Deactivation of poly(o-aminophenol) film electrodes by storage without use in the supporting electrolyte solution and its comparison with other deactivation processes. A study employing EIS

Abstract

The effect of storage time without use (STWU) in the supporting electrolyte solution on the charge-transport parameters of poly(o-aminophenol) (POAP) film electrodes was studied by electrochemical impedance spectroscopy. STWU decreases the charge-transport rate of the polymer. This effect is herein called deactivation. Impedance diagrams of both nondeactivated and deactivated films in contact with a solution containing the p-benzoquinone/hydroquinone redox couple were interpreted on the basis of a model formulated for homogeneous conducting polymers, where the bathing electrolyte contains a redox pair that provides the possibility for electrons to leak from the film surface. Dependences of diffusion coefficients for electron (D _e) and ion (D _i) transport and interfacial resistances related to ion $\left( {R_{\text{i}}^{{{\text{f}}|{\text{s}}}} } \right)$ and electron $\left( {R_{{{\text{m}}|{\text{f}}}} ,R_{\text{e}}^{{{\text{f}}|{\text{s}}}} } \right)$ transfer across the polymer/solution and metal/polymer interfaces, respectively, on the degree of deactivation (θ _d) of the polymer were obtained. These dependences were compared with those from previous work for POAP films deactivated by employing other procedures, such as high positive potential limits, soaking in a ferric ion solution, and prolonged potential cycling.

Appendix: interpretation of ac impedance diagrams

A particular interpretation of impedance data is based on the choice of a certain equivalent electrical circuit as a model for the system under study or by introducing a number of additional elements corresponding to peculiar features of the impedance spectra into the available circuits. However, a correct microscopic formulation of the problem of a modified electrode impedance and its solution for homogeneous conducting polymer films has been reported by Vorotyntsev in [28] and then, extended to the case where the bathing electrolyte contains a redox pair that provides the possibility for the electron to leak from the film surface [21, 29]. The general theory of Vorotyntsev et al. considers diffusion-migration transport of electrons and ions as mobile charge carriers in a uniform medium, coupled with a possibly nonequilibrium charge transfer across the corresponding interfaces at the boundary of the film [30]. “Essentially, the approach is based on the formulae of the multicomponent diffusion” [31] relating the electrochemical potential gradients of flux components. Standard Nernst–Planck–Einstein expressions are used for flux densities of both species (electrons and ions) taking account of both diffusion and migration transport mechanisms. On the basis of the experimental arrangement used in this work, i.e., a gold disk electrode of low surface roughness (high specularity) after deposition by evaporation of a thin gold film coated with a thick POAP film [19], the system could be considered as a good enough approximation to a uniform polymer layer deposited on a smooth electrode surface to apply a homogeneous electrochemical impedance model in the interpretation of experimental ac impedance diagrams. Then, the microscopic formulation of ac impedance of a modified electrode described by Vorotyntsev et al. in [21] was employed in this work to interpret impedance data of nondeactivated and deactivated POAP films. It should be remarked that the theory developed in [21] is strictly valid when the charging of interfacial double layers is negligible, i.e., it does not account for the charging of the film/substrate and film/solution layers in parallel with the injection processes of charge carriers. If this is not the case, a more complete model, such as the one developed by Vorotyntsev in [28], should be used. In this model [28], besides the traditional “double-layer” capacitance and interfacial charge-transfer resistances, two additional parameters for each boundary, “interfacial numbers” for each species and “asymmetry factors,” are introduced. Although we also fitted our experimental impedance diagrams with the model reported in [28], the fitting did not result much more precise than that using the model given in [21], and furthermore, the increasing mathematical difficulty of determining the numerous parameters of the model given in [28] from experimental data was a major drawback. Then, despite this last theoretical limitation, the model described in [21] concerning a uniform and nonporous film and no penetration of redox species from the solution was employed to interpret our experimental impedance diagrams.

As in the present case, one has the modified electrode geometry with a redox active electrolyte solution (m/film/es), Eq. (2) [21] must be applied.

$$Z_{{{\text{m}}\left| {\text{film}} \right|{\text{es}}}} = R_{\text{m|f}} + R_{\text{f}} + R_{\text{s}} + \, \left[ {Z_{\text{e}}^{{^{\text{f|s}} }} R_{\text{i}}^{\text{f|s}} + W_{\text{f}} Z_{12}^{\text{m}} } \right] \, \left( {Z_{\text{e}}^{f|s} + R_{{_{i} }}^{f|s} + \, 2W_{\text{f}} \coth \, 2\nu } \right)^{ - 1} ,$$

(2)

where

$$Z_{12}^{\text{m}} = Z_{\text{e}}^{{^{{{\text{f}}|{\text{s}}}} }} \left[ {{ \coth }\nu + \, \left( {t_{\text{e}} - t_{\text{i}} } \right)^{ 2} { \tanh }\nu } \right] + R_{{_{\text{i}} }}^{{{\text{f}}|{\text{s}}}} 4t_{\text{i}}^{ 2} { \tanh }\nu + W_{\text{f}} 4t_{\text{i}}^{2} .$$

(3)

In Eqs. (2) and (3), $\nu = \left[ {{{\left( {j\omega \phi_{\text{p}}^{ 2} } \right)} \mathord{\left/ {\vphantom {{\left( {j\omega \phi_{\text{p}}^{ 2} } \right)} { 4D}}} \right. \kern-0pt} { 4D}}} \right]^{ 1/ 2}$ is a dimensionless function of the frequency ω, ϕ _p is the film thickness, D is the binary electron–ion diffusion coefficient, and t _i and t _e are the migration (high frequency) bulk-film transference numbers for anions and electrons, respectively. D is defined as D = 2D _i D _e (D _e + D _i)⁻¹ and t _i,e = D _i,e (D _e + D _i)⁻¹, where D _e and D _i are the diffusion coefficients for the electrons and ion species, respectively.

$W_{\text{f}} = \left[ {{\nu \mathord{\left/ {\vphantom {\nu {j\omega \phi_{\text{p}} C_{\text{p}} }}} \right. \kern-0pt} {j\omega \phi_{\text{p}} C_{\text{p}} }}} \right] = \Delta {{R_{\text{f}} } \mathord{\left/ {\vphantom {{R_{\text{f}} } \nu }} \right. \kern-0pt} \nu }$ is a Warburg impedance for the electron–ion transport inside the polymer film. $\Delta R_{\text{f}} \left( {{{ = \phi_{\text{p}} } \mathord{\left/ {\vphantom {{ = \phi_{\text{p}} } { 4DC_{\text{p}} }}} \right. \kern-0pt} { 4DC_{\text{p}} }}} \right)$ is the amplitude of the Warburg impedance inside the film, and C _p is the redox capacitance per unit volume.

R _f (= ϕ _p/κ) is the high-frequency bulk-film resistance, R _s is the ohmic resistance of the bulk solution (κ is the high-frequency bulk conductivity of the film), R _m|f is the metal/film interfacial electron-transfer resistance, and $R_{\text{i}}^{{{\text{f}}|{\text{s}}}}$ is the film/solution interfacial ion-transfer resistance.

$Z_{\text{e}}^{{^{{{\text{f}}|{\text{s}}}} }} = \, \left( {R_{\text{e}}^{{{\text{f}}|{\text{s}}}} + W_{\text{s}} } \right)$ is the electronic impedance, where $R_{\text{e}}^{{{\text{f}}|{\text{s}}}}$ is the interfacial electron-transfer resistance at the film/solution interface, and W _s is the convective diffusion impedance of redox species in solution, which contains the bulk concentrations of ox(red) forms, c _ox(c _red), and their diffusion coefficients inside the solution, D _ox(D _red). Also, it contains the Nernst layer thickness, δ.

$R_{\text{e}}^{{{\text{f}}|{\text{s}}}}$ is defined as

$$R_{\text{e}}^{{{\text{f}}|{\text{s}}}} = RT\left( {nF^{ 2} k \, c_{\text{red}} } \right)^{ - 1} ,$$

(4)

where k is the rate constant of the reaction between the film and the redox active forms in solution. The diffusion of the redox forms from the bulk solution to the film/solution interface can be regarded as stationary through the diffusion layer thickness, expressed in cm by

$$\delta = { 4}. 9 8D_{{{\text{ox}},{\text{red}}}}^{ 1/ 3} \eta^{ 1/ 6} \varOmega^{ - 1/ 2} ,$$

(5)

where η is the kinematic viscosity of the solution in the same units as D _ox,red, and Ω the rotation rate of the disk electrode in rpm. The rest of the constants have their usual meaning. This model also includes the impedance behavior of the polymer contacting the inactive electrolyte (absence of the redox couple in solution) by considering $Z_{\text{e}}^{{^{{{\text{f}}|{\text{s}}}} }} \to \infty$ in Eq. (2).

A rigorous fitting procedure was performed employing Eq. (2). Six replicate measurements for each degree of deactivation were carried out, and the error structure was assessed following the method recommended by Agarwal et al. [32] and Orazem [33]. The standard deviation for the real (σ _Zr) and imaginary (σ _Zj) parts of the impedance followed the form proposed by Orazem (see Eq. (8) of Ref. [33]).

$$\sigma_{\text{Zr}} = \sigma_{\text{Zj}} = \left. \alpha \right|\left. {Zj} \right| + \left. \beta \right|\left. {Zr} \right| + \left. \gamma \right|\left. Z \right|^{2} Rm^{ - 1} + \delta ,$$

(6)

where Rm is the current measuring resistor used for the experiment, Zr is the real part of the impedance, and Zj is the imaginary part of the impedance. α, β, γ, and δ are constants that have to be determined. The values of these scaling factors were α = 0, β = 4.22 × 10⁻³ ± 0.005 × 10⁻³, γ = 2.5 × 10⁻⁵ ± 0.1 × 10⁻⁵, and δ = 4.8 × 10⁻³ ± 0.3 × 10⁻³. The error structure was found to follow the same model within the range of the degree of deactivation 0.05 < θ _c < 0.77. At θ _c values lower than 0.05, the error structure model parameters had different values, but these results are not reported here. Then, solid lines in Figs. 1, 2, 3 and point representation in Fig. 4 represent the weighted complex nonlinear least squares fit to the data. The regression was weighted by the inverse of the variance of the stochastic part of the measurement. Under all conditions, the weighted sum of the square of residuals was below one [33].