Cyclic Voltammetry Part 2: Surface Adsorption, Electric Double Layer, and Diffusion Layer

Abstract

This paper “Part 2: Surface Adsorption, Electric Double Layer, and Diffusion Layer” is the applicational part and is a continuation of “Part 1: Fundamentals” (https://doi.org/10.5796/electrochemistry.22-66082). This part explains the principles of cyclic voltammetry on adsorption, electric double layer, and diffusion layer with microelectrodes. Moreover, recent trends, such as polymer electrolyte fuel cells (PEFCs), electric double layer capacitors (EDLCs), and sensors, are highlighted. The relationship between the electrochemical surface area (ECSA) and electric quantity estimated on the basis of cyclic voltammograms is explained in the chapter on adsorption, where the adsorption of hydrogen and carbon monoxide on Pt is discussed. The following chapter introduces the pseudo-capacitance of activated carbon, which exhibits characteristic capacitor-like behavior, with Faradaic current flow on the surface. Finally, an explanation concerning the effect of diffusion-limiting currents on two types of microelectrodes and a practical case of enzyme sensing using a microelectrode is included.

1. Introduction

With the advancement towards the goal of a sustainable, carbon neutral society using renewable technology demand for electrochemical measurements has significantly increased, along with the corresponding increase in the demand for tutorials on electrochemical measurements. Although several textbooks are available,^1–9 there are only a few accessible tutorials for electrochemical measurements. Cyclic voltammetry provides useful information concerning, reversibility derived from electron and mass transfer processes, Faradaic and non-Faradaic electrode processes, surfaces and interfaces phenomena of surface adsorption, and formation of electric double layers and diffusion layers. This paper explains the principles of cyclic voltammograms (CVs) on adsorption, electric double layer, and diffusion layer with microelectrodes and discusses recent application trends, such as polymer electrolyte fuel cells (PEFCs), electric double layer capacitors (EDLCs), and sensors.

Chapter 2 explains the practical methods for the calculation of the electrochemical surface area (ECSA) of Pt based on the characteristic adsorption/desorption peaks of hydrogen underpotential deposition (UPD) and CO stripping peaks. The behavior of oxygenated species (such as –OH_ad and –O_ad) on Pt, which strongly affects the catalytic activity toward the oxygen reduction reaction (ORR), must be analyzed for understanding the cathodic reaction in PEFCs and the corresponding experimental methods.

Many studies have shown that CVs are primarily obtained using the Faradaic process, involving the current generated by the reduction or oxidation of certain chemical substances at an electrode. Chapter 3 focuses on non-Faradaic processes and explains the associated principles. Moreover, the pseudo-capacitance of activated carbon, which has the characteristic behavior of a capacitor, that is, Faradaic current flows on the surface, is explained.

When the electrode size approaches the thickness of the diffusion layer, the steady-state diffusion-limiting current can be rapidly obtained using non-linear diffusion. Chapter 4 explains the principles of the microdisk and microband electrodes. The CV shapes were changed by varying the scan rate. The sigmoid curve for the microelectrodes is obtained when the electrode potential sweep is scanned slowly enough to match the diffusion layer growth rate, while the curve more closely resembles a duck shape at higher scan rates, which is easily understandable visually and intuitively. Finally, a practice case concerning enzyme sensing using microelectrode is introduced, which allows the monitoring of the consumption of reactive substrates.

2. Surface Adsorption for Polymer Electrolyte Fuel Cells

The mixed-controlled CV mainly described in “Part 1 Fundamentals”¹⁰ is a system in which either the electrode reaction or mass transfer from the bulk is the rate-determining system. In addition to the voltammogram of the adsorption system described in Part 1, it is important to understand the voltammogram in the electrocatalyst field, particularly for PEFCs, where a redox-active substance exists on the surface of the electrode as an adsorbate. In this chapter, the behavior of voltammograms of substances adsorbed on metal electrodes, which are frequently employed in applications such as PEFCs, is explained.

2.1 Basic interpretation of voltammograms on adsorption system

The basic principle and tutorial of cyclic voltammetry on adsorption system in the reversible process are interpreted in Part 1,¹⁰ where it is mentioned that the current of a voltammogram shows the redox of adsorbed species on the electrode. As in Part 1, the one-electron reaction of the redox species is defined as follows:   

\begin{equation} \text{O} + \text{e$^{-}$} \rightleftharpoons \text{R}, \end{equation} (1)

where O, R, and e⁻ denote the oxidant, reductant, and electron, respectively. If the concentrations of the adsorbates (oxidants and reductants) existing on the surface are defined as Γ_O and Γ_R (typical unit: mol cm⁻²), respectively, the relationship between the surface concentration and the electrode potential based on the Nernst equation is expressed as follows:   

\begin{equation} \frac{\varGamma_{\text{O}}}{\varGamma_{\text{R}}} = \exp\left[\frac{F}{RT}(E - E^{\circ\prime}{}_{\text{ad}})\right], \end{equation} (2)

where E°′_ad is a formal potential that considers the interaction between the adsorbed species and the electrode. If the interaction between the oxidant and the electrode is close to that between the reductant and the electrode, E°′_ad can be equivalent to E°′. Taking the anodic current where the oxidant increases as positive, current (I) is expressed as follows:   

\begin{equation} I = FA\frac{\partial \varGamma_{\text{O}}}{\partial t} = FAv\frac{\partial \varGamma_{\text{O}}}{\partial E}, \end{equation} (3)

where F, A, E, t, and v denote the Faraday constant, the area of the electrode, potential, time, and scan rate (= ∂E/∂t), respectively. Equation 3 leads the important fact that the total amount of electricity is related to the amount of redox-active adsorbate species on the surface.

Integrating the oxidation current (I) with respect to E from a sufficiently negative potential (E_neg) to a sufficiently positive potential (E_pos) yields the total amount of the reductants (Γ_R,total) as shown in Eq. 4.   

\begin{equation} \varGamma_{\text{R,total}} = \varGamma_{\text{O}}(E_{\text{pos}}) - \varGamma_{\text{O}}(E_{\text{neg}}) = \frac{1}{FAv}\int_{E_{\text{neg}}}^{E_{\text{pos}}}I\text{d}E. \end{equation} (4)

If I is replaced by −I, it meets the case of the reduction of the oxidants.   

\begin{equation} -I = FA\frac{\partial \varGamma_{\text{R}}}{\partial t} = FAv\left(-\frac{\partial \varGamma_{\text{R}}}{\partial E}\right). \end{equation} (5)

The scan rate is equivalent to −∂E/∂t due to the negative scan in Eq. 5.

The integration direction is reversed from E_pos to E_neg, Eq. 5 yields the total amount of the adsorbed oxidants (Γ_O,total) as shown in Eq. 6.   

\begin{equation} \varGamma_{\text{O,total}} = \varGamma_{\text{R}}(E_{\text{neg}}) - \varGamma_{\text{R}}(E_{\text{pos}}) = \frac{1}{FAv}\int_{E_{\text{pos}}}^{E_{\text{neg}}} - I(-\text{d}E). \end{equation} (6)

If the total amount of adsorbates to be focused on is defined as Γ_total, the integration of the oxidation current from E_neg to E_pos or that of the reduction current from E_pos to E_neg can be bundled as Eq. 7.   

\begin{equation} \varGamma_{\text{total}} = \frac{1}{FAv}\int_{E_{\text{neg}}}^{E_{\text{pos}}}|I|\text{d}E. \end{equation} (7)

It should be noted that the integral divided by v has the dimension of coulomb in Eq. 7, which can be determined from data of CVs.

The method of determining the amount of adsorbed redox species from the amount of electricity is one of the most powerful electrochemical tools and is widely used in areas such as fuel cells, batteries, and sensors probably because of its ease of application in various cases, including multi-electron systems. Although the characteristic bell-shaped voltammogram can be obtained for the reversible adsorption system, as shown in Fig. 1, it should be noted that there are many cases where the reversible voltammograms cannot be obtained owing to the existence of interactions between adsorbed species and electrodes, resulting in distorted voltammograms with peak separations. However, reversibility is not necessarily indispensable to evaluate the amount of adsorbed redox species, as long as the total current in the voltammogram of the electrochemical reaction of interest can be integrated.

Figure 1.

Cyclic voltammogram of an adsorption system. Constants were substituted as follows: n = 1, AΓ_t = 1.0 × 10⁻⁹ mol, and v = 0.010 V s⁻¹, respectively. I_p is indicated in the graph. See Part 1 for theoretical details. (Γ_O = VC_O(t)/A, where V is equivalent to the volume of the adsorption layer.)

To evaluate Γ_total properly, I should be the faradaic current after the background current is carefully subtracted from the original data (see the previous part),¹⁰ especially when porous electrodes are used. In the next section, we describe examples for determining the electrochemical surface area of the porous Pt/C catalysts for PEFCs using the method mentioned in this section, that is, underpotential deposition (UPD) of hydrogen and CO stripping voltammetry on the Pt-based electrode.

2.2 Practical cases of adsorption system for PEFCs

Cyclic voltammetry of adsorption systems is widely used in the studies of PEFCs as a powerful tool for diagnosing the electronic state and the electrochemical surface area of the metal surface. This section describes UPD of hydrogen and CO stripping voltammetry on the Pt-based electrode.

UPD is a phenomenon in which cations, such as metal ions (Mⁿ⁺) and protons (H⁺), are reduced on a specific metal electrode at a more positive potential than E°′(Mⁿ⁺/M) and E°′(H⁺/H₂). Since UPD occurs on the metal surface of the electrode, it is hard to form multilayers at the UPD potential, which results in the formation of a monolayer with good reproducibility. It is known that hydrogen causes UPD on Pt. Therefore, UPD of hydrogen on Pt is intensively used to investigate the electrochemical surface area (ECSA) of Pt in the PEFC studies, where Pt-based catalysts are practically used in both cathode and anode. Figure 2 shows the CV of the Pt/C catalyst in an acidic electrolyte in an inert atmosphere. A characteristic peak of the UPD of hydrogen (H_UPD) was observed at a lower potential than 0.4 V vs. reversible hydrogen electrode (RHE). The peaks observed at the higher potentials are derived from the oxide formation on the Pt surface (not discussed in the paper in detail). The shaded area between the voltammogram and the horizontal line, which represents the electric double layer capacitance current of the electrode, can be considered as the charge amount of the desorption of the adsorbed hydrogen (H_desorp). In the single crystal electrodes, the UPD of hydrogen on the Pt surface shows a characteristic voltammogram depending on the index planes of Pt, and the charge amount of the UPD of hydrogen per unit surface area of Pt is estimated.^11,12 In the polycrystal electrodes, the value (210 µC cm⁻²) is widely adopted.¹³ By dividing both the charge amount of electricity and the weight of Pt, ECSA (m² g⁻¹_Pt) can be obtained (Fig. 2).

Figure 2.

Cyclic voltammogram of Pt/C-catalyst-modified glassy carbon electrode in 0.10 mol dm⁻³ HClO₄ at 25 °C in argon saturated condition. Scan rate was 0.010 V s⁻¹. The shaded area shows the total charge amount of the desorption of adsorbed hydrogen. ECSA was obtained as 81 m² g_Pt⁻¹ as a result of dividing the shaded area by 210 µC cm⁻².

The UPD method described above has good reproducibility and does not require any special equipment, reagents, or gas. Therefore, it is often used in both half-cell and membrane electrode assembly (MEA) as a powerful method to determine ECSA of Pt. However, it does not always give a reasonable value in alloy catalysts such as PtCo and PtNi, or core-shell catalysts, which have higher activity for the ORR than single Pt catalysts. Particularly, in the case of Pd, it is difficult to separate the peaks of UPD from the peaks caused by hydrogen storing. CO stripping voltammetry, which utilizes the strong adsorption of CO on Pt, is an applicable method for evaluating the ECSA of alloys/core-shell catalysts. An on-top CO_ad monolayer can be formed on the surface by passing CO through the electrolyte while maintaining an adequately low potential (∼0.3 V) in an inert atmosphere. A voltammogram can then be obtained derived from the oxidative desorption of CO_ad by sweeping the electrode in the anodic direction, as shown in the following equation.   

\begin{equation} \text{CO$_{\text{ad}}$} + \text{H$_{2}$O}\to \text{CO$_{2}$} + \text{2H$^{+}$} + \text{2e$^{-}$}. \end{equation} (8)

A typical voltammogram is shown in Fig. 3. The sharp peak derived from Eq. 8 is observed at ∼0.8 V. Assuming the on-top adsorption of CO on Pt, the charge amount of the desorption of CO_ad is equivalent to 420 µC cm⁻² per the unit surface area of Pt, which is the double amount of UPD of hydrogen, since CO oxidation is 2-electron reaction. In the example of the paper, the ECSA value evaluated by CO stripping voltammetry was close to that evaluated by UPD of hydrogen (Figs. 2 and 3). CO stripping voltammetry is widely utilized for the estimation of ECSA of alloys/core-shell catalysts containing Pt.

Figure 3.

CO stripping voltammogram of Pt/C-catalyst-modified glassy carbon electrode in 0.10 mol dm⁻³ HClO₄ at 25 °C in argon saturated condition. Scan rate was 0.010 V s⁻¹. The shaded area shows the total charge amount of the desorption of adsorbed CO. ECSA was obtained as 79 m² g_Pt⁻¹ as a result of dividing the shaded area by 420 µC cm⁻².

The overall electrochemical oxidation of CO (Eq. 8) proceeds by the electrochemical oxidation of CO_ad and by the oxidation of CO_ad by the oxidized species generated on Pt (Pt–OH).¹⁴ Therefore, the onset potential of CO stripping depends on the potential for the generation of Pt–OH. For example, it has been reported that the decoration of organic molecules on the core-shell catalyst shifts the onset potential in the positive direction, as demonstrated not only by cyclic voltammetry but also CO stripping voltammetry.¹⁵

3. Electric Double Layer for Capacitors

Basic information on electrochemical capacitors is provided in chapter 3 on polarization. Electrical double layer capacitors (EDLCs) fabricated using activated carbon as an active material are widely used in power- and load-leveling applications. On the other hand, pseudo-capacitors based on redox reactions have been widely investigated to achieve higher energy density. The energy density of pseudo-capacitors significantly increases using redox reactions while exhibiting rate characteristics comparable to those of EDLCs. This is because of the charge-discharge mechanism, which is called pseudo-capacity, with a mechanism different from the traditional redox reaction on the battery electrodes.

A pseudo-capacitor has electrochemical mechanisms that are completely different from those of a battery that also uses redox reactions. It is easy to make the mistake of treating an electrochemical reaction that should be considered a battery as a pseudo-capacitor. Therefore, this chapter describes the characteristics of pseudo-capacitors in addition to an explanation of cyclic voltammetry measurements of capacitors.

3.1 Cyclic voltammetry of electrochemical capacitors

When an ideal isosceles triangle charge-discharge profile (See Ref. 16) is obtained in constant current charge-discharge testing of electric double layer capacitors, evaluation by cyclic voltammetry is a complementary method. On the other hand, electrochemical analysis using cyclic voltammetry is effective when the shape of the charge-discharge profile is deformed from an isosceles triangle, when the Helmholtz layer structure, which greatly affects the capacitance of the electric double layer, changes with electric potential, or when evaluating new materials. For example, CV is an effective means to confirm side reactions and decomposition reactions caused by impurities, as well as reversible/irreversible redox reactions of surface functional groups when evaluating new carbon materials. Furthermore, cyclic voltammetry measurements are particularly valuable for understanding the potential and characteristics of their redox response in the case of electrode materials used in redox capacitors.

When cyclic voltammetry measurements are performed on an ideal EDLC, a nearly parallelogram-shaped response is observed, as shown in Fig. 4. The cyclic voltammetry method can also be used to calculate the charge/discharge capacity. ΔE/Δt is the scan rate (ν) in the cyclic voltammetry method, and the device capacitance C_dev is calculated as follows.   

\begin{equation} I = C_{\text{dev}} \cdot \nu \Leftrightarrow C_{\text{dev}} = \frac{I}{\nu}. \end{equation} (9)

However, the actual CV curve does not show a parallelogram shape. For example, because the current I changes with voltage, the average current is calculated as follows and introduced into Eq. 9 to calculate the capacitance.   

\begin{equation} \bar{I} = \frac{1}{E_{2} - E_{1}}\int_{E_{1}}^{E_{2}}I(E)\text{d}E. \end{equation} (10)

Figure 4.

An image of CV for EDLC.

3.2 Pseudo-capacitor

Both pseudo-capacitors^17–19 and batteries are energy storage devices that use redox reactions. The most important characteristic of pseudo-capacitors compared to the widely known properties of batteries is that charge/discharge operations can be completed in seconds to minutes. On the other hand, batteries can charge/discharge with their original energy density by taking more than 10 minutes, even with excellent charge/discharge characteristics. This is due to the difference in ion diffusion properties. In batteries, ion diffusion inside the solid is the rate-limiting factor, whereas in pseudo-capacitors, diffusion is not the rate-limiting factor.

3.3 Mechanisms of pseudo-capacity

Three mechanisms are considered the main factor for pseudo-capacitance.

1. i)    Underpotential deposition: Various metal cations adsorb on the electrode surface at a potential higher than the reduction potential as explained in the previous chapter. For example, copper adsorption on Pt.
2. ii)    Redox pseudo-capacity: Redox reactions are not limited to diffusion when ions in solution react with ions near the surface of electrode materials. For example, RuO₂ nanosheets.²⁰
3. iii)    Intercalation pseudo-capacity: Generally, an intercalation reaction is a reaction in which the diffusion of ions inside a solid is the rate-limiting factor, as observed in cathode materials for lithium-ion rechargeable batteries. However, intercalation electrode materials without crystal structure changes enable charge/discharge reactions in which diffusion is not the rate-limiting factor. For example, crystalline Nb₂O₅.²¹

Because the pseudo-capacitance electrode charge/discharge with adsorption/desorption mechanism as described above, the electrode potential is given as follows:   

\begin{equation} E = E^{\circ} - \frac{RT}{F}\ln \left(\frac{X}{1 - X}\right), \end{equation} (11)

where E is the potential, R is the ideal gas constant, T is the temperature, F is Faraday constant, and X is the degree of electrode coverage. The electrical quantity should be divided by the voltage to calculate the capacitance C; however, X should be multiplied to take into account the extent to which the reaction covers the electrode since pseudo-capacitance is a reaction on the electrode surface. The capacitance of a unit weight adsorbent can be shown as follows only when E vs. X maintains a linear relationship.   

\begin{equation} C = \left(\frac{F}{m}\right)\frac{X}{E_{\text{cell}}}, \end{equation} (12)

where E_cell is the voltage of the cell and m is the molecular weight of the active material.

One of the main features of the potential sweep method such as cyclic voltammetry measurement is that the time scale can be controlled by changing the scan rate. The response to a change in scan rate depends on whether the redox reaction is dominated by mass diffusion in the solid or by surface reactions. The Faradaic current is proportional to v^1/2 in the diffusion-limiting reaction. In contrast, the Faradaic current is proportional to v in the surface reaction. Therefore, the following general relationship is established.   

\begin{equation} I = k_{1}v^{1/2} + k_{2}v. \end{equation} (13)

By determining the values of k₁ and k₂ at each potential, it is possible to separate the diffusion-limiting current from the capacitive current (Fig. 5). The b-value evaluation is the technique to understand the ratio of the diffusion-limiting current to the capacitive current.   

\begin{equation} i = kv^{b}. \end{equation} (14)

The b-value ranges from 1/2 to 1, with 1/2 indicating a purely diffusion-limiting reaction and 1 indicating a pure capacitor. It is necessary to provide each value to evaluate k₁ and k₂ separately; however, the b value evaluation is valid to indicate the ratio of the capacitive current and the diffusion-limiting current since only the ratio of k₁ and k₂ is meaningful in this case. These measurement methods are often used to show the electrode operating as a pseudo-capacitor. However, the electrode that does not exhibit the characteristics listed below should not be treated as a pseudo-capacitor.

Figure 5.

CV analyzed to separate capacitive and diffusion contribution based on Eqs. 3–5.

Redox peaks are observed with cyclic voltammetry measurements at very low scan rates with intercalation type electrodes for batteries. The peak potentials of each oxidation and reduction are different because of the crystal structure change that occurs with the insertion and extraction of metal cations such as lithium. However, for electrodes that exhibit pseudo-capacitance, the peak potentials for oxidation and reduction are almost identical because no crystal structure change is associated with the redox reaction (Fig. 6). As mentioned in the previous chapter, time and voltage show linear relationships in constant-current charge-discharge tests of electrochemical capacitors. This does not change, even for quasi-capacitors. Therefore, it should be noted that electrodes that show a distinct plateau voltage should be treated as batteries, regardless of the b-value.

Figure 6.

Typical image of the CV of a pseudo-capacitor.

4. Microelectrodes and Sensors

Microelectrodes are electrodes having dimensions comparable to the diffusion layer thickness of the electrode active species. The limiting currents at microelectrodes easily reach the mass-transfer limited steady-state currents. Therefore, the microelectrodes can easily yield the sigmoidal voltammogram using cyclic voltammetry. Because the current is stable and reproducible, microelectrodes are suitable for sensor applications. Additionally, microelectrodes enable measurements in dilute electrolyte solutions or highly viscous solutions with low electrical conductivities because of the very small currents. According to the symmetry of mass transport around electrodes, microelectrodes are classified into two types: microdisk or microsphere (3D) and microrod or microband (2D). This section introduces the fundamentals of metal microdisk and microband electrodes, which are easy to fabricate.

4.1 Fabrication of microelectrodes

4.1.1 Microdisk electrodes

The microdisk electrodes are prepared by sealing a thin conductive wire in an insulator. Although glass is an excellent insulator, the sealing of gold thin wire in glass is difficult because the softening point of the glass is close to the melting point of gold and the difference between their expansion coefficients is large. A gold wire sealed in an epoxy resin, such as Torr Seal^®,²² was cut and the cross-section was ground with emery papers. It is important to pay attention to the gap between the metal and insulator. The electrolyte solution can easily penetrate the gap around the metal wire. This penetration can cause various problems to the microdisk electrode. For example, the penetration of the electrolyte solution increases the electrode surface area and the charging current. The penetration of the redox species provides unanalyzable data. Additionally, the polishing of microelectrodes frequently causes problems because of the malleability of metals, such as gold. The expanded electrode surface provides a larger Faradaic current than that expected from the cross-sectional area of the wire. In conclusion, it is difficult to determine the surface area of a microelectrode. The measurement of the redox current of the standard solution determines the real surface area of microdisk electrodes.

4.1.2 Microband electrodes

Microband electrodes are also fabricated by sealing thinner conductive films, such as metal foils, metal spattered films, and coating films of conductive inks with an insulator. The characteristics of microband and thin ring electrodes are practically the same. Waterproof adhesive tapes were used to insulate the metal foil.^23,24 A fresh cross-section of a metal foil sandwiched between the adhesive tapes can be easily obtained by cutting with a razor.²⁴

4.2 Characterization of microelectrodes

It is difficult to determine the shape and dimension of a microelectrode surface using microscopic observations. Generally, the characterization of the microelectrode is carried out based on the voltammetry of typical redox-active species. We used an aqueous solution of ferrocenedimethanol (Fc(CH₂OH)₂) because of its fast electrode reaction.²³ The voltammetry should be carried out at various scan rates (v). The gap between the conductor and the insulator can cause the charging current to be relatively larger than the Faradaic current. In several cases, it is necessary to deeply grind the surface to remove gaps at the microelectrode surface.

4.2.1 Current response of microelectrodes

The electrode reaction causes a concentration gradient around the electrode. The concentration gradient induces diffusion of the electrode active species, and the diffusion flux (f) is formulated from the diffusion equation as follows:   

\begin{equation} f(x,y,z) = -D_{j}\nabla c_{j}, \end{equation} (15)

where D_j and c_j denote the diffusion coefficient and concentration of species j, respectively. The equation is simplified to a one-dimensional form at the planar electrode surface. However, mass transfer around the microelectrode is a three-dimensional form and cannot provide an analytical form. The response of limiting current at the microdisk electrode (I_lim) can be formulated as follows:²⁵   

\begin{equation} \frac{I_{\text{lim}}}{4nFD_{j}ac_{j}} = \left(0.7854 + \frac{0.8862}{\sqrt{\tau_{\text{d}}}} + 0.2146\exp \left(-\frac{0.7823}{\sqrt{\tau_{\text{d}}}}\right)\right), \end{equation} (16)

where n denotes the number of electrons, a denotes the radius of the electrode, and τ_d denotes the dimensionless time defined as follows:   

\begin{equation} \tau_{\text{d}} = \frac{4D_{j}t}{a^{2}}. \end{equation} (17)

The solid line in Fig. 7 shows a chronoamperogram of a microdisk electrode. When t = ∞, the current converges to the steady-state value of 4nFD_jac_j. The steady-state characteristics of microdisk electrodes enable monitoring of the concentration of electrode active species.

Figure 7.

Dimensionless chronoamprograms for (solid line) microdisk and (broken lines) microband electrodes.

According to Eq. 16, the current at the microdisk electrode is proportional to a. Therefore, the current density at the microdisk electrode increases with a decrease in a. This implies that the ratio of the Faradaic current to the charging current increases with a decrease in the value of a. In several electrochemical measurements, the charging current is regarded as the background current. Therefore, microelectrodes are advantageous in terms of the limit of detection.

The time course of the limiting current at the microband electrode with width w and length l is defined as follows:²⁶   

\begin{align} \frac{I}{nFD_{j}lc_{j}} & = \left(\frac{1}{\sqrt{\pi\tau_{\text{b}}}} + 1\right)\quad \tau_{\text{b}} < \frac{2}{5}\\ & = \cfrac{\pi \exp \biggl(-\cfrac{2\sqrt{\pi\tau_{\text{b}}}}{5}\biggr)}{4\sqrt{\pi\tau_{\text{b}}}} \\ & \quad+ \cfrac{\pi}{\ln \biggl[\sqrt{64\exp (-0.5772156)\tau_{\text{b}}} + \exp \biggl(\cfrac{5}{3}\biggr)\biggr]}\quad\tau_{\text{b}} > \frac{2}{5}, \end{align} (18)

where the dimensionless time τ_b is defined as follows   

\begin{equation} \tau_{\text{b}} = \frac{D_{j}t}{w^{2}}. \end{equation} (19)

The time course from Eq. 18 is shown as a broken line in Fig. 7. The equation shows that I = 0 at t = ∞. Therefore, the current of the microband electrode never reaches a strict steady-state value. However, the current decay is quite slow and can be regarded as a pseudo-steady-state current.

According to Eqs. 16 and 18, when t ≈ 0 the equation is equal to the Cottrell equation for current decay at a planar electrode with an electrode surface area of A:   

\begin{equation} I = \frac{nF\sqrt{D_{j}} Ac_{j}}{\sqrt{\pi t}}. \end{equation} (20)

Therefore, even microelectrodes are regarded as planar electrodes in fast electrochemical techniques, such as fast-scan voltammetry or high-frequency AC measurements. According to the definitions of nondimensional time, the time for the transition from linear to non-linear diffusion depends on the diffusion coefficient and size of the electrode. In cases where the diffusion coefficient is quite small, that is, the substrate molecule is large or the viscosity of the medium is high, it is difficult to demonstrate the characteristics of microelectrodes. Conversely, the long-time chronoamperogram at a planar disk electrode under stationary conditions deviates from the Cottrell equation and converges to Eq. 16.²⁷

4.2.2 Voltammetry of microelectrodes

The reversible electrode reaction at microdisk electrodes is demonstrated in this section. Figure 8A shows the calculated voltammograms without the charging current at scan rates (v) of 10 (solid line), 100 (broken line), and 1000 (dotted line) mV s⁻¹. Despite the use of microelectrode, the voltammogram exhibited oxidative and reductive current peaks when v was high. When the scan was slow, the voltammogram exhibited a sigmoidal shape. The steady-state limiting current value was 7.7 nA and equal to the calculated value of 4nFD_jac_j. The scan-rate dependence of the shape of the voltammogram corresponds to the transition from linear to non-linear diffusion. Figures 8B, 8C, and 8D show the concentration profiles around the microdisk electrode at 300 mV for v = 1000, 100, and 10 mV s⁻¹, respectively. The diffusion layer at v = 1000 mV s⁻¹ is thinner than that at 10 mV s⁻¹. The transition of the diffusion corresponds to the shape of the concentration profile.

Figure 8.

(A) Calculated voltammograms of 1 mmol dm⁻³ substrate with D_O = D_R = 1 × 10⁻⁹ m² s⁻¹ and n = 1 at a microelectrode with a = 40 µm at 298 K. Scan rate is (solid line) 10, (broken line) 100, and (dotted line) 1000 mV s⁻¹. (B, C, and D) Concentration profiles of oxidized form at 0.3 V when v = 1000, 100, and 10 mV s⁻¹, respectively. The boundaries correspond to 0.2, 0.4, 0.6, and 0.8 mmol dm⁻³ in order of light color.

Microband electrodes also provided a sigmoidal voltammogram for the reversible electrode reaction. Figure 9A shows voltammograms for the oxidation of Fc(CH₂OH)₂ at a microband electrode with w = 100 nm and l = 2 cm. Although the voltammogram of the microband electrode is theoretically in the quasi-steady-state, the steady-state characteristics of the current are practically sufficient for analysis. The concentration dependence of the current at 0.6 V is shown in Fig. 9B. The current is proportional to the concentration of Fc(CH₂OH)₂. The linearity of the calibration curve demonstrates that microelectrodes are suitable for sensor applications.

Figure 9.

(A) Voltammograms of oxidation of Fc(CH₂OH)₂ at a microband electrode with w = 100 nm and l = 2 cm recorded at 10 mV s⁻¹ at 0, 0.2, 0.4, and 0.8 mmol dm⁻³ (from bottom to top) and (B) a calibration curve for Fc(CH₂OH)₂ based on the current at 0.6 V.

4.2.3 Monitoring by microelectrodes

The steady-state characteristics and quick responses of the microelectrode enable monitoring of the concentration of the electrode active species. For example, monitoring the reduction of Fc(CH₂OH)₂⁺ by glucose and PQQ-dependent glucose dehydrogenase.²³ The conversion of Fc(CH₂OH)₂⁺ to Fc(CH₂OH)₂ can be traced not only by the reduction current but also by the color change. The solid and dotted lines in Fig. 10 correspond to the remaining ratio of Fc(CH₂OH)₂⁺ in the buffer solution (R), simultaneously determined by the microelectrode and spectrophotometer, respectively. Both measurements yielded the same traces. Unfortunately, the agitation of the solution affects the diffusion-limiting current of the microband electrode. However, the advantage of electrochemical measurements is their tolerance to the turbidity of a sample.

Figure 10.

Monitoring of enzymatic reduction of Fc(CH₂OH)₂⁺ cation by glucose with PQQ-dependent glucose dehydrogenase. The solid and dotted lines show the electrochemically and the photometrically determined remaining ratio of Fc(CH₂OH)₂⁺, respectively. The arrow indicates the addition of enzyme under stirring. Reproduced from Ref. 16, Copyright (2015), with permission from The Japan Society for Analytical Chemistry, and modified in part.

5. Summary

CVs have been used in various research fields including batteries, fuel cells, capacitors, and sensors, because they provide useful information concerning electrochemical reactions. Through this tutorial, we aimed to improve the learning and utilization of electrochemistry for beginners, providing a comprehensive guide for some experts and promoting research advancement. Additionally, this paper summarized practical issues concerning recent trends in fuel cells, capacitors, and sensors. In chapter 2, the practical methods for the ECSA calculation of Pt are explained. Chapter 3 focuses on the non-Faradaic process, where the pseudo-capacitance of activated carbon is introduced. In chapter 4, the principles of microelectrodes are explained and enzyme sensing with microelectrodes is presented as a practice example. We believe that this paper can help enhance future research activities.

Data Availability Statement

The data that support the findings of this study are openly available under the terms of the designated Creative Commons License in J-STAGE Data at https://doi.org/10.50892/data.electrochemistry.21226994. The authors' profiles of this paper can be found on the preface.²⁸

CRediT Authorship Contribution Statement

Hirohisa Yamada: Writing – review & editing (Lead)

Kazuki Yoshii: Writing – review & editing (Equal)

Masafumi Asahi: Writing – original draft (Lead)

Masanobu Chiku: Writing – original draft (Lead)

Yuki Kitazumi: Writing – original draft (Lead)

Conflict of Interest

The authors declare no conflict of interest in the manuscript.

Footnotes

This paper constitutes a collection of papers edited as the proceedings of the 51st Electrochemistry Workshop organized by the Kansai Branch of the Electrochemical Society of Japan.

H. Yamada, M. Asahi, M. Chiku, and Y. Kitazumi: These authors contributed equally to this work.

H. Yamada, K. Yoshii, M. Asahi, M. Chiku, and Y. Kitazumi: ECSJ Active Members

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