Gravimetric Method for Hydrogen Evolution Measurements on Dissolving Magnesium

As mentioned above, the volume of gas produced per mole of H₂ can be approximated by means of the ideal gas law. At constant temperature, this volume will depend exclusively on the gas pressure. Although using standard conditions for pressure (1 atm) could be a reasonable approach, significant differences are observed for deviations from this standard value.¹⁸ Consequently, to accurately account for the current associated with the HER, a more realistic pressure for the H₂ gas generated needs to be determined.

When H₂ gas is produced, a gas/liquid interface is created. Once this interface appears, an evaporative process of the electrolyte takes place. The gaseous phase constituted initially by pure H₂ will eventually saturate with evaporated solvent until the equilibrium vapor pressure is achieved. Thus, the gaseous phase accumulated at the top of the inverted beaker as the result of the HER will be composed of H₂ and evaporated water vapor coming from the electrolyte. In a mixture of gases, each gas has a partial pressure, which is the hypothetical pressure of that gas if it alone occupied the volume of the mixture at the same temperature. The total pressure (P_T) of an ideal gas mixture is the sum of the partial pressures of each individual gas in the mixture. For the volume of gas accumulated at the top of the inverted beaker in the gravimetric set-up, P_T would be defined by the following expression:

where P_H2 is the partial pressure of the generated H₂, P_vapor(H2O) is the vapor pressure for water at a given temperature, and P_T has already been described. Because the beaker is fully immersed in the electrolyte, P_T will be the sum of the atmospheric pressure (P_atm) and the hydrostatic pressure exerted by the column of electrolyte on the top part of the beaker. Consequently, the partial pressure of the volume of produced H₂ will be described by:

where h₁ is the immersion depth, i.e. the distance between the top of the inverted beaker and the solution/air interface (see Fig. 1), P_vapor(H2O) is 0.03 atm at 25°C and the rest of the parameters have been previously described. For low density solutions and/or small immersion depths the second term in the right side of Eq. 7 will be on the order of 1 × 10^–4 atm, and thus could be neglected. However, the importance of considering the real atmospheric pressure has been previously discussed by Kirkland et al.¹⁸ and needs special attention.

Atmospheric pressure is caused by the weight of air above the measurement location and this parameter will vary with altitude. At points above the sea level, where the average pressure of 1 atm is taken as a reference, an exponential decrease in the atmospheric pressure is expected according to:²²

where P₀ is the average pressure at the sea level (1 atm), M is the molar mass of dry air (29 g mol⁻¹), h is the altitude above the sea level and the rest of the parameters have their usual meanings. Note that variation of the atmospheric pressure with local climatic conditions was not considered in the analyses performed in this paper. Considering the average local atmospheric pressure at the location where the experiments were carried out, about a 3% difference in the volume of generated H₂ would exist with respect to that assuming an atmospheric pressure of 1 atm. Furthermore, nearly a 7% error would be expected without corresponding corrections for both the vapor pressure and the atmospheric pressure. Note that this difference increases as conditions such temperature and height above sea level increase. For instance, at a local height of 650 m above the sea level and a temperature of 30°C, about a 15% difference in H₂ volume would be exhibited.

Following the previous rationale and taking into account the corrected value for vapor and atmospheric pressures, then the gas produced per mole of H₂ will occupy approximately 26.12 liters at 25°C. Using Faraday's law, a 140 μg s^–1 variation in the buoyant force associated with the mole of hydrogen generated by the corrosion reaction is equivalent to a current of 1 mA (considering a density value for the electrolyte of 1.037 g cm^–3, i.e. 1 M NaCl solution). This represents a 10% difference with respect to the expected buoyant force variation under standard conditions. When a 0.1 M NaCl solution was used (density value of 1.001 g cm^–3), a 135 μg s^–1 variation in the buoyant force was considered equivalent to a current of 1 mA.

To evaluate the accuracy of the experimental method for gravimetric HE collection, galvanostatic polarization measurements were conducted on a Pt foil electrode with a surface area of 1.34 cm² using different applied cathodic current densities, i_app, for a fixed period of time. A Pt electrode was chosen due to its low reactivity in aqueous media to avoid any interference from corrosion that might occur during polarization. The traditional volumetric HE collection method was also evaluated for comparison. The application of different cathodic current densities represents a reliable procedure to assess the accuracy of both HE collection methods based on the fact that, ideally, the calculated current densities associated with the HER should be equal to the applied cathodic current densities. For this to be applicable, no other electrochemical reaction in competition with HER should occur on the electrode surface. The current was applied for 900 and 1000 s for the volumetric and gravimetric methods, respectively. The longer period was used for the volumetric method because of the need to make a sufficient number of volume readings given the limitations in the accuracy of the burette, 0.1 mL. Measurements were performed every 100 s for a total of 10 measurements. For an applied cathodic current density of 1 mA cm^–2, longer experimental times were needed due to the low amount of H₂ production. In this case a total experimental time of 6000 s was used with volume measurements carried out every 600 s. For the gravimetric method the high precision balance allowed quantitative and automatic weight measurement every 5 seconds, providing a significantly higher confidence in HE rate determination.

Fig. 3 shows the volume of H₂ collected during the application of different cathodic current densities as a function of time in 1 M NaCl solution for the Pt foil electrode using the volumetric experimental set-up. As was observed in previous works on high purity Mg,^12,15 the HE rate was linear in all cases although an initiation time or period of lower rate was observed. The duration of this period was dependent on the applied current density value, being longer for lower current densities. This was particularly relevant for the initial stages of experimentation. H₂ gas is very soluble in aqueous environments and it is likely that some H₂ was lost by dissolution into solution.¹⁸ However, the dissolution of H₂ in the electrolyte appeared not to be responsible for this initial period of lower HE detection, as will be discussed below. The inset in Fig. 3a shows a magnified view of the initiation period. For applied cathodic current densities below 25 mA cm^–2, approximately 500 to 600 s were needed for the volume increase to be linear. For the applied cathodic current density of 1 mA cm^–2, Fig 3b, the time needed to observe linearity increased to approximately 1200 s. This confirms the unsuitability of the volumetric method when short immersion times or low current densities are investigated (i.e. low i_corr values associated with corrosion resistant materials).

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Fig. 4 shows the calculated volume of H₂ collected during the application of different cathodic current densities as a function of time in 1 M NaCl solution for the Pt foil electrode using the gravimetric experimental set-up. A linear-like behavior was exhibited during the whole time of experimentation where, in contrast to the volumetric method, no initiation time of lower rate was observed at the early stages of polarization. The inset in Fig. 4 shows that a reliable linear region was exhibited within the first minute of experimentation. The experimental conditions, such as applied cathodic current, temperature, volume of electrolyte and working electrode surface, were identical for the two different H₂ collection methods. Therefore, it is reasonable to assume that, for each particular current density applied, the same amount of H₂ dissolved into the electrolyte independently of the H₂ collection method used and that the time of lower HE detection exhibited at the beginning of the volumetric experiments was not caused by H₂ dissolution. The slower response of the volumetric method might be associated with the time for bubbles to form, detach from the electrode surface, and travel to the top of the burette. Note that even the bubbles still attached to the sample surface would create a buoyant force in the gravimetric method. It is also possible that more hydrogen would be lost by dissolution into the electrolyte in the volumetric method because of the long travel distance for the bubbles, but this effect is expected to be small. This high sensitivity to HE detection makes the gravimetric method more suitable than the volumetric method for the study of materials with high corrosion resistance, which evolve hydrogen at a slower rate. The gravimetric method also allows for the study of materials with limited size and/or thickness, where complete dissolution of the sample may occur before enough measurements from the burette could be taken for a reliable determination of the HE rate.

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The steady state HE rates were determined from the linear portion of the curves in Figs. 3 and 4 and are plotted in Fig. 5 as current densities as a function of the applied cathodic current density. The dashed lines in Fig. 5 represent the ideal response in HE detection with 100% accuracy (slope of 1) and were added to aid comparison. The expected linear-like behavior was observed for both volumetric and gravimetric methods. For the volumetric method, the i_HER values were lower than the applied current densities over the whole range of currents investigated. In contrast, higher values for i_HER were observed for the gravimetric method, especially when cathodic current densities higher than 15 mA cm^–2 were applied. From the linear fits of the data, the gravimetric method exhibited HE current densities closer to the expected ideal values than the volumetric method, with deviations in the slope of 0.12 and 0.16, respectively, from the theoretical value of 1. The calculated slopes suggest that the volumetric method was able to detect 84% of the H₂ produced over the whole range of applied current densities, whereas the gravimetric method detected 112%. However, this should be read with caution since a regression line is the straight line that best approximates all the individual data points. For this reason, to better determine the accuracy of both experimental methods for HE detection, each i_HER value should be evaluated individually.

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Fig. 6 shows the absolute value of the percentage error for the calculated i_HER value as a function of the applied cathodic current density. For applied cathodic current densities of 25 mAcm⁻² and greater, the gravimetric method exhibited error values very close to 10%, which is shown as a dashed line in the figure and assumed as the threshold below which the experimental values might be considered acceptable. The errors were much less for the low applied current densities. In contrast, significantly higher errors were observed for the volumetric method, particularly for the low applied current densities. This confirms the higher accuracy of HE detection shown in Fig. 5. It is interesting to note that the increase in the applied current density generated two different trends depending on the experimental method. While the error values progressively decreased in the volumetric method as the applied cathodic current density increased approaching the satisfactory threshold, the errors associated with i_HER for the gravimetric method increased to a relatively steady value close to 10%. This is a reasonable behavior for the volumetric method because as the HE rate increases, the higher amount of H₂ produced saturates the solution surrounding the electrode quicker, leading to a higher HE collection efficiency. Furthermore, it is likely that the copious generation of H₂ did not allow bubbles to attach to the electrode surface, neither to the walls of the funnel and the burette, decreasing the underestimation of the HE rate. However, it is somewhat surprising that, for the gravimetric method, higher amounts of H₂ were collected with respect to those expected from the cathodic current densities applied, especially for current densities over –15 mA cm^–2. The reason for this extra current is not yet clear, but the following points address this issue.

• (a)  
  In an aerated solution such as the one used in the present study, a certain amount of dissolved O₂ and N₂ are present in the electrolyte. The bubbling of the electrolyte with the produced H₂ gas may also lead to removal of some the gases dissolved in it by degasification. As observed in Fig. 6, a relatively steady amount of 10% extra weight was registered using the gravimetric method when the highest current densities were applied. This corresponds to an increase in the hydrostatic force of 1.18 grams as the result of an electrolyte displacement of approximately 1.1 mL for the highest current density (i.e. –70 mA cm^–2), that will be considered as the maximum amount of extra weight registered. The solubilities of O₂ and N₂ gases in an aqueous solution at standard conditions are approximately 5.8 and 10.9 mL/L, respectively.²³ Consequently, in the constant volume of 0.6 L of electrolyte used throughout the experiments, a total volume of approximately 10 mL of O₂ and N₂ gases was contained in the test solution. It is reasonable then that nearly a 10% if it could have been displaced by HE. It is interesting to note that the electrochemical cell was open to air. This may represent a potential source of O₂ and N₂ to be incorporated to solution. Furthermore, simultaneously to the production of H₂ at the working electrode, O₂ was produced at the counter electrode at a rate proportional to HE rate so that the test solution was continuously fed with O₂ during the whole time of experimentation.
• (b)  
  The solubility of a gas in a solvent is dependent on temperature, meaning an increase in temperature results in a decrease in the gas solubility in an aqueous solution. As discussed by Kirkland et al.,¹⁸ an increase in temperature may result in the release of a certain amount of the gases dissolved in the electrolyte, mainly O₂ and N₂. The electric current flow through the low conductivity region near the electrolyte associated with bubbles may cause Joule heating of the solution near the electrode surface, promoting a decrease in dissolved gas solubility. The amount of heat released by Joule heating is proportional to I²R so it should be stronger at higher applied current density. However, due to the relatively large volume of electrolyte used (approximately 600 mL) it is likely that this effect is negligible.

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Hydrogen evolution at the corrosion potential

Fig. 7a shows the volume of H₂ collected at the E_corr as a function of time in 0.1 M NaCl solution for the HP Mg electrode using the gravimetric experimental set-up. A 0.1 M NaCl solution was used to compare the results obtained using the gravimetric method with those previously reported using the volumetric method on the same HP Mg material as test specimen.¹² For clarity and with the aim of evaluating the corrosion process, Fig. 7a shows representative results from replicated experiments, which were similar. Fig. 7a also shows the evolution of the E_corr as a function of time. The volume of H₂ collected increased rapidly within the first hour of immersion, exhibiting a constant rate after about 2 h of experimentation. The evolution of the E_corr is in agreement with this behavior, exhibiting a stable potential value of circa –1.6 V_SCE after the electrode was immersed in the electrolyte for approximately 2 h. When the evolution of the H₂ volume collected at the E_corr using the gravimetric method is compared with that obtained by the volumetric method,¹² significant differences were exhibited (see Fig. 7b). Approximately 10 h of immersion were needed to start observing linearity in the volumetric data, although experimental timeframes of about 2–3 days were needed to determine a steady state value for the corrosion rate. Very similar immersion times were also reported in a previous work using the same HP Mg material.¹⁵ However, significantly shorter experimental times were required using the gravimetric method, where an 8 h period was enough to calculate a reliable corrosion rate value. Furthermore, almost no H₂ volume was collected using the volumetric method within the first 8 h of immersion.¹²

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Fig. 8 shows corrosion current density for the HP Mg for the different methods in 0.1 M NaCl solution at the E_corr. Current density values were calculated from the steady state HE rates. A slightly higher average i_corr value was obtained using the gravimetric method, but this difference is only about 10 μA/cm² and can be considered insignificant. However, it should be stressed that significantly shorter experimental times were needed to carry out the i_corr determination using the gravimetric method. These results confirm the higher sensitivity to HE detection of the gravimetric method with respect with the traditional volumetric method, exhibiting a better suitability for corrosion current determination on Mg and its alloys. Furthermore, in contrast with the volumetric method, the higher resolution of the gravimetric method when monitoring the corrosion process allows accurately differentiation of any possible variation in the instant corrosion rate that the electrode may experience during the time of experimentation. The high sensitivity of the gravimetric method for H₂ collection is worth noting, as current values of the order of tens of microamperes were detected.

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Anodic hydrogen evolution under galvanostatic polarization

Fig. 9 shows the volume of H₂ collected during the application of different anodic current densities as a function of time in 0.1 M NaCl solution for the HP Mg electrode using the gravimetric experimental set-up. As commented above, results will be compared with those obtained using the volumetric method on the same HP Mg as test specimen.¹² As previously shown for the Pt foil electrode (see Fig. 4), a linear-like response was exhibited during the whole time of experimentation. This is particularly relevant for the lower current densities, where reliable results were obtained even within the first minute of polarization, in contrast with the results exhibited when the volumetric method was used where lower rates were exhibited in the early times of measurement (as previously reported in Ref. 12). These results confirm the higher sensitivity to HE detection of the gravimetric method with respect to the traditional volumetric method when Mg is subjected to anodic polarization. Furthermore, the observation of a constant anodic HE rate from the early stages of polarization (when no corrosion product was visually detected on the electrode surface) presents important implications regarding some of the current interpretations on the mechanism of this phenomenon. Nevertheless, discussion about the origins of anodic H₂ on Mg is not the aim of this paper.

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Fig. 10 shows HE current density values for the HP Mg specimen determined from the linear fits of the curves in Fig. 9 plotted as current densities as a function of the applied anodic current density. Fig. 10 also shows the current density values associated with HE for the HP Mg electrode determined using the volumetric method for comparative purposes.¹² A linear-like behavior was observed for both H₂ collection methods over the whole range of anodic current densities applied. Note that an analysis analogous to that shown in Fig. 6 to determine the accuracy of the HE current density values using the gravimetric method could not be performed because a 1:1 relation in current is not expected when anodic polarizations are applied. However, according to the accuracy results when the Pt foil electrode was used, it is reasonable to assume that the gravimetric method exhibited error values within 10%, which might be similar here. Higher HE current density values were measured by the gravimetric method. From the linear fits of the data, nearly 10% more H₂ volume was detected using the gravimetric method than using the volumetric method. However, to evaluate the gravimetric method with respect to the traditional volumetric one, it is more useful to compare the differences between each individual i_HER value determined by both H₂ collection methods upon the application of a particular anodic current density. An average increase of 25 ± 8% in the current density values associated with the HER was exhibited using the gravimetric method. It is worth noting that the HE current density values using the volumetric method were determined by passing a total net charge of 20 C at different anodic current densities. This means that, with the exception of +25 mA/cm², longer periods of current application were used for the volumetric method than for the gravimetric method. This difference was significantly higher for the lowest current densities applied where, for the case of +1 mA/cm², a 19X increase in current application time was used between the volumetric and the gravimetric methods. These results show the higher suitability of the gravimetric method with respect to the traditional volumetric method for the study of anodic H₂ on Mg and its alloys. Additionally, the gravimetric method appears to be also suitable for the study of anodic H₂ on other materials where this effect has been reported such as Al and Al alloys.^24–26

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Hydrogen evolution detection under galvanodynamic polarization

An interesting characteristic of the gravimetric method is that, in contrast with the traditional volumetric one, it allows for real-time HE detection during dynamic polarization. Galvanodynamic testing was performed instead potentiodynamic polarization for the same reason that galvanostatic instead of potentiostatic polarization is often used: controlling the applied current allows for easy comparison with the rate of HE. Fig. 11 shows the galvanodynamic polarization response of the HP Mg in 0.1 M NaCl solution plotted against the measured potential. Fig. 11 also shows the absolute value of the calculated current densities for the HER obtained during polarization using the gravimetric method. These experiments were carried out in a quiescent electrolyte and in separate scans (i.e. anodic and cathodic polarizations). Representative results from replicated experiments are presented. The potential values presented are not corrected for ohmic potential drop.

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As shown by Curioni,²¹ during cathodic polarization a very good correspondence between the HE current densities and those measured by the potentiostat was exhibited. This behavior validates the use of the gravimetric method for H₂ collection during dynamic polarization measurements. When anodic currents were applied to the electrode, the current density values associated with HE presented lower values than those measured by the potentiostat during galvanodynamic polarization. It should be noted that the curve registered by the potentiostat corresponds to the net current of the HP Mg, whereas the current density values from the gravimetric method are associated with the local cathodic reaction, HE, taking place across the full range of potential (both above and below the OCP), and were calculated from the HE at the working electrode. During the anodic polarization of Mg, a cathodic current density associated with HE was measured because some of the electrons generated by the Mg oxidation reaction (Eq. 1) did not flow through the potentiostat to the counter electrode but rather were consumed by the HER on the Mg electrode surface, thus the net anodic current density applied was lower that the anodic current density associated with Mg oxidation. Using the accurate gravimetric detection of the HE current density, the total Mg dissolution current density is easily determined by the addition of the net anodic and the HE current densities. As observed in Fig. 11, the gravimetric method exhibited a very high sensitivity and resolution in HE detection during dynamic polarization and appears to be a reliable way for real-time monitoring the current density associated with Mg dissolution during anodic polarization.

More interestingly, when the absolute value of the HE current density values determined from the galvanostatic polarization experiments using the gravimetric method are plotted together with those calculated during the galvanodynamic measurements (Fig. 12), a very good correlation was observed over the whole range of potentials. Given that the HE rate exhibited a constant value from the beginning of the anodic current application (see Fig. 9), this indicates that, in a single galvanodynamic experiment, the current density value associated with HE at any applied current density of interest is easily determined by interpolation in a HE current density vs. applied current density plot. Therefore, the gravimetric method represents a quicker as well as a more reliable and straightforward procedure for the study of anodic H₂ on Mg and its alloys than the volumetric method. This is particularly useful not only when short timescales are needed but, more importantly, when limited amount of material is available to carry out a study over a large range of applied current densities.

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