Optical and Electrical A.C. Response of Polyaniline Films ... plots of the a.c. impedance of PANI can be explained by a dual rail .... It can be seen that at high fre-.
J. CHEM. SOC. FARADAY TRANS., 1991, 87(6), 853-860
853
Optical and Electrical A.C. Response of Polyaniline Films Maher Kalaji and Laurence M. Peter* Department of Chemistry, The University of Southampton , Southampton SO9 5NH, UK
The small-amplitude periodic optical transmittance response of redox polymer films is derived and related to the corresponding electrical behaviour. The combination of optical and electrical measurements allows Faradaic and non-Faradaic charging processes to be distinguished. The analysis of the modulated transmission data obtained for polyaniline films on indium-doped tin oxide coated transparent electrodes in 1.0 mol dm-3 H,SO, indicates that the capacitance measured in a.c. experiments is associated with redox transformations in the PAN1 film. The a.c. capacitance was found to be lower than the pseudo-capacitance derived from cyclic voltammograms and possible reasons for this discrepancy are discussed. The absorption coefficient of the polaron has been derived from the relationship between the modulated transmittance and the film capacitance which also shows that bipolaron states are formed at potentials more positive than 0.15 V vs. SCE.
The electrical and optical properties of polyaniline (PANI) continue to attract attention. The material is particularly interesting since its conductivity depends not only on its degree of oxidation but also on protonation equilibria. l P 3 Oxidation of the insulating leucoemeraldine form of PANI in acid solutions results in the formation of a conducting phase whereas upon further oxidation the polymer becomes insulating again. Several aspects of the behaviour of PANI are not well understood. It is not clear, for example, why the pair of voltammetric peaks associated with the insulator-conductor transition exhibit hysteresis which is independent of sweep rate.4,5At the same time, the origin of the apparent ‘charging current’ in the cyclic voltammogram for the oxidised (conducting) form of PANI remains c o n t r ~ v e r s i a l .There ~ * ~ is also disagreement about the interpretation of EPR data for oxidised PANI in terms of localised Curie spins as against Pauli susceptibility of metallic islands.8-’ Several of these key problems were highlighted during the recent Faraday Discussion on Charge Transfer in Polymeric Systems.’ Here we address the problem of distinguishing between Faradaic charge-transfer processes and charging of the electrical double layer around polymer strands. PANI films can be electrosynthesized on optically transparent electrodes (OTEs) constructed from indium-doped tin oxide (ITO) coated glass, and changes in the absorption spectrum associated with the subsequent oxidation and reduction of the polymer have been widely In this paper, we are concerned with the small-amplitude non-steady-state optical response of PANI. This contains additional information since the time-dependent absorbance changes can be related to the Faradaic component of the total current. The study has been restricted to the first insulator-conductor transition, since further oxidation leads to rapid film degradation. Recently, we have shown that the transient response of PANI-coated macroelectrodes is limited by the solution and electrode resistances’ (the latter is particularly important for ITO-coated OTEs). The kinetic processes involved in the oxidation-reduction mechanism are extraordinarily rapid and the transformation process can be resolved only if iR errors are minimized by using ultramicroelectrodes with radii as small as 10 pm. There are, however, two further processes which might be expected to influence the transient or periodic electrical response of PANI films. The first of these is the transport of counterions which is required to maintain electroneutrality during oxidation and reduction. If ion transport is diffusion controlled, an additional Warburg impedance should be observed in the ax. response. The second process that could be important is non-Faradaic charging of the elec-
trical double layer at the polymer/solution interface. It was suggested by Feldberg7 that the double-layer capacitance associated with this process should depend linearly on the fraction of the polymer converted to its conducting (oxidized) form. The experimental impedance behaviour of electrochemically synthesized PANI films has been discussed by several and it is clear that no Warburg behaviour is observed. It has been proposed by Albery et that the absence of a Warburg response in the complex plane plots of the a.c. impedance of PANI can be explained by a dual rail transmission line model in which the distributed resistance elements in the polymer and aqueous phases are equal, but this seems physically implausible (for a critical discussion of this model see ref. 13). There is also no compelling evidence for the existence of a double-layer capacitance corresponding to ‘metallic’ behaviour (i.e. arising from an excess of surface density of mobile electronic charge carriers and an ionic double layer in solution) of PANI in its oxidized state. However, it is not possible to distinguish between Faradaic pseudo-capacitance and double-layer capacitance on the basis of electrical measurements alone. In a recent c o m m u n i c a t i ~ nwe , ~ ~reported that an exact correspondence exists between the small-amplitude periodic electrical and optical responses of PANI films on OTEs. In particular, the characteristic relaxation frequencies of the two responses are identical and appear to be determined by the RC combination consisting of the Faradaic pseudocapacitance of the PANI film in series with the electrode and solution resistances. The modulated optical response was found to persist even when the film was converted to its conducting state, showing clearly that the apparent ‘double-layer charging current’ observed in the plateau region of the cyclic voltammogram is associated with a Faradaic process. In spite of its power, there have been few applications of modulated transmittance. Kankare and ParenZ5 have used a similar method to characterize poly(3-methylthiophene) and Keddam et aLZ6 have described modulated reflectance measurements on PANI films. In the present study, we consider the relationship between frequency-resolved periodic optical (transmission) and electrical (impedance) responses of PANI films grown electrochemically on I T 0 electrodes. Impedance and modulated reflectance measurements of PANI-coated platinum electrodes will be discussed el~ewhere.~ ~
1
Theory Relationship between Electrical and Optical A.C. Response The optical transmission of a film of thickness, d, is given by Itrans/ZO = exp( - ad) = exp( - 4nkd/R)
.
~
~
7
~
J. CHEM. SOC. FARADAY TRANS., 1991, VOL. 87
854
where I , is the incident light intensity (corrected for is the transmitted light intensity. Here a reflection) and Itran, is the absorption coefficient and k is the imaginary component of the complex refractive index at the wavelength, 1. For the present purposes, it is convenient to eliminate the film thickness by rewriting eqn. (1) in terms of the surface concentrations r, (mol mP2) of absorbing species and the corresponding molar absorption cross-sections, on (m2 mol - I ) . = ~ X P( Ern an)
Itransl'o
(2)
For a potential perturbation between two values a and b, the normalized change in transmission is related to the corresponding changes, Ar, in surface concentration
For small optical perturbations, eqn. (3) can be written in the linearized form
ATIT =
-mr,o,
-
s
~o)/nF]
(5)
Z F ( W ~ )dt
We can now relate the optical and electrical responses of the film by noting that the total a.c. current density, I,,, (which is the sum of the Faradaic and non-Faradaic components), is related to the perturbing voltage, V , by
I,,,
=
V/Z = VY
(6)
where Z is the film impedance and Y is the film admittance. The total a.c. charge density Qtotis related to the perturbing voltage by
Q,,, =
i
=
CV
(7)
5
(8)
= nF(AT/T)/[(oR -
Alternatively, we can consider the time derivative of the normalized transmission d(AT/T)/dt = [(OR
-
~o)/nF]Zdwt)
(9)
in order to derive the optical admittance, Y,,, x p t = {nF/[(oR
(1)
where R is the corresponding reduced species. Eqn. (4)then takes the form
AT/T = -(ArR
OR
+ A r p o p + ArB oB)
-
(11)
and although the relationship between AT/T and AQ will still be linear for small perturbations, the optical complex capacitance is less easy to define and AT/T will in general no longer be a linear function of the complex capacitance. This situation is considered in more detail in the discussion section.
The Effect of the Distributed Resistance of the I T 0 Electrodes When considering the impedance of PANI films on I T 0 substrate electrodes, it is necessary to take into account the distributed sheet resistance of the transparent oxide coating. In our experiments, the resistance measured between the ends of the I T 0 electrodes (1 cm square) was typically 20-30 Q. Some of this resistance is associated with the part of the I T 0 that is covered with insulating epoxy, and so it can be treated simply as a series resistance. On the other hand, the exposed part of the I T 0 electrode can be represented by a distributed resistive network28 which is connected via the impedance of the PANI film to the distributed resistance of the electrolyte solution. The equivalent circuit of the PANI-coated I T 0 electrode is shown in Fig. 1. The total impedance of the circuit shown in Fig. 1 is given by the sum of the contact resistance R,,,, and the distributed impedance Zdist,28 where
Zdist= (ZpRito)1/2cotanh[IRjto/(ZpRj3'/2] I,,, dt
where C is the complex capacitance, defined by C = Y dt. It follows from this discussion that AT/T should be linearly related to the Faradaic complex capacitance and it is therefore possible to define the optical complex capacitance, Copt, as Copt
P+P=B+R
(4)
The changes in surface concentration, Arn,are related to the Faradaic component of the current density (IF)and hence to the corresponding component of the charge density AQF . If, for example, we consider two species that are involved in the redox reaction R = 0 + ne, then ArB= -ArR= AQF/nF. For an a.c. perturbation, eqn. (4)then takes the form
AT/T = [(OR
The relationship between AT/T and the complex capacitance will no longer be linear if more than two species are involved in the redox equilibria. There is evidence from EPR measurements1'>12for the existence in the conducting state of PANI of unpaired spin radical cation states (polarons) and paired spin states (bipolaron or quinone imine). Equilibrium between the polaron (P) and bipolaron (B) states is expected to be established by the reaction
d(AT/T)/dt
(12)
Here I is the length of the IT0 electrode, 2, is the distributed impedance made up of the capacitance of the PANI film and the electrolyte resistance, and Rito is the distributed sheet resistance of the I T 0 electrode.
Ir
Rc o n t a c t
Rsneet
I
(10)
Finally, it may be of interest to obtain the optical impedance, Zopt,which can be defined as Zopt= Yoi: . It is important to note that the electrical terms C , Y , and Z become identical with their optical analogues Copt, and Zopt,only in the case where non-Faradaic processes make no contribution to the total current, i.e. It,, = I , . Provided that interference effects are negligible, the foregoing analysis can be extended to approximate the reflectance behaviour of thin films on a reflecting substrate by taking the increased optical pathlength into account. However, for thicker films it is necessary to use the three-layer
x,,
Cpolymer
Rsolutlo"
;
I
Fig. 1. Equivalent circuit of a PANI-coated I T 0 electrode. The impedance of the PANI film has been represented as a pseudocapacitance (valid for thin films)
855
J. CHEM. SOC. FARADAY TRANS., 1991, VOL. 87
real( impedance/l 0 n) real (admittance/l 0 - 2n-’) real(capacitance/l 0-4 F )
0 ) ?
0
log [frequency/Hz]
Fig. 2 (a) Complex plane plots of the impedance (+), admittance (a)and capacitance (0) corresponding to the equivalent circuit shown in = 10 R, Rsheet = 20 R cm-’, Cpolymer = 0.5 mF cm-’ and Rsolution= 0.2 R cm2; ( b ) Bode plot of the impedance of the Fig. 1 , where RcOntact equivalent circuit shown in Fig. 1 calculated using the same values as those given in Fig. 2(a); ( 0 )magnitude (0) phase angle
The effects of the distributed and series resistance on the impedance, admittance and complex capacitance are illustrated by Fig. 2(a) and (b). It can be seen that at high frequencies the impedance plot deviates from the vertical line corresponding to the simple series RC circuit, and the corresponding response in the admittance is manifest as a second high-frequency semicircle. By contrast, the complex capacitance plot is much less sensitive to the effects of the distributed sheet resistance, since it compresses the high-frequency response and emphasizes the low-frequency semicircle. This is demonstrated by Fig. 2(a) which shows that the complex capacitance plot forms an almost perfect semicircle. The Bode plot [Fig. 2(b)] gives the most balanced representation of the impedance. The low-frequency behaviour tends towards purely capacitive behaviour as expected, but the transition at high frequencies to near resistive behaviour proceeds via an intermediate region where the distributed impedance is important. This is evident in the change of slope in the log[Z]/logf plot from - 1 towards -0.5 and the corresponding flattening off in the phase-angle plot.
Experimental PANI films were grown p~tentiodynamically~~ on I T 0 electrodes by cycling the potential between -0.2 and 0.75 V us. SCE in a solution containing 0.1 mol d m - 3 of freshly dis-
tilled aniline (Aldrich ‘Gold Star’ grade) in 1.0 mol dm-3 H,SO, (BDH ‘Aristar’ grade). The potential was extended to 0.9 V for the first cycle to promote nucleation of the film. OTEs were constructed from 1 cm2 pieces of indium-doped tin oxide (ITO) coated glass (Hoya). Contacts were made with conducting silver paint and the contact area was insulated by a layer of epoxy resin. The PANI film thicknesses were calculated from the relationship between thickness and switching charge in the cyclic voltammogram established independently by e l l i p ~ o m e t r y . ~ ~ Electrochemical measurements were carried out in a threeelectrode cell controlled by a potentiostat constructed using high-bandwidth operational amplifiers. Frequency-resolved transmission measurements were performed at fixed d.c. potentials and wavelengths in a single-beam arrangement in which monochromatic light, provided by a tungsten lamp and a grating monochromator, was detected by a suitably positioned silicon photodiode. The output of the photodiode was measured with a wideband current amplifier with a d.c. offset facility and was fed to a Solartron 1250 frequencyresponse analyser, which in turn provided the smallamplitude a.c. modulation to the potentiostat. Impedance measurements were performed at constant d.c. potential under identical conditions using the Solartron frequencyresponse analyser. Data acquisition, treatment and presentation were carried out under microcomputer control.
J. CHEM. SOC. FARADAY TRANS., 1991, VOL. 87
856
obtained on the first cycle after holding the potential at the negative limit sufficiently long to ensure complete reduction of the PANI film (see ref. 17 for a discussion of the effect of multicycling on the anodic peak). The voltammogram obtained with the I T 0 electrode exhibits the familiar shape observed for PANI-coated platinum, although the background current at the negative limit is much smaller owing to the much higher overpotential for hydrogen evolution on ITO. The hysteresis observed in the voltammogram, which is typical of many conducting polymer systems, does not appear to arise from slow electron-transfer kinetics since the shape of the voltammogram remains unchanged at sweep rates of up to 1000 V s-'.I7 It seems more likely that a structural transformation of the type discussed by Heinze et aL4 and by Feldberg and Rubinstein' is responsible. However, more evidence is needed to support the proposed mechanisms or any other possibilities, such as film swelling during the influx of
counter ion^.^^
1
-0.2
1
1
1
1
1
1
1
0 0.2 0.4 potentialp vs. SCE
It is significant that the optical absorbance in Fig. 3(a) increases over the entire range of the forward potential scan, indicating that oxidation still takes place in the plateau region following the anodic peak. Fig. 3(b) shows that the hysteresis, exhibited in the absorbance plot of the forward and reverse potential scans, disappears in a plot of absorbance us. charge indicating that the composition of the film is determined by the charge rather than the potential (we note, however, that some hysteresis was observed in the absorbance-charge plots measured at 450 nm). Fig. 3(b) also shows that the absorbance does not increase linearly with charge, which indicates that more than two species are involved in the redox reactions. Zotti and Schiavon14 have analysed the non-linear charge dependence of the absorbance at different wavelengths in terms of the polaron-bipolaron equilibrium, and have obtained the polaron density as a function of oxidation charge and the corresponding association constan t. Impedance measurements were carried out on a range of PANI films on I T 0 electrodes. Fig. 4 contrasts the complexplane impedance, admittance and capacitance plots for a 26 nm thick PANI film on an I T 0 electrode at 500 mV us. SCE
1
0.6
40 h
$ v
Q,
m C
e v)
n
20
0
1 2 charge/mC cm-*
3
Fig. 3 (a) Cyclic voltammagram for an 80 nm PANI film on ITOcoated glass (1 cm') at 20 mV s - * . The figure also shows the simultaneously recorded change in the optical absorption of the film at 620 nm. The absorbance increases over the whole range of potential. (b) Plot of absorbance us. charge constructed from the data in (a). Note the absence of hysteresis and the deviation from linearity; (a) anodic sweep; (())cathodic sweep
0
'9 *
Results and Discussion
iw 0100 Hz
O
5 - p
---o 0
Fig. 3(a) illustrates the relationship between the cyclic voltammetric behaviour of a PANI film and the corresponding changes in optical transmittance at 620 nm. The data were
0 0
reaI(,ZJn) _ _ _____* ~ real(Y/Q-') -012 rea1(C/1o - F) ~ ___10 ~
4---- -
.
Fig. 4 Complex-plane impedance (+), admittance (a)and capacitance (0) plots of a 26 nm PANI film on an ITO-coated glass electrode (1 cm2) measured at 500 rnV us. SCE. Note the similarity between the experimental electrode response and the calculated plots shown in Fig. 2(a)
J. CHEM. SOC. FARADAY TRANS., 1991, VOL. 87
857
5 h
LL d
0
0.5
1
real (C/m F)
-
I
I
0.5
0
.,
real (C/m F)
Fig. 5 Complex plane plots of the complex capacitance of a 26 nm PANI film on an ITO-coated glass electrode (1 cm2) at different potentials us. SCE: (a) 0, 500 mV; 400 mV; 0 , 200 mV; 0, 150 mV; (b) +, 100 mV; 0 , 50 mV; 0, 0 mV. The data were obtained for d.c. potentials decreasing in steps from 0.5 V
[i.e. at a potential corresponding to the anodic limit of the cyclic voltammogram in Fig. 3(a)].Here, as in the simulations in Fig. 2, the impedance plot deviates at high frequencies from the vertical line corresponding to the series RC circuit. The remarkably good fit to the theory is manifest in the
admittance plot which shows the predicted high-frequency semicircle. By contrast, the complex capacitance appears to form an almost perfect semicircle since the high-frequency response is compressed. The presentation of the data in the form of the complex capacitance is particulary convenient since it allows the film capacitance to be obtained by extrapolation of the plot to zero frequency. The effect of potential on the a.c. response of the PANIcoated electrode is illustrated by the complex capacitance plots in Fig. 5(a) and (b) which were recorded for successively less positive values of the electrode potential in order to avoid the 'memory effects' associated with the reduced form of PANI. The extrapolation of the complex capacitance plots to zero frequency showed that the capacitance goes through a rather small maximum at around 150 mV on the reverse scan. Measurements for film thicknesses in the range 20-300 nm showed that the film capacitance increases and a,,, decreases approximately linearly with film thickness. The transition in the electrical behaviour of the film from capacitive at low frequencies to resistive at high frequencies is best illustrated in the Bode plot shown in Fig. 6. The resemblance between Fig. 6 and Fig. 2(b)further confirms the validity of the equivalent circuit of the PANI-coated I T 0 electrode shown in Fig. 1. Note that the PANI films considered here are sufficiently thin that no additional highfrequency semicircle appears in the complex plane impedance plot.20,21 Fig. 7 compares capacitance values derived from the impedance measurements with the apparent capacitance derived from the cyclic voltammogram by assuming that the measured current is given by the product of the sweep rate and the pseudo-capacitance. It is immediately clear that the capacitance measured using a small-amplitude perturbation at constant d.c. potential is considerably lower than the apparent capacitance derived from the cyclic voltammogram. Furthermore, the positions of the capacitance maxima do not coincide. This kind of behaviour has been noted for other
- 90
_ .
-1.0
0
1.0
2.0
3.0
4.0
log (frequency/Hz)
Fig. 6 Bode plot of the impedance of the same PANI film (26 nm) as in Fig. 5 at -200 mV ( 0 , magnitude; 0, phase) and 500 mV (m, magnitude; 0, phase)
J. CHEM. SOC. FARADAY TRANS., 1991, VOL. 87
858
I
4 rnF c m - 2
-1
-0.5
.o
-1.5
real(AT/T)/l 0-4
real(AT/T)/l 0 -
- 0.2
0 0.2 0.4 potentialp vs. SCE
Fig. 7 Comparison of the capacitance of a 66 nm PANI film determined from the impedance (0) with the pseudo-capacitance derived from the cyclic voltammogram
Fig. 8 Complex-plane plots of the modulated normalized transmittance AT/T at 630 nm for the same PANI film as in Fig. 5 for decreasing potentials from 0.5 V; (a) 0, 500 mV;W, 400 mV; 0 , 200 mV; ( b ) 0, 150 mV, 100 mV; .,50 mV
+,
The dependence of AT/T on oxidation charge is compared in Fig. 9 with the corresponding variation of the complex capacitance. For simplicity, the comparison has been restricted to the reverse sweep from 0.5 V. The first point to note is that no maximum is observed in the AT/T plot, in spite of the fact that the complex capacitance passes through a maximum at 0.15 V. In fact, the largest AT/T response is obtained at the anodic limit of 0.5 V, which is in the region where the plateau current in the cyclic voltammogram might be attributed to double-layer charging of the fully oxidized polymer. The optical response provides convincing proof that
polymer system^.^'.^^ In the case of PANI at least, the differences cannot be attributed to slow kinetics since cyclic voltammetry at microelectrodes has shown that the shape of the cyclic voltammogram remains unchanged even at sweep rates of up to loo0 V s-'. It must be concluded that smallamplitude periodic perturbation results in the reversible transfer of a smaller quantity of charge than is observed during a large potential excursion. The reasons for this are not clear at present, but it has been suggested that rapid electron transfer is accompanied by significant conformational 0.C changes in the polymer which occur on a longer time~cale.~ We note that the capacitance values obtained from the impedance measurements for increasing and decreasing d.c. potentials still show significant hysteresis, in spite of the fact that each measurement was made after waiting for three 0.C minutes. The first-order rate constants for the structural from the analysis transformation obtained by Albery et NI of spin-density transients are sufficiently high that we should expect the most stable conformation to be achieved on the L L timescale of our measurements. If this were indeed the case, E 0.4 the capacitance data should not exhibit hysteresis. At present we have no evidence that the hysteresis would disappear on longer timescales. The correlation between the complex electrical and optical capacitances can be seen by comparing Fig. 5 with Fig. 8 ; the latter shows the normalized modulated transmittance at 630 0.; nm of the 26 nm PANI film in Fig. 5. The correspondence between the electrical and optical responses is clearly demonstrated by the fact that their characteristic relaxation fre1 I 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 quencies are identical. This confirms our previous conclusion that the 'capacitive current' is associated with charge transQlQ,,, fer.24 As expected, the value of AT/T at zero frequency Fig. 9 Plots of complex capacitance (0) and modulated transmitincreases whereas w,,, decreases linearly with film thickness, as a function of oxidation charge normalized to charge at tance).( 0.5 V. All data were taken for the reverse sweeD following exactlv the behaviour of comdex caDacitance.
5
I
I
I
I
I
I
J. CHEM. SOC. FARADAY TRANS., 1991, VOL. 87
the charging in this potential region is still due to a redox process in the film. Eqn. (8) predicts that a plot of AT/T against the complex capacitance should be a linear function provided that the redox equilibrium is dominated by only two species and nonFaradaic charging is negligible. The EPR data” suggest that the initial oxidation leads to a radical cation or polaron state, whereas the bipolaron is stable only at more positive potentials. Fig. 10 shows that the initial part of the plot of AT/T against film capacitance is indeed linear, but as the degree of oxidation exceeds the value where bipolarons are presumed to form, the plot folds back as AT/T continues to rise but the capacitance falls again. Analysis of this part of the curve is difficult because a realistic model describing the polaronbipolaron equilibrium must include interaction parameters to explain the broadening of the voltammogram. Here we restrict attention to the first part of the plot which we analyse assuming that only polaron species are present in addition to the reduced form. According to eqn. (8), the plot of AT/T us. C should have a slope which is equal to (oR- ao)V/nF (in the case of the polaron, n = 1). Since the reduced form of the polymer is transparent at 630 nm,29it is possible to obtain an approximate value of the optical absorption cross-section of the polaron; the value estimated from the linear portion of the plot in Fig. 10 is 1.4 x lo7 cm2 molThe absorption coefficient of the PANI films has been determined as a function of wavelength and potential by ellip~ometry~’ at 633 nm; the value of k at 0.15 V on the reverse sweep is 0.12 corresponding to tl = 2.3 x lo4 cm-’. The molar volume V, of the polaron species at the upper limit of the linear plot can now be obtained since V, = op/tl. We find in this way that V, = 600 cm3 mol-’. If we assume that the polaron repeat unit consists of four benzene units and take the density of PAN132 to be 1.2 g cm-3, the mole fraction of polarons at the point where bipolarons begin to form is ca. 0.6, which is in reasonable agreement with the estimate obtained by Zotti and S ~ h i a v o n . ’ ~
’.
Conclusions The simultaneous analysis of the periodic electrical and optical responses of PANI films clearly offers a powerful new
12
10
d (0.9 2
LD
z l
a
2 2 9 4
2
0
-
~~
0.6
0.7 0.8 C/mF c m - 2 Fig. 10 Plot of A T I T us. capacitance [see eqn. (8)1 constructed from data in Fig. 9. Note that the plot is linear at low-oxidation charges where the polaron dominates, but folds round as the bipolaron is formed at higher charges. The linear portion of the plot can be used to derive the absorption cross-section of the polaron (see text)
859
approach to the characterization of this complex material, and the method should also find application to other modified electrode systems. The main conclusion of the study is that the a.c. response of PANI is dominated by Faradaic processes, but the problem of the discrepancy between the smallamplitude (a.c.) and large-amplitude (cyclic voltammetry) capacitance values remains unsolved. It seems unlikely that analysis of a.c. impedance data alone will offer any new insights into the mechanisms of conducting-polymer oxidation and reduction, and approaches based on complex equivalent c i r c ~ i t s ~ ~or , ~ ’ on invalid models involving non-Faradaic processes” have little to recommend them. A complete understanding of these complex systems will require simultaneous application of even more than the two techniques discussed in this paper. In this context, the introduction of the a.c. modulated mirobalance method34 may prove to be an important step forward since this method can, in principle, be used to deconvolute anion and cation fluxes during the cycling of conducting-polymer films. This work was supported by the SERC and the Ministry of Defence. The authors wish to thank the Hoya Corporation (UK) for the donation of I T 0 materials.
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Paper 0/04142D;Received 1lth September, 1990
