|December 1, 2000; pp. 754 A-760 A|
|Copyright 2000 American Chemical Society|
Eliminating or using very little supporting electrolyte provides opportunities for new types of voltammetry and amperometry experiments.
Brooklyn College of the City University of New York
Universtiy of Warsaw (Poland)
For many years, there has been a rule in electroanalysis: Before starting any voltammetric or amperometric measurement, add excess supporting electrolyte to the solution. There are good reasons for this. Excess supporting electrolyte significantly increases solution conductivity and, consequently, decreases the ohmic potential drop that causes electrode potentials to depart from the value imposed by the electrochemical instrument. Moreover, excess electrolyte suppresses ion migration in solution, allowing purely diffusional transport of ions and molecules. Thus, the mathematical modeling of the current–potential and current–time relationships, and, correspondingly, the obtained equations, is simpler. All of this assumes that the supporting electrolyte is soluble in the solution, does not interact with the analyte, and generates ions that are electroinactive in the desired potential window.However, excess electrolyte has its disadvantages. It usually significantly increases the ionic strength of the solution and affects the activities of ions and the mobilities of ions and molecules. (The mobilities of neutral molecules are only affected if the added supporting electrolyte measurably changes viscosity.) Moreover, the interactions between the supporting electrolyte and the analyte or the product of the electrode process can be significant and should not be completely ignored. Finally, adding supporting electrolyte is a time-consuming step and can introduce unwanted impurities.
In some cases, adding excess supporting electrolyte is difficult or even impossible—if the concentration of the analyte approaches the level of moles per liter, the solubility of supporting electrolyte is very low, or the analyte is in its solid state. (Note that the relative concentrations of the analyte and supporting electrolyte are important; however, the absolute concentration of either is not.)
Can supporting electrolyte be avoided altogether? The first current–potential waves with no supporting electrolyte were obtained more than 70 years ago (1, 2). Those experiments were possible due to the presence of ionic analytes, which provided sufficiently high conductivity. Nevertheless, because of the large ohmic potential drop, the voltammetry of uncharged species without supporting electrolyte was not possible until the 1980s.
The introduction of microelectrodes or ultramicroelectrodes, which have at least one dimension in the micrometer range, into electroanalytical practice has significantly reduced the ohmic potential drop and enabled voltammetric experiments in solutions with or without low levels of supporting electrolyte. The first well-defined steady-state voltammograms of uncharged molecules without added supporting electrolyte were obtained in the 1980s (3–5). Since then, microelectrodes have become widely accessible and primary tools for voltammetry in low ionic strength media, which can also be described as media with low electrolyte/analyte concentration ratios. Various microelectrode geometries have been used for low-electrolytevoltammetric experiments, including disk, hemispherical (or partial spherical), cylindrical, band, and ring microelectrodes, as well as microelectrode assemblies.
The changes in ion concentrations can be easily explained by the electroneutrality principle, which says that the total charge at any point in the solution equals zero. The assumption that the electroneutrality principle is always obeyed has frequently been made in theoretical derivations. However, Norton and co-workers have shown that this principle does not hold when the depletion layer is entirely included within the double layer (6). (The double layer is a thin layer of solution, typically up to 100 Å thick, in which cations and anions accumulate to counter the excess charge of the electrode that is polarized to a given potential.)
Based on their data, one can estimate that the depletion layer thickness can be assigned a value of 10r0, where r0 is the electrode radius, and the double layer thickness is ~1.5–1, where –1 is the Debye–Hückel length. This last value is determined by
–1 = (0kT/2c0z2e02) 1/2 (1)
in which c0 is the bulk z:z, z is ion charge, is the relative dielectric permittivity of solvent, 0 is the permittivity in vacuum, k is the Boltzmann constant, T is the temperature, and e0 is the elementary charge. For z = 1, the approximate -1 values are 10 nm, 100 nm, and 1 µm for electrolyte concentrations of 1 × 10-3, 1 × 10-5, and 1 × 10-7 M, respectively. Moreover, the larger the difference between the electrode potential and the zero charge potential (the potential at which the excess charge on the electrode equals zero), the smaller the Debye–Hückel length. Based on these equations, for typical sizes of microelectrodes (r0 > 1 µm) and a very low level of ionic impurities in a solvent (e.g., 10–6 M), the thickness of the double layer is significantly smaller than that of the depletion layer. Interestingly, if the radius of the electrode is <~0.1 µm, the electroneutrality principle may be violated, even with excess supporting electrolyte.
The key problem for the voltammetry of uncharged species without added supporting electrolyte is that the actual electrolyte/analyte ratio in the solution is not known, and it can vary widely over a range of solvents. In fact, neither the identity of the ions nor their concentrations are usually known. In water, these ionic impurities are usually metal ions and typical mineral anions. The initial level of ionic impurities can be estimated from conductance measurements or the shift in the half-wave potential from the value obtained with excess electrolyte (7).
When current flows in the cell, the concentration of ions near the electrode surface can increase or decrease. For example, if a cation of the dissolved compound C+A– is reduced, and the voltammetric current reaches the limiting current plateau, the cation and anion concentrations drop to zero at the electrode surface due to the electroneutrality principle. On the other hand, during the reduction process of a neutral species that produces anions, the cations (counterions) are drawn to the electrode surface, and the total ion concentration increases. The change in ion concentration near the electrode surface for a one-electron oxidation process of a neutral species is illustrated in Figure 1. The structure of the double layer is neglected in this figure. Figure 1a shows the situation before the electrode process, whereas Figure 1b illustrates conditions of flowing current.
It has been known for many years that the limiting currents of ionic species depend on the concentration of supporting electrolyte, because it contributes the migrational flux to the total flux (current) of the charged species (8). The total flux of species j can be represented as
where C and are gradients of concentration and electric potential, respectively; D is the diffusion coefficient; F is the faraday constant, and R is the molecular gas constant.
The experimental and theoretical treatments of diffusional and migrational transport with microelectrodes were reported in the 1980s. (We want to point out that the classical theoretical approach to migration at regular electrodes does not take into account the time dependence of the migrational transport or the type of spherical depletion field, which forms at microelectrodes.) The first theoretical elaboration of microelectrode behavior came from Bond et al. (9) and was followed by Amatore et al. (10), who derived expressions relating the current with the electrolyte/analyte ratio—also called the support ratio—for several types of electrode reactions. Amatore et al. obtained solutions for microcylindrical electrodes, because such electrodes were widely used for in vivo measurements. However, it became clear later that their predictions were correct for other microelectrode geometries. Oldham’s group described the problem for spherical microelectrodes using a very clear analytical derivation, and they offered some generalizations and expansions of the model (11–13). For the reduction or oxidation of cations or anions, respectively, to neutral species, Ciszkowska and Osteryoung added the influence of the type of supporting electrolyte to Oldham’s model (14).
Those papers predicted that, for the reduction of a cation or the oxidation of an anion in the presence of little supporting electrolyte, the limiting current will always be higher than that obtained with excess supporting electrolyte. This is because the transport of the charged analyte is enhanced by its migration. (In this case, cations are attracted to the cathode, and anions move faster in the electric field generated in the solution with or without little supporting analyte.) However, for the oxidation of a cation or the reduction of an anion, the current will decrease, because, in this case, the electric field generated slows down the transport of analytes to the working electrode.
Extensive tables with the appropriate data on the enhancement of voltammetric wave heights have been published (13). For example, in the absence of supporting electrolyte, the voltammetric one-electron reduction of a singly charged cation results in a current that is exactly 2 times higher than that obtained with excess supporting electrolyte, whereas for the one-electron reduction of a singly charged anion, this factor is 0.85.
By comparison, the limiting steady-state current i at microdisk or microsphere electrodes with excess supporting electrolyte is usually expressed as
i = gnFr0Dc (3)
in which n is the number of electrons transferred, c is the bulk analyte concentration, and g is the geometry constant of the microelectrode (4 for microdisks and 2 for microhemispheres). The oxidation and reduction currents of uncharged species should not depend on the electrolyte/analyte ratio, provided there is no variation in solution viscosity and a steady state is reached.
The electrode process without supporting electrolyte is very interesting, because, as the current increases, the concentration of ions near the electrode surface increases significantly (Figure 1), as was first indicated by Oldham (11). There is one type of electrode reaction called the charge reversal reaction (analyte-negative and product-positive and vice versa, which makes this reaction at least two-electron), for which the theory predicts an infinite rise of the current in the absence of supporting electrolyte (10). (There is no experimental confirmation of this finding, because the appropriate electrode system has not yet been found.) There are numerous examples of electrode processes—for example, the reduction of H+ to H2 and the reduction of Tl+, Pb+2, and Cd+2 to thallium, lead, and cadmium amalgams, respectively—for which the agreement between the experimental data and theory is very good (15–17).
However, there are also reports of electrode reactions for which there is no agreement among the predicted and experimental ratios of current in the absence (limiting current, il) or excess (diffusional current, id ) of supporting electrolyte, il/id (12). For example, il/id for the oxidation of Ru(II) to Ru(III) in a solution of Ru(COOEtbpy)3[PF6]2 (COOEtbpy = dicarboethoxy bipyridine) is 0.03, but theory predicts a value of 0.880. An opposite deviation was found for the reduction of the cation complex in [CoCp2][PF6], from +1 to 0; the experimental value of il/id is 2.8, but the theoretical value is 2.0. Most likely, unidentified chemical reactions associated with the electron transfer are responsible for these deviations.
Thus, care should be taken when applying the theoretical results in the cited references to the evaluation of experimental results, because some significant simplifying assumptions have been made. The most important assumption is that all diffusion coefficients are equal. Using digital simulation, Palys et al. have shown that, at spherical microelectrodes, il/id may change substantially if the diffusion coefficients for the ions in the electrode process differ significantly (18).
half-wave potential dilemma
Figure 2 presents a set of chronoamperograms at a constant potential, which illustrates how slow that process might be. The lower the electrolyte/analyte ratio, the longer the time required to reach the steady-state current (curves 1–4), whereas for an appropriately large electrolyte/analyte ratio, the curves look classical (curves 5, 6). Note that all chronoamperograms finally reach the limiting, steady-state value. This means that the electrode potential finally reaches a value corresponding to the plateau of the diffusional wave. Also note that, without supporting electrolyte, the resistance between the electrodes changes as the current increases. Therefore, the electronic iR compensation in commercial instruments does not work well. Most of these electronic compensators require an input with a constant resistance.
The half-wave potential contains thermodynamic and kinetic information about the redox couple. To extract this information, the contribution of ohmic potential drop to the half-wave potential should first be estimated. Extensive work on this subject has been published (19, 20). Amatore et al. noticed that, in addition to regular ohmic potential drop changes, half-wave potentials are affected by natural convection, but its contribution is difficult to estimate (19). Convection may slow the rate of counterion accumulation in the depletion layer, which may additionally increase the ohmic potential drop. In fact, there are two types of natural convection—one related to the vibrations of the laboratory environment and another due to gravity. The latter has been known for large electrodes, but surprisingly, it is also observed for microelectrodes with relatively large concentrations of analyte, which generates fluid density gradients during the electrode process (21).
Forced convection, such as that generated by the rotation of the disk or arising from the carrier in flow injection analysis, has the same influence on an electrode response as natural convection (22, 23). The currents are generally smaller, but the half-wave potentials still exhibit an additional shift.
Another phenomenon that can affect voltammograms and chronoamperograms is the formation of ion pairs with ionic products and counterions. The presence of ion pairs may cause changes in the limiting steady-state current, especially in solvents of low dielectric constant (24). Ion pairs may also affect the half-wave potentials by increasing the resistance between the electrodes.
Maintaining a constant level of electroinactive ions is especially difficult when the electrolyte/analyte ratio is very small and there are large differences among the concentrations of ions in the electrolyte bridge and the cell. To avoid any ion leakage, an electrolytic bridge filled with deionized water or another appropriate solvent should be used. This approach requires a very high input-impedance potentiostat. The ionic level is also kept constant by using a quasi-reference electrode, such as a platinum sheet electrode. The quasi-reference electrode, however, usually results in a 20- to 30-mV uncertainty in the measured potential. An internal reference, for example ferrocene or a similar uncharged electroactive compound, can be also used.
A mirror image to the above system is the electrolysis of undiluted ionic liquids (melts). An example of such a system is the perchlorate salt of cobalt (or iron) bipyridine complexes, in which the ligand has attached polyethers of varying chain lengths. Ionic and electronic migration effects are observed in these melts (33). This unexpected result was explained by a much higher diffusion coefficient value for the counterion ClO4– than for the complex cation. Another example is the chloroaluminate/1-ethyl-3-methylimidazolium melt. Voltammetric experiments in this ionic liquid at room temperature have been run without supporting electrolyte to determine anodic and cathodic limit reactions and to study the behavior of various electroactive systems (34, 35).
Another new field for voltammetric investigation, in which migration plays an important role, uses complex systems, such as solutions of polyelectrolytes (large polymers with one or more ionic groups per monomer), colloidal suspensions, and polymeric gels (36–41). In such systems, the electrostatic interactions between ionic polymers and simple counterions are strongest in solutions of very low ionic strength. These interactions affect the diffusion coefficients of the counterions (or electroactive probe ions). Because the steady-state current at microelectrodes is proportional to the diffusion coefficients of the electroactive species, any changes in these coefficients result in proportional changes in the current response. Thus, voltammetry offers an accurate and highly precise method for studying interactions in polyelectrolytic systems.
An example of probe-ion voltammetry in polyelectrolytic solutions is the detection of the thermal coil-to-double helix conformational transition of -carrageenan (42). In Figure 3, the transition region is better defined by the voltammetric plot than by changes in the circular dichroism spectrum. By plugging the measured values for diffusion coefficients of electroactive probes into the theoretical model, the uniform spacing between the polyion charges in the double helix and the coil forms can be estimated.
Voltammetry of solid conducting crystals is a somewhat different experiment (43). Those systems usually have a fixed electrolyte/analyte ratio before experiments, but the magnitude of the ratio is often unknown, and this can lead to erroneous interpretations of the measured transport coefficients. Simple, reverse-pulse voltammetric experiments allow the migrational contribution to the ion transport in solid analytes to be determined (44). Reverse-pulse voltammetry and double-pulse chronoamperometry are useful for determining the primary diffusion coefficients of the analyte without knowing the electrolyte/analyte ratio and the number of transferred electrons.
Recently, voltammetric investigations of homogeneous equilibria at low electrolyte/analyte concentration ratios have been of interest. A rigorous theoretical model that explains the unusual relationship between the height of the cathodic voltammetric waves of weak acids and the concentration of supporting electrolyte has been developed (45).
Researchers have also investigated selected inert complexes, which were studied with voltammetry in the presence of low levels of supporting electrolyte and with an appropriate theoretical model (46). Finally, Amatore et al. developed a general treatment for successive electron transfers under the conditions of diffusional and migrational transport (47).
Voltammetry and amperometry with little or no supporting electrolyte are particularly promising for analyzing biological, environmental, and industrial samples. Amperometric or voltammetric detection with no supporting electrolyte in flow injection and regular-flow analysis and after chromatographic separation may be technically and chemically simpler than the classical approach and more reliable for studies of speciation. The steady-state currents might not be reached and, thus, the linear ranges for the concentration calibration plots are smaller than those obtained with excess electrolyte. However, setting experimental parameters, such as electrode potential and the time-of-current sampling, appropriately should allow one to reach satisfactory analytical (current–concentration) dependencies (23, 48).
This work was supported by the Office of Naval Research under grant number N00,014-98–1-0244, the NATO Collaborative Research Grant number CRG.CRG 974399, the Polish State Committee for Scientific Research grant UM-947/11/99, and the PSC-CUNY Research Award number 61,353-00–30.
Malgorzata (Maggie) Ciszkowska is an assistant professor at Brooklyn College of the City University of New York. Her research interests include electrochemical and spectroscopic investigations of volume-phase transitions of polymeric gels, conformational transitions of ionic biopolymers, and new polymeric materials for electrochemical sensors and power sources. Zbigniew Stojek is professor at the University of Warsaw (Poland). His research interests include electroanalysis, host–guest interactions, modification of metal surfaces with amorphous alloys, and mathematical modeling of diffusion coupled to migration. Address correspondence about this article to Stojek at firstname.lastname@example.org Ciszkowska at email@example.com.