J. Phys. Chem. 1995, 99, 12294-12300
12294
Redox Activity of Vinylferrocene Copolymers by Electron Hopping Reaction in the Absence of Fluid Solvents Masayoshi Watanabe" and Hideaki Nagasaka Department of Chemistry, Yokohama National University, 156 Tokiwadai, Hodogaya-ku, Yokohama 240, Japan
Naoya Ogata Department of Chemistry, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102, Japan Received: March 21, 1995@
A series of novel copolymers consisting of a redox monomer, vinylferrocene, and an ion-conducting monomer, o-methacryloyl-a-methoxy-oligo(ethy1eneoxide) (average molecular weight = 470), have been prepared by radical copolymerization and characterized. Ionic conductivity and redox activity of the copolymers, complexed with lithium perchlorate, have been explored by using complex impedance spectroscopy and solid state voltammetry with microelectrodes, respectively. The copolymer/salt complexes exhibit ionic conductivity of S cm-' at room temperature and chemically reversible redox activity by themselves without any fluid solvents. The redox activity can be assigned to redox reactions of ferrocene sites in the bulk polymeric phases. The redox reactions are caused by propagation of oxidized (reduced) sites, generated at the electrode/ copolymer interface, by electron transfer (electron hopping) reactions between mixed valent ferrocene/ ferrocenium sites in the diffusion layer. Apparent electron diffusion coefficient for the electron transfer reactions, evaluated by potential step chronoamperometry, increases with increasing vinylferrocene composition in the copolymers. These copolymer/salt complexes are intrinsic redox conductors which exhibit appreciable ionic conductivity and redox activity by themselves without any fluid solvents and can be distinguished from conventional redox polymers.
Introduction Polymer electrolytes[ are solvent-free ion-conducting polymers which are mostly solid solutions of electrolyte salts in saltsolubilizing polymers like poly(ethy1ene oxide) (PEO) derivatives. Extensive studies have been conducted on syntheses, structures, properties, and applications of the polymer electrolytes. Most of the studies have been directed to ionic conductivity of the polymer electrolytes and their potential application as solid electrolytes in advanced electrochemical devices.' An interesting property of the polymer electrolytes, which is not found in inorganic solid electrolytes including glasses, is the ability to dissolve redox active solutes in the bulk phases, just like low molecular fluid solvents. Although electrochemical voltammetry had been traditionally constrained to experiments in fluid electrolyte solutions by the experimental requirements of ionically conducting media, the solute-solubilizing property of the polymer electrolytes as well as their appreciable ionic conductivity has made it possible ta conduct electrochemical voltammetry2 in the bulk polymeric phases.3 Facilitating developments, in addition to the polymer electrolytes, have been ultramicr~electrodes,~ which can compensate for iR drop problem during the electrochemical measurements due to poorer ionic conductivity of the polymer electrolytes than conventional fluid solvents. As in fluid electrolyte solutions, the electrochemical measurements in polymer electrolytes (solid state voltammetry) have provided a wealth of information concerning solutes in the polymeric media,2 such as the diffusion coefficients, the heterogeneous electron transfer rates at the polymer/electrode interface, and the formal potentials. It is also possible to exploit information of the solutes as tools to probe dynamics of the polymer itself.5 Furthermore, the electrode interfaces in contact ~
@
Abstract published
In
Adwnce ACS Absiructy, July 15. 1995.
0022-3654/95/2099- 12294$09.00/0
with the polymer electrolytes can be modified and functionalized6 in ways analogous to those demonstrated for chemically modified electrodes in fluid media.7 One of the characteristics in the solid state voltammetry is, first, extremely low diffusivity of redox solutes in the polymeric phases. The suppressed diffusivity enhances the importance of electron transfer reaction between the redox solutes in the charge transport process during electrochemical reactions, as can be expected by Dahms-Ruff's equation:* Dapp
= Dphys
+ (1/6)kexs2c
(1)
where Dappis the electrochemically-determined apparent diffusion coefficient, Dphysis the physical diffusion coefficient, k,, is the electron self-exchange rate constant, 6 is center-tocenter distance of the solutes at electron transfer, and C is concentration of the solutes. In fluid solvents Dphysof low molecular redox solutes are mostly 10-5-10-6 cm2 s-'. Under these conditions, contribution of the electron transfer reaction to Dappis small, even if kex of the solute is relatively high. However, Dphys of redox solutes in polymer electrolytes is typically 1 0 - ~ - i O - ' ~cm2 s-I or lower at room temperatures2 Thus, the contribution of the electron transfer reaction to Dapp can be experimentally d e t e ~ t e d .A~ typical example is the solid state voltammetry of LiTCNQ (lithium salt of anion radical of 7,7,8,8-tetracyanoquinodimethane)in network PEO polymer electrolyte^.^^,^ In this system, contribution of the electron transfer reaction to the charge transport process during the redox reaction is much larger for the oxidation of TCNQ- than for the reduction.9a This is due to the fact that k,, for the TCNQ-/ TCNQO couple is quite large; however, k,, for the TCNQ-/ TCNQz- couple is much lower. Second, the dynamics of polymeric molecules themselves, which would affect the dynamics of physical diffusion and electron transfer reaction 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 32, 1995 12295
Redox Activity of Vinylferrocene Copolymers
Polymer film
SCHEME 1: Structure of poly(VFc-co-MEOs)
*y-
e
45
10 pm
C 'O-(CH2CH2O),-CHJ
of the redox solutes, greatly changes with the changes in temperature and electrolyte salt concentrati~n.~?~ It has been reported that proportional correlation between the physical diffusivity of TCNQ- and the electron transfer reaction (kexd2) of TCNQ-/TCNQo couple is found in remarkably wide variety of the diffusivity (10-7-10-'2 cm2 s-l) in the LiTCNQ system.9b In this perspective, it is quite of interest to explore the effects of incorporation manner, concentration, and electron self-exchange rate constant of redox solutes and of the change in polymer dynamics on the electron transfer reactions. In this study, redox solutes have been incorporated into polymer electrolytes by covalently attaching them to ionconducting polymers;I0 i.e., copolymers consisting of an ionconducting monomer and a redox monomer have been synthesized. As the redox and ion-conducting monomers, vinylferrocene and o-methacryloyl-a-methoxy-oligo(ethy1ene oxide) have been selected, respectively. Distinguishable characteristics of this system, compared with solute solutions in polymer electrolytes, would be that the redox solutes could not individually diffuse over a long distance because of the covalent attachment to polymer backbone and that concentration of the solute could increase without the phase separation problem by changing composition of the polymers. We have intended to explore the following points in this study: first, whether redox response of the covalently attached solutes can be observed in the bulk polymeric phases in the absence of any fluid solvents; second, how electron transfer reaction between the redox centers is concerned with the redox reaction; and third, how change in the copolymer composition influences the electron transfer reactions.
Experimental Section Chemicals. Vinylferrocene (VFc) was purchased from Aldrich and purified by sublimation under reduced pressure (0.1 Torr) at 45 "C. o-Methacryloyl-a-methoxy-oligo(ethy1ene oxide) (MEO9, nominal average molecular weight = 470) was purchased from Polysciences and used as received. 2,2'Azobisisobutyronitrile (AIBN, Wako Pure Chemical) was recrystallized three times from methanol below 35 "C. Benzene was repeatedly washed with sulfuric acid, then washed with an aqueous sodium hydroxide solution and water, successively, dried over calcium chloride, and purified by fractional distillation. Diethyl ether was used after drying over 4A molecular sieves. Anhydrous LiC104 (Kishida Kagaku) was dried at 150 "C under vacuum for 24 h. Spectroscopic grade acetonitrile and methanol (Dojin Kagaku) were stocked over 4A molecular sieves before use. Copolymer Preparation and Characterization. The copolymers, poly(VFc-co-MEO9), having different compositions were prepared by radical copolymerization (Scheme 1). Into a glass ampule were injected a mixture of VFc and ME09 at a known ratio (7.5 mmol in total), 6.2 mg (0.5 mol % on the basis of total monomers) of AIBN as initiator, and 3 mL of benzene, it was evacuated by freeze-thaw cycles and sealed under vacuum. Polymerization was carried out at 60 "C. The copolymers were purified by repetitious reprecipitation (3 times) from a benzene solution into an excess of diethyl ether and dried in vacuo.
t
'
r
-I
REF.
WE. Ag
0
AUX.
glass
'
epoxy
Figure 1. Structure of microcell for solid state voltammetry.
Electronic spectra of the copolymers were measured in methanol by using a Shimadzu UV-240 spectrophotometer. The copolymer composition was determined by the maximum absorbance at 440-450 nm, assignable to the ferrocenyl group. Ferrocene was used as a standard substance for the composition determination: A,,, = 441 nm ( E = 9.0 x 10 M-' cm-I). Infrared spectra were measured by using a Shimadzu IR-435 spectrophotometer. H NMR spectra (JEOL GX270) were recorded at 270 MHz in CDCl3 with tetramethylsilane as internal standard. Gel permeation chromatography (GPC) was carried out with Shodex GPC KF-80M columns (two columns connected in series) at 40 "C using tetrahydrofuran (THF) as the elution solvent at a flow rate of 1 mL/min driven by a Shimadzu LC-1OAD pump. A UV-vis (JASCO 875-UV) detector and a refractive index (Shimadzu RID-6A) detector, connected in series from the upper to lower flow, were used for GPC analyses of the eluents. The columns were calibrated with narrow distribution poly(ethy1ene oxide) standards (Tosoh) by using the RI detector. Injected sample concentration and amount were 0.1 wt % and 100 pL, respectively. Differential scanning calorimetry (DSC) of the copolymers was conducted by using a Seiko Instruments DSC-200 calorimeter at a heating rate of 20 OC/min under nitrogen atmosphere. Glass transition temof the copolymer was taken at the onset temperperature (Tg) ature of heat capacity change observed during glass transition. Measurements. Ionic conductivity and electrochemical measurements were conducted on the copolymers doped with LiC104. The copolymer and LiC104 were dissolved in acetonitrile, and the solvent was completely removed in vacuo at 40 "C to obtain the copolymer/LiC104 complexes. Concentration of LiC104 in the copolymer was represented by the molar ratio of LiC104 to ether oxygen atoms in the copolymer and was kept at Li/O = 1/30 in this study. The copolymer/LiC104 complex, together with a poly(tetrafluoroethylene)ring spacer, was sandwiched between two platinum disk electrodes (effective diameter of 10 mm), and frequency dependence of the cell impedance was measured under argon atmosphere using a Yokogawa Hewlett Packard 4192A impedance analyzer at 500 mV amplitude in the frequency range of 5 - lo6 Hz under controlled temperatures. Ionic conductivity of the copolymer/LiC104 complex was evaluated by using complex impedance method.' I Electrochemical measurements (solid state voltammetry) were made by using three-electrode microcells, as shown Figure 1. The three-electrode microcell consists of tips of three electrodes:2 Pt microelectrode (10 pm diameter, sealed in soft glass capillary), and Pt and Ag wires (0.4 mm diameter) counter and pseudoreference electrodes, respectively, all sealed in an insulating epoxy cylinder. The surface of the microcell was polished by using diamond and alumina pastes (successively smaller
'
Watanabe et al.
12296 J. Phys. Chem., Vol. 99, No. 32, 1995
TABLE 1: Preparation and Characterizationof Copolymers monomer
copolymer VFc GPC data reaction conversion composn concn (wt %) VFc (mol %) (M) MdRIY' Mw(RI)" MwIMn(RI)' Mw(UVIb MwIMdUV)b Tg("C) (mol 8) time (h) 12.4 -64.2 54800 5.13 4430 8360 42900 22 79 3.69 80 137 -62.2 186000 4.31 43200 4.10 61 63 2.49 34400 141000 60 69 31900 113000 3.54 -63.0 85200 3.41 38 59 2.25 25000 60 276 158000 3.77 -60.5 3.76 41900 48 53 1.91 31900 12oooO 50 113 44200 169000 3.82 -64.0 3.89 50 48 1.65 32900 128000 40 109 C C -64.4 C C C C 44 32 0.96 20 20 GPC data monitored by UV-vis detector at 445 nm. No GPC data because of partial gelation. a GPC data monitored by RI detector.
in feed, VFc
down to 0.05 pm, Buehler), and the electrode surfaces were exposed. The microcell was cleaned by polishing and sonication before each use. The copolymer/LiClO4 complexes were contacted on the tips of the microcell electrodes by the solvent casting method, and the solvent was completely removed under vacuum. The thickness of the complex film on the microcell was made sufficiently thicker than the diffusion layer formed during electrolysis. The electrochemical measurements were carried out under argon atmosphere and controlled temperatures with a locally constructed highly sensitive potentio~tat~~ and a function generator (Hokuto Denko HB-104) in a Faraday cage, and the results were recorded on a Rikadenki RW-21 X-Y recorder.
0
20 40 60 80 VFc fraction in feed
100
Figure 2. Copolymer composition curve for poly(VFc-co-MEO9). Results and Discussion Characterization of Redox Copolymers. The copolymers obtained were orange-colored rubbery materials having viscoelastic property. Table 1 summarizes the results of preparation and characterization of the redox copolymers. When the VFc mole percent in feed was low, gelation of the polymerization solutions easily occurred. However, the redox copolymers having six different VFc compositions ranging from 30 to 80 mol % could be obtained by the radical copolymerization method. To characterize the copolymers, GPC data were collected by using the UV-vis and RI detectors, as shown in Table 1. At 445 nm where detection wave length of the Wvis detector was fixed, VFc moiety has a characteristic absorption maximum, whereas ME09 moiety has no absorption. The GPC data by the UV-vis detector, thus, reflect selective information of VFc moiety in the copolymers. On the contrary, the GPC data by the RI detector represent information of both VFc and ME09 moiety in the copolymers. The molecular weight and polydispersity data measured by the W - v i s and RI detectors (Table 1) reasonably coincide with each other.'* The reasonable agreement of the GPC data, irrespective of the detectors, confirms that a series of poly(VFc-co-MEO9) can be prepared by the radical copolymerization. It is also important to note that the GPC charts showed no elution peaks, assignable to VFc, MEO9, and their relating low molecular weight derivatives. This is the most significant criterion to discuss change transport property of the copolymers, as mentioned later. NMR and IR data also indicate the copolymer structure shown in Scheme 1, as follows: 'HNMR (6 from TMS): 3.8-4.3 (-C5H4 Fe CsHs), 3.6 (-0-CH2CH2-0-), 3.4 (-0-CH31, 0.9 (-CH3, a-methyl). IR (KBr): 3070 cm-' (YC-H, cyclopentadienyl), 2870 cm-' (YC-H, aliphatic), 1725 cm-' (YC-01, 1100 cm-' (YC-0,oxyethylene). Tg of the copolymers did not greatly depend on the copolymer compositions and ranged from -60 to -64 "C. Figure 2 shows VFc fraction in the copolymers plotted against VFc fraction in feed. Monomer reactivity ratios were estimated by using Kelen-TiidB~'~~ and Fineman-Ro~s'~~ methods. The results are given in Table 2. The rl and r2 values, determined by the two different methods, agreed with each other. The
TABLE 2: Monomer Reactivity Ratio ~~
MI M2 method rl r2 VFc ME09 Fineman-Ross 0.76 0.48 ME09 Kelen-TudBs VFc 0.77 0.55 copolymer composition curve in Figure 2, which was calculated by using the rl and r2 values determined by the Kelen-Tiid8s method, well represents the experimental data. The copolymer composition curve close to the diagonal line indicates random nature of the sequence distribution of VFc and ME09 in the copolymers. This fact implies that average concentration of VFc sites in the bulk copolymers and the local concentration which is an important parameter for the change transport between VFc sites (vide infra) are not appreciably different. The bulk concentrations of VFc sites in molarity are shown in Table 1.'* Redox Response of Covalently Attached Solutes. Electrochemical systems, where electronically conducting electrode materials are in contact with ionically conducting electrolyte materials and electrochemical reactions occur at the interfaces, presume appreciable ionic conductivity of the electrolyte materials because of the practical requirements of control of the electrode potential^.'^ In the solid state voltammetry studies of redox solutes dissolved in polyether-based polymer electrolytes, quantitative electrochemical measurements can be conducted2 by using ultramicr~electrodes~ which diminish the measuring current. This is owing to the fact that ohmic drop (iRdrop) is negligible even in the polymer electrolyte phases, though the ionic conductivity is much lower than that of fluid electrolyte solutions.I The experimental situation in the present study is different from that in the previous solid state voltammetry ~ t u d i e sin ~ .the ~ point that redox sites (VFc sites) in this study are covalently attached to the polymer backbone. However, it is also necessary for the copolymers to have appreciable ionic conductivity in order to conduct electrochemical measurements of the bulk polymeric phases. Figure 3 shows typical temperature dependence of ionic conductivity for poly(VFcco-ME09)(48 mol % of VFc) complexed with LiC104.I5 Although the VFc moiety, which does not contribute to the ionic conduction, is introduced in poly(VFc-co-MEO9), the ionic
J. Phys. Chem., Vol. 99, No. 32, 1995 12297
Redox Activity of Vinylferrocene Copolymers
(a) Physicaldiffusion
-3 4
(b) Electron hopping
I
-5
6
-E
.
(%
-7 -8
-in -9
Figure 5. Possible charge transport processes for redox reaction. -1 1 2.8
3.2
4.0
3.6
4.4
1000/T (K-I)
Figure 3. Arrhenius plots of ionic conductivity of poly(VFc-co-MEO9) (48mol % of VFc) complexed with LiC104 (Li/O = 1/30).
I O 1nA
-0.2
E I v vs. Ag
0.8
Figure 4. Cyclic voltammograms (10 mV/s) at Pt disk (10 p m in diameter) electrode for poly(VFc-co-MEO9) complexed with LiC104 (Li/O = 1/30) at 40 OC. Composition of VFc mol %: (A) 79; (B) 63; (C) 59; (D) 53; (E) 48;(F) 32.
conductivity reaching S cm-' at room temperature is comparable to that of the network PEO polymer electrolytes3 in which quantitative solid state voltammetry was possible.2 The ionic conductivity of the copolymer/LiC104 complexes tended to decrease with increasing VFc mol % in the copolymers. Figure 4 shows solid state cyclic voltammetry of the copolymers containing LiC104 at 40 "C. Oxidation waves, having formal potentials of ca. 0.3 V vs Ag, are well-defined in each copolymer. Judging from the formal potentials and the copolymer structures, these redox waves can be assigned to the redox reactions of ferrocene sites in the copolymers. It should be noted that the ferrocene sites undergo chemically reversible redox reactions, although these sites are covalently attached to the polymer backbone, and the experiment is conducted in the absence of any fluid solvents. The present electrochemical system is quite unique because the copolymers themselves
function as polymeric solvents to dissolve LiC104 and to give appreciable ionic conductivity to the copolymers and at the same time function as electroactive solutes. The redox current of the copolymer increases with increasing VFc composition, as seen in Figure 4. The peak-potential separation tends to increase with increasing VFc compositions, especially it is pronounced for the copolymer having the highest VFc composition (Figure 4A). This can be attributed to uncompensated iR drop because the copolymer having the highest VFc composition exhibited the lowest ionic conductivity. Redox Activity by Electron Hopping Reaction. Charge transport process during the reversible redox reaction, seen in Figure 4, is considered here. When the electrode is polarized, the appreciable ionic conductivity of the copolymer/LiC104 complexes allows to form predominant potential gradient at the copolymer/electrode interface. Charge imbalance at the interface made by the redox reaction can be compensated by ionic migration from the copolymer bulk. These molecular pictures at the electron transfer may be similar to those in low molecular weight redox solutes dissolved in fluid solvents.l4 However, the redox sites in these copolymers are covalently attached to the polymer backbone, and free diffusion of the redox sites is impossible. Under this situation, if only the redox sites in the vicinity of the electrode surface can transfer electrons, the voltammograms should have the feature of surface-confined reactions. However, the voltammograms in Figure 4 are of typical diffusion-controlled process. This clearly shows that the ferrocene sites far from the electrode surface transfer electrons toward and from the electrode (vide infra). Figure 5 shows two possible charge transport processes during redox reactions which accompanies charge transport from the bulk. In Figure 5a, the charge is transported by diffusion of redox molecules, followed by electron transfer reaction at the interface. The charge transport in Figure 5b is propagation of electrons (holes) of reduced (oxidized) species generated at the interface by electron hopping (homogeneous electron transfer) reactions. It is known that both of the processes contribute to electrochemical charge transport,8 though the contribution of the electron hopping process is negligibly small in fluid solutions of low molecular redox solutes, as described earlier. However, here we presume (vide infra) that the charge transport during electrochemical reactions of the present redox copolymers is conducted by the electron hopping process between adjacent ferrocene sites, since the ferrocene sites are covalently linked together and free diffusive displacement of the individual ferrocene site is impossible in the present copolymers. If the charge transport is the electron hopping process, the hopping rate can be evaluated by measuring apparent electron diffisivity, utilizing electrochemical techniques under diffusioncontrolled condition. Figure 6A shows typical Cottrell plots of the current-time curve (Figure 6B) for the copolymer, when the electrode potential was stepped from -0.2 to 0.6 V vs Ag.16 If diffusion profile during the electrolysis is linear and semi-
Watanabe et al.
12298 J. Phys. Chem., Vol. 99, No. 32, 1995 VFc composition / mol%
01020 3040 50 60 201,l
0.001 0.0
.
' 0.1
.
'
0.2
'
0.3
.
0 30
Time I
70
80
90
I
1
7
Figure 7. VFc concentration (composition) dependence of electron diffusion coefficient (Dapp)in poly(VFc-co-MEO9) at 40 "C.. The LiC104 concentration of Li/O = 1/30 is converted into the molarity of 0.61, 0.54, 0.51, 0.47, 0.44, and 0.29 M, from low to high VFc composition copolymers, respectively.
50 1
s
Figure 6. Typical Cottrell plot of poly(VFc-co-MEO9) (48 mol % of VFc) at 40 "C, A; its current-time curve at potential step chronoamperometry and the best fit to eqs 2 and 3, B.
infinite, the Cottrell plots should be linear having zero intercept. However, the Cottrell plots for the copolymer have definite intercept, which indicates that the diffusion profile is the mixture of linear and radial diffusion. The peak-shaped cyclic voltammetry, seen in Figure 4, and the time-dependent current, seen in Figure 6B, are the evidences for contribution of linear diffusion, while the definite intercept of the Cottrell plots, seen in Figure 6A, is that of radial diffusion. The electron diffusion coefficient (Dapp) at disk electrodes, where the diffusion profiles are the mixture of linear and radial diffusion, is estimated by fitting the experimentally obtained current-time (i-r) curves to Shoup-Szabo's equation,I7as reported elsewhere,2with changing D,, as adjustable parameter:
i = 4nFrDaP,C{0.7854 4-0 . 8 8 6 2 ~ - "4~ 0.2146 exp(-0.7823~-'/~)} (2) 2
I
VFc concentration / mol d W 3
540
z = 4Da,,t/r
1
I
-Experimental data - - - Calwlaled limr-curnnt curve by wing Szabo's equation
, 20
I
0.4
1 /A lSQ.5
0 0.0010
I
(3)
where n, F,r, and C are the number of electrons transferred at each reaction, the Faraday constant, electrode radius, and the concentration of redox sites, respectively. This equation reproduces i-t curves at disk electrodes, irrespective of the diffusion pr0fi1es.I~ The broken line in Figure 6B is the best fit to the experimental i-t curve by using eqs 2 and 3, and Dapp = 6.8 x lo-" cm2 s-I. Copolymer Composition and Electron Diffusivity. Figure 7 shows Dapp values plotted against VFc concentration (composition) in the copolymers.'* The D, values of the copolymers at 40 "C ranged from 10-l' to cm2 s-I and tended to increase with increasing the VFc composition. Although some scattering in the data is seen, we have confirmed that this tendency is observed at several different temperatures. l 9 Here, we reconsider the possibility of the physical diffusion process of ferrocene sites in the copolymers, as shown in Figure 5a, during the redox reactions. When we consider dynamics of the copolymers, both local segmental motion (microbrownian motion) and self-diffusion of the entire polymer chain (motion of the center of gravity) should be taken into since the measuring temperature is well above the Tgof the copolymer/ salt complexes. Of course, the latter dynamics is much slower
than the former.20 Although complexation of LiC104 with the copolymers raised the Tg,their T, still lie at ca. -50 "C irrespective of the copolymer composition. The relative importance of both the motions to the polymer dynamics is closely correlated with time scale of Dappmeasurements.20 In the Dapp measurements by chronoamperometry, the measuring time scale is in the order of 10' s, as typically shown in Figure 6B. Thickness of the diffusion layer during the measurement is given by (nDappt)"2 on the assumption of linear and semiinfinite cm2 s-I diffusion.*' By using the typical values, Dapp= and r = 50 s, the thickness of the diffusion layer is estimated as 1.25 x IO4 A. On the contrary, the length of the fully stretched polymer chain, assuming all trans zigzag conformation of the main chain, is only 9.4 x lo2 A even for the relatively high molecular weight copolymer (48 mol % of VFc, see Table 1). The large difference indicates that self-diffusion (centerof-gravity diffusion) of the entire polymer chain must be involved in the charge transport, if electronic charge for the redox reaction is transported only by the physical diffusion process. It is well-known that self-diffusion of polymer chains in the polymer melts is quite sensitive to the molecular eight.^^-^^ Below the characteristic molecular weight for entanglement (AIc),the self-diffusion coefficient is in proportion to M-' ( M = molecular weight), according to the Rouse theory.25 Sufficiently above M, and on the assumption that only reptation of polymer chain takes place, the Doi-Edwards theory26predicts that the self-diffusivity is in proportion to W2. Although we do not know the Mc of the each copolymer, there is no correlation between the copolymer molecular weight and the Dappvalue, by referring to Figure 7 and Table 1. This is a strong evidence that the charge transport in the copolymer is not carried out by the center-of-gravity physical diffusion process. The fact that the diffusion layer thickness is much larger than the length of the fully stretched chain thus proves the existence of the electron hopping process. Another evidence for the electron hopping process is found in the nearly linear increase of the Dappvalue, having zero intercept, with VFc concentration (Figure 7). This sort of increase in Dappwith redox site concentration has been found for charge transport process in some covalently attached redox polymers modified on electrode^,^ such as electrochemically polymerized Os(II) complex films by Murray and c o - w ~ r k e r s , ~ ~ ~ viologen polymers by Oyama and c o - ~ o r k e r sphenothiazine ,~~~ polymers by Morishima and c o - w o r k e r ~ and ,~~~ electrochemically polymerized Co(I1) complex films by Abruiia and cow o r k e r ~ . ~The ' ~ explanation of the concentration-D,,, relationship is based on, in most cases, disappearance of Dphysin eq 1 due to the covalent attachment of the redox sites to the polymer backbone, resulting in the linear increase of electron diffusivity with redox site concentration. If we consider that
J. Phys. Chem., Vol. 99, No. 32, 1995 12299
Redox Activity of Vinylferrocene Copolymers
Dphysin the present VFc copolymers is also negligible, the result in Figure 7 is also understandable. A remaining problem is how local segmental motion of the copolymers is concemed with the electron hopping process. Blauch and SavtantZ8recently presented the theory which represents the charge transport by electron hopping between redox centers which are irreversibly attached to supramolecular systems. They introduced a new concept-the bounded diffusion-which takes into account local displacement of the redox centers from equilibrium position in the supramolecular redox systems. When the local displacement is much faster than the electron hopping and the range of displacement (A) is larger than center-to-center distance between the redox centers at electron transfer (d), the electron diffusivity is expressed by
Dapp= ( 1/6)ke,Ch2
(4)
where h2 is expressed by
Ax2 = d2
+ 3A2
(5)
In this bounded diffusion model, the local displacement (A) of redox centers in addition to the electron transfer reaction at d contributes to the Dappvalues. In the present redox polymers, the local segmental mobility of VFc sites is quite high, because the copolymers are completely amorphous and their Tg is much lower than the measuring temperature of Dapp. The charge transport in the VFc copolymers by the electron hopping process, the behavior in Figure 7, can be understood in terms of the bounded diffusion model, and the local segmental motion of VFc sites may contribute to the Dappvalues. Additionally, redox site concentration ( C ) in eqs 1 and 4 should be local concentration that is concemed with the electron hopping reaction. As stated before (Figure 2), since the present copolymers have random nature in terms of the sequence distribution, we think that the local concentration and the average concentration, estimated by the copolymer compositions, do not differ appreciably. It is important to note that the electron hopping processes in the present polymeric systems involves both intramolecular and intermolecular hopping processes, which we cannot distinguish at the present. Since VFc concentrations in the copolymers (Table 1) are higher than LiC104 concentrations (Figure 7, caption), and further, the difference is pronounced with increasing the VFc concentration, it may be necessary to consider the migration e n h a n ~ e m e n tof ~ ~ electron diffusivity . However, we have concluded that the migration effect is minor for considering the charge transport, because of the following reasons. First, the migration enhancement of transient responses29cis pronounced, when true diffusion coefficient of electron hopping (De)is much higher than diffusion coefficient of electroinactive counterion (Di). The diffusion coefficient of C104- in the present copolymers is not available. However, there are ample data30 which anticipate that Di De. In the network PEO polymer electrolytes, structurally close materials to the present copolymers, DCIQ-at 40 "C is higher than cm2 s-], which is estimated by Dc1oa- = ~ D T c N Q -In. ~linear ~ PEO,Dcl04- and DSCN-at 40 "C, evaluated respectively by solid state NMR30a and radiotracer experiments,30bare higher than cm2 s-l. These data indicate that Di/D, and that the migration effect is negligible in the present copolymers. Second, we have foundI9 that local polymer dynamics effects dominate over the electron diffusivity, rather than the migration effect. The LiC104 concentration of Li/O = 1/30 was fixed, though the molarity is changing depending on the copolymer composition, so as to
--
adjust Tgof the copolymers at a constant value (ca. -50 "C). It should be noted that the linearly increasing tendency of the Dapp values with VFc concentration in the copolymers, as shown in Figure 7, is seen when Tg of the copolymers, i.e., their local dynamics, is similar. This may also support the validity of the bounded diffusion model to the present copolymers. Finally, the Dapp value extrapolated to 100 mol % of VFc in the present copolymers, 2.5 x cm2 s-l, is compared with those for PVFC.~'This value well agrees with the early work (Dapp = 2 x cm2 s-l from digital simulation of cyclic voltammetry) by Peerce and Bard31a for electrochemically deposited PVFc film in 0.1 M TBAFVCHsCN and with the recent work of Sullivan and Murray3Ib (Dapp= 7.9 x 1O-Io cm2 s-I from steady state limiting current) for mixed valent PVFc film on interdigitated array electrodes under dry N2 atmosphere. Although there have been several works3' which report somewhat higher and lower Dappfor PVFc modified electrodes in fluid electrolyte solutions than the present value, we have noticed that the D, values of the present copolymers are greatly influenced by the local polymer dynamics, as mentioned above. It is concluded that redox reactions of the copolymers, seen in Figure 4,are caused by the electron hopping between VFc sites (Figure 5b). The charge transport by electron hopping during redox reactions has been widely found in polymer modified electrode system (vide s ~ p r u ) , ~where . * ~ the electrodes coated by redox polymers are immersed in fluid solutions or plasticized by fluid solvents. However, most of the redox polymers exhibit redox activity only when they are in contact with fluid solutions, because the coated redox polymers themselves do not have appreciable ionic conductivity. On the other hand, the present copolymers complexed with LiC104 exhibit redox activity by themselves, in other words, in the absence of any fluid solvents. In this sense, these copolymer complexes are intrinsic redox conductors or intrinsic iodelectron mixed conductors and can be distinguished from conventional redox polymers.
Acknowledgment. This research was supported in part by a Grant-in-Aid for Scientific Research on Priority Areas (No. 236/6226228) from The Japanese Ministry of Education, Science and Culture and Kanagawa Academy of Science and Technology Research Grants (No. 95203). H.N. acknowledges JSPS fellowship for Japanese Junior Scientists. References and Notes (1) (a) Polymer Electrolyte Reviews Vols. 1 and 2; MacCallum, J. R., Vincent, C. A., Eds.; Elsevier Applied Science: London, 1987, 1989. (b) Armand, M. B. Annu. Rev. Mater. Sci. 1986, 16, 245. (c) Vincent, C. A. Prog. Solid State Chem. 1987, 17, 145. (d) Ratner, M. A,; Shiver, D. F. Chem. Rev. 1988, 88, 109. (e) Watanabe, M.; Ogata, N. Br. Polym. J . 1988, 20, 181. (0 Applications of Electroactive Polymers; Scrosati, B., Ed.; Chapman and Hall: London, 1993. (2) (a) Reed, R. A,; Geng, L.; Murray, R. W. J . Electroanal. Chem. 1986, 208, 185. (b) Watanabe, M.; Longmire, M. L.; Murray, R. W. J . Phys. Chem. 1990, 94, 2614. (c) Longmire, M. L.; Watanabe, M.; Zhang, H.; Wooster, T. T.; Murray, R. W. Anal. Chem. 1990,62,747. (d) Wooster, T. T.; Longmire, M. L.; Watanabe, M.; Murray, R. W. J . Phys. Chem. 1991, 95, 5315. (3) (a) Watanabe, M.; Nagano, S.;Sanui, K.; Ogata, N. Polym. J . 1986, 18, 809. (b) Watanabe, M.; Itoh, M.; Sanui, K.; Ogata, N. Macromolecules 1987, 20, 569. (4) (a) Wightman, R. M. Science 1988, 240, 415. (b) Ewing, A. G.; Dayton, M. A.; Wightman, R. M. Anal. Chem. 1981, 53, 1842. (c) Fleischmann, M., Pons, S., Rolison, D. R., Schmidt, P. P., Eds. Ultramicroelectrodes; Datatech Systems: Morganton, NC, 1987. (d) Chidsey, C. E. D.; Murray, R. W. Science 1986, 231, 25. (e) Wightman, R. M.; Wipf, D. 0. In Electroanalytical Chemistiy Bard, A. J. Ed.; Marcel Dekker: New York, 1989; Vol. 15, pp 267-353. (5) Pinkerton, M. J.; Le Mest, Y.; Zhang, H.; Watanabe, M.; Murray, R. W. J . Am. Chem. SOC. 1990, 112, 3730.
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Jp950800+
