Anal. Chem. 1997, 69, 5082-5086
An Electron Time-of-Flight Method Applied to Charge Transport Dynamics in a Cobalt Bipyridine Redox Polyether Hybrid Jeffrey W. Long, Roger H. Terrill,† Mary Elizabeth Williams, and Royce W. Murray*
Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290
An electrochemical time-of-flight technique is employed in the investigation of charge transport dynamics in a cobalt bipyridine redox polyether hybrid. Measurements of the apparent diffusion coefficient, DAPP, provide insight into electron self-exchange reactions in the undiluted molten metal complex. Results from time-of-flight measurements are compared to those from potential step chronoamperometry and cyclic voltammetry; good agreement is observed. Peak shapes are compared with simulations from a previous report; disparities noted are ascribed to differences in the potential pulse profile employed. Electroactive polymer films1 have experienced intensive research owing to their potential applications in chemical sensors, electrocatalysis, electrochromic devices, and energy storage. These materials include films of redox polymers,2 where an electroactive probe is covalently attached to a polymeric lattice, and polyelectrolyte membranes,3 such as Nafion, into which charged probes have been incorporated. The rate of electron hopping1,4 or electron self-exchange transport through the films is a property both of fundamental significance in electron-transfer dynamics and of practical importance since this process transports oxidizing or reducing equivalents through films in their applications. Electrochemical methods used to measure diffusion rates within these polymers have included transient ones like potentialstep chronoamperometry and chronocoulometry5 and cyclic voltammetry,6 and a variety of steady-state methods.7 † Beckman Institute, University of Illinois, Urbana, IL 61801. (1) Murray, R. W., Ed. Molecular Design of Electrode Surfaces; John Wiley & Sons, Inc.: New York, 1992. (2) (a) Elliott, C. M.; Baldy, C. J.; Nuwaysir, L.; Wilkins, C. L. Inorg. Chem. 1990, 29, 389. (b) Wrighton, M. S. Science 1986, 231, 32. (c) Chidsey, C. E. D.; Murray, R. W. Science 1986, 231, 25. (d) Murray, R. W. Annu. Rev. Mater. Sci. 1984, 14, 145. (e) Abruna, H. D. In Electroresponsive Molecular and Polymeric Systems; Skotheim, T. A., Ed.; M. Dekker: New York, 1988; Vol. 1. (3) (a) Haas, O.; Kriens, M.; Vos, J. G. J. Am. Chem. Soc. 1981, 103, 1318. (b) Oyama, N.; Anson, F. C. J. Electrochem. Soc. 1980, 127, 247. (c) Oyama, N.; Anson, F. C. Anal. Chem. 1980, 52, 1192. (d) Oyama, N.; Shinomura, T.; Anson, F. C. J. Electroanal. Chem. 1980, 112, 271. (4) (a) Facci, J.; Murray, R. W. J. Phys. Chem. 1981, 85, 2870. (b) Kaufman, F. B.; Engler, E. M. J. Am. Chem. Soc. 1979, 101, 547. (5) (a) Andrieux, C. P.; Saveant, J.-M. J. Phys. Chem. 1988, 92, 6761. (b) Miller, C. J.; Widrig, C. A.; Charych, D. H.; Majda, M. J. Phys. Chem. 1988, 92, 1928. (c) Goss, C. A.; Miller, C. J.; Madja, M. J. Phys. Chem. 1988, 92, 1937. (6) (a) Oyama, N.; Anson, F. C. J. Electrochem. Soc. 1980, 127, 247. (b) Widrig, C. A.; Majda, M. Anal. Chem. 1987, 59, 754. (c) Buchanan, R. M.; Calabresse, G. S.; Sobieralski, T. J.; Wrighton, M. S. J. Electroanal. Chem. 1983, 153, 129.
5082 Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
Our synthetic efforts have recently produced a new class of electroactive materials8 that while only oligomeric, have many polymer-like characteristics, such as high viscosity, lack of crystallinity above a glassing temperature, and very slow physical self-diffusion rates. These “redox polyether hybrids” consist of oligomeric poly(ethylene glycol) or poly(propylene glycol) chains attached to an electroactive species, are uniformly melts at room temperature, are highly concentrated in redox sites, and dissolve appreciable quantities of lithium and magnesium electrolytes. Among the redox species to which polyether “tails” have been attached are derivatives of ferrocene,8a porphyrins,8a tetrathiafulvalene,8b viologen,8c,d and metal bipyridines.8e,f Electrochemical measurements in the neat, molten state of the hybrids can provide information on physical self-diffusion rates and electron self-exchange dynamics of their oligomeric units, and since a huge range of values of diffusivity have been encountered (as large as 10-8 and as small as 10-18 cm2/s), it is important to explore a range of methodologies and to compare them so as to validate their mutual reliability. In this report, an electron time-of-flight method is employed in tests of charge transport dynamics in a redox polyether hybrid, the tailed cobalt-bipyridine complex [Co(bpy(CO2MePEG350)2)3](ClO4)2.
This metal complex has two metal-centered redox reactions that have widely divergent electron-transfer kinetics. In dilute solu(7) Surridge, N.; Jernigan, J. C.; Dalton, F.; Buck, R. P.; Watanabe, M.; Wooster, T. T.; Zhang, H.; Pinkerton, M.; Longmire, M. L.; Facci, J. S.; Murray, R. W. Discuss. Faraday Soc. 1990, 8, 1. (b) Pickup, P. G.; Kutner, W.; Leidner, C. R.; Murray, R. W. J. Am. Chem. Soc. 1984, 106, 1991. (c) Facci, J. S.; Schmehl, R. H.; Murray, R. W. J. Am. Chem. Soc. 1982, 104, 4959. (8) (a) Velazquez, C. S.; Hutchison, J. E.; Murray, R. W. J. Am. Chem. Soc. 1993, 115, 7896. (b) Velazquez, C. S.; Murray, R. W. J. Electroanal. Chem. 1995, 396, 349. (c) Hatazawa, T.; Terrill, R. H.; Murray, R. W. Anal. Chem. 1996, 68, 597. (d) Terrill, R. H.; Hatazawa, T.; Murray, R. W. J. Phys. Chem. 1995, 99, 16676. (e) Williams, M. E.; Masui, H.; Long, J. W.; Malik, J.; Murray, R. W. J. Am. Chem. Soc. 1997, 119, 1997. (f) Long, J. W.; Velazquez, C. S.; Murray, R. W. J. Phys. Chem. 1996, 100, 5492. S0003-2700(97)00701-4 CCC: $14.00
© 1997 American Chemical Society
tions9 of the untailed complex [Co(bpy)3]2+, the Co(II/I) redox couple exhibits a homogeneous self-exchange rate constant kEX ≈108 M-1 s-1 whereas the Co(III/II) redox couple undergoes selfexchange with a small rate constant kEX ) 2 M-1 s-1. Buttry and Anson9a were the first to address the implications of this difference for electrochemical measurements in polymeric media, showing that voltammetric currents for [Co(bpy)3]2+ incorporated in Nafion membranes are significantly enhanced for the [Co(bpy)3]2+/+ redox couple relative to the [Co(bpy)3]2+/3+ couple. The enhancement can be attributed to the rapid electron self-exchange reaction rate in the former couple. We have since observed analogous behavior for a variety of redox polyether hybrid couples.8 The coupling of physical diffusion mass transport and electron self-exchange can be described by the Dahms-Ruff equation,10 where DAPP is the measured diffusion coefficient, DPHYS the
DAPP ) DPHYS + DE ) DPHYS + kEXδ2C/6
(1)
physical diffusion coefficient, and DE the electron self-exchange hopping contribution to diffusion. DE can further be defined in terms of the parameters kEX, δ (the site-to-site distance at electron transfer), and C (the redox site concentration). Due to the facile electron-transfer kinetics, DAPP values measured for the [Co(bpy(CO2MPEG350)2)3]2+/1+ couple are dominated by the DE term. We originally introduced the electrochemical time-of-flight method11 in the context of charge transport across a redox polymer film bathed in an electrolyte solution and situated in the gaps of a 50-finger interdigitated electrode array. The method has not been applied to a solvent-free redox material or to transport rates as slow as encountered in the [Co(bpy(CO2MePEG350)2)3](ClO4)2 melt. Time-of-flight electrochemical measurements are based on the generation at a generator electrode using a potential pulse, of a concentration pulse of electron donor (in an originally electron acceptor material) or vice versa. The concentration pulse diffuses across the gap (which must be small) to a collector electrode where it is electrochemically detected by reoxidation or rereduction. The flight time between that of pulse generation and of detection of the maximal response, tMAX, can be related to the charge transport diffusion coefficient, DAPP, by the Einstein equation,
DAPPtMAX/d2 ) θ
(2)
where d is the gap distance between generator and collector electrodes and the constant θ is determined from simulations and is dependent on the cell geometry. In our initial report,11 interdigitated array (IDA) electrodes with up to 50 fingers each of generator and collector electrode were employed. Since an electrolyte solution bathed the redox polymer films, external counter (Pt coil) and reference (SSCE) electrodes could be used. In the present investigation of neat-phase transport (9) (a) Buttry, D. A.; Anson, F. C. J. Am. Chem. Soc. 1983, 105, 685. (b) Baker, B. R.; Basolo, F.; Neumann, H. M. J. Phys. Chem. 1959, 63, 371. (10) (a) Ruff, I.; Botar, L. Chem. Phys. Lett. 1988, 149, 99. (b) Ruff, I.; Botar, L. Chem Phys. Lett. 1986, 126, 348. (c) Ruff, I.; Botar, L. J. Chem. Phys. 1985, 83, 1292. (d) Ruff, I.; Friedrich, V. J. J. Phys. Chem. 1971, 75, 3297. (e) Ruff, I.; Friedrich, V. J.; Demeter, K.; Csaillag, K. J. Phys. Chem. 1971, 75, 3303. (f) Dahms, H. J. Phys. Chem. 1968, 72, 362. (11) Feldman, B. J.; Feldberg, S. W.; Murray, R. W. J. Phys. Chem. 1987, 91, 6558.
in [Co(bpy(CO2MPEG350)2)3](ClO4)2 melts, where there is no solvent, a microdevice with integrated counter and auxiliary electrodes was necessary, and attention was required to the meager ionic conductivities of the melts. To accomplish this, we employed lithographically fabricated devices having eight parallel, individually addressable, band electrodes, using an adjacent pair of these bands as generator and collector electrodes, and the large Pt pads located on either end of (and parallel to) the array of bands serving as counter and reference electrodes. The advantage of using paired bands (vs IDAs) is that there is a uniform resistance drop between the generator band and the reference pad. With an IDA in an integrated device, there is a distribution of distances between the finger electrodes and the reference electrode, and thus a distribution in resistance values and iRUNC potential drops. This can smear out the concentration pulse. Use of paired bands also simplifies the interpretation of chronoamperometry and cyclic voltammetry results. The results of the time-of-flight measurements are compared with DAPP values obtained from chronoamperometric experiments on the same paired band electrode device. Reasonable agreement is obtained when the electron flight times are much longer than the potential pulse times employed. The peaked shapes of the collector current responses are also compared with computer simulations. Differences noted between them are ascribed to differences between the shape of the potential probe assumed in the simulation and that actually employed. EXPERIMENTAL SECTION [Co(bpy(CO2MePEG350)2)3](ClO4)2 was synthesized as described previously.8f Films of this material were cast onto the microdevice from concentrated methanol solutions which also contained the desired amount of LiClO4. The methanol was evaporated under a stream of nitrogen and the film was further dried in vacuo at 70 °C for at least 24 h. The microdevice electrodes used consist of eight individually addressable, parallel Pt bands, separated by 1.6 µm gaps. Each band is a strip of metal 1.9 mm long and 0.2 µm high. The inner six bands are 3.2 µm wide while the outer two are 10 µm wide. Two adjacent, inner bands are selected to serve as generator and collector electrodes; the other bands are not connected. The band array is flanked on opposite ends by two large Pt pads [300 reference electrodes (Figure 1B)]. These microdevices are fashioned on a Si/SiO2 substrate and were generously donated by Dr. O. Niwa of Nippon Telephone and Telegraph. An Ensman bipotentiostat was employed in the four-electrode mode so that the potentials of the generator and collector electrodes could be separately controlled. Data acquisition was accomplished using a Keithley DAS-HRES 16-bit analog input/ digital output board in an IBM-compatible 386-25 computer using software written locally. Temperature control was obtained by mounting the electrode platform on a locally built heating/cooling stage. Ionic conductivities were determined by ac impedance using a Solartron SI 1287 electrochemical interface and SI 1260 phase analyzer using an IDA electrode consisting of 50 pairs of Pt fingers, each 3 µm wide, 0.1 mm high, and separated by 2 mm (also supplied by Dr. Niwa). Films ∼0.5 mm thick were cast onto the potential waveform, and after drying, a 0 V dc bias, an ac amplitude of 50 mV, and an ac frequency range of 1 M Hz to 1 Hz was applied across the IDA fingers. Temperature was controlled by a Lakeshore 330 autotuning temperature controller. Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
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Figure 1. (A) Diagram of potential-step technique employed for time-of-flight measurements. (B) Cross-section schematic of the band array electrode platform employed. Generator and collector bands are 3.2 µm wide and are separated by a 1.6 µm gap. Counter and reference bands are located ∼475 µm from the working electrodes and parallel to them.
A commercially available software package, Digisim 2.0 (Bioanalytical Systems) was used for digital simulation of cyclic voltammetry. RESULTS AND DISCUSSION Time-of-Flight Measurements. Figure 1A illustrates the scheme of potential control for a time-of-flight electrochemical measurement when a reduction reaction is to be studied as in the case of the [Co(bpy(CO2MePEG350)2)3]2+/1+ couple. The generator is initially set at an oxidizing potential until some time, t0, when the electrode is stepped to a reducing potential for a pulse time tp. The typical pulse time in these measurements is 1 s. The potential step is of a magnitude sufficient to reach the diffusion-limited “plateau” of the Co(II/I) wave. At the end of the pulse, the generator potential is returned to its initial value. The pulse is thus the equivalent of double potential-step chronoamperometry. The Co(I) concentration pulse produced at the generator electrode diffuses (predominantly by electron self-exchanges) across the gap to the collector electrode, which is maintained at a potential such that the pulse of [Co(bpy(CO2MePEG350)2)3]+ concentration is reoxidized, and an anodic current is recorded at the collector. Some typical collector current responses for the detection of [Co(bpy(CO2MPEG350)2)3]1+ pulses are shown in Figure 2. As the temperature of the film is increased, the flight times (tMAX) become shorter and the collector response more narrow. Diffusion coefficients can be derived from tMAX values according to eq 1. The factor, θ, in this equation varies with the cell geometry and film depth. Previous simulations11 suggest that 0.44 is an appropriate value for θ when a relatively thick film is employed, as is the case here. Rearrangement of eq 1 with this factor gives
DAPP ) 0.44d2/tMAX
(3)
Experimental values for tMAX and the resulting DAPP are compiled in Table 1 for the [Co(bpy(CO2MePEG350)2)3]2+/+ couple, with and without added LiClO4 supporting electrolyte. The TOF measurements confirm two of our previous observations8e,f in redox polyether hybrid melts: that (i) DAPP values are depressed as lithium perchlorate supporting electrolyte is added; and (ii) the charge transport processes have a strong temperature5084 Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
Figure 2. Collector responses for the detection of [Co(bpy(CO2MePEG350)2)3]+ concentration pulses at 25, 40, and 50 °C. Film contains 1.2 M LiClO4 as a supporting electrolyte. Figure inset shows current response at the generator to the forward and back potential pulse, at 50 °C.
Figure 3. Normalized collector current responses from Figure 2, for detection of [Co(bpy(CO2MePEG350)2)3]+ concentration pulses at 25, 40, and 50 °C. DAPP used for the normalization was measured from the peak maxima, tMAX, using the equation DAPP ) 0.44d 2/tMAX.
dependence and thus high thermal activation barriers. It should also be noted that the diffusion coefficients measured in these experiments are 1 order of magnitude smaller than in the previous11 time-of-flight experiments for redox polymers. Figure 3 shows the same set of time-of-flight collector current responses, where collector current (ICOL/ICOL,MAX) and time (DAPPt/ d2) are both normalized (where DAPP is the value determined from the time-of-flight experiments). Normalized in this manner, the peak shapes are obviously similar, except some broadening of the peak is observed at the lower temperatures where the flight time is longer. Comparison with Simulation. In the previous report, digital simulations were performed based on a two-dimensional mesh and using a potential pulse which was on-then-disconnect. Figure
Figure 4. Normalized collector responses for (b) experimental data for detection of [Co(bpy(CO2MePEG350)2)3]+ concentration pulse at 25 °C in a film containing 1.2 M LiClO4, and (O) simulated response assuming an on-then-disconnected potential pulse at the generator electrode11). Simulation also assumes a thick polymer film, so that θ ) 0.44.
4 shows a comparison between the time-of-flight simulation curve for an on-then-disconnect pulse (for a 1 µm thick film and θ ) 0.44), and the present experimental collector current response for a [Co(bpy(CO2MePEG350)2)3]+ concentration pulse. The experimental response has been normalized in the same fashion as for Figure 3, based on DAPP ) 1.8 × 10-10 cm2/s, as derived from eq 3. The experimental peak has a significantly narrower profile than the simulation, with the greater deviation evident at the trailing end of the peak. The dissimilarity with peak width can be ascribed to the difference in pulse techniques employed. The simulation assumes that, at the end of the generator potential pulse, the generator electrode is disconnected and the resulting concentration gradients are allowed to relax. A broad trailing current peak is then observed at the collector electrode. In the present work, we employ a forward and back potential step as the potential pulse profile. The result of the back potential step is that part of the concentration pulse is consumed at the generator electrode (see Figure 2, inset). The collector current response for this type of pulse is as a result, more narrow and more readily measured, especially for longer electron flight times. Comparison with Chronoamperometry. Our previous work8 with redox polyether hybrids has relied primarily on chronoamperometry, for quantitative DAPP measurements. Using this technique, large potential steps can be applied to the working electrode that overcome any iRUNC potential drop, so that the current transients can be measured in the diffusion-limited regime. To provide a comparison with the time-of-flight experiments, chronoamperometry was used to independently assess DAPP for the [Co(bpy(CO2MePEG350)2)3]2+/+ redox couple. Figure 5 shows Cottrell plots (i vs t-1/2) for potential steps at 25, 40, and 50 °C. As DAPP increases with temperature, the slopes of the Cottrell plots increase and more positive intercepts are observed on the current axis. The intercepts can be ascribed to the emergence of radial diffusion effects. A mixed linear-radial diffusion profile can be accounted for by treating the generator
Figure 5. Cottrell plots for potential-step chronoamperometry measurements of the [Co(bpy(CO2MePEG350)2)3]2+/1+ couple. Film contains 1.2 M LiClO4.
electrode as a microband electrode and applying the equation of Szabo and Wightman,12 x i(t) πe-(2 πτ)/5 π ) + nFDCl ln[(64e-γτ-1/2 + e5/3] 4xπτ
(4)
where τ ) Dt/w2, D is the diffusion coefficient, w is the width of the band, l is the length of the band, and C is the bulk concentration. The resulting values of DAPP taken from chronoamperometric measurements are shown in Table 1. In general, there is excellent agreement between chronoamperometry and time-of-flight experiments. At higher temperatures and larger DAPP, the agreement is less good, which is probably due to fact that the tMAX values are sufficiently small as to approach the potential pulse time (1 s). Cyclic Voltammetry. Cyclic voltammetry is generally less useful in semisolid redox materials for obtaining quantitative data on diffusion coefficients. The low ionic conductivities (such as found in the redox polyether hybrids) lead to significant iRUNC distortions in the voltammetry and ∆Ep values much greater than 60 mV. Another complication can be the emergence of mixed radial-linear diffusion geometries, which are evident in the Cottrell plots in Figure 5. Under these conditions, the standard voltammetric equations cannot be strictly applied, although more complex alternate theory is available.13 Digisim 2.0, a commercially available digital simulation program14 can be used to estimate DAPP. This program can readily (12) Szabo, A.; Cope, D. K.; Tallman, D. E.; Kovach, P. M.; Wightman, R. M. J. Electroanal. Chem. 1987, 217, 417. (13) (a) Aoki, K. Electroanalysis 1993, 5, 627. (b) Amatore, C.; Fosset, B. Anal. Chem. 1996, 68, 4377. (14) (a) Rudolf, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A. (b) Kovach, P. M.; Caudill, W. L.; Peters, D. G.; Wightman, R. M. J. Electroanal. Chem. 1985, 185, 285. (c) A microband can be approximated as a hemicylinder by equating the actual width of the microband to π, where the microband width is 3.2 µm, which corresponds to a hemicylinder radius of 1.0 µm.
Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
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Table 1. Apparent Diffusion Coefficients for the [Co(bpy(CO2MePEG350)2)3]2+/1+ Reaction DAPP × 10-10 cm2/s electrolyte conc
temp (°C)
tMAX, s
no electrolyte
25
7.0
1.2 M LiClO4
25 30 40 45 50 55 60
63 43 18 13 8.5 5.2 3.1
TOFa
CAb
16
12
1.8 2.6 6.3 8.9 13 22 37
1.4 2.3 5.4 7.7 11 16 24
CVHEMIc
CVPLANARd
0.9 1.8 4.5 6.8 10
1.3 3.0 8.0 15 24
a Time of flight, using t b c MAX from results like Figure 2 and eq 3. Chronoamperometry. Cyclic voltammetry based on hemicylinder approximation with rHEMI ) bandwidth/π ) 1.02 µm. d Cyclic voltammetry based on planar geometry with electrode area of 3.2 µm × 1.9 mm.
incorporate such factors as RUNC and electrode geometry into simulated current-potential curves. Ionic conductivity measurements (ac impedance) were used to derive RUNC values using equations specific to microband electrodes,15 and the mixed radial-linear diffusion profile can be accounted for by modeling the microband as a hemicylinder.14 The DAPP parameter can then be adjusted until optimal agreement is obtained between peak current and peak potentials in the voltammogram. DAPP values determined by CV simulation based on mixed diffusion and on planar diffusion are recorded in Table 1. Figure 6 shows such a comparison of simulated vs experimental cyclic voltammograms. The agreement in peak shape is far better when the microband is modeled as a hemicylinder as opposed to planar geometry, confirming the influence of radial diffusion contributions, particularly as the temperature increases. The agreement with time-offlight and chronoamperometry is quite good (again, better for the CV analysis by mixed diffusion, Table 1) in view of the multiple parameters involved in the simulation. CONCLUSIONS This study compares electrochemical strategies for measuring charge transport rates in molten redox polyether hybrids. Electrochemical time-of-flight measurements give good agreement with chronoamperometry and cyclic voltammetry. The potential pulse profile used differs from the previous report,11 and gives sharper peaks. With the current experimental microdevice, however, the range of DAPP values that can be measured by the time-of-flight method is limited. Smaller DAPP values correspond to longer flight times and smaller peak currents, so that current sensitivity becomes a problem. With short flight times (large DAPP) the measurement can become limited when tMAX approaches the potential pulse time. The optimum microdevice for a broader (15) (a) Porat, Z.; Crooker, J. C.; Zhang, Y.; Le Mest, Y.; Murray R. W. Anal. Chem. 1997, 69, 5073 (preceding paper in this issue). (b) Kasper, C. Trans. Electrochem. Soc. 1940, 77, 365. (c) Wehmeyer, K. R.; Deakin, M. R.; Wightman, R. M. Anal. Chem. 1985, 57, 1913.
5086 Analytical Chemistry, Vol. 69, No. 24, December 15, 1997
Figure 6. Cyclic voltammograms at a scan rate of 5 mV/s. Voltammograms shown are: experimental at 40 °C (s); simulation based on hemicylinder geometry (- - -), where hemisphere radius ) band width/π ) 1.02 µm; and simulation based on planar geometry (‚‚‚) where width × length ) electrode area ) 6.1 × 10-5 cm2.
range of DAPP value measurements would contain an assortment of gap sizes between generator and collector electrodes. ACKNOWLEDGMENT This research was supported in part by grants from the Department of Energy and the National Science Foundation.
Received for review July 2, 1997. Accepted October 2, 1997.X AC970701N X
Abstract published in Advance ACS Abstracts, November 15, 1997.
