ANALYST, APRIL 1993, VOL. 118 36 1 Poly(pyrro1e) Based Amperometric Sensors: Theory and Characterization * Michael E. G. Lyons, Cormac H. Lyons, Catherine Fitzgerald and Thomas Bannon Physical Chemistry Laboratory, University of Dublin, Trinity College, Dublin 2, Ireland The utilization of electropolymerized electronically conducting polymers as amperometric chemical sensors and electrocatalysts is described, with specific emphasis on poly(pyrro1e) based materials. A theoretical model describing the operational principles of the polymer sensor is also described. The processes of substrate transport t o the sensor surface, and subsequent substrate reaction at the latter, were analysed in the context of rotating disc v.oltammetry. Two distinct situations were considered. In the first, the substrate does not partition into the layer, but simply reacts, via Butler-Volmer kinetics, at the polymer/solution interface.The second situation arises when the substrate partitions into the polymer layer. In this instance, substrate diffusion and reaction within the film was analysed. The porous nature of the polymer film is specifically taken into account. The redox chemistry of poly(pyrro1e) films doped with CI- and DBS- ions was examined using cyclic voltammetry and complex impedance spectroscopy and the mechanism of redox switching in these materials was investigated. The electrode kinetics of the quinone-hydroquinone redox couple at the doped poly(pyrro1e) films was also examined using cyclic voltammetry and rotating disc electrode voltammetry, and the mechanistic pathway was elucidated.Keywords: Amperometric sensor; poly(pyrro1e) electrochemistry; electronically conducting polymer; theory The design, fabrication and application of novel ampero- metric chemical and biological sensors has been the subject of considerable research interest in recent years. The subject of chemically modified electrodes has also been a very fruitful area of research activity. With respect to the latter field of research, considerable emphasis has been placed on the fabrication and characterization of electroactive polymer (redox polymer and electronically conducting polymer) modi- fied electrodes. General surveys of the electrochemistry of electroactive polymers have been provided by Hillman,l Lyons' and Evans.3 The application of polymer modified electrodes in analytical chemistry is of increasing interest. The recent review by Wring and Hart4 provides a good summary of this topic. Some specific examples can be mentioned.For instance, osmium-containing redox active metallopolymers have been used to determine nitrite amperometrically using a flow injection system.' Enzymes can be immobilized in electronically conductive polymer films to form novel am- perometric biosensor devices.6.7 It should be noted, however, that much of the analytical work reported to date has been mainly qualitative in char- acter. With some exceptions,Gg little effort has been made to provide a quantitative description of the systems examined. This is surprising given the fact that such an analysis is necessary in order to ensure that the sensor design is conducted on a rational basis.Further, the mechanism by which electronically conducting polymers enhance or catalyse the rate of interfacial electron transfer processes has not been examined to any great extent.9-13 This is also surprising, given that this is the fundamental process that governs the operation of a chemical sensor operating in the amperometric mode. With respect to the latter comment the work of Jakobs et al.11 Haimerl and Merz,9 Miller and Bockris,l2 Mao and Pickup13 and Lyons and co-workers14,I' is of note. The sensitivity and limit of detection of a polymer based sensor will also depend mainly on the background current exhibited by the material. The latter will, to a great extent, be a function of the morphology of the polymer, which in turn will depend on the * Prescnted at the Sensors and Signals Symposium at The Royal Society of Chemistry Autumn meeting, Dublin. Ireland, September 16-18, 1992.electropolymerization conditions employed, 16 and on the nature of the dopant counter ion incorporated in the polymer matrix to ensure electroneutrality . Consequently, a thorough characterization of a polymer based amperometric sensor device should also include an examination of the redox switching characteristics of the polymer, although the latter topic has been the focus of considerable attention in recent years. 17 A number of these themes will be addressed in the present paper. In particular, a quantitative analysis of the operational characteristics of conducting polymer amperometric sensors is outlined.Further, the characterization of the redox chemistry of these materials using cyclic voltammetry and complex impedance spectroscopy is presented. Finally, the mechanism and kinetics of mediation of outer sphere electron transfer processes at poly(pyrrole) (PPy) based sensor materials is discussed. Amperometric Detection at Conducting Polymer Surfaces: A Theoretical Appraisal The following analysis will be concerned with amperometric detection at a conducting polymer coated rotating disc electrode (RDE). This specific electrode configuration was chosen for the following reason. The transport of substrate to an RDE surface is well defined hydrodynamically (the diffusion layer thickness can be evaluated quantitatively) and steady-state conditions pertain.The latter condition simplifies the mathematical analysis considerably. Further, ampero- metric detection is usually conducted under steady-state con- ditions. It is assumed that the sensor is operated at a potential such that the polymer is electronically conductive, although it will be shown later that a more physically correct description involves the invocation of a semiconducting band structure for the material. The problem is to obtain an analytical expression for the faradaic current under steady-state conditions. The situation is outlined schematically in Fig. 1. The general reaction sequence at a conducting polymer modified electrode can be represented as follows: k'D k'ME sm - sL - products where kID and represent the mass transfer and heterogeneous modified electrode rate constants, respectively362 Conducting polymer , 1 electrode Support I X = O x = L Fig.1 Schematic representation of operating as an amperometric chemical Solution a. conducting polymer film sensor (units: cm s-1). The former quantity is given by the following expression : where D is the substrate diffusion coefficient (.=lo-5 cmL s-1 for aqueous solutions), X, is the diffusion layer thickness, v is the kinematic viscosity, w is the rotation speed and B is the Levich factor, i.e., 1.550: v-i. Typical values for k'ME are not very numerous, but a value of 1 x 10-3 cm s-1 can be quoted from work reported by Haimerl and Merz' for the quinone- hydroquinone redox couple at PPy coated Pt electrodes in buffered aqueous media of low pH.This result should be compared with a value of about 1 x 10-6 cm s-1 obtained at uncoated Pt electrodes under similar experimental conditions. Values of klME = 1 X cm s-l have been reported8 for the oxidation of catechol at conductive composite electrodes consisting of Ru02 microparticles dispersed in Nafion matrices. Hence a significant acceleration in rate is observed as a result of surface modification using a Conductive matrix. Following an approach suggested by Albery and Hillman,l8 application of the steady-state approximation to the reaction sequence outlined above results in the following expression for the reciprocal of the steady-state current (i): klD = D/X, = 1.55D2/3~-'/6~'/2 = Bw1/2 (1) This is the Koutecky-Levich equation for the amperometric sensor where n = number of electrons transferred, F = Faraday constant, and A = geometric area of the electrode.Hence we note from eqn. (2) that a plot of reciprocal current versus w-t is linear, with slope yielding B-1 and intercept (corresponding to the situation of infinite rotation speed) giving the kinetically significant quantity k'ME-'. The Koutecky-Levich type of analysis outlined above is to be preferred to that analysing the shape of the cyclic voltammet- ric response9 in that the processes of solution phase material transport (k' term) and chemical reaction/diffusion within the layer ( k f M E term) are clearly separated. The essential theoretical problem, therefore, is to evaluate k f M E . Details of the mathematical solution to the differential equation describing the transport and reaction kinetics within the layer have recently been reported from this laboratory.15 In the present paper, discussion will be focused on the current response obtained using this analysis.Two possible modes of reaction can be considered. The first case corresponds to the situation where the polymer film is impermeable to substrate. Hence the substrate will simply react at the polymer/solution interface. We do not consider the case where the reaction may be limited by the rate of charge percolation through the layer, because the polymer is electronically conductive. This form of rate limitation must be considered if redox polymer films are used as amperometric sensors because the conductivity in these materials occurs via an electron hopping mechanism between localized redox sites attached to the polymer backbone, a process which will ANALYST, APRIL 1993, VOL.118 intrinsically be less efficient than the rather facile charge carrier transport along conductive organic polymer chains. Consequently, the situation at an impermeable conductive polymer electrode is exactly analogous to reaction at a conventional metallic electrode and the heterogeneous modi- fied electrode rate constant is given by the simple Butler- Volmer equation k ' M E = k'E = k"~xp[a@] (3) where klF is the heterogeneous electrochemical rate constant, cx is the transfer coefficient, k" is the standard rate constant and 0 is a normalized potential given by 0 = F(E - E")/RT. The second case represents the fundamentally more com- plex situation where the polymer layer is permeable to substrate.In this situation substrate transport and reaction kinetics within the layer must be evaluated. In the latter instance the total current is obtained by solving the bounded diffusion problem for substrate transport and chemical reac- tion within the layer, and can be shown to have the following form: i = nFADsDFks"{tanh[L/XK](~sxK -k kDFX[i t a n h [ L / X ~ ] ) ~ ' } (4) where XK represents the reaction layer thickness given by: X K = (DF/k'E)' ( 5 ) and k is the partition coefficient ( L is the layer thickness and XD is the diffusion layer thickness). In these latter expressions we have differentiated between substrate diffusion in solution (Ds) and in the layer (DF).The reaction layer thickness quantifies the distance into the layer the substrate travels before it is consumed via chemical reaction at the polymer strands. Diffusional transport in solution and diffusiodreaction processes in the polymer film can be readily separated by inversion of the current expression outlined in eqn. (4) to obtain nFAs"/i = X[,/Ds + ( x ~ / k D ~ ) c o t h [ L / X ~ ] (6) k'ME = (kDF/XK)tanh[L/XK] (7) We compare eqns. (2) and (6) to obtain and the current due to diffusiodreaction processes within the layer, iF, is given by iF = nFAkSWDFXKp'tanh[L/XK] ( 8 ) At this stage attention must be focused on the ratio L / X K , where L is the layer thickness. When LIXK >> 1 then tanh[L/XK] = 1 and the expression for iF outlined in eqn.(8) reduces to iF = nFAks"DFXK-L (9) Alternatively, if L/xK << 1 then tanh[LIXK] = L/xK, and eqn. (8) admits the form iF = nFAkDFswL/XK2 = nFAkfEksWL ( 10) We now note the following important point. The reaction layer thickness XK will depend on potential and we can write that X K = (Dt./k'~); = (DF/k")l exp[ - &@/2] (11) Therefore, as the applied potential 0 increases, the factor exp[ - a@] will decrease and consequently the reaction layer thickness XK will also decrease. Froin eqns. (9) and (11) we obtained that for L >> XK, i.e., thick layers, the current- potential response will admit the form iF = n FAks" D,ik"kxp[ a@/2] ( 12) and the experimentally determined transfer coefficient aexpl = d 2 . For a simple single electron transfer reaction LY == 0.5 usually. Hence for a similar reaction taking place at a porousANALYST, APRIL 1993, VOL.118 /' 363 ----- \------/-7 conducting polymer matrix one would expect that aexpl = 0.25, i . e . , for thick films the Tafel slope 6 = 2.303RT/01e,plF, will be twice that expected. This result has a physical basis. It is well established that thick electrodeposited layers of electron- ically conducting polymers are fairly porous. Hence, for large values of applied potential, XK becomes very small and only a small fraction of the inner surface of the pore will be utilized. The perceived sensitivity of rate to applied potential (expressed as a Tafel slope) will be less than that expected for a planar electrode because only a small proportion of the active surface is being utilized.The porous matrix will also be electronically conductive at high potentials and so the reactant will only have to diffuse a short way into the layer before it is consumed via chemical reaction. Hence, as noted in eqn. (13), the reaction rate iF will be independent of layer thickness. In contrast, for thin layers when L << XK, the current-potential expression obtained from eqns. (10) and (11) becomes 3 0 iF = nFAks" Lk"exp[ 0101 L In this instance normal Tafel behaviour is observed with O1expl = 01 and the entire layer is utilized. Further, the reaction rate will depend in a linear manner on the layer thickness. Hence the reaction kinetics of a solution phase substrate at a conducting polymer surface will only depend on the layer thickness for small values of the latter. If thick layers are used then the rate will be independent of layer thickness. This may account for the varied and inconsistent observations regarding rate/layer thickness dependencies reported in the liter- The prediction that the observed transfer coefficient aexpl can depend on the LIX, ratio has not been appreciated in previous studies reported in the literature.v.12 ature.'~.ll,l~ Experimental The PPy-DBS- (DBS- = dodecylbenzenesulfonate ion) polymer was formed via potential step electropolymerization (deposition potential, 800 mV versus Ag-AgCI) onto a Pt disc electrode immersed in a solution containing 50 mmol dm-3 pyrrole and 0.1 mol dm-3 C12H2sC6H4S03Na.A similar procedure was used to generate PPy-Cl-, except that in this instance the supporting electrolyte was NaCl (0.1 mol dm-3).Full experimental details have been published elsewhere. 14 The mechanism of nucleation and growth under controlled potential potentiostatic conditions has also been addressed in a recent paper,l6 and so will not be discussed here. All solutions were prepared using ultra-pure Milli-Q water and AnalaR-grade reagents. A conventional three-electrode electrochemical cell was used. Potentials were measured, and are quoted, with respect to an Ag-AgC1 (sat. KCl) reference electrode. A large surface area Pt foil served as counter electrode. Solutions were de-gassed with oxygen-free nitrogen prior to electrochemical measurements. Cyclic voltammetry and complex impedance spectroscopy measurements were conducted under microcomputer control using an EG&G PAR Model 378 complex impedance software package.The complex impedance of pre-grown polymers was determined in supporting electrolyte solution as a function of electrode potential in the frequency range from 100 kHz to 0.5 mHz. An EG&G PAR Model 5208 lock-in amplifier was used to measure the in phase and quadrature components of the impedance in the frequency range from 100 kHz to 5 Hz. For measurements conducted at lower frequencies, a fast Fourier transform technique was used. Redox Chemistry of Surfactant Doped PPy Films A specific example of a conductive polymer electrode that has been shown to be a very effective sensor material for the amperometric determination of ascorbate14JO will now be considered.The redox chemistry of a PPy film doped with the surfactant counter ion DBS- , C12H2sC6H4S03-, is described the redox characteristics of the latter material (PPy-DBS-) are compared with those exhibited by PPy doped with chloride ion (PPy-C1-). The voltammetric responses obtained for PPy-Cl- and PPy-DBS- in 0.1 rnol dm-3 NaCl are presented in Figs. 2 and 3, respectively. The layer thickness was about 2 pm in each instance. It is clear from these voltammograms that the dopant counter ion exhibits a marked effect on the shape of the voltammetric response. A broad ill-defined response is observed for the PPy-CI- layer, in which the charge distribu- tion is considerably broad along the potential axis, signifying the presence of considerable electrostatic repulsive interac- tions between the oxidized sites in the polymer layer.21-22 The observed broadness may also be attributed, in part, to counter ion transport effects within the polymer matrix.23 The standard redox potential lies in the range 80-90 mV.The latter range is quoted because the voltammetric peaks shift slightly on repetitive potential cycling around the redox switching region. The latter observation is due to polymer restructuring effects. 1 4 - 2 3 ~ 4 The material PPy-CI- is electron- ically insulating at -400 mV and electronically conducting at 500 mV. The voltammetric profile illustrated in Fig. 2 is also characterized by the pseudo-capacitative current plateau region located at potentials anodic to the oxidation peak where the material behaves as a plastic metal.Redox switching in PPy-CI - is accompanied by anion transport in the polymer film and can be described in terms of the following reaction: PPy + X-(as) % PPy+X-(pol) + e- (14) t .+ f 2 3 0 -0.4 0 0.5 E N Fig. 2 Cyclic voltammogram of PPy-CI- (35 mC deposition charge) in 0.1 mol dm-3 NaCl. Sweep rate, 25 mV s-1. First sweep (solid line), third sweep (broken line)364 ANALYST, APRIL 1Y93, VOL. 118 Hence polymer chain oxidation results in the generation of positive charges (polarons) on the backbone that are delocal- ized over four monomer units. In order that electroneutrality is preserved, ingress of anions from the electrolyte solution into the polymer matrix occurs. The reverse occurs on reduction: anions are ejected from the polymer matrix into the solution.This mechanism has been confirmed using the electrochemical quartz crystal microbalance (EQCM) tech- nique.25-27 This hypothesis can also be confirmed using cyclic voltammetry. The material PPy-CI- acts as a permselective membrane so that cations are excluded from the coating. The Nernst equation describing the redox switching reaction involving anion injection/ejection can be written as follows: E, = E,O + (RT/F) ln([P+]/[P"][X-I} (15) where [P+] and [PO] represent the concentrations of the oxidized and reduced units in the polymer, respectively, and E, denotes the apparent formal potential of the polymer redox couple. The quantity E i ) is the formal potential of the polymer redox couple. If we assume that E, is evaluated by taking the mean of the anodic and cathodic voltammetric peak potentials then under these conditions [P+] = [P"] and eqn.(15) reduces to E, = EpO -(RT/F)ln[X-] (16) We note, therefore, that a plot of E, versus log[X-] should be linear with a slope given by 2.303RT/F, i.e., the potential of the PPyO-PPy+ redox couple shifts in a negative direction by 59 mV decade-' increase in anion concentration [X-1. This prediction is valid for an ideal anion-selective permselective ion-exchange membrane. The shift in apparent formal poten- tial is simply caused by the existence of a Donnan potential difference between the anion-exchange polymer film and the supporting electrolyte solution in contact with it. This effect is illustrated in Fig. 4. The apparent formal potential does indeed decrease with increasing anion concentration in the solution.However, the slope has a super-Nernstian value of -80 mV decade-'. Super-Nernstian shifts have also been observed by other workers.28.29 The origin of this super- Nernstian shift is not clear at present. Work is currently being carried out in this laboratory to examine this effect further. At this stage it must be stated that the analysis of voltammetric peak shifts does not convey structural informa- tion. What it does convey is information on the stoichiometry of the redox process. The determination of redox reaction stoichiometry via analysis of shifts in voltammetric peak potentials is a well established procedure in electrochemistry. 100 50 > E G 0 - 50 -2.0 -1.0 0 Log(c/mol dmp3) Fig. 4 Plot of standard voltammetric peak potential versus NaCl concentration for a PPy-CI- coated electrode.The potential values were obtained by averaging the anodic and cathodic peak potentials recorded at a slow sweep rate, 5 mV s- 1 . T = 298 K A point of caution must also be noted here. Voltammetric profiles recorded for electronically conducting polymers are usually fairly broad. This can give rise to appreciable errors in the exact determination of peak potentials. This will not negate the observed trends, however, especially the sign of the dE, versus dlogc plot. The voltammetric peaks obtained for ppy-CI- are fairly broad. Hence the uncertainty in the assignment of peak potential may lead to an uncertainty in the assignment of the magnitude of the slope of the dE, versus dlogc plot for this material.A markedly different voltammetric response is obtained for the PPy-DBS- layer (Fig. 3). On the initial potential sweep a very marked well defined reduction peak is observed, which may be attributed to the ordering of the polymer matrix by the rather large surfactant DBS- counter ion. In contrast, the anodic part of the voltammogram is rather broad and ill defined. An approximate value for the apparent formal potential in 0.1 mol dm-3 NaCl solution is -525 mV. A more well defined response is observed if the voltammetry is carried out in phosphate buffer, pH 7 (Fig. 5 ) . In this instance the redox peaks are well defined and the standard potential is -445 mV. A further feature of interest can be noted from Fig. 3. Considerable polymer restructuring occurs on repeti- tive potential cycling, if the latter perturbation involves continuous redox switching. This restructuring effect results in a shifting of the reduction peak to more positive potentials together with a significant diminution of the peak current. The current response during the anodic sweep also changes, the charge being distributed over a wide potential window.This results in an increase in background current response at potentials more positive than 0 mV. Our experiments have indicated that the PPy-DBS- layer can be subjected to a repetitive potential cycling programme in the region from -300 to +600mV without any noticeable increase in back- ground current. This indicates that little restructuring and morphology change occurs under these conditions.Hence, restructuring effects occur only if the potential limits are extended to include the region of redox switching and will always be accompanied by layer reduction. The 'bottom line' from the viewpoint of electroanalytjcal application is that PPy-DBS- layers exhibit extremely stable electrochemical responses and minimal background currents provided that the layer is not operated in a potential region that involves redox switching. As the latter process occurs at fairly negative potentials, the material is electronically conductive over a fairly large potential window (about 1100 mV). This is a very desirable property from the viewpoint of amperometric sensor applications. 1 I I - 800 - 400 0 E/mV Fig. 5 Voltammetric profile recorded for PPy-DBS- in the region of redox switching in phosphate buffer solution, Ph 7.Sweep rate, 20 mV s-lANALYST, APRIL 1993. VOL. 118 365 The PPy-DBS- material exhibits a number of unusual features. Firstly, analysis by scanning electron microscopy has indicated30 that the electrodeposited layer exhibits a rather compact morphology. Secondly, the fact that a long chain alkylsulfonate ion is used as dopant, results in the imposition of a rather ordered polymer film. This is evident in the well resolved reduction peak in the voltammogram. Thirdly, we have previously noted14 that the material exhibits a very low pseudo-capacitative current in the oxidized state, compared with most of the other electrochemically deposited conducting polymers. The subject of pseudo-capacitative current has been a vexing problem in the area of electronically conducting polymers and has been examined by a number of workers in recent years.17,31,32 Some presume that the current is capacita- tive and others assign to it a faradaic origin.If the first assignment is valid then the low current response can be attributed to the rather dense polymer morphology: the layer is so compact that there is not great exposure of surface area to the pools of electrolyte within the polymer matrix. On the other hand, if the current in the plateau region is assigned a faradaic origin, then the very low current observed may be due to efficient layer oxidation caused by the ordering of the polymer imparted by the large surfactant DBS- ion. There are no unoxidized regions remaining in the polymer at potentials more positive than 0 mV.This is clearly not the situation for PPy-CI- (Fig. 2). In the latter material there is a certain amount of 'over oxidation' in the region of the current plateau and consequently the current response is significant. Finally, the DBS- ion is large and thus should not be readily transported through the polymer matrix. This implies that redox switching should be accompanied by cation rather than anion transport and the material should be cation permselec- tive. This is in contrast to the situation previously encountered with PPy-CI-. Consequently, polymer oxidation will be accompanied by cation ejection and reduction by cation injection as follows: PP~-C+RSO~-(POI) S PPy+RS03-(pol) + C+(aq) + e- (17) One can again apply a nernstian analysis to this reaction to obtain: E, = EpO + (RT/F)ln{ [PPy+RS03-]/[PPyRS03-C+]} + (RT/F)ln[C+] (18) In this instance we note that the apparent formal potential should vary in a linear manner with the log of the cation concentration and that dE,/dlog[C+] = 2.303RT/F, i .e . , +59 mV decade-'. In simple terms this means that an increase in cation concentration will result in a positive shift in the formal redox potential. This feature is clearly illustrated in Fig. 6. In this instance a slope of 56 mV decade-' is obtained, 460 I d I - 560 -2 - 1 0 Log(c/mol dm 3, Fig. 6 Plot of standard voltammetric peak potential versus NaCl concentration for a PPy-DBS- coated electrode. Experimental conditions are similar to those outlined in Fig.4 which indicates that PPy-DBS- behaves almost ideally as a permselective cation-exchange membrane. As redox switching in PPy-DBS- involves cation ejection/ injection, it is interesting to examine the effect of cation size on the efficiency of cation transport in the polymer matrix. The results of such a study are outlined in Fig. 7, in which the numerical value of the voltammetric charge corresponding to layer reduction is plotted as a function of the dehydrated cation radius. One can assume that this charge Q, represents an approximate measure of the ease of cation injection into the film. The significant feature exhibited from these data is that the reduction charge Q, decreases as the dehydrated radius of the cation increases. Hence the phenomenon is kinetic and reflects a simple size effect: large cations are transported less readily than small cations.Hence Cs+ is transported less efficiently than either Li+ or Na+. This observation can be explained in the following manner. The surfactant doped polymer can exhibit considerable hydrophobicity. This is due to the conditions employed during electropolymerization, where 50 mmol dm-3 pyrrole and 0.1 mol dm-3 DBS- were used. It should be noted that the concentration of surfactant employed was considerably greater than the critical micellization concentration, which is 1.2 x 10-3 mol dm-3.33 Consequently, it is probable that micellar aggregates form in the solution and that the deposited film is ordered such that the pyrrole chains orient themselves around the hydrophilic surface of the micelle.The polymer environment will, therefore, exhibit a marked hydrophobic character. Consequently, before the cation can enter the matrix it must lose a significant fraction of its hydration sheath: ion-solvent interactions (Born, ion-dipole, ion-quad- rupole, ion-induced dipole) must be disrupted. This concept of partial dehydration remains speculative at present. Studies utilizing the EQCM technique should enable one to evaluate the amount of water associated with the cations as they are transported through the polymer matrix during redox switch- ing. Complex Impedance Spectroscopy of PPy-Cl- and PPy-DBS- Films Complex impedance spectroscopy has proved to be a very useful method for the quantification of electronic and ionic resistivities in electronically conducting polymer films.In principle, if the range of frequency over which the impedance response is examined is very large then both the electronic resistance RE and the ionic resistance RI can be determined. The mathematics of the impedance response of an electronic- ally conducting polymer film has recently been developed largely by Albery and co-workers34-3h and Fletcher.37 The analysis is based on the porous nature of electronically 2'5 r--- cs + 0 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 rlnm Fig. 7 Plot of the voltammetric charge for layer reduction corres- ponding to the facility of cation transport within the PPy-DBS- matrix as a function of cation radius. The voltammograms were recorded at a slow sweep rate, in a number of metal chloride solutions366 ANALYST, APRlL 1993, VOL.1113 conducting polymers. A full quantitative theory which can be used for data analysis is lacking at present. As a consequence, the impedance response obtained for the doped polymers will only be discussed in a qualitative manner. A full quantitative analysis of the data will be presented in a subsequent paper. The mathematical model employed is based on a dual rail transmission line (Fig. 8). One rail of the transmission line represents the electronic conductivity, the other rail, the ionic conductivity in the pores. The two rails are connected via a circuit element associated with interfacial redox reactions involving polaron and bipolaron states at the pore wall. Typical complex impedance spectra obtained for PPY-CI- and PPy-DBS- layers in contact with 0.1 mol dm-3 NaCl and 0.1 mol dm--7 NaDBS solutions, respectively, are illustrated in Figs.9 and 10. These spectra were obtained when the polymers were in the oxidized, conductive state. For the C1- doped material (Fig. 9), the applied d.c. potential was 400 mV and the deposition charge was 100 mC. A number of features can be noted from the impedance spectrum such as the presence of two semicircles at high frequencies. This feature was predicted in a recent paper by Fletcher.37 The small semicircle at very high frequencies is related to conduction processes associated with polaron motion along the polymer backbone (intrachain conduction) and between chains (inter- chain conduction). The former is associated with regions of high structural order and is, therefore, very fast, while the latter is associated with regions of low structural order and is, therefore, slower.The second semicircle at lower frequencies is attributed to an RC (resistancekapacitance) circuit element describing charge transfer reactions involving the localized polaronic and bipolaronic states at the pore wall. Clearly this feature dominates the over-all response in the high-frequency region. At lower frequencies a Warburg-like feature can be noted, while in the very low frequency region a vertical capacitative response is observed. The response at inter- Fig. 8 A dual rail transmission line model for electronically conducting polymers. RE denotes the electronic resistance, RI is the ionic resistance and Cis the distributed capacitance of the polymer. Rs represents the uncompensated solution resistance 80 ,G G 0 100 140 Z'IR 0.67 Hz .mediate and low frequencies is governed totally by reactions at the pore walls and not by processes occurring within the bulk polymer. A similar situation is found for the PPy-DBS- material (Fig. lo). In this instance the applied d.c. potential was again 400 mV and the deposition charge 75 mC. Only one semicircle is observed at high frequencies, and a quasi-vertical response is observed in the lower frequency domain. The impedance response totally reflects interfacial redox processes at the pore walls. The impedance spectra recorded for the doped PPy materials in the reduced, insulating states are illustrated in Figs. 11 and 12.The applied potential in both instances was -900 mV. Tn Fig. 11, for the C1- doped polymer, two semicircles are noted. The impedances are much greater in this instance, as expected. The response obtained for the DBS- doped material (Fig. 12) is less well defined, but exhibits the shape predicted by Fletcher,37 who has noted that the shape of the response corresponding to the interphasial electrochemistry at the pore walls will depend on the ratio of the double layer capacitance of the pore wall to the pseudo- 0 2.5 Z'IkR Fig. 10 Complex impedancc spcctrum for PPy-DBS- in 0.1 rnol dm-3 NaDBS. The applied potcntial was 400 mV. Deposition charge, 75 mC. The layer is in the oxidized, conductive state . . . . 40 ....-._. I I , 0 40 80 120 Z'IkO Fig. 11 Complex impedance spcctrum for PPy-CI- in 0.1 mol dm-3 NaCl.The layer is fully reduced and insulating. Applied potential = -900 mV. Same deposition charge as in Fig. 9 30 Fig. 9 Complex impedance spectrum for PPy-Cl- in 0.1 rnol dm--l NaCl. The layer is fully oxidized and conductive. Upper frequency limit, 100 kHz; lower limit, 0.67 Hz. Applied d.c. potential = 400 mV. Deposition charge = 100 mC 180 0 37 Z'IkQ Fig. 12 Complex impedance spectrum recorded for PPy-DBS- in 0.1 mol dm--l NaDBS. The layer is fully reduced and insulating. Applied potential, -900 mV. Same deposition charge as in Fig. 10ANALYST, APRIL 1993, VOL. 118 367 capacitance describing the charge/discharge reactions of the polaronic and bipolaronic states. A defined semicircle will only be observed if this ratio is very small.If this is not true, and the ratio is appreciable, then a response similar to that illustrated in Fig. 12 is predicted. The major point to note from this qualitative analysis is that over most of the available frequency range, the impedance response is dominated by interfacial redox chemistry involving localized polaronic and bipolaronic states, and not by the intrinsic conductivity of the polymer chains. This point has not been fully realized by other workers. Mediation of Outer Sphere Electron Transfer Reactions at Doped PPy Films The redox chemistry of the quinone-hydroquinone redox couple at doped PPy films will now be discussed. It is well established3840 that the quinone-hydroquinone redox transformation in solutions of low pH follows a 2e-, 2H+ process at unmodified electrode surfaces.The redox stoichiometry can be readily confirmed by cyclic voltammetry, and determining the way in which the voltammetric peak potentials vary with changes in solution pH. We have shown41 that a similar mechanism operates at a PPy coated electrode. As illustrated in Fig. 13, the voltammetric peak potentials for the Q-QH2 reaction at PPy films vary in a regular manner with changes in solution pH. The voltammetric response was examined as a function of pH for both a slow (2 mV s-1) and a fast (100 mV s-1) sweep rate. In all instances it can be seen that the slope, dE,/dpH, is close to the value of -0.059 V decade-’, when the voltammograms are recorded - at 298 K. In general we can write that dE,/dpH = -(2.303RT/F)(rn/n) 0.6 0.5 0.4 0.3 3 0.2 0.1 0 where rn denotes the number of protons transferred and n represents the number of electrons transferred in the redox process. Hence if rn = n , the predicted slope at 298 K is -0.059VpH-1.Hence, as n = 2 for the Q-QH2 reaction, then the stoichiometry of the reaction in low pH solution is Q + 2H+ + 2e- + QH2 (20) A typical voltammogram for the quinone-hydroquinone redox couple (1 mmol dm-3 in each component) at a PPy- DBS- coated glassy carbon electrode in McIlvine buffer, pH 2.2, is illustrated in Fig. 14. In this instance the sweep rate employed was 5 mV s- 1 . A corresponding voltammogram recorded at a PPy-Cl- coated electrode at the same pH is outlined in Fig. 15. The scan rate employed was 10 mV s-1. In both instances the peak separations (190 mV for the DBS- doped material and 210 mV for the CI- doped material) indicate that the redox process is quasi-reversible.One can utilize the peak separation values to determine the hetero- geneous electrochemical rate constant using a protocol originally proposed by Nicholson.42 One can relate the observed peak separation WE, to a parameter c. The latter is related to the standard electrochemical rate constant via c = (Do/D,).’*ko/[Donv(n~/R~]~ (21) where Do and DR denote the diffusion coefficients of the oxidized and reduced forms of the redox couple, and v is the scan rate. The other symbols have their usual meanings. Clearly n = 2. The required value of c was obtained from the published working curve relating nWE, values to c. Further, Do = DR = 3.46 x 10-5 cm2 s-1 for the quinone-hydroqui- none couple at PPy-CI- and Do = 1.92 X 10-5 cm2 s-1, DR = 1.67 x 10-5 cm2 s-1 for the reaction at PPy-DBS-.If these 0 I I I I I I 1 2 3 4 5 6 PH Fig. 13 Variation of voltammctric peak potentials with solution pH for the quinone-hydroquinonc rcdox couple at a PPy-DBS- electrode. The data were recorded at 2 and 100 mV s-l. Note that d F /dpH = -59mVdecade-1 (Y = 2mVs-1) and -60 mrdecade-1 (Y = 100 mV s-1). The corresponding anodic slopes wcrc slightly higher with dE,,/dpH = -64.3 mV decade-’ (Y = 100 mV s-1). Hence the ratio of protons to electrons is unity. 0, Anodic; and 0, cathodic. A, 100; and B, 2 mV s-l 0.3 E N 0.6 Fig. 14 Voltammetric response for quinone-hydroquinone at a PPy-DBS- coated clectrode. Conditions are similar to those outlincd in Fig.14, but thc sweep rate in this instance is 10 mV s-1 0 0.7 E N Fig. 15 Voltammetric response for the quinone-hydroquinone (1 mmol dm-3 in each Component. McIlvinc buffer, pH 2.2) redox couple at a PPy-Cl- coated electrode. Sweep rate, 5 mV s--l368 ANALYST, APRIL 1993, VOL. 118 t Y c i?! 13 0 t Y t 2 3 0 -0.1 0.3 0.8 EN I I I -0.1 0.4 0.8 EIV Fig. 16 Typical RDE voltammograms recorded for the quinone-hydroquinone redox couple at (a) PPy-CI- and (b) PPy-DBS- electrodes. Sweep rate, 2 mV s--l. Rotation speed, 500 rev min-1. Experimental conditions are similar to those outlined in Fig. 14 - values are substituted into eqn. (21), then the heterogeneous rate constant for the quinone-hydroquinone reaction at PPy-Cl- is 9.2 x 10-dcms-1, and at PPy-DBS-, 4.52 x 10-4 cm s-1 (oxidation) and 4.84 x 10-4 cm s-1 (reduction).The mechanism of the Q-QH2 reaction can be determined by a detailed analysis of the current-potential response curves. A typical rotating disc voltammogram recorded for the Q-QH2 couple at a PPy-DBS- coated electrode at a rotation speed of 500 rev min-1 is illustrated in Fig. 16. Again, the shape of the RDE voltammogram indicates quasi-reversible electrode kinetics. This voltammogram was recorded at the slow sweep rate of 5 mV s-1. The current-potential data are illustrated in a Tafel format in Fig. 17. A dual Tafel slope behaviour is observed for reduction, whereas only a single Tafel region is observed for oxidation. The numerical values of the Tafel slopes are b, = 0.053 V decade-', b,, = -0.39 V decade-' (low potentials) and bc2 = -0.291 V decade-' (high potentials).As the overall Q-QH2 reaction sequence involves the transfer of both protons and electrons, the reaction pathway can be described in terms of a square scheme.39-JO.43 As a buffer solution is being used, the proton transfer processes can be assumed to be at equilibrium. Hence, formally, the kinetics can be analysed in the context of a simple consecutive EE sequence, in which the heterogeneous electrochemical rate constants for the individual electron transfer steps depend on pH. The RDE voltammograms were recorded in a low pH buffer (pH 2.2). Under such conditions the general nine- member square scheme reduces to the following CECE (chemical, electron transfer chemical, electron transfer) reaction sequence: Q + H+-+QH+ QH+ + e - -+= QH' QH* + H+ + QH2+* QH2+* + C- + QH2 This sequence can be used to explain the observed kinetic data (Fig.17). We firstly consider the Tafel plot for reduction. The Tafel slope at low potentials is 40 mV decade-1, correspond- ing to a = 3/2. This corresponds to the second electron -10 --I1 3 - I= -I -12 -13 0 0 cr 0.1 0.3 E N 0.5 Fig. 17 Tafel plot analysis for quinone-hydroquinone reaction at PPy-DBS-. Voltammetric conditions as outlined in Fig. 16. General experimental conditions as in Fig. 14. 0, Cathodic; and 0, anodic transfer in the reaction sequence being rate determining. At higher potentials there is a change in the nature of the rate-determining step as implied by the change in observed Tafel slope.If the first electron transfer becomes rate determining under these conditions then the expected slope would be 120mV decade-' or a = 1/2. However, the observed slope is about 290 mV decade-' (corresponding to a = 0.2), slightly over twice the expected value. This observa- tion is in good accord with the theory outlined earlier in this paper. The apparent doubling in the Tafel slope value is due to the porous nature of the polymer layer. The first electron transfer step is rate limiting, but only a small portion of the polymer layer is reactive and eqn. (12) pertains. Hence the data reported support the theoretical analysis presented here. The dual slope Tafel behaviour and the changeover in the identity of the rate-determining step is in exact accord with the Hammond postulate.Hence, the harder a reaction is driven, the earlier will be the transition state. The observed Tafel slope of about 50 mV decade-' observed for the correspond- ing oxidation reaction again points to an assignment that the second electron transfer is rate determining in this instance. A full kinetic analysis of this system will be presented else- where.41 We are currently examining the redox chemistry of a number of redox couples at conducting polymer coated electrodes in order to test fully the applicability of the theoretical analysis presented here. The results of this work will be published in a subsequent paper. This is a contribution from the Electroactive Polymer Research Unit, Trinity College. 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