Anal. Chem. 1997, 69, 2337-2342
Potentiometric Response of Conducting Polymer Electrodes for Oxygen in Neutral Aqueous Solutions Jouko Kankare*
Department of Chemistry, University of Turku, FIN-20014 Turku, Finland Igor A. Vinokurov
Department of Chemistry, St. Petersburg University, 198904 St. Petersburg, Russia
The effect of oxygen on the potential of electrodes coated with a thin layer of various conducting polymers and immersed in aqueous neutral buffer solution has been studied. A theoretical equation describing the dependence of the potential on the concentration of oxygen has been derived and shown to be in conformity with the experimental results for polyaniline, polypyrrole, and poly(3-methylthiophene). The theory is based on the formation of charge-transfer complexes between oxygen molecule and the reduced (undoped) form of conducting polymer. A fast and simple determination of dissolved oxygen in aqueous solutions is important in various fields such as environmental monitoring, physiological measurements, etc.1 The most important oxygen sensor for this purpose has been the Clark electrode, which is essentially a voltammetric cell. Its main problems are the proper choice of materials, leakage of electrolyte solution, and somewhat complicated construction. Also the construction of a subminiature version is not without problems. A direct potentiometric sensor would be simpler and more amenable for miniaturization. Unfortunately, due to the irreversible nature of oxygen reduction at almost any electrode material, proper electrodes with the stable and reproducible potentiometric response have been difficult to come by. It was recently shown by Park et al.2 that a platinum electrode coated with polyaniline can be used as a satisfactory potentiometric sensor for dissolved oxygen. In general, conducting polymers are interesting sensor materials because of their nearly infinite variability which, in principle, allows the construction of selective electrodes for different purposes. Polyaniline is interesting because of its easy synthesis, inexpensive monomer component, and stability in aqueous media. However, there are numerous other, already “classical” conducting polymers which deserve to be studied in this respect. The mechanism of interaction of oxygen with conductive polymers is still somewhat obscure, and reports in the literature are controversial. Park et al.2 suggested charge transfer from leucoemeraldine to oxygen whereupon superoxide is formed. Superoxide ion is unstable in aqueous solution and disproportionates to hydroxide and peroxide ions. Polyaniline has been (1) Hitchman, M. L. Measurement of Dissolved Oxygen; Wiley: New York, 1978. (2) Shim, Y. B.; Stilwell, D. E.; Park, S.-M. Electroanalysis 1991, 3, 31-36. S0003-2700(96)01217-6 CCC: $14.00
© 1997 American Chemical Society
studied in strongly acidic solutions,3,4 and a two-electron reduction of oxygen to hydrogen peroxide by the reduced form of polyaniline has been suggested. In a more recent paper Cui and Lee5 studied the effect of polyaniline on oxygen reduction in buffered neutral solution. Although the total reduction seems to be a four-electron process, the rate-determining step is the one-electron reduction of the adsorbed dioxygen molecule. Furthermore, the presence of the polyaniline coating on glassy carbon seems to enhance the adsorption of oxygen. Polypyrrole is known to show only little activity for the catalytic reduction of oxygen. Okabayashi et al.6 reported no catalytic activity at all, whereas Jacobs et al.7 showed some activity. However, it is well-known that molecular oxygen reacts with pristine (undoped) polypyrrole. Investigations of this type have been conducted by Street et al.,8-10 Son and Rajeshwar,11 and very recently by Lei and Martin.12 Street et al. correlated measurements of oxygen uptake by pristine polymer with conductivity and EPR data, providing evidence for the polaron and bipolaron concepts in polypyrrole. The nature of the interaction of oxygen with polymer was not elucidated. Lee and Martin12 used FT-IR, XPS, and electrochemical data to show that this interaction may take different forms, depending on the time scale. The first stage is the formation of a molecular association complex, essentially a charge-transfer complex with a partial charge transfer. The measured doping level is only 0.06 although XPS shows that 0.34 O is introduced. Hence, the majority of oxygen is as a molecular association complex. On prolonged exposure to oxygen, the pyrrole nitrogen is deprotonated with a subsequent irreversible reaction. It is most likely that the formation of charge-transfer complexes between oxygen and conductive polymers is a general (3) Mengoli, G.: Musiani, M. M.; Zotti, G.; Valcher, S. J. Electroanal. Chem. 1986, 202, 217-230. (4) Doubova, L.; Mengoli, G.; Musiani, M. M.; Valcher, S. Electrochim. Acta 1989, 34, 337-343. (5) Cui, C. Q.; Lee, J. Y. J. Electroanal. Chem. 1994, 367, 205-212. (6) Okabayashi, K.; Ikeda, O.; Tamura, H. J. Chem. Soc., Chem. Commun. 1983, 684-685. (7) Jacobs, R. C. M.; Janssen, L. J. J.; Barendrecht, E. Electrochim. Acta 1985, 30, 1433-1439. (8) Street, G. B.; Clarke, T. C.; Krounbi, M.; Kanazawa, K. K.; Lee, V.; Pfluger, P.; Scott, J. C.; Weiser, G. Mol Cryst. Liq. Cryst. 1982, 83, 1285-1296. (9) Pfluger, P.; Krounbi, M.; Street, G. B.; Weiser, G. J. Chem. Phys. 1983, 78, 3212-1328. (10) Scott, J. C.; Krounbi, M.; Pfluger, P.; Street, G. B. Phys. Rev. B 1983, 28, 2140-2145. (11) Son, Y.; Rajeshwar, K. J. Chem. Soc., Faraday Trans. 1992, 88, 605-610. (12) Lei, J.; Martin, C. R. Chem. Mater. 1995, 7, 578-584.
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phenomenon. In a recent publication, Holdcroft et al.13 showed that poly(3-hexylthiophene) and molecular oxygen form a reversible charge-transfer complex. They used UV-visible-near-IR spectroscopy to observe the charge-transfer band and showed unequivocally the reversible influence of oxygen on the conductivity of the polymer film by using a thin-film field effect transistor. It is the purpose of this report to present results of our studies of polyaniline, polypyrrole, and poly(3-methylthiophene) as potentiometric oxygen electrodes. The emphasis is on getting basic knowledge of the behavior these materials in contact with oxygencontaining aqueous solution and later on to embrace the studies to include full feasibility tests. THEORY The open circuit potential of a conductive polymer electrode depends on the redox state of the polymer. The redox state can be influenced by either injecting electric charge or adding a reagent that interferes with the redox equilibrium. The main problem in the theoretical treatment of the redox processes in conductive polymers is the ambiguity in choosing the reactive species in the polymer network that participate in these processes. The reactive species could be “polarons” and “bipolarons”, i.e., singly and doubly charged sites in the polymer chain with their neutralizing counterions. Also, the corresponding neutral unoccupied sites that are conformationally fitted to receive the charge and counterions could be considered as independent species. In order to keep our minds open, we do not use any special name for these reactive sites. The second question is whether we assume that equilibrium prevails in the entire system. In that case, we could deal with the system in an easy way by using expressions derived from the chemical equilibria and electrochemical potentials of the species. In particular, the equilibrium potential could be treated on the basis of the Nernst equation. However, in the potentiometric measurement, it is sufficient to assume that the net current passing through the interface is zero. In the presence of several redox processes, we are then dealing with the stationary potential in analogy with the theory of corrosion processes. Let the active sites in the polymer be denoted by A and the reduced site by D. Let us first assume that oxygen forms a charge-transfer complex with both of these species. Then we have the following three redox processes: jc1
A+e\ {j } D jc2
jc3
(3)
where ja and jc refer to the anodic and cathodic current densities, respectively. In the stationary state j ) 0, the net current is zero:
(4)
If we assume that the mechanisms of processes 1-3 are reasonably similar, then we may assume that their transfer coefficients (13) Abdou, M. S. A.; Orfino, F. P.; Xie, Z. W.; Deen, M. J.; Holdcroft, S. Adv. Mater. 1994, 6, 838-841.
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R)FEj)0/RT] + k0a2xDO2 exp[(1 - R)FEj)0/RT] + k0a3xD(O2)2 exp[(1 - R)FEj)0/RT] (5) Here x’s are the mole fractions of the six species, Ej)0 is the potential difference between the metal and polymer, and k0’s are rate constants at Ej)0. This potential difference can be solved as
Ej)0 )
0 RT kc1 ln 0 + F k a1
0 0 0 0 RT xA + (kc2/kc1)xAO2 + (kc3/kc1)xA(O2)2 ln (6) F x + (k0 /k0 )x + (k0 /k0 )x D
a2
a1
DO2
a3
a1
D(O2)2
It is reasonable to assume that the mole fractions of the species DO2 and D(O2)2 are linearly related to the mole fraction of free D and to the concentration of oxygen cO2 and its square, respectively:
xDO2 ) βD1xDcO2
(7)
2 xD(O2)2 ) βD2xDcO 2
Here the stability constants of the 1:1 and 1:2 donor-oxygen complexes are denoted by βD1 and βD2, respectively. Similar relations are assumed to be valid for the acceptor A. On the other hand, the total mole fractions of the oxidized and reduced species can be represented as 2 xtot A ) xA + xAO2 + xA(O2)2 ) xA(1 + βA1cO2 + βA2cO2)
(8)
2 xtot D ) xD + xDO2 + xD(O2)2 ) xD(1 + βD1cO2 + βD2cO2)
Substitution of (7) and (8) into (6) gives 0 tot RT kc1xA ln 0 tot + F k x a1 D
(2)
a3
jc1 + jc2 + jc3 ) ja1 + ja2 + ja3
k0c3xA(O2)2 exp(-RFEj)0/RT) ) k0a1xD exp[(1 -
Ej)0 )
a2
A(O2)2 + e \ {j } D(O2)2
k0c1xA exp(-RFEj)0/RT) + k0c2xAO2 exp(-RFEj)0/RT) +
(1)
a1
AO2 + e \ {j } DO2
R are equal, and we may write the equivalent Butler-Volmer equations for (4):
2 0 0 0 0 RT 1 + (kc2/kc1)βA1cO2 + (kc3/kc1)βA2cO2 ln + F 1 + β c + β c2 A1 O2
A2 O2
2 1 + βD1cO2 + βD2cO RT 2 ln (9) 2 0 0 0 F 1 + (ka2/ka1)βD1cO2 + (ka3/k0a1)βD2cO 2
There is a large number of parameters that may be reduced by chemical reasoning. It is plausible that because the oxygen molecule is an electron acceptor, it forms a charge-transfer complex of any significant stability only with an electron donor; i.e., the stability constants βA1 and βA2 are so small that the terms 0 containing them can be ignored. Also the rate coefficients ka2 0 and ka3 for the oxidation of the donor-oxygen complexes are
0 certainly much smaller than the rate coefficient ka1 for the oxidation of the donor itself. This is related to the fact that the acceptor-oxygen complex is considerably weaker than the donor-oxygen complex. Hence we obtain a much simpler expression for the potential:
RT 2 ln(1 + βD1cO2 + βD2cO Ej)0 = E°′ + ) 2 F
K′2 ) xD(O2)2/xD-O2cO2; K′′2 ) xD(O2)2/xO2-DcO2
(11)
(
K ) (β′D1 + β′′D1)
(20)
K ) 4(β′D1/K′2)
(21)
This gives
If we assume that the two oxygen molecules in the 1:2 complex have no mutual interaction, we have β′D1 ) K′2 and K ) 4. If there is mutual attraction between the oxygen molecules complexed with D, the value of K will be diminished. Let the interaction energy be U. Then we may write
It is interesting to note that if the interaction energy U is zero, eq 10 behaves mathematically as if only a 1:1 complex is formed and the number of electrons exchanged is equal to 1/2.
(13)
By making the assumption that the donor forms a 1:2 complex with oxygen, we have also assumed that there are two sites in the donor moiety capable of binding an oxygen molecule. Hence, even in the case of 1:1 complexes we have in fact two equilibria:
D + O2 a D-O2 D + O2 h O2-D
(14)
with the corresponding microscopic equilibrium constants
β′D1 ) xD-O2/xDcO2; β′′D1 ) xO2-D/xDcO2
(15)
We see that
βD1 ) β′D1 + β′′D1
(16)
Correspondingly the 1:2 complex may form from these two 1:1 complexes:
D-O2 + O2 a D(O2)2 (17) O2-D + O2 a D(O2)2
(22)
(12)
E ) E°′ + K)
(19)
β′D1 ) β′′D1 and K′2 ) K′′2
K ) 4e-U/RT
It is easily seen that this constant is obtained from the cumulative equilibrium constants βD1 and βD2:
β2D1/βD2
)
1 1 + K′2 K′′2
Making now a reasonable assumption on the equivalency of the oxygen binding sites, we obtain
which can be described by the equilibrium constant 2 K ) xDO /xD(O2)2xD 2
(18)
Comparing eqs 15-18 to eq 12 we see that
(10)
Here E°′ is the short-hand notation for the first term in the expression 9. It can be taken as a constant because no significant current is flowing during the potentiometric measurement, and on the other hand, due to the assumed mechanism, no net electron transfer is occurring between the polymer and redox-active species tot in solution. Hence, the ratio xtot A /xD is constant. This expression contains only three adjustable parameters, and it can be easily applied to experimental results. One should note that exactly the same expression can be derived on the basis of the assumption that, instead of the steady state assumed here, a complete equilibrium prevails in the system, where only the donor forms complexes with oxygen. Of considerable interest is the disproportionation reaction
D(O2)2 + D a 2DO2
The equilibrium constants for these reactions can be written as
RT 2 ln(1 + βD1cO2 + βD2cO ) 2 F
) E°′ +
RT 2 ln(1 + βD1cO2 + 1/4β2D1cO ) 2 F
) E°′ +
2RT ln(1 + 1/2βD1cO2) F
(23)
EXPERIMENTAL SECTION Apparatus. Electropolymerizations and voltammetric determinations were done on a potentiostat/galvanostat Model PAR 283 (EG&G, Princeton Applied Research) and M270 software. For potentiometric measurements, a digital multimeter Fluke Model 8860 equipped with a high-impedance (∼1014 Ω) preamplifier was used. Reagents. Aniline (E. Merck) and pyrrole (Aldrich) were distilled in vacuo over zinc dust. 3-Methylthiophene (Aldrich), acetonitrile (Baker, HPLC), and lithium perclorate (Aldrich) were used as received. Aqueous solution of phosphate buffer (5 × 10-2 M Na2HPO4/KH2PO4, pH 6.9) was prepared from sodium phosphate and potassium dihydrogen phosphate (Merck). Nitrogen used for deaeration was of the highest purity available (99.999%). Electropolymerization. Polymer films were synthesized under potentiostatic conditions on a platinum wire electrode (Metrohm) with the surface area of ∼0.2 cm2 in solutions containing 0.1 M concentration of monomer and 1 M lithium perchlorate in acetonitrile. Ag/AgCl electrode filled by saturated LiCl in ethanol (Metrohm) served as a reference electrode during Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
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Figure 1. Potentiodynamic curves of a rotating glassy carbon disk electrode in aqueous phosphate buffer containing various concentrations of dissolved oxygen. The rotation speed is 420 rad s-1, and the scan rate 20 mV s-1. The vertical dotted line shows the potential at which the current values were recorded. The nearly horizontal dotted line shows the base line.
electrosynthesis (potential vs NHE +143 mV at 25 °C). The values of applied potential were 2 V for polyaniline, 1.3 V for polypyrrole, and 2 V for poly(3-methylthiophene). The polymerization time in each case was 20 s. Oligomers were partially soluble in the course of synthesis, and hence the amount of polymer grown on the electrode cannot be characterized by the total amount of electricity consumed during the synthesis. After electrosynthesis, the polymer electrodes were washed with acetonitrile for 1 h and stored in aqueous phosphate buffer at least 24 h before the potentiometric measurements were started. Measurements. The measurements of potential of polymer electrodes were carried out in phosphate buffer at pH 6.9 containing different concentrations of oxygen at 25 °C. A calomel electrode (Metrohm) filled with a saturated aqueous solution of KCl was used as a reference electrode. All the potentials are given with respect to this electrode. To determine the concentration of oxygen during the potentiometric measurements, the cathodic potentiodynamic curves of oxygen reduction were simultaneously recorded by using a rotating disk glassy carbon electrode (Beckman, diameter 0.62 cm) placed in the same solution (together with both a stainlesssteel auxiliary electrode and an additional SCE). The potential values of the polymer electrodes and potentiodynamic curves with the RDE were successively recorded starting from air-free buffer solution saturated with nitrogen and proceeding gradually toward oxygen-containing solutions by allowing the solution to make contact with atmospheric oxygen. The contact time with the ambient air was a few seconds at low oxygen concentrations and several minutes at higher concentration levels. The equilibration times before the potentiometric reading was taken varied from some tens of seconds at the low end to some minutes at the high concentration end, each time waiting until only insignificant drift in potential was observed. The parameters of eq 10 (or alternatively by substituting K for βD2 from eq 13) were obtained by fitting the equation to experimental data points by using the nonlinear fitting program of ORIGIN (Microcal, Inc.). Figure 1 shows an example of a set of current vs potential plots for the rotating disk electrode in phosphate buffer solution. It can be seen that, on glassy carbon electrode, oxygen is reduced in a single wave with E1/2 ≈ -0.8 V. The wave height depends 2340
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Figure 2. I-1 vs ω-1/2 for a glassy carbon RDE in air-saturated phosphate buffer at -1.25 V with the scan rate 20 mV s-1.
strongly on the rotation rate of the disk (ω). Limiting current (I) estimated at -1.25 V and the rotation rate dependence were analyzed by plotting I-1 vs ω-1/2 at the ambient oxygen concentration. A good straight line was obtained with an insignificant intercept on the I-1 axis (Figure 2), confirming that at this potential the reduction of oxygen is almost entirely mass transport controlled.14 The estimation of oxygen concentration (CO2) was performed by using the Levich equation 2
1
1
I ) -0.62zFAD /3ω /2ν- /6 CO2 applied to the limiting current (I) of the oxygen reduction process:
O2 + 2H2O + 4e f 4OHwhich is shown to be the predominant stoichiometry in neutral aqueous solutions on a glassy carbon electrode.15 The following parameters were used: z ) 4; F ) 9.648 × 104 C/mol; A ) 0.302 cm2; D ) 2.3 × 10-5 cm2 s-1;16 ω ) 420 rad s-1, ν ) 1 × 10-2 cm2 s-1. RESULTS AND DISCUSSION Often the calibration of an oxygen sensor is performed by utilizing aqueous oxygen solutions made by bubbling gas mixtures of oxygen and nitrogen through the aqueous phase. Usually due to the tedious procedure only a few data points are used and the calibration curve is made by rather rough interpolation. In the present work special attention was paid to the accurate determination of dissolved oxygen by a voltammetric method based on the use of a RDE. By a thorough deaeration with highly purified nitrogen and gradual dissolution of atmospheric oxygen, a reasonably large concentration range of oxygen could be reached. The reason for the choice of the RDE voltammetric method of the oxygen determination was that in this way a reasonably calibrationfree method could be used. An alternative would be some commercial dissolved-oxygen meter but it was felt that one cannot completely rely on the manufacturer’s specifications, especially at low oxygen concentrations. The in situ determination of oxygen (14) Bard, A. J.; Faulkner, L. R. Electrochemical Methods. Fundamentals and Applications; J. Wiley: New York, 1980; p 290. (15) Taylor, R. J.; Humffray, A. A. J. Electroanal. Chem. 1975, 64, 95-105. (16) Zwetanova, A.; Ju ¨ ttner, K. J. Electroanal. Chem. 1981, 119, 149-164.
Table 1. Cumulative Stability Constants of the 1:1 and 1:2 Complexes and Disproportionation Constant of the Neutral Forms of Conductive Polymers with Oxygen and the Interaction Energy U of Oxygen Molecules in the 1:2 Complex
Figure 3. Potential of Pt wires coated with polypyrrole, polyaniline, and poly(3-methylthiophene) vs SCE in phosphate buffers at pH 6.9 and different concentrations of dissolved oxygen.
allowed a reasonably convenient and reproducible way of concentration variation. The large range of oxygen concentration and its accurate determination allows one to draw conclusions on the mechanism of potential formation. Polyaniline, polypyrrole, and poly(3-methylthiophene) were chosen as representatives of typical conductive polymers not only because they are the most commonly used and most thoroughly studied conducting polymers, but also because they represent different types of these materials. Polyaniline is the most hydrophilic of these three polymers, and it has the special property of being dopable by protonation. Poly(3-methylthiophene) is a representative of highly hydrophobic polymers. Although 3-methylthiophene cannot be polymerized in aqueous solutions as aniline or pyrrole, the polymer made in a nonaqueus solution is stable in water. Polypyrrole is between polyaniline and poly(3methylthiophene) in hydrophobicity. Pyrrole is easily polymerized even in neutral aqueous solutions, and the resulting polymer is commonly used as a substrate for various kinds of biosensors because of the mild polymerization conditions and compatibility with large biomolecules. The electropolymerizations were carried out in acetonitrile using the same electrolyte in every case. In this way we could assure that swelling caused by the incorporation of solvent and electrolyte were comparable. Although the preparation was carried out in nonaqueous solvent, conditioning of the electrode was done in the same solvent where the potentiometric measurement was to be done, i.e., in aqueous phosphate buffer. From the practical point of view, neutral aqueous solution was considered as the best alternative, although it was realized that, for example, polyaniline is essentially electrically inactive at this pH and previous measurements by other researchers were done in strongly acidic solutions.2 The results of the potentiometric measurements are summarized in Figure 3 together with the fitted curves according to
polymer
log βD1
log βD2
log K
U (298 K), kJ/mol
polyaniline polypyrrole poly(3-methylthiophene)
3.90 ( 0.09 4.34 ( 0.10 4.79 ( 0.03
8.52 ( 0.02 8.79 ( 0.04 8.87 ( 0.02
-0.72 -0.11 0.71
7.5 ( 1.1 4.1 ( 1.2 -0.6 ( 0.4
eq 10. It can be seen that the proposed equation fits rather well in all three cases. The numerical values of the stability constants and the interaction energies U are shown in Table 1. The cumulative stability constants are surprisingly close to each other, especially the values for the 1:2 complexes. The interaction energies U have a lower precision, but still one can rather clearly see that the interaction of the two oxygen molecules in the poly(3-methylthiophene) complex is nearly zero, meaning that the second oxygen molecule reacts equally easily with the donor moiety as the first one. In the more polar polymers, polyaniline and polypyrrole, oxygen molecules have a strong attraction, meaning that the reaction of the first oxygen favors the reaction of the second one with the same moiety. If the formation of the 1:1 and 1:2 donor-oxygen complexes is hypothetically assumed to involve full electron transfers, the difference in the interaction energies U may reflect the differences in the mutual stabilities of polarons and bipolarons in these three polymers. (The authors are grateful for this suggestion to one of the reviewers.) However, one should be cautious with further speculations, especially as the existence of polarons and bipolarons in conjugated polymers is still a controversial subject and constitutes a research field of its own, as very recently reported by Furukawa.17 The values of the stability constants may seem to be rather high for stability constants of charge-transfer complexes. It is customarily thought that the charge-transfer complexes generally are quite labile and unstable. However, one should take into account that these equilibria are heterogeneous and they include the phase-transfer distribution of oxygen from water to a solid organic medium. CONCLUSIONS Although the derived eq 10 is in rather good conformity with the experimental measurements, thus seemingly supporting the proposed mechanism, it is not completely solid evidence of the formation of charge-transfer complexes between oxygen and conducting polymer and their role as potential-determining species. It is quite possible that some other mechanism may lead to the same equation. The simplest explanation is that the oxidative power of oxygen may change the oxidation/reduction quotient or “doping level” of the polymer, which leads to the change of potential. However, one should note that the full electron transfer from the conducting polymer to the oxygen molecule leads to the formation of oxygen anion and superoxide radical, which are not stable in an aqueous system. Consequently, the fully irreversible nature of oxygen reduction may not produce the stable potential observed in the present neutral aqueous system. Of course it is quite possible that the oxygen anion radical formed (17) Furukawa, Y. J. Phys. Chem. 1996, 100, 15644-15653.
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in the charge transfer does not diffuse away but remains as a stable ion pair with the oxidized polymer segment. But this leads exactly to the same equation as the partial charge transfer. The similar behavior of the three very different polymers is noteworthy. It seems that the polarity of the polymer medium is not a determining factor in complex formation. The only significant differences can be observed in the disproportionation reactions 11 and the derived interaction energies of oxygen molecules in the 1:2 complexes. How the strong attractive interaction in the more polar polymers, polypyrrole and polyaniline, can be explained, remains at the level of speculation. The practical analytical exploitation of conducting polymers as dissolved oxygen sensors is a promising possibility. The very
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small size of coated-wire electrodes may allow different interesting biological and physiological applications. Considerable research and development is still needed in improving the stability and studying possible intereferences. ACKNOWLEDGMENT Financial support from the Academy of Finland and the Nordic Council of Ministers is gratefully acknowledged. Received for review December 3, 1996. Accepted March 25, 1997.X AC9612178 X
Abstract published in Advance ACS Abstracts, May 1, 1997.
