Elucidation of Band Structure of Charge Storage in Conducting

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Elucidation of band structure of charge storage in conducting polymers using a redox reaction Asfiya Qais Contractor, and Vinay Anant Juvekar Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/ac500440d • Publication Date (Web): 26 May 2014 Downloaded from http://pubs.acs.org on June 3, 2014

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Analytical Chemistry

Elucidation of band structure of charge storage in conducting polymers using a redox reaction Asfiya Q. Contractor and Vinay A. Juvekar Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India Abstract: A novel technique to investigate charge storage characteristics of intrinsically conducting polymer films has been developed. A redox reaction is conducted on a polymer film on a rotating disk electrode under potentiostatic condition so that the rate of charging of the film equals the rate of removal of the charge by the reaction. The voltammogram obtained from the experiment on polyaniline film using Fe2+/Fe3+ in HCl as the redox system shows five distinct linear segments (bands) with discontinuity in the slope at specific transition potentials. These bands are the same as those indicated by ESR/Raman spectroscopy with comparable transition potentials. From the dependence of the slopes of the bands on concentration of ferrous and ferric ions, it was possible to estimate the energies of the charge carriers in different bands. It is shown that the charge storage in the film is capacitive. Key words: conducting polymer, steady-state voltammetry, redox reaction, energy bands, capacitive charging, polyaniline. Introduction Understanding how electric charge is stored in an intrinsically conducting polymer (ICP) is important from the point of view of its use as a charge storage device. It is wellknown that charge is stored in ICPs in different energy bands. For example, in polyaniline, five bands, namely, leucoemeraldine, polaron, polaron lattice, bipolaron and pernigraniline have been identified[1,2]. Transition from one band to the next is discontinuous and these discontinuities allow one to detect the transitions. Three techniques which have been reported in the literature to detect these transitions are ESR spectroscopy, Raman spectroscopy and optical absorption spectroscopy[1,2]. When polyaniline is subjected to a sufficiently high positive potential, charge is injected into the polymer in the form of polarons (radical cations). Polarons have unpaired spins and therefore they can be detected by electron spin resonance (ESR) spectroscopy. Raman spectroscopy is sensitive to rotational and vibrational modes in the polymer structure which change due to oxidation. Optical absorption spectra also confirm the existence of five structural forms in polyaniline because each structural form shows a distinct absorption wavelength. In the present work, we have developed a new technique in which we use a suitable redox reaction, conducted on the ICP, to detect these

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bands. The principle of this technique is as follows. A redox reaction on an ICP can be written as R + P+ ⇔ O + P

(1)

where R is the redox species and O is its oxidized form. P + and P are respectively, the charged and the uncharged sites of the polymer. Since the rate constants of the forward and the backward reactions depend on the energy states of P + and P , they differ from band to band. Hence by measuring the net rate of the reaction at different electrode potentials, it is possible to discern the energy bands and locate their transitions in the conducting polymer film deposited on the electrode. Moreover, it is possible to estimate the energies associated with these bands through estimation of the equilibrium constants of the reaction. The technique adopted here is steady-state voltammetry on rotating disk electrode. The measured current density is corrected for the diffusion effects of redox species using Koutecky-Levich plots. The corrected current density, which we call the reaction current density, when plotted against the electrode potential shows distinct straight line regions with different slopes. Each straight line corresponds to a distinct band and the transition from one band to the next is marked by an abrupt change in the slope. By analyzing the dependence of the slopes on concentrations of the redox species, we have been able to estimate the equilibrium constants of reaction (1) in different bands. We have illustrated the technique using polyaniline as the model ICP and Fe2+/Fe3+ as the model redox system. Some experiments have also been performed using quinhydrone, which is a 1:1 adduct of benzoquinone (oxidant) and hydroquinone (reductant). The five band-transition potentials of polyaniline, obtained using this technique are compared with those reported in the literature based on electron spin resonance (ESR) spectroscopy and Raman spectroscopy (both performed under steady state).

Materials and methods All chemicals were analytical grade and purchased from reputed companies. Aniline was distilled to a colorless product before use. Ferrous ammonium sulphate and ferric ammonium sulphate were used as sources of ferrous and ferric ions respectively. Concentrations of ferrous and ferric ions in the solution were estimated using colorimetric techniques [3].


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All experiments were performed at ambient temperature (298 K). Both the deposition of the film and the redox reaction were conducted in a single compartment three electrode cell. Saturated calomel electrode was used as the reference electrode and a platinum rotating disk electrode (Pine Instrument Company) having 5 mm disk-diameter was used as the working electrode. The film was deposited on the electrode at a disc speed of 4000 RPM, from a solution containing 0.1 M aniline and 0.5 M sulfuric acid. Prior to deposition, the electrode was polished using 0.05 µm alumina paste and was activated by potential cycling between -2.0V and 0V in 0.5M HCl. During film deposition, electrode potential was cycled between -0.2V and 1.0V at the sweep rate of 50mV/s until a specified amount of charge (synthesis charge) was consumed during the preparation of the film. In most experiments, synthesis charge of the film was kept constant at 30±1 mC (i.e. 1527±50 C.m-2 of the apparent surface area of the electrode). The redox charge of the film was measured and found to be in the range of 100±10 C.m-2 of the apparent surface area of the electrode, which corresponded to a film thickness of about 0.47 µm based on the criterion provided by Thyssen et al. [4]. Some films having synthesis charge of 45 and 60 mC were also used. After deposition of the film, the electrode was rinsed with deionized water and then immersed in aqueous hydrochloric acid solution containing known concentrations of ferrous/ferric ions. In most experiments 0.5M HCl was used. The experiments were performed under potentiostatic condition. The electrode potential was stepped down from 0.7V to -0.2V in small steps of 25-50 mV. After each step-change, sufficient time was allowed for the system to attain steady state. The steady state current was recorded as a function of the electrode potential. In most cases, the steady state was attained within about 5s. However, the steady current was recorded 20 seconds after the step change. To confirm that the current does not vary significantly after 20s, a few experiments were conducted where the time interval of 2000s was allowed after the step change; current did not differ from that after 20s by more than 2%. The potential of the working electrode was not exceeded beyond 0.7V in most cases because it is known that polyaniline undergoes significant hydrolytic degradation in 1M sulfuric acid at potentials beyond 0.8V (versus Ag/AgCl electrode) [5]. In view of the fact that the acid used by us was milder, (0.5M HCl) we expect negligible degradation of the film during the experiments. This was also confirmed by reversibility of the voltammogram as shown later. Only in few cases, it was necessary to go beyond 0.7V. For example, pernigraniline band could be distinctly detected when the



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potential was well beyond 0.7V. However, the data needed for the quantification of the rate of reaction was obtained only in the range from -0.2V to 0.7V. At a fixed electrode potential, steady current was measured at seven different disk speeds in the range from 100 RPM to 4000 RPM for the purpose of preparing KouteckyLevich (KL) plots. These are plots of the reciprocal of the observed current versus ω −1/ 2 . They are based on the following equation which is derived from the Levich equation and assumes that the reaction is first order with respect to the redox species [6]. 1 1 = kω −1 / 2 + I IR

(2)

where ω is the speed of revolution of the disc, I is the total current and I R is the current that would be observed at infinite disc speed, where the mass transfer resistance is absent. I R therefore represents contribution to the current from the surface reaction as well as other internal resistances (such as pore diffusion resistance) associated with the film. We term this current as the reaction current. We found Koutecky-Levich plots to be excellent straight lines from which we obtained reliable estimates of the reaction current. Due to slow deterioration of the polyaniline film in acid medium [5], it was used immediately after preparation and was discarded at the end of the experiment. It was also not possible to reproduce films with identical current-potential characteristics, even when the synthesis charge was kept constant (Lack of reproducibility in film preparation is a wellknown fact [7]). However, we defined certain ratios associated with the film characteristics which exhibited consistent trends among different films and provided us insights into the doping/dedoping characteristics of the films.

Results and Discussion: Figure 1(a) shows a typical plot of reaction current density versus electrode potential for a film immersed in 0.5 M HCl solution containing a 3:1 ratio of ferrous to ferric ions. Figure 1(b) is the corresponding plot for quinhydrone which is a 1:1 adduct of benzoquinone and hydroquinone. These plots may be called ‘reduced steady-state voltammograms’ because they represent the steady state current from which the mass transfer contribution has been eliminated. The potential was decreased in small steps from 0.9V up to -0.2V. Each plot is seen to consist of five straight line segments, each segment having a distinct slope. Transition


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from one straight line to the next one is sharp, indicating discontinuity in the first derivative

diR dE at the point of transition. These straight lines are numbered on the plot from 1 to 5 in the direction of increasing electrode potential. The regions described by the lines are termed, respectively, as leucoemeraldine, polaron, polaron lattice, bipolaron and pernigraniline. These terms are consistent with the polyaniline molecular structure in these potential domains [1]. These potential domains represent five different energy bands in the conducting polymer.

Figure 1 Reaction current density versus electrode potential on (a) 31.79 mC polyaniline film immersed in an electrolyte solution containing a mixture of 37.5mM Ferrous ions and 12.5mM Ferric ions, and (b) 29.2 mC polyaniline film immersed in an electrolyte solution containing 10mM Quinhydrone in 0.5M hydrochloric acid.

To check the reversibility of the voltammogram, experiments were conducted where the electrode potential was first stepped in the backward direction from 0.7V to 0V and then in the forward direction from 0V to 0.7V. A typical result is shown in Figure 2. The steady state voltammograms obtained from the forward and the reverse stepping are superimposable within experimental error indicating that the process is reversible in this potential range.



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Figure 2. Demonstration of reversibility of voltammogram. Voltammograms for forward and reverse potential stepping between 0V and 0.7V have been superimposed. The inset shows forward and reverse steady-state voltammograms between 0.3V to -0.2V. The arrows indicate the direction of potential stepping. (electrolyte: 0.5 M HCl; synthesis charge:30mC; redox ion concentration: 9.60mM Ferrous + 9.60mM Ferric; reference electrode: SCE).

In the range of potential from -0.2V to 0V, the forward and the reverse scans were not superimposable (see inset of Figure 2). The voltammogram exhibited a negative slope when the potential was stepped in the direction of decreasing potential (the negative slope is more pronounced in Figure-1a). During forward stepping in this potential region, the voltammogram is nearly horizontal. Thus a hysteresis loop is formed in the potential range between -0.2V and 0.1V. However, this hysteresis does not affect the reversibility of the voltammogram beyond 0.1V as seen in the inset. This indicates that no irreversible changes occur in the film in the potentail range between -0.2V and 0.7V. It is also evident from Figure 1 that there are definite electrode potentials at which transition from one region to the next occurs. These transition potentials were found to be independent of the acid type (H2SO4 and HCl) and concentration, film thickness/charge. They were also same for the two redox systems employed here. The average values of transition potentials observed in different experiments are listed in Table-1 below along with the width of the potential band in which they lie.


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Table-1: Transition potentials for polyaniline films in acid medium in the potential range of -200mV to 1000mV. Transition Potential, mV Leucoemeraldine - Polaron

75 ± 26

Polaron - Polaron lattice

290 ± 27

Polaron Lattice - Bipolaron 482 ± 29 Bipolaron- Pernigraniline

654 ± 23

The reduced steady-state voltammograms have been overlaid with the Raman spectrogram [1] and ESR spectrogram (esrogram [2]) in Figures 3(a) and 3(b) respectively. Note that both these spectra have been obtained under steady state conditions. The transition potentials where structural shifts are predicted in the Raman spectrum are in good agreement with the transition potentials obtained from our reduced steady-state voltammograms.

Figure 3(a) Data from Raman spectroscopy (ratio of quinoid band area to total –CH bendings area) in 0.1M HCl [Error! Bookmark not defined.] (b) Esrogram recorded under steady-polarized condition in 1 M HCl[Error! Bookmark not defined.]; Both these spectra are compared with reduced steady state voltammogram on 30mC polyaniline film in 1M HCl. The inset in Fig 3(b) shows variation in ESR linewidth with potential [Error! Bookmark not defined.].

Comparison with the esrogram (Figure 3b) shows that transitions indicated by the voltammogram coincide with the points of inflection in the esrogram. For example, the transition from polaron band to polaron lattice band occurs to the right of the peak in the esrogram. Some authors [2] have suggested that the point of transition should coincide with the peak. We observe that at the peak of the esrogram, the spin intensity is maximum and hence it should have highest concentration of unpaired spins (isolated polarons). Moreover, the ESR linewidth (shown in the inset of Figure 3b) is narrowest at the peak, indicating



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minimum spin-spin coupling. Hence this region does not represent a polaron lattice. Polaron lattice is identified by low ESR intensity and broad linewidth, due to appreciable spin-spin coupling. These conditions are fulfilled at potentials well beyond the peak of the esrogram. The same is true for the other transitions also. Therefore, we conclude that the transition potentials obtained from our reduced steady state voltammogram are in good agreement with ESR data. We now discuss the other characteristics of the reduced voltammograms shown in Figure 1. The first characteristic is the potential at which the voltammogram crosses from cathodic to anodic region. This is the point at which the current is zero and should correspond to the equilibrium potential of the redox system. For Fe2+/Fe3+ system, we determined the equilibrium potential for different ratios of concentrations of Fe2+ to Fe3+. The plot of the

([

equilibrium potential (not shown here) versus ln Fe2 +

] [Fe ]) was a straight line, which 3+

matched closely with the corresponding plot obtained on the bare electrode (platinum disk). That the equilibrium potential of the redox reaction is not altered by the nature of the electrode is theoretically justified and has been previously verified on conducting polymers [8]. The second important characteristic of the voltammogram is that its linear trend persists over a broad range of potential across the equilibrium point. If the charge transfer resistance were present at the electrode-film interface, the reaction current would have shown a Butler-Volmer type of dependence on electrode potential and the voltammogram would have exhibited a marked curvature on the two sides of the equilibrium potential corresponding to transition from linear to Tafel region. The lack of curvature is indicative of the absence of charge transfer resistance. Piecewise linear dependence of the current on the electrode potential also indicates that the doping process is probably capacitive and its capacitance is constant in a given energy band. Moreover, the slopes, diR dE , of all segments of the voltammogram exhibit linear dependence on concentrations of both ferrous and ferric ions. The dependence on


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ferrous ion is depicted in Figure 4(a) and that on Ferric ions in Figure 4(b).

Figure 4. Effect of concentrations of ferrous ions (a) and ferric ions (b) on the slope ( diR dE ) of the reduced voltammograms in different bands. Voltammograms are prepared on 30mC polyaniline films in 0.5M HCl. Key: Red circles (Polaron band); Blue triangles(Polaron lattice band); Green squares(Bipolaron band); Pink diamonds (Pernigraniline band). (All potentials are relative to saturated calomel electrode).

From Figure 4(a) we observe that the dependence of diR dE on ferrous ions progressively increases as we move up from polaron to pernigraniline band, on the other hand, the dependence on ferric ions increases as we move down from pernigraniline to polaron band. Linear dependence of the reaction current on both the electrode potential and the redox ion concentrations suggests the following model for the reaction. When the electrode potential is increased, charges are injected into the film, converting the undoped polymer sites, P , into doped sites, P + . These sites react with the redox species according to the reaction Fe 2 + + P + = Fe 3 + + P

(3)

The reaction is assumed to be first order in each of the redox species as well as the polymer sites. At steady state, the current flowing from the electrode into the film equals that consumed by the redox reaction. Hence we can express diR dE (in each band) in terms of the net rate of the redox reaction, which can be expressed in terms of concentrations of the redox

] [ ] sites in the polymer ( [P ] and [P ] respectively). [

species in the solution ( Fe2+ and Fe3+ ) and the surface densities of undoped and doped +



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[ ][

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 d P+ diR d [P ] 3+ = F  k f Fe 2 + − kb Fe dE dE dE 

]

[

]

(4)



Here, k f and kb are the rate constants for the forward and the backward surface reactions,

[ ]

respectively. The surface densities [P ] and P+ are based on unit area of the substrate electrode. Both the forward and the backward rate constants of the reaction can be treated as constants in a given energy band. If the surface density of the total accessible sites (doped plus undoped) is assumed to remain constant at [S ]0 , so that

[P] + [P + ] = [S ]0

(5)

[ ]

we can replace d [P ] dE by − d P + dE in Eq 4 and obtain the following equation

[ ]( [

diR d P+ =F k f Fe 2 + + kb Fe3+ dE dE

] [

])

(6)

[ ]

From Eq 6 it can be deduced that if, in a given band diR dE is constant, then d P + dE should also be constant, indicating that charging is a linear capacitive process. We denote the differential capacitance in band j , by c f , j and write

[ ]

 d P+ F   dE

 = cf , j j

(7)

Eq 6 can therefore be written for band j as

( [

]

[

 diR  2+ 3+   = c f , j k f , j Fe + kb , j Fe  dE  j

])

(8)

Eq 8 implies that diR dE should scale linearly with concentrations of ferrous and ferric ions, with slopes c f , j k f , j and c f , j kb , j respectively. This linear dependence is consistent with trends seen in Figure 4. Although, in both leucoemeraldine and pernigraniline bands, diR dE does not depend on either of the redox ion concentrations, the current density itself shows a strong and linear dependence on ferric ion concentration in leucoemeraldine band, and linear dependence on ferrous ion concentration in pernigraniline band as shown in Figure 5. In these experiments, to begin with, we have used a solution containing 5mM concentration of each of the two


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redox ions and measured the current after each subsequent addition of redox ions. From these plots we also observe that the reaction current does not depend on the concentration of Fe 2 + in leucoemeraldine band and is independent of the concentration of Fe 3 + ions in

pernigraniline band.

Figure 5(a) Dependence of the reaction current density on redox ion concentrations in the Leucoemeraldine band (0mV). (b) Dependence of the reaction current density on redox ion concentrations in the Pernigraniline band (700mV). Key: Black squares([Fe2+]) and Red circles([Fe3+]).

Since in the leucoemeraldine band, the only reaction happening in the film is the reduction of ferric ions, the current density in the leucoemeraldine band (band-1) can be written as

[

i1 = − Fkb,1[S ]0 (1 − ε l ) Fe3+

]

(9)

where, ε l is the fraction of [S ]0 in charged state in leucoemeraldine band and kb ,1 is the rate constant of the reaction between ferric ions and the uncharged sites. In the pernigraniline band, the reaction current density is independent of ferric ion concentration (see Figure 5b) indicating the absence of the forward reaction. If we assume that fraction ε p of

[S ]0

is in the charged state at 0.7V, then the current density i5 in this

region can be represented as

[

i5 = Fε p [S ]0 k f ,5 Fe2 +

]

(10)

Our goal in this work is to derive some intrinsic characteristics of the bands from the reduced voltammogram. For example, we can obtain c f , j k f , j and c f , j kb , j from the slopes of the linear segments corresponding to different bands by performing, on a single film,



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experiments involving different ratios of ferrous and ferric ion concentrations. However, it would need a large number of experiments to be performed on a single film. These would need a few days. Owing to deterioration of the film in acid medium, we decided against this scheme. It was decided to perform only one full potential scan on one film at a fixed concentration ratio of redox ions. In order to overcome the effect of the lack of reproducibility of the films, we adopted the procedure which is illustrated below. In Figure 6a, we have plotted i1 (current density in leucoemeraldine band) as a function of ferric ion concentration and i5 (current density in pernigraniline band) as a function of ferrous ions concentration, for a large number of films. Although these data show clear dependence of current densities on the concentrations of redox ions, there is significant scatter in the data caused by the variability of the films (correlation coefficients of the lines are 0.931 and 0.944 for i1 and i5 respectively). In Figure 6b, we have plotted the ratio,

[

R1 = −i1 i5 versus Fe3+

] [Fe ] . 2+

The plot is a straight line passing through the origin, which

is expected from Eq 11 below (obtained by combining Eq 9 and 10).

[

k (1 − ε l ) Fe3+ i1 = − b,1 i5 k f ,5ε p Fe2 +

[

]

]

(11)

Moreover, the scatter in the data around the straight line is much lower (correlation coefficient = 0.988). This indicates that when we use the ratio of the two different characteristics of the film, the effect of the variability can be considerably reduced. This implies that the variability affects both characteristics equally. We have made use of this fact in the further analysis.


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Figure 6(a) Violet line: linear fit of current density i5 in pernigraniline band versus concentration of ferrous ions (R2 = 0.944); Pink line: linear fit of current density i1 in leucoemeraldine band versus

[

][

]

concentration of ferric ions (R2 = 0.931); (b) Linear fit of the ratio − i1 i5 versus ratio Fe 3+ Fe 2+ (R2 = 0.988). All plots correspond to polyaniline films in 0.5M HCl. Key: 30mC (black square), 45mC (blue triangle), 60mC (green circle)

Another important observation from Figure 6 is that the values of both i1 and i5 for films with 45mC and 60mC synthesis charge fall within the error band around the mean line corresponding to films having 30mC synthesis charge. That the rates of redox reactions do not depend on the film thickness (which is directly proportional to synthesis charge) has been reported by several workers [9,10,11]. Based on this observation, they have concluded that the reaction does not occur over the entire bulk of the film, but within a thin region of the film in the vicinity of polymer-solution interface [10,11,12,13] A reason cited for this confinement of the reaction zone in the case of ferrous/ferric system is that these redox ions are excluded from the interior of the film [11,14]. This fact prompted us to ignore the pore diffusion resistance. We have used current density i5 to normalize the slopes

(di

dE ) j of the

voltammogram in different bands. By dividing Eq 6 by 10 we get

Rj =

(di dE ) j i5

=

[ [

 Fe3+  Fk f ,5ε p [S0 ]  Fe2+ c f , j kb , j

] + c ] Fk

f , jk f , j f ,5ε p

(12)

[S0 ]

[

Eq 12 implies that if we plot the ratio (di dE ) j (i5 ) against Fe3+

] [Fe ] we should obtain a 2+

straight line having slope equal to c f , j k f , j F k f ,5ε p [S 0 ] and intercept equal to c f , j kb , j Fk f ,5ε p [S 0 ] . More importantly, the ratio of the slope to the intercept yields



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K j = k f , j k b , j (13)

where K j is the equilibrium constant of the redox reaction in the j th band. The plots of ratios R1 (= −i1 i5 ) , R2 ( = (di / dE )2 i5 ), R3 ( = (di / dE )3 i5 ) and

[

R4 ( = (di / dE )4 i5 ) versus Fe3+

] [Fe ] are shown in Figure 7. They all follow linear trends, 2+

which confirm Eq 12. We find that the plot of R2 shows significant scatter (this scatter was found to be an inherent characteristic of polaron band) while the rest show very low scatter. We also see that R2 and R3 exhibit very small intercepts, whereas

R4 shows a large

intercept.

[

][

]

Figure 7. Normalized film characteristics, R1 , R2 , R3 , R4 , versus Fe 3+ Fe 2+ in different bands. All data are recorded on polyaniline films in 0.5M HCl. The inset shows an enlarged view of initial portion of the plots to clearly indicate the points corresponding to 45 and 60 mC films. Key: R1 (black squares with red line); R2 (red circles with black line); R3 (blue triangles with pink line); R4 (dark cyan inverted triangles with gray line); Points corresponding to 45mC film are shown by navy blue circles and those for 60mC film by light blue inverted triangles.

Table-2 lists the slopes and intercepts of the plots. The equilibrium constants K j = k f , j kb, j are obtained from the slopes and the intercept using Eq 12 and are also listed

in Table-2. The error bars in the computation of the slope and the intercepts are listed in the table, from which the error bars in the equilibrium constants are estimated.

Table-2: Characteristics of the energy bands of Polyaniline film.


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Polyaniline Potential StructureErr Range or! Bookmark V not defined.

Slope of Eq 15

Intercept of Eq 15 c f , jk f , j

0.05-0.3 0.3-0.5

0.5-0.7

∆GTj0

0 ∆GCj

K Cj

kJ .mol −1

kJ .mol −1

× 10 9

c f , j kb, j

F [S ]k f ,5

3.49 ±0.116 2.32 ±0.060

1.018 ±0.385 1.005 ±0.200

0.383 ±0.208 0.435 ±0.097

2.810 ±1.507 2.125 ±0.562

40.898 ±1.507 41.583 ±0.562

80.69 ±43.81 52.72 ±11.76

0.389 ±0.04

4.502 ±0.119

11.7 ±1.39

-6.076 ±0.296

49.784 ±0.296

1.89 ±0.23

F [S ]k f ,5

Polaron (band-2) Polaron lattice (band-3) Bipolaron (band-4)

K j = k f , j kb , j

Among the values listed in Table-2, the equilibrium constant in the bipolaron band is most accurate, whereas that in polaron band is least accurate (due to the scatter in the data). It was not possible to estimate the equilibrium constant in the leucoemeraldine band because of the absence of reactivity of ferrous ions in that band. The same was true for pernigraniline band due to the absence of reactivity of ferric ions. We see from Table-2 that K j increases as we move from polaron to bipolaron band. This implies that as we move in this direction, it becomes easier for the charge carriers to oxidize ferrous ions to ferric ions but more difficult for ferric ions to oxidize the undoped sites to doped sites. This indirectly implies that the energy of the charge carriers increases as we move up from the polaron band to bipolaron band. We can quantify the energy levels of these bands using the following argument. The overall reaction, (expressed by Eq 2) can be split into two steps Fe 2 + = Fe3+ + e − (∆GR0 ) (14)

(

0 P = P + + e− ∆GCj

)

(15)

0 In these equations, ∆GR0 and ∆GCj are respectively, the standard free energies of the

redox reaction step and polymer doping step (in band j). The standard free energy of the overall reaction ∆GTj0 is therefore equal to the difference between the standard free energies of the constituent steps, that is 0 ∆GTj0 = ∆GR0 − ∆GCj (16)



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where ∆GTj0 is related to the equilibrium constant K j by the following equation

∆GTj0 = − RT ln K j (17) The values of ∆GTj0 , obtained from Eq 17 are listed in Table-2. The standard free energy ∆GR0 is estimated from the formal potential (0.453 V in 0.5 M HCl both on polyaniline and platinum electrode) as 43.708 kJ.mol-1. The values of ∆GCj0 can now be estimated using Eq 16. These values are listed in Table-2. The corresponding values of the equilibrium constants can be estimated using the following equation and are also listed in Table-2. 0 ∆GCj = − RT ln K Cj (18)

It is seen from Table-2 that K Cj decreases by a factor of 40 as we move from the polaron band to the bipolaron band. This means the energy of the charge carrier substantially increases when we move up from the polaron to bipolaron band. Although, it is not possible to determine the energies of leucoemeraldine and pernigraniline bands by the present method, we can infer from the locations of these bands that the charge carriers in leucoemeraldine band will have the lowest energy and those in the pernigraniline band will have the highest energy.

Conclusion The present method allows us to quantify charge storage characteristics of conducting polymer films under steady state. Great simplification is achieved since the dynamics of double layer and the associated counterion diffusion can be eliminated. Since the rate of charge transport and relaxation must match with the rate of reaction, it is possible to investigate charge relaxation steps of different time constants by choosing redox reactions with appropriate rate constants. The following are the salient observations from our studies: 1. The charging process is capacitive. The capacitance of the film is a result of faradaic oxidation of polyaniline. Moreover, there is an absence of both the charge transfer resistance at the substrate electrode-film interface and the resistance to electronic conduction through the film. 2. There are five distinct energy bands in polyanailine. The transition potentials from one band to the next are in good agreement with ESR and Raman spectroscopy data.


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3. Band energies computed by the present technique show that energies of bands increase in the order: Uleucoemeraldine< Upolaron< Upolaron lattice< Ubipolaron< Upernigraniline. The energies of some of the bands have been estimated by this technique. 4. The differential capacitance of the film is constant in each band. This observation is supported by independent measurements of the film capacitance which were carried out by us and are reported in the supporting information.* The method developed here is general and can be applied to investigate charge storage characteristics of other instrsically conducting polymers. *This information is available free of charge via the internet at http://pubs.acs.org/. References: 1. Bernard, M,C.; Hugot-Le Goff, A. Electrochimica Acta, Vol. 52, 2006, p 595-603. 2. Zhuang, L.; Zhou, Q.; Lu J. J. Electroan. Chem., Vol. 493, 2000, p 135-140. 3. Jeffery, G.H.; Bassett, J.; Mendham, J.; Denney, R.C.; Vogel's Textbook of Quantitative Chemical Analysis, Fifth Edition, Longman Sceintific and Technical: England, 1989, p 690. 4. Pfeiffer, B.; Thyssen, A.; Schultze, J.W. J. Electroanal. Chem., Vol. 260, 1989, p 393-403. 5. Stilwell, D.E.; Park, S. M. J. Electrochem Soc., Vol. 135, 1988, p 2497-2502. 6. Rocklin, R.D.; Murray, R.W. J. Phys. Chem., Vol. 85, 1981, p 2104, 2112. 7. Heinze, J.; Frontana-Uribe, B.A.; Ludwigs, S.; Chemical Reviews, 2010, 110, 47244771. 8. Deslouis, C.; Musiani, M.M.; Pagura, C.; Tribollet, B.; J. Electrochem. Soc., Vol. 138, No. 9, 1991, p 2606-2612. 9. Oyama, N.; Anson, F.C. Anal. Chem., Vol. 52, 1980, p 1192-1198. 10. Mandić, Z.; Duić, L. J. Electroan. Chem., Vol. 403, 1996, p 133-141. 11. Maksymiuk, K.; Doblhofer, K. Electrochimica Acta, Vol. 39, No. 2, 1994, p 217-227. 12. Ikeda, T.; Leidner, C.R.; Murray, R.W. J. Electroan. Chem., Vol. 138, 1982, p 343-365. 13. Deslouis, C.; Musiani, M.M.; Tribollet, B.; J. Electroanal. Chem., Vol. 264, 1989, p 37-55. 14. Yano, J.; Ogura, K.; Kitani, A.; Sasaki, K. Synthetic Metals, Vol. 52, 1992, p 21-31.



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Comparison between optical absorption spectrum and reduced steady state voltammogram. The reduced steady state voltammogram was obtained on a 30mC polyaniline film in 1M HCl. Optical absorption spectrum showing intensity of 1/1.5eV transitions in HCl of pH 1 was extracted from reference: “Bernard, M,C.; Hugot-Le Goff, A. Electrochimica Acta, Vol. 52, 2006, p 595-603.” 216x121mm (96 x 96 DPI)


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Elucidation of Band Structure of Charge Storage in Conducting

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