Iterative Absolute Electroanalytical Approach to Characterization of Bulk Redox Conducting Systems

Abstract

A novel electroanalytical approach is proposed here, and it is demonstrated with the direct and simultaneous determination of two unknowns: the concentration of redox sites and the apparent diffusion coefficient for charge propagation in a single crystal of dodecatungstophosphoric acid. This Keggin-type polyoxometalate serves as a model bulk redox conducting inorganic material for solid-state voltammetry. The system has been investigated using an ultramicrodisk working electrode in the absence of external liquid supporting electrolyte. The analytical method requires numerical solution of the combination of two equations in which the first one describes current (or charge) in a well-defined (either spherical or linear) diffusional regime and the second general equation describes chronoamperometric (or normal pulse voltammetric current) under mixed (linear-spherical) conditions. The iterative approach is based on successive approximations through calculation and minimizing the least-squares error function. The method is fairly universal, and in principle, it can be extended to the investigation of other bulk systems including sol-gel processed materials, redox melts, and solutions on condition that they are electroactive and well behaved, they contain redox centers at sufficiently high level, and a number of electrons for the redox reaction considered is known.

Solid-state electrochemical behavior of Keggin-type borotungstic acid single crystal

“…Structure analysis of the α-[BW 12 O 40 ] 5− Keggin anion reveals a central, regular {BO4} unit, in agreement with 11B solid-state NMR data [42][43][44]. According to our previous work [25,26,45], application of electroanalytical approaches allow us to determine both the concentration (C 0 ) of redox centers and the apparent diffusion coefficient (D app ) for a single crystal of silicotungstic, phosphotungstic acids, or Prussian Blue in a sol-gel matrix, by solving a system of two equations with two unknowns (D app and C 0 ). Moreover, the obtained apparent diffusion coefficients were compared with the values of the real diffusion coefficient (transport coefficient free of migration influence) calculated by using the analysis of transient currents in the double potential step chronoamperometric experiment (DPSC) [46,47].…”

“…Similar electrochemical behavior was described when these compounds were introduced into organic polymers or a silica matrix [6,23,24,[37][38][39][40][41]. Kulesza et al [21,22,25] studied solid-state electrochemistry of these heteropolyacids and showed that the electrochemical behavior of both acids was almost the same as the behavior observed in solutions, namely: well-separated and reversible reduction peaks. Moreover, by combining various electroanalytical techniques, they found that these single crystals are characterized by high effective diffusion coefficients and large concentrations of mixed-valence redox centers (W or Mo) [21,36].…”

“…On the basis of two appropriately different scan rates of 50 Vs −1 and 4 mVs −1 (short-time and long-time regimes), a system of two equations with two variables (the concentration of redox sites and the transport coefficient) were obtained for the results shown in Fig. 4 [22,25]. Consequently, this allowed us to estimate both parameters: C o and D app .…”

“…Moreover, to minimize such parameters as ohmic resistance and migration effect, the concentration of charged species, like mobile ions and electrons, should be fairly large in the system. Examples of the mixed-valence inorganic bulk redox systems utilized in solid-state voltammetry are Keggin-type polyoxometalates (POMs), such as heteropolyacids of tungsten or molybdenum [21][22][23][24][25][26]. Generally, Keggin-type polyoxometalates have a central XO 4 (X = B, Si, Ge, P, As) tetrahedron surrounded by 12 MO 6 octahedrons arranged in four groups of three-octahedral subunits, M 3 O 13 .…”

“…POMs have been studied as monolayers or organic-inorganic hybrids in contact with different supporting electrolytes [34,35], and as single crystals in the absence of external liquid phase [21][22][23][24][25][26]. The electrochemical analysis of the most popular Keggin-type POMs (phosphotungstate and tungstosilicate) in the presence of acidic solution revealed three reversible reduction peaks originating from two one-electron processes followed by one two-electron process [17,21,22,36].…”