the cover of the Faraday cage was shut. The Rcell was stable at about 50 GΩ during the carbon powder was flowing, and then it became immeasurably high after all the powder passed (t = ∼2 min). Figure 2B shows the Rcell of the cell (1) in the absence of streaming carbon powder electrode. An immeasurably high Rcell was observed soon after the Faraday cage was shut. These results indicate that the Volta potential difference can be measured only when the carbon powder is supplied, and that the tip of the stainless-steel hopper does not work as an electrode. A brief examination by a digital multimeter showed that the carbon stream of about 5-mm length from the tip of the hopper was electrically in contact. Probably, the Rcell is determined by the 1-mm air gap between the surfaces of the carbon powder in contact and the electrolyte solution at the upper opening of the glass tube. The carbon powder released must be the carrier of charge and responsible for the electric conduction at the air gap. The Rcell of 50 GΩ is small enough to carry out potential measurements by the high-input-impedance voltmeter of 200 TΩ.
Time course of the resistance of the cell (1) at cKCl = 0.020 M in the presence (A) and absence (B) of streaming carbon powder electrode.
The compensation potential (Ec) of the cell (1) was measured by the Kenrick method with the streaming carbon powder electrode. Figure 3 shows the results at the KCl concentration (cKCl) of 0.010 M. The Ec reached an almost constant value within 30 s and did not change so much until the carbon powder was over. In our previous study with a dropping carbon fluid electrode,26 the Ec gradually changed for several minutes, and it finally became stable at about 10 min. Here, an almost constant value of Ec was obtained quickly. From Fig. 3, we sampled the potential data for 60 s at the interval of 1 s after it became stable, and obtained Ec = −0.124 ± 0.008 V as an average. The value with “±” indicates the standard deviation. The average and the standard deviation were calculated from 360 data (60 data points for each experiment with 6 times repetition). Similar replicate measurements of Ec were performed with seven different cKCl between 0.002–0.020 M. No significant difference in Ec was observed when the whole set of the apparatus was placed in a polyethylene bag filled with Ar gas, suggesting that oxygen gas did not affect the measurement.
Time course of replicate measurements of Ec with 0.010 M KCl at streaming carbon powder electrode.
By streaming the aqueous solution (aq) and the conductive powder (cp) in the vertical tube, no charge is built up on their surfaces, so that it can be assumed that there is zero Volta potential difference between them:3,24
| \begin{equation} \psi^{\text{aq}} = \psi^{\text{cp}} \end{equation} | (2) |
| \begin{equation} E_{\text{c}} = \frac{1}{F} (\mu_{\text{Ag}}^{\circ} + \alpha_{\text{Cl${^{-}}$}}^{\text{aq},\circ} + RT\ln a_{\text{Cl${^{-}}$}} - \mu_{\text{AgCl}}^{\circ} - \alpha_{\text{e${^{-}}$}}^{\text{cp},\circ}) \end{equation} | (3) |
In order to determine $\alpha_{\text{Cl}^{ - }}^{\text{aq}, \circ }$, we employed the method of extrapolation to zero ionic strength, as described previously.3,24 Figure 4 shows the plot of Ec corrected for the activity of KCl against the square root of ionic strength, I1/2. The mean activity of KCl, designated as aKCl, was calculated using experimental values of mean activity coefficients of KCl.30 Within the concentration range tested (0.002 M ≤ cKCl ≤ 0.020 M), aKCl can be approximated to $a_{\text{Cl}^{ - }}$.3,20 The standard value $E_{\text{c}}^{ \circ }$ for the limit of infinite dilution was determined from the intercept of the regression line by Eq. 4.
| \begin{align} E_{\text{c}}^{\circ} &= E_{\text{c}} - \frac{RT}{F}\ln a_{\text{Cl${^{-}}$}} = \frac{1}{F} (\mu_{\text{Ag}}^{\circ} + \alpha_{\text{Cl${^{-}}$}}^{\text{aq},\circ} - \mu_{\text{AgCl}}^{\circ} - \alpha_{\text{e${^{-}}$}}^{\text{cp},\circ}) \\ &= 0.005 \pm 0.025\,\text{V} \end{align} | (4) |
Plot of Ec corrected for the mean activity of KCl against I1/2. Error bars show the standard deviations. Broken line is the regression line.
The graphite powder was replaced by other conductive powders and the $E_{\text{c}}^{ \circ }$ values were obtained to be 0.159 ± 0.034 V and 0.165 ± 0.067 V for silver powder and tin powder, respectively. Work functions of three conductive powders were estimated by an ultraviolet photoelectron yield spectrometer in air, as summarized in Table 1. From Eq. 4 with the experimental values of $\alpha_{\text{e}^{ - }}^{\text{cp}, \circ }$, and with literature values of the lattice free energy of AgCl ($\mu_{\text{AgCl}}^{ \circ } = - 848.5$ kJ mol−1)31 and the negative value of the gas-phase free energy of formation of Ag+ ion ($\mu_{\text{Ag}}^{ \circ } = - 974.5$ kJ mol−1),31 we obtained the $\alpha_{\text{Cl}^{ - }}^{\text{aq}, \circ }$ values with carbon, silver, and tin powders. The results are summarized in Table 2. Of course, these values should be independent of the electrode material. The values obtained with silver and tin powders were close to each other, and to the literature values obtained with mercury jet electrode,18,20,24 as well as to our previous result with dropping carbon fluid electrode.26 However, the value obtained with carbon powder deviated negatively from them by about 20 kJ mol−1. Although this disagreement might be derived from the random error of the present Volta potential measurement with very high cell resistance, the standard deviation of the $E_{\text{c}}^{ \circ }$ was about 0.03–0.07 V, which corresponds to at most 3–7 kJ mol−1 deviation of $\alpha_{\text{Cl}^{ - }}^{\text{aq}, \circ }$, as indicated in Table 2.
| Conductive powder | Work function/eV | $\alpha_{\text{e}^{ - }}^{\text{cp}, \circ }$/kJ mol−1 |
|---|---|---|
| Graphite | 4.86 | −469 |
| Silver | 4.85 | −468 |
| Tin | 4.81 | −464 |
| Electrode | $\alpha_{\text{Cl}^{ - }}^{\text{aq}, \circ }$/kJ mol−1 |
|---|---|
| Mercury | −318a, −324b |
| Carbon fluid | −320c |
| Carbon powder | −343 ± 3 |
| Silver powder | −327 ± 4 |
| Tin powder | −322 ± 7 |
a; Calculated from Randles’ data.18 b; Calculated from Farrell and McTigue’s data.20 c; Ref. 26.
The study by McTigue et al. with mercury jet electrode is certainly one of the finest measurements of Volta potential difference.20–23 They reported highly precise results of $E_{\text{c}}^{ \circ }$ with a relative standard deviation of 0.04 %. However, the real potentials of ions, which are calculated from the $E_{\text{c}}^{ \circ }$ and the work function of the probe electrode, include uncertainty in the both measurements. When the former can be determined accurately and precisely, the uncertainty of the real potential is entirely derived from the latter, as Trasatti pointed out.32 Although 4.50–4.52 eV is widely accepted as the work function of mercury,3,32–34 it is reported that the accurate value is very difficult to obtain due to its instability.35,36 McTigue et al.20–23 and other researchers who used mercury jet electrode for the measurement of Volta potential difference16–19 did not evaluate the work function of their probe electrodes at the temperature and pressure of their experimental condition. Thus, the validity of the real potentials they obtained is questionable.
Similarly, the uncertainty of the real potential in our study is considered to be from the evaluation of the work functions of the electrodes, but it is difficult to estimate it. The values with “±” in Table 2 do not include the uncertainty in the measurement of the work functions. In the present work, we employed a photoelectric method and assumed that the photoelectrons were emitted from the Fermi level of the conductive powders. However, as pointed out by Hansen and Hansen,13 the source of photoelectrons may be an insulating photoactive surface layer, whose electrons are not directly correlated with the Fermi level of the substrate. In the case of tin powder, although not insulating, the surface is covered with a thin semiconductive SnO2 film, in which the Fermi level is supposed to be inside the band gap. Therefore, the photoelectric work function estimated here may not be the same as the true work function of metallic Sn, which is in electronic equilibrium. With respect to silver, the oxide film on the surface of the powder can be neglected, but it is known that the surface can corrode by the formation of Ag2S even in ambient laboratory air with very low concentrations of H2S.37,38 Ag2S is a semiconductor and thus the photoelectric work function may be different from that of metallic Ag. If we assume that the work functions of Ag and Sn are 4.30 and 4.38 eV according to the literature values,3,33 the $\alpha_{\text{Cl}^{ - }}^{\text{aq}, \circ }$’s calculated from our results are −274 and −281 kJ mol−1, respectively, both of which are remarkably more positive than the Randles’ and McTigue’s values (−318 and −324 kJ mol−1, respectively). Taking into account the absolute value of the solvation free energy of Cl− ion reported (−304 kJ mol−1),3,24 those values of −274 and −281 kJ mol−1 are improbable, since they require negative surface potential of water. It is known that the surface of graphite has also impure structures with oxygen atoms, such as carbonyl and carboxyl groups. We are not certain about their influence on the emission property at the surface of the graphite powder, but the situation may be similar to silver and tin. If we take the literature value of work function of HOPG, 4.48 eV,13 the $\alpha_{\text{Cl}^{ - }}^{\text{aq}, \circ }$ is calculated to be −306 kJ mol−1, which is rather close to the Randles’ and McTigue’s values.
Accordingly, at the present stage, it is difficult for us to establish an appropriate procedure for accurate values of real potentials. The key point is the validity of work functions of the probe electrodes. Gold and tungsten are often used as the reference surface in the measurements of work function.36 Further study with these materials may give more reliable values of real potentials.
This work was supported by JSPS KAKENHI Grant Number JP21K05109. The authors wish to thank Dr. Yoshiyuki Nakajima (Riken Keiki) for his valuable advice and assistance in the measurements of the work function of conductive powders.
Hirosuke Tatsumi: Conceptualization (Lead), Funding acquisition (Lead), Investigation (Lead), Supervision (Lead), Writing – original draft (Lead), Writing – review & editing (Lead)
Keita Sato: Methodology (Lead)
Manami Yoshimura: Data curation (Lead), Formal analysis (Lead)
Mariko Sakamaki: Data curation (Supporting), Formal analysis (Supporting)
Mizuki Sunagawa: Data curation (Supporting), Formal analysis (Supporting)
Fumiki Takahashi: Supervision (Supporting), Writing – review & editing (Supporting)
Jiye Jin: Supervision (Supporting), Writing – review & editing (Supporting)
The authors declare no conflict of interest in the manuscript.
Japan Society for the Promotion of Science: JP21K05109
H. Tatsumi: ECSJ Active Member
