Introduction

Experiments with the use of micro- or nanoelectrodes are especially good and useful in student lab courses. It can be shown that just a substantial drop in the electroactive electrode area results in a significant change in the voltammogram shape, which is a result of a change in the shape of the depletion layer and of a strong decrease in the ohmic potential drop. Particularly eye-catching is the fact that this microelectrode response can be easily generated and canceled by changing the time of experiment, e.g., by changing potential scan rate in voltammetry.

Also, a very attractive experiment may be an experiment involving the constant-potential amperometry of an uncharged electroactive species in the absence of deliberately added supporting electrolyte. Under such conditions the current starts with a low value and, in time, will reach finally the steady-state value for excess supporting electrolyte.

Next, in the paper, we will show how it is possible to determine both: diffusion coefficients of substrate and product of electrode reaction. This can be done only in the absence of excess supporting electrolyte, so the employment of microelectrodes is required. Finally, a brief discussion on qualitative analysis with anodic stripping voltammetry at a nanoelectrode will be given.

To enhance understanding and utility of the material presented, the relevant terms used in this work are defined in Table 1.

Table 1 Definitions of basic terms used in this work
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Relativity in microelectrode phenomenon

Up to seventies of the twentieth century, a regular voltammetric electrode of size in the range of single millimeters was usually called a microelectrode. So, a hanging mercury drop electrode and a regular Pt disk electrode belonged to the group of microelectrodes. In time, the electrodes of much smaller size were successfully prepared and used in electrochemical experiments. It appeared that the voltammetric curves obtained with the electrodes of size in the range of micrometers differed from those of classical electrodes by shape; they were wave-shaped and did not form sigmoidal peaks seen in the case of regular electrodes. A comparison of voltammograms obtained for the reduction of hydrogen cation at a regular electrode (sigmoidal peaks are seen) with those obtained with a microelectrode (waves were formed) is presented in Fig. 1. Two concentrations of perchloric acid were used in those experiments. The peak distortions seen at the regular-electrode voltammogram for the higher acid concentration were caused by evolution of gaseous hydrogen [1]. No distortions caused by hydrogen bubbles were seen at the microelectrode voltammograms because of much faster transport of the electrode product to the solution bulk.

Fig. 1
figure 1

Voltammetric waves for reduction of hydrogen cation at a microelectrode (11.25-μm-radius Pt disk, top) and at a conventional electrode (0.15-cm-radius Pt disk, bottom). Conditions: linear scan voltammetry, 20 mV s.−1; T = 20 °C; supporting electrolyte, 1 mM LiCI04. HCI04: 0.005 (1), 0.025 M (2). Copyright Analytical Chemistry, reprinted from [1]

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It was established that the wave shape of the microelectrode voltammograms was a result of a substantial alteration in the analyte transport to the electrode surface [2,3,4,5]. The diffusion/depletion layer at a regular electrode, where the analyte concentration is lower than in the solution bulk, is usually flat (except for the electrode edges) and uniformly spread over the electrode surface. Its thickness is a small fraction of the electrode radius. In this situation, scientists talk about “linear” diffusion of the analyte to the electrode surface. At the microelectrode surface, at the same time interval, the diffusion-layer thickness can be more than 10 times bigger than the electrode radius, and, as a result, its shape becomes spherical/hemispherical, and correspondingly, the diffusion to the electrode surface is called “spherical.” In such a layer, the analyte transport to the electrode surface is considerably faster/more efficient and the current density at the electrode surface is much bigger. Similarly, as it was mentioned in the discussion of Fig. 1, the faster was the transport of the electrode product to the solution bulk. This is why the rather slow process of nucleation of gas bubbles did not manage to start at the microelectrode surface under the conditions of Fig. 1, curve 2. The difference in the depletion-layer shapes, in the case of disk electrodes (regular and micro), is illustrated in Fig. 2. Going back to the nomenclature, the name “microelectrodes” was quickly assigned only to very small electrodes.

Fig. 2
figure 2

Transport of analyte to the surface of regular electrode and microelectrode

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It is important to stress here that the wave-shaped voltammograms cannot be obtained with microelectrodes under all conditions. Scientists demonstrated that a sigmoidal peak characteristic for regular electrodes can be also obtained with a very small electrode. Such a situation will take place when the experimental time is very short, e.g., when potential scan rate in the linear-scan voltammetry is fast enough. Then, the diffusion/depletion layer cannot become sufficiently thick and spherical, and the layer thickness will remain much smaller than the electrode size (radius). This situation is illustrated in Fig. 3. So, the microelectrode size does not guarantee the microelectrode behavior [6]. Figure 3 also shows that the theoretical voltammograms (one considering and the other eliminating the natural convection) are superimposed which indicates the absence of significant perturbation by natural convection. Taking into account the above relativity facts, in 2000 the IUPAC published a technical report with an “elastic” definition of microelectrode. It is suggested, in that report, that while it is conventionally assumed that a microelectrode has dimensions of tens of micrometers or less, down to submicrometer range, a more rigorous look should be applied in the definition of microelectrodes. It can be said that microelectrode is any electrode whose characteristic dimension is, under the given experimental conditions, comparable to or smaller than the diffusion layer thickness, d. Under these conditions, a steady state or a pseudo steady state (cylindrical electrodes) is attained [7].

Fig. 3
figure 3

Theoretical (solid lines) and experimental (symbols) cyclic voltammograms obtained with a 12.5 μm radius Pt electrode at various potential scan rates. Solution: 2 mM K4Fe(CN)6 in 1 M KCl. E° = 0.238 V. Simulations were done assuming the presence and absence of natural convection. The two theoretical voltammograms are superimposed establishing the absence of significant perturbation by natural convection. Copyright Electrochemistry Communications, reprinted from [6]

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Microelectrodes can have a variety of forms. We can talk about microspheres and sphere fractions, microdiscs, microcylinders, bands or lines, and assemblies of microelectrodes. The most popular microelectrode types are disc and cylinder. Also, in many publications, the use of assemblies of microelectrodes is reported. Interestingly, in eighties and nineties of the twentieth century, microelectrodes became a big new perspective for electrochemistry. The feeling was they will become the first, most important tool in electroanalysis. This prediction appeared to be over-optimistic. However, the need to prepare electrodes smaller and smaller was strong. Nanoelectrodes seemed to be especially useful in nanobiosensing and electrochemical scanning microscopy [8,9,10,11].

Electrochemistry in the absence of supporting electrolyte

It is clear that nanoampere- and picoampere currents cannot generate in the cell a substantial ohmic potential drop. Therefore, the use of microelectrodes in electrochemistry made the quantitative measurements in solutions without deliberately added supporting electrolyte possible [12]. It was found that under the conditions of severe deficiency of supporting electrolyte the obtained voltammograms were well defined and reproducible. Interestingly, pulse voltammetry gave also satisfactory replies. Particularly stimulating was the fact that under the constant-potential conditions, in the absence of purposely added supporting electrolyte, the obtained microelectrode steady-state current for uncharged substrates was, sooner or later, identical to the fully diffusional current. The height of the stationary current/wave did not depend on the support ratio (the ratio of concentrations of supporting electrolyte and analyte) [13, 14]. The above behavior was in a good agreement with the results of digital simulations which are presented graphically in Fig. 4. The reported ability of microelectrodes can be explained by the continually increasing conductivity of the depletion layer and the corresponding decrease of the ohmic drop while the electrode process lasted. In other words, in time the accumulation of ionic species (the product and the counterion) in the electrode neighborhood took place.

Fig. 4
figure 4

Theoretical time dependencies of currents, normalized with respect to the limiting current under the purely diffusional conditions, calculated for the oxidation (reduction) of uncharged substrate and for several values of support ratio: 10−4 (1), 10−3 (2), 10−2 (3), 1 (4), and 102 (5). Dashed line refers to the purely diffusional conditions (excess supporting electrolyte). Copyright Encyclopedia of Analytical Chemistry, reprinted from [14]

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Exercise on examination of mass transport at microelectrodes

As mentioned above, very small size of the active parts of microelectrodes results in very small faradaic currents (down to pA level) flowing through the solution/working electrode interface. This leads to relatively small ohmic potential drops even if the measurements are performed in solutions without deliberately added supporting electrolyte. Under such conditions, the transport of charged species to the electrodes is driven by both diffusion and migration. The problem of mixed diffusion-migration transport to microelectrodes was extensively studied by several groups [2, 3, 13]. The analytical expressions derived for the steady-state conditions can be employed for the quantification of some vital parameters characterizing both the redox species and the electrochemical system. These include diffusion coefficients of both the substrate and the product of the electrode process, charge numbers of the electroactive species, the supporting electrolyte level, and ohmic potential drop across the cell.

The voltammetric oxidation of Fe(CN)64− at microelectrodes in aqueous solutions containing no and sufficient excess of supporting electrolyte under the steady-state conditions is a convenient example for the exploration of the above possibilities of microelectrodes in electroanalysis and for the verification of the predicative features of the expressions derived for the transport phenomena at microelectrodes.

Redox system characteristics

The Fe(CN)64− system gives a 1 − e wave-shaped voltammetric response. Due to the migration contribution, the limiting current for the oxidation process Fe(CN)64−  → Fe(CN)63−  + e carried out under the absence of supporting electrolyte is increased compared to the purely diffusional conditions. Assuming equal diffusion coefficients of the substrate and the product, the theoretical value of the ratio of the limiting currents recorded in the absence of supporting electrolyte and in the presence of its excess is equal to 1.128 [3]. According to the generalized theoretical predictions derived by Hyk and Stojek [15], the inequality of the substrate and the product diffusivities, which is the case for hexacyanoferrates, should make this ratio distinctly larger.

Experimental details

Two pieces of platinum foil can be used as the counter and the quasi-reference electrodes to eliminate a possible leak of ions from the bridge. Platinum disk microelectrodes of radii less than 25 μm are used as working electrodes.

Before each experiment, the working electrode is polished with aluminum oxide powders of various sizes (down to 0.05 μm) on a wet pad and was rinsed with a direct stream of deionized water (conductivity of ∼0.056 μS/cm). The electrodes are dried using ethyl alcohol. After the measurements, the electrode surface is inspected optically with a microscope. To minimize the electric noise, the electrochemical cell is kept in a grounded Faraday cage.

Potassium hexacyanoferrate(II) (K4Fe(CN)6, 99 + %) serves as the redox probe system while potassium chloride (99 + %) is used as supporting electrolyte.

Voltammetric measurements are performed at room temperature in 20 mM aqueous solutions of the redox system, Fe(CN)64−, containing either no or 50-fold excess of KCl. Ten replicates of the background-corrected voltammograms are recorded at the scan rate of 10 mV/s.

To avoid the photochemical decomposition of hexacyanoferrate(II), the electrochemical cell is shielded from light.

Transport control of the electrode process

To make sure that electroactive species do not adsorb on the working electrode surface during the oxidation process and the electrode process rate is mass-transport controlled, a correlation of the limiting currents (obtained for the supporting electrolyte excess, IdL) with the microelectrode radius (e.g., 5.0, 10, 12.5, and 25.0 μm in radius (re)) is analyzed. The linear dependence (IdL vs. re), with the correlation coefficient, r, not smaller than 0.99, is expected if the mass transport controls the electrode process rate. By taking the accepted literature value of the electrode-process substrate diffusion coefficient, DS, equal to 6.32 × 10−10 m2/s, the theoretical value of the slope (a = 4FDScSb, where cSb is the bulk concentration of the electroactive species (Fe(CN)64−)) of that dependence can be confronted with the empirically found value. The linearity of the tested dependence and a good agreement between theoretical and experimental values of the slope indicates the transport-controlled nature of the process examined. The perfectly flat and very well reproducible voltammetric wave plateaus may serve as additional proof for the absence of Fe(CN)64− adsorption at the concentration level used. The reproducibility of the results expressed by the coefficient of variation of the steady-state current should be less than 5%.

Diffusion coefficient of the electrode process substrate (Fe(CN)6 4−)

The value of the Fe(CN)64− diffusivity can be easily extracted from the height of the diffusional voltammogram recorded for any of the microelectrodes employed for experiments. To improve the accuracy of the determination process, it is recommended to apply the slope (a) of the calculated linear dependence (IdL vs. re) from the previous step of the experimental procedure The expression a/4FcSb yields the value of the Fe(CN)64− diffusivity at a given temperature.

Diffusion coefficient of the electrode process product (Fe(CN)6 3−)

The determination of diffusion coefficient of the electrode reaction product is not possible under conditions of excess supporting electrolyte. The elimination of supporting electrolyte opens this possibility. For the redox species examined, the experimental value of the ratio of the limiting currents obtained in the system with no supporting electrolyte to that in the presence of excess supporting electrolyte (I L/IdL) determines the ratio of the product to substrate diffusivity (θ = DP/DS = D(Fe(CN)63−)/D(Fe(CN)64−)) as it is predicted by Eq. 37 in [15]. The diffusivity ratio θ given by

$$\theta =\mathrm{exp}\left(\frac{\frac{{I}^{L}}{{I}_{d}^{L}}-1.1277}{0.4575}\right)$$

and combined with the diffusion coefficient of the electrode process substrate found in the previous step of the experimental procedure yields the value of the Fe(CN)63− diffusivity at the given temperature. The number obtained should be confronted with the values found in the literature: 7.17 × 10−10 (∼1 mM Fe(CN)63−, 0.5 M KCl, T = 25 °C), 7.4 × 10−10 (10 mM Fe(CN)63−, no supporting electrolyte, T = 20 °C), 7.61 × 10−10 (1 M KCl, T = 25 °C) [16,17,18].

The limiting ohmic potential drop across the cell

The experimental value of the ratio of diffusion coefficients of the product and the substrate θ can be used for the estimation of the limiting electrostatic potential at the interface (ΨL) by employing Eq. 29 in [15]. The number obtained allows one to estimate the IR drop across the electrolytic cell in mV:

$$IR=1000\frac{RT}{F}{\Psi }^{L}$$

where

$${\Psi }^{L}=\frac{4\theta -3}{16\theta -15}\mathrm{ln}\left(\frac{16}{15}\theta \right)$$

R is the gas constant and T denotes temperature.

Electroanalysis with nanoelectrodes

In general, the experiments carried out with nanoelectrodes (i.e., electrodes for which, by definition, at least one dimension does not exceed 100 nm) are similar to those with microelectrodes. However, extremely increased efficiency of the mass transport to nanoelectrodes results in the steady-state current conditions in ultrashort times. Nanoelectrodes and ultramicroelectrodes have many advantages; they open new possibilities of measurements performed at nanoscale, including the transport studies in extremely resistive media. On the other hand, in a real experiment with nanoelectrodes, a researcher must demonstrate a lot of experimental skills, since nanoelectrodes are extremely susceptible to electrostatic, mechanical, and electrochemical damage that leads to formation of lagooned electrodes with reduced current response.

Fabrication of carbon and platinum nanoelectrodes

Microelectrodes can be obtained commercially, nanoelectrodes rather not. The procedure of fabrication of carbon nanoelectrodes usually starts with pulling quartz capillaries by a laser-based micropipette puller. Non-etched side of the fabricated micropipette is placed inside the silicon tube connected with a gas supplying system. Provided acetylene is heated with a gas burner. The pyrolysis of acetylene results in the formation of a graphite clog inside the etched-side capillary. After that, a copper wire is inserted to provide an electrical connection for voltammetric measurements [19].

An alternative to the use of a micropipette puller is electrochemical etching. This is especially useful for the fabrication of Pt nanoelectrodes. Platinum wires with diameters in the range 25–100 μm are immersed in an aqueous solution composed of CaCl2 and HCl. The wires serve as the working electrodes in the two-electrode system. A high voltage applied to the electrodes dissolves electrochemically Pt and makes the Pt working electrode thinner. The following reactions take place in the system:

$$\mathrm{Pt}+{6\mathrm{Cl}}^{-}\to \mathrm{Pt}{{\mathrm{Cl}}_{6}}^{2-}+4\mathrm{e}$$
(1)
$${4\mathrm{H}}^{+}+4\mathrm{e}\to 2{\mathrm{H}}_{2}$$
(2)

The etched tips are cleaned in concentrated nitric acid (V) and then in ethanol and acetone to remove impurities. The etched wires can be then visualized with a scanning electron microscope in order to initially estimate the size of the tips. The cleaned wires are placed in borosilicate capillaries; then, one end of the capillary is melted to cut off the air supply. Next, the electrodes are polished mechanically and manually to expose the conductive surface. After that, a copper wire is inserted into the capillary to provide an electrical connection for voltammetric measurements [19].

Voltammetry at nanoelectrodes

The measurements of the steady-state diffusion-limited currents with the fabricated nanoelectrodes in a solution containing excess supporting electrolyte are reasonably reproducible, and the waves are well defined (see Fig. 5A). They are usually performed for the rough estimation of the active size of the working nanoelectrode. The geometry of the fabricated nanoelectrodes is rather undefined; therefore, each electrode is characterized by the so called geometry factor, g, by using the steady-state diffusion-limited current expressed in the following way:

$${I}_{d}^{L}=gnF{D}_{S}{c}_{S}^{b}$$

where IdL is the steady-state current measured in the system with excess supporting electrolyte and the typical substrate is a ferrocene derivative, e.g., ferrocenemethanol or ferrocenedimethanol.

Fig. 5
figure 5

A Cyclic voltammetry of 1,1’-ferrocenedimethanol (5 mM) at Pt nanoelectrode under the conditions of supporting electrolyte excess (0.1 M NaNO3). The nanoelectrode radius estimated from the diffusion-limiting current is 280 nm. B Cyclic voltammetry of 2.5 μM Cu.2+ at mercury film deposited at Pt nanoelectrode (characterized in A) in the absence (blue curve) and presence (red curve) of tenfold excess supporting electrolyte (NaNO3)

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Thin-film mercury nanoelectrodes, prepared by employing a well-documented procedure [20], extend electroanalytical usefulness of nanoelectrodes towards the quantification of metal ion species at very low concentrations in aqueous media. The anodic stripping signal [21] can be further magnified if supporting electrolyte is withdrawn from the system as it is demonstrated in the case of Cu ions in Fig. 5B.

The voltammetric measurements at nanoelectrodes in the systems containing severe deficit of supporting electrolyte are rather poorly reproducible [19]. The possible reason for it may be partially related to the breakdown of the electroneutrality in the region adjacent to the nanoelectrode. It should be emphasized that the electroneutrality assumption in mathematical modeling is generally valid if the electrical double layer occupies an insignificant fraction of the transport depletion layer. This becomes questionable when the size of the working electrode approaches the nanometer range. The elimination of supporting electrolyte is another factor leading to an increase in the double layer thickness that leads to an increase in the ratio of double layer thickness and the depletion layer thickness. The structure of the layer adjacent to the nanoelectrode surface during the electrode process in a system with no supporting electrolyte added is illustrated schematically in Fig. 6. In the absence of supporting electrolyte, the double layer at a nanoelectrode is practically composed of the ionic electroactive species.

Fig. 6
figure 6

Schematic representation of the layer adjacent to the nanoelectrode surface in the system with no supporting electrolyte. S and P denote substrate and product of the electrode process; arrows indicate direction of mass transport, and φ is potential at characteristic points in the electrical double layer. SEM image presents the tip of carbon nanoelectrode

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Final remarks

At the end of the paper, it is reasonable to discuss the advantages and disadvantages of microelectrodes and nanoelectrodes compared to macro/regular electrodes. The voltammograms obtained with macro electrodes often enable more precise and deep analysis of complex electrochemical reactions and their mechanisms and parameters. However, these analyses can only be performed under the conditions of supporting electrolyte excess which could make the determined parameters affected by the increased ionic strength. The handling of regular electrodes in voltammetric experiments is easy. The work with micro- and nanoelectrodes is more demanding; however, they are superior for voltammetry in low ionic-strength solutions, at high potential scan rates, in examination of various very small samples and in scanning electrochemical microscopy.