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Dubna, Russian Federation August 26-30, 2012

Cyclic voltammetry of electrodes modified by pristine and metalcomposite polymer films
Valery V. Malev1,2 and Oleg V. Levin1
1)Department 2)

of Chemistry, St. Petersburg State University, Universitetskii pr.26, Petrodvoretz, St.Petersburg, 198504 Institute of Cytology, Russian Academy of Sciences, Tikhoretsky pr. 4, St. Petersburg 194064

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The Laviron equation of a quasi-equilibrium reaction proceeding in a compact film adsorbed onto an electrode
· Cyclic voltammetry is probably the most frequently used method of electrochemical research. A great influence on its application to studying the electrode reactions that proceed in an adsorbed state of reacting particles has had brilliant works by Laviron. His widely known equation
2 2

· ·
·

i= (nF) Am RT(1+)

,

where = exp{nF(E- Ep)/RT} and E = Ei ­ t (, the rate of potential change; Ei , the initial value of E in linear potential sweep voltammetry), was derived for reversible reaction O + ne R proceeding in a compact film adsorbed onto an electrode of surface A. A series of inferences from this equation, namely: (1) the appearance of peak current ip at potential value E = Ep (i.e. = 1); (2) the equality of adsorption densities of reduced (R) and oxidized forms (O) to each other at peak (or formal) potential Ep (O(Ep) = R(Ep)= m /2); (3) symmetry of i(E)-curves with respect to the peak potential and (4) the fact that "the width of the peak at mid-height is equal to 90.6/n mV" is considered as a complex of experimental criteria that can be used to establish the absence of specific (short-range) interactions between particles forming such films (or the Langmuir type of adsorption in case of monolayer films).
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Is it possible to reformulate the Laviron's criteria of the absence of short-range interactions within polymer films?
· To perform such reformulation is necessary due to the fact that the Laviron's consideration had been performed for monolayer films of adsorbed particles O and R, whereas modifying polymer films have a phase character; they are so thick, that the electroneutrality condition takes place practically for their entire interior. This means that the charge consumed to reduce/oxidize the film fragments (Qf) is strictly compensated by the opposite one of counter-ions entering/leaving such films. The concentration of these ions, Cm, and, hence, charge

Qf = - zmF Cm dz
·

0 zL

(here, L is the film thickness; zm is the charge of counter-ions) is determined by electric potential 0 of the film bulk. As potential 0 differs from electrode one E , the derivative of the film charge with respect to time t or potential E (taking into account that dt = ± dE/ in the conditions of cyclic voltammetry) should contain derivative d0/dE, which changes the final result for passing current i as compared to that given by the above Laviron's equation.

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Electroneutrality condition for p- and n-doped polymers
Thus, one can conclude that the electroneutrality condition plays the key role for the further consideration of red/ox processes Red - e Ox, which are accompanied with entering/leaving the counter-ions of charge Zm. Three following cases will be considered below I. (I.1) Charge Z0 of the oxidized form equal to 1 and Z0 = - 1 (p-doped film, the polaron formation); (I.2) Z0 = 0, Zm = 1 (n-doped film) II. (II.1) Charge Z0 = 2, Zm = - 1 (polaron / bipolaron system; (II.2) Z0 = -1, Zm = 1 (n-doped film) III. (III.1) Charge Z0 = 1, Zm = - 1 (p-doped film), but the oxidation process is accompanied with binding the formed polarons into ionic associates with counter-ions: P + A PA; (III.2) Z0 = -1, Zm = 1 (ndoped film) and the reduction process is also accompanied with ionic associate formation The electroneutrality condition: Z0COx + (Z0 -1)CRed + ZmCm = 0 Here, CK are the concentrations of corresponding species (K = Ox,

Red, m) 4


ip /const
0,006

ip /2const
0,003



i/const /V

-1

1
0,000

const =

F 2 ALk m C
RT

0

2

-0,003

-0,006

Ep'
-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5

·

Quasi- equilibrium CV-curves of electrodes modified by p-doped (curve 1) and n-doped (curve 2) polymer films at z0 =1, 0, correspondingly

E/V

·



, the velocity of scanning the electrode potential;

A,

the electrode area; L, the film thickness;

km,

the partition coefficient of counter-ions; C0, their concentration

·

is a semi-width of CV-curves that, in the case considered, is equal to
5.1RT/F (131 mV at room temperature)

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Comparison between CV-curves corresponding to different values of charge z0 of the reduced film fragments

Reduced CV-curves in case of p-doped polymer at different charges z0 of its oxidized fragments, const = vF2AL/RT. Curves 1 and 2 correspond to z0 = 1 and z0 = 2, respectively. 1 = 131 mV and 2 = 108 mV, the mid-width of curves 1 and 2. Both curves were calculated at ke = km = 0.1, C = C0 = 10-3 mol/cm3.

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Influence of binding the counter-ions with reduced fragments of polymer films

Reduced CV-curves in case of p-doped polymer in the presence of ionic association between counter-ions and charged film fragments, const = vF2AL/RT. (a) kp = 1000, k1 = 1, km = 1 (curve 1) and km = 0.1 (curve 2), the obtained mid-width value = 3.80RT/F; (b) kp = 100, other parameters are the same as those of figure a, the obtained mid-width value = 4.32RT/F; (c) kp = 10, other parameters are the same as those of figure a, the obtained mid-width value = 4.93RT/F.
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Conclusions from the above consideration of quasi-equilibrium CV-curves
(Electrochimica Acta 80 (2012) 426-431)
· 1. Current and potential values in singular points of CV-curves, as well as the semi-widths of such curves depend on charges of red / ox film fragments and counter-ions, and binding of the film fragments with counter-ions. 2. This means that any general formulation of the only set of criteria of the absence of short-range interactions within polymer films is impossible, since the shape of CV-curves of modified electrodes changes with variations in the system parameters. 3. Cyclic voltammetry is, therefore, only a primary method of studying charge transfer processes in modified electrodes and should be used in a combination with other instrumental methods.

·

·

Obviously, the question arises whether there exists an optimum combination. In some cases indicated further on, such combination might be indicated.
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Problems of modeling the electrode processes in pristine and composite films of electroactive polymers
· Modified electrodes are often used for electroanalytical determinations of different substances inclusive of biologically active ones. Meanwhile, details of the corresponding processes underlying such applications have mostly remained to be unclear. As it is known, real polymer films are porous systems (see the next slide). This, in particular, means that reactions of the determined particles can proceed not only on the visible ("outer") film surface, but also on an "inner" surface of pores penetrating completely or partly such films. The same situation probably takes place for electrode reactions in composite films, the metal inclusions of which are predominantly settled in film pores. Such porous character of polymer films in some extent complicates a quantitative description of electrode processes in these objects. The problem seems to be more complex in case of composite films. However, the problems have their solutions in some cases, at least.
9

·

·

·


SEM-image of a PEDOT/Pd film. Pd particles are deposited by dipping of previously reduced polymer . film for 60 s into 5·10-3 M PdCl2 / 0.1 M H2SO4 solution. Separate palladium clusters are indicated by arrows. 10


TEM-image of a PEDOT/Pd film. Pd particles are deposited by dipping the previously reduced polymer film for 120 s into 5·10-3 M PdCl2 / 0.1 M H2SO4 solution. Separate palladium clusters are indicated by arrows

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e


e

II

e

I III

solution



substrate

film

Possible paths of tested particles' diffusion
I. Reaction on the electrode substrate II.Reaction on the film/solution interface including the "inner" surface of pores III.Reaction within the film volume (the case of metal-composite films)

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Left figure: open points within the film correspond to metal clusters. White line of the figure represents the tested particles' distribution. Right figure: metal clusters included partly or completely into an arbitrary film layer of the thickness equal to 2, where , the mean radius of film clusters

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Cylindrical and slit pores
· LEFT: ri is the radius of
cylindric pores of the i-th kind · RIGHT: rj is the width of slit pores of the j-th kind

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Description of electrode processes with participation of tested particles
In the three cases considered, the concentration Ck of tested particles satisfies the following equation: C k /t = Dk 2Ck/z2 ­ K (z, ri )Ck , where Dk, the diffusion coefficient of tested particles; K (z, ri ) is some effective rate constant (see V.V. Malev, O.V. Levin , Electrochimica Acta 56 (2011) 3586-3596; Russian J. Electrochemistry (2012) ). The final equation for current I resulted from the reduction/oxidation of tested particles on film surface Atot = (Ain + A) is as follows -ACk0/I = 1/Kk(1+ Ain/A) + Ilim/Dk , where Ain , the total inner surface of all possible kinds of pores (cylindrical, conic, slit, wedge-shaped, and so on); Ilim = 0.62nF ADk2/31/2-1/6Ck0 is the limiting current to a rotating disc electrode of surface A; Kk is the rate constant of the reaction K ± ne Kred or Kox. Definitions of constant Kk are given in the next slide.
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Continuation of the preceding slide
· constant value in the limit of E (sign of E depends on the electrode reaction nature). Though the above Levich-Koutecky `s representation is valid for arbitrary values of electrode potential E, I'll further consider only the cases of limiting currents, which have a different nature in different cases. Case I: through pores and the tested species' reaction on the electrode substrate. In this case, Atot A, while constant Kk is determined by the film porosity and equal to Kk = Dk/L , where , the substrate surface fraction free of a modifying film; L and Dk, the film thickness and the diffusion coefficient of tested particles. Case II: reaction on the film physical border (including lateral surface of pores). In this case, Atot A, while constant Kk is determined by both the concentration of redor ox-fragments of the film and the electric potential drop on the film/solution interface. As the latter in the limit of high electrolyte concentrations is practically equal to zero, the intercept of the dependence (ACk0/I(1/2)) gives the reversal product of three quantities: Kk0C (1 + Atot /A), where Kk0, the true value of the constant and C, the total concentration of film fragments. Case III: reaction on the metal clusters' surface. In this case, quantity (1 + Atot /A) should be treated as the ratio of the clusters' surface to the visible electrode one if all clusters are of the same radius, r0. At this condition, Kk = Dk/r0; more complicated expressions for these quantities are valid in the general case of different ri . 16 In all the cases considered, Kk is a potential dependent quantity that tends to a

· · ·

·


Experimental results; poly-o-phenylenediamine + hydroquinone (case I of through pores)

Effects of the PPD film on the oxidation wave of hydroquinone. 0.01 M Na2B4O7 · 10H2O was used as electrolyte; (1) pure glassy-carbon disk without any hydroquinone additions, (2) glassy-carbon disk coated with a PPD film without any hydroquinone additions, (3) glassy-carbon disk coated with a PPD film in solutions with hydroquinone at concentrations indicated below, and (4) pure glassy-carbon disk in solution with hydroquinone at 6 â 10­4 M

Dependences of the limiting penetration current on the hydroquinone concentration (1) pure glassy-carbon electrode and (2)­(4) PPD- coated electrode for film thicknesses L (nm) of (2) 150, (3) 330, and (4) 390
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Experimental results; poly-o-phenylenediamine + hydroquinone (case I of through pores)

The Levich-Koutecky representation of the dependences of the limiting penetration current on the RDE frequency. The hydroquinone concentration is 6 â 10­4 M; (1) pure glassy-carbon electrode, (2)­ (4) PPD-coated electrode, film thickness L, nm: (2) 150, (3) 330, (4) 390. Russian Journal of Electrochemistry, 2008, Vol. 44, No. 1, pp. 98­103
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Experimental results; PB+H2O2 (case II: reaction on the real physical film surface)
20 15 10 5 0 P r u ssi an b l u e G l assy car b o n P r u ssi an b l u e + 2. 3 10
-3

M 2

2

Anodic branch

I, A

-5 -1 0 -1 5 -2 0 -2 5 -3 0 - 400 - 200 0 200 400 600 800 1 000 1200

Cathodic branch

E, m V

Cyclic voltammograms of glassy carbon and PB-modified electrodes with hydrogen peroxide added. H2O2 = 2.3·10-3 , v=20 mV/s

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Experimental results; PB+H2O2 (case II: reaction on the real physical film surface)
Anodic limiting current at 1.1 V: H2O2 ­ 2e O2+ 2H+
5

Cathodic `limiting' current at - 0.3 V: H2O2 + 2e + 2H+ 2H2O
5

Cathodic branch -3 [H2O2] = 1.2* 10 [H2O2] = 2.3* 10
-3

0

0

I, A

I, A

-5

-5

Anodic branch -3 [H2O2] = 1.2x10 [H2O2] = 2.3x10
-3

-10 -500 0 500 1000

-10 -500 0

500

1000

E, mV

E, mV

0.1 KCl, pH=3 Partial currents of the hydrogen peroxide electroreduction/electrooxidation on a PB modified electrode at different concentrations of H2O2 (Unpublished data).
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Experimental results; PB+H2O2 (case II: reaction on the real physical film surface)

f

Calculated current, Icalc, ·105 (C (H202)= 1.2 ·10-3)

Calculated current, Icalc, ·105 (C (H202) =2.3·10-3M)

Experimental current, Iexp, ·105 (C (H202) =1.2 ·10-3M) E=-0.3 V -1.1 -1.1 -1.0 -0.9

Experimental current, Iexp, ·105 (C (H202) =2.3 ·10-3M) E=-0.3 V -1.4 -1.4 -1.3 -1.2

Experimental current, Iexp, ·105 (C (H202) =1.2 -3M) ·10 E=1.1 V 0.7 0.6 0.7 0.6

Experimental current, Iexp, ·105 (C (H202) =2.3 ·10-3M) E=1.1 V 1 1 1 0.9

2500 2000 1500 1000

±16 ±14.5 ±12.5 ±10

±31 ±28 ±24 ±20

Comparison between the experimental limiting currents and those calculated according to the Levich equation
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Experimental results; PB+H2O2 (case II: reaction on the real physical film surface)
Current change with increasing the film thickness in 1.2·10-3 H2O
15
2

30

10

-I, A

I, A
5

20

10

-0.3 V forward direction backward direction
0
0 5 10
-1

1.1 V forward direction backward direction
20

0

15

0

5

10

L , m

-1

L , m

-1

-1

15

20

Similar results were published by U. Scharf and E. W. Grabner (Electrocatalytic oxidation of hydrazine at a Prussian blue-modified glassy carbon electrode / Electrochimica A. (1996), 41, 233)

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Experimental results; PEDOT/Au + H2O2 (case III of metal-composite films)

RDE voltammetry curves of GC/PEDOT electrode in solution of PBS in the absence (1) and presence (3) of 0.001 M H2O2 and those of GC/PEDOT/Au electrode in PBS solution in the absence (2) and presence (4) of 0.001 M H2O2 (substrate - GC disk of 0.07 cm2, f =2500 rpm, scan rate 10 mV s-1). Duration of gold loading from solution of 1·10-3 HAuCl4 + 0.1M H2SO4 is 60 s
23


Experimental results; PEDOT/Au + H2O2 (case III of metal-composite films)

Partial RDE voltammetry curves for the hydrogen peroxide reduction on Auparticles in PBS solution plus 1·10-3 M H2O2. Durations (s) of gold loading from solution of 1·10-3 HAuCl4 +0.1M H2SO4 are as follows: 1 - 60, 2 - 150, 3 - 240, 4 24 - 330, 5 - 560, 6 - 720.


Experimental results; PEDOT/Au + H2O2 (case III of metal-composite films)

Mass-transfer corrected Tafel plots for the hydrogen peroxide reduction on Auparticles in PBS solution plus 1·10-3 M H2O2 at different durations of gold loading, s: 1 - 60, 2 - 150, 3 - 240, 4 - 330, 5 - 560, 6 ­ 720.
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PEDOT/Au + H2O2 (case III of metal-composite films)

Koutecky-Levich plots of 1/Id() vs. -1/2 for the hydrogen peroxide reduction on composite PEDOT/Au film in PBS solution plus 1·10-3 M H2O2 at different durations of gold loading from solution of 1·10-3 HAuCl4, s: 1 - 720, 2 ­ 60, 3 ­ 60 (partial currents). Curve 3 represents partial limiting currents of H2O2 reduction on gold particles.
Hydrogen peroxide electroreduction on composite PEDOT films with included gold nanoparticles; Journal of Solid State Electrochemistry December 2011, Volume 15, Issue 11-12, pp 2383-2393 26


Acknowledgements:

This work was supported by the Russian Foundation for Basic Research (grants Nos.: 10-03-00793, 10-03-00609, 10-08-00895) and the Saint Petersburg State University (grants Nos. 12.38.15.2011, 12.38.77.2012).

Thank you for attention

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