摘要:

Faraday Discuss. Chem. SOC., 1989, 88, 123-131 Probe Beam Deflection Spectroscopy as a Tool for Mechanistic Investigations of Modified Electrodes Otto Haas Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Probe beam deflection spectroscopy together with cyclic voltammetry was used to analyse reaction mechanisms at redox polymer-coated electrodes. With this method, the direction of the concentration gradient at the electrode surface can be probed while a cyclic voltammogram is obtained. If a simple binary electrolyte like HCIO, is used in such an experiment, the direction of the beam deflection can be used to determine whether perchlorate ions or protons are used to compensate the charge of the electron exchange process in a characteristic part of the cyclic voltammogram, and may help to elucidate the reaction mechanism of an electroactive electrode coating.Results obtained from electrodes coated with [ Ru( bpy),Clpoly(4-vinyl- pyridine)]Cl (I) and poly-( 1-hydroxyphenazine) (11) are discussed. The deflection signal clearly indicated that the electron transfer in the polymer ( I ) was accompanied by an anion movement whereas polymer (11) showed a mixed mechanism which uses protons and anions to compensate the charge exchanged during the oxidation and reduction of the polymer. In order to fully understand the results, a numerical simulation of the interfacial process at the polymer coated electrode was necessary. The system of non-linear differential equations which describes the physical and chemical processes at the polymer coated electrode is presented.Using appropriate numerical methods and boundary conditions, it should be poss- ible to calculate the concentration profile for different potentials of the voltammogram. A direct correlation between the magnitude of the slope of the calculated concentration profile and the beam deflection is expected. Recently, Cairns et al.'?' successfully used optical probe beam deflection spectroscopy (PDS) and photothermal deflection spectroscopy as an in situ technique for the investiga- tion of electrochemical interfaces. Probe beam deflection spectroscopy yields informa- tion about concentration and thermal gradients adjacent to the electrode. The refractive index is a function of the concentration and temperature of the electrolyte and the refractive index gradient can be characterized by passing a probe laser beam parallel to the electrode surface (fig.1 ) . The beam will be deflected in the same direction as the vector gradient of the electrolyte refractive index. Deflections of the probe beam normal to the electrode surface were measured with a linear position detector after the laser beam passed the electrode. In this paper, we examined the interfacial concentration gradients due to electrochemical reactions when the electrode potential was cycled. For this purpose, we used the transverse probe beam geometry (fig. l ) , but without illumination of the electrode. The plots generated by this technique have been referred to as cyclic deflec- tograms.3 Deflection measurements require fewer restrictions on cell geometry and alignment than those for interferometric measurements of concentration gradients.' It has been shown that this simple technique leads to very useful information about the electron transfer process at redox polymer coated electrode^.^ Results obtained from a [ Ru( bpy),Cl( PVP)]CI- and a poly( 1 -hydroxyphenazine)-coated electrode are presented in this paper.123124 Mec ha n is t ic In vest iga t ions of Modijied Electrodes working electrode laser Fig. 1. ( a ) Electrochemical cell arrangement for the recording of the cyclic deflectogram. ( b ) Positive deflection of the probe beam resulting when the concentration gradient is positive. ( c ) Negative deflection obtained when the concentration gradient adjacent to the electrode is negative.Experimental Electrochemical Cell The electrochemical cell used for the cyclic deflectogram was mounted in a 1 cm x 1 cm x 5 cm glass cuvette (fig. 1 ) using a polymer-coated glassy carbon (GC) plate as a working electrode. A Pt screen, mounted in front of the working electrode, was used as a counter electrode. The spacing between the working and the counter electrode was ca. 7 mm, which eliminated interference from concentration gradients at the counter electrode. A hydrogen electrode was used as a reference electrode, and was connected to the cell with a Luggin capillary filled with the same electrolytic solution as the experimental cell. The PDS and the cyclic voltammograms were started at positive potentials and scanned continuously. The plots shown are the average of ca.15 scans obtained at 10 mV s-I. The zero points of the deflection curves were arbitrary. A reference point for horizontal concentration gradients had to be taken before the experiment at open circuit or at a fixed potential where no permanent current could be registered. Probe Beam Deflection Refractive index gradients in the electrolyte were detected with the same equipment as described previously,'924 a Uniphase HeNe probe Iaser (model 1303P) and United Technology (UDT) linear position sensor (model LSC-SD) were used. A lens was mounted on the laser to focus the beam to a diameter of ca. 80 pm at the electrode. Electrochemical Synthesis [ R U ( ~ ~ ~ ) ~ C ~ ( P V P ) ] C I was a gift from Dr J. G. Vos. It was synthesized using the procedure previously de~cribed.~ The [ Ru( bpy),Cl( PVP)]Cl-coated electrodes were prepared according to ref.(6) using the spin-coating technique.0. Haas 125 0.60 0.70 0.80 . 0.90 1 .oo 1.10 E / V us. NHE Fig. 2. ( a ) Cyclic deflectogram at a [Ru(bpy),CI(PVP)]Cl-coated electrode. Scan rate 20 mV sC1, r = 5 x rnol cm-*. ( b ) Typical cyclic voltammogram of a [Ru(bpy),CI(PVP)]Cl coated electrode in 1 rnol dmP3 HCI, experimental conditions as in ( a ) . 1 -hydroxyphenazine and poly( 1 -hydroxyphenazine) films were prepared as described previously.’ The electrodes were cycled between -200 and 1200 mV vs. SCE using a solution containing 0.002 mol dm-3 1-hydroxyphenazine in 1 mol dm-3 H2S04. This procedure was continued for several hours until the desired surface concentration of poly( 1-hydroxyphenazine) was obtained.In some cases the polymer was produced using NH4S208 as an oxidizing agent in acidic solution at room temperature and in the presence of catalytic amounts (ca. 0.2 mg cm-’) of FeSO,. The brown product obtained was filtered and washed with 1 mol dm--3 H2S04 and small amounts of ethanol and then air dried. The polymer could be dissolved in acetone and tip or spin coated onto the substrate.6 Results and Discussion [ Ru( bpy),CL( PVP)]Cl coated electrodes have been investigated exten~ively.~”~~ It is an interesting example of a polymer with inorganic redox centres, and has an almost ideal electrochemical behaviour with a rapid one-electron exchange per incorporated Ru centre. A typical cyclic voltammogram of a [ Ru( bpy),CL( PVP)]Cl coated electrode is shown in fig.2( b ) . Counterions maintained charge neutrality in the film as the electrode potential was cycled. This charge-compensating process generated an ion flow to or from the coated electrode, which led to concentration gradients inside and outside the film. The formation and the direction of the gradient outside the film were detected by cyclic deflectograms. Fig. 2( a ) shows the deflectogram obtained with this redox polymer coated electrode in 1 mol dm-’ HCl. It shows a positive deflection (deflection away from the electrode) when the polymer is oxidized and a negative deflection during the reduction cycle. This behaviour is expected for charge compensation by anion incorpor- ation. The beam was deflected towards the more concentrated region (which assumes that the refractive index is larger at higher concentration).The deflections would be reverse if protons or cations were used to compensate the charges of the electron exchange process.126 Mechanistic Investigations of ModiJied Electrodes -600 0 + 600 I 7 0.5 ( b ) - 0.5 E E 2, -0.5 0.5 - 0.5 -0 -0.5 0.5 l l I 1 -600 0 + 600 E / V us. SCE Fig. 3. Cyclic voltammogram of ( a ) 0.001 rnol dm-3 1-hydroxyphenazine in 1 mol dm-3 HC104. ( b ) Poly( 1-hydroxyphenazine) in (I) 1 rnol dmW3 HC104, (11) 3 rnol dmP3 HC104. ( c ) Poly(1- hydr0xyphenazine)-coated GC electrode (I) in 1 mol dmP3 HC104. (11) 0.1 mol dmP3 HC104 + 0.9 mol dm-3 NaClO,. The deflection signal lags behind the CV signal because of the time required to establish the concentration gradient 50-100 pm away from the electrode surface.A certain sweep rate dependence is also expected for thicker films when the electron transfer process within the film is slow relative to the sweep rate. This would also cause the CV to increase the peak separation. At slow sweep rates, the delay of the deflection signal is smaller, along with the decreased gradient (and deflection signal). Cyclic Voltammetry of Poly( 1-hydroxyphenazine)-coated Electrodes It has been shown that 1-hydroxyphenazine can be anodically polymerized on glassy carbon or noble metal electrodes.’ Although the 1 -hydroxyphenazine (monomer) has well behaved reversible peaks [fig. 3( a ) ] , electrodes coated with electrochemically polymerized 1-hydroxyphenazine give rise to cyclic voltammograms in 1 mol dmP3 HClO, with two overlapping peaks, where, the second reduction peak is poorly resolved and behaves like a capacitive tail of the first peak [fig.3 ( b ) ( I ) ] . In 3 mol dm-3 HClO, with electrodes having rather low coverages (su;face concentration < loP8 mol cmP2), better resolution was obtained for the CVs [fig. 3 ( b ) (II)]. It is likely that the polymer is linked by the hydroxy group of the monomer, thereby forming ether bridges between adjacent phenazine groups. The different states are thought to be made up from the monomeric 1-hydroxyphenazine redox states. There are three different redox states distinguishable, as in polyaniline:0. Haas 127 (1) Structural formula of singly protonated H I , X- 1-hydroxyphenazine ([ N,NH]+X-).OH I H (2) Structural formula of singly protonated 1 -hydroxyphenazine radical (polaron) ([ NH,NH]+X-). 1 H (3) Structural formula of 1-hydroxydihydrophenazine (NH,NH). The redox centres in the polymer are probably interacting centres but we can nevertheless assume that each phenazine centre passes through the three different forms while the film is electrochemically oxidized or reduced. The first reduction wave (positive potential) shows a sharp peak for the cathodic scan. This peak is probably due to depletion of protons inside the film during the cathodic scan. Since the diffusion in the film is several orders of magnitude slower than in the electrolyte, the reduction rate slows down considerably as soon as the acid in the pores and other intra-polymer spaces inside the film is consumed.This interpretation is consistent with the fact that the area (in coulomb) under this pre-peak is ca. ten times larger in 1 mol dm-3 HClO, than in 0.1 mol dmP3 HClO, [see fig. 3( c ) (I) and (II)]. A flatter peak follows the anodic peak. This second part of the first reduction peak is probably controlled by diffusion of the acid from outside the film. In 3 mol dm-3 HClO, [fig. 3 ( b ) (11)], this second part almost disappears. Interference measurements? on poly( 1 -hydroxyphenazine) films show that the poly- mer swells by a factor of two when it is soaked with the electrolyte, corresponding to a redox centre concentration of ca. 2.5 mol dm-3. In the pH range 0.5-2 the first reduction wave moves 60 mV towards more negative potentials when the pH is increased by one unit [fig.3 ( c ) (I), (II)]. This indicates that t Reflectance spectra of poly( 1-hydr0xyphenazine)-coated electrodes show an interference pattern which can be used to measure the film thickness while the electrode stands in an electrolytic solution. (For that measurement the assumption was made that the refractive index of the film is 1.35, a value which is most certainly not incorrect by more than loo/,.)128 Mechanistic Investigations of Modijied Electrodes E / m V us. NHE H H -1 00 0 100 200 300 400 500 600 E j m V cs. NHE Fig. 4. ( a ) Cyclic deflectogram and ( b ) cyclic voltammogram of poly( 1-hydroxyphenazine)-coated GC plate electrode in 1 mol dm-3 HzSO4. Scan rate: 10 mV s-'. Surface concentration = 3 x lo-' mol cm-2.there was a proton transfer involved in this first reduction step. Unfortunately, the pH dependency of the second wave could not be easily determined but it appears that the potential of the second wave is pH independent. In order to discuss the reaction mechanism, it is essential to know the degree of protonation of the different redox states in our acidic electrolytes. Unfortunately, this information is not easily obtained, since the polymer is oxygen sensitive in its reduced state and its reflection spectra show redox state dependent interference patterns superim- posed on the absorption spectra. A spectrophotometric pH titration with phenazine, phenazine radical and dihydrophenazine gives as a result pK,(phenazine) = 1.3, pK,(phenazine radical) = 0.5 and pK,(dihydrophenazine) =: -0.7.'' Owing to its low solubility and its oxygen sensitivity the pK, value of dihydrophenazine can only be estimated.Grabowska and Pakula" measured pK, = 1.3 and pK2 = -4.3 for phenazine. The pK, value l o of poly(1-hydroxyphenazine) is probably similar, as the CV of poly( 1-hydroxyphenazine)-coated electrodes starts to become irreversible at pH > 2,9 which seems to be a consequence of deprotonation. Under our acidic experimental conditions, the phenazine centres are probably singly protonated when the polymer is in its oxidized state and in its first reduced state (radical). The dihydrophenazine state, however, is probably not protonated, as it has low solubility in our acidic electrolyte. Therefore, the simplest mechanism for the two-electron transfer process in the poly( 1-hydroxyphenazine) is: [(N,N)H]'X + e +H' ---* [(N,NH)H]+X- (3) (4) [I (N,NH)H]'X ~ + e- - NH,NH + X-.Cyclic Deflectogram of a Poly( 1-hydroxyphenazine)-coated GC Electrode Fig. 4(a) shows the cyclic deflectogram and fig. 4(6) the cyclic voltammogram of a poly( 1-hydr0xyphenazine)-coated electrode in 1 mol dmP3 H,SO,. During the cathodic scan the PDS signal rises sharply, as predicted by reaction (3) for the decrease of acid concentration at the electrode. To preserve electroneutrality, the gradients for protons and anions should be equal (in the absence of other ions).0. Haas 129 However, only the protons diffuse towards the electrode and the anions remain stationary as charge compensating ions.The gradient reaches a maximum at a potential close to the minimum of the cyclic voltammogram. The PDS signal and the concentration gradient decrease and change sign at ca. +125 mV us. NHE. Then, the probe beam is deflected towards the electrode indicating an increase in acid concentration at the electrode. The PDS signal passed through a minimum at the potential where a shoulder of the CV peak indicates the second reduction wave. According to reaction (4), the polymer loses its charge at potentials more negative than the second CV wave and rejects anions from the film in this potential region during the cathodic scan. This causes an increase in anion concentration at the electrode surface, and the probe beam deflects towards the electrode. Since the anion flux is exhausted at potentials more negative than 0 mV us.NHE, the gradient starts to flatten out in this potential region. Finally, at -200 mV the gradients disappear and the PDS signal returns to its starting point. At the second redox step the opposite occurs with respect to concentration gradients and ion flows. To maintain electroneutrality at the second wave, the proton concentration gradient is equal to the anion concentration gradient, but this time only anions are transported and the protons are stationary (except the proton flow which is needed to establish the gradient, this small flux, however, is in the reverse direction to the anion flux). The cathodic PDS signal is in agreement with the mechanism proposed in reactions (3) and (4). To be consistent with this mechanism, the anodic scan processes should exhibit the opposite behaviour.On the return scan, the signal is increasing, indicating a flux toward the electrode (which corresponds to the expected incorporation of anions in this part of the anodic scan). It then decreases and at ca. +300 mV us. NHE the beam becomes slightly deflected towards the electrode. The fact that only protons are transpor- ted in the first reduction step and only anions in the second step is of some importance; protons diffuse much faster than anions, we expect higher gradients and thus stronger deflection at the peak with the anion transport. This explains why the amplitude of the deflection signal at the anodic scan (300-500 mV us. NHE) is small. Fig. 4(b) shows that reaction (3) is very fast, therefore at the cathodic scan (between 300 and 100 mV us.NHE) a rather high positive concentration gradient is obtained even though proton transport is causing this concentration gradient. In order to understand better the results obtained, we work on a program to simulate the process numerically. With this program, we calculated the concentration profile of the electrolyte inside and outside the coating at different potentials of the voltammogram. The calculations were based on the following plausible reaction mechanism. The electrode-electrolyte interface can be divided into a polymer layer, a diffusion layer and the bulk electrolyte. In the polymer layer we have an immobile redox polymer. Diffusion and migration allows the electrolyte to move within the polymer phase.An electron hopping mechanism can account for the electron exchange through the immobile redox polymer. In the diffusion layer the electrolyte moves from the polymer layer to the bulk and vice versa. In the bulk, we have uniform electrolyte concentrations. In the whole region of polymer, diffusion layer and bulk we have assumed electroneutrality. Heterogeneous redox reactions occur on the surface of the electrode with the polymer. At the polymer/electrolyte interface, the Donnan membrane equilibrium and the Donnan potential are assumed to be established. It is, however, questionable if these equilibria are always established. For the study of transient phenomena a double layer capacitance at the electrode surface was also taken into account.All these physical and chemical processes can be expressed by the following equations in the polymer layer. dc,/dt= Dk d2ck/dx2+zkuk F d / d x ( c k d@/dx)+ fhom,k if k is mobile I - diffusion’ migration redox chemistry130 Mechanistic Investigations of ModiJied Electrodes dck dt =fhop,k if k is immobile 2 ( z k C k ) = O k where ck(x, t ) are concentrations of species k, Dk is the diffusion coefficient, z k is the charge, uk the mobility, F is the Faraday constant, F(x, t ) is the electric potential, t is time, x is distance from electrode, fhop,k is the electron-hopping kinetic factor, fhom,k the homogeneous kinetic factor ( e.g. protonation and disproportionation in two electron- exchanging redox centres). The boundary conditions can be described as follows: where x is the electrode/polymer interface if k is mobile where x is the electrode/polymer interface if k is immobile where x is the polymer/diffusion layer interface if k is mobile Dk dck d x + ~ k U k F ( ~ k d@/dx)= Hk where x is the polymer/diffusion layer interface if k is immobile, where Gk is the rate of the heterogeneous electrode reaction which can be expressed by the Tafel law and Hk is the flux in the diffusion layer at the boundary to the polymer layer.Electroneutrality is also maintained at the boundaries. The system of non-linear equations above can be solved using the method of lines,I2 using orthogonal cubic Hermite polynomials for the spatial part of the profiles to transform the partial differential equations into a system of ordinary differential equations.These equations can be solved by a semi-implicit method. This model allows us to study any complex systems of homogeneous and heterogeneous reactions and we can investigate a variety of possible mechanisms, by changing fhom,k, fhop,k, g k and the diffusion and migration constants. A direct correlation between the magnitude of the slope of the calculated concentra- tion profile and the beam deflection is expected. Conclusions To our knowledge cyclic deflectograms have not been used to analyse the reaction mechanism of redox polymer-coated electrodes. The concentration gradient and thus the direction of the ion flow gives valuable information concerning the charge compensa- tion process inside the film. To avoid confusion, it is advisable to use electrolytes which have only one anion and one cation as charge carriers.The results obtained with the two polymers are reasonable. However, we must remember that even though the CV and the deflection signal do not contradict the mechanism, the deflection signal is not conclusive. It does verify that the proposed mechanism is a viable explanation. But it is possible that another mechanism would lead to a similar result. This work was supported by Swiss National Science Foundation grant no. 2.915-0.85 and the National Energy Foundation. Most of the practical work was carried out at Prof. E. J. Cairn’s laboratory, at the Lawrence Berkeley Laboratory, University of California and thus was supported by the DOE contract 98.1. Helpful discussion with Prof. E. J. Cairns and J. Rudnicki are appreciated. For the formulation of the simulation I also acknowledge the help of Dr C. Daul and Dr E. Deiss and for the critical reading Dr J-F. Equey and Dr R. Moy.0. Haas 13 1 References 1 R. E. Russo, F. R. McLarnon, J. D. Spear and E. J. Cairns, J. Electrochem. Soc., 1987, 134, 2783. 2 J. D. Rudnicki, R. E. Russo, Frank R. McLarnon and E. J. Cairns, Spring Meeting, Los Angeles, 3 M. A. Tamor and M. Zanini, J. Electrochem. SOC., 1986, 133, 1399. 4 0. Haas, J. Rudnicki, F. R. McLarnon and E. J. Cairns, in press. 5 0. Haas and J. G. Vos, J. Electroanal. Chem. 1980, 113, 139. 6 0. Haas and B. Sandmeier, J. Phys. Chem., 1987, 91, 5072. 7 0. Haas, M. Kriens and J. G. Vos, J. Am. Chem. Soc., 1981, 103, 313. 8 C. P. Andrieux, 0. Haas and J. M. Saveant, J. Am. Chem. SOC., 1986, 108, 8175. 9 0. Haas and H. R. Zumbrunnen, Helu. Chim. Acta, 1981, 64, 854. 10 F. Holzer, Diplomarbeit (Ingenieurschule Burgdorf, 1989). 11 A. Grabowska and B. Pakula, Photochem. Photobiol., 1969, 9, 339. 12 E. Deiss, C. Daul and 0. Haas, to be published. California, May 1989, Extended Abstracts Volume 89-1 Abstract no. 543 p. 771. Paper 9/02240€; Received 26th May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800123

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Furuday Discuss. Chem. Soc., 1989, 88, 133-138 GENERAL DISCUSSION Prof. C. A. Vincent (University o f S f Andrews) turned to Dr Latham: It is interesting to speculate on what happens in a polymer electrolyte when a ‘crystalline complex’ melts. For example, how much of the structure described by Chatani’ and Okamura for 3 : 1 PEO-NaI persists in the amorphous phase? The work you have described refers exclusively to amorphous polymer electrolytes. Have you any results for systems which contain a significant proportion of crystalline complex phase, and if so, how different are their EXAFS spectra to those of’ totally amorphous material? 1 Y. Chatani and S. Okamura, Puljmer, 1987, 28, 1815. Dr R. J. Latham (Leicester Polytechnic) replied: We have examined the EXAFS of PEO-ZnCl, films both at room temperature and at temperatures in the range 80-130 “C. No difference could be observed between the spectra for samples which were fully amorphous and those for samples which contained a crystalline complex phase. Prof.R. W. Murray (University qf North Carolina) said: I have two questions to put to Dr Latham. First, is not the observation of the absence of calcium ion-halide ion nearest-neighbour interactions in the EXAFS surprising in view of the observations by others of ‘ion-pairing’ in the alkali-metal salt-polymer solutions? Is it important in this sense to distinguish between solvent-separated and contact ion pairs? Secondly, the variation in zinc ion coordination numbers, i.e. 1,2, 1, in the halide series, C1-, Br-, I-, respectively, is interesting.Is there an explanation for the difference between Br- and C1- or I - ? Dr Latham replied to the first question: What we find for calcium is that the divalent cation is surrounded by a large number (ca. 10) of ozygen nearest neighbours and there is no evidence for the presence of anions within 6 A of the cation. This is in contrast to the zinc system, which resembles the structure in fig. 3(b) of the paper by Cameron e f al. The cation is within a matrix composed of both oxygens and anions, each species being as close to the cation as their respective sizes will permit. EXAFS studies of the anion location may very well help in discussions about the issue of contact ion pairing. He then addressed the second question: It was a surprise to us, as well as to Prof. Murray, that the coordination number for bromine was greater than that for iodine and chlorine.We think that the explanation is not due to any technical factors within the EXAFS technique because the statistical cross-checking employed gave sufficient confidence in the reported data. Prof. G. G. Cameron (University ofAberdeen) remarked: It is well known that many polyether-salt complexes become unstable at a certain critical tempeature above which the salt crystallises. (The misnomer ‘salting out’ for the phenomenon should be avoided!) Spectroscopic evidence indicates that precipitation is preceded by ion pairing and aggregation. Has Dr Latham considered applying EXAFS to the study of the molecular/ionic events leading up to salt precipitation? Dr Latham replied: We have carried out a number of preliminary experiments at temperatures ranging from below Tg to above T,,, for zinc systems.The cryostat path- length and window opacity restrict the variable-temperature study for calcium. In both cases there is no evidence within the timescale of the EXAFS experiment for the phenomenon commonly, but erroneously, known as ‘salting out’. We are grateful for the suggestion that EXAFS studies could be carried out to examine whether changes 133134 General Discussion in coordination number, indicative of incipient phase separation, occur as the tem- perature is increased. We hope to follow this suggestion and that of Dr Cameron by studying the detailed temperature dependence of the EXAFS of non-divalent species such as PE0,-RbI.Prof. M. Cheradame (E.F.P., St Martin d’Heres) said: In addition to Dr Cameron’s comment I have at least one piece of evidence, concerning networks crosslinked with siloxane units, that at high temperatures and salt concentrations there is production of higher aggregates, indicating that the salt becomes less soluble at higher temperatures. This behaviour is similar to that of organic solutions. Dr P. G. Bruce (Heriot- Watt University, Edinburgh) commented: EXAFS may be applied to probe the local environment in both amorphous and crystalline phases and Latham et al. have shown that the local environment around a cation appears to be very similar in both the amorphous and crystalline phases of a particular polymer-salt system. In view of this, it is important to determine the full atomic structure of crystalline polymer-salt complexes.Only a few systems [ e.g. poly(ethy1ene oxide)-NaI] have been studied because of the difficulty of obtaining good single-crystal diffraction data; further- more such data obtained on oriented fibres may be unrepresentative of the spherulites in polymer-salt films. Powder X-ray diffraction techniques, incorporating Rietveld refinement of the entire diffraction profile should, however, be well suited to the complete determination of crystal structures even from polycrystalline polymer films. Dr M. D. Ingram (University of Aberdeen) said: Latham et al. have concentrated their EXAFS experiments on polymer electrolytes containing zinc salts. Can this work be extended to univalent salts? Such experiments might provide valuable information on the existence of solvent- shared and contact ion pairs in these systems.This question lies at the heart of current controversies concerning transference numbers in polymer electrolytes. Dr Latham replied: Lithium cannot be studied and the K-edge energy for sodium is at the absolute limits of the experimental facility. Potassium, rubidium and caesium are accessible. Indeed, studies of PEO complexes with some rubidium salts have been reported in ref. (3) of our paper, and strong evidence for ion pairing was found. Dr S . J. Higgins (University of Liverpool) asked: The work in this paper concentrates on results obtained using the absorption edges of the cations. Have the authors tried similar experiments using, for example, the bromine K-edge, or other anion edges? If so, what results did they obtain? Dr Latham answered: We agree that anion EXAFS is particularly interesting because the location of the anions has been a major question within the field of polymer electrolytes for some time.Iodine L l l l and bromine K-edge EXAFS regions are experi- mentally accessible. We have, in fact, obtained anion EXAFS spectra for many different samples. In a few cases it is possible to deconvolute the spectra to reveal one cation neighbour. In the majority of cases, however, no significant EXAFS spectra could be recorded, presumably because the environment is excessively disordered and heavy near neighbours are absent. The impliction is that ion pairing or clustering does not occur in the latter cases.Prof. M. Armand (E.N.S.E.E.G., St Martin d’Heres) turned to Dr Wright: For the TCNQ-/O complexes with discrete ions solvated by crown ethers, the best conduc- tivities have been obtained with alkaline-earth-metal cations (Ca, Ba). One explanationGeneral Discussion 135 is the closer distance imposed by the divalent charge. Have you tested some of these cations in PEO? Dr P. V. Wright (University of Shefield) replied: In these exploratory experiments we have worked almost exclusively with the PEO-Na' helix because highly Crystalline, oriented PEO-NaI films and fibres are readily fabricated and handled. We briefly investigated the use of the PEO-LiI system and confirmed that PEO-LiTCNQ materials could be made using analogous procedures to those we had employed for the Na' complexes but we experienced greater difficulty in preparing well organised structures, partly as a consequence of the greater hygroscopicity of the Li' system and perhaps also because Li' may be a poorer 'fit' within the helical cavity than Na' as indicated by thermal analyses of a range of PEO-Na' and Li+ complexes.Thus we measured lower conductivities in the Li' system than in the analogous Na' system. This finding correlates with the conductivities of the alkali-metal-TCNQ salts in which conductivities increase with increasing cation size although the effective cation size may be increased by complexation with the PEO helix. We have not studied the PEO-Ca2+ system and the possibility of preparing TCNQ complexes with PEO-M2+ adducts should be investigated.The crystalline PEO com- plexes with divalent cations are presumably not based on the same 2, helical structure as the Na+ and Li+ systems and bearing in mind the propensity for divalent cations to form amorphous complexes with PEO the preparation of highly organised structures with the iodide salts may present difficulties. Recalling the investigations by Potember et al. [ref. (18) of our paper] of switching in TCNQ salts we are interested in the possibility of incorporating metals having more than one oxidation state within the PEO lattice with a view to detecting similar field-induced effects. Dr Latham added: Under certain preparation conditions, crystalline complexes can be formed for a range of PEO-divalent salt systems.Crystallographic information on these phases is currently being obtained by Thomas and his group in Uppsala, and also by other workers, [ref. (9) of paper by Latham et a,.]. Dr P. N. Bartlett (University of Warwick) said: TCNQ stack structures frequently show anisotropy in their conductivities. Has Dr Wright observed any anisotropic effects in the conductivity of his PEO-sodium iodide complexes with TCNQ? Dr Wright replied: We have studied anisotropy of conduction in our PEO- NaTCNQ/PEO-NaI bilayers. We found [ref. (6) of our paper] the conductivity to be approximately a factor of five greater (at ambient temperature) perpendicular to the draw direction. The perpendicular and parallel conductivity data converged at approxi- mately 100 "C. We attributed this unexpected result to the microfibrillar morphology of the film.Parallel to the draw there are periodic interruptions to the continuity of organised structure (see plate 2 of our paper) in the form of amorphous polymer. Transmission electron microscopy (TEM) of carbon replicas of the oriented precursor PEO-NaI also reveals voids bridged by microfibrils. There is, therefore, more extensive intercrystalline contact of organised material perpendicular to the draw. However, the TEM also suggested that the crystalline layers apparent in plate 2 represent integral crystalline material. If so, the crystalline lamellae of the oriented precursor appear to be unusually thick (ca. 0.5 pm) when compared with the lamellae of the unoriented spherulitic material [ref. (13) of our paper] which are of a thickness (ca.200 A ) normally observed in flexible crystalline polymers. It seems likely, therefore, that the greater lamellar thickness is a major factor in accounting for the superior electronic conductivity of the oriented material (fig. 3 of our paper). It wou!d be of interest to prepare PEO-NaTCNQ from precursor fibre or film drawn from the melt in which the interlam- mellar material should have a greater degree of orientation and should include fewer voids than are present in the material deposited from solution.136 Genera 1 Discussion Prof. R. W. Murray ( University of North Carolina) asked Dr Wright: The observations on TCNQ-containing PEO implicitly assume that the crystalline phase behaviour is an essential part of the conductivity behaviour. Is there evidence, say from measurements on amorphous materials, that the crystalline phase is indeed a crucial component or that there is a contribution from transport in the amorphous phase? Dr Wright replied to Prof.Murray: We have not studied the conductivity of amor- phous PEO-NaTCNQ explicitly. In most of our work with this system we have studied oriented material in which the non-crystalline component may be significantly anisotropic. However, the proportion of non-crystalline material in the precursor PEO- NaJ should increase with increase in x( =[ E0]/[ Na’]), where x >3, and this is reflected in an increase in the ionic conductivity of this material although the ambient temperature conductivity is very low (fig. 3 of our paper).Following exchange with TCNQ, the same increase in x gives rise to a decrease in conductivity in PEO-NaTCNQ (fig. 4 of our paper). (The surface conductivities for x = 5 and 6 in this material were too small to be measured by the four-point probe method.) The linearity and reversibility of slow sweep voltage-current data suggest that in these materials the conductivity is essentially electronic in nature and is dependent on the extent of intercrystalline contacts which decreases with increase in x. Voltage-current sweep data also suggest that conduction in PEO-NaI, is essentially electronic, although we have studied only the x = 3 system in this case. However, it must be conceded that ionic mobility between crystallites, not detected by our sweep experiments, may exert some influence on the level of conduc- tivities observed in both PEO-NaTCNQ and PEO-NaI, ; complex impedance analysis should give more information regarding the extent of ion mobilities in these cases.In the case of PEO-NaTCNQ-I2 materials at least two kinds of structure are observed over the range of compositions studied. As we showed in our short presentation, optical reflection micrographs of material in which x = 3-4 reveal extensive phase separation of gold, needle-shaped microcrystallites (ca. 1 p m in length). Wide-angle X-ray analysis confirms that the microcrystals have the same structure as those obtained by treatment of NaTCNQ with I, and suggests that the matrix is essentially amorphous PEO having Iz dissolved within it. The decrease in conductivity over x = 3-4 in this material may thus be ascribed to a corresponding decrease in microcrystalline contacts within the composite structure and may be controlled to a significant degree by ionic conductivity of polyiodide ions in the amorphous PEO as discussed by Lerner and coworkers [ref.(20), our paper]. This would account for the non-linearity and irreversibility of the voltage-current sweep data for this material presented in fig. 5 of our paper. However, for PEO-NaTCNQ-I2 with x = 5, the voltage-current sweep data are remarkably linear (sweep rate = 1 mV s-I) and, as we showed in our presentation, there is no evidence of microcrystallite separation in the optical micrographs. Although WAXS analysis of this material remains to be done, we tentatively attribute the significant increase of almost three orders of magnitude in the conductivity of the exchanged layer over the range x = 4-5 (fig.4 of our paper) to the formation of a new molecular complex with PEO. The schematic arrangement shown in fig. 6 of our paper is an ‘alloy’ of PEO-NaTCNQ and PEO-NaI, complexes (where n signifies polyiodide ions). The ionic lattice is now expanded by neutral TCNQ molecules so that complex formation with the polymer should be rendered thermodynamically more favourable than for lower x values by the lowering of electrostatic interactions between ionic components which also promote electron transfer along the TCNQ-I, stack. The required structural reorganisation from the poorly conducting PEO-NaTCNQ (x = 5-6) material to the expanded lattice is facilitated by the back-oxidation by iodine of TCNQ anions to the neutral species which are the more mobile within the PEO lattice.In the schematic structure of fig. 6 (our paper), the compositional parameter, x, is equal to 6. The sample of PEO-NaTCNQ-I,, x=6, giving the conductivity shown in fig. 4 (our paper) hadGeneral Discussion 137 undergone some relaxation of the oriented structure and ‘islands’ of the gold TCNQ complex are clearly visible in optical micrographs. These discontinuities in the structure are partly responsible for the reduction in conductivity over the range x = 5-6 in fig. 4 of our paper. In summary, we conclude that ionic mobility may play minor roles in the PEO-NaI, (x = 3) and PEO-NaTCNQ systems and a more significant one in the PEO-NaTCNQ-I2 (x = 3 - 4), salt-separated systems.However, we have not detected any significant ionic conductivity in the most highly conducting PEO-NaTCNQ-I, (x = 5 - 6) systems for which we propose a new molecular complex alloy structure. (University of Bristol) turned to Dr Haas: Your probe beam deflection experiments give information on the uptake/ expulsion of species by the polymer film. First, is it possible to distinguish concentration (refractive index) changes caused by ion transfer from those caused by solvent transfer in the opposite direction? Secondly, have you attempted to correlate the ion flux (from the deflection data) with the electron flux, for example in a deflection us. charge plot? Dr 0. Haas (Paul Schemer Institute, Villigen) replied: The beam deflection probes the concentration gradient adjacent to the electrode.However, we are not able to distinguish between a concentration gradient produced by ion transfer or by solvent transfer in the opposite direction. In practice, additional experiments with different electrolyte concentrations or techniques such as microbalance or radio tracer experiments may be necessary to estimate solvent transfer contributions to the beam deflection. It is, however, difficult to imagine that solvent transfer could completely mask the very substantial counterion transport across the redox polymer interface. Oxidation and reduction of the polymer is accompanied by a counterion concentration change within the film of at least 1 mol dm-’. Turning to the second question; so far our beam deflection experiment has not been used for quantitative measurements of the ion flux.This is difficult since the probe beam deflection is a result of the whole concentration profile and not just the gradient at the interface. As you have seen, we always register the beam deflectogram together with the cyclic voltammogram which leads directly to a qualitative correlation between the electron flux and the concentration gradient at the electrode. Prof. T. J. Lewis (University College of North Wales, Bangor) said: I would like to ask Dr Haas whether the probe beam monitors only the refractive index changes resulting from density changes or whether, in some circumstances, dipole orientation and molecular ordering in the strong field likely at an electrode interface could also cause a beam deflection.I assume that the local fields themselves are never large enough to induce optical effects in a polarized laser beam. Prof. A. L. Smith (Unilever Research, Port Sunlight Laboratory) said: Significant refractive index gradients resulting directly from electric fields near the surface rather than via concentration gradients will be restricted to very short distances (< 1 nm) and are, therefore, not likely to affect the measurements reported by Dr Haas. Dr Haas added: At our polymer-coated electrode we are looking at the polymer- electrolyte interface which normally exhibits only a small electric field due to the Donnan potential. In addition, this interface always has some roughness and even if effects due to dipole orientation and molecular ordering do exist, they most probably could not be detected.At a nicely polished metal electrode molecular ordering at the electrode surface is more likely, but as mentioned by Professor Smith, the refractive index gradient obtained by such a layer (1 nm) would deflect only minor part of the probe beam (ca. 80 000 nm diameter). We therefore do not expect any measurable deflection from local fields and dipole orientation at the electrode surface. Dr A. R. Hillman138 General Discussion Prof. Cheradame asked: Is it possible to use a tunable laser light source with your system so as to obtain at the same time the spectrum of the species which is moving? Secondly, is it possible to use your system in solid electrolytes, i.e. at the electrode- polymer interface? Dr Haas replied: In principle it is possible to measure the spectrum of the moving species with a tunable laser beam and an appropriate detector.This may be interesting if the moving counterions have a distinct spectrum. From an experimental point of view, however, it is easier to take spectra of the electrode surface and its adjacent diffusion layer using photothermal beam deflection spectroscopy, as described in ref. ( 1 ) of our paper. With this method a tunable chopped-light source shines perpendicular to the electrode and an alternating deflection signal can be measured. In some cases it is possible to distinguish between the spectrum of the electrode surface and the diffusing species in solution by looking at the in-phase and out-of-phase signals separately. Dr L. M. Peter (The University, Southampton) said: An important aspect of the method discussed by Dr Haas concerns its time resolution, which is of the order of d 2 / D , where d is the width of the solution sampled by the laser beam and D is the mean diffusion coefficient of the ions concerned (in the present case this corresponds to 1-10s). Since Dr Hillman has suggested that different ions may move on different timescales, it is clearly important to improve the time resolution of PBDS. I would like to suggest to Dr Haas that this could be done by applying an a.c. modulation to the electrode potential which would generate a damped concentration wave in the boundary layer. The width of this layer would be determined by the frequency of modulation. The corresponding a.c. component of the beam deflection, although small, could be detected readily by conventional lock-in techniques which would, in any case, greatly enhance the signal-to-noise ratio. Dr Haas replied: A beam deflection signal can be detected even if only part of the beam is deflected. The time resolution is therefore somewhat better than you calculated since d might only be a fraction of the laser beam diameter. In our case the signal is still increasing when the sweep rate is steadily increased from 10 to 50mVs-'. The deflection signal, however, is somewhat delayed. Your suggestion to employ a.c. modulation to the electrode is certainly worth trying.

ISSN:0301-7249    

DOI:10.1039/DC9898800133

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1989, 88, 139-149 Transport and Kinetics in Multicomponent Chemically Modified Electrodes Michael E. G. Lyons, Declan E. McCormack and Orla Smyth Physical Chemistry Laboratory, University of Dublin, Trinity College, Dublin 2, Ireland Philip N. Bartlett Department of Chemistry, University of Warwick, Coventry CV4 7AL Analytical expressions quantifying the transport and kinetics in polymer- modified electrodes containing a homogeneous distribution of spherical microparticulate catalysts are presented. In particular the dependence of the flux on the number of catalytic particles per unit volume, the layer thickness, the substrate and mediator concentrations, the particle radius and the electrode potential are outlined for the situation of conducting polymer catalyst and ionomer-mediator-catalyst composites.A strategy for optimis- ing the electrocatalytic behaviour of these multicomponent micro- heterogeneous systems is also outlined. The use of microscopic particles of metals or metal oxides dispersed within polymeric films deposited on electrode surfaces has many attractive features for electrocatalysis. Such microheterogeneous catalytic systems have a number of practical advantages. First, they are easy to prepare. Secondly, the functions of catalysis and electron transport between the support electrode surface and the catalytic site are distinct. Thirdly, the microscopic particles can act as catalytic sites for multi-electron transfer processes. Finally, the polymer matrix appears to stabilise the small particles.This has been noted in the work of Kuwana and co-workers' who noted that platinum particles dispersed in poly( aniline) films display excellent long-term stability for methanol oxidation in aqueous acid solution compared with bulk platinum electrodes operating under similar conditions. Three types of microheterogeneous system may be distinguished: those based on the use of microscopic particles dispersed within electronically conducting polymers;'-' those using ionically conducting polymeric matrices;'-'* and, finally, those utilising the combination of dispersed catalytic microparticles in a redox polymer film.I3-l6 We are interested in the design of such microheterogeneous systems for efficient electrocatalysis. Although the transport and kinetics of reactions in chemically modified electrodes have been analysed and approximate analytical solutions are available, I7-I9these treatments are not directly applicable to the situation considered here.This is because for microscopic catalytic particles it is necessary to include explicitly both the spherical diffusion to the particle surface within the polymer matrix, and the electrode kinetics of the reactions at the particle surface. In this paper we present the results of a theoretical analysis of the mass transport and kinetics within such microheterogeneous systems. We also compare the theoretical predictions with available experimental data, and discuss the implications of the use of these multicomponent systems in electrocatalysis. Theory In this section we discuss the balance between kinetics and diffusion for reactions at microscopic metallic particles uniformly distributed in either an electronically conducting 139140 Multicomponent Chemically Modijied Electrodes ( a ) electrod 0 j e l u t i o n 2- 0 0 Ks, sp her ica I ' catalyst particle x = L x = o x = L Fig.1. The model and notation for modified electrodes with immobilised, microheterogeneous catalyst particles. ( a ) Particles immobilised in an electronically conducting polymer matrix; ( b ) particles immobilised in an ionomer or redox polymer matrix. polymer (such as polypyrrole), fig. l ( a ) , or in an ionomer (such as Nafion), fig. l(6). In the former case, the metallic particles are assumed to be in intimate electrical contact with the polymer and, hence, the supporting electrode.Thus, we can assume that each particle is held at the same potential. In the latter case, an electron transfer mediator, usually an inorganic redox couple, is also a necessary component of the system, and functions as an electron relay between support electrode and catalytic site. On each particle the rate of reaction is determined by the balance between the reaction of mediator and of substrate. Consequently, the electrochemical potential of each particle throughout the film need not be the same. We begin by considering the reaction on a single particle. Diffusion to a spherical microelectrode is described by the following equation: d's 2 ds (dr' dr) D, -+ - = OM. E. G. Lyons et al. 141 where Ds is the diffusion coefficient for the reactant S in the film, s denotes the substrate concentration, and r is the radial distance from the centre of the particle.We can consider the reaction in two ways.”’ First, we can treat the reaction as a heterogeneous process at the particle surface so that where kE is the potential-dependent heterogeneous rate constant for the reaction of S at the particle surface, N is the number of catalyst particles per unit volume, A denotes the surface area of the particles ( 4 7 ~ 3 , and so is the surface concentration of S. Alternatively, we can treat the reaction as a conventional second-order process between S and the particles. In this case we have where k2 is the effective second-order rate constant, s(x) denotes the concentration of S bathing the particle, and c is the concentration of particles.If we then define a pseudo-first-order rate-constant for the reaction as k = k,c, we can derive the following expression for k : *OJ’ 1 1 k-4.rrr:N k , (4) In this equation the first term describes the effect of heterogeneous kinetics, and the second term describes the spherical diffusion. When kE >> Ds/ro mass transport of S to the particle surface by spherical diffusion within the film is rate-limiting. When kE << D,/ ro reaction at the particle surface is rate-limiting. Having established an expression for the pseudo-first-order rate constant we can now consider the effect of coupled reaction and macroscopic diffusion within the film. Provided that the particles are small compared to the film thickness and that particle loadings do not exceed 3% by volume, we can separate the effect of ‘macroscopic’ planar diffusion through the film from that of ‘microscopic’ spherical diffusion to an individual particle.Conducting Polymer-Microparticulate Catalyst Composites We begin by considering the case where the particles are embedded within an electroni- cally conducting polymer.” Under these circumstances the diffusion equation is of the following form: d2s dx D s T - k s = O where x is the distance normal to the supporting electrode and k,$ is given by eqn (4). The boundary condition at the electrode surface is x=O; ds/dx=O ( 6 ) whereas at the polymer/solution interface we have: x = L ; s=KsCC (7) where L denotes the film thickness, ss is the concentration of S in solution and K is the partition coefficient for S into the film.142 Multicomponent Chemically Modijied Electrodes Fig.2. Case diagram illustrating the interrelation between cases for catalyst particles immobilised in a conducting polymer matrix. The letters in the square boxes distinguish diffusion (D) and kinetic (K) cases. The inset in the lower left-hand corner shows the way in which changing the experimental variables of kE (with potential), r,, L and N will move the system. Table 1. Expressions for the flux,j, and mechanistic indicators for micro- heterogeneous catalysis at conducting polymer electrodes reaction order w.r.t. case j s" L r, c (or N ) k, I 4 m, NDs Ks" L 1 1 1 1 0 1 1 2 0 I1 4 mi NkE Ks" L 1 1 2 Iv KS"(47Tri&Nk~)~" 1 0 1 - 1 1 - I11 D , K ~ " ( ~ T ~ , N ) " ~ 1 0 - 2 2 Solution of eqn ( 5 ) with these boundary conditions gives the following expression for the flux, j : j = Ks"Ds [ 4m:N ( kE/ro )]"'tanh{L[lar~N( kE'ro )I1'*].(8) DS/ rO + k E Dsl ro + k E We can identify four limiting cases from eqn (8), and these are shown in fig. 2. Table 1 gives the appropriate limiting forms for j in each case. For cases I and I1 there is no concentration polarisation of S through the film. In case I spherical diffusion to the particle is rate-limiting, whereas in case 11, the heterogeneous reaction at the particle surface is rate-determining. In cases I11 and IV, S is consumed in a first-order reaction layer at the film surface. For case I11 the spherical diffusion to the particle is rate-limiting, whereas for case IV the heterogeneous kinetics are again rate-limiting.M. E.G. Lyons et al. 143 Returning to table 1, we can see that the four cases can be distinguished by the characteristic dependences of the flux on the experimental parameters s", L, r,, N and electrode potential. Ionomer-Mediator-Microparticulate Catalyst Composites We now consider the situation where one utilises an ionomer film loaded with microscopic catalytic particles. In this situation a mediator is used to shuttle charge between the support electrode and the particle [fig. l(b)]. In this case, in addition to the diffusion equation for the substrate S given by the expression: d2s dx2 Ds-- kss = O we must also consider the diffusion equation for the mediator A: (9) The rate constants ks and kA reflect diffusion to, and electrode kinetics at, the spherical catalytic microparticles and are expressed in the form: 47rri Nk: Dx D,+ kkr, kx = For this situation, in the steady-state, the rates of reaction of A and S on each individual particle must balance and so we write k&so = kaao (12) (13) where k; and ka are the electrochemical rate constants and are of the general form: kj, = kj,,, exp [*taF(E - EO)/RT] ka = (ka,,k;,,s/ a ) 1/2 and so, a, denote the substrate and mediator concentrations at the particle surface. It can be shown that:22 (14) and k& = (ka,,k&,,a/s)'/'.Substitution from eqn ( 1 l ) , (14) and (15) into eqn (9) and (10) gives us two differential equations describing the transport and kinetics within the film. These expressions are of the form: and d2s 4.rrriNDs( kX,ok;,o)1/2( as)'/2 dx2 Ds-- [ Ds+ ro( k~,ok$,o)'/2( ~ / s ) ' / ~ ] = These differential equations have to be solved subject to the following boundary condi- tions: x=O; dsldx-0; a=a" (18) and x = L; s = Ks"; da/dx = O .144 Mult icompon en t Ch em ical ly Mod i$ed Electrodes Table 2.Expressions for the flux, j , and mechanistic indicators for microheterogeneous catalysis at ionomer- or redox-polymer-modified electrodes reaction order w.r.t. case j a" sm L c (or N ) r, I I1 I11 IV V VI VI I VIII ~ ~ ~~~ 4rrO ND, Ks" L 0 1 1 1 4 nr0 NDA a"L 1 0 1 1 47rr; NL( k ~ , , k & , , a " K ~ " ) ' / ~ + + 1 1 [4~r;ND,Ks"(kk ok~,oamKsm)'/2]'/2 f $ 0 - 1 (4 Tr0 N ) 'I2 D, Ks" 0 1 0 2 KD,S"/ L or DAa"/L 0 1 -1 0 2 1 0 1 0 0 1 2 I (4TroN) ' I 2 DA Q O0 [ 4 ~ r ; NDAa "( k;,, k&,,a " Ks") 'I2] 4 d O 1 1 2 1 0 1 2 - I 2 1 I B O L I1 O L Fig.3. Case diagram illustrating the interrelation between the different cases for catalyst particles immobilised in an ionomer or redox polymer film. The diagram is drawn for L < XK, where XK = (47rrON)-'/* and is the kinetic length. The system is characterised by the two dimensionless parameters p = (amDA/Ks"Ds)'/2 and y = ro(k;,ok&,o/ DADs)'/'. Concentration profiles are shown for A and S in each case. Although it is not possible to obtain an analytical solution to these non-linear second- order differential equations, it is possible to identify a number of limiting cases and obtain approximate analytical expressions for the These are given in table 2 and the relationship between the various cases is shown in fig.3 and 4. For cases 1-111 (fig. 3), the film is thinner than the reaction layer thickness [ L < X K , where XK = (4.rr0N)-'/*] and the reaction takes place throughout the film. For case I,145 VII O L Fig. 4. As fig. 3 but now with L > XK. the kinetics are controlled by the spherical diffusion of S to the particles, for case I1 by the spherical diffusion of A to the particles, and for case 111 by the balance of kinetics on the particle. When L > X K there is concentration polarisation within the film and we can identify five additional cases. This situation is outlined in fig. 4. In cases IV and V, S is consumed in a first-order reaction layer at the polymer surface.For case IV the heterogeneous kinetics at the particle surface are rate-limiting, whereas for case V spherical diffusion to the particles is rate-limiting. Cases VII and VIII are similar but now A is consumed in a first-order reaction layer at the electrode surface. In case VII the reaction is diffusion controlled, and in case VIII it is kinetically controlled. Finally, there is an interesting situation, case VI, where A and S react together somewhere in the middle of the film. This 'titration' situation is analogous to the case of a layer reaction zone (LRZ) found in the corresponding treatment of Albery and HillmanI8 for a conventional chemically modified electrode. Returning to table 2, we can see that each case is distinguished by a unique set of dependences on the experimental parameters urn, srn, L, r, and N.Thus, it is again possible to determine which case applies by careful systematic variation of the experi- mental parameters. Note that this same model can be applied to catalysis by particles immobilised in redox polymer films since the mediation process can be formally described in a similar manner. Discussion We now discuss the application of the theoretical analysis to a number of specific situations, and consider some implications for electrocatalysis.146 ‘0 Multicomponent Chemically ModiJed Electrodes \ a I I 2 Fig. 5. Plot of the logarithm of the normalised limiting current ( I , proportional to j / N d ) versus the particle radius for data taken from table 6 of ref. (2). The lines are drawn with a slope of -2 as predicted for case I. Data for three different rotation speeds are outlined; 0, 100 r.p.m.; 0, 800 r.p.m.; (>, 3600 r.p.m.From table 1 we can see that for microheterogeneous particles immobilised in a conducting polymer matrix the particle size is a very useful mechanistic indicator to distinguish between the four cases. In most of the published studies of systems of this type systematic measurements of the particle size have not been reported. One exception is the work of Yassar et aL2 who have studied the reduction of oxygen at electrodes modified with films of poly(thiophene) containing palladium particles. These workers note that ‘the electrocatalytic activity of the electrodes increases markedly when the average size of the Pd particles decreases’.Analysis of the data given in table 6 of their paper (fig. 5 ) , suggests that they were in case I where the reaction is controlled by diffusion to the spherical particles. This is sensible since the data outlined in their table relate to the limiting currents at high overpotential when, presumably, the reaction is being driven hard at each particle. Further evidence as to the applicability of our theoretical analysis is provided from the results of some preliminary experiments conducted in our laboratory on the electrochemical oxidation of hydrogen at platinum particles dispersed within a poly(pyrro1e) film. These studies were conducted in 0.5 mol dm-3 H 2 S 0 4 at 298 K using a glassy carbon support. The platinum particles were incorporated into a preformed polymer layer [the latter being formed potentiostatically at 645 mV (us.Ag/AgCl) from an aqueous pyrrole-LiC 10, solution] according to procedures previously described by Vork et al., Our RDE studies concentrated on determining the variation of flux with catalyst loading and layer thickness.M. E. G. Lyons et al. 147 - 2.0 - 3.0 n d 3. L Y 00 - -4.0 - 5.0 - 5.5 - 5.0 -4.5 - 4.0 Fig. 6. Plot of the logarithm of the current (corrected for concentration polarisation effects in solution) uersus the logarithm of the catalyst loading for hydrogen oxidation at platinum particles immobilised in a surface-deposited poly(pyrro1e) layer. The dashed lines outline slopes of 1 and 1/2. Regions ( a ) and ( b ) , see text. The results of these experiments are outlined in fig.6 and 7. It is interesting to note that the variation of current (corrected for concentration polarisation effects in solution) with catalyst loading exhibits a dual-slope behaviour. In region ( a ) which corresponds to loadings less than 30 pg cm-*, the slope is very near 0.5. A much larger slope (ca. 4) is obtained at higher loadings, region ( 6 ) . This latter value cannot be rationalised in terms of our model. However, the intersection point between the low- and high-slope regions corresponds to a 7% catalyst loading per volume, a figure which is in very good agreement with our theoretical prediction of the maximum allowable catalyst loading under which our analysis is valid. A series of RDE experiments as a function of layer thickness (0.1-0.5 pm) were also carried out.The resultant Koutecky-Levich plots were found to be essentially independent of layer thickness (fig. 7). It must also be noted that the data illustrated in fig. 6 and 7 were extracted from the limiting current region of the RDE voltammogram. Consequently, the flux remains independent of applied potential under these conditions. For table 1 we note that a reaction order of 0.5 with respect to loading and zero with respect to layer thickness and kE (and hence electrode potential), indicates that case I11 is operative. Hence hydrogen is consumed in a first-order reaction layer at the film surface, and the spherical diffusion of substrate to the platinum particles is rate-limiting. This result is in good agreement with, and indeed extends, the previous interpretation of Vork et aL4 who simply noted that the non-linear Levich plots obtained for hydrogen oxidation could be ascribed to the slow diffusion of the substrate through the polymer film.It is of interest to consider which of the cases for the two systems discussed in the paper represents the optimum strategy for the utilisation of the dispersed catalytic particles for electrocatalysis.148 Multicomponent Chemically ModiJied Electrodes 10 8 - 6 I h 4 L ci 2 - 4 2 0 0 0.2 Fig. 7. Typical Koutecky-Levich plots for hydrogen oxidation as a function of layer thickness. Note that the intercept remains effectively independent of layer thickness. First, let us consider the catalytic particles immobilised in a conducting polymer matrix. In cases I11 and IV only the outer region of the film takes part in the reaction since the substrate does not penetrate throughout the film.This is inefficient in the use of catalyst particles because not all the particles are being utilised. In case I the current is limited by spherical diffusion to the surface of each particle and not by the electrode kinetics on the particle surface. Consequently, this also is an inefficient strategy because the overpotential applied is now excessive. The only efficient strategy is that of case 11, where all the catalyst particles are being used and the rate of reaction is determined by the heterogeneous kinetics on the particle surface. Under these circumstances the current is greater by a factor of 4.rrr&YV over that which would be found at a macroscopic electrode of the same projected geometric area.Secondly, we consider the ionomer or redox polymer systm. We can again identify the optimum strategy. We reject all cases in which the flux depends upon the concentra- tion of the mediator, a*, since we could presumably increase the mediator loading if necessary. This leaves cases I, V and possibly VI. In cases V and VI only a fraction of the catalyst particles are being used since the substrate does not penetrate the whole film; we therefore also reject these two cases. Thus we are left with case I where the reaction occurs throughout the film at a rate controlled by the spherical diffusion of reactant to each catalytic particle. The support of the Trinity Trust and the Commission of the European Communities Stimulation Action Program (grant number 86300283FRI8PUJUl) is gratefully acknowl- edged.D.E.McC. acknowledges receipt of a Trinity College postgraduate award.M. E. G. Lyons et al. 149 References 1 K. M. Kost, D. E. Bartak, B. Kazee and Y. Kuwana, Anal. Chem., 1988, 60, 2379. 2 S. Holdcroft and B. L. Funt, J. Electroanal. Chem., 1988, 240, 89. 3 A. Yassar, J. Roncali and F. Gamier, .I. Electroanal. Chem., 1988, 255, 53. 4 F. T. A. Vork, L. J. J. Janssen and E. Barendrecht, Electrochim. Acta., 1986, 31, 1569. 5 E. W. Paul, A. G. Ricco and M. S. Wrighton, J. Phys. Chem., 1985, 89, 1441. 6 G. Tourillon and F. Gamier, J. Phys. Chem., 1984, 88, 5281. 7 G. Tourillion, E. Dartyge, H. Dexpert, A. Fountaine, A. Jucha, P. Lagarde and D. E. Sayers, J. 8 A. Michas, J. M. Kelly, R. Durand, M. Pineri and J. M. D. Coey, J. Membr. Sci., 1986, 29, 239. 9 K. Itaya, H. Takahashi and J. Uchida, J. Electroanal. Chem., 1986, 208, 373. Electroanal. Chem., 1984, 178, 366. 10 W. H. Kao and T. Kuwana, J. Am. Chem. Soc., 1984, 106, 473. 11 D. E. Bartak, B. Kazee, K. Shimazu and T. Kuwana, Anal. Chem., 1986, 58, 2756. 12 H. Y. Liu and F. C. Anson, J. Electroanal. Chem., 1983, 158, 181. 13 R. N. Dorniney, N. S. Lewis, J. A. Bruce, D. C. Bookbinder and M. S. Wrighton, J. Am. Chem. Soc., 14 J. A. Bruce, T. Murahashi and M. S. b’righton, J. Phys. Chem., 1982,86, 1552. 15 R. A. Simon, T. E. Mallouk, K. A. Daube and M. S. Wrighton, Znorg. Chem., 1985, 24, 3119. 16 D. J. Harrison and M. S. Wrighton, J. Phys. Chern., 1984, 88, 3932. 17 C. P. Andrieux, J. M. Dumas-Bouchiat and J. M. Saveant, J. Electroanal. Chem., 1982, 131, 1; J. 18 W. J. Albery and A. R. Hillman, J. Electroanal. Chem., 1985, 170, 27. 19 A. R. Hillman, in Electrochemical Science and Technology of Polymers 1, ed. R. G. Linford (Elsevier, 20 W. J. Albery and P. N. Bartlett, J. Elecrroanal. Chem., 1982, 131, 137. 21 M. E. G. Lyons, D. E. McCorrnack and P. N. Bartlett, J. Elecfroanal. Chem., 1989, 261, 51. 22 M. E. G. Lyons and P. N. Bartlett, manuscript in preparation. 1982, 104, 476. Electroanal. Chem., 1984, 169, 9. London, 1987), pp. 103-291. Paper 9/02068C; Received 15th May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800139

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1989, 88, 151-163 Charge Transport in Electroactive Polymer Films A. Robert Hillman,* David C. Loveday, Marcus J. Swann and Ruth M. Eales School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1 TS Andrew Hamnett and Simon J. Higgins Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR Stanley Bruckenstein and C. Paul Wilde Department of Chemistry, University at Buflalo, State University of New York, Buflalo, New York 1421 4, U.S.A. The electrochemical quartz crystal microbalance (EQCM) and ellipsometry have been used to study directly the movement of ions and solvent into/out of electroactive polymer films. The systems studied were polyvinylferrocene (PVF), polybithiophene (PBT) and polythionine (PTh).The overall mass changes accompanying oxidation/reduction indicate that film sources of counter-ions (required to maintain electroneutrality) can be significant. The extent of participation of these species depends on the nature and concentra- tion of the bathing electrolyte solution. In the case of PVF, optical data also indicate a structural change: reduced PVF appears to be a homogeneous compact film, whilst oxidised PVF+ is a more diffuse, inhomogeneous film, whose polymer content decreases with distance from the electrode. Voltam- metric experiments at rapid (and in some cases even moderate) scan rates show that transport of mobile species can be quite slow. It was generally observed that ingress into the polymer was slower than egress of the same species from the polymer.Charged species, notably proton in hydrated systems, move faster than neutral species, such as solvent, due to the influence of the field. Surface-immobilised electroactive polymer films have potential applications in areas as diverse as electrocatalysis, optical/electronic devices, sensors and energy storage. Frequently, performance is limited by the rate of charge transport in the polymer film.4 This can restrict such quantities as the overall reaction flux in electrocatalytic applica- tions, sensitivity or response time in sensors, and charge/ discharge rates in batteries. That the electrochemistry of redox polymer films is affected by the nature of the counter-ion has been recognised from the However, the role of solvent and co-ions, alone or in ion aggregates, has been acknowledged comparatively recently.Consideration of counter-ions alone corresponds to the assumption that electroneutrality alone determines ion populations within the film (in membrane terminology, that the film is permselective). In fact, the conditions of high ionic strength employed in most electrochemical experiments are those where permselectivity is least likely. Here, elec- troneutrality is not the only consideration. Thermodynamics demands that, at equili- brium, the activities of all mobile film species must be the same as those of their counterparts in solution. We have recently described a thermodynamic model for this situation.’ Clearly, to improve the characteristics of devices employing conducting polymers, it is necessary to improve their charge-transport properties.Before this can be achieved, information about the underlying physical processes occurring during charge transport must be obtained. A range of electrochemical techniques has been developed for 151152 Electroactive Polymer Films monitoring the flux of electrons across electrode/ polymer interfaces. This includes steady-state [ rotating-disc electrode (RDE)] and transient (chronocoulometric) methods. However, exclusive reliance on electrochemical techniques means that the role of electroinactive species (for example, solvent,' counter-ions and ion pairs) cannot be directly deduced. Recently, electrochemists have developed a number of in situ spectroscopic tech- niques. Unfortunately, these can suffer from the fact that it is difficult to distinguish between species in the film and the vast excess of the same species in solution.Two techniques which theoretically offer both sensitivity and surface specificity are ellip- sometry and the electrochemical quartz crystal microbalance (EQCM). Furthermore, since these techniques depend on entirely different principles, their combined use lowers the risk of data misinterpretation. We have employed these techniques to study charge transport in polyvinylferrocene (PVF), commonly used as a model system for electroactive polymer poly- bithiophene (PBT),'13'2 and polythionine ( PTh),I3-l6 and report our results in this paper. Experiment a1 A more detailed account of the operation of the ellipsometer is given in another paper in this volume." The working electrodes were thin films of Au or Pt coated onto glass microscope slides (supplied by Dr M.Lee, Imperial College). During film deposition and subsequent potential cycling experiments, ellipsometric parameters were recorded as functions of time or potential; where appropriate, averaging over multiples of the basic ellipsometer sampling period (20 ms) was employed. The apparatus and technique for simultaneously recording mass vs. potential and current vs. potential have been described previously.'* The working electrodes were metal films (area 0.23 cm2) on 10 MHz AT cut quartz crystals (International Crystal Manufacturing Co., Oklahoma City, USA), either Au (as received) or Pt-coated (by Dr Lee, Imperial College, London) onto blanks supplied by the manufacturer. Equilibrium or slow-scan voltammetric data were recorded using an analogue system. Transient and faster scan voltammetric data were captured using a Keithley SOFT500 data acquisition system, interfaced to an IBMATX computer.All potentials were measured and are quoted with respect to the aqueous saturated calomel electrode (SCE). Experiments were performed at room temperature, 20 * 2 "C. The duration of a single experiment was sufficiently short that any temperature effects are negligible. Reagents, water, acetonitrile, and argon were of similar quality to those used in ref. (12), (16) and (19). The PVF, prepared according to ref. (20), had an average molecular weight of 26 500. Monomeric thionine16 and bithiophene" were purified as described previously.Polyvinylferrocene (PVF) films were deposited electrochemically, by the application of a potential step from 0.0 to 0.7 V, from 0.1 mol dm-3 tetraethylammonium perchlorate (TEAP)/CH2C12 solutions containing PVF (0.01 mol dm-3 in ferrocene moieties). Coated electrodes were transferred to aqueous media (see figure captions for electrolyte concentrations) for the experiments described here. They were then taken through two voltammetric cycles, from -0.1 to +0.75 V at 5 mV s-l, before recording data on sub- sequent cycles. Polybithiophene films were deposited from acetonitrile solutions of the monomer as described previously.12 Their properties were investigated in monomer-free solutions of the same background electrolyte, 0.1 mol dmP3 tetraethylammonium tetrafluoroborate (TEAT).Deposition of polythionine films from aqueous acid media was petformed according to the standard procedure. l 3 Films were characterised in monomer-free aqueous sol- utions, whose compositions are given in the relevant figure legends.'4. R. Hillman et al. 153 I I 1 I 1 o-a O6 EIV 0' 02 0-4 Fig. 1. ( a ) Current-voltage and ( b ) mass-change-voltage curves for a PVF film on Au during a cyclic voltammetric experiment in 0.01 mol dm-3 NaClO,. The scan-rate was 5 mVs-'. Ellipsometric data analysis was performed using a procedure described elsewhere. l9 In all cases, the possibility of inhomogeneous films was considered. Results and Discussion Polyvinylferrocene (PVF) Fig. 1 shows EQCM data obtained on potential cycling of a PVF film in 0.01 mol dmP3 NaClO,.Similar data were acquired for a series of electrolytes, employing different anions and cations, as a function of concentration.2' At low concentration (< 1 mol dm-3 for NaClO,) the mass changes accompanying oxidation of PVF to PVF+ show four characteristics. First, the film mass increases by an amount independent of electrolyte concentration. Secondly, the mass increase is greater than expected solely on the basis of uptake of one counter-ion per redox site. Thirdly, the mass increase varies approxi- mately linearly with anion molar mass, but is independent of the cation for a range of perchlorate salts. Fourthly, the variation of formal potential for surface-immobilised PVF/PVF+ is Nernstian (ca. -60 mV per decade).From these we deduced*l that, at electrolyte concentrations below 1 mol dm-3, PVF oxidation is accompanied by the ingress of one anion per redox site and some solvent (ca. 6-9 H 2 0 per redox site). There is no net movement of cations, either alone or as part of an aggregate.154 Electroactive Polymer Films -88.1 -88.2 -88.3 3 -88.4 0 -8a.E -88. t -88.' -88.1 - 2 -0.1 0 0.1 0.2 0.3 Q.& 0.5 0.6 0.7 ' -31 . / 5 -31.5 - 31.55 -31.6 0 \ -3 -31.65 -31.7 -31 .75 -31.8 -31.85 -31.9 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fig. 2. Ellipsometric data for an experiment under the conditions of fig. 1. Curves ( a ) and (b) show A and $, respectively. The monitoring wavelength was 450nm, the sampling rate was 1 point s-', and the concentration was 0.01 mol dm-3 NaClO,. We have employed ellipsometry to investigate the variation of film thickness with oxidation state.Fig. 2 shows data acquired during a similar voltammetric experiment (in aqueous background electrolyte) to that shown in fig. 1. We were unable to measure film thickness during the deposition of polymer (as PVF') from CH2C12, because of the small change and large scatter in the intensity data. Recourse was therefore had to independent optical data22 obtained during in situ electronic spectroscopic studies ofA. R. Hillman et al. 155 Table 1. Variation of PVF film thickness with oxidation state and NaClO, electrolyte concentration ~~~~~ ~ film thickness/A concentration /mol dmb3 reducedn oxidisedb 0.01 1 .o 3 .O 3 50 515* 10 417 580* 10 412 610* 10 Homogeneous film; inhomogeneous film (see text for details).PVF and PVF' films. Together with the experimentally significant intensity changes in the aqueous ellipsometric experiments, this allowed us to arrive at the semi-quantitative picture of PVF film structure changes during redox switching, described below. Coulometric estimates of the amounts of polymer deposited were obtained by integrating the current peaks in aqueous (background electrolyte) voltammetric experi- ments. This is preferred to use of coulometric data from the deposition process, since the deposition efficiency of ferrocene-containing polymers is 10w.l~ For the film of fig. 2, 1.1 x lo-' mol cm-2 of ferrocene sites were present. Assuming that the volume of a vinylferrocene monomer unit is approximately the same as that (determined by X-ray crystallography) for acetylferrocene, 250 A3,23 this would correspond to a film ca.170 A thick. This figure represents the minimum possible (solvent and ion-free) thickness for reduced PVF. Use of the data in fig. 2, employin a single homogeneous the film contains approximately 45% solvent, 55% polymer. The low molar ratio of solvent to redox sites, ca. 7 H20 per ferrocene (or less if NaClO, is present), is in agreement with the hydrophobic character of the reduced polymer. The refractive index of the reduced film at 450 nm is 1.392 - 0.0086i. The value of n is between those for the solvent and a range of f e r r ~ c e n e s ; ~ ~ that of k shows the ferrocene entities to be rather weak chromophores, like their monomeric counterpart^.^^ Analysis of the data for the oxidised, PVF+, film is more complex.Previous (trans- mission) electronic spectroscopy experiments indicated that at 450 nm the films are less absorbing in the oxidised form.22725 However, in these ellipsometric experiments, we observe that the reflected light intensity is lower for the oxidised material. These two pieces of information suggest that the film becomes inhomogeneous upon oxidation. This was confirmed by the failure of a simple homogeneous film model to provide physically realistic fits to the data at 0.7 V in fig. 2. We therefore employed a model in which the film was described as a set of (eight) equal thin homogeneous films, whose optical properties varied (linearly) from the electrode/polymer interface out to the polymer/electrolyte interface.The properties of the outer film were those of the solvent. The three parameters to be fitted are then the refractive index of the inner film ( nI, k , ) and the total film thickness. The results of this procedure are summarised in table 1, for an initial kL product for the reduced film of 3.0. Artificial increase of the reduced film kL product was explored to test the validity of the results. It was found that the reduced film L Val could be increased by up to ca.25% without failure of the fitting routine, but that this produced essentially proportionate increases in the oxidised film thicknesses. In other words, there is an uncertainty of ca. 12% on the absolute values of film thickness, but conclusions regarding changes in film thickness (swelling) on oxidation are unambiguous.film model, suggests that the film, in its reduced state, is 300 1 thick. In other words,156 Electroactive Polymer Films As shown in table 1 , the film thickness increases on oxidation, from 350 to ca. 500 A. The refractive index of the inner part of the film is 1.438-0.01Oi. Simple volume arguments show that the inner ‘layer’ in this linearly graded composition model contains ca. 72% by volume polymer. This explains the higher real component of the inner film refractive index, and shows that the extinction coefficient (on a molar basis) at 450 nm is decreased upon oxidation (by ca. 10%). The important conclusion, however, is that there appears to be a structural change induced by the redox state change, and concomitant changes in ion and solvent popula- tions.We are aware that a similar model has been invoked to explain redox state- switching processes in polyaniline.26 At higher concentrations ( c > 1 mol dm-3 for NaClO,), the mass increase is larger.2’ We attribute this to the participation of cations, i.e. the failure of permselectivity. Departure of the formal potential from the Nernstian relationship is in accord with this view. From this we predict that the transient charge-transport process within a PVF film may be different at high and low concentrations. In concentrated electrolytes, co-ions (Na’ here) have the obligation to participate at long times (equilibrium), and the opportunity to do so at short times. We now explore the latter aspect in a kinetic experiment.The data described are for voltammetric experiments, where the time variable is scan rate ( v ) . For the film thicknesses and scan rates examined, the total mass change and charge are not very dependent on scan rate. This is because, by the end of the scan, sufficient time has elapsed for equilibrium to be approached. In order to answer the more searching question of the time required for the various equilibria to be established we compare mass and charge data during the redox transformation. A simple measure of the relative rates of charge and mass transfer involves comparison of the potentials at which half the charge and mass change have occurred, E 1 / 2 , q and E 1/2,rn 9 respectively. In a preliminary comm~nication,~~ we showed that, for the PVF+/PVF couple in 3 mol dm-3 NaClO,, E1/2,q and E l l ? , , diverge from their low scan-rate values above ca.100 mV s-’. We are now able to explore this in more detail. Fig. 3 shows a plot of the mass change vs. charge injected into a neutral PVF film. By plotting the data in this way the effect of charge hysteresis in the potential (time) domain is separated out. The important observation is that the mass and charge responses are nearly in step throughout reduction, but not during oxidation. Tn the latter case, this is only so at slow scan rates (10 mVs-’ for the film shown). At higher scan rates (500 mVs-’ here), the mass response lags the charge and, by comparison with slow scan rate data, is incomplete at the end of the scan. An interesting observation is that the initial mass response proceeds along a line similar to that predicted by the motion of anion alone.The implication here is that counter-ions, being driven by both concentra- tion and potential gradients, move more rapidly than solvent or ioii pairs. The latter (neutral) species only move by diffusion. Thus the simple counter-ion response is seen at sufficiently short times, but thermodynamics prevails, as it must, at long times. Polybithiophene (PBT) In the ‘doping’ of electronically conducting polymers, such as PBT, an important issue is the correlation of dopant uptake with passage of electronic charge. The EQCM provides a direct measure of dopant ingress/egress. Fig. 4 shows current-voltage and mass-change-voltage curves for PBT dopinglun- doping during a voltammetric experiment.Fig. 5 presents the data in the form of a mass-change vs. charge (normalised by the Faraday) plot. If BF, were the only species to move in response to the removal/injection of electronic charge, the data would fall on a straight line of slope 87 g mol-’ (the molar mass of BF,). (The analogous issueA. R. Hillman et al. 157 E' a E a --. 0 0,2 0.4 0.6 1 q / qT Fig. 3. Mass-change us. charge plot for a cyclic voltammetry experiment on PVF in 3 mol dmP3 NaCIO,. The scan rate was 500 mVs-'. Charge and mass are referred to their values at 0 V, and are normalised with respect to their overall changes. The line represents the calculated mass change for the injection of one counter-ion per electron removed. for a sulphonate-functionalised polypyrrole has been considered by other authors.*') Furthermore, electroneutrality would result in no hysteresis.Although the net mass change, averaged over duplicate experiments using 0.1 mol dmP3 TEAT, 83 (*7) g mol-', is close to the 'expected' value, there is clear hysteresis, the extent of which increases with scan rate. Additionally, the overall mass change depends slightly on the electrolyte concentration, decreasing from 95 ( * 7 ) to 76 (*6) g mol-' on going from 0.01 to 1 .O (fig. 4 and duplicates) mol dm-3 TEAT. These observations suggest the movement of more than one species. This is supported by the fact that oxidation peak potentials at slow scan rates do not show a Nernstian dependence on BF, concentration. We suggest a mechanism involving both anion ingress and cation egress, together with some solvent transfer, upon PBT oxidation.The extents of cation and solvent transfer vary with concentration, so that the overall mass change will vary with concentra- tion. The details of this hypothesis are now under further study. Polythionine (PTh) The polythionine system, represented in scheme 114 is more complex in several respects. The most obvious of these is that there are coupled protonic equilibria. This has important consequences, discussed below. Ellipsometric dataI5,l6 show that the films are extremely compact, ca. 50% polymer by volume. Inclusion of a minimum estimate of counter-ion content (based on electroneutrality alone), 25% by volume, shows that the (maximum) water content is very low, ca. 25%.This corresponds to barely three water molecules per redox site. In the discussion below, we consider the source(s) of the required species, for example counter-ion, and their rates of access. Both these158 0.6 0.4 N I 0 , 2 < E 2 Eo -0,2 - - 0-- - -0,4 ' 1 I I I 1 I I I I I 0 0.2 0.4 0.6 0.8 1 1,2 E I V -0.2 0 0.2 0.4 0.6 0.8 1 1.2 ( E N Fig. 4. ( a ) Current-voltage and ( b ) mass-change-voltage curves for a PBT film on Pt during a cyclic voltammetric experiment in 1 mol dm-3 TEAT. The scan-rate was 100 mV s-'. issues affect the observed charge-transport rate. H Scheme 1. Fig. 6 and 7 show data from voltammetric EQCM experiments on polythionine films in strong (perchloric) and weak (acetic) acid solutions, respectively. The first, qualitative, point to note is that the mass changes are in different directions.Reduction results in an increase in mass in the 0.05 mol dm-3 perchloric acid solution (fig. 6), and a decrease in mass in the 0.1 mol dm-3 acetic acid solution (fig. 7). These observations should be compared with prediction of a simple permselective film model [based on the chemistryA. R. Hillman et al. 1.5 1 - 0,5 0 . 159 - - 0 5 10 15 20 qf-'/nmoI cm-2 Fig. 5. Mass-change us. ( q / F ) plot for the experiment of fig. 4. Charge and mass are referred to their values at 0 V. 16.3 Hz rw 179 ng Fig. 6. ( a ) Current- ( b ) charge- and (c) mass-change-voltage curves for a cyclic voltammetric experiment on PTh. The electrolyte was 0.05 mol dm-3 HC104. The scan rate was 100 mV s-'.160 Electroactive Polymer Films T / \ f + E - Fig.7. ( a ) Current- ( b ) charge- and ( c ) mass-change-voltage curves for a cyclic voltammetric experiment on PTh. The electrolyte was 0.1 mol dm-3 CH3C02H at pH 2.9. The scan rate was 5 mV s-'. of scheme (l)], that the film mass should increase upon reduction, by (3MH++ MA-) g mol-', where Mi is the molar mass of species i. The failure of the permselective model, even at a qualitative level, to describe the behaviour of polythionine in acetic acid media is explained as follows. Independent gas-phase acetic acid absorption experiment^^^ show that acetic acid is incorporated into the film (to the extent of ca. 2 molecules per redox site) and is strongly bound. Consequently, under the conditions of the experiment in fig.7, undissociated acetic acid will compete successfully with water for sites in the film. The reason anions do not need to enter the film during its reduction is that they are already present, as HA. This also provides one of the protons (scheme l ) , the other two coming from solution. Under the conditions of the experiment, there is also some solvent ejection on reduction. The kinetics of this process are particularly interesting. If anion ingress into the very compact polythionine film were required, one might expect it to influence the rate of reduction. However, since HA is present in the film, electroneutrality only requires the movement of protons. These latter species are able to move rapidly between the waters (in a Grotthus-type mechanism) and/or polymer amine sites.Expulsion of water is also facile, so the mass and charge changes parallel each other (see fig. 8) during reduction. Contrastingly, mass lags the charge during oxidation. This is shown qualita- tively by visual comparison of the mass and charge traces of fig. 7, and quantitatively by the E 1 / 2 , q and E 1/2,m vs. scan-rate plots of fig. 8. During oxidation, proton movement required to satisfy electroneutrality is rapid, but solvent ingress, into a compact film and unaided by the field, is slow.A. R. Hillman et al. " 161 P 1 I I ib :* E '1. 100 4 . . n l I scan rate/mV s-' Fig. 8. E1,2,q and E l l z , , us. scan rate for PTh in 0.1 mol dmP3 CH,C02H (pH 2.9). Symbols are q(a) W; m(a) 0; q(c) + ; m(c) 0 (a = anodic scan, c = cathodic scan). h > 4 1 5 0 r 100 0 + 0 + -to 0 01 I I I I I 0 20 40 60 80 100 1 0 scan rate/mV s-' Fig.9. E ,/z,q and El12,, us. scan rate for PTh in 0.05 mol dm-3 HC104. (Symbols as in fig. 8.) Our interpretation of the strong-acid experiment of fig. 6 is a little more complex, as befits the situation. Here the net mass change is in the expected direction, but quantitative data show that it is much smaller than anticipated, ca. 15-20 g (mol Th)-' at this concentration of HC104, as compared to 102Sg(molTh)-' (=3H +ClO,). Analogous to the acetic acid case, we postulate an anion source within the film, H,O+ClO,. A fundamental difference here is that the break-up of the ion pair liberates H20. Two issues then arise. First, how much of this water is expelled and how much of the ion pair is replenished by partition from solution? Secondly, how rapidly do these processes occur? The answer to the first question depends on the external electrolyte concentration;21 for the conditions of fig.6, the result is a net increase in mass. In this paper we focus on the second question. That different mobile species are transferred at different rates is unambiguously demonstrated by the fact that non-monotonic mass changes are observed (during reduction in fig. 6 and oxidation in fig. 7). Differences in ingress and egress rates are demonstrated by the fact that mass and charge changes are differently correlated during oxidation and reduction. Again, E$,q and Eh,m vs. scan-rate plots are helpful, as shown in fig. 9. In 0.05 mol dm-3 perchloric acid, the mass lags the charge response during162 Electroactive Polymer Films reduction (cf.fig. 8). Although the overall picture is more complex, because more species are involved, the common feature is that ingress of species (leading to a mass increase) is more difficult than egress. Conclusions The conclusions of this work fall into two areas: the sources/sinks of the mobile species and their relative rates of utilisation. We conclude that film sources of counter-ions may be significant. In our studies, they took the form of ion pairs or undissociated acids. The extent to which these species participate is very dependent on the bathing electrolyte nature and concentration. Since the solvent content of most electroactive polymer films is low, and the density of charged redox sites is usually high (> 1 mol dm-’), activity effects will be important in determin- ing these equilibrium populations.We note that the conditions of high ionic strength often employed in electrochemical measurements are those where permselectivity is likely to break down. The studies described here provide direct evidence for the participation of film sources of counter-ion in electroactive polymer redox state switching. Clearly, thermodynamics prevails, given time. However, equilibria associated with electronic, ionic and solvation processes may be established on quite different time-scales. Despite the apparent diversity of behaviour, we are able to postulate some general rules. First, the high concentration and immediate proximity of film sources leads to the expectation that they will take temporal precedence over solution sources.On longer timescales, equilibrium considerations may redress this imbalance. Secondly, the demands of electroneutrality will, in general, cause the motion of charged species (assisted by the field) to be faster than that of neutral species. This means that solvation equilibria may be only slowly established. Thirdly, for any given species, its ingress into the film is likely to be more difficult than its egress from the film. Although there may be exceptions to this ‘difficult ingress, rapid egress’ (DIRE) mechanism, we suggest that all cases may be explained by consideration of the appropriate activity gradients. Finally, we note that the rather special nature of protonic transport in water appears to have a parallel in hydrated electroactive polymers, such as polythionine.Here, because of the very different mobilities of protons and other ions, protons alone assume responsi- bility for maintaining electroneutrality immediately following injection of electronic charge. Given that coupled protonic equilibria are common in organic redox systems, we would not be surprised if other polymer films showed similar behaviour. We thank the S.E.R.C (grant no. GR/E/32946) and the U.S. Air Force Office of Scientific Research (grant number 87-0037) for financial support. A.R.H. and S.B. thank NATO Scientific Affairs Division for a Collaborative Research Award (grant number 86/0830). M.J.S. and R.M.E. thank the S.E.R.C. for studentships, and S.J.H. thanks the S.E.R.C.for a PDRA award. References 1 R. W. Murray, in Electroanalytical Chemistry, ed. A. J . Bard (Marcel-Dekker, New York, 19841, vol. 13, p. 192. 2 A. R. Hillman, in Electrochemical Science and Technology of Polymers, ed. R. Linford (Elsevier, London, 1987), vol. 1, chap. 5 and 6, pp. 103-292. 3 Conducting Polymers, Special Applications, ed. L. Alcacer (Reidel, Dordrecht, 1987). 4 W. J. Albery and A. R. Hillman, J. Electroanal. Chem., 1984, 170, 27. 5 S. Bruckenstein and A. R. Hillman, J. Phys. Chem., 1988, 92, 4837. 6 P. J. Peerce and A. J. Bard, J. Electroanal. Chem., 1980, 114, 89. 7 P. Daum, J . R. Lenhard, D. R. Rolison and R. W. Murray, J. Am. Chem. Soc., 1980, 102, 4649. 8 S. Chao, J. L. Robbins and M. S . Wrighton, J . Am. Chem. Soc., 1983, 105, 181. 9 C. M. Carlin, L. J. Kepley and A. J. Bard, J. Electrochem. SOC., 1985, 132, 353.A. R. Hillman et al. 163 10 P. T. Varineau and D. A. Buttry, J. Php. Chem., 1987, 91, 1292. 11 Handbook of Conducting Polymers, ed. T. A. Skotheim (Marcel-Dekker, New York, 1986). 12 A. R. Hillman and M. J. Swann, Electrochim. Acta, 1988, 33, 1303. 13 W. J. Albery, A. W. Foulds, K. J. Hall and A. R Hillman, J. Electrochem. SOC., 1980, 127, 654. 14 W. J. Albery, M. G. Boutelle, P. J. Colby and A. R. Hillman, J. Electroanal. Chem., 1982, 133, 135. 15 A. Hamnett and A. R. Hillman, J. Electroanal. Chem., 1985, 195, 189. 16 A. Hamnett and A. R. Hillman, J. Electroanal. Chem., 1987, 233, 125. 17 A. Hamnett, S. J. Higgins and P. Christensen, Faraday Discuss. Chem. Soc., 1989, 88, 261. 18 S. Bruckenstein and M. Shay, Electrochim. Acta, 1985, 30, 1295. 19 A. R. Hillman, D. A. Taylor, A. Hamnett and S. J. Higgins, J. Electroanal. Chem., accepted for 20 T. W. Smith, J . E. Kuder and D. Wychik, J. Polym. Sci., Pol-vm. Chem. Ed., 1976, 14, 2433. 21 A. R. Hillman, D. C. Loveday and S. Bruckenstein, J. Electroanal. Chem., submitted for publication. 22 A. R. Hillman and Z. X. Shu, unpublished work. 23 K. Sato, M. Katuda, H. Sano and M. Konno, Bull. Chem. SOC. Jpn, 1984, 57, 2361. 24 Handbook of Chemistry and Physics, (CRC Press, Cleveland, 56th edn, 1975), pp. C692-C695. 25 Y. S. Sohn, D. N. Hendrickson and H. B. Gray, J. Am. Chem. SOC., 1971, 93, 3603. 26 S. Gottesfeld and J. Rishpon, personal communication. 27 S. Bruckenstein, C. P. Wilde, M. Shay, A. R. Hillman and D. C. Loveday, J. Electroanal. Chem., 1989, 28 J. R. Reynolds, N. S. Sundaresan, M. P Pomerantz, S. Basak and C. K. Baker, J. Electroanal. Chem., 29 C . P. Wilde, S. Bruckenstein and A. R. Hillman, unpublished work. publication. 258, 457. 1988, 250, 355. Paper 91025125; Receiued 14th June, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800151

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1989, 88, 165-176 Ion Transport in Pyrrole-based Polymer Films Huanyu Mao, Jolanta Ochmanska,? Chris D. Paulse and Peter G. Pickup* Department of Chemistry, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1 B 3x7 Ionic resistivities and counterion diffusion coefficients for polypyrrole, poly- [ l-methyl-3-(pyrrol-l-ylmethyl)pyridinium] (poly-MPMP+) and pyrrole,- [R~(2,2'-bipyridine)~(3-( pyrrol-1-ylmethyl)pyridine)Cl]+ copolymer films have been obtained by chronoamperometry using the single-pore model. For poly-MPMP+ both the electronic resistivity and the ionic resistivity can be simultaneously determined. Finite-difference simulations have been used to confirm the validity of the equations used and to extend the applicability of the model.Counterion diffusion coefficients in polypyrrole and poly-MPMP+ have also been determined by rotating-disc voltammetry and d.c. conductivity measurements. Where possible the results have been confirmed by the use of two independent methods. Diffusion coefficients for I-, CI-, ClO, and Fe(CN);f- in the above polymers in water and/or acetonitrile are compared and discussed. It is concluded that: ( a ) polypyrrole and poly-MPMP+ are solvated and swollen to a much greater extent in water than in acetonitrile, ( b ) permanent cationic sites increase the permeability of polypyrrole in water but not in acetonitrile and (c) the permeability of polypyrrole in acetonitrile can be increased by the incorporation of bulky metal complexes. There has recently been much interest in the determination and enhancement of ion- transport rates in conducting polymer One source of impetus for this research is the potential applications of these materials in batteries, displays, and other electrochemical devices.On a more fundamental level, studies of ion-transport rates, and how they vary from one polymer film to another, can enhance our understanding of the structure of polymer films that are in contact with, and swollen by, an electrolyte solution. Our recent work has been aimed at developing a range of experimental techniques for measuring ion-transport rates in conducting polymers. I 4 , l 6 Specifically, we have applied chronoamperometry, rotating-disc voltammetry and d.c. ionic conductance measurements to the measurement of anion transport in pyrrole-based polymers.We have been using these techniques to explore the influence of permanent ionic sites16 and bulky metal complex sites on anion transport through substituted polypyrrole films. These studies are yielding important insights into the structure and swelling of polypyrrole-based materials. In this paper we focus on the use of chronoamperometry to measure ClO, transport rates in polypyrrole and poly-[ 1 -methyl-3-( pyrrol- 1 -ylmethyl)pyridinium] (poly- MPMP+, I).18 We also summarize and discuss results for pyrrole,-[ Ru(bp),(prnp)Cl]' copolymer films (11) " [bp = 2,2'-bipyridine, pmp = 3-( pyrrol-1-ylmethy1)pyridinel and t Permanent address: Laboratory of Electroanalytical Chemistry, Department of Chemistry, Warsaw University, Pasteura 1, 02093, Warsaw, Poland.165166 electrode Ion Transport polymer f i l m e I ect rol y te solution Fig. 1. Equivalent circuit for the single-pore model. R, = 100Ri, RE = 100R,, C,= lOOC,, and A&,, is the potential difference between the two stars. results obtained using rotating-disc voltammetry and d.c. ionic conductance measure- ments. '0 p Me I I1 We have previously shown that chronoamperometric data for polypyrrole should be analysed using a migration model (e.g. the single-pore model of a porous electrode") rather than the commonly used diffusion model (Cottrell equation). In this work the single-pore model is applied to the full reduction/oxidation of polypyrrole and to the modified polypyrroles specified above. The Single-pore Model According to the single-pore model, a porous conducting electrode can be treated as a finite transmission line in series with the uncompensated solution resistance Rs (fig. 1).The electrode is characterized by the electronic resistance (RE) of its solid phase, the ionic resistance ( R , ) of its electrolyte phase, and its total double-layer capacitance ( CF). When the electronic resistance of the electrode material is negligible compared to its ionic resistance and the solution resistance (RE<< I?, and &), the potentiostaticH. Ma0 et al. N 167 Fig. 2. Cyclic voltammogram (10 mV s C ' ) of a 1.7 pm thick polypyrrole film in acetonitrile containing 0.1 mol dm-3 TEAP (-). The dashed line is a theoretical voltammogram based on the Feldberg model" with a@ = 129 pF, a-' - Epzc = 0.82 V, Eo = -0.20 V and g = 0.54 (see text).behaviour is described by2* where IT is the total current, AEstep is the magnitude of the potential step, RF = R 1 , T = RFCF, p = Ro/RF, Ro= Rs and values of m are the positive roots of m tan (m) = l/p. The solution resistance ( R , ) and film ionic resistance ( R , ) have been designated as Ro and R F , respectively, since we will use eqn (1) to treat a case which involves more complex combinations of RE, R , and R s . Thus RF and Ro are parameters obtained from current us. time data using eqn (1). For the treatment of chronoamperometric data for polypyrrole, eqn (1) is valid only for potential steps in the 'double-layer charging region' between ca. 0.1 and 0.6 V (fig. 2). It is only in this region that the capacitance and resistance (ionic and electronic) are approximately independent of potential. In this region, the analysis of chronoam- perometric transients for polypyrrole films in both water and acetonitrile, according to eqn ( l ) , yields a good fit and accurate Rs and R , v a l ~ e s .' ~ In order to apply the single-pore model more generally to potentiostatic experiments on conducting polymers, the following additional factors must be considered: ( a ) the electronic resistance of the film (RE); ( b ) the variation of the polymer capacitance (C,) with potential [this is crudely given by a cyclic voltammogram (e.g. fig. 2) where CF = dQ/dE = current/scan speed]; ( c ) variation of the polymer electronic" and ionic3 resistance with potential.The effects of these factors are most conveniently assessed by using digital simulations. The finite-difference is used here. Finite-difference Simulations Simulations of the behaviour of the circuit shown in fig. 1 were carried out using FORTRAN programs on a Vax 8800 or a Vax 11/780. An equivalent circuit consisting of 100 capacitors representing 100 equal thickness layers of the polymer film perpendicular to the electrode surface was used. A time increment of 10 ps (ca. 5 x 10-5RsCF) was168 Ion Transport generally found to be satisfactory. Simulations were routinely checked by also running them at half of this time increment. Many of the parameters used in the following treatment are defined by fig. 1. The general procedure for the simulations is as follows.The initial charge for each capacitor (Q,) is first calculated from the initial potential. Then, for each time increment, the total current (IT) and the current through each capacitor ( I , ) are calculated. The individual capacitor currents are multiplied by the time increment and added to the charge on the capacitor. The new potential difference across each capacitor (AE,) is then calculated from its new charge. Case 1: R, and R, >> RE, C, independent of E The result for this case is given analytically by eqn ( l ) , it was used to test the simulation procedure. Since only changes in charge and potential are relevant, initial values of Q, and AE, were set at zero. The relevant equations used in the simulation were: I T = (AEstep-AEl)/(Rs+ Ri/2) (2) and I, = ( AE, - 1 - A E, )/ Ri - ( AE, - AE,+ I ) / Ri .(3 The first term in eqn (3) is I T for n = 1 and the second term is zero for n = 100. Simulated current transients were indistinguishable from those obtained using eqn (1). This confirms the validity of both the simulation method and eqn (1). Case 2: RI and RE of similar Magnitude, CF independent of Potential This case applies to chronoamperometry of poly-MPMP+ with potential steps in the ‘double-layer charging region’ (ca. 0.9-1.1 V). Again, only changes in charge and potential are relevant so initial values can be set at zero. The total current is given by I T = (AEstep-AEtiirn)/(Rk) (4) where and R & = Rs+ Re/2+ Ri/2. The current through each capacitor is given by I n = In., - It, ~ I .e In,,=[I,R,+ 100(AE,+, -AEn)I/(RI+RE) where (7) and I100 = I T - I99.e - (10) This simulation was tested by applying it to Case 1.For RE > Rs >> R, and RI > R, >> RE the results were the same as those given by the Case 1 simulation and by eqn (1) with RF equal to RE and R , , respectively. A plot of log IT us. t for the simulated transientH . Ma0 et al. 169 could be analysed according to eqn (1) l 4 to yield the parameters used in the simulation (e.g. R , = 5000 0, Rs = 500 0, RE = 1 a, CF = 100 pF). Simulations with RE = RI > Rs (e.g. RI = 5000 f17 RE = 5000 0, Rs = 500 f17 CF = 100 pF) could also be analysed in this way; however, the RF value obtained (2500 0) was equivalent to a parallel combination of RE and R , whereas Ro (3000 0) was a series combination of RF and Rs.This is in agreement with equations given by Johnson and Newman for this case.24 According to Johnson and Newman’s treatment, Ro and RF are given by: R, = Rs+ I / ( K +a) (11) and” where K = l / R I and a = l / R E . Although K and u were originally defined as conduc- tivities, it is more convenient here to define them as conductances. For RE> R , > R, and R,> R E > R,, analysis of simulations according to eqn (1) yields Ro and RF values in only fair agreement with those used in the simulation [converted to Ro and RF using eqn (11) and (12)]. For example, a simulation with RF = 6.2 ka, Ro = 2.6 kCl and C , = 0.5 mF, yielded RF and Ro values of 9.2 and 1.9 k 0 , respectively, when analysed according to eqn (1).Furthermore, the fit between the simulated current transient and that generated from eqn ( l ) , (11) and (12), using the same parameters was not excellent. Case 3: R, and CF are Potential Dependent, R, > Rs >> RE This case will be applied to complete and partial reduction and oxidation of polypyrrole. Values of charge and potential must now be specified relative to reference points. Qn is set at zero for a fully reduced film and hE, is set at zero at the formal potential (-0.2OV us. SSCE). The dependence of C, on potential will be described using Feldberg’s The relationship between charge and potential will be given here since that is actually used in the simulation. ~ = ( ~ - ~ , , , + a - ~ ) a ~ I ‘ e x p ( j E ) / [ l + e x p (jE)]= IOOQ,, (13) were E is the potential relative to the formal potential ( = A E , ) , Epzc is the point of zero charge for the polymer, a is a constant relating the faradaic charge to the double-layer capacitance, Qy, is the maximum faradaic charge for the whole film and f= g F / R T .We have added an empirical factor ( g ) into the exponential term to account for activity effects which lead to a broadening of the voltammetric wave.27 Our function for the dependence of R , on potential is based on the work of Burgmayer and Murray.3328 These authors have shown that the ionic conductivity of polypyrrole decreases by over three orders of magnitude when the polymer is reduced. This can easily be accounted for by considering the relationship between resistance and the concentration of ion-exchange sites ( CIF) given by the same authors3 R , = R T d / F’ADC,, (14) where D is the diffusion coefficient of counterions in the film and d is the thickness of the film.Since CIE goes to zero when the film is reduced, it is inevitable that the ionic resistance of the film will increase considerably. Since C,, is directly related to the charge state of the film (Clb = Q / F A d ) , eqn (13) and (14) can be used to obtain the potential dependence of R , . The simulation of this case uses the same basic equations as for Case 1. However, for each time increment and each capacitor, eqn (13) is used to obtain the new potential170 Ion Transport difference across the capacitor from its new charge. Values of Ri between each pair of capacitors are calculated from the charge on the first capacitor of the pair using Rfl,i = R?Q0/ l0OQfl (15) where Ry is the ionic resistance at a charge of Qo.Experimental Electrochemistry Electrochemical experiments were carried out in conventional three-compartment glass cells under an argon atmosphere at 23 f 2 "C. A 0.0045 cm2 Pt disc electrode sealed in glass, a R wire counter electrode and a saturated sodium chloride calomel electrode (SSCE) reference electrode were used. All potentials are quoted with respect to the SSCE. Chemicals 1-Methyl-3-( pyrrol-1-ylmethy1)pyridinium tetrafluoroborate (MPMPBF,) was prepared as previously described." Pyrrole (Aldrich) was purified on a dry alumina column. Tetraethylammonium perchlorate (TEAP, Fluka), tetraethylammonium tetrafluorobor- ate (TEABF,, Fluka) and acetonitrile (Fisher, HPLC grade) were used as received.Preparation of Polymer Films Polypyrrole was prepared by constant current (0.33 mA cm-2) polymerization of pyrrole (0.1 mol dmP3) from a 0.1 mol dm-3 TEAP/acetonitrile solution. MPMPBF, was elec- tropolymerized from a 0.05 mol dm-3 acetonitrile solution containing 0.1 mol dm-' TEABF, at a constant current density of 0.8 mA cm-2.'8 Film thicknesses were estimated from the polymerization charge using conversion factors of 0.24 C cm-* = 1.0 pm' and 0.15 C cm-2 = 1.0 pm,18 respectively, for polypyr- role and poly-MPMP+. Equipment A Pine Instruments RDE4 potentiostat/galvanostat was used with a BBC MDL780 X-Y recorder. A Tatung TS-7000 microcomputer, interfaced to the potentiostat via a Data Translation DT2801 ADC/DAC card, was used to collect and analyse chronoam- perometric data.Results Poly pyrrole Fig. 3 shows chronoamperometric transients for 0.2 * 0.4 V and 0.2 * -0.4 V potential steps applied to a polypyrrole film (1.7 pm thick) in acetonitrile containing 0.1 mol dm-3 TEAP (solid lines). The 0.2 ++ 0.4 V potential steps are in the double-layer charging region of oxidized polypyrrole (see fig. 2) and can therefore be analysed as log I , us. t plots according to eqn (1) as shown previously. Owing to the difficulty in obtaining Ro from the intercept of such a plot,'" an alternative procedure was used here. The initial current following any potential step is given by eqn (16). IT( t = 0) = AE,te,/ R" (16) where R, is the total uncompensated resistance of the cell and will include Rs and a parallel combination of RE and R , .In this case, R, = Rs = Ro. Thus extrapolation ofH. Ma0 et al. 171 0 0.5 0 0 2 .o 4 .O time/s Fig. 3. Current transients from chronoamperometry on a 1.7 pm thick polypyrrole film in acetonitrile containing 0.1 mol dm-' TEAP. Dashed lines are case 3 simulati,ons with R,. = R , = Rr=3.7kCl, RS=0.80kR, QU=170pC,aQ~=129pF,a-'-~E,,,=0.82V,Eo =-0.20V and g = 0.54 (see text). ( a ) 0.2- 0.4 V; ( h ) 0.4- 0.2 V; ( c ) 0.2- -0.4 V; ( d ) -0.4- 0.2 V. the current transient to t = 0 allows the determination of R,. In practice this extrapola- tion is achieved by dividing the first experimental current point [at 7 ms for the data in fig. 3 ( a ) ] by a current decay factor determined from eqn ( 1 ) .Since the use of eqn (1) requires a knowledge of RF, which in turn requires knowledge of Ro, an iterative procedure must be used. First, Ro is estimated by assuming that the initial current ( r = 0) is equal to the first experimental current point. This value of Ro and eqn ( I ) are used to estimate RF from the slope of the log IT us. t plot. The current decay to the first point is calculated and a new R, is estimated. The procedure is repeated until Ro becomes constant. This procedure was tested on data generated using eqn (1); its accuracy requires a large number of the terms to be used, and 50 terms were routinely used. Analysis of the transients shown in fig. 3 ( a ) and ( b ) , yielded RF values of 3.2 and 4.2 k n , and R, values of 0.78 and 0.82 kR, respectively.C, was 129 pF. The average Ro value (800 0) is close to the uncompensated solution resistance previously determined for the electrode and cell used (ca. 700 0). The average RF value (3.7 kR) corresponds to a resistivity oc98 kR cm, which is in reasonable agreement with the value of 41 kR cm previously reported by this group. " The average parameters determined above were used in case 3 simulations to generate the theoretical curves shown in fig. 3 (dashed lines). Other parameters used in the simulations were obtained from the charge required to oxidize the film from -1.0 to +0.4 V ( QT,() ') and from C,( = Z7,0 J v ) as described by Feldberg.'6 Thus 6' - Ep,c = 0.82 V and aQ:= 129 p F . A g value of 0.54 was chosen to match approximately the anodic peak height of the theoretical cyclic voltammogram with that of the experimental voltammogram.The theoretical voltammogram generated using these parameters in the172 Ion Transport I 1 1 I 1 I I 1 1 0 2 .o 4.0 6.0 8.0 time/s Fig. 4. Current transient for a 1.0-0.9 V potential step on a 12 pm thick poly-MPMP' film in acetonitrile containing 0.1 mol dmP3 TEAP. The dashed line is a case 2 simulation with RE = 1.94 kn, R , = 10.6 kil, R, = 700 Cn and CF = 0.488 mF. A cyclic voltammogram (100 mV sC1) of a 0.3 p m thick poly-MPMP+ film is shown in the inset. Feldberg model is shown in fig. 2 (- - -). Note that i', E,,, and Q: do not need to be determined independently. The above combinations are sufficient to define the i us. E and Q us. E relationships. In this treatment we have neglected the decrease in RE at potentials below ca.0 V2' since R, is assumed to remain significantly higher than R E . However, in a typical experiment, RE becomes larger than Rs at potentials below ca. -0.2 V. In chronoam- perometry this is manifested predominantly as a decrease in the initial current for anodic steps from potentials below -0.2 V. We have not made any distinction between faradaic and capacitive currents and charges because we are not convinced that such a distinction is possible or reasonable.29 In this work, this distinction would only be required if the faradaic process was slow relative to the timescale of the chronoamperometric experiments ( 1- 14 s). We have seen no evidence of this. We have used Feldberg's model, which does distinguish between faradaic and capacitive currents (charges), merely because it yields a current (charge) us.potential function that approximates the behaviour of polypyrrole. Pol y - MPM P -+ A chronoamperometric transient for a 1.0-0.9 V potential step on a poly-MPMP' film (12 pm thick) in 0.1 mol dm ' TEAP/acetonitrile is shown in fig. 4. Analysis of this transient according to eqn ( 1 ) with R,( = Ro) determined from the initial current (use of the intercept of the log 1 us. t plot consistently produced poor estimates of R,) yielded an R, value of 2.3 kSZ and an RF value of 6.8 k 0 . This R, value is much higher than the uncompensated solution resistance (ca. 0.7 kiZ) indicating that R E and R , are both higher than R, (case 2). Calculation of R F and R , from these results using eqn (11) and (12) yielded values of 1.9 and 10.6 kR. Note that at this stage it is not possible to decide which of these values corresponds to RE or R , .A case 2 simulation using theseH. Ma0 et al. 173 Table 1. Electronic and ionic resistivities of poly- MPMP+ in 0.1 mol dm-' TEAP/acetonitrile from chronoamperometry (1.0-0.9 V) resistivity/kn cm film thickness/pm electronic ionic 4.0 7.3 52 5 .O 4.7 29 8.0 1.6 41 12 8.6 39 16 16 51 average 7.6 * 5.4 42*9 parameters yields a theoretical transient that matches the experimental data well [fig. 4 (- - -)I. A similarly good fit is obtained from eqn (1) using the above-noted values of R,(=R,) and RF. The film resistances obtained from this analysis (1.9 and 10.6 k a ) can be assigned to RE and R , , respectively, by comparison with known or estimated values for the electronic and ionic resistivity of poly-MPMP+.The ionic resistivity in 0.1 mol dmP3 TEAP/acetonitrile can be estimated from the counterion diffusion coefficient ( D ) using eqn (14). D is 5.4 x lo-'' cm2 s-' for I - and can be expected to be similar for ClO,. l 6 Thus the ionic resistivity of poly-MPMP+ will be ca. 90 kfl cm in 0.1 mol dm-3 TEAP/acetonitrile. We have recently measured the electronic resistivity of poly-MPMP+ as ca. 10 k n cm. For the film used in the present experiment these resistivities correspond to resistances of RE = 3 k a and R, = 20 kfl. The agreement with the resistances obtained by chronoamperometry is remarkable and leaves no doubt as to the assignment of these values. Electronic and ionic resistivities determined by chronoamperometry for a number of poly-MPMP+ films are presented in table 1.The independence of these values on film-thickness supports further the validity of these data. Clearly, chronoamperometry can be used to measure simultaneously both the electronic and ionic resistivity of these films. The value of the case 2 simulation here has been to confirm the approximate validity of eqn (1 1) and (12). The origin of the slight discrepancy between the theoretical curves generated from eqn ( l ) , (1 1) and (12), and those produced by the simulation is not clear. Discussion The first purpose of this paper is to demonstrate that the single-pore model is appropriate to the treatment of potentiostatic data for conducting polymer films.We have done this by ( a ) showing that the model yields current us. time functions that are in good agreement with those obtained experimentally, and (6) verifying that correct physical parameters (resistances) are obtained using the model. The excellent fit between the theoretical (simulated) curves and the experimental data shown in fig. 3 ( a ) , 3(b) and 4 is clear evidence that the model is appropriate. However, perhaps the best evidence appears in fig. 3(c) and (d). Here, the model has been applied to the full reduction and reoxidation of polypyrrole for the first time. The cathodic and anodic transients are quite different because of the decrease in ionic conductivity as the polymer is reduced, and the asymmetry (about the peak potential) of the capacitance us.potential behaviour of the polymer. When these factors were incorporated into the model, a similar difference between the simulated cathodic and174 Ion Transport Table 2. Counterion diffusion coefficients in polypyrrole, poly-MPMP+ and a pyrrole,.,-[ RU(bp),(pmp)C1]+ copolymer ( PP,,,RU) ion/solvent polypyrrole poly-MPMP+ PP, "Ru method ref. C10;/CH3CN ( 2 . 3 f 0.4) x (' (l.O*O.l)x lo-9'' 0.05 x ' 1 x lo-" 1.1 x lo-9 I -/CH,CN 5.4 x Cl-/H,O 1 x lo-' I - / H 2 0 1.5 x lo-' 3.5 x lo+ 3.3 x Fe ( C N) :-/ H 2 0 2.6 x lo-" CA CA CA CA RDV RDV IC CA IC RDV 14 this work 17 this work 16 16 16 14 14 16 a Average for 15 film in the thickness range 2-12 pm. ( b ) Average for 2 film in the thickness range 1-2 pm. ( c ) Prepared at 1.15 V from 1.7 mmol dm-, pyrrole, 0-2 pm.CA= chronoamperometry, RDV = rotating-disc voltammetry, IC = d.c. ionic conductivity measurement. anodic transients was observed. The change in ionic conductivity turned out to be the most important factor. The modified model yields a remarkably close fit to the experi- mental data [fig. 3 ( c ) and ( d ) ] considering the complexity of the experimental system. The fit is even more remarkable considering that all parameters used in the simulations were determined directly from experimental data and no adjustments were made. [The g parameter in eqn (13) was chosen rather arbitrarily but it has only a minor influence on the simulated transient.] Verification of some of the parameters obtained using the single-pore model [eqn ( l ) , (11) and (12)] is given in table 2 where they are compared with values obtained using other methods.To facilitate this comparison all ionic resistivities have been converted to counterion diffusion coefficients using eqn (14). Where meaningful com- parisons can be made, there is good agreement. Specifically, there is excellent agreement between chronoamperometry (using the single-pore model) and ionic conductivity measurements for CI- in polypyrrole in water. The diffusion coefficient for ClO, in poly-MPMP+ in acetonitrile determined by chronoamperometry is in good agreement with that determined for I - by rotating-disc voltammetry. It should be noted that the single-pore model also yielded the correct electronic resistance for poly-MPMP'. The second purpose of this paper is to discuss the influence of polymer structure, ion size/charge and solvent, on ion transport in pyrrole-based polymers.To facilitate this, our recent data are summarized in table 2. The following conclusions can be drawn. 1. Incorporation of a high concentration (5.6 mol dm-') of permanent cationic sites into polypyrrole (poly-MPMP') has a negligible effect on its permeability in acetonitrile, but significantly increases its permeability in water. This indicates that solvation and swelling of the polymer are much more significant in water than in acetonitrile. 2. Both polypyrrole and poly-MPMP' are much more permeable in water than in acetonitrile. This again is a strong indication that swelling of these polymers is more significant in water.3. The diffusion coefficient of ClO, in polypyrrole in acetonitrile increases with increasing film thickness. This has previously been reported by Osaka et a!." for polypyrrole in propylene carbonate and by usI4 for polypyrrole in water. It can be attributed to formation of a less dense polymer as the polymerization progresses, possibly due to a build-up of oligomers in the solution close to the electrode. This effect is mostH. Ma0 et al. 175 significant over the first few pm and is insignificant for films thicker than 10 pm. It is much more apparent in water than in acetonitrile, perhaps due to the higher degree of solvation/swelling in water. 4. Polypyrrole prepared from dilute pyrrole solutions (e.g. 1.7 mmol dm-') and at high potential ( e .g . 1.15 V) is much less permeable than polypyrrole prepared under 'normal' conditions (0.1-1 mol dm-' pyrrole, 0.8-0.9 V). 5. The permeability of polypyrrole can be significantly increased by the incorporation of a bulky metal complex (e.g. [Ru(bp),(pmp)Cl]+). This is an expected effect because metal-polypyridyl complex polymers are more permeable than polypyrrole.3' It is extremely significant from a practical point of view because it shows that the incorpor- ation of an electrocatalyst into polypyrrole can have the added benefit that the rate of diffusion of the substrate into the polymer will be increased. 6. The diffusion coefficients of ClO,, I - and C1- are all similar in poly-MPMP'. However, the diffusion coefficient of Fe(CN):- is almost four orders of magnitude lower.This is presumably due to both the larger size and the larger charge of this ion. Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and Memorial University of Newfoundland is gratefully acknowl- edged. We would also like to thank S. Feldberg for suggesting the use of finite difference simulations. Glossary constant relating faradaic charge to double-layer capacitance (V-') film capacitance capacitance of d / 100 thick layer of film (= C,/ 100) counterion diffusion coefficient film thickness potential us. formal potential point of zero charge of film formal potential potential difference across capacitor n magnitude of potential step potential difference between stars in fig. 1. = g F / RT empirical parameter added to Nernst equation total current current through capacitor n current through electronic resistor n current through ionic resistor n charge on capacitor n maximum faradaic charge for whole film ionic resistance of film ionic resistance of d / 100 thick layer of film (=RE/ 100) film resistance from eqn ( I ) ionic resistance of film ionic resistance of d / 100 thick layer of film (= R , / 100) ionic resistance between capacitors n and n + 1 uncompensated resistance from eqn (1) uncompensated solution resistance uncompensated resistance from initial current scan speed176 Ion Transport References 1 R.A. Bull, F-R. F. Fan and A. J. Bard, J. Electrochem. SOC., 1982, 129, 1009. 2 E. M. Genies, G. Bidan and A. F. Diaz, J. Electroanal. Chem., 1983, 149, 101.3 P. Burgmayer and R. W. Murray, J. Phys. Chem., 1984, 88, 2515. 4 G. Nagasubramanian, S. Di Stefan0 and J . Moacanin, J. Phys. Chem., 1986, 90, 4447. 5 S. H. Glarum and J. H. Marshall, J. Electrochem. SOC., 1987, 134, 142. 6 J. Tanguy, N. Mermilliod and M. Hoclet, J. Electrochem. Soc., 1987, 134, 795. 7 P. Marque, J. Roncali and F. Gamier, J. Electroanal. Chem., 1987, 218, 107. 8 T. Shimidzu, A. Ohtani, T. Iyoda and K. Honda, J. Electroanal. Chem., 1987, 224, 123. 9 J. B. Schlenoff and J. C. W. Chien, J. Am. Chem. Soc., 1987, 109, 6269. 10 1. Rubinstein, E. Sabatani and J. Rishpon, J. Electrochem. Soc., 1987, 134, 3078. 11 E. W. Tsai, T. Pajkossy, K. Rajeshwar and J. R. Reynolds, J. Phjx Chem., 1988, 92, 3560. 12 T. Osaka, K. Naoi and S . Ogano, J. Electrochem. Soc., 1988, 135, 1071. 13 R. M. Penner, L. S. Van Dyke and C. R. Martin, J. Phys. Chem., 1988, 92, 5274. 14 C. D. Paulse and P. G. Pickup, J. Phys. Chem., 1988, 92, 7002. 15 Handbook of Conducting Polymers, ed. T. A. Skotheim (Marcel Dekker, New York, 1986). 16 H. Mao and P. G. Pickup, J. Phys. Chem., 1989, 93, 6480. 17 J. Ochmanska and P. G. Pickup, J. Electroanal. Chem., in press. 18 H . Mao and P. G. Pickup, J. Electroanal, Chem., 1989, 265, 127. 19 R. De Levie, in Advances in Electrochemistry and Electrochemical Engineering, ed. P. Delahay and C. W. Tobias (Interscience, New York, 1967), vol. 6. 20 F. A. Posey and T. Morozumi, J. Electrochem. SOC., 1966, 113, 176. 21 B. J. Feldman, P. Burgmayer and R. W. Murray, J. Am. Chem. SOC., 1985, 107, 872. 22 S. W. Feldberg, Electroanal. Chem., 1969, 3, 199. 23 A. J. Bard and L. R. Faulkner, Electrochemical Methods- Fundamentals and Applications (Wiley, New 24 A. M. Johnson and J. Newman, J. Electrochem. Soc., 1971, 118, 510. 25 P. G. Pickup and R. A. Osteryoung, J. Electroanal. Chem., 1985, 195, 271. 26 S. W. Feldberg, J. Am. Chem. SOC., 1984, 106, 4671. 27 P. G . Pickup, W. Kutner, C. R. Leidner and R. W. Murray, J. Am. Chem. SOC., 1984, 106, 1991. 28 P. Burgrnayer and R. W. Murray, J. Am. Chem. SOC., 1982, 104, 6139. 29 P. G. Pickup and R. A. Osteryoung, J. Am. Chem. SOC., 1984, 106, 2294. 30 T. Osaka, K. Naoi, S. Ogano and S. Nakamura, J. Electrochem. Soc., 1987, 134, 2096. 31 T. Ikeda, R. Schmehl, P. Denisevich, K. Willman and R. W. Murray, J. Am. Chem. Soc., 1982, 104,2683. York, 1980). Paper 9/01982K; Received 8th May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800165

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1989, 88, 177-187 GENERAL DISCUSSION Dr K. Doblhofer ( ~ r ~ t z - ~ a 6 e r - I n ~ f ~ t u t , Berlin) said: Preparing homogeneously dis- persed metal particles in polymer films may be more difficult than suggested by Lyons et al. Hexachloroplatinate reduction on electrodes coated with polyvinyl- pyridinium films [see ref. (l)] leads to the production of spherical particles exclusively at the interface between the electrode and the polymer film. 1 A. Kowal, K. Doblhofer, S. Krause and G. Weinberg, J. Appl. Elecrrochem., 1987, 17, 1246. Dr M. E. G. Lyons (University of Dublin) replied: Dr Doblhofer is quite correct in stating that the preparation of homogeneously dispersed metal particles in polymer films is not a trivial procedure. It may be readily achieved in certain circumstances, however.For instance, Holdcroft and Funt’ have produced dispersions of Pt particles in poly- pyrrole films by electrochemical deposition. In this work the concentration profile of the particles was determined by Auger electron spectroscopy and it was shown that by suitable manipulation of the experimental procedure the metal particles could be deposited primarily at the polymer/solution interface, at the metal/polymer interface, or uniformly throughout the layer. Our theoretical studies have been pursued in tandem with a related experimental programme. A number of results have been examined with a view to the incorporation of metal or metal oxide particles (distributed both homogeneously and inhomogeneously) in polymeric matrices, where the latter are in the form of free-standing membranes or thin films deposited on support electrode surfaces.In this work we have made extensive use of the technique of electron microprobe analysis (EMPA) to examine the form of the particle concentration profile within the polymeric matrix. For the sake of brevity we will confine our remarks to the deposition of metal oxide particles in free-standing Nafion 117 membranes (nominal thickness 200 pm).’ We have shown that by variation of the reaction conditions one can precipitate metal oxide particles (e.g. RuOz - HzO, TiO- , Fe203) both at (one or both) membrane surfaces or homogeneously throughout the membrane. Fig. 1 ( a ) - ( d ) illustrates how this has been achieved for TiOz .3 Upon incorporation of Ti3+ from N,-stirred aqueous solution, the membrane develops an appreciable violet colouration after ca.15 min. Exposure of the hydrated Ti”-exchanged membrane to air or aerated water causes the membrane to become clear after ca. 30s, suggesting formation of the metal oxide within the membrane [fig. l(a)]. Heating the Ti3+-exchanged membrane in water to 150 “C under high pressure (i.e. in an autoclave) also results in a clear membrane. Again [fig. l ( b ) ] the concentration profile appears quite flat, indicating a homogeneous particle distribu- tion throughout the membrane. KOH. After 15-20min the membrane changes from its initial pale violet to a very dark blue colour, indicating possible formation of the higher oxides, Ti,03 (purple/violet) and Ti,OS (blue/black).However, after CLI. 60 min the membrane becomes opaque and white indicating TiO, formation. The EMPA profile [fig. l ( c ) ] indicates that after 30 min all the incorporated titanium is at or very near to the membrane surface. The deposition procedure suggested by Bard et d4 using methanol rather than aqueous solutions was also attempted and the resultant EMPA profile is outlined in fig. l ( d ) . However, the concentration of particles is not as sharply distributed near the membrane surfaces in this case. Hence, in conclusion, this example clearly shows that one can selectively precipitate metal oxide particles either homogeneously within a polymer matrix or within a very thin layer near the membrane surface. Precipitation was also effected by basic hydrolysis in aqueous 0.2 mol dm 177178 General Discussion -a 0 v) U a 0 distance Fig.1. 1 S. Holdcroft and B. L. Funt, J. ElectroanaL Chem., 1988, 240, 89. 2 A. Michas, J. M. Kelly, A. Durand, M. Pineri and J. M. D. Coey, J. Membr. Sci., 1986, 29, 239. 3 M. E. G. Lyons and D. E. McCormack, unpublished work. 4 A. J. Bard, H. Y. Liu and F. A. F. Fan, J. Phys. Chem., 1985, 89, 4418. Prof. W. J. Albery (Imperial College, London) said: I was very interested in the break that occurs between sections ( a ) and (6) of the results displayed in your fig. 6 . Section ( b ) has a gradient of 4 as opposed to the gradient of 1/2 for section ( a ) . In your paper you comment that the break arises at the point where the loading of the polymer is such that the spherical diffusion fields of the individual particles are beginning to overlap.However, when this happens, I would expect that the current would be less and not greater than that observed for section ( a ) . The overlapping diffusion fields would mean less material being transported to each individual particle. So first, have you any other explanation for the gradient of 4 and secondly, have you any further results at higher concentrations ?Genera 1 Discussion 179 Dr Lyons and Dr P. N. Bartlett (University of Warwick) replied: We agree with Prof. Albery that the break observed in fig. 6 of our paper is quite interesting. It is difficult to propose a fundamental theoretical explanation to account for the sharp rise in current at high catalyst loadings. We feel, however, that our result may be explained in the context of the experimental procedure used to deposit the Pt particles within the conducting polymer layer.The platinum particles were incorporated into the layer via cathodic electrodeposition. Our model assumes that the distribution of particles throughout the layer is homogeneous. This condition may not pertain when the catalyst loading is high. It is quite possible that under such conditions one may have a concentration of Pt particles in the outermost regions of the film near the polymer/ solution interface. Our experimental data indicate that hydrogen is consumed in a first-order reaction layer at the film surface, and that the spherical diffusion of substrate to the particles is rate determining. It is therefore reasonable to presume that the surface enrichment of catalytic particles would lead to an experimentally observable rate greater than that predicted from our model.We propose to examine the electrodeposition process at polypyrrole layers in some detail, and to examine the concentration profile of Pt particles within the layer as a function of catalyst loading using ESCA. _This should help to clarify the situation. Prof. T. J. Lewis (University College of North Wales, Bangor) said: In connection with the work reported by Lyons and co-workers, I ask whether there might be similarities between the situation where micro-particulate catalytic particles are held in a polymer matrix and electron transfer is required in catalysis and that in a photographic emulsion where silver grains are also held in a polymer matrix, albeit a hydrated one, and an electron transfer is a necessary step in the initiation of growth and development of the grains? Dr Lyons replied: Prof.Lewis has made a very valid point. There are striking similarities between the situation of polymer-bound microparticulate catalytic particles, and that of a photographic emulsion. Photographic materials consist of microcrystals of AgX (X = halide ion) typically ca. 100-1000 nm in size dispersed in a gelatin layer coated on a flat support. Absorption of light by a grain results in the generation of mobile electrons within the crystal lattice, and these photoelectrons are trapped at specific grain sites. One then has charge-transfer reactions involving the photoelectrons and Ag' ions to form Ag atoms.The Ag atoms form clusters, and for a grain to be subsequently developable one must have at least a four-atom cluster. Prof. P. G . Pickup (Memorial University of Newfoundland) (communicated): Con- cerning Dr Lyons' paper, in the oxidation of hydrogen at platinum particles in the polypyrrole layer (fig. 6 of your paper), is it possible that the reaction occurs pre- dominantly at particles on the surface of the polymer? Your model assumes that H? must diffuse through some polymer to reach a Pt particle. Can you distinguish between these two cases? Dr Lyons replied: The comment raised by Prof. Pickup is interesting. His question may be best answered by reference to the recent work reported by Schultze and co-workers' who examined oxygen and hydrogen evolution processes at polyaniline- coated metal electrodes.In this work a diffusion coefficient of H2 molecules within the polymer matrix of ca. lop5 cm2 s-l was estimated. Hence, assuming that a similar value pertains for polypyrrole films, it is reasonable to suppose that hydrogen molecules will diffuse through some polymer and react at a Pt particle located within the reaction layer near the polymer/solution interface, rather than react directly at a particle located at the polymer/solution interface. Finally, it is possible to distinguish between these two180 General Discussion cases, since in the latter situation (i.e. a purely surface reaction), one would simply have reaction at an array of Pt microelectrodes. This situation has been described in the literature.1 B. Pfeiffer, A. Thyssen and J. W. Schultze, J. Elecrroanal. Chem., 1989, 260, 393. Prof. P. G. Zambonin (Universitci di Bari) said: Starting from some findings of the paper presented by Dr Hillman I wish to make a comment which is likely to reflect a quite general problem. In the oxidation process of polybithiophene at electrolyte concentrations lower than 1 mol dmP3 the authors suggest a mechanism involving both anion ingress (BF,) and cation egress (Et,N+). Recent results obtained in our labora- tory'32 on the same polymer by using similar concentrations of a different electrolyte (LiC104) indicate a low anion mobility. The evidence for this claim is readily apparent from the charge-corrected XP spectra reported in fig.2, where the signal of the dopant ClO, is still present after reduction. However, other authors3 working on various materials, including Hillman's and our polymer-electrolyte systems, gave evidence that reduction is accompanied only by the expulsion of anions. According to the authors the phenomena were demonstrated by XPS data. In fact, the original spectra relevant to the Cl0,- and BFT-doped polythiophenes are not reported in the paper; however, it seems likely that no signal due to the two dopant anions was present in the reduced samples. Similar examples of controversial results are not rare in the literature. They seem to suggest that often, systems considered similar must actually be different, e.g. s 2s h I I I I 230 222 21L 206 binding energy/eV Fig. 2.XPS profiles of the S 2p+C12p region for samples of C10,-doped polybithiophene: a specimen of a pristine ( a ) and a specimen of reduced pristine ( b ) . Slight qualitative differences between the XP spectra can be explained' on the basis of different chemical environments.General Discussion 181 because of different polymer porosity induced by the deposition conditions, moisture content in the solvent, electrolyte and so on. It seems to be confirmed by various authors that galvanostatic or potentiostatic depositions produce different morphologies in the deposit and the electrolyte concentration can influence charge transport through the polymer as Hillman and co-workers found. At the present state of knowledge, it seems critical to search, select and consider judiciously many parameters, even those which are apparently minor.There is, otherwise, the real risk of producing good pieces of work on unreliable, or insufficiently characterized polymer systems. 1 C. Malitesta, G. Morea, L. Sabbatini and P. G. Zambonin, Poster, presented at Faraday Discussion 88. 2 C. Malitesta, G. Morea, L. Sabbatini and P. G. Zambonin, work in preparation. 3 G. Tourillon and F. Gamier, J. Electroanal. Chew., 1984, 161, 51, and references quoted therein. Dr A. R. Hillman (University ofBristo1) answered: Prof. Zambonin makes an impor- tant point: the structure and properties of polymer films can depend markedly on the polymerisation/deposition conditions, subsequent history and environment. In the work reported here, we focus on the effect of bathing electrolyte composition on polymer transport properties.We find significant effects regarding the sources/sinks of, for example, counterions. In previous work on thiophene-based systems, we have examined the role of polymerisation conditions (potential, monomer concentration, etc.). Not surprisingly, we found the rate, and sometimes, of course, the reaction to vary. The similarity of quantitative data, for example optical parameters, to those of other workers was noticeably dependent on the similarity of preparation conditions. In summary, we agree on the importance of the full reporting of experimental conditions and procedures. Mr X-B. Wang ( University College of North Wales, Bangor) (communicated): Accord- ing to Hillman et al. the ingress of the ClO, counterion into the PVF film during oxidation is slower than the egress of ClO, from the PVF film during reduction.Therefore, the oxidation process should be slower than the reduction process. Secondly, table 1 in their paper shows that the relative concentration of vinylferrocene units in the oxidized form of the polymer is smaller than that in the reduced form as the reduced form is thinner (i.e. the average distance between the vinylferrocene units is smaller). Based on these two pieces of data, the conclusion that may be drawn is that the oxidation peak current should be smaller than the reduction peak current. However, in fig. 1 of their paper, the oxidation peak is almost twice as big as the reduction peak. This is the reverse of what should be expected.Can the author please give an explanation for this result? Dr Hillman replied: There is no inconsistency in the observations. It is important here to note the positions of the peaks, as well as their heights. The low ionic content of the reduced PVF film results in an appreciable iR drop at the start of the oxidation process. Oxidation is thus ‘delayed’ until the more positive applied potentials. However, once oxidation begins, the influx of ions lowers the film resistance. There is then an overpotential driving the redox conversion, so the current rises rapidly. This delayed, but sharp current response as a consequence of ohmic drop effects has been observed and explained by Gottesfeld et al. for polyaniline films’ 1 Gottesfeld et al., J. Electroanal. Chem., 1989, 265, 15.Prof. M. Armand (E.N.S.E.E.G., St Martin d’Heres) said: When studying intercala- tion redox processes we have found that when using polyelectrolytes we could diff erenti- ate between the species involved in the redox processes. If a polymeric cationic PE with discrete and mobile anions is used, no electrochemical activity is observed; if a polymeric anionic PE with counter charges is used, the reduction process is always182 Genera 1 Discussion observed. Such experiments indicate that the ingress of cations for reduction processes in the solid state is always favoured over the egress of anions. We could not find any exception to this behaviour, although we did not test redox polymers such as PT or PF,. Dr Hillman replied: First, I should clarify one point.In those cases where we have been able to differentiate between the rates of ingress and egress of a given species, ingress has been the slower process. As one might expect, rates of ingress for different species are different. Comparison of different species, moving in opposite directions across the polymer/solution interface can thus produce either result. As an extreme case, proton motion in aqueous systems is sufficiently rapid that its transfer in either direction appears faster than, for example, solvent transfer in either direction. Dr 0. Haas (Paul Schener Institut, Villiger) added: We think that charge compensation in redox polymers is possible with anions and/or cations depending on the nature of the polymer. If the redox polymer has anion-exchanging properties the charge is most likely to be compensated by anions and vice versa.We have evidence for both examples, cation and anion insertion into redox polymers. Prof. A. L. Smith (Unilever Research, Port Sunlight Laboratory) commented: Rather than referring to ‘balancing activities’ it would be preferable to refer to uniformity of electrochemical potentials throughout the system. Dr Hillman replied: This is correct. However, the central issue we are trying to convey is the importance of activity effects. The message is to avoid thinking in terms of concentrations. Prof. R. W. Murray (University of North Carolina) said: I believe that the generality ‘slow ingress, rapid egress’ may have many exceptions. For example, in the loading, by potential sweeping, of Fe( CN)2-’4- into polyvinylpyridinium films, the Fe(CN)2-/4- goes in more rapidly than it egresses, and accumulates as Anson and Oyama showed.I think the key to this is that the Fe(CN)2-/4- ions are less mobile in the polymer than the electrolyte ions. So the generality in the paper may be limited to polymer redox processes where the net polymer ionic composition is not changed very much during the process observed. Dr Hillman replied: I think that an important point is made at the end of Prof. Murray’s remark. In the PVP. Rf-Fe(CN),3-’4- system, entry of the Fe(CN),”-/4- species results in a marked structural change, termed ‘electrostatic cross-linking’ by Anson. One is then not comparing ingress to and egress from the same polymer. Our studies have involved the exchange of simple ions/molecules which do not result in such effects.The ‘DIRE’ mechanism is postulated as an explanation for those systems for which we have data, and is intended to be tested. Dr H. H. Girault (University of Edinburgh) asked: How would you explain the rule you mentioned earlier that ingress motions are slower than egress motions? Do you think it is related to the difference of order between the polymer and the electrolyte and therefore to the difference of activation energy for ionic motion in the different phases? Dr Hillman replied: We should emphasise at this point that this is a common feature for the systems we have studied. Naturally, we seek a rule of general applicability, but would prefer to examine additional systems before stating that this is the rule itself, rather than a particular manifestation under the type of conditions employed here.General Discussion 183 Our suspicion is that the underlying principle requires consideration of the gradients of the electrochemical potential associated with the two processes.It would appear that activity effects, prevalent at the high charge site densities in the polymer films studied, cause these gradients to be greater when redox state switching 'instantaneously' generates high internal activities of species. This generates a large driving force for their expulsion. Conversely, the demand for species from solution (film deficiency) generates less extreme gradients and the ingress is slower. As stated in our reply to Prof. Murray's remark, for different species, transfer in both directions may be rapid or slow.We do not think that our polymers are particularly ordered systems, and thus cannot comment on your final point. Prof. Albery said: Like Dr Hillman we also have evidence for polythionine that changes in the oxidation or reduction of the coat involving the passage of current can take place on a different timescale to changes involving protonation. In our case' we have used a ring-disc electrode made of bismuth oxide to measure the proton fluxes at the polymer-electrolyte interface on the disc. The electrode works in the potentiometric mode and is capable of measuring fluxes as low as lo-'' mol dm-* s-'. To achieve this sensitivity one must have very little buffering capacity in the solution.Hence in our case we find that the protonic changes often lag behind the electronic changes because the supply of protons is limited by mass transport from the bulk of the solution. We have shown that C1- can be measured similarly using an Ag/AgCl electrode.2 I believe that the ring-disc electrode used in this way is a valuable method of identifying a species and measuring its flux at the polymer electrolyte interface. 1 W. J. Albery and A. R. Mount, J. Chem. SOC. Faraday Trans., 1, 1989, 85 1189. 2 W. J. Albery and A. R. Mount, J. Chem. SOC. Faraday Trans., 1, 1989, 85, 3717. Prof. Lewis said: My question refers to the paper by Hillman and co-workers. Apart from the need to establish electroneutrality the ingress of ions must be controlled, perhaps to a considerable extent, by the free volume available to accommodate them, small ions being more easily accommodated.Egress of ions into the electrolyte from the polymer would not be expected to be controlled in the same way. Are static and dynamic free-volume characteristics an important factor, therefore, in determining ion behaviour under cyclic conditions? Dr Hillman replied: It is our expectation that the behaviour of the relatively compact polymer films we have studied will be influenced strongly by free-volume effects. These are likely to be more readily observed under transient conditions. In extreme cases they may cause different species to be responsible for maintaining electroneutrality on different timescales. Prof. Murray commented: In response to the point raised about free-volume availabil- ity in electroactive polymers into which solvent and ions penetrate, the permeability of the polymer (as a membrane) to molecular species of various sizes gives a measure of the free-volume factor.We have observed in our electropolymerized films, molecular permeability to vary systematically with permeant size, so one can say, in the free-volume sense, free-volume requirements of a permeant have direct importance. Prof. W. J. Albery and Dr A. R. Mount (Imperial College, London) (communicated): We have further considered the polythionine results presented by Hillman et al. We wonder whether the existence of the maxima in the mass curves for the reduction of the coat in HClO, and the oxidation in acetic acid (fig. 6 and 7 of their paper) may be partly explained by the local consumption of electrolyte species at the polymer electrolyte interface.Writing the species in their scheme I as ThH' and LH;' we have in acetic acid that the overall reaction on oxidation is: LH:t+2A;o,,+2A,, -+ ThH'A,',,,+3HAc,,,,+2e.184 General Discussion If the A- at the surface becomes depleted, then the initial reaction becomes LH:'+2A:o,t + ThH'+A;,,,+ HAc,,,+2H:q+2e. There is an initial loss of H+ giving a decrease in mass followed by a slower uptake of HA when it becomes available. Similarly, for the reduction in HCIO, the overall reaction is: If the HCIO, becomes temporarily depleted then this reaction would be replaced by ThH'+C10,,o,,+2HC10,,,,,,+2e + LH~+C10,,,,,+2C10~,,,. Again the expulsion of ClO, carrying the current would lead to the loss of weight.There would then be a slower uptake of HCIO,. In our work with polythionine we find that the kinetics of the current transients are the same whether one is reducing or oxidising the coat. I believe that Dr Hillman found the same when he was at Imperial College; the current response to a series of small potential steps had similar kinetics at all potentials and in either direction. For these reasons we prefer the scheme outlined above, as opposed to the DIRE explanation at the end of Dr Hillman's paper. Dr Hillman replied: The key point is made in Prof. Albery's comment regarding the conditions under which his excellent potentiometric rotating ring-disc electrode detector is constrained to operate.Those RRDE experiments necessarily operate at or near neutral conditions in unbuffered media to obtain maximum potentiometric sensitivity. In contrast, our experiments have been conducted in media where there is considerable buffering capacity, typically 0.1-1 mol dm-3 total acetate within two pH units of the pK, for the weak acid case. An instructive calculation is to use an integrated form of Fick's law to obtain the total (integrated) amount of free counterion available from the solution as a function of time: j dt = 2(DAt/n)"?q, I where Cb is the bulk anion concentration and D A is its solution diffusion coefficient. Each redox site (total coverage T/mol cm -?) requires effective movement of one counter- ion during redox conversion. The timescale on which these species can be provided by the solution is thus given by 2( Dt/ T ) '''c,, = r.For example, suppose we take the rather extreme conditions (see below) of fig. 7 of our paper, 0.1 mol dm-' total acetate, p H ~ p K , , - 2 . Here, Cb is ca. O.Olc,, i.e. lop6 rnol cm-3. Inserting r = 5 x lo-" rnol cm--, we find that this can be done in ca. 1 s. The timescale of the experiment in fig. 7 (scan rate 5 mVs-') is an order of magnitude slower. Furthermore, this argument does not use the possibility of solution- HA dissoci- ation and proton motion away from the surface-both relatively rapid processes. This would raise the effective value of Cb by two orders of magnitude. In fact, we still find maxima in the mass curves for 1 mol dm--3 total acetate solutions near the pK, in slow scan voltammetric experiments, where the effective value of cb is very large and the available timescale is very long.For these reasons, we do not feel that the 'solution depletion' explanation fits our data. These conditions are rather different from those associated with the RRDE experiment described by Prof. Albery.General Discussion 185 Dr C. D’Silva ( Univesity College of North Wales, Bangor) (communicated): Hillman et al. claim that ‘PVF oxidation is accompanied by the ingress of one anion per redox site and some solvent (ca. 6-9 H 2 0 per redox site).’ This appears to be in direct contradiction to the result reported by Varineau and Buttry [ref. (10) of the same paper]. They reported that for oxidation the charge compensation is achieved by anion insertion (1 : 1) with essentially no accompanying solvent.Can the authors please give an explana- tion for this difference between results? Dr Hillman replied: There are two facts worth noting here. First, the PVF films studied by Buttry et al. are markedly thicker than ours. There is no a priori reason why thin and thick films should have the same structures and properties. Indeed, there is evidence for other systems that such structural differences do exist. Secondly, Buttry’s data relate to measurements made at a single electrolyte concentration. Thermodynamic considerations’ predict, in general, that solvent motion will accompany redox switching and ion transfer. Our data merely exemplify this point, and show that electrolyte concentration has an effect on the overall transfer process.This highlights the dangers inherent in interpreting single-concentration measurements. 1 S. Bruckenstein and A. R. Hillman, J. Phys. Chem., 1989, 92, 4837. Dr L. M. Peter (The University, Southampton) said to Professor Pickup: I notice that you have used Feldberg’s model’ in his simulation of the potential dependence of the ‘capacitance’ of polypyrrole. As eqn (13) of his paper shows, this interesting model clearly attributes part of the charge accumulated in the conducting polymer to an electrical double layer at the solid/solution interface-the polymer is treated, in fact, as an ideally polarisable porous metal with a defined point of zero charge, with the volume fraction of the metallic component increasing as oxidation proceeds. I should like to point out that frequency-resolved optical measurements have allowed us to distinguish between this non-Faradaic charge and the charge arising from Faradaic charge transfer [see our paper and ref.(2)]. In the case of polyaniline films, we have found an exact correspondence between the integrated a.c. admittance and the simul- taneous a.c. modulation of the optical density, indicating that the charging behaviour observed beyond the first pair of voltammetric peaks is entirely due to oxidation of the polymer. Preliminary results for polypyrrole films3 support the same conclusion, and we therefore believe that Feldberg’s model is inappropriate for these systems. It is worth pointing out that electrical measurements alone cannot provide the solution to problems of this kind.1 S. W. Feldberg, J. Am. Chem. SOC., 1984, 106, 4671. 2 R. S. Hutton, M. Kalaji and L. M. Peter, J. EIecrroanal. Chem., 1989, 270, 429. 3 L. M. Abrantes, J . Mesquita, M. Kalaji and L. M. Peter, unpublished results. Prof. Albery said: We have used the same transmission line model as you have. It is interesting that, as shown in eqn (11) of our paper, the distributed capacitance can include contributions from the Nernst term describing the redox centres on the polymer, the Donnan term describing the counterions and a Feldberg term describing the double- layer charging of the interface. Although the model includes the Feldberg term, for the reasons stated in our paper, we do not believe the Feldberg model. Prof. Pickup replied: As pointed out in our paper, we do not believe that Feldberg’s model provides a realistic description of polypyrrole electrochemistry.However, it does provide a convenient way of mathematically approximating the charge vs. potential behaviour of the polymer. Our use of a model originally applied to porous metallic electrodes appears to have created the impression that we view polypyrrole as a porous metal. This is not the case. We believe that it would be more appropriate to describe electrolyte-wetted oxidized186 Genera 1 Discussion polypyrrole as a solvent-swollen polyelectrolyte, similar to a redox polymer. This type of ionic conductor/electronic conductor composite film can be viewed as the superimpo- sition of two continua and theoretically treated without specifying its microstructure, as first demonstrated by Newman and Tobias.’ A finite transmission line describes the electrical behaviour of this generalized model.? 1 J.S. Newman and C. W. Tobias, J. Electrochem. Soc., 1962, 109, 1188. 2 A. M. Johnson and J. Newman, J. Electrochem. Soc., 1971 118, 510. Dr Lyons said: The work reported by Pickup and co-workers is most interesting. I can accept that the porous electrode model is especially suitable to analyse transients in potential regions where polypyrrole is electronically conducting. The situation pertain- ing in potential regions where full electronic conductivity has not been attained may be quite different, however. Has Prof. Pickup any intuitive feelings on the matter of the mechanism of charge percolation in this latter potential region? It may be noted that Martin and Penner’ have suggested that reduced polypyrrole behaves quite like a redox polymer material in these potential regions. Note that these workers have applied a diffusion-based model to analyse their complex impedance results.Specifically for the situation of reduced polypyrrole, it was shown that’ the concentration of supporting electrolyte within the polymer matrix was quite high (gryater than 1 mol drnp3) and therefore could carry the requisite migration current. 1 R. M. Penner and C. R. Martin, J. Phj-s. Chem., 1989, 93, 984. 2 R. M. Penner, L. S. Van Dyke and C. R. Martin, J. Phps. Chem., 1988, 92, 5274. Prof. Pickup replied: For reduced polypyrrole, below ca. -0.4 V, the electronic resistance will become greater than the ionic resistance. The latter will be maintained at a constant level by supporting electrolyte in the polymer matrix, as you say.Under these conditions I believe that charge transport occurs by an electron-hopping mechan- ism, as in a redox polymer, and can be treated using a diffusion model as done by Martin and co-workers. However, the behaviour of the film could also be modelled using the finite transmission line represented in our fig. 1, where R F would be related to the electron diffusion coefficient by the Nernst-Einstein relationship.’ 1 H. Mao and P. G. Pickup, J. Am. Chem. Soc., in press. Dr Doblhofer said: The potential step -0.4 to +0.2 V [fig. 3 ( d ) ] is, according to fig. 2 (of the same paper), applied to the coated electrode while the film is in the electronically and ionically insulating state. Other comparable experiments (e.g. fig. 2A of Zhong et al. ’), show a considerable initial rising current in the chromoamperometric transient, in which the ‘barrier’ properties are overcome. Why is this barrier behaviour of the film neither observed nor expected (theoretical curve) in the results shown in fig. 3 ( d ) of this paper? 1 C. Zhong, K. Doblhofer and G. Weinberg, Faradav Discuss. Chem. Soc., 1989, 88, 307. Prof. Pickup replied: At -0.4 V, under the conditions of our experiments, polypyrrole is oxidized to an extent of ca. 0.002 holes per pyrrole molecule and its electronic and ionic conductivities are both ca. lo-‘ K’ cm-’. It is not sufficiently insulating to exhibit the initial rising current characteristic of ‘barrier’ behaviour. At lower potentials, the film becomes more insulating and does exhibit a current peak in potential step experi- ments. A -0.6to +0.2 V potential step on the film used for our fig. 3 gave a current transient similar to that shown in your fig. 2A(i). Dr Hillman asked: Could you use your data to determine whether the oxidation and reduction processes proceed outwards from the electrode polymer interface or inwards from the polymer/electrolyte interface? Prof. Pickup replied: From our simulations we can obtain concentration profiles for the oxidized polymer sites as a function of time. The course of an oxidation (or reduction)General Discussion 187 depends on the relative magnitudes of the film’s ionic and electronic resistances. In the normal case, where the electronic resistance is much lower than the ionic resistance, the redox reaction begins at the polymer/solution interface. However, if the electronic resistance is highest, the reaction begins at the polymer/electrode interface. If the electronic and ionic reistances are equal then the reaction begins simultaneously at both interfaces.

ISSN:0301-7249    

DOI:10.1039/DC9898800177

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1989, 88, 189-201 A Simple General Model for Charge Transfer in Polymers T. John Lewis Institute of Molecular and Biomoleculur Electronics, University College of North Wales, Bangor, Gwynedd LL57 1 UT A general but simple model is described to account for charge transport which is applicable not only to insulating polymers but also to those that have been doped to higher levels of conductivity. Charge transport is considered to occur by tunnelling transitions between localized states where the reorganization energy is an essential part of the localization. Expressions are obtained for the transient, a.c. and d.c. conductivities which, in their temperature and time and frequency dependences, are in agreement with experimental results for a number of polymers.An important feature is that these dependences can be used to determine the energy distribution of the localized transport states. It is concluded that these states correspond to the Urbach states at the optical absorption band edge of the polymer. The doping role of metal electrodes is also discussed. Organic polymers are generally electrically insulating or semi-insulating solids, although there now exists a group which, by appropriate control of morphology and by doping with electroactive molecules, can be made highly conductive. The emphasis in recent years has been on the conjugated polymers; polyacetylene, for example, can be doped to metallic levels gf conductivity. This polymer is unique in that charge transport within the molecular chain can be conceived in terms of soliton and polaron motion which is a specific property of the bond alternation of the chain.A considerable literature on it, especially of a theoretical nature, now exists2 The success of this has tended to obscure the fact that the soliton and related transport modes are properties of the idealized chain, whereas the measured conductivity of a polymer represents a macroscopic property in which chain configuration, interchain contacts and overall morphology must be important. Doping, whether deliberate or adventitious, involves the accommodation of molecules and requires a local reorganiz- ation of the polymer which is quite unlike the doping of an elemental semiconductor crysta~.~ That dopants can have a general conductivity-inducing role is highlighted by the recent report by Thakur4 that conjugation is not necessary for conduction and that iodine doping of natural rubber (cis-polyisoprene) can increase the conductivity by 10 orders of magnitude and also by the earlier work on iodine-doping of polyethylene.’-’ In spite of the considerable advances in understanding charge transport in polyacety- lene at the molecular level, the overall modes of conduction in this and other polymeric solids are less well understood.The present objective is to develop a model for electron and hole transport which wi!l be applicable to a wide range of polymers. Many relevant and detailed models have already been proposed for non-crystalline solids, but the present general approach relying on concepts established in electrochemistry has the advantage of simplicity.At the molecular level, a polymer is an ordered sequence of monomer units. The degree of unsaturation and conjugation influences ‘free’ electron transport via the orbital overlap within a molecular chain, but it is worth emphasising that conjugation is not a requisite for delocalization and electron energy bands. Even a short a-bonded polyethyl- ene chain generates extended-state bands.8 189190 Charge Transfer in Polymers Fig. 1. Extended band and localized electron states of polymer chain. Table 1. Polymer energy states E, X polyethylene 8.8 -0.5 polypeptide 5.0 1 .o polyacenes 0 3.9 rruns- polyacetylene 1.6 3.1 The one-dimensional nature of electron transport in the molecular chain is obscured by the intervention of chain folds, kinks and ends and by the need for charge transfer via the weak van der Waals intermolecular bonds if long-range transport is to occur.The connectivity of the transport network is also influenced to a marked degree by the presence of dopant molecules. Not only will these generate carriers (electrons or holes) by ionizing the polymer but they will also reorganize the structure, possibly provide intermolecular links and set up a micro-field pattern influencing electron and hole motion. It has been mentioned that relatively few monomer units are needed before electronic energy bands characteristic of the extended polymer chain arise. Thus the conventional band picture shown in fig. 1 with valence and conduction bands is applicable as much to a-bonded polyethylene8 as to a,v- bonded polyacetylene.Typical electron affinities x and energy gaps, E, = E,- E,, are given in table 1. E , and E , may be viewed as defining molecular states for the polymer chain or for segments of it. Thus E , represents a donor state, and removal of an electron from it will produce an oxidized positive ‘molecular’ ion. Likewise electron addition at E , produces a reduced negative ‘molecular’ ion. Any disturbance of the periodicity of the potential along the polymer chain induces a localized energy state. This occurs at chain ends and kinks and, in polyacetylene, where bond alternation occurs, leads to soliton and polaron mid-gap states.? Localization also arises in the neighbourhood of ionized dopant molecules because of the Coulomb field.Charged States Because the energy gap E , is likely to be much greater than 1 eV (see table l ) , the intrinsic conductivity will be very low. Introduction of oxidizing or reducing agents, however, will generate holes or electrons in the valence or conduction bands and at the same time produce molecular ions. The residual conductivity of highly insulating polymers such as polyethylene and polypropylene has been attributed by Tavakoli and Hirsch’ to such impurities at the level of a few ppm. Deliberate doping by strongT. J. Lewis 191 oxidizing agents such as iodine or arsenic pentafluoride or by reducing agents such as alkali metals, will markedly increase the hole or electron populations. Whether charge transfer occurs or not on introducing dopant molecules to a polymer depends on the redox energies of the two systems since electrons will transfer from a high to a low redox energy.Thus while iodine and arsenic pentaffuoride oxidize polyacetylene to produce holes, only the latter will oxidize poly( p-phenylene) which has a lower redox energy (E,+x), by ca. 0.8 eV,'O than polyacetylene. It is interesting that polyethylene with a very low redox energy (ca. -9 eV) will interact weakly with iodine to give enhanced condu~tivity.~-~ It is possible that the reaction is at terminal vinyl groups. Band transport in a field direction will be hindered by adverse chain orientation, by chain kinks and ends and by the pinning action of relatively unscreened ionized dopant molecules. Sets of donor and acceptor states, localized at the band edges E, and E, of the polymer, will appear (fig.1). States in each set can exist in oxidized or reduced form and will have redox energies Ered, appropriately measured with respect to the band edge. There will also be a local reorganization of the matrix in response to the charge-polymer interaction. Reorganization serves to change the energy of the charge state and to restrict the motion of charge in it. This self-trapping or polaron formation is a key factor in determining charge transport in polymers as will be described below. Emin" has discussed the nature of the polaron generated, stressing that the degree of localization is particularly dependent on the quasi-one-dimensional nature of the poly- mer system. The polaron formation energy is the same as the so-called reorganization energy, A, a key factor in the solvation of ions in electrolytes.It has two components. The first, an inner sphere microscopic component is measured in terms of the force constants, kJ, and displacements of the bond lengths AxJ in the immediate vicinity of the charge. The energy is then C k,A2xJ. The second, outer-sphere macroscopic component, is due to a collective polarization response of the remaining surrounding medium treated in terms of the average dielectric properties. It can be written as e ' / 8 7 ~ ~ ~ a ( K,-d - K,') where KO, and K , are the optical and static dielectric constants and a is an effective radius for the polaron with charge *e. Both components are key elements in the theory of electron transfer in solution and have been extensively treated by Marcus" and others.In the case of polymers where strong localization can occur in a medium which is not strongly polarizable, the major contribution to A will come from the inner-sphere components which will be influenced by the low dimensionality of the polymer system. Doping may have an effect on A in altering both the polarizability of the medium and the force constants k,. The effect of the reorganization energy A on the energy states of the polymer is of considerable significance. Any localized state characterized by a redox energy Ered will have energies E , and E , in oxidized and reduced forms shifted as shown in fig. 2. The amount of shift A will depend on the environment of the site of the state.It will be different in amorphous and crystallite regions and at the polymer surface. It may also depend on whether E r e d refers to a donor or an acceptor centre; E , will be a positive ion in the former and E, a negative ion in the latter. The Coulombic field of an ionized dopant will also influence the value of A. Thus a distribution in A values can be expected. Of considerable importance for charge-transfer processes will be the fluctuations in A, and therefore in E, and E,, brought about by thermal motions. It is possible to show that for a fluctuation in thermal energy A E,, , the corresponding fluctuation in an energy state El to E is given by13 ( E l -E)'=4A1AEth. Since A, can be quite large (values of 1 eV or more have been suggested for many polymer s y s t e m ~ ' ~ ) , the fluctuation in AE, can be large compared with k,T. Since the192 Charge Transfer in Polymers Fig.2. Localized energy-state energies, and Ered is the distributions n ( E ) , E, and E, are oxidized and reduced redox energy of a donor or acceptor state of the polymer. state probability density for a thermal fluctuation AEth is exp (-A&/ k , T ) the probability density function for the fluctuation of a state Ei to a state E is given by Di( E ) = ( 4 7 ~ A ~ k , T ) - ’ ’ ~ exp [-( Ei - E)2/4Aik,T] which is normal with a variance (4AikBT)’”. Thus, as shown in fig. 2, there will be distributions of the localized E , and E, states. At temperatures below the quantum limit, a modified form of D i ( E ) will be required. Electron and Hole Transport When an electric field is applied the localizing potentials will be distorted and both the electron and hole and the dopant ion systems will be displaced. In the present treatment the ions are immobile.The movement of electrons and holes in the bands of extended states will be facile, but scattering by lattice interactions will occur to give a mobility e d 2 w / 8 h 2 , where T is a scattering time, 1 is the lattice spacing and w is the bandwidth. Application of the uncertainty principle WT > h then gives a lower limit of band mobility e d 2 w / 8 h which is of the order of lop4 m V-’ s-’ for narrow-band polymers. In most cases this will be an unlikely situation and the mobility is more likely to be determined by hopping transfer between localized states.Drift of charge in a field direction through localized states will involve intra- as well as inter-molecular transitions. For convenience we consider only donor doping which puts electrons in acceptor states near E , (fig. 1 ) . The conditions for an electron transition between two such states a and b is illustrated in fig. 3 ( a ) . Localization is controlled by the potential energy V ( r ) and initially the electron is in state a. E, and Eb are the redox energies of the two sites referred to a quasi-free state at E , and a is a reduced and b an oxidized acceptor.T. J. Lewis 193 Fig. 3. Pair states. ( a ) Likely form of the potential energy V( r ) . E, and Eb are the redox energies of the two acceptor states. ( b ) Simplified one-dimensional version [after ref.(16)]. The rate of transfer Pab from a to b at an energy E depends on wavefunction overlap expressed in terms of the transition matrix element T a b ( E ) of the appropriate Hamil- tonian. Using the Fermi Golden rule” Pab = 2 T / fl DL( E ) T:b( E ) @ ( E ) d E (2) I where Di( E ) is the probability density function, eqn (l), for a fluctuation of the reduced state at a to a state E, and Dg(E) is a corresponding function for the oxidized state at b. Integration is over all possible energies E. Electron-lattice coupling is taken care of by the reorganization energy A which broadens the levels at each site. Following Redi and HopfieldI6 it is possible, by combining eqn ( 1 ) and (2) to obtain the approximation 2?T/h exp {-[(A,+ A ~ ) - ( E ~ - E , ) ] 2 / 2 ~ 2 } T Z , b ( E m ) / ( 2 ~ ~ 2 ) ” 2 ( 3 ) Em = (EaAb+ E b h a ) / ( A a + A b ) (4) where and The approximation is valid provided Tab( E ) does not vary rapidly in the neighbourhood of Em, the energy of the most strongly contributing transition state. The evaluation o f Tab for other than the simplest potential well structure is difficult although the general form will be the product of an energy and a tunnelling transmission probability through the potential barrier at energy E [fig.3 ( a ) ] between the states. We adopt the simple representation [fig. 3 ( b ) ] consisting of a pair of weakly coupled one-dimensional semi-infinite square wells evaluated by Redi and Hopfield,16 as where rn is the electron mass, d is the width of each well and R is the separation.Additional conditions are (2rnd2E,/h2)’/2 >> 1 and (2rnR2Em/h2)’/2 >> 1; these are necessary to ensure strong location in each well and weak overlap. More realistic V ( r ) representations will lead to modified Em without loss of the essential ‘tunnelling’ characteristic of T a b . For transitions in which the displacement R is along the polymer backbone, the representation of fig. 3( 6) will be a reasonable approximation, but it will be less accurate for interchain transitions. Eqn (3) and (6) combined can be written in the form (7) Pab = vab exp (-qab) = z’ab exp (-2aabR) exp (- wab/ k, T )194 Charge Transfer in Polymers where, evaluating the constants and d and R are in 8, and Em, A,, Ah and kBT are in eV. Eqn (7) corresponds to the well known formula for hopping transport in amorphous solid^.'^ The frequency factor v&, often taken as an upper phonon frequency of ca.10" Hz, depends on the width of the wells, the most probable transition energy Em and the reorganization energies A,, Ab and is also temperature dependent. The activation energy Wab could in principle become zero when E, - Eb = A,+ A b . The very different roles of lattice vibrations in band and localized hopping transport should be noted. In the former they are responsible for scattering and a reduced mobility, while in the latter they provide energy for activated transport. The tunnelling factor exp ( -2aabR) is strongly dependent on R and on Em, the dominant transition state, eqn (4). Response to an Electric Field Charge in localized states will be distributed throughout the polymer matrix and the resultant polarization in the direction of an applied field F ( t ) at time t is where f; is the probability that a state is occupied by an electron at time t, ri is the distance between the site and some convenient origin and 8 is the angle between r, and F ( t ) .The summation is made over all donor D and acceptor A states in the polymer, including those of dopants and impurities. The polarization current is then ~ ( t ) = P ( r ) = -eV-' C j ; , cos 8, (12) I where the summation is over all states and where pij is the transition rate from state i to state j . f ( i I j ) is the conditional probability that state i is occupied if state j is occupied and is a measure of the correlation between states.A formal solution of this equation is unmanageable in practiceIx and approxima- tions are necessary. The usual one is the pair approximation in which each charge is confined almost entirely to transitions between a pair of states a, b which are spatially and energetically favourable and makes only rare transitions to other states. Defining f d and fb as the probabilities of occupancy of the two states of such a pair, f a = P b a f b - Pabfa (14) where f,+fb is effectively unity. Apart from the convenience of this assumption there are also physical arguments for it which relate to the reorganization processes already discussed. When a transition occurs from a to b, the centroid of the phonon system at a will relax from that appropriate to E, and begin to reform for that appropriate to E,.The electronic state E ( t ) at time t after the transition from a to b can be written as E ( t ) = E , + ( E , - E , ) exp ( - t / ~ ) (15)T. J. Lewis 195 where T is a relaxation time which will depend on the connectivity of the system. Thus the probability of a return transition from b to a will be enhanced during the early stages of the relaxation and pair states once formed are likely to continue. From eqn (12)-( 14) we find that the current contributed by a pair element in response to a field F ( t ) will be AJ = -e[f,(m) -fA(0)]R cos 0 @ab exp ( - m , b t ) ( 1 6 ) where =pab+pba and Ja<o), fd(m) are the initial and final values of Pb,/@ba. The application of a step field F at t = 0 will change the effective redox energy difference Eb- E, by an amount -eFR cos 8.Thus if P&, PLb represent the rates before and after the application of the field AJ = -eR COS 8 ( p ~ , t . c ) , b - P b a W ~ b ) eXp ( - U L b t ) / W , b . Pkb = Pat,{ 1 + eFR COS 8[ ( A , + At,) - (E, - Eb)]}/[2k~ T ( A, + hb)]. (17) If the field is weak ( F < lo7 V m-'), the transition rate in first order is (18) Substituting this expression for PLb in eqn (17) and summing over all pair states the current response to a step field F becomes where cos2 8 has been replaced by $, the average over all angles since a random orientation of elements can be expected. If the polymer is strongly oriented, J ( t ) will be anisotropic according to the orientation of F relative to the chain direction. The volume density of polymer pair states, N, is equal to i N : , where N, is the density of single states and P( R, P a b , Pb,) is the compound probability density that a pair state has transition parameters R, Pab, Pb, and is singly occupied.The integrand in eqn (19), considered as a function of q a b , qba [eqn (7)], has a very sharp maximum where these variables are equal to In (2v,,t) provided R2P( R, P a b , &a) varies smoothly in the region of the maximum. Then provided vabt >> 1, a condition likely to be readily satisfied in practice, and vab is at best a weak function of q a b , q b , where qab == q b a = In ( 2 v a b f ) . (21) An important conclusion is that the major contribution to J ( t ) at time t comes from pair states satisfying eqn ( 2 1 ) and thus having equal redox energies, E , = Eb .There are two classes of pair states; those between dopant and polymer states and those between only polymer states. The former are unlikely to have equal redox energies and will make a negligible contribution to J ( t ) . The initial charge transfer on doping will be between dopant molecule and proximal polymer site, but subsequently some diffusion of polymer charge away from the immediate dopant site can be expected and polymer pair states will be generated. In equilibrium the number of polymer pair states will equal the number of ionized dopants. The response to an alternating field F sin ot can be found from J ( I ) , eqn (20), using the Duhamel theorem,I9 to give dielectric functions196 Charge Transfer in Polymers -7 -9 - I 5 gJ -11 c: b 1 - -13 2 94 Fig.4. log ~ ( o ) versus frequency at temperatures indicated. (-) 70% trans-, 30% cis-polyacety- lene, ref. (21). (- -) I,-doped polyphenylacetylene, ref. (22). and qab = qba = In (2 vab/@ 1- (24) The major contribution to J ( t ) at time t or to a( 0) at a frequency w comes from polymer pair elements satisfying eqn (21) or (24). The conditional probability for single occupancy of a pair state in P involves the probability that one site of a pair is occupied while the other is unoccupied. Up to at least moderate levels of doping the probability for single occupancy of a pair state will be Pa+ P b , where % is the probability for occupancy of a single site. If the reduced states of the dopant molecules are at the single level Ed and the reduced polymer states are normally distributed about an energy Ea-Aa, then the probability that a polymer pair state is singly occupied can be expressed to a good approximation as provided ( E , - ha- Ed) >> kBT. It has been assumed that the donors are not strongly ionized.The other factor in P depends on the model chosen for the transitions. The random range model [see for example ref. (20)] requires the assumption that all pair sites are of equal energy and R is a random variable. The a.c. conductivity a(o) then varies with frequency and temperature as W T - ’ In4 L2w-l exp ( w a b / k , ~ ) ] , where w& is con- stant. The result is that a(o) varies approximately as over some 4 or 5 decades of frequency. The corresponding variation of J ( t ) would be t-0.86.The characteristics of typical polymers of which some insulating and semiconducting examples are shown in fig. 4-6 are not always of this form, although the more insulating ones often show reasonable agreement. For the semiconducting polymers (fig. 5 and 6 ) the In a(w)-frequency dependence varies from almost zero to unity as the frequency is increased and the dependence on temperature is strong. Since temperature dependence 2( N d / N s ) ” 2 exp [ - ( E a - Aa - Ed)/2kB TIT. J. Lewis r I I 1 1 I I -1 0 -1 2 -1 4 5 7 9 11 13 lo3 K / T Fig. 5. log a( o) versus T-' at constant frequency for polyacetylene from fig. 4. -10 t- I \ -12 - -14 I I I -1 ~~ L -2 0 2 4 197 Fig. 6. Response J ( t ) to step field +F, (+), followed by -F, (-).(-) polypropylene, ( a ) at 293 K and ( b ) at 373 K, ref. (9). (--) polyethylene terephthalate at 373 K, (c) carrier-injecting and ( d ) non-injecting electrodes, ref. (23).198 Charge Transfer in Polymers Fig. 7. Probability density function g(A,) for reduced acceptor states. The possible form of g for small A, is shown by the broken line. will be determined mainly by the factor exp (- Wab/ k, T) in eqn (7), it is reasonable to consider a model in which exp (-2aahR) is constant which will occur if the polymer sites are uniformly distributed. It is also reasonable to assume that the two sites of a pair have equivalent environments so that A, = hh = A. Thus from eqn (23) qab = qba = In (2 v,b/ 0) = 2aab R + Wab/ k~ T. (26) The appropriate form of P is found from the slope d (In a ) / d (In o) = s ( o ) of the experimental plots.From eqn (25), assuming that vab is a constant v, we find s ( w ) = 1 - d (In P ) / d q (27) and from eqn (7) and (10) dq = dA,/2kBT so that d (In P)/dA,=(l -S)/2kBT or P=Poexp[(l-S)A,/2kBT] (30) where Po is a normalization constant. E, - A,, and if these have a probability density distribution The polymer states to be considered are the reduced acceptor states with energies g(A,) = Go exp [ - m l ) l (31) P=2G~(Nd/Ns)"'eXp (-26) eXp [-(E,-h,-Ed)/2k~T] (32) (33) where 6 is to be determined then whence by comparison with eqn (30) we find where GL now includes the temperature-sensitive factor exp [-( E , - Ed)/2kBT]. An increase in o at constant T will, from eqn (7) and (24), mean a decrease in W and A,, while it corresponds experimentally to an increase in s from zero towards unity.Thus the expected form of g ( h , ) would be as in fig. 7. If at high frequencies a(o) tended g = GA exp (-Sh,/4k~T)T. J. Lewis 199 to become independent of w again (s-+O) then g(A,) would reach a limit at small A,. For a chosen frequency, an increase in T increases A,, eqn (7) and (24), and will cause a decrease in s towards zero provided the general form of g(A,) does not alter with T. This condition can be explored from log a ( w ) us. T-' plots at constant frequency. From eqn (23) where p is the thermal expansion coefficient of the polymer accounting for the change of R with T and (Ed- Ed)/kBT is assumed to be constant. Pike24 has described how ( E , - Ed) will be influenced by the Coulombic interaction energy - e 2 / ( ' T T E T , ~ ) , where Tad is the separation between donor and polymer sites.( E , - Ed) will increase with temperature because Tad will increase. Thus ( E , - Ed)/ kBT is likely to be only weakly dependent on T. At constant o, an increase in T will mean that pair states of increased A, will become effective and according to fig. 7 will cause a decrease in s. Thus ds/dT will be negative. According to eqn (34), d (In a ) / d (1/ T) will not only decrease with increasing T-' at constant frequency but (ignoring the term in p ) may also go to zero as T-' approaches (In 2v/w -2aR) I ds/dTI. Moreover this situation will be reached at lower T-' as w increases. This behaviour is illustrated in fig.5 where the term in p probably prevents zero slope. It is clear that a single-valued activation energy indepen- dent of T is not to be expected even at very low frequencies. us, J ( t ) will vary as t-'. The characteristics for the polymers in fig. 6 after subtracting a steady-state current (see below) indicate a constant s = 1 over a long timescale and thus a simple exponential for the distribution g(A,). The form of g(A,), eqn (33), is strikingly similar to the Urbach optical absorption edge found for amorphous solids,'5 which is believed to arise from a distribution of states extending out from the fundamental absorption band edge. The distribution of A, is measured from E, = Em which, provided the conditions of eqn (6) are satisfied, can be close to the extended-state band edge of the polymer.Thus the distribution of reorganization energies could be the same as that of the Urbach edge, and useful comparison between studies of optical absorption and photoconductivity at the absorp- tion edge and the corresponding a.c. conductivity measured could be made. Examples of absorption tails for a number of polymers have been given by several authors, that by Orenstein" for trans-(CH). has a tail that extends a considerable way into the band-gap. The model should be readily applicable to soliton- or bi-polaron-supporting poly- mers. If inter-soliton hopping occurs the redox energy of the dominant transition state Em would correspond to the mid-gap energy of the soliton, and the linear extent of the soliton state would correspond roughly to the width d of the well.At high levels of doping, inter-soliton hopping should become more difficult because the probability for single occupancy of a soliton pair state will decrease and hopping conductivity would saturate. Corresponding to a(o) Steady Currents The response at very low frequencies or long times involves pair states with very low transition rates. As a consequence the rare transitions from pair states into new states which have been neglected become more significant. Without the restrictions imposed by the frequency or time relationships given in eqn (24) and (21), all transitions will contribute to the d.c. conductivity. Following Mott and Gurney,?' the effective drift velocity of a charge moving from site a to site b in a field F will be 2Rp,, sinh (eRF6 cos 0) where, as earlier, we have200 Charge Transfer in Polymers assumed that the effect of the field is manifest only in wab [eqn ( l o ) ] and 4 = averaging over a random orientation of R, becomes 2eR24pab/3.The d.c. conductivity can now be expressed as [ A , + h b - ( E , - E b ) ] / [ 2 k ~ T ( h , + h b ) ] . If eRF<< kBT the mobility Of this charge, after R 2 4 p a b P ( E , , Eb, A , , A b , R)dE,dEhdA,dhbdR ( 3 5 ) where P(E,, E b , A,, hb R ) is the conditional probability density that the sites a and b have the parameters E,, Eb, A, and hb, and 9 is the probability that site a is occupied and site b is empty. We assume that the sites are uniformly distributed in space (R is constant) and that occupancy of site a implies that site b is empty so that 9= ( N , / NS)”’ exp 1-( E, - A, - &)/kBT], where Ef is the Fermi energy of the system.If E,, Eb, A,, hb are independent variables and each is distributed normally with a mean f i , then, provided &#q& varies smoothly in the neighbourhood of each maximum, a reasonable approximation will be CTDC = N,e2R2p,bg(3k~T) (36) where we have assumed E, = Eb = E and h, = i b = 1 so that 4 = (2k,T)-’. Using eqn (7)-(10) p,b=2.4~ 1020[Ed6(2k,TA)’”]-’ eXp [-(1.8E1’’R +h/2kBT)] 9 = ( ND/ N,) eXp [ - ( E - - &)/ k~ TI. (37) ( 3 8 ) (39) We now find, if 9 is independent of T, d (In CTD,)/d ( r - ’ ) = - [ h / 2 k B - ~ T + 2 P ( l -0.9E1/2R)T2]. The effective activation energy of uDC thus tends to a constant value h at low T (high T-I). At high temperatures the activation energy can either increase or decrease with T according to the sign of ( 1 -0.9E’”R).The assumption that A, is distributed normally means that g(A,), fig. 7, also has a normal distribution. This is plausible and implies that s could be negative for A, sufficiently small, which would correspond to J ( t ) at very short times or o ( w ) at very high frequencies. The low-temperature limit of constant activation energy A should be compared with the zero-frequency extrapolation of a.c. behaviour, eqn (34). Replacing [log (2 v / w ) - 2aR] in eqn (34) by A(@, T)/2kB where A(w, T ) is the selected value at a given w and T, and ignoring terms in p, the two activation energies become [ - T ds/d TA ( w , T)/2kB - $( 1 - s) TI and ( A / 2 k ~ -;T) and at high enough temperatures they should become the same.In practice it may be difficult to distinguish a true steady d.c. current from J ( t ) because at times long after the application of a step field, the response will come from pair elements-for which q = In 2ut, eqn ( 2 1 ) , and these will have effective A(?, T ) approaching A. The concepts are also applicable to conditions at metal electrode-polymer contacts. Charge transfer occurs at these whether it be in passive contact ~harging,~’.~’.’~ in high-field induced conduction of insulating polymers or in electrochemical redox doping of conducting ones. The metal electrode is equivalent to a strong doping source capable of oxidizing or reducing polymer states to some distance inside the polymer.The situation for a donor contact in which the work function 4 of the metal was less than that of the polymer [ ca. (x + E,/2), see fig. 11 would be that electrons populated acceptor states near E,. If at the same time ( 4 - x) was small, a high proportion of the acceptor states near the interface, including those of small A,, could be populated, although under low a.c. fields bulk states of small A, would not be greatly occupied. Then a(o)T. J. Lewis 201 at high frequency (small A,) would be generated by the interface states and be metal- dependent. Under high fields the high density of populated interface states would become the source of steady current (fig. 6 ) . The model thus provides a general basis for charge transport in polymers.It can be developed further to cover interfacial and surface mechanisms and also the situation, at high doping levels, where electronic transitions through the dopant network itself become likely. Inclusion of thermally induced fluctuations in the reorganization energy suggests that it would also apply to problems of ion transport and could give new insights into conduction in polymer electrolytes. References 1 N. Basescu, Z-X. Liu, D. Moses, A. J. Heeger, H. Naarmann and N. Theophilou, Nature (London), 1987, 327, 403. 2 A. J. Heeger, S. Kivelson, J. R. Schrieffer and W-P. Su, Rev. Mod. Phys., 1988, 60, 781. 3 D. C. Bott, in Handbook of Conducting Polymers, ed. T. J. Skotheim (Marcel Dekker, New York, 1986), 4 M. Thakur, Macromolecules, 1988, 21, 661. 5 D. W.Swan, J, Appl. Phys., 1967, 38, 5051; 5058. 6 T. J . Lewis and D. M. Taylor, J. Phys. D, 1972, 5 , 1664. 7 G. T. Jones and T. J. Lewis, Symp. Faraday SOC., 1974, 9, 192. 8 W. L,. McCubbin, J. Chem. Phys., 1965, 43, 983. 9 M. Tavakoli and J. Hirsch, J. Phys. 0, 1988, 21, 454. vol. 2, chap. 33, p. 1191. 10 R. L. Elsenbaumer and L. W. Shacklette, in Handbook of Conducting Polymers, ed. T. J . Skotheim (Marcel Dekker, New York, 1986), vol. 1, chap. 7, p. 213. 11 D. Emin, in Electronic and Structural Properties of Amorphous Semiconductors, ed. P. G . Le Comber and J. Mort (Academic Press, London, 1973), chap. 7, p. 261. 12 R. A. Marcus, J. Chem. Phys., 1965, 43, 679. 13 S. R. Morrison, Electrochemistry at Semiconductor and Oxidised Metal Electrodes (Plenum Press, New 14 C. B. Duke, Surf: Sci., 1978, 70, 674. 15 L. I . Schiff, Quantum Mechanics (McGraw-Hill, New York, 2nd edn, 1955), p. 199. 16 M. Redi and J. J. Hopfield, J. Chem. Phys., 1980, 72, 6651. 17 N . F. Mott, Adu. Phys., 1967, 16, 49 18 J. 1. Beeby and T. M. Heyes, J. Phys. C , 1971, 4, 1757. 19 V. V. Daniel, Dielectric Relaxation (Academic Press, London, 1967), p. 68. 20 N. F. Mott and E. A. Davis, Electronic Processes in Non-crystalline Alaterials (Oxford University Press, Oxford, 2nd edn, 1979). 21 A. J. Epstein, in Handbook of Conducting Polymers, ed. T. J. Skotheim (Marcel Dekker, New York, 1986), vol. 2, chap. 29, p. 1068. 22 A. P. Bhatt, W. A. Anderson and P. Ehrlich, Solid State Commun., 1983, 47, 997. 23 J. Hirsch, A. Y-Y. KO and A. Y. Irfan, IEEE Trans. Electr. Insul., 1984, EI-19, 190. 24 G. E. Pike, Phjx Rev. B, 1972, 6, 1572. 25 J . Tauc, in Amorphous and Liquid Semiconductors, ed. J. Tauc (Plenum Press, London, 1974), chap. 4, p. 178. 26 J. Orenstein, Handboclk of Conducting Polvmers, ed. T. J. Skotheim (Marcel Dekker, New York, 1986), vol. 2, chap. 36, p. 1320. 27 N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (University Press, Oxford, 2nd edn, 1948), p. 43. 28 T. J. Lewis, IEEE Trans. Elecr. Insul., 1086, EI-21, 289. 29 C. B. Duke and T. J. Fabish, J. Appl. P h j x , 1978, 49, 315. York, 1980), p. 37. Paper 9/02282A; Received 26th May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800189

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC. 1989, 88, 203-211 Charge Transfer in Conducting Polymers Striving toward Intrinsic Properties Alan J. Heeger Department of Physics, Institute for Polymers and Organic Solids, University of California, Santa Barbara, California 93106, U.S.A. A principal goal of the field of conducting polymers is to strive for advances in materials quality that will enable the exploration of the intrinsic electrical properties. In this context, we summarize the requirements for achieving high performance conducting polymers with electrical conductivities greater than that of copper. To avoid localization onto one-dimensioal polymer chains (with bandwidth 4t,), interchain charge transfer (f3d) is required. For crystalline materials in which the chains have precise phase order, the mean distance along the chain between defects must be L/ucrys,nlllne >> to/ t,, .In the case where there is good chain extension and good chain alignment, but when that alignment is nematic (i.e. with random interchain phase along the chain), the criterion is more severe: L/a,,,,,,, >> ( t O / j j d ) I . When the appropriate inequality is satisfied the transport is that of an anisotropic three-dimensional metal, and the conductivity will increase in proportion to the mean distance between chain interruptions, cross-links, sp3 defects etc. If the mean defect scattering time, TClef = ( L / OF), becomes sufficiently long that phonon scattering limits the mean free path, then the conductivity takes on a metallic temperature dependence, and the system is in the clean and intrinsic transport limit.1. Introduction Although improvement of solid-state properties through higher-quality materials is a general goal of materials science, until recently there had been little optimism that this would be successful for the electrical conductivity of polymers. The reason for this is that in order to achieve 'metallic' behaviour, doping to a relatively high level is required; the resulting charged impurities might then be expected to cause scattering and localiz- ation. Thus, the need for doping would negate any improvement toward macromolecular chain perfection. Recent studies have shown that this is not the case in polyacetylene; improvements in synthesis and orientation have resulted in electrical conductivities as high as los S ~ m - ' .' - ~ Furthermore, the absence of a metallic temperature dependence with resistivity decreasing as the temperature is lowered'-4 implies that the measured conduc- tivity is still limited by material imperfections. Consequently, it is quite clear that the intrinsic electrical conductivity of polyacetylene and, by implication, of other conducting polymers, may be significantly greater than that of copper. Why is the high concentration of (partially) disordered charged impurities so ineffective in scattering the conduction electrons? The answer is that in a very funda- mental sense, conducting polymers are self-organizing systems. The stiff conjugated chains self-consistently force the dopant counterions to go into channels or planes within the structure. The details of this self-organization have been demonstrated in an in situ study of the evolution of the structure of polyacetylerie during electrochemical doping.' Because of this self-organization, the charged dopant ions are spatially removed from 203204 Striving Towards Intrinsic Properties the quasi-one-dimensional conduction path, and resistive back-scattering is suppressed. The situation is analogous to that which occurs in artificially layered semiconductors (quantum-well heterostructures) where the high-mobility carriers are confined to layers spatially separated from the alternate layers which contain the dopant ions.This effect is enhanced for conducting polymers by a combination of the ariisotropic screening and the quasi-one-dimensional nature of the transport6 (only the 2 k , Fourier component of the scattering potential is important).The conclusion is that in high-quality chain-aligned materials, scattering from the charged counterion impurities can essentially be ignored.6 Other limitations (molecular weight, interchain packing and order, sp’ defect density etc.) can be removed by a combination of improvements in synthesis and by better processing, i.e. by the methodology of materials science. A principal goal of the field of conducting polymers is, therefore, to strive for advances in materials quality that will enable the exploration of the intrinsic electrical properties. With knowledge of these intrinsic properties, we will be in a position to begin to understand in detail the fundamental transport processes in this class of materials.2. Conducting Polymers: ‘Dirty’ Conductors or True Metals With Delocalized Carriers? The electrical conductivity (u) of a metal can be expressed as a product of the number of carriers per unit volume ( n ) times the carrier mobility ( p ) : where e is the electronic charge. To optimize the conductivity, one wants to achieve the highest carrier density, and one wants these carriers to have high mobility. In the context of nearly-free electron theory, where T is the mean scattering time and m” is the carrier effective mass. Since the carrier densities are of the order of 10” or greater, and since these carriers go into relatively broad energy bands, the Pauli exclusion principle demands that they form a degenerate Fermi gas.Thus, the typical carrier velocity is the Fermi velocity, uF, of the order of 10’ cm s-’. Consequently, the mean distance between scattering events (the ‘mean free path’) is given by The shortest possible mean free path is one lattice constant (a); in the limit where A = a, the transport is better described as due to hopping of localized carriers, rather than scattering of free carriers. If we consider the hopping limit (mean free path of about one carbon-carbon distance), A == 10 ’ cm, then T = 2 x 10 To get a moderately high density of carriers per unit volume is relatively easy. For example in polyacetylene, a doping level of 10% per carbon can be achieved, correspond- ing to a carrier concentration of ca. 4 x 10” cm-3. This is a typical number for conducting polymers such as polyacetylene, poly(paraphenylenevinylene), poly(paraphenylene), etc.The addition of side-chains, as in the poly(3-alkylthiophenes), reduces the maximum carrier density somewhat simply because of the smaller fractional volume occupied by the conjugated backbones. For the emeraldine salt of polyaniline, there is one carrier per (B-NH-B-NH)+ repeat unit; again n = 5 x 10”. We conclude that in the hopping limit, the conductivity of a typical conducting polymer would be given by eqn ( 1 ) with n = 10’’ cm-’ and p (0.2 cm’ V-’ s-’, i.e. u < 30 S cm-’. For maximum doping levels, the smaller conductivities that are often reported in systems such as polypyrrole, polyaniline, etc., imply that the carriers are truly localized and that the transport is via thermally activated hopping, as for example by means of the famous phonon-assisted variable-range hopping mechanism.’ u = nep (1) p = eT/m” (2) A = V ~ T .(3) s and p = 0.2 cm’ V s-’.A. J. Heeger 205 This elementary analysis of the electrical conductivity demonstrates that there are two important classes of heavily doped polymers. ( 1 ) ‘Dirty’ conductors with electrical conductivities of the order of 1 S cm-’ or less. Such systems can be achieved with relative ease; all that is required is a moderately high density of carriers. Carrier delocalization is neither required nor implied by such values. In such cases, the heavily doped polymers are highly disordered systems which can be considered as examples of the ‘Fermi glass’ concept.* Indeed, n-conjugation is not even needed to achieve this low level of conductivity in polymers.’ (2) True metals in which the carrier mean free path is at least a few lattice constants.This only becomes relevant for those polymers in which the electrical conductivities are in excess of several hundred S cm-’. In such systems, the molecular weight is sufficiently high, interchain order is sufficiently good, and the defect density is sufficiently low that delocalization occurs leading to ‘free’ metallic carriers with mean free paths much greater than a carbon-carbon repeat unit. Note that the same ‘polymer’ could fit into both categories, depending upon how it was synthesized and processed. Obvious examples are conjugated systems made by the precursor polymer route, e.g.polyacetylene made by the Durham route” and polyphenyl- enevinylene (and its derivatives).’ ’ If the amorphous precursor polymers are simply converted to the conjugated polymers, these are disordered systems dominated by localization and hopping, and with electrical conductivities of a few S cm-’. If processed during conversion so as to achieve significant chain extension and chain alignment, these become true metals with delocalized carriers and electrical conductivities of several thousands of S cm-’. 3. The Intrinsic Electrical Conductivity: Mean Free Path Limited by Phonon Scattering When the conjugation length is sufficiently large, the conductivity will reach the intrinsic level, and the electronic mean free path will no longer be limited by static defects and imperfections.In this ‘clean’ limit, the electron mean free path is determined by phonon scattering, i.e. by scattering from the deviations from the regular periodic atomic spacings due to thermal motion of the atoms about their ideal equilibrium configurations. The intrinsic back-scattering rate resulting from thermal phonons has been calcu- lated:6 ( 1/ T ~ ~ ) =. [ 8a’/ Mwoto] exp - ( hao/ k , T ) (4) where w, is the frequency of the 2kF phonon, a is the electron-phonon coupling constant, M is the mass of the repeat unit (e.g. the CH mass in polyacetylene) and to == 2.5-3 eV is the n-electron transfer matrix element (4t, is the v-band width). On substitution of Tph into eqn ( 1 ) and (2) with the effective mass appropriate for a nearly half-filled one-dimensional energy band, m* = (nh/aV,), one obtains gII: A similar exponential temperature dependence, exp ( Amo/ k , T ) , is expected for all quasi-one-dimensional polymers; the important parameters are the carrier density ( n ) , the bandwidth (4t,) and Ao,/k,T.For polyacetylene, 0 a 4 . 1 eV &’ and hwO= 0.12 eV. Using these values, we estimate a room-temperature value for the intrinsic conductivity of metallic trans-(CH), which is 2 x lo6 S cm-’, about four times greater than that of copper. In the intrinsic regime, the temperature dependence will be dominated by the exponential factor. Since hwo/ k , T =: 4-5 at room temperature, decreasing the tem- perature to 150 K would lead to an increase in uII by more than a factor of 50-loo! This large vdue for tiwo/kHT originates in the stiffness of the carbon-carbon bond.206 I‘ Striving Towards Intrinsic Properties I ‘ I i l I I Fig.1. An array of aligned polymer chains, each with a few defects, as in an oriented fibre. The defects might be either chain ends or sp3 defects, etc. which interrupt the r-conjugation. i However, since even the best materials produced to date, with crll (300 K) in the range (0.2-1) x los S cm-’, show no indication of this strong temperature dependence,’-l it is clear that the intrinsic room-temperature conductivity of polyacetylene and all other conducting polymers is still severely limited by the quality of the material. I I ‘ I 4. An Analysis of Limiting Factors: What Are the Requirements? I I Dramatic improvements in the physical properties of polymers through chain extension and chain alignment are not unfamiliar in polymer science.For example, ordinary polyethylene is useful in a wide variety of low-value applications, but it is certainly not considered a high-performance material. On the other hand, ultra-high molecular weight polyethylene, which has been chain aligned through gel-spinning and subsequent tensile drawing is one of the strongest materials known;” in this case, the measured strength approaches the intrinsic theoretical limit set by the strength of the carbon-carbon bond. The question before us in the field of conducting polymers is whether or not we can reach the same level. Can we make conducting polymers with sufficient quality that the mean-free-path is limited by the intrinsic scattering from thermal vibrations of the lattice (phonons)? The principal problem is that of localization; quasi-one-dimensional electronic systems are especially prone to localization of electronic states due to disorder.The origin of this tendency to localize is easy to understand. Consider an array of polymer chains, each with a few defects, as shown schematically in fig. 1 . We imagine the defect density (e.g. sp’ sites) to be such that the typical distance, L, between defects is many lattice sites, but is still considerably less than the physical molecular weight. A carrier on a typical chain will then move with the Fermi velocity until it comes to such a defect at which point it back-scatters and moves in the opposite direction until it back-scatters from the next defect on the same chain, etc.This multiple resonant scattering localizes the electronic wave-function; the resulting ‘conjugation length’ is much less than the chain length. The result is localization with carrier transport limited by phonon-assisted hopping.’ Note that in this case, the conductivity is inherently small and would go to zerc as T - , 0, in contrast to the behaviour of a metal. To avoid the localization inherent to one-dimensional systems, one must have the possibility of inter-chain charge transfer. In the case of relatively high molecular weight and relatively few sp’ defects, even weak inter-chain coupling ( r3d < 0.1 eV) is sufficientA. J. Heeger 207 to avoid one-dimensional localization. The problem is essentially three-dimensional so long as there is a high probability that an electron will have diffused to another chain between scattering events.If T is the back-scattering lifetime and P( t ) is the probability that an electron which was initially on a specific chain will still be on that chain a time t later, then the criterion is6 P(T)<< 1. (6) For scattering off chain-breaks separated by a mean distance L, T = L/uF = ( a / u , ) x , where x = L/a. For a well ordered crystalline material in which the chains have precise phase order, the inter-chain diffusion is a coherent process. In this case, the inequality (8) (below) is satisfied so long as x >> ( t o / f3d). (7) Thus, for any value of t 3 d , the transport becomes three-dimensional when the material is sufficiently good that6 L/ a Icrystalline >> f3d - (8) In the case where there is good chain extension and good chain alignment, but when that alignment is nematic ( i e . with random inter-chain phase along the chain), the criterion is more severe6 This is a much more stringent condition than expressed in eqn (8).For example, in polyacetylene,'3 ( t 3 d / r,) = 0.03, so that the case of coherent inter-chain motion (8) would require L / a >> 30, whereas in the incoherent case the chain-defect concentration would have to be well below or L / a >> lOOO! Note that in the first case, (S), X-ray diffraction would yield Bragg spots along the chain direction, whereas in the second case, (9), the scattering would be in the form of sheets.In reality, with finite longitudinal structural coherence lengths we expect the physical condition to be somewhere in between those expressed in (8) and (9). Even if ( f 3 d / to) is reduced by extending the inter-chain spacings through addition of side-chains to the conjugated backbone [as in the poly(3-alkylthiophenes)], it is still possible to satisfy the inequalities (8) or (9). However, since L / a would have to be correspondingly greater, the implied difficulties for the polymer scientist would be that much greater! When the appropriate inequality is satisfied the transport is that of an anisotropic three-dimensional metal, and the conductivity is given by eqn ( 1 ) and (3) with A = L uI1 = (nez/rn*)(L/uF). (10) In this case, the conductivity should increase in proportion to the mean distance between chain interruptions, cross-links, sp' defects, etc.If the mean defect-scattering time, Tdrf = ( L / u,), becomes sufficiently long that phonon scattering limits the mean free path then eqn (5) becomes valid, and the system is in the clean and intrinsic transport limit. An analogous argument can be constructed for understanding the requirements for achieving the intrinsic strength of a p ~ l y m e r . ' ~ If one imagines a fibre like that shown in fig. 1, what is the requirement that the chains do not slip with respect to one another, such that the ultimate strength is determined by that of the carbon-carbon bond? If E,, is the energy required to break the carbon-carbon bond and E 3 d is the weaker interchain bonding energy (from van der Waals forces and hydrogen bonding for saturated poly- mers, or from inter-chain transfer, z~~ for conjugated polymers), then the requirement is coherence over a length L such that L / a >> & / E 3 d .In this limit the large number ( L / a ) of weak inter-chain bonds add coherently such that the polymer yields by breaking a carbon-carbon bond. Note that for a conjugated polymer, this criterion is less stringent,208 Striving Towards Intrinsic Properties since t3d is typically much greter than the energy expected from van der Waals forces or from hydrogen bonding. Moreover, the increased bond-order due to the 7.r-bonds will increase Eo over that expected for a saturated polymer. Thus, chain-aligned conju- gated polymers should have exceptional mechanical properties at lower chain lengths than their saturated counterparts.The need for high molecular weight conducting polymers that can be processed into the chain-aligned configuration is two-fold. Clearly the molecular weight (and chain perfection) must be sufficient to satisfy the appropriate inequality, (8) or (9). More important, however, is the need for sufficiently high molecular weight to enable the processing that will yield the chain-extended and chain-aligned material.”‘” 5. Is ‘Metallic’ Polyacetylene a Metal? The analysis given in the previous sections assumes that at heavy doping concentrations, polyacetylene (and other conducting polymers) have the electronic structure of metals. Only in a few cases has this been checked in detail.For example, the existence of a temperature-independent Pauli susceptibility has been established for p~lyacetylene’~ and polythiophene,“ indicative of a metallic system with a finite density of states at the Fermi surface. For polyaniline, a Pauli contribution to the susceptibility has been inferred,” but it only dominates in the most crystalline materials.’’ Nevertheless, even for polyacetylene, the electronic structure is not that of a simple metal in which the bond-alternation and the ~ - 7 . r ~ gap have gone to zero; there are infrared-active vibrational modes (IRAV) and a pseudo-gap.” This is indicated by the spectra” in fig. 2 which demonstrate the remarkable similarity between the doping- induced absorption found with heavily doped trans-( CH) y, and the photoinduced absorption spectrum observed in the pristine semiconductor containing a very few photoexcitations.Not only are the same IRAV mode spectral features observed, they have almost identical frequencies. The ‘metallic’ regime in polyacetylene is characterized by three important aspects of the data:19 (1) The IRAV modes are absorption bands; there is no indication of Fano-like anti-resonances studied in the one-dimensional charge transfer salts.*’ In addition, since there is no indication of free carrier Drude absorption, the intraband contribution to a ( w ) must be in the far-infrared” below 450 cm-’. Therefore, there is a gap in the excitation spectrum (or a pseudo-gap where a is small but non-zero) with magnitude of ca. 1500 cm-’ ( ~ 0 .2 eV). (2) The intensities of the IRAV modes increase linearly with the dopant concentration with essentially the same slope as observed at more dilute concentrations.” This implies that all the doping-induced charges are involved and that the IRAV in the ‘metallic’ state are not due to a small number of residual inhomogeneities (or non-uniformities) in the charge distribution. (3) Since the IRAV mode frequencies are essentially identical to those observed with photoexcitation, the pinning of the r-electron charges which cause the IRAV [ i.e. all the charges, see (2)] has virtually disappeared. These three conclusions are not consistent with the excitation spectrum of the simple metal which would result if the Peierls’ gap had been reduced to zero (there would be no gap and no IRAV modes).As noted above, the free-carrier contribution which extrapolates to the measured a ( 0 ) must be in the far-i.r. below 450cm-’.lS Nevertheless, most of the r-electron oscillator strength remains in the broad absorption band above 0.2 eV. An alternative which appears to be in agreement with the essential experimental facts is that polyacetyl- ene is an example of a polaronic metal.” The polaron lattice with a half-filled polaron band is certainly consistent with the observed susceptibility. In the case of a polaronA. J. Heeger 209 I I I I 1000 2000 3000 4000 frequency/cm-‘ Fig. 2. A direct comparison of the infrared absorption spectrum of the heavily doped sample (at 80 K) with that of the photoinduced absorption spectrum of pristine trans-(CH), (at 80 K). latti~e,~’ the IRAV modes are expected and would be bathochromically shifted from the Raman modes provided that the pinning is weak.Although the intensity of the IRAV modes was initially calculated to be much too weak, this calculation ignored the effect of the counter ion^;^^ the counterion Coulomb potentials may lead to sufficient non-uniformity in the charge density to yield the observed IRAV mode intensities.2’ For the polaron lattice, a ( w ) would have two contributions with a ‘gap’ in between: (i) a free-carrier contribution corresponding to the mobile carriers in the lattice of polaron-like distortions; (ii) an interband contribution: for hole polarons the transition is from the filled T band to the Fermi level in the lower polaron band; for electron polarons, the transition is from the Fermi level in the upper polaron band to the empty T* band.The concept of the polaronic metal has been applied to polyaniline as well,” and may be a more general feature of the metallic state in conducting polymers. In the context of the discussions presented in Sections 1-4, the polaronic metal is indeed a ‘metal’ and the analysis given is appropriate. In particular, the importance of the self-organisation of the doped polymer (to avoid counterion scattering) and the need to avoid localization etc. are of clear importance. 6. Discussion Although the ability to dope conjugated polymers (and thereby change their conductivity by many orders of magnitude) is well known, disorder introduced by the same doping process had been previously thought to render such materials intrinsically ‘dirty’ conduc- tors.Because of the self-organizing capability of the conjugated chains and because of the anisotropic screening in such systems,6 this is not the case. While the dopant potential will certainly lead to an inhomogeneous charge distribution ( e . g . a polaron with its mean charge density peaked in the vicinity of the dopant counterion), so long as there is reasonably good local order this potential causes almost no back-scattering. Thus, the electrical conductivity of conducting polymers is not necessarily limited by scattering from the dopant ions.210 Striving Towards Intrinsic Properties There are certainly other sources of disorder which are present in real conducting polymers, e.g.there are strains, gentle bends, twists, kinks and jogs, etc. of the polymer backbone, and there are regions where neighbouring polymer chains are imperfectly aligned. Although these have not been treated explicitly, none of these sources of disorder are expected to be seriously limiting, since the conductivity is only sensitive to the component of the disorder potential at 2 k F . Only sharp, localized defects on the polymer chain (e.g. chain ends or cross-links etc.) will have a significant effect on the conductivity. This is in accord with recent experimental which demonstrate increases in conductivity (to values in excess of lo5 S cm-’) as the number of sp3 defects is reduced, evenothough the structural coherence length as obtained from X-ray scattering is only ca.100 A. For a tangled or cross-linked amorphous polymer, metallic transport with A >>a cannot be expected (nor can high stiffness and strength). Such systems will always fall into the category of ‘dirty’ conductors with modest conductivities. Nevertheless, since a wide range of conductivity levels can be useful, both classes of materials can potentially be important in applications. High molecular weight, chain-aligned conducting polymers will be the high-performance polymers of the field. For more routine requirements, conducting polymers from the ‘dirty’ conductor category may be sufficient. Note, however, that composites made up of only a small fractional volume of (phase-separated) connected regions of the high performance component in the medium of a second polymer may yield conductivities that are of broad interest.However, it is from materials of the high-performance category that we will learn in more detail about the metal physics of conducting polymers and about the various contributions to the scattering which limit the mean free path and thereby limit the electrical transport. To produce such materials, we must strive for advances in the synthesis of high-molecular-weight polymers, and we must develop novel methods of processing these polymers into the chain-aligned configuration. Based upon these results, there is good reason to expect that conducting polymers can be made as high performance materials with electrical conductivities significantly greater than those of even the best conventional metals.To achieve these high conduc- tivities, methods must be developed to synthesize oriented conducting polymers with high molecular weight and with a high degree of chain perfection. However, it is not necessary that the material be crystalline, since the electronic mean free path can be much greater than the structural coherence length as measured in a scattering experiment. Since the phonon frequencies are higher than in conventional metals, and since only the 2kF phonon is relevant, the intrinsic conductivity should be very high at room temperature, and it will grow exponentially as the temperature is lowered. These high phonon frequencies are a direct manifestation of the strength of the carbon-carbon bond, which ultimately offers the promise of making such polymers truly high-perform- ance materials with conductivities significantly greater than copper and with strengths greater than steel by an order of magnitude.This paper was stimulated by an EPRI workshop in Baltimore (March 1989) and was prepared under support from EPRI. Many of the specific results were drawn from earlier work. In particular, I thank Prof. S. Kivelson for many important discussions and many detailed results. Any insight on the relationship of electrical and mechanical properties in polymers is due to my interactions with Prof. Paul Smith. References 1 H. Naarmann and N . Theophilou, SJwth. Met., 1987, 22, 1. 2 N. Basescu, Z-X. Liu, D. Moses, A. J. Heeger, H. Naarmann and N. Theophilou, Narirre (London), 1987, 327, 403.A. J.Heeger 211 3 T. Schimmel, W. Reiss, G . Denniger, J. Gmeiner, M. Schwoerer, H. Naarmann and N. Theophilou, 4 N. Theophilou, D. B. Swanson, A. G . MacDiarmid, A. Chakraborty, H. H. S. Javadi, R. P. McCall, 5 M. Winokur, Y. B. Moon and A. J. Heeger, Phys. Rea. Lett., 1987, 58, 2329. 6 S. Kivelson and A. J. Heeger, Synth. Met. 1988, 22, 371. 7 N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Marerials (Oxford, Clarendon Press, 1979). 8 ( a ) P. W. Anderson, Commun. Solid State Phys., 1970, 2, 193; ( b ) L. Fleischman and P. W. Anderson, Phys. Rev. B, 1980, 21, 2366; (c) H. Kamimura, in Modern Problems in Condensed Marrer Science, ed. V. M. Agranovich and A. A. Maradudin (North Holland, Amsterdam, 1985), vol. X, p. 555. Solid State Commun., 1988, 65, 147.S. P. Treat, F. Zuo and A. J. Epstein, Svnth. Met., 1989, 28, D35. 9 M. Thackur, Macromolecules, 1988, 21, 1379. 10 W. J . Fest, Handbook on Conducting Polymers (Marcel Dekker, New York-Basel, 1986), vol 1, p. 1. 11 ( a ) D. R. Gagnon, J. D. Capistron, F. E. Karasz, R. W. Lenz and S. Antoun, Polymers, 1987, 28, 567; D. R. Gagnon, F. E. Karasz, E. L. Thomas and R. W. Lenz, Synrh. Met., 1987, 20, 85. ( b ) T. Momii, S. Tokito, T. Testsui and S. Saito, Chem. Left., 1988, 1201. ( c ) S. Yamada, S. Tokito, T. Tetsui and S. Saito, J. Chem. Soc., Chem. Commun., 1987, 1448. 12 ( a ) P. Smith and P. J. Lemstra, J. Muter Sci. 1980,15,505. ( h ) P. A. Irvine and P. Smith, Macromolecules, 1986, 19, 204. 13 ( a ) P. M. Grant and I . Batra, J. Phys. (Paris) Colloq., 1983, 44, C3-437.( b ) P. Vogl and G . Leising, S?.nth. Met., 1989, 28, D209. 14 Y. Termonia, P. Meakin and P. Smith, Macromolecules, 1986, 19, 154. 15 ( a ) T-C. Chung, F. Moraes, J. D. Flood and A. J. Heeger, Phvs. Rev. B 1984, 29, 1341. ( h ) F. Moraes, J. Chen, T-C. Chung and A. J. Heeger, Svnth. Met., 1985, I I , 271. ( c ) J. Chen and A. J. Heeger, Phys. Reti. B, 1986, 33, 1990; J. Chen and A. J. Heeger, Synth. Met., 1988, 24, 311. 16 F. Moraes, D. Davidov, M. Kobayashi, T-C. Chung, J. Chen, A. J. Heeger and F. Wudl, Synth. M e t , 1985, 10, 169. 17 J. M. Ginger, A. F. Richter, A. G. MacDiarmid and A. J. Epstein, Solid Stare Commun., 1987, 63, 97. 18 C. Fite, Y. Cao and 4. J. Heeger, Solid Srate Commun., in press. 19 Y. H. Kim and A. J. Heeger, Phys. Ret.. B, in press. 20 ( a ) M J. Rice, L. Pietronero and P. Breusch, Solid State Commun., 1977, 21, 757. ( h ) Y. H. Kim, M. Nowak, Z. G . Soos and A. J. Heeger, J. Phys. C., 1988, 21, L503. 21 H. S. Woo, D. B. Tanner, N. Theophilou and A. G. MacDiarmid, Meeting of the American Physical Society, St. Louis, March, 1989; the results presented in this report indicated an increase in ~ ( w ) toward the measured ~ ( 0 ) at frequencies below 100 cm-'. 22 ( a ) A. J. Epstein, H. Rommelmann, R. Bigelow, H. W. Gibson, D. M. Hoffman and D. B. Tanner, Phys. Rev. Lett., 1983,50, 1866. ( h ) X . (2. Yang, D. B. Tanner, M. J. Rice, H. W. Gibson, A. Feldblum and A. J. Epstein, Solid State Commun., 1987, 62, 335; Mol. Cryst. Liq. Crvst., 1985, 117, 267. ( c ) X. Q. Yang, D. B. Tanner, G. A. Arbuckle, A. G. MacDiarmid and A. J. Epstein, Synth. Met., 1987, 17, 277. ( d ) D. B. Tanner, G. L. Doll, A. M. Rao, P. C . Eklund, G . A. Arbuckle and A. G . MacDiarmid, Proc. ICSM '88, Sjxth. Met., 1989, 28, D141. 23 S. Kivelson and A. J. Heeger, Phys. Rev. Lett., 1985, 55, 308. 24 ( a ) H. Y. Choi and E. J. Mele, Phys. Rtw B., 1986, 34, 8750. ( b ) J. C. Hicks, J. Tinka Gammel, H-Y. 25 S. Kivelson, personal communication. 26 S. Stafstrom, J. L. Bredas, A. J. Epstein, H. S. Woo, D. B. Tanner, W. S. Huang and A. G. MacDiarmid, Choi and E. J. Mele, Synrh. Met., 1987, 17, 57. Phjqs. Reti. Lett., 1987, 59, 1464. Paper 9/01999E; Received 12th May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800203

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1989, 88, 213-222 Charge Injection in Conjugated Polymers in Semiconductor Device Structures Richard H. Friend* and Jeremy H. Burroughes Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE The realisation of interesting electronic properties in materials which can be processed to form useful device structures has provided an important impetus to the field of conjugated polymers, and in recent years much progress has been made in understanding their electronic structure and properties. The semiconductor physics of these polymers is much affected by the ‘one-dimensional’ character of the electronic structure of the polymer. In contrast to three-dimensionally bonded semiconductors, the addition of an extra charge to the structure leads to local reorganisation of the 7r electron bonding, and to the formation of a self-localised excitation, usually termed a polaron.For the special case of trans-polyacetylene, the excitation is topological, separating regions of the chain with different senses of bond alternation, and is usually termed a soliton. The introduction of charge into a semiconductor is traditionally achieved by three routes: chemical doping, photoexcitation of separated electron-hole pairs, and by charge injection to form space-charge or surface-charge layers in semiconductor device struc- tures. We discuss here in particular the last of these, and review the measurements we have carried out on various semiconductor device struc- tures constructed with polyacetylene produced by the Durham precursor route.1. Introduction Conjugated polymers have proved to be versatile materials in that they are of interest to different groups for very different properties. The list includes their use as electrochemical insertion electrodes, as high-conductivity, low-density metals, as materials for non-linear optics, and as semiconductors. There are themes common to most interests, and among these are the ways in which charge can be stored on the polymer chain, and the ways by which it can be moved both along and between polymer chains. Associated with the very anisotropic properties of these materials are excitations of the chain which are strongly coupled to the local bond order and which show, therefore, a strongly non-linear response. Our interests are very much with the semi- conductor properties of these polymers, and in this paper we discuss how the formation of self-localised excitations of the polymer chain determines the operation of a variety of semiconductor device structures.In for example, the MISFET (metal-insulator- semiconductor field-effect transistor), the charges of interest to us are introduced into a region of surface charge at the semiconductor/insulator interface by the application of a strong electric field across the insulator, but in many ways these show the same properties as those introduced through chemical or electrochemical doping, and we hope that comparison between the two types of experiment is valuable. Despite the considerable progress in the past decade that has been made in the understanding of the electronic properties of conjugated polymers, there has been relatively little work reported on their use as the active component in semiconductor device structures. There are several reasons for this; the most important of which is that most conjugated polymers cannot be processed conveniently to the forms required 2 13214 Polymeric Semiconductor Devices F3HF3 - A 6 C Fig.1. The Durham route to polyacetylene. in these devices. Most conjugated polymers are not readily soluble in easily handled solvents and are infusible. This has severely limited the scope for the construction of Improvements in the processing of conjugated polymers, through electrochemical deposition during polymerisation, and the use of solution-processible poly(3-alkyl thiophenes) have allowed better device f a b r i ~ a t i o n , ~ ' ~ and the use of model oligomers which can be deposited by vacuum sublimation has recently been r e p ~ r t e d .~ There are also reports of field-induced conductivity measured in MISFET A major advance in the control of the polymer processing is in the use of a solution-processible precursor polymer which can be converted to the conjugated poly- mer after processing. This was first demonstrated by Edwards et al."-" for the prepar- ation of polyacetylene (the Durham route) and it is polyacetylene produced by this route that we have used in the present studies. We have made thin-film devices by spin-coating the precursor polymer, poly((5,6-bis(trifluoro-methyl)-bicyclo[2,2,2]octa- 5,7-diene-2,3-diyl)-1,2-ethenediyl), in solution onto the required substrate, followed by heat treatment to convert to the polyacetylene by elimination of hexafluoro-xylene.'"-I8 The Durham precursor route is shown in fig. 1; the precursor polymer is soluble in common solvents such as acetone and 2-butanone, and the heat treatment to achieve the thermal conversion from precursor to polyacetylene is achieved at temperatures of up to 100°C. The precursor polymer has very good film-forming properties, and it is straightforward to control the thickness of the resultant polyacetylene film over the range 100 8, to several pm. We have investigated a range of unipolar devices: Schottky- barrier diodes, MIS (metal-insulator-semiconductor) structures and MISFETs.'"-" By careful control of the processing, with rigorous exclusion of oxygen, we have been able to get the device performance up to levels respectable enough to learn about the detailed functioning of the device.For the Schottky diodes we routinely measure rectification ratios of ca. 500 000, and for the MIS and MISFET structures we can demonstrate that the devices show 'textbook' formation of charge accumulation and depletion layers at the polyacetylene/insulator interface. A semiconductor device such as the MISFET provides an excellent experimental tool for investigating many of the basic electronic properties of the semiconductor used. This is well exemplified by the investigation of the Anderson transition in the silicon MISFET inversion layer and subsequently in the same device, the discovery of the quantum Hall effect.In the present devices, the easy control of the charge concentration with gate voltage allows quantitative investigation of the electronic relaxation following charge injection. It is established that there is a structural relaxation around charges present on the polymer chains, both when charges are added to the polymer chain through chemical doping, or separated following photoexcitation. For polyacetylene, the localised states are bond-alternation defects, or solitons.27T22 Charge injected into the polyacetylene in these device structures should similarly be stored in soliton states. We illustrate schematically how this is achieved following the injection of two electrons onto a polyacetylene chain in fig. 2. Turning to the various regimes of behaviour that are exhibited in a MISFET structure, we can expect that the formation of a depletion layer in polyacetylene should remove the charged solitons introduced through theR. H.Friend and J. H. Burroughes ( ‘ ) 4 n: conduction band r e laxat i on vale nc e ban d 215 Fig. 2. Schematic representation of the formation of a pair of solitons on a polyacetylene chain. ( a ) Shows the undistorted chain and ( b ) shows the associated band scheme. The interband T - T* optical transition is shown as a dotted arrow. If two electrons are introduced onto the chain, initially into the conduction band as shown in ( b ) , the chain relaxes to the form shown in ( d ) , with a reversed sense of bond alternation in the centre of the chain separated by two solitons.Associated with the two solitons are non-bonding T states in the gap, created from one (doubly occupied) valence and one (empty) conduction band state. These two states are doubly occupied, as shown in (c), and each carries a negative charge. New optical transitions from the soliton level to the conduction band are indicated with a dotted arrow; the oscillator strength for the interband transition is weakened through the loss of the band states. A complementary picture holds for positive charge, which is accommodated as unoccupied soliton levels. extrinsic doping. However, with the formation of an accumulation or inversion layer we have a new means of charging the polymer chains, with charge at the interface between the polymer and insulator layers without the presence of charge-balancing counter-ions.Our principal motivation in carrying out this study of the device physics of polyacetylene was to find out how the relaxation of injected charges to form charged solitons controls the device operation and distinguishes this class of polymeric semi- conductor devices from traditional structures. Besides the range of electrical measure- ments that characterise the device performance, we have carried out an extensive range of optical measurements, since the clearest evidence for the formation of solitons in polyacetylene is through the appearance of additional optical absorption below the band gap, associated with the vibrational and electronic excitations of the solitons.24 For Durham polyacetylene prepared in the way used here the ‘mid-gap’ absorption feature due to transitions between the ‘mid-gap’ levels on the solitons and the band edges is seen at ca. 1.0 eV for chemically doped samples,lh and at 0.55 eV for photoexcited charges.” We expect, therefore, to see changes in the optical properties of the poly- acetylene in these devices; depletion should reduce the ‘mid-gap’ optical absorption, whereas accumulation or inversion layer formation should introduce ‘mid-gap’ states onto previously undistorted chains, and increase the mid-gap optical absorption.2. MISFET Construction and Electrical Properties Polyacetylene as produced by the Durham route is an extrinsic semiconductor with a concentration of p-type carriers of ca. 1016cmp3. This is established both from the216 Polymeric Semiconductor Devices I drain source 2?iniun te Fig.3. Schematic diagram for a polyacetylene MISFET structure. Dimensions shown are to scale, except the channel width (20 p m ) and length (1.5 m). capacitance versus voltage characteristics of Schottky barrier junctions formed with low work function metals such as Al and In’9320 and also from the sign, magnitude and temperature variation of the thermopower.” This is a convenient level of doping for the construction of many devices, and we have been able to use the polyacetylene without further doping. Of crucial importance for the operation of these devices is that the dopants responsible for the presence of the extrinsic carriers are not mobile. For the extrinsic carriers in polyacetylene this appears to be the case, though the concentration of these carriers is very low and we are not able to establish where they come from (we consider that a likely origin lies in the presence of catalyst residues at the polymer chain ends). We emphasise that the chemical and electrochemical methods commonly used to ‘dope’ conjugated polymers, in which doping is achieved by diffusion of dopants through the solid polymer at room temperature, are quite inappropriate here.Apart from the problem of dopant mobility, it is very difficult to control doping levels at the very low dopant concentrations required ( mol %), and at such low levels it is very unlikely that the doping would be homogeneous. A variety of device structures has been prepared. For two-terminal devices, such as the Schottky diode and the MIS structure, the device is fabricated as a series of layers.For example, to construct an MIS structure we have used silicon as substrate with a doped layer to act as gate and a native oxide layer on top as the insulator. This structure is then coated with polyacetylene and finally capped with an evaporated thin gold top contact. For the MISFET structure it is convenient to put the source and drain contacts onto the insulator layer, and put the polyacetylene layer down on top as the last stage in the construction. In the example of the MISFET structure shown in fig. 3, the source and drain contacts are of poly-n-silicon; we have also made structures with gold. The MIS structure allows the possibility of band bending ar the insulator/semi- conductor interface through the Fermi level to produce a surface-charge layer which may be the same carrier sign as the majority carriers (accumulation layer) or as the minority carriers (inversion layer).’“ The formation of accumulation, depletion and inversion layers may be demonstrated through the behaviour of the device capacitance with respect to the bias voltage.The measured capacitance, C, is that of the series combination of the insulator capacitance, Ci , and the capacitance of the active region of the semiconductor, Cd, and is given by C = c i c d / ( Ci + C,). Since C d is large for the accumulation and inversion layers, C is equal to the geometric capacitance of the insulating layer, but C falls to a lower value for movement of the depletion layer.The capacitance versus bias voltage curve for a polyacetylene MIS structure is shown in fig. 4. As expected, the capacitance for negative gate voltages flattens o u t to the geometric capacitance of the insulator, indicating the formation of an accumulation layer. TheR. H. Friend and J. H. Burroughes 217 11 10 71 I I I I -40 -20 bias voltage/V Fig. 4. The differential optical transmission, dln T / J V at 0.8 eV, and differential capacitance, d Q / d V versus bias voltage for the MIS structure. Measurements were made at 500 Hz and with an a.c. modulation of 0.25 eV. V,JV Fig. 5. I,, versus V,, at constant V,, (-lOV) for a MISFET with poly n-silicon source and drain contacts, as shown in fig. 3. decrease in the measured capacitance for positive voltages displays the formation of the depletion layer.Saturation of the capacitance for large positive biases sets in when the depletion layer extends across the polyacetylene film (estimated to be about 1200 A for this device). Demonstration that the charges at the polyacetylene/insulator interface in the MIS structure are mobile is made in a MISFET structure, in which source and drain contacts allow measurement of the conductance of the surface-charge layer. The choice of the material used for construction of the source and drain contacts should determine whether the device operates in inversion or accumulation mode. The MISFET shown in fig. 3 is constructed with n-silicon source and drain contacts, which might be expected to make ohmic contacts to n-type polyacetylene, and thus give enhanced channel conduc- tance from formation of an n-type inversion layer for positive gate voltages.Fig. 5 shows the variation of IDS with V,, at constant VDs. The channel conductance has a218 Polymeric Semiconductor Devices I 1 1 I 0.4 0.6 0.8 1.0 1.2 energy/eV Fig. 6. Voltage-modulated transmission for a MIS diode, [ T(0)-T( V ) ] / T(0) versus the photon energy, for various values of V (all negative with respect to the gate). minimum at VGs = +10 V (full depletion) and rises for gate voltages both more positive (inversion layer) and more negative (accumulation layer), with a maximum onloff ratio for this structure of 100 000 ( VGs = -40 V to VGs = +10 V). We see, therefore, the behaviour expected for positive bias, though the strong enhancement of the conductivity for negative bias indicates that the accumulation layer is still able to make good contact to the source and drain electrodes.It is unusual to find a device able to operate in both modes, and we consider that the n-silicon work function matches that of the mid-gap ‘soliton’ band in polyacetylene, and that in contrast to traditional semiconductors, the Fermi level does not move far from the mid-gap band with addition of either p or n carriers. The MISFET structure provides a very convenient means of controlling the charge carrier concentration in the surface layer of the semiconductor. We have determined the carrier mobility from conductance measurements as a function of gate voltage, and find low values, typically cm*V-’s-’.Similar values for the mobility are estimated for photogenerated carriers, and the extrinsic carriers in the as-made p~lyacetylene.~’ We discuss mechanisms for charge transport further in section 4. 3. Self-localisation of Injected Charge As discussed in section 1, charge is stored in polyacetylene in ‘soliton’ localised states, which have non-binding pz ‘mid-gap’ states associated with them. We expect to see, therefore, a modulation in the optical properties of the active semiconductor region of these devices with applied bias voltage. The devices described above have all been constructed so that it is possible to pass sub-band-gap light through the structure and thus to observe the changes in optical properties as the gate voltage is varied. For the MIS and MISFET structures we expect a decrease in the device transmission below the band-edge as the device is driven towards accumulation, and new charged solitons are introduced onto the polyacetylene chains at the interface with the insulator.The experiment is easily performed by modulating the gate voltage at a convenient frequency and monitoring with a lock-in amplifier the optical transmission signal that is modulated by the gate voltage. The electromodulation spectrum between 0.4 and 1.2 eV in fig. 6 shows that there is a decrease in the transmission through the device for negative bias. The peak value of A T / T is at 0.8 eV. If all the charge at the polymer-insulator interfaceR. H. Friend and J. H. Burroughes 219 is stored in soliton-like states then aln T/d V should scale with dQ/d V , the differential capacitance, as the bias voltage is varied.This is shown to be the case in fig. 4, in which dlnT/dV and the differential capacitance are both plotted against bias voltage. The ratio of alnT/ V and a Q / d V gives the optical cross-section per charge injected, and in the accumulation regime we find a value at the peak in the ‘mid-gap’ absorption as 1.2 x cm2, in very close agreement with the value measured from dopant-induced ab~orption.~~ Besides the electronic transitions associated with the soliton state, there is extra IR activity due to new vibrational modes which couple to motion of the charged soliton along the polymer chain. These are the translation modes of the soliton, and are seen in the polyacetylene accumulation layer at 1379 and 1281 cm-’ (the lowest mode is obscured by absorption by the silicon substrate).19320 There are additional vibrational modes of the soliton, including the width-modulating amplitude mode which is Raman active. This again has been observed in the polyacetylene accumulation layer” at a frequency ca. 50 cm-’ lower than the corresponding modes of the dimerised chain. 4. Charge-transport processes Charge transport in doped conjugated polymers has been extensively investigated but remains poorly understood. There was considerable early interest in the nature of the ‘insulator-metal’ transition achieved by chemical doping. It was observed that the conductivity reaches a metallic level at ca. 1% doping, whereas the magnetic susceptibility remains low up to ca.6% doping, at which level a transition to a Pauli-like behaviour is seen. There was considerable discussion as to whether the conduction processes in this intermediate regime were due to sliding of self-localised charged solitons along the polymer chain, but it is now clear that the transitions seen at ca. 6% doping are due at least in part to a phase transition between different ordering of the dopant ions around the chains.” In the limit of low charge carrier concentrations it is clear that carrier mobilities are low, and it is generally accepted that the rate-limiting process is that of charge transfer between chains. For the particular case of trans-polyacetylene, the topological character of the soliton raises some problems here, since it cannot move from one chain to another.There are two models developed for interchain charge transfer. The first of these is due to Kivelson28 and relies on the presence of a substantial concentration of neutral ‘soliton’ states. The process of interchain charge transfer is then achieved by transfer.of charge from a charged soliton on one chain to a neutral soliton on an adjacent chain. This process, termed ‘intersoliton hopping’ is clearly specific to polyacetylene, both because of the particular nature of the soliton excitation and because of the requirement for both charged and neutral solitons. The second model is one in which the charged solitons are present in pairs on a single chain, and constrained (by for example interchain coupling or finite chain lengths) to remain close to one another.The doubly charged excitation may then be treated as a bipolaron, and the process of interchain charge transport is then controlled by the rate at which these can hop (or possibly tunnel) between chains.25 The ‘bipolaron model’ is implicit in the scheme shown in fig. 2 for charge injection onto the polyacetylene chain. We consider that there is very strong evidence that this is the correct mechanism, for charge transport for carriers introduced through chemical doping, photoexcitation, and through charge injection. The intersoliton model depends crucially on the presence of ‘neutral solitons’ which can be readily ionised and thus participate in the charge transport. trans-Polyacetylene, produced either by the Shirakawa route or by the Durham route, does contain a high concentration of spin defects which are detected in ESR experiments, and which can be shown to be due to the presence of non-bonding pz states with wavefunctions spread over some 10-20 carbon sites.These spins appear during the thermal isomerisation220 Polymeric Semiconductor Devices from cis to trans, and are typically present in concentrations of 1018-1019 cm-’. However, the bulk of the evidence gathered from photoexcitation experiments is that though they may be ‘soliton-like’ in the nature of their wavefunctions, they do not possess energy levels within the gap, and are not involved in the production of metastable photoexcited StateS.25.29,30 Turning to the experiments we have performed with charge accumulation layers, we are able to achieve rather higher levels of charge injection than obtained in the photoexcitation experiments.At the higher gate voltages used in the data shown in fig. 6, the surface charge density is up to 4 x 10” cm-’ (at -40 V). We consider that the charge accumulation layer is strongly localised to the interface with the insulator, probably within 2 nm. The total areal concentration of the neutral spin defects within such a layer is a factor of 2 lower than the charge concentration (at Vg = -40 V), and we do not therefore consider that the charge injected into the polymer is stored on the spin defects. As previously discussed,2s-30 we consider that the neutral spin defects are present on disordered regions of the chain, which possess a high T - V * energy gap, and are thus excluded from participation in the electronic processes that take place within the gap. The ‘bipolaron model’ is generally applicable for conjugated polymers, whether or not they may in principle possess a degenerate ground state.As discussed by Chance et al.,” like-charged soliton pairs are analogous to bipolarons and are not topologically restrained from inter-chain hopping. The process by which they do this will involve an intermediate stage in which one of the two charges has transferred to an adjacent chain, and the instantaneous description is of two polarons on adjacent chains. If the second charge then follows the first, the bipolaron has moved from one chain to another, and has surmounted an energy barrier equal to the stabilization energy of the bipolaron (or soliton anti-soliton pair).Townsend and Friend” show that there is a well defined activation energy for the mobility of photocarriers, of about 0.31 eV, and identify this as the bipolaron stabilisation energy. The general expression for the hop rate of a self-localized carrier is R = w exp { - W,/ k , 8 } where W, is the hop energy and w is the attempt-to-hop frequency,” and this is shown to be consistent with the room-temperature mobilities observed if the average distance between hops is set at 2.1 nm. For the case of photocarriers, Townsend and Friend” were able to identify from spectroscopic measurements that they are present as like-charged pairs of solitons; hence the description of the transport in terms of bipolaron motion along and between chains.For carriers introduced through chemical doping the situation is less clear because in general we have less spectroscopic information. It is interesting to compare the properties of as-made samples of Durham polyacetylene. These contain the usual level of spin defects, as already discussed, and they also contain a low concentration of charges which are responsible for the d.c. conductivity. Measurements on Schottky barrier diodes formed between aluminium and the p o l y a ~ e t y l e n e ’ ~ ~ ~ ~ do provide the necessary information to characterise the charges present. From the current-voltage and capaci- tance-voltage characteristics we know that the charge carriers are p-type and present in a concentration of ca. 10’‘ cm-’, and that this does not vary strongly with temperature.From the differential optical transmission measurements through the depletion regime we also know that these p-type carriers show the same ‘mid-gap’ optical absorption signatures that are found in photo-induced absorption for the photocarriers, with a peak in absorption at 0.55 eV. The mobility of the dark carriers is now easily fixed by the value of the dark conductivity. The room temperature carrier mobility inferred from the conductivity (3 x lo-* S cm-’) is ca. 2 x lop5 cm’ V-I s-I, and it shows an activation energy of ca. 0.4eV.” These values are rather similar to those we have established for the photocarriers, and we consider that the same model for transport is appropriate for both the extrinsic carriers and the photocarriers.Turning to the carriers present in the accumulation and inversion layers in the MISFET structures, we have established that the mobilities are comparable to those ofR. H. Friend and J. H. Burroughes 22 1 the extrinsic carriers in the as-made polyacetylene and to those of the photocarriers. The MISFET structure provides a very versatile system for the control of the carrier density and for the systematic measurement of the transport properties, and this is an area for future study. It is important to recognise that the accumulation or inversion layer in the MISFET structure is confined to the interface between the polymer and insulator, and is thus very sensitive to the surface structure of the polymer. The optical characterisation of the self-localised states created to store the injected charges that we are able to perform gives a very powerful method for characterising the 7~ electron system of the polymer chains on which the charge is stored.We have previously noted'9720 that the 'mid-gap' electronic absorption in these structures is very dependent on the construction of the device. For devices which use silicon dioxide as the insulator layer the 'mid-gap' electronic absorption is at 0.8 eV. This is high, well above the value of 0.55 eV found for photo-excited charges in the bulk,'5 and indicates that the local band gap for the polyacetylene chains which form the surface layer is higher than in the bulk. In contrast, devices built with a polymer, such as poly(methylmethacrylate), as the insulator show a 'mid-gap' electronic absorption at 0.55 eV, and we consider that the polyacetylene formed at this interface is no more disordered than in the bulk.Clearly, control of the electronic structure of the polyacetylene on which the accumulation layer is formed is important in the study of electronic transport processes in these surface charge layers. We are currently extending our measurements to tackle this important area. References 1 P. M. Grant, T. Tani, W. D. Gill, M. Krounbi and T. C. Clarke, J. Appl. Phys. 1980, 52, 869. 2 J. Kanicki, in Hankbook on Conducting Polymers ed. T. J. Skotheim (Marcel Dekker, New York, 1986), 3 F. Garnier and G. Horowitz, Synth. Merals, 1987, 18, 693. 4 H. Tomozawa, D. Braun, S. Phillips, A. J. Heeger and H. Kroemer, Synth.Metals, 1987, 22, 63; 1989, 28, 687. 5 F. Garnier, G. Horovitz and D. Fichou, Svnth. Metals, 1989, 28, 705. 6 E. Ebisawa, T. Kurokawa and S . Nara, J. Appl. Phps., 1983, 54, 3255. 7 H. Koezuka, A. Tsumura and T. Ando, Synth. Mefals. 1987, 18, 699. 8 H. Koezuka and A. Tsumara, Synth. Metals, 1989, 28, 753. 9 A. Assadi, C. Svensson, M. Willander and 0. Inganas, Appl. Phps. Lett., 1988, 53, 195. pp 544-660. 10 J. H. Edwards and W. J. Feast, Polymer Commun., 1980, 21, 595. 11 J. H. Edwards, W. J. Feast and D. C. Bott, Pol-vmer, 1984, 25, 395. 12 W. J. Feast and J. N. Winter, J. Chem. Soc., Chem. Commun., 1985, 202. 13 R. H. Friend, D. C. Bott, D. D. C. Bradley, C. K. Chai, W. J. Feast, P. J. S. Foot, J. R. M. Giles, M. E. Horton, C . M. Periera and P. D. Townsend, Philos.Trans. R. Soc. London, Ser. A, 1985, 314, 37. 14 R. H. Friend, D. D. C. Bradley, C. M . Pereira, P. D. Townsend, D. C. Bott and K. P. J. Williams, Synth. Metals, 1986, 13, 101. 1.5 D. C. Bott, C. S. Brown, C. K. Chai, N. S. Walker, W. J. Feast, P. J. S. Foot, P. D. Calvert, N. C . Billingham and R. H. Friend, Synth. Metals, 1986, 14, 245. 16 R. H. Friend, D. D. C . Bradley, P. D. Townsend and D. C. Bott, Synth. Metals, 1987, 17, 267. 17 R. H. Friend, D. D. C. Bradley and P. D. Townsend, J. Phys. 0, 1987, 20, 1367. 18 R. H. Friend, H. E. Schatfer, A. J . Heeger and D. C . Bott, J. Phj-s. C, 1987, 20, 6013. 19 J . H. Burroughes, C. A. Jones and R. Id. Friend, Nature (London), 1988, 335, 137. 20 J. H. Burrougr,es, C. A. Jones and R. H. Friend, Svnth. Metals, 1989, 28, 735. 21 R. A. Lawrence, J. H. Burroughes and R. H. Friend, in Electronic Properties of'Conducting Poljlmers, ed. H. Kusmany et al. (Springer Series on Solid State Sciences, 1989) in press. 22 W. P. Su, J. R. Schrietfer and Heeger, A. J., Phys. Rec. Lett., 1979, 42, 1698; PhJs. Rec. B, 1980, 22, 2099; erratum, 1983, 28, 1138. 23 M. J. Rice, Phys. Lett. A, 1979, 71, 1.52. 24 J. Orenstein, in Handbook on Conducring Po!,,mers, ed. T. J. Skotheim (Marcel Dekker, New York, 25 P. D. Townsend and R. H. Friend, Synth. Metals, 1989, 28, 735; Phys. Rev. B, 1989, 40, 3112. 26 S. M. Sze, Physics of Semiconductor Deuices (Wiley-Interscience, New York, 2nd edn 1981 ). 27 A. J. Heeger, in Handhook on Conducting Polymers, ed. T. J . Skotheim, (Marcel Dekker, New York, 1986), pp. 1297-1396. 1986), pp. 729-756.222 Polymeric Semiconductor Devices 28 S . Kivelson, Phys. Rev. B, 1982, 25, 3798. 29 P. D. Townsend and R. H. Friend, J. Phys. C, 1987, 20, 4221. 30 N. F. Colaneri, R. H. Friend, H. E. Schaffer and A. J. Heeger, Phys. Rev. B, 1988, 38, 3960. 31 R. R. Chance, J-L. Bredas and R. Sibley, Phys. Rev. B, 1984, 29, 4491. 32 N. F. Mott, Conduction in Non-Crystalline Materials, (Oxford University Press, Oxford, 1987). Paper 9/02294E; Revised 3 1 st May, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800213

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年代:1989

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Faraday Discuss. Chem. SOC., 1989, 88, 223-233 Charge Transport in Conducting Polymers Siegmar Roth," Hartmut Bleier and Wojciech Pukacki Max-Planck-lnstitut f u r Festkorperforschung, Heisenbergstrape 1, 0-7000 Stuttgart $0, Federal Republic of Germany Experimental data on the electrical conductivity of conducting polymers is reviewed. Polyacetylene is regarded as a prototype and the conductivity is studied as a function of doping level, temperature, frequency and conjugation length. The consistency of the data with a model of anisotropic variable range hopping is pointed out, with the exception of very highly doped samples, where in addition to hopping also temperature-independent tunnel- ling between large conducting domains has to be assumed. 1. Introduction Most polymers are insulators.There are some polymers, however, which become electrically conducting, if they are treated with strong oxidizing or reducing agents. The chemical structure of the most important of these polymers is shown in fig. 1. A common feature of all of them is the existence of long strands of conjugated double bonds. Typical oxidizing agents are 12, BrZ, AsF,, SbF5 and FeC13 ; typical reducing agents are the alkali metals. Usually the all-trans form of polyacetylene is considered as the - \ 000000 /--\ / - \ / - \ / - \ / - \ / - pol yacet y Lene polyphenylene po I y pyr ro Le po\yt hiophene - \ 0 /-- -0- 1 - 0 - 1 -0-z - polyaniline poly (phenylene- vinylene 1 Fig. 1. Chemical structure of the most important polymers with conjugated double bonds. 223224 Charge Transport in Conducting Polymers lo6 - copper - platinum lo4 - bismuth - graphite lo2 - 100 - 10-2- germanium 10-4 - 10-6- - - - - silicon - 10-8- polyethylene diamond 1o-iil quartz Fig.2. Comparison of the conductivity of conjugated polymers with that of conventional materials. prototype of conducting polymers. This is the substance which has been most widely investigated in this class of materials, and it is also the substance in which the highest conductivity values have been obtained up to now.' In addition, it was the observation of dopant-induced metallic conductivity in polyacetylene,' which has brought the conju- gated polymers to the attention of the one-dimensional metal community. In fig. 2 the electrical conductivity of conjugated polymers is compared to that of conventional substances.The arrow indicates the conductivity range that can be spanned by conduct- ing polymers. The hatched area corresponds to the recent progress after preparing polyacetylene by a new method.' Some review articles on conducting polymers can be found in ref. (3)-(7). For further details the proceedings of the three Kirchberg winter schools might be helpful.8 2. Results In this section we summarize the most important experimental results on the conductivity of conjugated polymers. There is no claim for completeness, nor do the references imply historical priority. Most data were taken on trans-polyacetylene, but the other conduct- ing polymers behave similarly. 2.1. Dependence on the Doping Level In fig. 3 the d.c.conductivity of trans-polyacetylene is shown as a function of the dopant concentration. Doping agents AsF, and I2 were used; they are oxidizing agents and withdraw electrons from the conjugated polymer. The oxidants are incorporated as 13S. Roth, H. Bleier and W. Pukacki 225 Fig. 3. dopant concentration (mole% ) Dependence of the conductivity of polyacetylene on the doping level. and as AsF, ions into the polymer. The dopant concentration is given in mol %, taking one CH unit as a mole. The values shown were measured at room temperature in standard samples prepared by the Shirakawa technique. We note that upon increasing the doping level the coiiductivity rises by many orders of magnitude, but there is no sharp transition from an insulating to a metallic state.Already very light doping, far below 0.1%, has a drastic effect on the conductivity. Apparently, there is no finite percolation threshold. Reasonable analytical fits to the curve in fig. 3, in the limit 0.1% < y < 10~0, are9 and"' aary' In (TE -y-' where (T is the conductivity, y the dopant concentration, and y a value between f and 4. These fits are of importance when the data are compared with the predictions from theoretical models, as discussed later. 2.2. Temperature Dependence Fig. 4 shows the temperature dependence of the d.c. conductivity for a series of iodine-doped polyacetylene samples. We see that for highly doped samples the conduc- tivity varies only slightly with the temperature, whereas for low doping levels the temperature dependence is very drastic.In no range, however, do we observe a typically metallic behaviour, i.e. a negative temperature coefficient of the conductivity. The most highly doped samples behave like very dirty metals or disordered alloys, in which the conductivity is nearly temperature independent. Phenomenologically, the curves of fig. 4 can be quite well described by (T = a, exp [ -( T / (3)226 Charge Transport in Conducting Polymers 16'. 0 0 2.2% 3.3 % n lo5 I 2 3 5 10 203050 K 3 0 2 0 0 4 temperature/ K Fig. 4. Temperature dependence of the d.c. conductivity of polyacetylene for a series of iodine- doped samples. where go and To are fitting parameters and, as in eqn (2), This formula, of course, is inspired by Mott's variable range hopping," in which case y depends on the dimensionality, d, of the hopping process: y = l / ( d + 1).(4) 2.3. Frequency Dependence In disordered materials the electrical conductivity can usually be decomposed into a frequency-independent d.c. part and an a x . contribution, which increases more or less linearly with frequency. This behaviour is also observed in conductive polymers. In fig. 5 the conductivity of nearly undoped polyacetylene is plotted versus the frequency at various temperatures.12 We see that above a certain threshold frequency the a.c. contribution dominates. The strong temperature dependence of the d.c. part causes also a strong dependence of the threshold on temperature. In doped samples the d.c. conductivity is by many orders of magnitude higher and the frequency dependence of the total conductivity is only revealed if the experiment is carried out at much higher frequencies.In fig. 6 the d.c. and a.c. conductivities at the microwave frequency of 9.9 GHz are compared for two polyacetylene samples doped to 3 and 4.5% of i ~ d i n e . ' ~ Again we see the dominance of the a.c. contribution at temperatures where the d.c. part is sufficiently frozen out.S. Roth, H. Bleier and U? Pukacki 227 frequency/ Hz Fig. 5. Frequency dependence of the conductivity of nearly undoped polyacetylene at various temperatures. (-) Theory (Ehinger et ~ 1 . ’ ~ ) ; (0) experiment (Epstein et a1.I2). 2.4. Anisotropy A common feature of all conducting polymers is the existence of extended strands of conjugated double bonds. Because of these strands at least locally the structure of conducting polymers is very anisotropic and this anisotropy should somehow show up in the electrical conductivity.There are various methods available to obtain a macro- scopic anisotropy of the polymer samples. By stretching polyacetylene films a preferen- tial orientation of the polymer chains can be achieved.14 Often it is more convenient to stretch a precursor polymer and to convert it into the final conjugated polymer after stretching. l 5 , I 6 Furthermore, the polymerisation can be carried out on oriented sub- strates.” The conductivity of stretch-oriented samples differs considerably if measured once parallel and once perpendicular to the stretching direction. The temperature dependence for the d.c. conductivity in both directions is shown in fig.7.l’ The observed anisotropy is larger than one order of magnitude. Sometimes such macroscopic measurements are criticized because microcracks parallel to the polymer chains might pretend an enhanced anisotropy. Independent of possible contaminations by microcracks are measurements of the schubweg (carrier migration distance) in the transient photoconductivity experi- ments. Because of the short migration distances of the photoexcited charge (ca. 100 %.) this method is actually a local probe. Again an anisotropy of ca. 50 in favour of carrier motion along the stretching direction and hence along the chains’’ is obtained. Of course, we would not expect the same value of the anisotropy in dark conductivity measurements. The measurements are not only on different timescales; in addition, the photoconductivity has been measured on undoped and the dark conductivity on doped samples.It is known that the packing order of the polymer chains and hence the dis- tance between two adjacent chains changes upon doping. Furthermore, different228 Charge Transport in Conducting Polymers 0.3 0.4 0.5 0.6 Fig. 6. Comparison of d.c. and microwave conductivity of iodine-doped polyacetylene as a function of temperature. ( a ) truns-(CHI,,,,)y, (6) C ~ ~ - ( C H I ~ ~ ~ ~ ) ) , . 0, 30 Hz; 0, 9.9 GHz. temperature/ K Fig. 7. Temperature dependence of the d.c. dark conductivity of stretch-oriented polyacetylene, measured parallel and perpendicular to the stretching direction."S, Roth, H. Bleier and W. Pukacki 229 Fig.8. Conjugation-breaking defect in ‘segmented’ polyacetylene. l o 3 I02 10’ 100 10-1 10-2 1 o - ~ 10-f+ 10-6 10-7 10-8 0 2 0 LO 60 80 100 120 conjugation length/A Fig. 9. Effect of conjugation length on the d.c. conductivity of polyacetylene (the samples were doped to 3.5% of iodine after chemically introducing the defects of fig. 8). Different symbols correspond to different series of samples. mechanisms of charge transport are responsible in these two cases. For the d.c. dark conductivity the carriers have to move macroscopically, in the initial response of the photocurrent, which is considered for the evaluation of the schubweg, the deplacement of charge carriers is much more local. 2.5. Dependence on the Conjugation Length There is an important question concerned with the length of the conjugated strands necessary for high conductivity. How is the conductivity related to the conjugation length? It is often speculated that the recent progress in high-conductivity polyacetylene’ is due to very long and perfect strands, but conjugation lengths beyond a certain value, say 50 A, are difficult to measure.Therefore, to study the influence of the conjugation length, several groups have shortened the conjugated strands by deliberately introducing conjugation-breaking defects, such as that depicted in fig. 8. Here an oxygen atom is bound to a carbon atom, with two protons at the neighbouring carbon atom, so that the sequence of alternating double bonds is interrupted by three adjacent single bonds. The average distance between two defects in such ‘segmented’ polyacetylene is the conjugation length lConj.230 Charge Transport in Conducting Polymers 1 4 1 - 2 intra-chain \ 2-3 inter -chain 3 - 4 inter -fibre 1 - 4 superposition of above Fig.10. Schematic view of inhomogeneities in polyacetylene to illustrate the superposition of various conduction mechanisms. The effect of conjugation-breaking defects on the conductivity is very drastic. As can be seen from fig. 9, the conductivity decreases rapidly with decreasing conjugation length, namely by eight orders of magnitude, if the conjugation length is decreased from its pristine value (perhaps 100 A) to ca. 10 A. The analytical form of the relation between conductivity and conjugation length cannot be determined very accurately.Both and In D a lConj In D cc - ( I ~ ~ ~ ~ ) - ” ~ are consistent with experimental data.” 3. Tunnelling and Hopping Conductive polymers are built of polymer chains, but these chains are not perfect. They consist of strands of conjugated double bonds interrupted by defects. In standard Shirakawa polyacetylene the chains are bundled as fibres of 100-10008, in diameter and these fibres form a loose fleece-like structure. A schematic view of such a polyacety- lene sample is given in fig. 10. Macroscopic charge transport will be a superposition of the various local transport mechanisms, uiz. within a conjugated strand, from strand to strand, and from fibre to fibre. Other types of polyacetylene and other conductive polymers will not form a fleece; nevertheless there will be inhomogeneities on a fairly large scale (crystalline and amorphous regions, doped and undoped domains etc.), so that fig.10 can even be regarded as an idealisation of these polymers. Most interesting is the conductivity within a conjugated strand: This could be called ‘intrinsic conductivity’. It would be governed by the physics of conjugated double bonds and one-dimensional metals and reveal such concepts of one-dimensional physics as metal-non-metal transitions, solitons, electron-phonon coupling etc. There is little experimental access to this intrinsic conductivity. In the models discussing the charge transport from strand to strand and from fibre to fibre the intrinsic conductivity is usually assumed to be infinite.S. Roth, H. Bleier and W.Pukacki 23 1 Fig. 11. Handwaving argument for the assumption that the localisation length is proportional to the conjugation length. For the non-intrinsic transport mechanisms various hopping and tunnelling models have been suggested. If the charge carriers move by tunnelling between individual localized states, variable range hopping is appropriate. This model has been proposed by Mott to describe the conductivity in amorphous semiconductors." Hopping is an abbreviation for 'phonon-assisted quantum-mechanical tunnelling'2o and phonons are necessary to find an unoccupied hopping site. Each site c a be occupied by one electron only (for each spin direction) and free sites will usually be higher in energy. At high temperatures many phonons are available and even hops to energy-rich states are frequent. At low temperatures only few states are within the allowed energy range, and the smaller the energy range the further apart will be the next accessible hopping site.Consequently the average hopping distance depends on the temperature, hence the term variable-range hopping. Since low-temperature hops are over long distances, they are very rare. Therefore the overall conductivity increases with the temperature. The theory leads to the formulae quoted in eqn (3) and (4). In several papers it has been shown that the temperature and frequency dependence on the conductivity of slightly and moderately doped polyacetylene is quite well described by this mechanism. 13.' ','? The dependence of the conductivity on the conjugation length finds a simple explana- tion if the model of variable-range hopping is modified to take the chain structure of the polymers into account.This model of anistropic variable-range hopping lo assumes that the wave-function of the hopping site is not spherically symmetric but rather ellipsoidal. The short axes of the ellipsoid are in the order of magnitude of the distance between neighbouring chains, and the long axis is proportional to the conjugation length. A handwaving argument for this proportionality is given in fig. 11.' Segmented polyacety- lene is assumed to consist of conjugated strands of average length lconj and of barriers of length lbarrler. Within the strands the amplitude of the wavefunction is constant, in the barrier region it decays. We assume that in the absence of any conjugated strands the localisation lengths were a;'.In the presence of conjugated strands the localisation length is apparently because there are rn strands, along which the charge carriers 'get a free ride'. Evidently, rn = ail/lbarrier. If rn is large enough the second term in eqn (7) can be neglected and the localisation length in the chain direction becomes proportional to the conjugation length.232 Charge Transport in Conducting Polymers In Mott’s variable-range hopping the parameter T,, from eqn (3) is related to the localisation length a-’ via TOK ( . ’ / W F ) (8) where n(E,) is the density of (localised) states near the Fermi level. Only these states participate in the hopping process. For anisotropic variable-range hopping eqn (8) changes to TOK &+m4 a: C n , / n ( EF) * and with all cc I& [from eqn (7)] to To If eqn (10) is inserted into eqn ( 3 ) we obtain u = a, exp {-[ TIcon,rz(EF)/a:]py} ( 1 1 ) and for y = $ (dominance of hops in chain direction) we obtain eqn (6) In OX -(/con-i)-”2 which had been found above to describe the data of fig.9 on the conjugation length dependence of the conductivity. To check whether the dependence of the conductivity on the doping level is consistent with variable-range hopping, we have to look for an expression for the density of states near the Fermi level, n ( E F ) in eqn (8)-(10). When we simply assume that the density of states is proportional to the doping level n(EFPY (12) and substitute into eqn (1 1 ) we obtain In U K --vp’” consistent with eqn (2).The assumption of eqn (12) is not unreasonable. In the idealized case of soliton doping’-5 the number of states at the Fermi level is just identical to the doping level. If polarons and other (less specific) defects are allowed as well, the proportionality will still hold. The assumption just means that oxidized strands are hopping sites and the number of free sites is linearly increased by the oxidation reaction. So far all experimental data presented in this paper have been found to be consistent with anisotropic variable-range hopping, with one important exception: the temperature dependence of the conductivity of highly doped samples (fig. 4). At zero temperature the hopping conductivity should go to zero, since there are no more phonons around to assist the hopping process, as, among others, Kaiser has pointed out recently.23 Therefore, for highly doped samples tunnelling between conducting particles is assumed instead of (or in addition to) phonon-assisted tunnelling.This model has been developed to describe the electrical conductivity of granular metals and of polymers filled with carbon-black or aluminium Tunnelling between large particles differs from tunnelling between individual grains in an important aspect. In a large particle there is a substantial reservoir of accessible states at the Fermi level. Therefore this process is independent of the temperature and only determined by the geometrical parameters of the barriers between the particles. If the particles get smaller and smaller a carrier, which has hopped from one particle to another, will create a potential difference between the two particles.At finite tem- peratures spontaneous hops will occur by thermal fluctuations and all particles will be at slightly different and thermally fluctuating potentials. The detailed analysis shows that the net tunnelling current consists of a temperature-independent part and a tem- perature-dependent part.23 This concept has been successfully applied by Philipp et al.’5 to highly doped polyacetylene. At that time it was thought that the tunnellingS. Roth, H. Bleier and W. Pukacki 233 process would be between the fibres of fig. 10. Recently, however, Plocharski2' has tried to modify the interfibrillar contacts and hence the tunnelling barriers, but apparently without any noticeable effect on the conductivity.Therefore, it is more reasonable to assume that temperature-independent tunnelling occurs between other domains within the samples (amprphous and crystalline or doped and undoped regions). 4. Conclusion We have seen that most of the experimental data on the electrical conductivity of conducting polymers are in agreement with the transport mechanism of variable-range hopping. This is particularly true for the temperature dependence in lightly doped and moderately doped samples, for the frequency dependence and the dependence on the doping level. The dependence on the conjugation length is explained if the chain structure of the polymers is taken into account and a model of anisotropic variable-range hopping is formulated.The temperature dependence of the conductivity of highly doped samples, however, is in disagreement with any kind of hopping model. To explain the finite conductivity in the low-temperature regime temperature-independent tunnelling between fairly large conducting domains has to be assumed. It should be pointed out that conceptually there is a continuous transition from tunnelling between domains to variable range hopping between individual sites. Actually, a conjugated segment of a polymer chain can be regarded either as a small conductive domain or as a fairly extended localized state. References 1 H. Naarrnann, in Electronic Properties ojConjugated Polvmers, ed. H. Kuzmany, M. Mehring and S. Roth (Springer, Heidelberg; 1987), p. 12.2 C. K. Chiang, C. R. Fincher Jr, Y. W. Park, A. J. Heeger, H. Shirakawa, E. J. Louis, S. C. Gau and A. G . MacDiarrnid: Phvs. Reu. Lett., 1977, 39, 1098. 3 S. Roth and H. Bleier, Adc. Phys., 1987: 36, 385. 4 A. J. Heeger, S. Kivelson, J . R. Schrieffer and W. P. Su, Reu. Mod. Phys., 1988, 60, 781. 5 Yu Lu, Solitons and Polarons in Conducting Polymers (World Scientific, Singapore, 1988). 6 Handbook qfconducting Polymers, ed. T. A. Skotheirn (Marcel Dekker, New York, 1986), vol. 1 and 11. 7 S. Roth, in Hopping Transport in Solids, ed M. Pollak and B. I . Shklovskii (Elsevier, Amsterdam; in press). X Electronic Properties of' Pol~~mers and Related Compounds, ed. H. Kuzrnany, M. Mehring and S. Roth, (Springer, Heidelberg, 1 st edn, 1985). Electronic Properties sf Conjugated Polymers, ed. H. Kuzrnany, M. Mehring and S. Roth (Springer, Heidelberg, 2nd ed, 1987); (Springer, Heidelberg, 3rd edn, 1989). 9 H. Shirakawa and H. Nemoto, Polym. Prep. Jpn, 1982, 31, 372. 10 D. Schafer-Siebert, Ph.D. Thesis (Karlsruhe, 1988). 1 1 N. F. Mott and E. A. Davis, Electronic Processes in Non-Cr!,stalline Materials (Clarendon Press, Oxford, 2nd edn, 1979). 12 A. J. Epstein, H. Rornrnelrnann, H. Abkowitz and H. W. Gibson, Mol. Cryst. Liq. Cryst., 1981, 77, 81. 13 K. Ehinger, S. Summerfield, W. Bauhofer and S . Roth, J. PhJx C, 1984, 17, 3753, 14 C. R. Fincher Jr, A. G. MacDiarrnid, A. J. Heeger, M. A. Druy, Y. Matsarnura, H. Shirakawa, D. L. Peebles and S . Ikeda, Solid State Commun., 1978, 27, 489. 15 H. J. Edwards and W. J. Feast, 1980, PoiJ*mer 21, 59.5. 16 G. Leising, Po1j.m. Bull., 1984, 11, 401. 17 K. Araya, A. Mukoh, T. Narahara, K. Akagi and H. Shirakawa, SJwth. Metuls, 1987, 17, 247. 18 J. Plocharski, W. Pukacki and S. Roth, to be published. 19 H. Bleier, S. Roth, H. Lobentanzer and ( 3 . Leising: Europh!is. Lett., 1987, 4, 1397. 20 R. Zallen, The Phjxics of Amorphous Solids (New York, Wiley, 1983). 21 J. Chroboczek and S. Summerfield, J. Ph1.s. (Paris), 1083, C3, 517. 22 K. Ehinger and S. Roth, Philos. Mag. Src,t. B., 1986, 53, 301. 24 P. Sheng, Phys. Rev. B, 1980, 21, 2180. 23 A. B. Kaiser in Electronic Properties of'Conjugated Pol~-mers, ed. H. Kuzmany, M. Mehring and S. Roth (Springer, Heidelberg, 3rd edn, 1989). 25 A. Phillipp, W. Mayr and K. Seeger, Solid Stute Commun., 1982, 43, 857. 26 J. Plocharski and S. Roth, Synth. Mrtuls, 1989, 30, 109. Puper 9/02544H; Received 15th June, 1989

ISSN:0301-7249    

DOI:10.1039/DC9898800223

出版商:RSC    

年代:1989

数据来源: RSC