Interplay of Electron Hopping and Bounded Diffusion during Charge

Nov 8, 2012 - co-workers,28 in particular, used this model to interpret charge transport .... relative sensitivity factors in CASA software. Functiona...
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Interplay of Electron Hopping and Bounded Diffusion during Charge Transport in Redox Polymer Electrodes Abhinav Akhoury, Lev Bromberg, and T. Alan Hatton* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States S Supporting Information *

ABSTRACT: Redox polymer electrodes (RPEs) have been prepared both by attachment of random copolymers of hydroxybutyl methacrylate and vinylferrocene (poly(HBMA-co-VF)) to carbon substrates by grafting either “to” or “from” the substrate surfaces, and by impregnation of porous carbon substrates with redox polymer gels of similar composition. An observed linear dependence of peak current on the square root of the applied voltage scan rate in cyclic voltammetry (CV) led to the conclusion that the rate controlling step in the redox process was the diffusive transfer of electrons through the redox polymer layer. The variation in the peak current with increasing concentration of the redox species in the polymer indicated that the electron transport transitioned from bounded diffusion to electron hopping. A modified form of the Blauch-Saveant equation for apparent diffusivity of electrons through a polymer film indicated that bounded diffusion was the dominant mechanism of electron transport in RPEs with un-cross-linked polymer chains at low concentrations of the redox species, but, as the concentration of the redox species increased, electron hopping became more dominant, and was the primary mode of electron diffusion above a certain concentration level of redox species. In the cross-linked polymer gels, bounded diffusion was limited because of the restricted mobility of the polymer chains. Electron hopping was the primary mode of electron diffusion in such systems at all concentrations of the redox species.

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INTRODUCTION Polymeric materials with redox properties are used in applications as diverse as biofuel cells,1−3 batteries,4,5 bioelectronics,6 responsive membranes,7 and biosensors.8−14 Redox polymers containing the ferrocenyl or vinyl ferrocene group as an electroactive functionality, in particular, are wellstudied because they possess high redox activity and chemical stability,15 with electrochemical behavior quite similar to that of free ferrocene in solution. One application of poly(vinylferrocene) is as a polymeric mediator in the fabrication of glucose biosensors.16−18 These biosensors have been prepared by a variety of means, such as cross-linking ferrocene-containing acrylamide−acrylic acid copolymers or ferrocene-containing poly(allylamine) with glucose oxidase on the surfaces of glassy carbon electrodes,19,20 electrochemical codeposition of the redox monomers and enzymes on the surfaces of platinum electrodes, and cross-linking and immobilization of the polymers and enzymes within carbon paste, resulting in the formation of stable electrodes based on ferrocene-containing polymers.21 We have recently developed a novel redox responsive copolymer of hydroxybutyl methacrylate and vinylferrocene (poly(HBMA-co-VF)) with tunable hydrophobicity, and demonstrated its potential for the reversible extraction of organics dissolved in water.22 The successful implementation of these gels requires that they be associated with the electrode materials themselves in the form of porous redox polymer electrodes (RPEs) by either being grafted onto, or being impregnated within, mechanically stable and conductive substrates. It is desirable that such electrodes be © 2012 American Chemical Society

characterized quantitatively in terms of their electron transport properties, an important consideration in the design and scaleup of any process that is to take advantage of the reversible systems for chemical processing applications. This is the goal of the present study. Control of electron transfer kinetics in RPEs requires an appreciation of the mechanisms by which charge transfer in redox polymers takes place. Several theories have been forwarded to explain the diffusion of electrons through polymer films, notably by Dahms,23 Ruff,24 Laviron,25 Andrieux and Saveant,26 and most recently by Blauch and Saveant,27 whose model has been cited widely over the past two decades in studies on electron transport in different redox systems. Bu and co-workers,28 in particular, used this model to interpret charge transport observations in redox gels comprised of acrylamide and ferrocene, and to explain the concentration dependence of the measured diffusivity in terms of the parameters in the Blauch-Saveant model. In this work, we extend the approaches put forward by these researchers to provide a mechanistic interpretation of the charge transport properties of poly(HBMA-co-VF) attached to conducting carbon substrates. We elucidate the effect of variables such as concentration of redox species and cross-linkers on the way in which electrons move through the polymer layers by electron hopping from one center to the other, or by diffusional interactions between the Received: March 5, 2012 Revised: November 4, 2012 Published: November 8, 2012 333

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redox centers to allow for the transport from one redox moiety to the next through the polymer film.

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EXPERIMENTAL SECTION Materials. Hydroxybutyl methacrylate (HBMA) (94%, mixture of isomers), vinylferrocene (VF) (97%), n-butyllithium (1.6 M in hexanes), tetrahydrofuran (THF) (anhydrous, 99.9+ %), 4,4′-azobis(4-cyanovaleric acid) (ACVA) (98+%), 2,2′azobis(isobutyronitrile) (AIBN) (98%), ethyleneglycol dimethacrylate (EGDMA) (98%), dimethyl sulfoxide (DMSO) (99.5+%), 2-picoline (98%), 1,4-dioxane (99+%), methanol (anhydrous, 99.8%), aluminum chloride (AlCl3) (anhydrous, powder, 99.99%), aluminum (flakes, trace metal basis, 99.99%), hydrochloric acid (HCl) (1.0 M), poly(tetrafluoroethylene) powder (1 μm particle size), and 2-propanol (IPA) (99.5+%) were purchased from Sigma-Aldrich. A sample of conductive Vulcan XC-72R carbon black was obtained from Cabot Corporation (Billerica, MA). Toray carbon paper (grade ECTP1-060) was purchased from Electrochem, Inc. (Woburn, MA). Teflon sheets were purchased from McMaster Carr. All other chemicals were from commercial sources and were of highest purity available. Preparation of Redox Polymer Electrodes (RPEs). RPE1: Redox Polymer Grafted “from” Surface of Carbon Black. Poly(HBMA-co-VF) was synthesized by grafting “from” the surface of carbon black particles through a series of chemical reactions analogous to the reaction sequence detailed by Tamaki and Yamaguchi.1 Carbon black particles were first treated with n-butyl lithium in hexane and anhydrous THF to introduce hydroxyl groups on the surface.29 After allowing the reaction to proceed for 2 h, unreacted n-butyl lithium was consumed by careful dropwise addition of water. Thereafter, the carbon black particles were washed with excess water, filtered and dried in vacuum at 110 °C. Then, 2.5 g of the carbon black particles functionalized with hydroxyl groups were reacted with 0.5 mL of tolylene-2,4-diisocyanate and 0.5 mL of 2-picoline in a solution of dehydrated DMSO. After allowing the reaction to proceed for 4 h at 60 °C under nitrogen, 2 g of cyanovaleric acid (ACVA) dissolved in 10 mL of dehydrated DMSO was added to the reaction mixture. The reaction with ACVA was allowed to proceed overnight to functionalize the carbon black particles with azo groups. The azo-modified carbon black particles were washed with methanol and dried in vacuum. 0.3 g of azo-modified carbon black was added to a solution of 1 mL of HBMA and 0.4 g of VF in 10 mL of dioxane. The mixture was kept at 70 °C for 24 h for grafting to take place. The azo groups decomposed to produce free radical sites on the surfaces of the carbon black particles which, in turn, acted as initiators for the graft polymerization of the copolymer of HBMA and VF from the carbon black surface.1 At the end of 24 h, the carbon black particles with the attached redox polymer were washed with excess methanol and dried under vacuum. RPEs were prepared by painting a mixture of redox polymer modified carbon particles and PTFE (in 3:1 weight ratio) with IPA on the surface of carbon paper, following which the added IPA was allowed to evaporate to obtain the RPE. The resulting electrodes were stored in dark at 4 °C prior to their use. The reaction sequence is shown in Figure 1. RPE-2: Redox Polymer Grafted “from” Surface of Carbon Paper. Carbon paper is composed of conducting carbon fibers held together by a binder. To graft poly(HBMA-co-VF) “from” the surfaces of carbon fibers in the carbon paper, the fibers were functionalized first with hydroxyl groups and then with azo

Figure 1. Reaction sequence outlining the grafting of poly(HBMA-coVF) on carbon black particles (carbon black particles are denoted by large, black filled circles).

groups. Grafting of poly(HBMA-co-VF) from the surface of the azo modified carbon paper was then carried out. The hydroxyl modification, azo modification, and polymer grafting were achieved through a series of chemical reactions analogous to the reactions used for the modification of carbon black particles described in the preceding section and outlined in Figure 1. After the completion of these reactions, carbon paper with attached redox copolymer of HBMA and VF was obtained. This modified carbon paper was then used as an RPE in further studies and characterization experiments. RPE-3: Redox Polymer Grafted “onto” Surface of Carbon Paper. In contrast to RPE-1 and RPE-2 that were prepared using grafting of redox polymer “from” the surface of conducting substrates, a third RPE was prepared by using the grafting “to” approach for polymer attachment. Poly(HBMAco-VF) was synthesized by dissolving 1 mL of HBMA and 0.4 g of VF, and 30 μg of ACVA in 10 mL of dioxane, and carrying out free radical polymerization under nitrogen at 70 °C for 24 h. After the completion of the polymerization reaction, solvent was evaporated to obtain the copolymer of HBMA and VF. The resulting polymer had a number average molecular weight of close to 7500 with a polydispersity index, PDI, of 1.52. The copolymer was then grafted “to” the surface of carbon fibers constituting a piece of carbon paper through ligand exchange reaction as described previously.30,31 A piece of unmodified carbon paper measuring 1 cm2 in area was added to a 10 wt % solution of poly(HBMA-co-VF) in 1,4dioxane. A total of 0.1 g of anhydrous AlCl3 and 5−10 μg of anhydrous aluminum powder were added to the flask under nitrogen in a glovebox. The flask was then sealed, and the grafting reaction was allowed to proceed at 80 °C for 24 h. The reaction was then stopped by addition of excess methanol to quench AlCl3. Carbon paper was removed by filtration, and was washed thrice with excess methanol and dioxane in turn to remove the ungrafted polymer from the surface of carbon paper. The adsorbed AlCl3 was removed by washing the carbon paper with 1 M HCl solution. The grafted carbon paper was dried under vacuum to obtain RPE-3. RPE-4: Carbon Paper Impregnated by Redox Polymer Gel. A total of 0.4 g of VF was dissolved in 1 mL of HBMA with 334

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brief sonication at room temperature. Next, 30 μg of AIBN and 30 μL of EGDMA were dissolved in the solution of VF in HBMA to result in a solution of 2.5 mol % AIBN and 1.5 mol % EGDMA.22 Then, 200 μL of the reaction mixture was added dropwise to a square piece of carbon paper measuring 6 cm2 in area placed over a Teflon sheet in a flat-bottom beaker. After addition of the reaction mixture, a second Teflon sheet was placed gently over the carbon paper. The assembly of impregnated carbon paper and Teflon sheets was then pressed using a metal weight weighing 100 g, and the whole assembly was placed into a glovebox and sealed using a rubber stopper. Thereafter, the sealed beaker was removed from the glovebox and placed in an oven preheated to 70 °C and the free radical polymerization initiated by thermal decomposition of AIBN was allowed to proceed resulting in the synthesis of a redox polymer gel around the carbon fibers in the carbon paper. Formation of the poly(HBMA-co-VF-co-EGDMA) gel was complete after 24 h. The carbon paper impregnated with the redox polymer gel was gently detached from the Teflon sheet, and used as an RPE in further studies. RPE Characterization. Detailed, stepwise characterization of RPEs was carried out using techniques reported by other researchers for evaluation of similarly prepared electrodes.1,30,31 The results of these characterization experiments were consistent with those reported in literature, further corroborating our choice of techniques for RPE preparation. Our methodology for these characterization experiments, and a comprehensive set of results and conclusions based thereon have been reported elsewhere.32 Cyclic voltammetry (CV) was used for electrochemical analysis of the RPEs, employing a Gamry Instruments Series G 300 potentiostat. A saturated calomel electrode (SCE) was used as the reference unless noted otherwise, and platinum foil was used as the counter electrode. The size of the counter electrode was chosen so as to ensure that its area was larger than that of the working electrode. Unless mentioned otherwise, the working electrodes in the CV experiments were RPEs containing 22 mol % VF in the attached redox copolymer. Typical voltammetric scans were carried out between 0.0 and 0.7 V (with reference to SCE) at different scan rates, ranging from 5 to 100 mV/s. A 6% (v/v) butanol−water solution containing 0.1 M NaNO3 was used as the electrolyte. Background correction of voltammograms obtained for RPEs was performed using the current response of the conducting substrate in the absence of the redox polymer. The attachment of redox polymer to the conducting substrates was confirmed using thermogravimetric analysis. The weight loss of samples was measured as a function of temperature in a TGA Q 5000 instrument (TA Instruments, Inc.). The samples were heated in nitrogen atmosphere with a temperature ramp of 20 °C/min from ambient temperature to 900 °C. The elemental compositions of selected samples were measured by Columbia Analytical Services (Tucson, AZ). Since carbon fiber surfaces are complex, it was not possible to discern the multiple functionalities in the attached redox polymers through direct XPS measurements on the electrodes. Thus, an alternate method was used, in which the redox polymers were grafted on silicon wafers and the elements on the substrate surfaces were detected using XPS survey scans performed on a Surface Science Instruments SSX-100 with operating pressure less than 2 × 10−9 Torr. Monochromatic AlK-α X-rays (1486.6 eV) with a 1000 μm beam diameter were used. An electron flood gun was used for charge neutralization.

Photoelectrons were collected at a 55° emission angle. A hemispherical analyzer collected photoemission electrons, with a pass energy of 150 V for the survey scans. The energies analyzed correspond to the 1s level in carbon, nitrogen, oxygen, and fluorine, the 2s level in silicon (153 eV), and the 2p level in iron. Atomic concentrations were determined using the Scofield relative sensitivity factors in CASA software. Functional groups in the grafted polymers were analyzed using FT-IR spectroscopy. Redox polymer was deposited on the surface of special grade IR transparent silicon wafers using initiated Chemical Vapor Deposition.33 Details of the process are described in the Supporting Information. Silicon wafers were purchased from Wafer World. FT-IR spectroscopy of redox polymer coated wafers was performed on a NEXUS 870 FTIR spectrometer (Thermo Nicolet, Inc.). Spectra were recorded over the wavenumber range between 4000 and 400 cm−1 at a resolution of 4 cm−1 and are reported as the average of 64 spectral scan. SEM was performed using a Jeol ISM-6060 Scanning Electron Microscope. Samples were mounted on a piece of double-sided conducting tape on aluminum stubs and sputtercoated with gold before micrographs were taken at appropriate magnification. Contact angle measurements were performed using a VCA2000 goniometer (AST, Inc.). Advancing and receding contact angles were measured by using droplets of volume close to 5 μL placed on the substrate.

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RESULTS AND DISCUSSION We prepared four different redox polymer electrodes and investigated their electron transport properties, interpreting the results in terms of the Blauch-Saveant model. The chemical and physical characteristics of the RPEs are described below, followed by the detailed electrochemical characterization and assessment of the electron transport properties of the four electrodes. Polymerization of VF has been shown to be slow and challenging.34,35 Copolymerization of VF with other monomers such as acrylamide and methyl methacrylate is particularly difficult because ferricenium ions act as free radical scavengers, and it has been observed in the literature that the molar ratio of VF units in a copolymer can be much lower than in the bulk monomer solution.34,36 In our work, however, elemental analyses indicated that there was little, if any, difference between the compositions of the reaction mixtures (22.2 and 3.4 mol % VF in monomer solutions for polymers A and B, respectively) and those of the HBMA-VF copolymers (21.5 and 3.3 mol % VF in polymers A and B, respectively) synthesized in dioxane via free-radical polymerization using ACVA as the initiator. It was thus assumed that copolymers of HBMA and VF grafted on conducting substrates to make RPEs had the monomers in the same ratio as in the reaction mixture used for the synthesis. The relative amounts of polymer attached to the substrate surfaces (either carbon black or carbon paper) were determined by TGA, as shown in Figure 2. In all cases, while the unmodified carbon black and carbon paper showed essentially no change in mass up to 700 °C, there was a significant loss of mass from the polymer-modified substrates between 200 and 500 °C, the same temperature range over which pure poly(HBMA-co-VF) also degraded significantly (about 90 wt %). The relative loss amounts were nearly 40 wt % for the grafted carbon black, and 2.2 and 3.5 wt % for the two grafted redox polymer electrodes, RPE-2 and RPE-3, respectively. The 335

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Figure 2. Weight loss of samples of (a) unmodified carbon black, pure poly(HBMA-co-VF), and carbon black after grafting of poly(HBMAco-VF) measured using TGA, and (b) of unmodified carbon paper, RPE-2, and RPE-3 measured using TGA.

grafting on carbon paper was less than that on carbon black on a per unit mass basis because of lower specific area and lower concentration of modifiable functional groups on the surface of carbon paper fibers relative to carbon black particles. The polymer loading on the carbon black particles was further confirmed by elemental analysis; while unmodified carbon black was found to have insignificant or trace amounts of iron, this element was easily detected in the elemental analysis of carbon black after redox polymer grafting; the recorded value agreed within five percent of that calculated using the weight of redox polymer attached to the particles (obtained using TGA) and assuming that the composition of the grafted copolymer was identical to the composition of the monomer solution from which it was synthesized. The SEM micrographs in Figure 3 show the unmodified carbon paper fibers, with smooth, unblemished surfaces, together with the two polymer-grafted carbon papers. It is evident that the clean fiber surfaces of the unmodified carbon paper had undergone modification. The attached polymers clustered on the fibers did not coat them uniformly, and did not affect their overall thickness appreciably. The impregnated redox polymer electrode, RPE-4, was prepared by creating a chemically cross-linked network of redox polymer chains around the carbon fibers, with no direct chemical linkages between the polymer chains and the carbon fibers in the carbon paper. The weight of carbon paper before and after gelation indicated that 31 mg of redox polymer gel was present per square centimeter of RPE-4. The successful impregnation of the porous fiber matrix by the redox polymer gel was possible because the monomer solution of HBMA and VF containing EGDMA and AIBN wet and spread throughout the bulk of the carbon paper. The wettability of the unmodified carbon paper by the monomer mixture was confirmed by contact angle measurements showing advancing (30.4°) and receding contact (18.1°) angles that were much smaller than the critical contact angle of 90°.

Figure 3. SEM micrographs of (a) unmodified carbon paper, (b) RPE2, and (c) RPE-3. Scale bar denotes 10 μm.

The elemental and functional composition of the redox polymer grafted on conducting carbon substrates was analyzed indirectly by depositing the redox polymer on chemically modified IR-transparent silicon wafers using initiated Chemical Vapor Deposition, as detailed in the Supporting Information. The presence of iron on the surface of the polymer coating on silicon wafers was determined by XPS. The XPS spectrum (Figure 4a) showed a peak at 709 eV which is characteristic of the 2p orbital of iron. The atomic percent of iron on the surface (determined using CasaXPS software) indicated that if it is assumed that the surface is completely covered with the redox polymer, then the ratio of VF units to the HBMA units is somewhere in between 1:3 and 1:4. This agrees with the molar ratio HBMA to VF equal to 1:3 used to prepare the monomer solution that was used for the redox polymer grafting. Moreover, the XPS scan of the surface of a silicon wafer that was not subjected to polymer grafting but was simply immersed in a solution of HBMA and VF under identical conditions to act as control showed a much weaker signal attributable to iron. The ferrocene functionalities in the redox polymer layer were evident from the peak characteristic of ferrocene at 3090 cm−1 in the FT-IR spectrum of the redox polymer modified silicon wafer after polymer grafting (Figure 4b). Control silicon wafers immersed in HBMA-VF solution under identical conditions without allowing for the grafting of the redox polymer to proceed did not show a peak at 3090 cm−1, confirming that the ferrocene groups were covalently attached to the chemically modified silicon wafer, and were not simply adsorbed on the surface. 336

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been employed for studying phenomena at plane electrochemical interfaces, were not pursued in this work in light of reports by Tamaki and Yamaguchi of limited success of impedance spectroscopy for observing electron transfer behavior through porous electrodes.1 The voltammogram for the modified carbon black particles, electrode RPE-1 (Figure 5a), shows a broad, distinct peak at 0.60 V during oxidation and a similar peak at 0.16 V during reduction, resulting in a mean potential of 0.38 V, which falls within the range of 0.20−0.50 V reported in literature for the redox potentials of ferrocene-containing polymers and surfactants.37−41 No such peaks were observed in the CV of unmodified carbon black particles, however, indicating that the electrochemical activity can be attributed to the reversible redox reactions of the ferrocene groups attached to the polymer chains. Moreover, the presence of a single peak during the oxidation and reduction sweeps is consistent with a oneelectron reversible redox reaction, again a characteristic of the redox activity of ferrocene. The broadness of the peaks, observed also by Tamaki and Yamaguchi1 with similar RPEs, suggests that there is a range of local chemical environments for the ferrocene moieties in the polymer, each of which imparts slightly different oxidation and reduction potentials. The voltammograms showed significant, large charging currents during both the oxidation and the reduction halves of the cycle, as also observed elsewhere, 1 signaling high electrode capacitance. High capacitive currents with no discernible peaks (Figure 5a), also observed with electrodes prepared using unmodified carbon black particles, were a result of the large surface area of the carbon black particles. An unchanging current response of the electrodes over multiple voltammetric scans signaled the electrochemical stability of the electrode. Further, this indicated that all the ferrocene centers were covalently attached to the polymer chains, which in turn were attached to the carbon black particles by strong chemical bonds that prevented the dissolution of the redox sites in the electrolyte.

Figure 4. (a) XPS spectrum, and (b) FT-IR spectrum of the surface of silicon wafer after redox polymer grafting.

Electrochemical Characterization of Electrodes. Cyclic voltammetric characterization of the electrochemical activity of the electrodes was carried out to establish the reversible nature of the redox reactions at the electrodes, and to provide further evidence of the attachmentchemical or physicalof the redox polymer to the conducting substrate that facilitated the transfer of electrons from the substrate to the polymer. Typical voltammograms for the four redox polymer electrodes, generated at a voltage scan rate of 20 mV/s, are shown in Figure 5. Cyclic voltammetry provided an effective technique for estimation of the diffusion coefficient of charge in RPEs, as is evident from the work of Bu et al.28 Dynamic electrochemical techniques such as impedance spectroscopy, which have often

Figure 5. Voltammograms obtained by CV of (a) RPE-1 (solid line) and electrode made using unmodified carbon black (dashed line), (b) RPE-2, (c) RPE-3, and (d) RPE-4. 337

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Figure 6. Dependence of peak current obtained in CV on the square root of scanrate for (a) RPE-1, (b) RPE-2, (c) RPE-3, and (d) RPE-4.

Figure 7. Experimental results (filled circles) with the best-fit Blauch-Saveant model curve (red line) showing the variation of peak current with mole fraction of ferrocene in the electrodes (a) RPE-1, (b) RPE-2, (c) RPE-3, and (d) RPE-4. The blue and green dashed curves show the variation of peak current if only bounded diffusion or electron hopping, respectively, contributed to electron transport.

reaction mixture to catalyze the ligand exchange reaction; the noise was removed manually by postprocessing of the data using filtering commands in MATLAB. Moreover, the presence of distinct, single peaks in the oxidation and reduction halves of the cycle, again attributed to the one-electron redox reaction of the ferrocene moieties in the polymer attached to carbon paper, indicated that the charging effects were considerably less important than the redox effects. The electrodes showed no loss of electrochemical activity over multiple CV cycles. The CV of the electrode RPE-4 obtained by impregnating carbon paper with 31 mg/cm2 of redox polymer gel in Figure 5d shows distinct peaks at 0.47 and 0.29 V, with a mean redox potential of 0.38 V, again in agreement with the location of peaks of ferrocene-containing polymers in the literature.37−41 The peaks are broad and separated by 0.18 V. The measured current response was stable over multiple voltammetric scans.

Cyclic voltammograms of unmodified carbon paper under identical conditions to those described above did not result in any discernible peaks, while single distinct oxidation and reduction peaks were observed for the polymer-grafted carbon paper electrodes RPE-2 and RPE-3, as shown in Figure 5b,c. Anodic and cathodic peaks in the voltammogram of RPE-2 were observed at 0.40 and 0.26 V, respectively, with a mean redox potential of 0.33 V, and for RPE-3, at 0.43 and 0.29 V, respectively, with a mean redox potential of 0.36 V. These mean redox potentials again fall in the range of redox potentials characteristic of ferrocene containing polymers.37−41 Similar to RPE-1, the repeatability of the current response over multiple voltammetric scans for each of the carbon paper electrodes indicated a stable and reversible electrochemical process. The current response to repeated voltammetric scans of RPE-3 was, however, noisy, attributable to incomplete removal of the aluminum powder, an easily oxidized metal, added to the 338

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Identification of Rate-Limiting Step for Electron Transport. The linear dependence of the peak current on the square root of the scan rate shown for all four electrodes in Figure 6 indicated that the electron transport from the working electrode to the counter electrode, primarily through the polymer film, was diffusion-controlled, in accord with the Randles-Sevcik equation.42 These results were for a copolymer with 22 wt % vinylferrocene. The peak current can be expected to vary with the concentration of the redox centers within the polymer film, as discussed by Blauch and Saveant,27 who developed a model to describe electron motion in polymer films using percolation concepts. When the physical motion of the segments is either nonexistent or is very slow, the charge transfer takes place primarily via percolation through interconnected clusters of redox centers. If the concentration of the redox groups is less than a critical concentration so as to result in mutually disconnected clusters, no charge transport should be possible. However, the physical displacement of the redox centers around the anchoring points, if rapid enough, could lead to reorganization of the clusters making electron transport possible in a process called ‘bounded diffusion.’ To elucidate the mechanism of electron transport in our polymer films, we prepared a series of electrodes with different VF concentrations using each of the four techniques described above. Peak currents, ip, measured for these electrodes are plotted in Figure 7a−d as a function of the concentration of the redox species in the polymer. The variation in the case of RPE1, -2, and -3 shows a general pattern in that the current rises sharply from zero at low concentration, then levels off before increasing again. This inverted ‘S’-shaped variation of ip with the concentration of the redox species in the polymer indicates an interplay between the two different mechanisms, electron hopping and bounded diffusion, one dominant at low concentrations, and the other at high concentrations, with a range of concentrations in between where transition from one mechanism to the other takes place. The curves shown in these plots are a fit of a modified version of the Blauch-Saveant model to the data, as described below. The apparent diffusivity, which can be assumed to be the sum of the diffusion coefficient due to bounded diffusion, Dbd, and that due to electron hopping, Deh, was shown by Blauch and Saveant to be described well by the equation Dap = Dbd + Deh = where

hopping distance; and te and tp are the time constants characterizing electron hopping and physical motion of the chains, respectively. This model predicts a nonlinear concentration dependence for the apparent diffusivity, Dap, of the redox species. However, Deh varies linearly with concentration because the electron hopping distance, δ, is constant for a given redox polymer system. Bu et al. assumed that the physical motions of the ferrocenyl groups in their polyacrylamide copolymer gels were much more rapid than the rate of electron hopping, that is, they assumed that tp ≪ te. In this limit, ρ ≫ 1, and the expression for the apparent diffusivity simplifies to Dap =

⎛ ρ ⎞ ⎛ ω ⎞2 λ 2⎜ ⎟≈⎜ ⎟ ⎝ 1 + ρ ⎠ ⎝ cn ⎠

kactc ⎛ 2 ρ ⎞ ⎜3λ ⎟ 6 ⎝ 1 + ρ⎠

and

Deh =

kactc 2 (δ ) 6

(4)

where ω and n are positive parameters specific to a given redox polymer system. Thus, our modified form of the BlauchSaveant equation is Dap =

(1)

⎞ kactc ⎛ ω 2 2 ⎜ 3 2n + δ ⎟ 6 ⎝ c ⎠

(5)

The advantage of writing the Blauch-Saveant model in this form is that it allows ready estimates to be made of the relative contributions of bounded diffusion and electron hopping to the apparent diffusivity for limiting values of c. The value of n must be greater than 0.5 to ensure that the bounded diffusion of the polymer chains has the correct qualitative trends with changing concentration, that is, bounded diffusion is the dominant contributor to Dap at small values of c, while at high ferrocene concentrations, electron hopping will be the dominant mechanism; diffusion by electron hopping will continue to increase linearly with c while the bounded diffusion contributions will become smaller and smaller as the mean displacement of the ferrocene about its equilibrium point decreases with greater crowding of these moieties. Therefore, at low c, when bounded diffusion dominates

The individual contributions are Dbd =

(3)

showing that Dap should vary linearly with concentration, since λ is defined to be a concentration-independent constant in the original Blauch-Saveant model. The experimental results of Bu and co-workers were not consistent with this assumption, however, as they showed a pronounced nonlinear variation in diffusivity with ferrocene content. Indeed, if we do not constrain ρ to be much larger than unity, the bounded diffusion contribution will exhibit concentration dependence through the ρ/(1 + ρ) term. We found, however, that this concentration dependence is not sufficiently strong to capture the variation with concentration observed by Bu et al., most likely because the time constant for the physical motion of the chains is itself dependent on ferrocene concentration, which is not accounted for in the Blauch-Saveant approach. We have correlated the bounded diffusivity results reported by Bu et al. well in terms of a power law variation, observing that what Bu et al. reported as λ varied inversely with concentration raised to the 0.7 power, that is, λ ∝ [1/(c)0.7]. In accord with this observed power law variation and with the knowledge that λ by itself is meant to be a concentration-independent parameter in the original Blauch-Saveant model, we approximate the bounded diffusion contribution to the apparent diffusivity by

⎞ kactc ⎛ 2 ρ + δ 2⎟ ⎜3λ 6 ⎝ 1+ρ ⎠

⎛ 1 − c /ctot ⎞⎛ fc δ 2 ⎞⎛ te ⎞ ⎟⎟⎜⎜ ⎟⎟ ρ=⎜ ⎟⎜⎜ ⎝ c /ctot ⎠⎝ 3λ 2 ⎠⎝ t p ⎠

kactc (3λ 2 + δ 2) 6

(2)

In this equation, kact is the bimolecular activation-limited rate constant, c is the concentration of the redox moieties in the polymer, and λ = (2kBT/fs)0.5 is the mean-displacement of a redox molecule attached irreversibly to the polymer backbone about its equilibrium position, where kB is the Boltzmann constant, T is the temperature, and fs is an effective, concentration-independent spring constant. The total concentration of all monomeric units in the polymer is ctot; fc is a concentration-dependent correlation factor; δ is the electron 339

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and

Dap ≈

kactc ⎛ ω 2 ⎞ ⎜ ⎟ 6 ⎝ c 2n ⎠

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Table 1. Values of Parameters in the Modified BlauchSaveant Model Obtained by Curve Fitting to the Experimental Data Points

(6)

while at high c, where electron hopping dominates the process, we have ω2 ≪ δ2 c 2n

and

k c Dap ≈ act (δ 2) 6

electrode RPE RPE RPE RPE

(7)

For diffusion controlled electrochemical processes, the peak current ip measured during cyclic voltammetry is proportional to the square root of the diffusivity, Dap, and linearly proportional to the concentration of the redox species, c, according to the Randles-Sevcik equation 0.5 0.5 ip = 2.69 × 10−5n1.5ADap cυ

(8)

(9)

at low concentrations when bounded diffusion is the dominant mechanism, and, at high c, when electron hopping dominates, ip ∝ c1.5

(10)

Note that physically the peak current must approach zero as the concentration of the redox species is reduced, and this then places an upper limit of 1.5 on the allowable values of n. The modified form of Blauch-Saveant model given by eq 5 for describing electron transport mechanisms in redox polymer electrodes coupled with the Randles-Sevcik equation yields an expression for the peak current under diffusion limiting conditions of the form

⎞ ⎛ ω2 ip = K ⎜3 2n + δ 2⎟c1.5 ⎠ ⎝ c

(11)

A constant value of δ = 0.6 nm has been reported for ferrocenecontaining polymers.28 The values of the other parameters, K, ω2, and n, were determined by fitting the model to the experimental data for each electrode using a constrained optimization routine in MATLAB with the following constraints K > 0; ω 2 > 0; 0.5 < n ≤ 1.5

1 2 3 4

n

11.58 16.02 20.06 1.02

1.33 1.26 1.34 1.50

concentration increased, the contribution of bounded diffusion became less important and electron hopping began to contribute significantly to the electron transport until it dominated, as per eqs 7 and 10. By extrapolating the curves in the plot, it is expected that in electrodes with even higher ferrocene concentrations, electron hopping would become the principal mechanism for electron transport. These conclusions are in accord with those drawn by Bu et al.,28 who attributed the U-shape of the dependence of apparent diffusivity on ferrocene concentration to high bounded diffusion at low ferrocene concentrations, and fast electron hopping at very high ferrocene concentrations. For the three RPEs with un-cross-linked chains of copolymers of HBMA and VF, the numerical values of ω and n obtained from the optimization were found to be close to one another, with values ranging between 10 and 20 pm for ω, and varying slightly around 1.30 for n. The bounded diffusivity, Dbd, therefore varies inversely with c1.60. These values are specific to the HBMA-VF polymer systems used in this work, and are expected to be different for other redox polymers. The redox polymer electrode prepared by impregnation of the carbon paper with the redox polymer gel, RPE-4, is more intriguing. The value of the parameter ω obtained from the best-fit curve is an order of magnitude smaller than that obtained for the electrodes containing un-cross-linked polymer chains. This indicates that bounded diffusion played less of a role in electron transport in these cross-linked films than it did in the un-cross-linked films. Moreover, the value of n obtained from optimization was very close to 1.5 indicating that the contribution of bounded diffusion to the diffusion coefficient was nearly constant over the concentration range of ferrocene in the polymer explored in this paper. These conclusions can also be drawn based on the general shape of the best-fit curve to the experimental data points which is concave upward over the entire range of ferrocene concentration studied unlike the inverted ‘S’-shaped curve obtained in the case of RPE-1, -2, and -3. As further confirmation of the insignificance of bounded diffusion in electron transport in RPE-4, the effect of crosslinker concentration in the redox polymer gel on the measured peak current was investigated. Bounded diffusion takes place by physical motion of the polymer segments around an anchoring point. Therefore, an electrode with higher cross-linker concentration is expected to have a lower bounded diffusion contribution toward electron transport than another electrode with lower cross-linker concentration (maintaining the redox site concentration fixed) because cross-links between polymer chains reduce polymer segment fluidity making the structure more rigid.28 A series of RPE-4 electrodes were prepared by impregnating carbon paper with HBMA-VF gels having 1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 mol % of the cross-linker, EGDMA, keeping the concentration of VF fixed at 22 mol %. Within experimental error, the measured values of the peak current

Thus, based on our modified Blauch-Saveant model given by eq 5, the dependence of ip on c under the two limiting conditions should be

ip ∝ c1.5 − n

-

ω (10−3 nm)

(12)

The fitted curves are shown as solid lines in Figure 7, while the variations in the peak current with concentration that would be observed if either electron hopping or bounded diffusion were to dominate the electron transport process over the entire concentration range are shown using dashed lines. The values of the fitted parameters ω and n are given in Table 1 for the four RPEs studied here. Because the concentration of VF was expressed in terms of mole fraction, which is dimensionless, ω has the same units as δ, that is, nanometers. Visual inspection of Figure 7 indicates that in the electrodes with un-cross-linked redox polymer chains, that is, RPE-1, -2, and -3, transport of electrons occurred by both electron hopping and bounded diffusion of redox centers due to polymer chain motion. Which of the two mechanisms was dominant depended on the concentrations of these redox sites. At low ferrocene concentrations, where the electron transport processes are described by eqs 6 and 9, sharp rise in the peak current was due to rapid bounded diffusion. As the ferrocene 340

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The Journal of Physical Chemistry B were not significantly different from each other for this set of six electrodes. The indifference of the peak current to the crosslinker concentration along with the concave variation of the peak current with VF concentration over the entire range of VF concentrations investigated proved that electron hopping dominated over bounded diffusion as the mechanism for charge transport in RPEs made using cross-linked polymer chains.

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CONCLUSIONS

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The redox polymer was attached to silicon wafer using a stepwise process starting with iCVD functionalization of the wafer. The reaction steps and characterization experiments are discussed and presented. This material is available free of charge via the Internet at http://pubs.acs.org.

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ACKNOWLEDGMENTS

This work was funded by the DuPont-MIT Alliance (DMA). We acknowledge the support of Cabot Corporation, Columbian Chemicals, and Marktec, Inc., for providing free samples of chemicals and materials for use in this study. The authors would also like to thank Prof. Paula Hammond and Prof. Karen K. Gleason in the Department of Chemical Engineering, Massachusetts Institute of Technology for providing access to equipment in their laboratories. A.A. would like to acknowledge the help of Dr. Avni Argun and Dr. J. Nathan Ashcraft for training in electrochemical techniques and in-depth discussions. A.A. would also like to thank Dr. Mahriah Alf, Mr. Shreerang Chhatre, Ms. Jaisree Iyer and Dr. Sreeram Vaddiraju for their help in running certain characterization experiments and in model fitting.

Electron transport in RPEs prepared by attaching copolymers of HBMA and VF to conducting substrates such as carbon black and carbon paper was found to occur primarily via diffusion in the RPEs. A modified form of the Blauch-Saveant model permitted easy comparison of the relative importance of two mechanisms for electron diffusionbounded diffusion and electron hopping. It was found that both bounded diffusion and electron hopping were important contributors to the diffusion of electrons when the polymer chains attached to the substrates were un-cross-linked. Bounded diffusion effects were dominant over electron hopping effects at low redox species concentration in such RPEs, whereas the relative contribution of bounded diffusion and electron hopping was reversed at high concentrations of redox species. In RPEs with un-cross-linked poly(HBMA-co-VF) chains, bounded diffusivity, Dbd, in HBMA-VF systems varied inversely with c1.60, that is, Dbd ∝ [1/(c)1.60]. Diffusivity due to electron hopping, Deh, was linearly proportional to the redox species concentration irrespective of the linkage between the polymer chains. If, however, the polymer chains in the RPE were cross-linked, as in RPE-4, the mobility of the polymer chains was severely restricted and bounded diffusion no longer played the dominant role at low concentrations. Electron hopping was found to be the dominant mechanism of electron transport in such RPEs with cross-linked polymer chains over the entire VF concentration range studied. The characterization and analysis of redox polymer electrodes presented here will be of value in the design and preparation of such electrochemically responsive systems for a range of applications, including their use as reversible absorbents for chemical separations, the application of interest to us. In particular, a quantitative description of these transport processes will permit the a priori design and evaluation of integrated systems for the extraction and release of targeted compounds in feed solution.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 617.253.4588. Fax: 617.253.8723. E-mail: tahatton@ mit.edu. Notes

The authors declare no competing financial interest. 341

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