Journal of Electroanalytical Chemistry 466 (1999) 129–143 Review Voltammetry in solutions of low ionic strength. Electrochemical and analytical aspects Malgorzata Ciszkowska a,*, Zbigniew Stojek b a Department of Chemistry, Brooklyn College, The City Uni6ersity of New York, 2900 Bedford A6e., Brooklyn, NY 11210-2889, USA b Department of Chemistry, Uni6ersity of Warsaw, ul. Pasteura 1, PL-02-093 Warsaw, Poland Received 2 October 1998; received in revised form 22 February 1999; accepted 19 March 1999 Abstract Recent progress in microelectrode voltammetry in solutions without or with low concentrations of supporting electrolyte is reviewed. The following points are addressed: mathematical treatment of transport, experimental setup, steady state and non steady state transport, migration coupled with homogeneous equilibrium, voltammetry in undiluted redox liquids, studies on the mechanism of the electrode processes, transport of ions in solutions of polyelectrolytes and colloids, and analytical applications. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Voltammetry; Migration; Microelectrodes; Low support ratio; Absence of supporting electrolyte 1. Introduction lowering of the ohmic drop. This is an increase in ionic strength in the depletion layer while the electrode reac- Voltammetric measurements in solutions of very low tion of an uncharged substrate advances. The ionic ionic strength, including those without deliberately strength increases as a result of the formation of the added supporting electrolyte, became possible by using charged products accompanied by drawing of appropri- microelectrodes, electrodes with at least one essential ate amounts of counterions from the bulk solution. dimension in the range of micrometers or less. Voltam- This allows voltammetric measurements in solutions of metric measurements without supporting electrolyte de- low conductivity, e.g. solutions without added support- parted significantly from the traditional way such ing electrolyte or simply solutions of low support ratio, measurements were performed. ‘Traditional’ voltamme- g, which is the ratio of the concentration of supporting try required an excess of electroinactive ions to make electrolyte to the concentration of the reactant. It the solution sufficiently conductive, to make a compact should be mentioned here that it is possible to have double layer, and to suppress migration of electroactive both a relatively high conductivity and a low support species. Electrode processes at microelectrodes are usu- ratio; this is the case with a very high concentration of ally associated with very low currents in the range of electroactive species. For neutral reactants, the use of nano- or picoamperes. Consequently, it might seem regular-size electrodes, with sizes in the range of mm, straightforward that even in solutions of very high was practically not possible in solutions of low ionic resistance, the ohmic IR drop is very low. However, strength. Consequently, some media that were not ac- there is one specific phenomenon which contributes to cessible for voltammetric studies are now open for measurements with microelectrodes. Eventually, the ex- * Corresponding author. Tel.: +1-718-951-5456; fax: +1-718-915- perimental interest in no supporting electrolyte voltam- 4607. metry triggered work on development of rigorous E-mail address: [email protected] (M. Ciszkowska) mathematical models. 0022-0728/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S0022-0728(99)00141-2 130 M. Ciszkowska, Z. Stojek / Journal of Electroanalytical Chemistry 466 (1999) 129–143 Measurements without supporting electrolyte were to obtain the total flux across the hemisphere of radius initiated already in the 1930s, in parallel to the growth r. This flux is not only invariant with time, but is also of polarography [1,2]. However, those basic studies uniform in space. were limited to ionic species. Instrumentation was poor, The transport dynamics of each species is described and insufficient attention was given to the presence of by the following equation: adventitious, unwanted ions in the solutions. (c ( 2c 2 (c There is a number of reviews on the characterization i −D i + i (t i (r 2 r (r and application of voltammetry with microelectrodes [3–14]. The recent intensive progress in the area of z F ( 2f (c (f 2c (f −D i c + i + i =0 voltammetry in low ionic strength media inspired us to i RT i (r 2 (r (r r (r present an overview of the current status and opportu- i=S, P, A or C (2) nities for electroanalytical techniques in media of low support ratio. The following aspects are selected and and this equation together with appropriate boundary discussed in this paper: mathematical treatment of conditions is used to calculate the transient currents, see transport, experimental setup, steady-state, non steady- for example Refs. [23–26]. state and convective voltammetry, migration coupled The first successful attempt to predict the current for with homogenous equilibrium, voltammetry in undi- the reduction of a cation (or the oxidation of an anion) luted liquid organic substances, studies on the mecha- in the absence of supporting electrolyte was presented nism of the electrode processes, studies in by Amatore et al. [15]. The authors used Eq. (2) in an polyelectrolytes and colloids, and analytical equivalent form for cylindrical diffusion, and by em- applications. ploying the Nernst layer approach and assuming the steady- or quasi steady-state conditions they obtained a solution, which was correct for all types of microelec- 2. Mathematical treatment of transport trodes. This was shown in their next paper [16], in which the mathematical solution was extended to all Under steady state conditions, a spherical diffusion simple electrode processes. The same year, using Eq. field is formed at the surface of disk- or spherical (1a), Oldham presented a more rigorous treatment, (hemispherical) microelectrodes. This and substantial including the analysis of the ohmic drop [17]. After mathematical simplifications are accountable for choos- assuming that the electroneutrality principle is obeyed, ing of the transport equations in spherical coordinates it can be shown that the total solute concentration ( ci) to model (in most theoretical treatments) migrational is uniform throughout the solution [15,17,18]. currents at microelectrodes. Consequently, before any Steady-state theoretical voltammograms can be also comparison with the theory, experimental steady-state obtained by using the chronopotentiometric approach currents for disk microelectrodes should be corrected and assembling the I–E pairs [27]. by a factor of p/2, while those obtained with hemi- If the electroneutrality principle is not obeyed (see spherical microelectrodes can be compared directly. the discussion in Section 2.1) then either Poisson’s The transport of species i is described by its flux, Ji, equation [28] according to the Nernst–Planck equation, which in the ( (f F % spherical coordinates can be written as: ( ( =−oo zjcj(r, t) (3) r r o j (c z F (f i i or the equivalent displacement current equation [29] Ji =−Di ( −Di ci ( i=S, P, A or C (1) r RT r must be used to treat the electrical migration problems. where S denotes the substrate, P denotes the product, Generally, to solve any system of equations that con- and A and C refer to the anion and the cation of tains Eq. (2) and possibly Eq. (3) one should turn to digital simulation. Successful implementation of various supporting electrolyte, respectively. Di, ci and zi are the diffusion coefficient, concentration, and the charge of digital simulation methods can be found for example in ith species, respectively. f is the electrostatic potential Refs. [24,28,29]. (See also the references in Sections 5.1, in the solution, and R, T, and F have their usual 5.2 and 7.) meanings. Eq. (1) was used to model systems under steady- and non-steady state conditions [15–22]. As 2.1. Electroneutrality was shown by Oldham [17,18], it is convenient to transform Eq. (1) to the following form: It is usually assumed that the electroneutrality princi- ple is obeyed at any point in the solution (c z =0). J (c z F (f i i i i i c (1a) Norton et al. [28] have shown that this principle does p = + i 2 Di ( 1 RT ( 1 not hold when the depletion layer is entirely or in a r r significant part included in the double layer. On the M. Ciszkowska, Z. Stojek / Journal of Electroanalytical Chemistry 466 (1999) 129–143 131 basis of their data, one can make the following conclu- cannot be used for estimation of the ohmic drop. Eq. sions. The depletion layer thickness can be estimated as (4a) presents how, for example, the cell steady state 10r0, where r0 is the electrode radius, and the thickness resistance, RSS, changes with current, I, for the oxida- of the double layer is ca. 5k−1, where k−1 is the tion of an uncharged substrate, S, under the conditions k−1 oo o 2 2 1/2 Debye–Hu¨ckel length, =( okT/2c z e 0) , where of deficiency of supporting electrolyte [17]. o is the bulk z:z electrolyte concentration. For a c RT D c bI m univalent electrolyte in aqueous solution, the approxi- R = ln 1+ S S (4a) SS IF 2D c b I mate k−1 values are 10 nm, 100 nm and 1 mm for P C l −3 −5 −7 concentrations of 10 ,10 and 10 M, respec- where Il is a limiting current, P is product of the tively. This thickness will diminish significantly if the electrode reaction and C is a counterion. The ohmic electrode potential departs from the potential of zero drop during electrolysis with an excess supporting elec- charge by more than 0.02 V. For the usual sizes of trolyte is a function only of the flowing current. m microelectrodes (r0 larger than 1 m), and the concen- Before steady-state is reached, for a low concentra- tration of electrolyte not lower than 10−6 M, the tion of electrolyte, both current and resistance change double layer thickness becomes insignificant compared with time.