Kinetic and Mechanistic Aspects of a Poly(o-Toluidine) - American

Article pubs.acs.org/JPCC

Kinetic and Mechanistic Aspects of a Poly(o-Toluidine)-Modified Gold Electrode. 2. Alternating Current Electrogravimetry Study in H2SO4 Solutions J. Agrisuelas,*,†,§ C. Gabrielli,†,‡ J. J. García-Jareño,§ H. Perrot,†,‡ and F. Vicente§ †

Laboratoire Interfaces et Systèmes Electrochimiques (LISE), UPR 15 du CNRS, Centre National de la Recherche Scientifique (CNRS), 4 place Jussieu, 75005 Paris, France ‡ LISE, Université Pierre et Marie CurieParis 6 (UPMC), 4 place Jussieu, 75005 Paris, France § Departament de Química Física, Universitat de València, C/Dr. Moliner 50, 46100 Burjassot, València, Spain ABSTRACT: Electrodeposited poly(o-toluidine) (POT) on gold electrodes was investigated in 0.5 M H2SO4 aqueous solutions using alternating current electrogravimetry (simultaneous electrochemical impedance and mass transfer functions). The kinetic aspects of the three different redox transitions proposed for this polymer (leucoemeraldine− polaron transition, polaron−bipolaron transition, and bipolaron−pernigraniline transition) and the species involved, cation (hydrated proton), anion (bisulfate ion), and free solvent (water), are studied by means of the mass impedance technique. An ionic transfer model is proposed with coherent results where anion transfer is the fastest process and hydrated proton transfer is the slowest process (Grotthuss mechanism). The flux and counterflux of water molecules due to the conformational structure changes of the polymer and exclusion effect governed by the anion transfer are also discussed. polymers,11−14 and actually, they are improving this technique in the high-frequency mass transfer responses.15 By comparison with cyclic electrogravimetry, ac electrogravimetry integrates the mass response associated with the current response and the possibility to change the frequency of modulation. This possibility allows the different involved processes to be distinguished by their relative characteristic time constants. ac electrogravimetry has been clearly shown to be a powerful technique which does not have the limitation of cyclic electrogravimetry.16 Among ICPs, poly(o-toluidine) (POT) is one of the most studied polymers.17−25 In part 1 of this series (preceding paper in this issue),26 a general scheme with three different redox reaction steps was proposed for the global leucoemeraldine (LE)−pernigraniline (PN) transition observed during a potential scan (vs Ag|AgCl|KClsatd reference electrode) in 0.5 M H2SO4 solution at 100 mV s−1 thanks to a deep analysis of both cyclic electrogravimetry and visible−near-infrared spectroscopy results. During this transition, POT was shown to have two different intermediate forms, the polaron form (P) and bipolaron form (BP), which are considered as single entities with individual properties and characteristics:

1. INTRODUCTION The physicochemical properties of intrinsically conducting polymers (ICPs) are directly related to the oxidation state of their active sites, which can be controlled by electrochemical modulation. During this perturbation, electron transfer between the electrode and the polymer, electron or ion transport in the polymer, and ion, as well as solvent molecule, transfer between the solution and the polymer may occur. The apparent kinetic descriptions of a polymer/electrode system are controlled by the slowest of these processes related to the charge compensation mechanism and require also the knowledge of the polymer reconfiguration. For many years, the electrochemical processes of this kind of polymer have been studied by means of classical electrochemical techniques.1−3 In the past 10 years, a new technique was developed:4−10 alternating current (ac) electrogravimetry. This technique couples electrochemical impedance spectroscopy (EIS) with mass impedance spectroscopy (MIS) using a fast electrochemical quartz crystal microbalance (EQCM) which provides simultaneously the electrochemical impedance, ΔE/ ΔI(ω), and a mass/potential transfer function, Δm/ΔE(ω). The originality of this technique is its ability to discriminate between cation and anion transfers involved in the charge compensation process and the participation of uncharged molecules of solvent to satisfy activity constraints. Gabrielli et al. have already explained in detail the theory of the ac electrogravimetry technique for characterizing electroactive © 2012 American Chemical Society

Received: April 21, 2012 Revised: June 6, 2012 Published: June 12, 2012 15630

dx.doi.org/10.1021/jp303859m | J. Phys. Chem. C 2012, 116, 15630−15640

The Journal of Physical Chemistry C LE + x1HSO4 − ⇄ P + x1e− + 2x1H 2O

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fast enough. The equation describing the insertion/expulsion law characterizing the species i transfer is

at (1)

E°′ ≈ +0.240V P + x 2 HSO4 − ⇄ BP + x 2e− + 4x 2 H 2O

ΔCi −Gi (ω) = ΔE jωdf + K i

at (2)

E°′ ≈ +0.430V

BP ⇄ PN + x3e− + x3H3O+

at

E°′ ≈ + 0.520V

where i is related to an anion (a), a cation (c), or the free solvent (s), Ci is the concentration of species i in the polymer, j = √−1, ω is the pulsation equal to 2πf, where f is the perturbation frequency, and df is the polymer film thickness. Gi and Ki are the partial derivatives of the flux of species i crossing the polymer/solution interface during the potential perturbation, ΔJi, with respect to the concentration and potential, respectively:

(3)

where xi represents the amount of sites inside the polymer where molecular species could be inserted or expulsed during redox reaction step 1, or eq 1, redox reaction step 2, or eq 2, and redox reaction step 3, or eq 3, and LE = ⟨POT, x3H3O+, (4x2 + 2x1)H2O⟩, P = ⟨POT, x3H3O+, 4x2H2O, x1HSO4−⟩, BP = ⟨POT, x3H3O+, (x2 + x1)HSO4−⟩, and PN = ⟨POT, (x2 + x1)HSO4−⟩. Thus, the aim of this work was to delve into the kinetic aspects of the POT response during the electrochemical modulation in aqueous acidic solution (0.5 M H2SO4). ac electrogravimetry was used to complete the results discussed in part 1, where these three reaction steps were proposed.

2. AC ELECTROGRAVIMETRY THEORY To compensate the electron charge which enters or leave the polymer, ions have to enter or leave it. These ions can be inserted in one or several types of sites. 2.1. Model of Anion and Cation Insertion in Independent Sites. The doping mechanism of an electroactive film polymerized on a working electrode can be described by the following equations related to anion and cation insertion (expulsion) to (from) the electroactive film during the electrochemical reactions:

−

where ⟨P⟩ is the host electroactive polymer and ⟨P , nA ⟩ and ⟨Pn−, nC+⟩ are the polymers doped with anions and cations (Figure 1). In ac electrogravimetry, the ion exchange n+

(8)

(9)

where Ci,sol is the concentration of species i in the solution, Ci,max is the maximum concentration of the sites available for the insertion in the polymer, C i,min is the minimum concentration of the sites occupied, and ki and ki′ are the kinetic rate constants of transfers which are potential dependent (ki = ki00 exp[bi(E − E°′)] and ki′ = ki00 exp[bi′(E − E°′)], E°′ being the formal potential and bi and bi′ the Tafel coefficients related to the number of electrons involved in the faradic process.14,27 On the basis of this model and according to eq 6, the theoretical electrochemical impedance, ΔE/ΔI(ω), is obtained:

(5)

kc

⎛ ∂J ⎞ K i = ⎜ i ⎟ = ki + ki′Ci,sol ⎝ ∂Ci ⎠ E

= −biki(Ci − Ci ,min) + bi′ki′(Ci ,max − Ci)Ci ,sol

kc ′

⟨P⟩ + ne− + nC+ ⇄ ⟨Pn −, nC+⟩

(7)

i

(4)

ka ′

ΔJi = −jωdf ΔCi = K iΔCi + GiΔE

⎛ ∂J ⎞ Gi = ⎜ i ⎟ ⎝ ∂E ⎠C

ka

⟨Pn + , n A−⟩ + ne− ⇄ ⟨P⟩ + n A−

(6)

ΔE (ω) = ΔI Ru +

1 ⎡ G ⎤ jωCdl + jωAdf F ∑i = a,c zi⎢⎣ jωd +i K ⎥⎦ + f i

1 Rp +

1 jωC p

(10)

where Ru is the uncompensated solution resistance, Cdl is the polymer/solution double layer capacity, zi is the valence of ion i, F is the Faraday constant, and A is the electrode area. In some cases, an Rp, Cp series circuit has to be taken into account when a parallel reaction occurs on the polymer film surface without changing the mass (e.g., hydrogen evolution or oxygen reduction). Another transfer function can be calculated by subtracting the nonfaradic contributions to obtain complementary information, the electrical charge/potential transfer function, Δq/ΔE(ω), which gives the number of different charged species participating in the electrochemical processes:

Figure 1. Scheme of the electrode/polymer/solution-modified electrode where df is the polymer film thickness and A− and C+ are the anions and cations involved in the charge balance, respectively.

phenomena are modified when a small sine wave potential perturbation, ΔE, is applied. In this approach, previously justified for very thin films,11,7 only the ionic and free solvent transfers at the polymer/solution interface are taken into account as rate-limiting steps since the ionic and solvent transports inside the film and in the solution are supposed to be

Δq 1 (ω) = jω ΔE

1 ΔE (ω) ΔI

− Ru

− Cdl (11)

By using eqs 6 and 10, this theoretical transfer function is equal to 15631


The Journal of Physical Chemistry C Δq (ω) = AFdf ΔE

∑ zi i = a,c

Gi 1 + jωdf + K i jωR p +

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G1 = −b1k1(C1 − C1,min) + b1′k1′(C1,max − C1)C A−,sol 1 Cp

(22)

(12)

G2 = −b2k 2(C2 − C2,min) + b2′k 2′(C 2,max − C 2)C A−,sol

Finally, the mass/potential transfer function, Δm/ΔE(ω), is easily deduced from eq 6: Δm (ω) = Adf ΔE

∑ i = a,c,s

δimi

Gi jωdf + K i

(23)

At steady state dCi/dt = 0, for i = 1 and 2, so G1 = (b1′ − b1)(C1,max − C1,min)

(13)

where mi is the molar mass of the charged or neutral species involved in the electrochemical process and δi only reaches values of +1 or −1. δa = +1 indicates that the mass decreases (increases) if the polymer is reduced (oxidized); therefore, the anion is the counterion involved in such an electrochemical process. In this case, eq 13 describes a loop in the first quadrant (upper right quadrant of a complex x−y plot). On the contrary, if a cation exchange takes place, δc = −1 and the mass impedance spectrum appears in the third quadrant (bottom left quadrant of a complex x−y plot).8,11 2.2. Model of an Ionic Insertion in Two Structurally Different Sites. An ion is supposed to be inserted in the polymer by means of two different processes which occur at formal potentials E1°′ and E2°′ in two different structural configurations of the polymer. Process 1 inserts the ions in concentration C1 in structure 1, and process 2 inserts the ions in concentration C2 in structure 2 of the same polymer. In the case of anions A− k1′

+

−

−

k2

k1 + k1′C A−,sol

(24)

and G2 = (b2′ − b2)(C2,max − C2,min)

k 2k 2′C A−,sol k 2 + k 2′C A−,sol

(25)

If the Tafel coefficients are taken equal to b1 = (1 − β1) b1′ = −β1

n1′F RT

n1′F RT

and

and

b2 = (1 − β2)

b2′ = −β2

n2′F RT

n2′F RT

(26)

(27)

where β represents the charge transfer coefficient and n′ the apparent number of electrons involved in the electrochemical reaction, the kinetic parameters are n′F (E − Ei°′) RT ⎛ n′F ⎞ ⎟(E − E °′) = ki2 exp⎜ −βi i ⎝ RT ⎠

ki = ki1exp(1 − βi )

k1

⟨P1+ , A−⟩ + e− ⇄ ⟨P⟩ + A− at potential E1°′

k1k1′C A−,sol

(14)

(28)

Then −

⟨P2 , A ⟩ + e ⇄ ⟨P⟩ + A at potential E2°′ k 2′

b1′ − b1 = b2′ − b2 n′F at 298 K is about −40 V −1 for n′ =− RT

(15)

The insertions of anions are distinguished because they have different kinetics of insertion as they are inserted in different environments in the polymer, ⟨P1+, A−⟩ and ⟨P2+, A−⟩. In this way, the changes of the concentrations of the anions over time, which are inserted in ⟨P⟩ at the polymer/solution interface to counterbalance the current density j(t) of the electrons which cross the electrode/polymer interface to maintain electroneutrality, are equal to dC1 = −k1(C1 − C1,min) + k1′(C1,max − C1)C A−,sol dt

(16)

dC 2 = −k 2(C2 − C2,min) + k 2′(C2,max − C2)C A−,sol dt

(17)

(29) =1 From eq 6 and then, by adding eqs 18 and 19, the change of the total concentration C of the ions is equal to

jωdf ΔC = jωdf (ΔC1 + ΔC2) = −K1ΔC1 − K 2ΔC2 − (G1 + G2)ΔE

as ΔC = ΔC1 + ΔC2

(18)

jωdf ΔC2 = −K 2ΔC2 − G2ΔE

(19)

jωdf ΔC = −K1ΔC1 − K 2(ΔC − ΔC1) − (G1 + G2)ΔE (32)

jωdf ΔC = −K1

(20)

K 2 = k 2 + k 2′C A−,sol

(21)

⎛ −G1 −G1 ⎞ − K 2⎜ΔC − ⎟ jωdf + K1 jωdf + K1 ⎠ ⎝

− (G1 + G2)ΔE

(33)

Finally, the total change of concentration of the inserted anions is equal to K G − K 2G1 − (G1 + G2)(jωdf + K1) ΔC (ω) = 1 1 ΔE (jωdf + K1)(jωdf + K 2)

where K1 = k1 + k1′C A−,sol

(31)

so

where Ci,max and Ci,min are the maximum and minimum concentrations of the sites of insertion in the polymer in sites i = 1 and i = 2. Thus, a total concentration C = C1 + C2 of the anions is globally inserted in the polymer. For a small potential perturbation ΔE, in the frequency domain the changes of the concentrations C1 and C2 using eq 7 are jωdf ΔC1 = −K1ΔC1 − G1ΔE

(30)

(34)

As an example, a simulated diagram of (ΔC/ΔE)(ω) is plotted in the complex plane in Figure 2 considering E1°′ = 0 V and E2°′ = 0.4 V (β1 = 0.1, β2 = 0.7, k01 = 1 cm s−1, k02 = 0.07 15632


The Journal of Physical Chemistry C

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Figure 4. K(E) simulation with the parameters of Figure 2 at each potential.

Figure 2. Simulation in the complex plane of (ΔC/ΔE)(ω), eq 34, with β1 = 0.1, β2 = 0.7, k01 = 1 cm s−1, k02 = 0.07 cm s−1, C1,max − C1,min = 1 mol cm−3, C2,max − C2,min = 0.6 mol cm−3, CA−,sol = 1 mol cm−3, and df = 50 nm at E = 0.1 V.

When K(E) is graphically evaluated, by using the value of G/ K(E) obtained from eq 35, it is easy to calculate the value of G(E) (Figure 5). It is remarkable that G(E) has only one preponderant peak located in the E1°′ − E2°′ potential range.

cm s−1 C1,max − C1,min = 1 mol cm−3, C2,max − C2,min = 0.6 mol cm−3, CA−,sol = 1 mol cm−3, and df =50 nm at E = 0.1 V). In spite of considering two different transfers, the diagrams are close to a single semicircle whatever the observed potential. Consequently, the low-frequency limit, (ΔC/ΔE)(0), is a good evaluation of −G/K for each anion transfer: K G − K 2G1 − (G1 + G2)K1 G G ΔC (0) = 1 1 =− 1 − 2 ΔE K1K 2 K1 K2 (35)

where G1 = (b1 − b1′)(C1,max − C1,min) K1

(

exp −

n1 ′ F (E RT

(1 + exp(−

− E1°′)

n1 ′ F (E RT

)

Figure 5. G(E) obtained from Figure 4 with the parameters of Figure 2 at each potential.

2

− E1°′)

))

(36)

Here, when two different sites of insertion are considered for the same kind of ion, K(E) also shows only one peak in the middle of E1°′ and E2°′. On the contrary, the values of K(E) show a minimum for the formal potential when only one sort of site is considered, as expected for a sum of exponential functions. It is clear that the simulation depends on the values used in the parameters, but this example was chosen because it is very similar to the experimental results found in this work.

The same type of expression can be established for process 2. Therefore, G/K(E) shows two peaks at the formal potentials E01′ and E02′ as is plotted in Figure 3 (in this simulation they are well separated).

3. EXPERIMENTAL SECTION The electrochemical polymer deposition and characterization were controlled by cyclic voltammetry (CV) through an AUTOLAB potentiostat−galvanostat (PGSTAT302). The three-electrode cell involved a KCl reference electrode (saturated calomel electrode, or SCE, Tacussel XR 600) and a platinum counter electrode. The working electrode was a gold electrode patterned on a 9 MHz AT-cut quartz crystal resonator (TEMEX, France). The potential of the working electrode is always referred to that for the reference electrode. All solutions were freshly prepared with deionized and doubledistilled water. The polymerization procedure is described in part 1 of this series.26 ac electrogravimetry experiments of the POT-modified electrode were performed in 0.5 M H2SO4 from 0.55 to 0.1 V vs SCE at decreasing potentials. The solution characterization allows the protonated forms of POT to be assumed.26 For this purpose, a laboratory-made oscillator acted as a microbalance

Figure 3. G/K(0) simulation with the parameters of Figure 2.

To determine G and K separately, it should be necessary to estimate the characteristic frequency which is correlated to K(E) (this frequency is represented by a times sign on the semicircle diagram in Figure 2). Therefore, we have chosen to plot the diagrams at each potential and to determine graphically the characteristic frequency (Figure 4). 15633



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coupled with a four-channel frequency response analyzer (FRA, Solartron 1254) and a potentiostat (SOTELEM-PGSTAT Z1). The EQCM was used in the dynamic regime; the modified working electrode was polarized at a selected potential, and a sinusoidal small amplitude potential perturbation (10 mV rms) was superimposed. The microbalance frequency change, Δf m, corresponding to the mass response, Δm, of the modified working electrode, was measured simultaneously with the alternating current response, ΔI, of the electrochemical system through a frequency/voltage converter. The resulting signals were sent to the FRA, which allowed the electrogravimetric transfer function, Δm/ΔE(ω), and the electrochemical impedance, ΔE/ΔI(ω), to be simultaneously obtained at a given polarization potential. The experimental data were fitted to the theoretical functions by means of an optimized version of the Levenberg−Marquardt method for minimizing the residual sum of squared errors by means of Mathcad.

4. RESULTS AND DISCUSSION In this work, the thickness of the polymer was not estimated to avoid possible errors since df may change depending on the polarization potential as demonstrated in other permselective polymers.16,28−30 Therefore, the concentration of species inside the polymer must be expressed in terms of surface concentration considering only a bidimensional surface. Therefore, eq 6 is rewritten as df

ΔCi ΔΓi −Gi −Gi (ω) = (ω) = = ΔE ΔE jω + K i / d f jω + K i′

Figure 6. (a) Charge/potential transfer function, Δq/ΔE(ω), and (b) electrogravimetric transfer function, Δm/ΔE(ω), at E = 0.5 V and E = 0.15 V vs SCE in 0.5 M H2SO4. The continuous lines are the theoretical curves calculated from Δq/ΔE(ω), eq 38, and Δm/ΔE(ω), eq 39.

(37)

where Ki/df is a new apparent kinetic parameter, Ki′. Figure 6 shows examples of the two experimental transfer functions, Δq/ΔE(ω) and Δm/ΔE(ω), at two representative potentials, E = 0.15 V and E = 0.5 V. In the same graphs, the theoretical curves obtained by fitting are also represented using the theoretical transfer functions given in eqs 12 and 13 involving eq 37:

Table 1. Values of the Parameters Rp and Cp for the Parallel Reaction Obtained for the Fitting of the Experimental Data with Eq 38

⎛ ⎞ G H3O+ G HSO4− Δq ⎟ (ω) = F ⎜⎜ + − αH O+ (jω)αHSO4 + K HSO4−′ ⎟⎠ ΔE ⎝ (jω) 3 + K H3O+′ 1 + 1 jωR p + C p

(38)

(δ H2Om H2O)G H2O (jω)αH2O + K H2O′

Rp (Ω cm2)

Cp (mF cm−2)

0.25 0.20 0.15 0.10

12213 7176 5474 5501

4 11 28 20

place. This indicates the insertion of an anion when POT is oxidized. In agreement with cyclic electrogravimetry,26 the hydrated proton participation is negligible at this potential since Δm/ΔE(ω) does not have a loop in the second or third quadrant. At the polarization potential of 0.5 V, the Δq/ΔE(ω) transfer function is only related to hydrated proton transfer, and in this case, the bisulfate ion transfer is negligible. The Δm/ ΔE(ω) transfer function shows a loop in the third quadrant owing to an increase (decrease) of mass on the electrode during the reduction (oxidation) process. Between 0.1 and 0.45 V, the transfer of anions is taken into account, while the flux of hydrated protons when POT is reduced takes place from 0.3 to 0.55 V. In the whole range of potentials, the Δq/ΔE(ω) transfer function can be well fitted considering a fast transfer for anions and a slow transfer of the hydrated protons where the transfer function has six free parameters (Figure 6a). This mechanism has already been observed in other similar polymers.31 Anion transfer should be mainly involved in the charge balance as counterion and proton transfer could be governed by a Grotthuss mechanism where the transfer is achieved through

(δ H3O+m H3O+)G H3O+ (δ HSO4−m HSO4−)G HSO4− Δm (ω) = + − αH3O+ (jω) (jω)αHSO4 + K HSO4−′ ΔE + K H3O+′ +

E (V vs SCE)

(39)

At the polarization potential of 0.15 V, the Δq/ΔE(ω) transfer function shows a quasi-vertical branch in the low frequency range which demonstrates the occurrence of a concomitant parallel reaction p. Between 0.25 and 0.1 V, the parallel reaction must be taken into account since it contributes to the charge transfer process. Taking advantage of the fitting procedure, the characteristics values of the capacitance, Cp, and the resistance, Rp, can be found. Rp decreases when the applied potential is more cathodic (Table 1), which indicates that it is a cathodic reaction. The Δm/ΔE(ω) transfer function at 0.15 V shows a loop in the first quadrant due to an increase (decrease) of mass on the electrode when the oxidation (reduction) process of POT takes 15634



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the hopping of protons between donor and acceptor amine groups.32 The protonation/deprotonation of electroactive sites should imply a slower transfer of protons which is observed at low frequencies despite the fact that it is the smallest ion. Once the kinetic parameters for the charged species were obtained by fitting the experimental Δq/ΔE(ω) transfer function with eq 38, they were fixed to fit the experimental mass data to the theoretical Δm/ΔE(ω) transfer function. Moreover, the transfer direction and molar mass (δimi) of the involved species can be fixed in eq 39. Hence, the hydrated protons enter POT during the reduction reactions, δH3O+mH3O+ = −19 g mol−1, while the bisulfate ions leave the polymer, δHSO4−mHSO4− = +97 g mol−1, as was justified in part 1 of this series.26 In this manner, all free parameters can be fixed if we consider only these two contributions in Δm/ΔE(ω). However, the mass transfer function does not show good fittings with respect to the experimental results. Therefore, the contribution of free solvent must be considered, and it confirms the results obtained in part 1 by CV. δH2OmH2O can be fixed at −18 g mol−1 in eq 39, and finally, we have only three free parameters referred to water transfer in the fitting procedure of the mass transfer function (Figure 6b). These assumptions were reasonable in the complete experimental range of potentials of this work. To complete the explanation of the fitting procedure, it is important to note that the insertion model presented in section 2 defines perfect semicircles in the impedance plane plot (complex plane) whereas sometimes the experimental results show depressed semicircles. This discrepancy is phenomenologically replicated in that field by using constant-phase elements (CPEs), in other words, introducing the term (jω)αi in eqs 12 and 13. Concerning the impedance, many factors can affect this value scuh as the charge distribution, the surface roughness,33,34 transport phenomena inside the film, resistivity distributions in the film,35 local changes of pH, and interactions between parts of the adsorbed polymer. For mass measurements, similar causes can be evoked. If the thickness of the polymer layer is not uniform, such a behavior can be observed. Some distribution of the polymer film thickness has already been shown to affect the impedance of the modified electrode by a polymer.36−38 Concretely, it was found that the exponent of the CPE depends on the thickness, the surface morphology, the electrolyte concentration, and the polarization potential in POT-modified electrodes.39 The different expressions given for the CPE underline that the physical meaning of this element is not clear. In this work, the introduction of αH3O+, αHSO4−, and αH2O in the theoretical functions, eqs 38 and 39, was used to improve the fitting procedure. The results indicate that the POT deposited on the gold electrode can be considered like a thin film with a very uniform surface morphology since the exponent is very close to unity (about 0.9). The kinetic parameter Gi can be interpreted as the inverse of a charge transfer resistance at the polymer/solution interface or, in other models, mathematically equivalent to 1/FGi = Rct.14,40 Therefore, it can be considered as the rate/ease the insertion (expulsion) of species i in (from) the polymer during the redox processes. As was expected from section 2.1 for the dependence on potentials of this kinetic parameter for the hydrated proton transfer, GH+ shows a maximum at about 0.45 V where the BP− PN transition takes place (Figure 7a). One apparent transfer process is also obtained for GHSO4− (Figure 7b) and for GH2O (Figure 7c) with maximum ease of transfer at 0.35 V. This fact

Figure 7. Kinetic parameter, Gi, for hydrated protons (a), bisulfate ions (b), and water molecules (c) at different polarization potentials in H2SO4 (0.5 M) obtained by fitting Δq/ΔE(ω) and Δm/ΔE(ω) with the theoretical functions, eqs 38 and 39, respectively.

agrees with the reactions proposed in the theoretical section (see section 2.2) as these species are involved in two transitions, eqs 1 and 2. Therefore, Gi shows only one peak for the insertion of anions and solvent although they are inserted at two different sites. As shown by the spectroscopic results in part 1 of this series,26 the structure of POT in the LE−P transition is different from the polymeric structure in the P−BP transition, which affects the kinetic characteristics of the species transferred. Even at the more anodic potentials where it mainly occurs, the hydrated proton has serious difficulties transferring between the polymer and the solution compared with the other species with maximum values of GH3O+,max of about 1 μmol s−1 cm−2 V−1 in spite of the relatively small size of this species. This fact may be due to a Grotthuss-type mechanism of proton transport inside POT. The protons hop between neighboring sites along the polymer structure by a protonation/deprotonation process 15635



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associated with the LE−P transition and monitors the formation of compact coil structures when the anions interact strongly with the C−NH+C group. The structure of POT developed at this potential enhances the transfer of species between the film and the solution. Therefore, both the redox process and other factors such as structural changes can influence the kinetic aspects of species transfer in POT. Hillman et al. have suggested that a slow-moving solvent counterflux with a fast anion exchange for the POT film in HClO4 occurs from the results of the combined EQCM and probe beam deflection instrument.45 In this work, the transfer of water molecules is also proposed, but the similar profiles for both kinetic parameters (Ki′ and Gi) shown by the fast transfer of the bisulfate ion and the opposite free solvent transfer allow a coupled free solvent−bisulfate movement to be postulated, in agreement with the exclusion effect assumed in the cyclic electrogravimetry results.26 Free solvent molecules are replaced by bisulfate ions during the oxidation reaction. The exit of anions from POT leaves vacancies which can be rapidly occupied by the incoming free solvent molecules during the reduction reaction. If the exclusion effect is the only mechanism which governs water transfer during the LE−P and P−BP transitions, the transfer rate should be the same for anions and free water molecules. Here, it is observed that the transfer rate of water is faster than that of bisulfate ions. Therefore, the neutral nature of the molecule and structural changes of POT can help in the transfer of water molecules. The derivative of the surface insertion law with respect to the potential at ω = 0, dΓi(E)/dE, can be obtained from the Gi/Ki′ ratio.46,47 In a manner similar to that of the derivation of eq 36 for transfer process i, one has

which would be the rate-limiting step of this transfer. The transfer processes of both bisulfate and free solvent have values of Gi,max of about 5 and 17 μmol s−1 cm−2 V−1 (parts b and c, respectively, of Figure 7). The transfer of free solvent is about 4 times easier than the bisulfate ion transfer owing to its smaller size. These results confirm that the transfer of these species is particularly easier during the polaronic transition (P−BP transition). Around 0.35 V, POT shows electron localization greater than that of PANI because it has both a larger interchain separation due to the −CH3 group and more disorder in the interchain separations induced by a random location of this group on the aromatic ring.41,42 This fact favors the formation of time-stable bipolarons and allows this polaronic structure to be detected at 710 nm in this potential range during the cyclic voltammogram.26 The accumulation of the radical cations balanced by anions in the POT chain at more anodic potentials than the LE−P transition could be accompanied by a structural reorganization of the chains.43,44 Thus, the transfer of anions and free solvent between the polymer and the solution is improved during the polaronic P−BP transition. The change of the apparent kinetic parameter, Ki′ obtained from the fittings at different polarization potentials is presented in Figure 8. The slowest transfer corresponds to the hydrated

Gi (E) = (bi′ − bi)(Γi ,max − Γi ,min) K i′ exp((bi′ − bi)E) (1 + exp((bi′ − bi)E))2

(40)

By fitting the experimental results with the expression of dΓi(E)/dE, it is possible to determine the kinetic parameters bi′ − bi and Γi,max considering Γi,min = 0. Finally, the resulting expression is

Figure 8. Apparent kinetic parameter, Ki′, at different polarization potentials in 0.5 M H2SO4 obtained by fitting Δq/ΔE(ω) and Δm/ ΔE(ω) with the theoretical functions, eqs 38 and 39, respectively.

proton transfer due to the transfer limited by the Grotthuss mechanism, between 0 and 10 s−1. Bisulfate ions and associated water molecules have a higher kinetic rate by reaching maximum values around 70 s−1. The above-mentioned highest ease of the bisulfate ion and water transfers related to the changes of the structure of POT during this transition induces the highest kinetic rates at similar potentials, which is also in agreement with the model proposed previously. This fact agrees clearly with the change of the physicochemical properties of POT between 0.25 and 0.4 V. In this range of potentials, the increasing conductivity of POT during the LE−P transition (insulator-to-conductor transition) is improved by the P−BP transition (a conductor-to-conductor transition). The analysis of the kinetic parameters confirms that the formation of the bipolaronic form of POT cannot be solely considered like the amount of polarons in the macromolecular chain of the conjugated system since it forms a separate entity with defined kinetic characteristics (Figures 7 and 8). Around 0.35 V, the proportion of anions corresponding to the LE−P transition are almost completely inserted in POT and the proportion corresponding to the P−BP transition are partially inserted. The absorbance at 810 nm studied in part 1 of this series26 is

Γi ,max dΓi b ′ − bi (E ) = i ( b ⎡ i dE 4 cosh2 ′ − bi)(E − Ep,i) ⎤ ⎢⎣ ⎥⎦ 2 =

(dΓi/dE)max ⎡ (bi ′ − bi)(E − Ep,i) ⎤ cosh2⎣⎢ 2 ⎦⎥

(41)

where Ep,i is the peak potential for transfer process i. This equation has similarities to the theoretical derivation of a voltammetric response of a redox process (charge, mass, or absorbance) involving the insertion/expulsion of species in part 1 of this series.26 Accordingly, Ep,i in eq 41 can be considered the peak potential in the cathodic sense since we apply polarization potentials from 0.55 to 0.1 V. This experimental potential range was chosen because POT degrades in any further anodic potential.48 A green degradation product close to the electrode surface was observed when we tried to reach more anodic potentials. This fact can be neglected at higher scan rates with CV techniques. On the contrary, the parallel catalytic reaction observed at more cathodic potentials could seriously limit the species flux. From the experimental results, all redox 15636



Article

transitions proposed previously can be fairly characterized and completed in a more extended potential range. In particular, this function also allows the dΓi(E)/dE curves of anions and solvent transfer to be separated for LE−P and P− BP transitions (Figure 9). The parameters used in eq 41 to

Table 2. Parameters Used in the Simulated Curves of dΓi(E)/dE in Eq 41 from the Data of Figure 9 for Species ia BP−PN Γi,max (nmol cm−2) bi′ − bi (V−1) Ep,i (V vs SCE)

P−BP

LE−P

−

−

+

H3O

HSO4

39 −20 0.547

15 −20 0.380

H2O

HSO4

49 −20 0.380

20 −20 0.145

H2O 69 −20 0.140

a LE−P is the leucoemeraldine−polaron transition, P−BP the polaron−bipolaron transition, and BP−PN the bipolaron−pernigraniline transition.

In steady-state conditions, the parameter bi′ − bi obtained by eq 41 in all transfer processes is also in accordance with the values obtained by cyclic voltammetry in part 1 of this series,26 −20 V−1. Thus, the scan rate does not have a decisive influence on the values of bi′ − bi. This parameter governs the curve shape at the width of half-height peak, ΔEp,i(1/2) = (Ep,i(1/2) − Ep,i(−1/2)), and it corresponds to 181.2/n′ mV (T = 298 K), which also can be calculated graphically from Figure 9. This fact is representative of repulsive interactions in permselective redox films assuming a Frumkin-type isotherm characteristic of thin polymers adsorbed on an electrode where lateral interactions between random distributed electroactive sites may take place during the redox reactions.49−52 However, the existence of a previous chemically controlled step of the monoelectronic transfers could also explain these results, and we may consider n′ = 0.5 in eq 29 with the same numeric result.53 Deeper studies from a molecular perspective are necessary to give an explanation of this uncertainty, since the surrounding environment of the electroactive sites also plays an important role and influences the electrochemical behavior of the films. Figure 10 shows the variation of the global insertion law for all the involved species for the three transitions (LE−P, P−BP,

Figure 9. Derivative of the insertion law with respect to the potential, dΓi(E)/dE, at different polarization potentials in 0.5 M H2SO4 obtained by fitting Δq/ΔE(ω) and Δm/ΔE(ω) with the theoretical functions, eqs 38 and 39, respectively. The lines are the simulated curves of dΓi(E)/dE, eq 41, using the parameters in Table 2 between −0.5 and +1 V (LE−P is the leucoemeraldine−polaron transition, P− BP the polaron−bipolaron transition, and BP−PN the bipolaron− pernigraniline transition).

Figure 10. Global insertion law for all the involved species in the three redox transitions by integration of simulated curves of dΓi(E)/dE, eq 41, using the parameters in Table 2 between −0.5 and +1 V.

and BP−PN) obtained by integrating the simulated insertion law, dΓi(E)/dE, when the polarization potential decreases. From Figure 10, it should be noted that the highest surface concentration in POT corresponds to the free solvent transfer during the LE−P transition with ΓH2O,max = 69 nmol cm−2, with a mass contribution (mH2OΓH2O) of about 20%. The highest mass contribution is for the bisulfate ions at 31% and a surface concentration of 20 nmol cm−2 in the same redox transition. The hydrated protons have a mass contribution of about 12% owing to their smaller size. Considering the ideal redox reaction of one electroactive site, one bisulfate ion and one hydrated

simulate all transitions are summarized in Table 2. Starting at the more anodic potentials, the peak potential of the hydrated proton transfer, Ep,H3O+, is close to 0.55 V (BP−PN transition). For the P−BP transition and LE−P transition, the peak potentials are about 0.38 and 0.14 V, respectively. These values are very close to the formal potentials estimated by cyclic voltammetry at a 100 mV s−1 scan rate (about 0.52, 0.43, and 0.24 V, respectively). 15637



Article

5. CONCLUSIONS Direct kinetic information on the redox transitions and the hydrated proton, bisulfate ion, and free solvent transfers occurring at the POT/solution interface during the potential perturbation was investigated using ac electrogravimetry in H2SO4 aqueous solutions. The rigorous analysis of the experimental data from this technique allows three different transitions with their respective species transfer to be separated. In the reduction direction, the BP−PN transition, the P−BP transition, and the LE−P transition occur. A model where the transfer of anions is the fastest process and the transfer of hydrated protons is the slowest process (Grotthuss mechanism) is proposed with coherent results. The stoichiometric flux or counterflux of water molecules owing to these conformational structure changes of the polymer and the exclusion effect governed by the anion transfer respectively is also proposed. The better electrochemical properties of POT take place in the conductor-to-conductor transition (P−BP transition), corroborating the results in part 1 of this series26. The coupling of different in situ techniques opens new perspectives mainly for the development of new methodologies allowing a better evaluation and understanding of the kinetics and mechanistic aspects in the conducting POT and more widely in other permselective materials. Moreover, a theoretical model which can explain the experimental results has been developed. In this model, the kinetic transfer of one species would depend on the conformational structure of the redox site where it is inserted.

proton are necessary for the charge compensation of two electrons. Accordingly, the hydrated proton surface concentration can be similar to that of the sum of the surface concentration of bisulfate ions in the LE−P−BP transition. From the simulations, the calculated surface concentration of the hydrated protons is 39 nmol cm−2 and the total surface concentration of bisulfate ions is 35 nmol cm−2. This fact provides some validity of the simulated curves obtained from the experimental data in Figure 9. The amount of water transferred between the film and the bathing solution depends significantly on the counterion.54,55 The ratio ΓH2O,max/ΓHSO4−,max could be an estimation of the number of water molecules transferred for each anion of the coupled free solvent−bisulfate ion transfer.10 At potentials between −0.2 and +0.4 V where the LE−P transition is supposed to occur, about 3.5 water molecules are expulsed (inserted) for each bisulfate ion inserted (expulsed) in steadystate conditions. Similarly, the ratio is 3.3 for the P−BP transition between 0.2 and 0.7 V. Using the commercial software ChemBio3D Ultra v. 12.0 ChemBioOffice 2010, the dimensions of the bisulfate ion and the water molecules were estimated from the Connolly solvent-excluded volume. Accordingly, one molecule of bisulfate ion could replace five molecules of water and vice versa taking into account the volume calculated for bisulfate ions (∼45 Å3) and the volume calculated for water (∼10 Å3). Consequently, two molecules of water are not excluded owing to the conformational changes of the polymeric structure of POT above assumed in these redox transitions. In this manner, POT should act like a molecular pump promoting the transfer of neutral species by two different mechanisms (exclusion and conformational changes), and this may allow the hydration extent of the POT to be controlled. From all these results, the general scheme proposed in part 1 of this series26 from only one cyclic voltammetry scan rate can be stoichiometrically and kinetically completed more accurately during the global PN−LE transition in the experimental conditions of this work (0.5 M H2SO4 solution in the cathodic sense): k1

LE + x1HSO4 − ⇄ P + x1e− + 3x1H 2O

■

APPENDIX For a redox process involving the insertion/expulsion of a charged species, e.g., for the insertion of anions, A−, in electroactive sites ⟨P⟩ during the oxidation of the host polymer p, eq 4, one has J = −k(C − Cmin) + k′(Cmax − C)Csol G=

at

and

k1′

Ep ≈ +0.140V vs SCE

K=

(42)

k2

P + x 2 HSO4 − ⇄ BP + x 2e− + 3x 2 H 2O

k′(Cmax − C)Csol = k(C − Cmin)

Ep ≈ +0.380V vs SCE BP ⇄ PN + x3e− + x3H3O+ k 3′

∂J = k + k′Csol ∂C

As at steady state J = 0

at

k 2′

k3

∂J = −bk(C − Cmin) + b′k′(Cmax − C)Csol ∂E

(43)

at

then G = (b′ − b)k′(Cmax − C)Csol

Ep ≈ + 0.550V vs SCE

and

(44)

where xi represents the amount of sites inside the polymer where molecular species could be inserted or expulsed during redox reaction step 1, or eq 42, redox reaction step 2, or eq 43, and redox reaction step 3, or eq 44, LE = ⟨POT, x3H3O+, (3x2 + 3x1)H2O⟩, P = ⟨POT, x3H3O+, 3x2H2O, x1HSO4−⟩, BP = ⟨POT, x3H3O+, (x2 + x1)HSO4−⟩, and PN = ⟨POT, (x2 + x1)HSO4−⟩. Moreover, the redox reactions where the bisulfate and water molecules are involved are faster than the redox reaction where the hydrated proton is involved; in other words, k1 > k3 and k2 > k3 in the oxidation direction and k1′ > k3′ and k2′ > k3′ in the reduction direction.

G = (b′ − b)

k′k(Cmax − Cmin)Csol k′Cs + k

for each redox process. If the rate constants are supposed to be activated by the potential, such as k′Csol = k 0′Csol exp(b′E) = k 00 exp(b′(E − E°′)) k = k 0 exp(bE) = k 00 exp(b(E − E°′))

where 15638


The Journal of Physical Chemistry C ⟨P⟩ ⟨Pn+, nA−⟩ ⟨Pn−, nC+⟩ ΔE/ΔI(ω) Δm/ΔE(ω) Δq/ΔE(ω) Cdl ΔEp,i(1/2) K′ Rct df Ci ki and ki′

n′F RT

b′ = (1 − β)

b = −β

Article

n′F RT

and ⎛ ⎛ n′F ⎞ n′F ⎞⎟ k 00 = k 0′Csol exp⎜(1 − β) E°′ = k 0 exp⎜ −β E°′⎟ ⎝ ⎠ ⎝ RT ⎠ RT

then

b′ − b =

n′F RT

and

Gi

⎛ n′F ⎞ k′Csol (E − E°′)⎟ = exp⎜ ⎝ RT ⎠ k

J Ki f j α β δ ω zi

where R is the gas constant, T is the absolute temperature, E° is the formal potential of the modified electrode, and n′ is the apparent number of electrons transferred during the electrochemical reaction. Accordingly n′F ⎡ ⎤ Fk 00 (Cmax − Cmin)exp⎣(1 − β) RT (E − E°′)⎦ G= n′F RT 1 + exp⎡⎣ RT (E − E°′)⎤⎦

(

)

■

If β = 1/2 and n′ = 1, then ⎡ F ⎤ Fk 0 (Cmax − Cmin)exp⎣ 2RT (E − E°′)⎦ G= F RT 1 + exp⎡⎣ RT (E − E°′)⎤⎦

(

G=

(

)

and K=

∂J = k + k′Csol ∂C

From eq 6 at each potential

■

REFERENCES

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)

2Fk 0 (Cmax − Cmin) RT cosh F (E − E°′) 2RT

host electroactive polymer polymer doped with anions polymer doped with cations electrochemical impedance mass/potential transfer function charge/potential transfer function polymer/solution double layer capacity width of half-height peak (Ep,i(1/2) − Ep,i(1/2)) K/df charge transfer resistance polymer thickness concentration of species i kinetic rate constants of the direct and inverse reactions biki(Ci − Ci,min) − bi′ki′(Ci,max − Ci)Ci,sol of species i flux of the species crossing the polymer/solution interface ki + ki′Ci,sol of species i perturbation frequency √−1, imaginary number exponent of the CPE charge transfer coefficient +1 or −1 2πf valence of the ion

ΔC −G (ω = 0) = ΔE K

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Part of this work was supported by CICyT Project CTQ201128973/BQU. J.A. acknowledges his position to the Generalitat Valenciana.

■

NOMENCLATURE56 CPE constant-phase element EIS electrochemical impedance spectroscopy MIS mass impedance spectroscopy SCE saturated calomel electrode 15639



Article

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