Choosing the Correct Internal Reference Redox Species for Overcoming Reference Electrode Drift in Voltammetric pH Measurements

Abstract

Reference electrode (RE) drift is a common problem when electrodes are used for pH determination, especially over extended periods of time or in complex media. For voltammetric pH measurements, one method to mitigate against RE drift is to add a second pH insensitive redox species (the internal reference, IREF) and measure the difference in peak potential, E _diff, between the signal associated with the pH sensitive species, E _pH, and IREF, E _IREF. This work strategically explores how to choose the correct IREF species. For these studies, a quinone-functionalized boron doped diamond (BDD-Q) electrode is employed as the pH sensing electrode over the pH range of 4–9. To avoid errors in reporting of the real E _pH and E _IREF values, there must be a minimum separation between the two peaks. Moreover, the distance on the potential axis between a peak and that of the current response pertaining to water electrolysis must also be considered. For the BDD-Q pH electrode, an operable potential window for IREF is established and the IREF redox species, hexachloroiridate (IrCl₆ ^2–/3–), is determined to be most appropriate, showing an ∼0.08 pH error over the pH range of 4–9 and reducing to ∼0.02 pH error over the pH range of 6–8. The use of E _diff is further assessed via the voltammetric measurement of dissolved carbon dioxide (CO₂) in a Stow-Severinghaus arrangement over the partial pressure range of 30.4–152.0 mmHg. The R ² linearity of the calibration line (=0.998) is shown to be equivalent and in agreement with theory when plotting either E _diff or E _pH versus CO₂ partial pressure. This data bodes well for the use of E _diff as a measurement signal in Stow-Severinghaus dissolved CO₂ transcutaneous sensors, where continuous measurement of pH over several days is required.

Introduction

In electroanalysis, attention is often focused on the sensing (working) electrode, but this means the vital role of the reference electrode (RE) can be overlooked. The RE provides a stable, well-defined potential against which the potential at the sensor electrode is controlled and measured. RE drift is a significant challenge in any electrochemical sensor system, where an output voltage is the measurement signal. This includes both the more common potentiometric sensor and the voltammetric sensor, with the latter operating under conditions in which the potential for a characteristic (often peak) current is the measurement signal of interest.

RE drift can arise for many reasons. In systems which use glass fritted REs such as the silver, silver-chloride electrode (Ag|AgCl|Cl^– _(aq)) and the saturated calomel electrode (SCE), mechanical damage to the frit can result in loss of potential determining chloride ions from the filling to the test solution. Extended use, especially in real water samples, can also result in clogging of the frit due to precipitate or biofilm formation. For sensing devices where miniaturization and ease of construction is important, a Ag|AgCl quasi reference electrode (QRE) is typically used. This consists of a Ag wire coated in AgCl, which sits directly in the solution of interest. Whilst the rapid rate of dissolution of the sparingly soluble AgCl controls the concentration of Cl^- in the vicinity of the AgCl (especially in Cl^- free solutions), this reference electrode is more susceptible to local changes in the analyte solution.

One of the most important solution parameters measured electrochemically for both laboratory-based and real-world solutions is the pH. pH sensors typically output a characteristic potentiometric voltage using, e.g., glass pH sensitive electrodes or metal oxides or voltammetrically using, e.g., quinone-based systems that undergo proton coupled electron transfer (PCET). pH can also be used to inform indirectly on dissolved carbon dioxide (CO₂) concentrations via measurement of the pH change in a bicarbonate buffer solution, the Stow-Severinghaus electrode. − Dissolved CO₂ measurements also have a wide range of applications ranging from environmental (fresh, sea, and aquarium water monitoring) to corrosion control, beer brewing, and medical care. Due to RE drift, the frequency of calibration required in such settings often precludes their use for long-term applications such as, e.g., continuous blood-gas monitoring over the period of a week.

For potentiometric pH measurements, as only a voltage is measured, the instrumentation is simpler; however, this means there is far less scope for adapting the actual measurement protocol to build in methods to account for RE drift. In contrast, for voltammetric pH measurements, it has been demonstrated as early as the 1980’s how addition of a pH independent redox species, referred to as the internal reference (IREF), can be used as a possible RE drift mitigation strategy. Addition of an internal standard (or reference redox species) is common for non-aqueous systems, but the reasoning is different and is due to the difficulties of finding a suitable reference electrode in such solvent systems.

For the aqueous system, as the pH changes, the potential associated with the peak current of the pH dependent species moves with respect to that of IREF, which, ideally, remains fixed in position. The difference in potential between the two signals, referred to as E _diff, is used as a metric for determining solution pH. , If RE drift occurs, while the peak currents for both the pH sensitive and pH insensitive species shift, E _diff remains unaffected and an accurate measurement of pH is obtained. This concept is schematically shown in Figure . Square wave voltammograms (SWVs) are typically used in analysis due to the sharper peaks obtained in the current–voltage response compared to those in cyclic voltammograms (at macroelectrodes).

1.

(a) Schematic depicting SWV scans in solutions of decreasing pH (from left to right); E _pH is the peak potential of the pH dependent peak whilst E _IREF corresponds to the peak potential for the pH independent, IREF species. (b) E _diff plotted vs pH to form a calibration line.

In the original work, either a pH sensitive conducting polymer (polyaniline) or quinone containing species (chloranil) was immobilized on Pt wires in the presence of Nafion encapsulated Ru­(bipy)₃ ²⁺ (IREF). For polyaniline, pH values could only be measured up to ∼8 and reproducibility issues were raised. Whilst the chloranil system was found to be more stable, it was necessary to consider the oxidation/reduction state of the Pt and pH values could only be measured up to pH ∼6. Further studies extended this concept to self-assembled monolayers or drop cast “inks”, containing both the pH sensitive and pH insensitive molecules. This work, and others that followed, used ferrocene (Fc) or Fc derivatives as IREF, immobilized on macro- and micro-sized gold electrodes, glassy carbon electrodes, and screen printed graphite electrodes. , However, each of these studies presented its own complications. In the original gold microelectrode work, the Fc IREF potential moved by ∼50 mV (estimated from Figure 4 in ref ) over the pH range of 1–8, which is almost a pH unit given that the Nernstian pH responses shift by 59 mV/pH at 298 K. By decreasing to a pH range of 5–9, the variation in IREF was reduced to 15 mV (estimated from Figure 3 in ref ), and by moving to an even narrower range (pH 7.30–7.50), the IREF variation was reduced further to 7 mV. This work was expanded by using two working electrodes, one as the sensor and the other to correct RE drift (the calibration electrode). However, the peak potential of the calibration sensor varied by 50 mV over the pH range of 2–13 (estimated from Figure 2 in ref ). In other work, the Fc and quinone groups were combined into one molecule and drop cast onto glassy carbon; however, a reduced linearity in the pH–E _diff calibration slope (R ² = 0.969) was found. Finally, in only one other study, have different redox couples been explored. Here, two redox polymers containing an osmium redox couple (IREF) and a pH sensitive phenothiazine moiety were electrochemically deposited on a gold microelectrode; no quantification was made of E _IREF stability.

Given the prior literature, which shows non-negligible variations in the IREF potential with pH, in this paper, we explore the different factors that must be considered when identifying the ideal IREF redox species for voltammetric pH measurements. For these studies, we use boron doped diamond (BDD) electrodes functionalized in defined locations with a very robust form of oxygen-terminated sp² carbon, , given they have shown considerable promise as voltammetric pH sensors. The sp² carbon regions contain surface integrated quinones (Q’s), which undergo 2e^–2H⁺ PCET up to a pH value associated with the first pK_a of the quinone (typically ca. pH = 12). , The electrodes show Nernstian behavior, in both buffered and unbuffered solutions. Whilst we apply the study to quinone-functionalized boron doped diamond (BDD-Q) pH electrodes, operating over the pH range of 4–9, the principles established will apply to any voltammetric pH sensor, over the required pH range of interest. This pH range covers environmental and medical fluids including seawater, fresh water, and blood. The IREF E _diff method is further demonstrated by using, for the first time, the BDD-Q pH electrode as a Stow-Severinghaus dissolved CO₂ sensor. The use of the IREF methodology for measuring pH and dissolved CO₂ is compared against the conventional reference electrode approach to determine its viability for use with pH/dissolved CO₂ BDD-Q sensors.

Experimental Section

Solutions and Chemicals

All solutions were prepared using ultra-pure Milli-Q water (Millipore Corp.) with a resistivity of 18.2 MΩ cm at 25 °C. Oxidative acid cleaning of the BDD used potassium nitrate (KNO₃, 99%, Fisher Scientific) and concentrated sulfuric acid (H₂SO₄, 98%; Sigma-Aldrich). Reagecon buffers (Reagecon Diagnostics Ltd., Calibre Scientific) of pH 4.00, 6.00, 7.00, 8.00, and 9.00 (±0.01) were used to perform the BDD-Q pH tests. Carmody buffers were made in the pH range of 4–9 for electrode calibrations and were prepared using boric acid (H₃BO₃, 99.97%; Sigma-Aldrich), citric acid (C₆H₈O₇, ≥99.5%; Sigma-Aldrich), and tertiary sodium phosphate (Na₃PO₄, ≥95%; Sigma-Aldrich). For dissolved CO₂ measurements, 20 mM potassium bicarbonate (KHCO₃, ≥99.95%, Fisher Scientific; Sigma-Aldrich) was used. The IREF redox species investigated were ferrocenylmethyltrimethylammonium, FcTMA⁺, hexafluorophosphate (made in house), potassium hexachloroiridate­(IV), IrCl₆ ^2– (99.99%, Merck; Sigma-Aldrich), and tris­(1-10-phenanthroline) iron­(II), Fe­(phen)₃ ²⁺, sulfate (0.25 M, Fisher Scientific). Potassium chloride (KCl, ≥99%, Fisher Scientific) with concentrations up to 0.2 M and KNO₃ with concentrations up to 0.09 M were used as supporting electrolyte for electrochemical measurements. Solution pH was measured using a glass pH probe (InLab Expert Pro ISM, SevenEasy, Mettler Toledo). The probe was calibrated using a four-point calibration, employing NIST standard pH solutions (pH 2.00 ± 0.01, pH 4.01 ± 0.01, pH 7.00 ± 0.01, and pH 10.00 ± 0.01; Sigma-Aldrich), as per manufacturer guidelines.

Electrode Manufacture

The BDD was cut from a 357 μm thick, free-standing wafer of polycrystalline, electroanalytical grade BDD (electrode E in ref ), Element Six Ltd, Oxford. The growth face was polished to <5 nm RMS surface roughness and used as the electrode surface. 1 mm diameter BDD cylinders were cut from the wafer using a 355 nm Nd:YAG 34 ns laser micromachining system (E-355H-ATHI-O system, Oxford Lasers). Oxidative acid cleaning, using boiling concentrated H₂SO₄ saturated with KNO₃, was used to remove any loosely bound sp² carbon introduced after the micromachining process. The cylinders were annealed electrode face-down in air at 600 °C for 5 h to significantly reduce sp² carbon on the cylinder walls, arising from the laser cutting processing. Spatially controlled regions of sp² carbon were laser micromachined into the electrode face of the cylinder, as described in detail in ref , before undergoing a second oxidative acid clean. 10 nm of titanium and 400 nm of gold were sputtered (Moorfields MiniLab 060 platform sputter/evaporator) onto the back (nucleation side) of the cylinders, which were annealed at 400 °C for 5 h in air, again electrode-face down, to ensure an ohmic contact. Finally, the cylinders were sealed in heat-pulled glass capillaries (o.d. 2 mm; i.d. 1.16 mm; Harvard Apparatus Ltd., Kent, UK) and polished to reveal the glass-sealed electrode as described in ref .

Electrochemical Setup

All electrochemical measurements were conducted by using a CH1040a potentiostat (CH Instruments Inc., USA). All experiments were conducted at a temperature of 21 ± 2 °C. A BDD-Q electrode was used as the working electrode, either an SCE or silver chloride coated Ag foil (Ag|AgCl) as the RE, and a coil of platinum wire (diameter = 1 mm, ∼10 mm length immersed in solution) as the counter electrode. The Ag|AgCl RE was prepared by anodization of an annealed Ag foil (0.5 mm thick, Premion, Thermo Fisher Scientific, 99.9985%) cut to ca. 5 mm in width and 30 mm in length. Ag was held at +0.54 V vs SCE with a Pt mesh counter electrode (to provide a large surface area compared to the silver) in a saturated KCl solution for ca. 10 min or until the foil visibly changed color from silver to brown. Solutions containing the IREF redox species were made using concentrations of 100 μM, in up to 0.2 M KCl supporting electrolyte.

For SWV measurements, scans were carried out in the cathodic direction with an amplitude of 0.1 V, a step increment of 0.001 V, a frequency of 100 Hz, and a quiet time of 2 s. These settings had been previously determined as being suitable for pH measurements using the BDD-Q electrode. For all BDD-Q voltammetric measurements, six SWVs were recorded consecutively. The first scan was discarded, and the current of the remaining five was averaged to provide a mean current across the potential range. The mean SWV was smoothed using a Savitzky–Golay (adjacent-averaging) filter with a polynomial order of three over 21 data points to provide sufficient smoothing without compromising the data. As a SWV scan with a 1 V potential range and a frequency of 100 Hz has 1000 data points, the smoothing window equates to ∼2% of the data points. Voltages corresponding to the peak SWV current were determined from the mean SWV. MATLAB R2021b was used to average SWV scans and to find the peak potentials. The MATLAB code used can be found in Supporting Information (SI)-1. For electrode voltage vs pH calibrations, Reagecon buffer standards, Carmody buffers, or bicarbonate solutions (depending on the final system being measured) with pH values in the range of 4–9 were used. Linear regression analysis of a plot of SWV peak potentials vs solution pH (with pH values measured using a calibrated Metler Toledo glass pH probe) was made using Origin 2021b (OriginLab).

Mass Flow Controller Setup to Control Dissolved CO₂ Concentration

Mass flow controllers, MKS Instruments, 100 standard cubic cm per minute (sccm), were used to control the partial pressure, pCO₂, flowing into the 20 mM bicarbonate solution. CO₂ and Ar were bubbled through the solution to produce pCO₂ values in the range of 30.4–152.0 mmHg. Parafilm (Amcor) was used to seal the electrochemical cell and limit evaporation of solution. pCO₂ values in the range of 35–48 mmHg are typical for blood. , pCO₂ values were calculated using eq :

$${\mathrm{pCO}}_2=760\mathrm{mmHg}\%{\mathrm{CO}}_2$$ 1

where 760 mmHg is atmospheric pressure and %CO₂ is the sccm of CO₂ compared to the total sccm gas flow through the cell (Ar and CO₂).

Results and Discussion

Figure a displays the SWV response of the BDD-Q pH sensor, shown in the inset of Figure b, in buffer solutions of pH 4, 7, and 9. The SWV peak observed is due to the 2e^–2H⁺ PCET reaction occurring at the Q sites integrated into the sp² carbon surface in the BDD electrode. Figure b shows the shift in the PCET peak potential, E _pH, with solution pH. A slope of −56 mV/pH unit is observed, very close to theory (−58 mV/pH for a temperature of 21 °C) with an R ² value of 0.9993.

2.

(a) SWV scans (100 Hz frequency, 0.001 V increment, 0.1 V amplitude, 2 s quiet time) for 2e^–2H⁺ PCET at a BDD-Q electrode (scanning from 0.5 to −0.3 V vs SCE) in buffer solutions of pH 4 (yellow), 7 (green), and 9 (blue). (b) Resulting calibration curve of E _pH versus solution pH (measured by using a glass pH probe). The inset shows an optical image of the BDD-Q electrode; the dark circular regions represent the laser machined sp² carbon regions.

There are five key requirements for an IREF redox species for any voltammetric SWV (or CV) pH measurement. (1) The IREF SWV response shows no dependence on pH over the pH range of interest. (2) IREF is chemically stable in the solution of interest for the time period required. (3) The SWV peak is sufficiently separated from the PCET pH peak, such that the two can be easily resolved, with (4) no peak interactions, due to the proximity of the two peaks, which result in an apparent shift of either peak from their true peak positions. (5) The redox species undergoes fast electron transfer, which results in narrower SWV peaks, with no follow up reactions. Additional requirements reflect the chemistry of the BDD voltammetric pH sensor. Specifically, there are no interactions (e.g., chemical or redox) between the redox species and surface integrated quinones of the BDD electrode, which detrimentally impact the IREF peak position.

Three fast electron transfer redox species, FcTMA⁺, Fe­(phen)₃ ²⁺, and IrCl₆ ^2–, were chosen for the investigation, ,, with formal electrode potentials of 0.392, 0.861, and 0.695 V vs SCE, respectively (Figure S1, SI-2), which lie outside the E _pH range, −0.05 V to +0.23 V vs SCE (Figure a). SWVs for the reduction of 100 μM (a) FcTMA⁺, (b) Fe­(phen)₃ ²⁺, and (c) IrCl₆ ^2– at a 1 mm diameter BDD-Q pH electrode in buffered solutions of pH 4, 7, and 9 are shown in Figure a–c.For SWV, given the potential is continuously switched between forward and backward pulses, we can choose to start scanning from either the positive or negative potential direction. The decision to scan in the negative potential direction was made to allow scope for scanning further in the negative direction, if required for future experiments, for example, to simultaneously voltammetrically measure dissolved oxygen, as well as pH/dissolved CO₂.

3.

SWV scans (parameters as in Figure ) on a BDD-Q electrode in buffer solutions of pH 4 (yellow), 7 (green), and 9 (blue) in the presence of 100 μM (a) FcTMA⁺ (scanning from 0.7 to 0.1 V vs SCE), (b) Fe­(phen)₃ ²⁺ (1.15–0.6 V vs SCE), and (c) IrCl₆ ^2– (0.85–0.35 V vs SCE).

All three IREF redox species showed good peak potential stability over a range of 5 pH units (pH 4–9); FcTMA⁺, Fe­(phen)₃ ²⁺, and IrCl₆ ^2– varied in E _IREF (peak potential of the internal reference species) by only 3, 9, and 5 mV, respectively, over the three measurements (when considering the maximum difference in E _IREF between the three SWVs). This corresponds to a maximum error of 0.05, 0.15, and 0.08 pH units (assuming a theoretical −59 mV/pH calibration at 298 K). The peak shape of the SWV is controlled by the SWV parameters employed (see Experimental Section). E _IREF values versus pH for the three IREF redox species are displayed in Table S2, SI-3.

For FcTMA⁺, despite displaying the smallest E _IREF shift, at a concentration of 100 μM, when scanning from a more positive start potential to reveal the pH peak, the separation between E _pH and E _IREF is not sufficient to resolve the pH peak for pH values ≤ 7, as shown in Figure S2a, SI-4. Whilst decreasing the FcTMA⁺ concentration (to 40 μM, Figure S2b) results in the pH peak at pH 7 being resolved, the pH 4 peak is still obscured by that associated with IREF, eliminating FcTMA⁺ as an IREF candidate over this pH range. Moreover, even if both peaks are prominent, depending on their separation and relative peak heights with respect to each other, the experimentally measured E _pH and E _IREF values may no longer be reflective of the actual E _pH and E _IREF values.

This concept is illustrated in Figure S3, SI-5, where for mathematical modeling simplicity the two peaks are treated as Gaussian in shape, with a peak width at half height of 200 mV (the latter reflecting the data in Figure a, where the peak width at half height is 200 mV for FcTMA⁺). The peaks going from left to right represent the pH and IREF peaks, respectively, as in real experimental data. The IREF peak is defined with an E _IREF of 0.4 V. The data is plotted for peak current (amplitude) ratios of pH:IREF of 1.0, 0.5, and 0.25 (the latter reflective of experimental data) and peak-to-peak separations of 0.2, 0.25, 0.3, and 0.34 V. A 0.34 V separation between the two peaks is shown to be the minimum separation required for the two peaks to be considered non-interacting, irrespective of peak current ratio. As the peak separation is decreased, the apparent peaks shift toward each other with respect to their actual positions. This results in an error in the measured values for E _IREF, E _pH, and E _diff and is exacerbated for the smaller peak, especially when the ratio of peak current pH:IREF is decreased. When Gaussian shaped peaks and a minimum peak separation of 0.34 V between E _IREF and the most positive E _pH value (at pH 4) is assumed, there is a requirement for IREF to have an E _IREF > 0.57 V vs SCE. Note, whilst our focus here is on apparent shifts in peak position on the voltage axis, peak separations should also be taken into account when analyzing closely spaced peak currents in multiple analyte measurements. The impact of peak seaparation on reporting the true peak current is shown in Table S3, SI-5.

The position of the IREF peak with respect to the commencement of water oxidation was also considered. When the solution pH increases, the potential at which oxidation of water begins becomes less positive. Figure b shows the impact of water oxidation on the SWV for Fe­(phen)₃ ²⁺, which has the most positive E _IREF of the three species. As the pH is increased from 4 to 7 and 9, the SWV response for water oxidation becomes more noticeable. At pH 10, there is no peak evident in the SWV for Fe­(phen)₃ ²⁺ due to its proximity to water oxidation (Figure S4, SI-6). Whilst the IREF peak is still visible at pH 9, the close spacing of the two responses has resulted in a small positive apparent shift of E _IREF. Therefore, despite no convolution with the pH peak (data not shown), this couple is unusable at the higher pH values. Furthermore, given that water oxidation results in a local decrease in pH, in unbuffered solutions, due to proton generation, it is always advisable to minimize current flow arising from water oxidation during a voltammetric measurement of solution pH. Taking into account the proximity of the IREF SWV to the SWV response for water oxidation and the pH peak(s), for pH 4–9, for a BDD-Q electrode, this sets E _IREF to within 0.57–0.70 V vs SCE.

Figure c shows the SWV response for 100 μM IrCl₆ ^2– over the pH range of 4–9; E _IREF is 0.670 V vs SCE, which sits at sufficient distances from both the pH and water oxidation SWVs such that the peaks can be treated as non-interacting. The response for water oxidation becomes increasingly visible as the pH increases. As highlighted above, the pH error is ∼0.08 pH due to the maximum 5 mV E _IREF variation. This is further reduced to 1 mV (∼0.02 pH error) for a pH of 6–8 (Table S2, SI-3). This latter range is appropriate for dissolved CO₂ measurements in blood. This redox species was, therefore, used for all further measurements. Whilst these variations are smaller than all reports in the literature to-date, additional reasons for variations in E _IREF are currently the subject of further investigation.

To test the suitability of IrCl₆ ^2– as an internal reference and the use of E _diff as a measurement signal, initial experiments used a standard reference electrode (SCE) and a silver chloride coated Ag foil (Ag|AgCl) RE in three different buffer solutions of pH 4, 6, and 8. The Cl^‑ concentration was kept fixed for the Ag|AgCl RE experiments at 0.1 M, resulting in an E _Ag|AgCl of +0.049 V vs SCE (at 21 °C). A BDD-Q electrode was used to measure the solution pH via SWV referenced against (i) a SCE (black squares); (ii) a SCE in the presence of 100 μM IrCl₆ ^2– (red circles), and (iii) a Ag|AgCl|Cl^– (0.1 M) RE in the presence of 100 μM IrCl₆ ^2– (blue triangles), Figure . The SWVs recorded in the presence of IrCl₆ ^2– show both pH and IREF peaks, allowing E _diff to be calculated. Figure has two y axes, E _pH (no IrCl₆ ^2–) and E _diff (IrCl₆ ^2– present). As can be seen from the linear regression values, while the intercepts may be different, a negligible difference in linearity and slope gradient is observed whether using E _diff or E _pH (R ² values >0.999). Both of the calibration lines, which use E _diff, fall within the 95% confidence interval (CI) of the BDD-Q SWV SCE calibration line.

4.

Buffered pH calibration for the BDD-Q electrode (SWV parameters as in Figure ). On the left, E _pH is plotted with (i) SCE as the reference electrode (black squares) with a 95% CI (grey band). On the right, E _diff is plotted with (ii) IrCl₆ ^2– as the IREF vs SCE (red circle) and (iii) IrCl₆ ^2– as the IREF vs a Ag|AgCl|Cl^– (0.1 M) RE (blue triangle).

In order to assess the ability of the IrCl₆ ^2– IREF system to account for RE drift, AgCl coated Ag foil was again employed as the RE and the concentration of Cl^– deliberately varied from 0.01 to 0.1 M to cause a quantifiable shift in the RE potential. For these experiments, the total salt concentration was kept at 0.1 M via additions of KNO₃ (SI-7), removing any potential influence from ohmic drop. In practical applications, RE drift is very unlikely to be associated with a significant decrease in solution conductivity. Figure a,b shows SWV scans for a BDD-Q electrode in three pH 5 Carmody buffer solutions containing 0.01, 0.03, and 0.1 M KCl, with all solutions containing 100 μM IrCl₆ ^2–. In (a), a commercial SCE is used as the RE, while in (b), a Ag|AgCl foil RE is employed. As shown in Figure c, when measuring E _IREF vs SCE (black squares) for IrCl₆ ^2– in the three different chloride concentration solutions, there is very little change in potential (3 mV). In contrast, E _IREF shifts by 53 mV when measured using the Ag|AgCl foil RE (black circles), due to the potential determining Cl^– ion concentration changes. In accordance with the Nernst equation, a change in Cl^– concentration from 0.01 to 0.1 M is theoretically expected to result in a potential change at the Ag|AgCl RE of 58 mV (at 21 °C), close to that observed here. E _diff values for the three different Cl^– solutions (purple triangles) were found to be almost identical as expected in a pH buffered solution: −496 mV (0.01 M), −495 mV (0.03 M), and −494 mV (0.1 M), highlighting the ability of the E _diff measurement to accommodate a shift in RE potential. The E _diff values can be converted to pH via the calibration line shown in Figure S5, SI-8, giving pH values of 4.97 (0.01 M), 4.96 (0.03 M), and 4.94 (0.1 M).

5.

SWV (parameters as in Figure , scanning from 1.0 to −0.4 V) of pH and IREF (IrCl₆ ^2–) in KCl concentrations varying from 0.01–0.1 M, using (a) a SCE, and (b) a Ag|AgCl foil RE. (c) Plot of (left) E _IREF for a SCE RE (black squares) and Ag|AgCl foil RE (black circles); (right) E _diff versus log₁₀ Cl^– concentration (purple triangles) for the data from (b).

Further proof-of-concept experiments were carried out using the BDD-Q electrode in a Stow-Severinghaus dissolved CO₂ sensor arrangement, − to verify whether E _diff could be used instead of E _pH as the SWV measurement signal. For these measurements, 100 μM IrCl₆ ^2– was added to a solution containing 20 mM KHCO₃ and 0.2 M KCl. Different partial pressures of CO₂ (pCO₂) in the range of 30.4–152.0 mmHg (corresponding to 4–20% CO₂ of the total gas flow) were achieved by changing the composition of CO₂:Ar flowing into the solution (SI-9). As the % of CO₂ in the gas bubbled through the solution increases a buffer system is established (albeit weak given the concentrations of dissolved CO₂ and HCO₃ ^– involved). The dissolved CO₂–pH relationship can be described using a modified form of the Henderson-Hasselbalch equation (eq ), where, 0.034 is the Henry’s Law constant for dissolved CO₂, in mmol L^–1 mmHg^–1 and

$$\mathrm{pH}={\mathrm{pK}}_{\mathrm{a}}+\log \left(\frac{[{{\mathrm{HCO}}_3}^{-}]}{0.034\times {\mathrm{pCO}}_2}\right)$$ 2

pK_a is the acid dissociation constant, equal to 6.3. Equation can be simplified to a log–linear relationship when a known HCO₃ ^– concentration is added to the electrolyte solution. In this case, 20 mM KHCO₃ is used, giving eq , which predicts that an increase in pCO₂ is associated with a decrease in pH.

$$\mathrm{pH}=-\log ({\mathrm{pCO}}_2)+9.06$$ 3

Figure a shows BDD-Q SWVs recorded in a solution containing 20 mM HCO₃ ^–, 200 mM KCl, and 100 μM IrCl₆ ^2– (IREF) for different pCO₂ values in the range of 30.4 to 152 mmHg. As the pCO₂ levels increase, the pH peak can be seen to shift to the right (by 40 mV) as expected for a solution that is decreasing in pH. Also shown is the SWV peak associated with 100 μM IrCl₆ ^2–. E _IREF changes by no more than 4 mV (a change of 0.07 pH units or log­(pCO₂) units) over the course of the experiment.

6.

(a) SWV data (parameters as in Figure , scanning from 0.9 to −0.2 V vs SCE) showing the BDD-Q SWV pH peak and the IREF IrCl₆ ^2– peak in one voltammetric scan. The arrow indicates the movement of the pH peak as pCO₂ increases. (b) BDD-Q pH vs change in pCO₂ calculated using calibration lines for E _pH (black squares) and E _diff (purple circles), the latter using 100 μM IrCl₆ ^2– as the IREF. (c) Calibration plot of E _pH (left y-axis, black squares) and E _diff (right y-axis, purple circles) versus log­(pCO₂). For (b) and (c), n = 3 where measurements were made using the same BDD-Q electrode in fresh solutions.

In Figure b, the resulting BDD-Q pH values, calculated from calibration plots using E _pH, i.e., without IrCl₆ ^2– (black squares) and E _diff, i.e., with (purple circles) IrCl₆ ^2– IREF, are plotted vs log­(pCO₂); the pH varies from 6.7 to 7.4. The corresponding E _pH and E _diff calibration plots are shown in SI-10 and are recorded in the same bicarbonate electrolyte system used for Figure . Calibration line 1 plots BDD-Q E _pH versus the glass probe pH, resulting in a calibration slope of −56 mV/pH unit (R ² = 0.9995), Figure S6a, SI-10. Calibration line 2 (which uses IREF) plots E _diff versus the glass probe pH, resulting in a calibration slope of −61 mV/pH unit (R ² = 0.9985), Figure S6b, SI-10. The gradients of the two plots in Figure b are very close to −1 pH unit per mmHg pCO₂, with a y-intercept just below the expected 9.06 pH units (R ² > 0.999 for both sets of data, n = 3). Hence, the BDD-Q CO₂ sensor follows the predicted response (eq ) for both scenarios where either a standard reference (E _pH) or IREF (E _diff) is utilized. Figure c shows plots of E _pH (black squares) and E _diff (purple circles) against log­(pCO₂), which is a simpler form of calibration, as it does not require conversion of either potential to a pH value first. For both, a linear line is expected with a Nernstian slope of 59 mV/log­(pCO₂) unit (at 298 K), derived as shown in SI-11. Slopes very close to these values of 58 mV/log­(pCO₂) (E _pH) and 63 mV/log­(pCO₂) (E _diff) are obtained, with R ² > 0.99 and n = 3. Figure b,c highlights the validity of the IREF (E _diff) approach for measuring the dissolved CO₂.

Conclusion

For suitability as an internal reference redox species for voltammetric pH determination, IREF must display a SWV response sufficiently removed from the pH and water electrolysis responses such that they can be considered non-interacting. If present, apparent shifts in IREF/pH peak position are seen, resulting in errors in measurement of E _pH, E _IREF, and E _diff. Whilst this concept applies universally, for the BDD-Q pH electrode, E _IREF was estimated as needing to fall within the range of 0.57–0.70 V vs SCE for pH 4–9. IrCl₆ ^2– was found to be the most promising IREF for this pH measurement system, showing a maximum variation in SWV peak potential of only 5 mV over a five orders of magnitude change in proton concentration, equivalent to a pH error of ∼0.08. Reducing the pH range to that of importance in medical applications, pH = 6–8, resulted in a pH error of ∼0.02. Current applications would be determined by the level of pH accuracy required. The study was extended to show, for the first time, the versatility of the E _diff method in measuring dissolved CO₂ concentrations via the pH response of a weakly buffered bicarbonate solution.

Currently, IREF is added to the solution and is thus appropriate for sampled solutions analyzed in a laboratory or for sensors where the electrolyte solution is separated from the analytical solution by a solution-impermeable membrane. For making membraneless measurements at the source, e.g., directly in an environmental sample, integration of IREF into the surface of the electrode, via surface grating or drop casting of a film, is required. Furthermore, while the variation in IREF peak potential as a function of pH is at best 1 mV over pH 6–8 (at worst 5 mV, over pH 4–9), there is still scope for further improvements. Although IrCl₆ ^2– has shown promise, it is more expensive compared to the Fe-based redox couples. Thus, there is the option for producing cheaper metal centered redox species where the functional groups attached to the metal center have been tuned to result in redox potentials that fall within the window of interest, here 0.57–0.70 V vs SCE.

There is also a need to explore the impact of elevated temperatures or significant use time scales. Both are of importance for dissolved CO₂ Stow-Severinghaus transcutaneous sensors where the electrolyte is heated to 43 °C during extended use on a patient. These measurements typically run continuously for up to 1 week at a time. Continuous long-term monitoring is where we see the IREF methodology offering most advantages, due to the greater possibility of RE drift, and is where future work is directed.

The concepts discussed here with respect to ensuring there are no peak interactions can be extended to other voltammetric pH sensors used in conjunction with IREF and alternative sensing methods. For the latter, this includes, for example, where the peak current is related to analyte concentration for multiple analyte detection using the same sensor. Finally, it is also possible to consider data processing, post-collection, to deconvolute closely spaced and overlapping peaks. This would extend the workable potential range for the IREF and enable a wider pH range to be accessed.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acselectrochem.5c00138.

• 1: MATLAB Code; 2: Cyclic Voltammetry of Reversible Redox Species on BDD-Q Electrodes; 3: pH Stability of Redox Species; 4: SWV FcTMA⁺ Overlap with BDD-Q pH peak; 5: Mathematically Determining Required Peak Separation; 6: 100 μM Fe­(phen)₃ ²⁺ in pH buffers 4, 7, 9 and 10; 7: Conductivity of Solutions Used for Drifting Reference Experiments; 8: E _diff vs pH Calibration for Changing [Cl^–] Experiment; 9: Carbon Dioxide and Argon Compositions for CO₂ Experiment; 10: CO₂ Calibration Curves; 11: Potential vs log­(pCO₂) Theory (PDF)

The authors declare no competing financial interest.