Anal. Chem. 1992, 64, 1118-1127
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Use of Microelectrode Arrays To Determine Concentration Profiles of Redox Centers in Polymer Films Ingrid Fritsch-Faules and Larry R. Faulkner* Department of Chemistry, University of Illinois, 1209 West California Street, Urbana, Illinois 61801
Electrochemically-generatedconcentration proflies of redox mdacuks bound in a polymer film were expertmentally determined by using microfabricated arrays of Au band mlcroelectrodes in an open-face sandwich configuration. The concentration proflles should deviate from linearity lf charge and mass transport are influenced by oxldation-state-de pendent morphokgks or by mlqatkn in the motbw'esttkthre medium. A thln film of methylquaternized poly(4vlnyC pyridine) (OPVP, ca. 5000 A thick) contalning eiedrorrtatically-bound Fe(CN)?-"- coated the array, which was knmersed in either KNO, or potassium p-toiuenesulfonate (KOTs) aqwous eiectrotyte. Two flanking electrodes (50 p n ~ X 2 mm and 188 pm apart) of the array edablkhod a steady-state concentration gradlent, because one was held at an oldazlng, and the other at a reducing, potmtlai. Fitteen smakr electrodes (4 pm X 2 mm and 8 pm apart) potentiometrically probed the Intermediate chemlcai envlronment. The measured potentlak were translated into the relative concentrations d the oldazed and rwluced species In the llhr via CCrWbratloncurves estabkhd In the hmedlateiy folbwhg companlon paper. Concentratlon profiles in the OPVP/Fe(CN),,-"- system were linear, in spite of known changes in film fiuldlty with the state of oxldation. The communication across the array takes place by a combination of physical diffwlon of redox species through the film, differentlai partltioning between film and solution, and diffusion through the solutlon. The transport k dominated by dlffudon through 0iutlon, since dining causes the concentration proflies to d e viate from linearity.
INTRODUCTION Wective communication by transfers of electrons, ions, and molecules in supramolecular networks is central to the understanding of advanced materials and has implications in sensor technology, photochemical conversion, and electrocatalysis. Of particular importance is the study of electron transfer among redox species in polymer networks. This matter is central in the field of modified electrodes, which makes use of thin films of materials on electrodes.'P2 Several factors may control electron motion in networks of redox centers. These include the ease with which counterions compensate charge, long-range and short-range physical motion of the redox centers, and intersite electron transfer kinetics. These factors result, in turn, from the electronic nature of the redox centers, the supporting electrolyte, the chemical composition of the polymer matrix, the interactions between the polymer and the redox centers (e.g. electrostatic attraction or coordination to the backbone), and the degree of cross-linking between neighboring branches of the polymer. Information from typical electrochemicalexperiments reflects only the region next to the electrode and is transient
* To whom correspondence should be addressed. 0003-2700/92/0364-1118$03.00/0
in nature. From such experiments in complex systems, like modified electrodes, it is difficult to probe dynamic processes in the bulk of the material (which may depend on the state of oxidation) or to separate electron transport from transient effeds due to double layer charging and restrictive counterion motion. Thus, it is of interest to evaluate the concentration profiles experimentally,so that the motion of charge and mass may be understood more directly. In this paper, we report the development of an electrochemical method for determining concentration profiles of redox centers in fluid or rigid molecular networks. Figure 1 illustrates the important features of the technique. The concentration profile is set up in the medium (a polymer f i i containing redox centers, in the actual case) between large flanking anodic and cathodic generator electrodes of a microelectrode array in an open-face sandwich configuration. The smaller inner electrodes probe the chemical environment that is established between the generator electrodes. We use a steady-state methodology in order to eliminate time-dependent charging and transient effects controlled by counterion motion. Under steady-state conditions, oxidationstate-dependent morpholq$ea of polymers that affect electron transport can be detected from the shapes of the concentration profiles for the oxidized (0) and reduced (R)species. Kittlesen, White, and Wrighton3previously used a similar system, involving individually addressable electrodes, to measure the potential distribution in a film of conducting polymer, but their experiments were not aimed at concentration profiles. Much attention has been given to the theoretical prediction of concentration profiles in well-behaved thin films under a variety of electrochemical condition^.^ Ideal steady-state profiles between two electrodes bridged by polymers hosting redox sites are usually assumed to be lir1ear.%*P9~,~ This is true as long as the morphology of the polymer is independent of the state of oxidation of the f i i , the heterogeneous electron transfer is chemically reversible, and there is no convection or migration. The linear steady-state concentration profile for R is expressed by eq 1,which is readily derived from Fick's
fiist law, where n is the number of electrons transferred per molecule of R oxidized, F is the Faraday constant, DR is the diffusion coefficient of R, i, is the steady-state current across the film, x is the distance between the generator electrodes, ACR is the difference between concentrations of R at the cathode and at the anode, and A is the cross-sectional area of the diffusion field, which is the product of the f i i thickneas and the length of the electrodes. When counterion concentrations become small, migration effects are not negligible, and nonlinear profiles are sometimes expected? In motion-restrictive films, additional factors may contribute to nonlinear profiles. The polymer films can develop inhomogeneities as the state of oxidation changes. For example, when electzostatically-bound,multiple-charged redox centers undergo oxidation or reduction, the degree of elec0 1992 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 64, NO. 10, MAY 15, 1992 ElectrolyteSolution
Film
Generator
O
R
.
Generator Potentiometric Probes of P I and [RI Figure 1. A cross section of the microelectrode array canflguration used for cancentration profile measurements. The film contains redox centers that may be Coordinathretyof electrostatica~bound to the film
matrix.
Scheme I
trostatic m l i n k i n g in the polyelectrolyte may change. This can affect the diffusivities of both redox species. For example, poly(styrenesulfonate)films containing electrostatically-bound redox centers exhibit significant changes in structure and local composition upon oxidation or reduction.2eJ*q Majda and Faulkne+ showed electrochemical and s p e c t ” p i c evidence for the formation of electroinactive Ru(bpy)t+ domains in the polymer. One would expect to see flatter concentration gradients in regions of increased fluidity, since more facile molecular motion (much of it segmental) homogenizes the system and results in faster electron diffusion. The redox-polymer system chosen for this study was cross-linked methyl-quaternized poly(4-vinylpyridine) (QPVP), containing electrostatically bound ferri- and ferrocyanide (Scheme I). It offers several useful features: (1) reversible redox properties, (2) reproducibility, (3) a formal potential, E”’, that allows us to hold a potential 300 mV more positive thanthis value without oxidizing gold electrodes, and (4)a morphology that depends on the oxidation state of the redox centers. Several studies in the literature have illuminated characteristics and dynamics of the system.abf*Qm**e Some reportsshow that the chemical identity of the electrolyte has a large impact on the rigidity of QPVP.2”*b*h*i The effect of electrolyte on rigidity is relevant to our investigation here. Several groups have described spatially-resolved concentration measurements within diffusion layers near electrodes in solutions containing electroactive molecules. The techniques include refractive index mapping by interfer0metry;JO deflection spectrometry:’ W-visible absorption spectrometry,12Raman microprobe spedros~opy,’~ and electrochemistry with microelectrode ~r0bes.l~ However, neither transient nor steady-state concentration profiles in rigid media or in networks of redox centers, like polymer-modified electrodes, have been determined experimentally. Electrochemical steady-state measurements have been achieved at rotating disk electrodes: in “closed-face”sandwich
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cells,Bb*P*hand in “open-face” sandwich ceUs.ld@iJsJs In open-face structures, two or more coplanar electrodes contact the overlying electroactive polymer film, and migration and other counterion effects are minimized because the motion of the electrolyte is generally perpendicular to the lateral motion of the electrons. Probably the simplest open-face structure is a ringdisk electrode.2” Band electrodes have also been fabricated for use in an “open-face” configuration by several techniques.17 Electrode widths of lesa than 10 nm have been achieved.18 Microlithography, a fabrication technique for integrated circuits, has been used to construct microstructures for use in electrochemicalsystems. For example, Wrighton and cow o r k e r have ~ ~developed ~ ~ ~ chemical-sensing ~ ~ ~ ~ molecular devices based on microelectrode arrays. Murray and coworkers have studied various electroactive filmswith arrays.w Diffusion of molecules through materials covering a coplanar array of microelectrodes has been investigated to understand the morphology and transport properties of the materials.3*3*5J9*21*22 Wrighton and co-workers3 have also demonstrated the use of potential measurements in conducting polymers across an electrode array. T h e ~ r e t i c a l l ~and ~J~*~ digital simulation23c*d*24 studies of diffusion to ultramicroelectrodes of this geometry are documented in the literature. In this paper, we report electrochemicalexperiments that have been performed at a microlithographically-fabricated gold microelectrode array, coated with a thin QPVP/Fe(CN)63-/4film (ca. 5000 A) in two different electrolytes, KN03 and potassium p-toluenesulfonate (KOTs). T w o large outer electrodes (50 pm X 2 mm and 188 pm apart) establish a diffusion field. Fifteen smaller electrodes (4 pm X 2 mm and 8 pm apart) probe the resulting local potentials defined by the relative concentrations of the oxidized and reduced species in their vicinities. Redox dynamics, potential profiles, and concentration profiles are discussed herein. The companion paper immediately following%presents an experimentallydetermined relationship between potential and the concentration of oxidized and reduced species that is used here to convert the potential profiles to concentration profiles. In a third paper,% the experimental concentration profiles are compared with digital simulations.
EXPERIMENTAL SECTION Materials. Methylquatemized poly(4vinylpyridine)(QPVP) was prepared from poly(4-vinylpyridine)and methyl p-toluenesulfonate by adapting a procedure described by Braun et aL2” A mixture of 25.2 g of methyl p-toluenesulfonate (Aldrich) and 20.0 g poly(4vinylpyridine) (MW = 50OO0,Polysciences, Inc.) in 500 mL of methanol (Fisher) was heated in heavy-walled Pyrex tubes at 71-76 “C for 4 days, concentrated in vacuo, precipitated with diethyl ether, and extracted twice by refluxing with hot diethyl ether overnight Further purification by precipitation with diethyl ether from methanolicpolymer solutions and drying in vacuo gave an amber-brown product in -98% yield, with 77% quaternization as determined by elemental analysis. Anal. Calcd (found): C, 63.6 (61.8);H, 5.96 (6.33);N,5.64 (5.39);S,9.93 (9.55). Potassium p-toluenesulfonate (KOTs)was prepared as described by Oh and Faulkner.2b l3quivalent.s of potassium hydroxide (Fisher) and p-toluenesulfonic acid (Aldrich) were combined in methanol, and then the product was recrystallized from hot water. The product was verified by elemental analysis. And Calcd (found): C, 39.98 (40.18);H, 3.36 (3.41);S,15.25 (15.48); K, 18.59 (18.30). Reagent-grade KSFe(CN), (Baker), KNOs (Baker), and a,&dibromo-m-xylene (97%, Aldrich) were used without further purification. All aqueous solutions were prepared from water treated with a Milli-Q Water Purification System (Millipore). Particulates were removed from methanolic stock solutions of 22% w/v QPVP and cross-linking reagent by centrifuging for 1 h and taking the top 95% of the supernatant. The cross-linkingsolution was prepared the same day in which the polymer was spin-cast onto substrates, since a,d-dibromo-
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 10, MAY 15, 1992 1. HMDS 2. Spincoat PR 3. Prebake 90"C, 20min.
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QPVP/F8(CN),”/’- In 0.1 M KNO,. Each curve corresponds to the flanking electrodes being heM at dlfferent potentlals: at open clrcult (rest), both at 4-300 mV vs Eo’ (+300 mV/+300 mV), the left one at +300 mV and the other at -300 mV vs Eo’ (+300 mV/-300 mV), and an agltated s o l a over an array with flanking electrodes at +300 mV/-300 mV.
t Flgura 8. A representatbe chronoamperogram at the flanking electrodes, numbered 1 and 10, of any array coated wlth QPVP/Fa (CN)83-/CIn 0.1 M KNO,. Both electrodes are hew at oxMlrlng potentlals Inltlalty, then no. 10 electrode Ls swltched to reducing potentlals. The swltchlng tlme Is about 1 h, and the steady-state current Is about 1 nA.
slowly levels off. At the cathode, there is a large initial current transient as the double layer charges and as the oxidized species reduce. The current decreases rapidly; however, instead of approaching zero at long times, the current reaches a steady state, since there is a continuous flux of oxidized species from the anode. The current at the anode rises as reduced species arrive from the cathode. At the anode, the expression for steady-state current in the film is simply a rearrangement of eq l.2p932 Ideally, the currents at the two electrodes should become equal in magnitude, but opposite in sign. However, there is a high background current that contributes to the overall current at the cathode. It may be partially due to the reduction of Fe(CN)6” redistributed from other parta of the film. Nevertheless,the Fe(CN)64-species that is oxidized at the positive electrode can only be due to the reduction of Fe(CNl6“ at the negative electrode. Thus, the steady-state current (i,) characterizing transport across the array was taken as the change in current at the electrode that was held at +300 mV vs Eo’ after the other flanking electrode is made reducing. See Figure 8 for an illustration of this measurement. Over three experiments on different samples, i, values averaged 1.03 f 0.09 nA. Static KNOa Electrolyte: Steady-State Potential Profiles. The potentials relative to EO’, measured at each probe under various conditions, are shown in Figure 9. The abscissa represents the normalized distance across the array between the inner edges of the flanking electrodes. The rest potentials are positive of E O ’ , because the film initially contains redox centers in the oxidized form. The error bars for the rest potential profile are large because the electrodes are all unpoised in the rest condition. Small perturbations of the concentrations by electrochemical experimenta that had been
performed on the probe electrodes prior to the rest potential measurements therefore lead to sizable variations in potential. The reproducibility of the steady-state profiles from sample to sample in experiments where the flanking electrodes are held at +300 and -300 mV vs ED‘is excellent. The profiles are better understood in terms of concentration, rather than potential, as discussed in the next section. Static KN03Electrolyte: Steadystate Concentration Profiles. There are two ways that the measured potentials can be related to concentrations of the oxidized and reduced species. If the electron transfer is reversible, the Nernst equation could readily provide a ratio of concentrations of the two redox forms. However, researchers have cautioned against the assumption of reversibility in some modified electrode ~ y s t e m s .Consequently, ~ empirical calibration by LPCC was used to determine the dependence of potential on the concentrations. Establishing the linkage between the potential at a probe electrode and the concentrations of species in ita vicinity requires careful attention to experimental protocol and an extensive body of measurements. Consequently, we discuss this aspect of the work separately in the immediately following companion paper.% Important conclusions from the companion paper are (a) that differential partitioning plays an important role and (b) that the potential-concentration relationship is remarkably nernstian. The concentration profiles corresponding to the potential profiles are shown in Figure 10. In treating modified electrodes, it is often assumed that the total concentration of redox forms is constant over a range of potentials. The calibration curves show that this is not necessarily true for systems in which redox centers are electrostatically bound into a polymer matrix. The potential profiles are strongly influenced by small concentration changes when the quantity of one redox form greatly exceeds the other. This is because of the logarithmic dependence of potential on concentration. For example, it might appear from the curve in Figure 8 which corresponds to both flanking electrodes held at +300 mV vs E O ’ , that the concentration of Fe(CN)63-across the array is not uniform. Figure 10 shows that the uniformity in the dominant species is actually very good. Figure 10 presenta the concentrations of the redox species relative to the maximum concentration of the oxidized form
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 10, MAY 15, 1992
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Normalized Distance Figure 10. Concentration profiles Of Fe(CN),” (0)and Fe(CN)6C(R) in QPVP reletive to the “umconcetWatbn of the oxidized spedes. The electrolyte was 0.1 M KNO,. Plots are shown for flanking electrodes at rest, both held at +300 mV vs Eo‘, the rlght one held at 400 mV vs Eo‘ while the lett one Is held at +300 mV vs Eo‘ (+300 mV/-300 mV), and for an agltated supporting electrolyte for the condition +300 mV/-300 mV.
at +300 mV vs E O ’ . This representation eliminates the need to know the film thickness. Typical values for QO,marand QR+,=are 3.8 and 1.7 pC, respectively, and were obtained at the flanking electrodes immediately after the completion of the steady state experiments by running LPCC with an additional quiet time of 60 s. The oxidizing electrode was stepped from +300 to -300 mV vs EO‘, whereas the reducing electrode was stepped from -300 to +300 mV vs EO’. Typical concentrations corresponding to these Q values are CoFmrU = 0.82 M and CR,” 0.36 M. Thus QR,mJQO,mm = CRSmar/ COW = 0.44 & 0.04. These results are consistent with those from calibration curve determinations% and reemphasize the reproducibility of the film partitioning characteristics of Fe(CN),3-/4-. The concentrations of the Fe(CN),& across the array at open circuit (at rest) are not as high as the concentrations when both flanking electrodes are held at oxidizing potentials. This may be due to a loading solution that was not 100% oxidized or to reduction that may have occurred during the preparation of the loaded f h . Because of the larger partition coefficient for Fe(CN)63-,there is additional loading of Fe(CN),$ when the flanking electrodes are both held at +300 mV vs E O ’ . The steady-state concentration profiles in Figure 10 are very nearly linear for the fully polarized condition (+300 mV/-300 mV), as one would expect for a homogeneous system. The slopes of the profiles for the reduced and oxidized forms differ because the partition coefficients and diffusion coefficients differ for 0 and R.% One can see a slight sigmoidal character in these relationships, but the departures from linearity probably do not exceed the error ranges on the points. The error bars on potential are several millivolts, implying error bars on concentration of 5-10%. In addition, one must recognize that the data are not actually “points”on the horizontal axis because of the finite width of each probe electrode. These eledrodes are expected to mediate the redistribution of charge and maas above themselves so that conditions become nearly uniform over them. Given the blurring of the data by statistical uncertainty and finite spatial resolution, we doubt that an interpretation of the slight apparent curvature is warranted. Since the fluxes at anode and cathode are equal a t steady state, the diffusivities of both 0 and R can be calculated from is, as long as the profiles are linear and their concentrations
are known a t the two electrodes. For our arrays at steady state, CO= Co,, and CR= 0 at the anode, while Co = 0 and CR = Cat the cathode. A typical D , is 6.3 X lo4 cm2/s, as obtamed from a rearrangement of eq 1 by substituting the experimental values for ,i and ACR = CR,-. A Do,, of 2.8 X cm2/s was obtained in a similar way, where ACO = This value is 5 times larger than the Do,fb. This significant difference may be explained by a large component of lateral diffusion of the redox centers outside of the film, where solution diffusion coefficients are = 7.14 X lo4 cmz/s and DR,soln= 6.23 x lo4 cm2/s.= Agitated KN03 Electrolyte. One can imagine a mechanism in which most lateral transport of charge occurs in the solution above the f i . If the movement of redox ions to the polymer/solution boundary is rapid enough, then agitation of the solution should influence the concentration profile. On the other hand, if electron transport is solely controlled by electron hopping or physical diffusion within the film, then agitation of the solution should not have any effect on the profile. Both flanking electrodes were held at +300 mV vs Eo’ in static solution and the current was monitored for 1.5 h. A Dremel “moto-tool”, which provided the agitation,3l was turned on and the current rose immediately by 1.7 nA and continued to rise slowly at 1.4 nA/h. After 2 h of agitation, the Dremel was turned off and the current dropped quickly a t first (over 14 min), and then approached its previous magnitude over 1h. When the Dremel was turned on again, the current increased in the anodic direction immediately and was already 2.5 times higher than in the unagitated solution after 24 min. The current continued to rise at a rate of about 2 nA/h. The resulting potential profiles (Figure 9) and concentration profiles (Figwe 10) were significantlydifferent from those in a static solution. The Dremel was turned off again and the steady-state current dropped, but never reached the pre-agitation steady-state current. After 3 h, it was still 1.6 times the preagitation value. However, the concentration profile in the static electrolyte was extremely reproducible. The concentration profile for the agitated system is indicative of a solution-assisted electron transport mechanism. A large drop in concentration a short distance away from the flanking electrode and more uniform concentration across the middle of the array are observed. This would be the expected behavior when agitation breaks up the profile that is established in the solution over the array. We conclude that lateral diffusion through the film between the flanking electrodes is probably much less important than transport through the solution. Static KOTs Electrolyte. Oh and Faulkner studied the effect of electrolytes on the permeation characteristics of loaded QPVP films.2a,b IR spectroscopy revealed that in QPVP+X- (X- = ClO,, OTs-, NO,), perchlorate substantially dehydrates the polymer, OTs- allows some hydration of the film, and NO3- yields substantial hydration.2a The investigators concluded that the anions have a strong effect on the internal structure, and thus, on the fluidity of the redox/ polymer network. These results triggered our interest in establishing concentration profiles in a film exposed to an electrolyte other than KNOB. Experiments are described below that involve the less hydrated supporting electrolyte, KOTs. Several differences in the CV measurements between the KNOBand KOTs systems are of note. A major difference is that the Eo‘ value for the KOTs system ( ~ 1 3 mv) 6 is negative of that for the KNOBsystem by 22 mV. Another difference in the characteristics of the two systems lies in the peak splittings (AE,).In fast CV (100 mV/s) AE, is about 20 mV greater than that for the KN03 system. This may be a result
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 10, MAY 15, 1992
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Normalized Distance Figure 11. Potential profiles for an electrode array coated with QPVP/Fe(CN),""- In 0.1 M KOTs. Each curve corresponds to the flanklng electrodes being held at different potentials: at open circuit (rest); both at +300 mV vs E"' (+300 mV/+300 mV); and the left one at +300 mV and the other at -300 mV vs E"' (+300 mV/-300 mV). of the resistance toward electron transfer, because KOTs causes the film to be more compact. However, at slow scan rates (5 mV) Upof the KOTs system (25 mV) is similar to that in the KNOBsystem (32 mV). The slower scan rate may allow the film more adequate time for solvation as the potential is scanned negatively. The chronoamperometry at the flanking electrodes in this system was similar to that in the KNO, system. However, upon application of the +300 mV/-300 mV field, the current at the anode rose initially when the other electrode was switched to -300 mV v8 E"' and then rolled over and decreased gradually as the current approached steady state. A smaller effect was observed in some of the experiments in KNO,. This transient hump in the chronoamperogramis actually predicted in our digital simulations26as consequence of producing a faster-moving species (Le. the reduced form) at the switched electrode. The KOTs system is more compact and rigid than the KNOBsystem. Although the maximum concentrations of 0 and R (Co,- = 0.78 M and CR- = 0.29 M) are similar to those for the KNOBsystem, the Do* value was 2.3 X lo4 cmz/s, which is only about one-third of that for the KNOB system. This result confirms that motion is more restricted in the film in the presence of KOTs. However, the diffusion coefficients obtained from the steady-state current (i, = 0.75 nA) are Do- = 2.0 X lo4 cmz/s and DRgs= 5.1 X cm2/s, both being 1order of magnitude greater than Do- In fact, the D, values compare much more closely than the Do,fh values between the two electrolyte systems. These data suggest that, just as in the KNOBsystem, there is a significant contribution to the steady-state current from the physical diffusion of redox species outside the film. The potential and concentration profiles from experiments performed on QPVP/Fe(CN)63-/" in KOTs are given in Figures 11and 12. The profides resemble those for the KNO, system, but slight differences in KOTs are exhibited in a crossing point in the concentration profie cloeer to the cathode and a smaller slope for the R concentration profile. Both probably arise because of a slightly smaller relative partition coefficient for the reduced species in KOTs than in KN03.26 The sigmoidal character in the profiie for the reduced form under full polarization (+300 mV/-300 mV) is greater in the KOTs system in Figure 12 and may be significant. The profile
0.0
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No r m alized Distance Figure 12. Concentration proflies of Fe(CN)," (0)and FNCN)eC (R) in WVP relathre to the maximum concentration of the oxidized specles. The electrolyte was 0.1 M KOTs. Plots are shown for flanking eiectrodes at rest; both held at +300 mV vs E"'; the right one is held at -300 mV vs Eo' while the left one is held at +300 mV vs E"' (+300 mV/-300 mV); and (for comparison) for 0.1 M KNOBfor the condition +300 mV/-300 mV. The points and llnes for the oxidired form under the +300 mV/-300 mV condition in KNO, and KOTs electrolyte are not easily resolved in this figure. curves with a similar (but suppressed) pattern to that of the agitated KNO, system. Perhaps there is a larger contribution of solution diffusion and natural convection to the overall profile for the KOTs system. Oxidation-state-dependent diffusion probably does not affect our observations, since the curvature of the profiles is small and does not trace that of the digital simulations well.26
CONCLUSIONS In the QPVP/Fe(CN)63-/" system, the redox couple is electrostatically bound in the polyelectrolyte and cross-links the polymer but leaches into the supporting electrolyte (especially when in the reduced state), changing the Concentration in the f i . Doblhofer and co-workers suggest that diffusion in QPVP/Fe(CN)63-/4-/KC1is controlled by the changes in the film structure with oxidation state. In general, a nonlinear steady-state concentration profile would be expected for our systems if diffusion of redox species could be restricted to the film. However, the geometry of our microelectrode array allows diffusion of the redox molecules to aid the electron transport, not only through the film, but as we discovered, around it as well (the "path of least resistance"). This was confirmed by showing that the concentration profiles are dramatically affected by agitating the electrolyte. The experimental results presented here are consistent with a model that involves (1)electron transport from the cathode perpendicularly (and to some extent, laterally) through the film by segmental or physical diffusion to the film/solution boundary, (2) partitioning of oxidized and reduced species at the film/eledrolyte interface, (3) fast diffusion of redox species through the solution (about 3 orders of magnitude faster than in the f i b ) , (4) exchange of electrons along the way between species in the solution and in the film, and ( 5 ) electron transport back throughthe f ilm toward the oxidizing electrode. The probe electrodes sense the concentrations of oxidized and reduced species that result from overall equilibration between concentration gradients established jointly in the solution and in the film. Digital simulations concerning fii/solution partitioning, diffusion, and f i i fluidity support the conclusions we have drawn here.26
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The electrochemical methodology demonstrated here is a powerful means for studying the dynamia of redox networks. Unlike other methods for determining concentration profdes, this one does not require an interpretation of refractive indices; thus, one can determine the spatial distributions in highly complex systems. Although we did not obtain curved concentration profiles that have a dependence of diffusivity on the oxidation state of the system, we have shown that actual diffusion coefficients can only be obtained from the steadystate currents if the relative contributions of diffusion in the film and in the solution, the partitioning, and concentration profiles are known. In combination with typical electrochemical techniques, like CV and CC, the chronoamperometric response at the generating electrodes and the concentration profiles provide a great deal of information, both qualitative and quantitative. Continued studies would most importantly involve the use of molecular networks in which the redox centers (or states) are immobilized, so that communication via electron transfer remains within the f i b . Suggested systems include polymers containing redox centers, such as PVP-[Fe(CN)5]n,35solidstate systems, such aa Prussian Blue and ita analogues,%vapor-saturated films,2da*k and conducting p o l y m e r ~ . ~ J ~ JIn ~&~' addition, the smaller diffusion coefficients of polymer-confined redox centers might require an electrode array design with smaller distances between outer flanking electrodes so that measurable steady-state currents may be detected in a shorter time.
ACKNOWLEDGMENT We thank Mr. Tim Brock and Dr. Fred Sharifi for many helpful discussions on microlithography. We acknowledge the University of Illinois Compound Semiconductor Microelectronics Laboratory and the Materials Research Laboratory for use of their microfabrication facilities. We are also grateful to the National Science Foundation, the Division of Analytical Chemistry of the American Chemical Society, and the Procter and Gamble Company for graduate fellowships to I.F.F. The support of the National Science Foundation for research cosb under Grant CHE-86-07984 is also acknowledged. Registry No. QPVP, 103747-18-8; KNOB,7757-79-1; Au, 7440-57-5; KOTs, 16106-44-8;Fe(CN)6*, 13408-62-3;Fe(CN),", 13408-63-4.
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for review
24, lgg2* Accepted
7, 1992.
Relationships between Measured Potential and Concentrations of Redox Centers in Polymer Networks Ingrid Fritscb-Faules and Larry R. Faulkner* Department of Chemistry, University of Illinois, 1209 West California Street, Urbana, Illinois 61801
We have shown that a nernrtlan relationship exlsts between
the comentratkrw, C,of fed- (0) and ferrocyanide (R) and the applied potentlal in thin films of methylquatemizedpdy(4-vinylpyrklh) (OPVP) on d.Ctrode8 In aqueorw KNO, and potassium p-toiuenewlfonate (KOTs) electrolytes. Plots of E Eo' versus in (CdC,) cioseiy foikw expected nenwtlan behavior (ideally, dope = 25.5 mV and intercept = 0 mV at 22 "C). For the KNO, system,the observed slope was 26.4 f 0.3 mV and the Intercept was 3.6 f 0.14 mV. For the KOTs system,the cdope was 29.3 f 0.3 mV and the intercept was 7.8 f 0.11 mV. The nearfy nernstlan behavlor k somewhat wrprlrlng, considering the complex dynamics and thmnodyrwnics of QpVP/Fe(cN),~'c/c,where (a) both f m of the rodox coupb parlttion to Merent extents between f i h and rdutlon, (b) the mass transport In the film Is oxidationstate dopendent, and (c) the full-wknhs at haif maxlmum of peaks in cyclk voitammetry are greater than the nernstian responm of 89.7 mV. Callbration curves in the form of CdCo,- or CdCo,- versus E - Eo' allow us to convert the potontld p r d h In our companion pcrper to concentration profhs. Here CO,nurIs the maximum (equiilbrium) concentration of 0 at € - Eo' = +300 mV. Llkewb, CR,- Is the eqMbdum concentration of R at a strongly reducing potential ( € - Eo' = -300 mV). Concentratlons of 0 and R were determined by preconditioning the flhn for 1 h at a glven potential, folkwed with kng-pukswldth (20 000-32 000 ms) chn"ary (LPCC) featuring a step to either -300 mV or +300 mV M P O ' , wpectively. Experiments were carried out at 50-pm X 2" electrodes with the experimental arrangement described in the companion paper. The ratlo of ConuJCR- Is 0.44 tor KNO, Md 0.37 fOr KOTS electrolytes, suggesting that tho partitioning Is almost independent of the ldontfty of the electrolyte.
-
INTRODUCTION In the preceding companion paper,l we have shown that potential measurements a t a microelectrode array can probe the spatial distribution of electrochemically-generated redox species within a polymer film. The experimental system
* To whom correspondence should be addressed. 0003-2700/92/0384-1127$03.00/0
involved electrostatically-bound ferri- and ferrocyanide (Fe(CN)63-/4-)in cross-linked methyl-quaternized poly(6vinylpyridine) (QPVP). In this paper, we report conversion of the potential measurements into redox center concentrationsusing calibration curves that were obtained experimentally with long-pulse-width chronocoulometry (LPCC). For a homogeneous, reversible redox system
uoO + ne- a uRR
(1)
the relationship between the potential and the concentrations of oxidized and reduced species is the Nernst equation2
where Eo is the standard potential of the couple, (0) and (R) are the activities, Co and C R are the concentrations, vo and U R are the stoichiometric coefficients, and yo and Y R are the activity coefficients for the oxidized and reduced species, respectively. Since the formal potential Eo' = Eo + (RT/nFj In (yoYo/yR~), eq 2 becomes
(3) If the relationship between E and Co or CRis nernstian, and if variations in activity coefficients are negligible, one can plot E - Eo' vs In (Co/Cd (YO = vR = 1 in our case) and obtain a straight line with an intercept of zero and a slope of RT/(nF) (= 25.5/n mV a t 22 "C). Polymer-modified electrode systems are not prone to ideal behavior. Although the electron exchange a t the electrode/solution interface may be very fast: there is usually a decrease in heterogeneous rate for a redox couple when incorporated in a confining polymer film; thus, a nernstian equilibrium may be difficult to establish. Possible causes include partial blocking of the electrode4 or an increase in electron-transfer activation energy. Interactions between electroactive species can also cause variations in activity coefficients as concentrations change in the film.6 QPVP/Fe(CN)63-/4-systems, in particular, demonstrate variable dynamic behavior,- some aspects of which can be explained by the partitioning of the oxidized and reduced species between the f ilm and electrolyte solution. Partitioning directly affects film concentrations and fluidity and is influenced by the concentration of redox centers in the electrolyte 0 1992 American Chemical Society
