2614
J . Phys. Chem. 1990, 94, 2614-2619
A Study of Ferrocene Dlffusion Dynamics in Network Poly(ethy1ene oxide) Polymer Electrolyte by Solid-state Voltammetry M. Watanabe,*>+M. L. Longmire, and Royce W. Murray* Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290 (Received: July 17, 1989)
The diffusion rates of five ferrocene derivatives dissolved in an amorphous, cross-linked poly(ethy1ene oxide) (PEO) polymer electrolyte are measured by an electrochemical technique which detects the rate of their transport to an oxidizing microdisk cm2 electrode. The diffusion coefficients in dilute ferrocene/polymer solutions at 65 OC vary from 3 X lo-' to 2 X S-I depending on the size of the ferrocene derivative. The diffusion coefficients decrease with increasing ferrocene concentration, increasing LiC104 electrolyte concentration, and decreasing temperature; values approaching 1O-Io cm2 s-I are encountered at room temperature. The concentration dependencies conform to a simple free volume model. The qualitative similarities of the temperature and concentration dependencies of the ferrocene diffusion rates to the behavior of ionic conductivity of network PEO/LiC104 solutions suggest that the decrease in ionic conductivity observed at high electrolyte concentration is due to a decrease in the ionic diffusivity.
oxide); measurements reported here were made with LiC104 a s The experimental requirement of a strongly ionically conducting electrolyte. The diffusion coefficients as measured by cyclic medium has traditionally constrained electrochemical voltammetry voltammetry and by chronoamperometry are found to decrease interpretable by Fickian diffusion mathematics to experiments at higher electrolyte concentration and at higher ferrocene conin fluid electrolyte solutions. The situation has recently changed, centrations. (In ordinary fluid electrolyte solutions, diffusion and it is now possible to perform quantitative voltammetry of coefficients usually vary little or not at all with concentration.) molecular solutes and to discuss electron-transfer and mass The concentration and temperature dependencies of the diffusion transport phenomenal4 in rigid and semirigid polymer solvents. This development offers important new approaches to solid-state rates are compared to those of small molecules and ions in rubbery chemistry. Facilitating developments have been thin-film ionSand polymers, are found to be similar to the behavior of ionic conelectron conducting6polymers combined with ultra micro electrode^^ ductivity in network PEO, and yield insight into the ionic conduction process in the polymer electrolyte. and miniaturized electrochemical cells,',* which can compensate for the problem of the typically meager ionic conductivity in In a quantitative transport study, the network polymer electrolyte offers advantages over a polymer solvent previously used'*g nonfluid media and permit manipulation of ionic conductivity by, for polymer voltammetry, high molecular weight linear PEO for instance, organic vapor plasticization. electrolyte, since it is a completely amorphous, single-phase The polymer solvents that we use are called polymer electromaterial. Using a single-phase isotropic polymer solvent removes l y t e ~ which , ~ are solvent-free, ion conducting, solid solutions of dissociable electrolytes in salt-solubilizing polymers like the poly(ethy1ene oxide) (PEO) families. For our purposes, polymer (1) (a) Reed, R. A,; Geng, L.; Murray, R. W. J. Electroanal. Chem. 1986, electrolytes have the important property of also dissolving many 208, 185. (b) Geng,L.; Reed, R. A.; Longmire, M.; Murray, R. W. J . Phys. electroactive monomers,' which diffuse in the polymer just as in Chem. 1987,91, 2908. (c) Geng, L.; Reed, R. A,; Kim, M.-H.; Wooster, T. a fluid electrolyte solution (except more slowly). This latter T.; Oliver, B. N.; Egekeze, J.; Kennedy, R. T.; Jorgenson, J. W.; Parcher, J. F.; Murray, R. W. J . Am. Chem. SOC.1989, 1 1 1 , 1619. (d) Oliver, B N.; property provided the basis for quantitative solid-state voltamEgekeze, J. 0.;Murray, R. W. J. Am. Chem. SOC.1988,110,2321. (e) Reed, metric investigations, in poly(ethy1ene oxide) and related polymer R. A.; Wooster, T. T.; Murray, R. W.; Yaniv, D. R.; Tonge, J. S.; Shriver, electr~lytes,l*'~~ of mass transport rates,lbvcelectron-transfer dyD. F. J. Electrochem. SOC.1989, 136, 2565. namics,lCand formal potentialsla of monomer solutes dissolved (2) (a) Skotheim, T. A. Synth. Met. 1986, 14, 31. (b) Skotheim, T. A,; Florit, M. I.; Melo, A.; O'Grady, W. E. Mol. Cryst. 1985, 121, 291. (c) in the polymeric media. Solid-state voltammetry also probes the Skotheim, T. A.; Inganas, 0. Mol. Cryst. Liq. Cryst. 1985, I Z Z , 285. (d) dynamics of the polymer i t ~ e l f .Electrode ~ interfaces contacted Skotheim, T. A.; Florit, M. I.; Melo, A.; OGrady, W. E. Phys. Rev. B 1984, by polymer electrolytes can be modified and f u n c t i ~ n a l i z e d ' ~ ~ ~30,4846. ~ ~ ~ (e) Inganas, 0.;Skotheim, T. A,; Feldberg, S. W. Solid State tonics in ways analogous to those known for chemically modified elec1986, 18/19, 232. (3) (a) Watanabe, M.; Ogata, N. Br. Polym. J . 1988, 20, 181. (b) Watrodes6 in fluid media. tanabe, M.: Tadano. K.; Sanui. K.: Ogata. N. Chem. Lett. 1987, 1239. Our knowledge, however, of the chemistry of polymer solutions (4) (a) Jernigan, J. C.; Chidsey, C.-E. D.; Murray, R. W. J. Am. Chem. of electroactive materials and of the characteristics of solid-state SOC.1985,107, 2824. (b) Jernigan, J. C.; Murray, R. W. J. Am. Chem. Soc. voltammetry remains limited. Mass transport and electron-transfer 1987, 109, 1738. (c) Jernigan, J. C.; Murray, R. W. J . Phys. Chem. 1987, 91, 2030. dynamics in polymer solvents can depend on many factors (some (5) (a) MacCallum, J. R.; Vincent, C. A,, Eds. Polymer Elecrrolyre Renot requiring particular attention in fluid electrolyte solutions), views 1; Elsevier Applied Science: London, 1987. (b) Ratner, M. A.; Shriver, including the nature and concentration of incorporated solutes D. F. Chem. Reu. 1988,88, 109. (c) Vincent, C. A. Prog. Solid State Chem. and salts, temperature, plasticization, and phase structure of 1987, 17, 145. (d) Armand, M. B. Annu. Reu. Mater. Sci. 1986, 16, 245. (6) Murray, R. W. Annu. Rev. Mater. Sci. 1984, 14, 145. polymeric media. We have described several plasticization ef(7) (a) Wightman, R. M. Science 1988, 240, 415. (b) Ewing, A. G.; f e c t ~ l ~and , ~ have . ~ analyzed9 plasticization of the polymer elecDayton, M. A.; Wightman, R. M. Anal. Chem. 1981, 53, 1842. (c) trolyte P(E0) 1s-LiCF3S03by sorbed acetonitrile vapor, which Fleischmann, M.; Pons, S.; Rolison, D. R.; Schmidt, P. P., Eds. Ultramienhanced both the diffusion coefficient of an electroactive metal croelectrodes; Datatech Systems: Morganton, NC, 1987. (8) (a) Chidsey, C. E. D.; Murray, R. W. Science 1986, 231, 25. (b) complex solute and the ionic conductivity in terms of free volume Wohltjen, H.; Barger, W. R.; Snow, A. W.; Jarvis, N. L. IEEE Trans. theory. Electron Deoices 1985, ED-32, 1170. (c) Kittelsen, G. P.; White, H. S.; This paper describes a quantitative study of diffusion rates of Wrighton, M. S. J. Am. Chem. SOC.1985, 107, 7373, and references therein. a series of ferrocenes dissolved in an amorphous, plasticizer-free (d) Sanderson, D. G.; Anderson, L. B. Anal. Chem. 1985,57, 2388. (9) Geng, L.; Longmire, M. L.; Reed, R. A,; Parcher, J. F.; Barbour, C. network polymer.10 Network PEO is a cross-linked poly(ethy1ene Permanent address: Department of Chemistry, Sophia University, Chiyoda-ku, Tokyo 102, Japan.
0022-3654/90/2094-2614$02.50/O
J.; Murray, R. W. Chem. Mater. 1989, 1, 5 8 . (10) (a) Watanabe, M.; Nagano, S.; Sanui, K.; Ogata, N. Polym. J . (Tokyo) 1986, 18, 809. (b) Watanabe, M.; Itoh, M.; Sanui, K.; Ogata, N. Macromolecrtles 1987, 20, 569.
0 1990 American Chemical Society
Ferrocene Diffusion Dynamics in Network PEO
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2615
uncertainties in interpretation of diffusion results arising from possible nonuniform distribution of electrolyte and electroactive solute between crystalline and amorphous, (conduction) polymer phases." Also, the absence of phase changes within the temperature range of interestlo facilitates relating the ferrocene voltammetric results to the desired mass transport parameters in the polymer solvent. Experimental Section Electrochemical Microcell. The three-electrode electrochemical microcell used for voltammetric studies consists of the tips of three wires exposed in a polished insulating plane: a small-diameter (IO- or 25-pm diameter) Pt wire working electrode sealed in a glass capillary (1.2-mm diameter) and Pt and Ag wires 0.35 mm in diameter, auxiliary and reference electrodes, respectively. The microcell structure differs from that reported earlier' only in that the three electrodes were sealed together in a cylinder of epoxy resin (EPON 828, Miller-Stephenson Chemical), instead of thermally shrinkable plastic, to improve thermal durability of the microcell. The wire tip/epoxy surface was polished with diamond and alumina paste (successively smaller down to 0.05 pm, Buehler), and a film of the network polymer electrolyte was cross-linked on the surface. Network Polymer Electrolyte. PEO triol (Daiichi Kogyo Seiyaku; M , = 3000) was dried under reduced pressure at 80 OC for 48 h. Anhydrous LiC104 (Aldrich) was stored and used in a N2-filled glovebox. Tolylene 2,4-diissocyanate (TDI; Polysciences) was purified by reflux distillation under reduced pressure and stored in the glovebox. Dibutyltin dilaurate (Aldrich) was used as received. Methyl ethyl ketone (MEK) was purified by distillation and stored over 4-A molecular sieves. Trimethyl(ferrocenylmethy1)ammonium hexafluorophosphate (Cp,FeN+PF{) was prepared by an ion-exchange reaction from the iodide salt ( K & K Laboratories); purity was ascertained by cyclic voltammetry. The other ferrocene derivatives-ferrocene (Cp,Fe), decamethylferrocene ( C P * ~ F ~ ferrocenecarboxylic ), acid (Cp,Fe-COOH), and sodium ferrocene carboxylate (Cp2FeCOO-Na+)-were purchased and purified by sublimation or recrystallization. Stock solutions of PEO triol in MEK containing the tin catalyst (0.1 wt % based on PEO triol) and LiC104 in MEK were prepared and stored in the glovebox where network polymer electrolyte films were prepared. After confirming complete dissolution of a weighed amount of the ferrocene derivative in a mixture of appropriate volumes of PEO and LiC104 stock solutions, an appropriate amount of TDI (PEO triol:TDI = 2:3 molar ratio) was added, thoroughly mixed, and warmed at 70 OC for several minutes to initiate cross-linking as detected by an increase in the solution viscosity. A droplet of this solution was then cast on the microcell surface. The microcell was fixed and sealed in an air-tight glass container through which electrical contact to the microcell electrodes could be made. The glass container, equipped with a thermocouple in the vicinity of the microcell and stopcocks for evacuation, was removed from the drybox, heated at 70 OC for 1 h to complete the cross-linking reaction, and stripped of remaining solvent by vacuum evaporation at room temperature for 18 h. Before making voltammetric measurements, the glass container was also purged with dry Ar gas and resealed. The resulting network polymer electrolyte films contacting the three-microcell electrodes were at least 100 pm thick, to ensure that the polymer solvent was much thicker than the diffusion layer of the electroactive solute under typical experimental conditions. The concentration of LiCIO, in the polymer electrolytes is expressed as a Li/O molar ratio (0is PEO ether oxygen) following previous practice with polymer e l e c t r ~ l y t e s . ~ J ~ Measurements. Small current voltammetric responses were measured with a locally constructed p ~ t e n t i o s t a t ,and ~ ~ PAR (1 1 ) (a) Minier, M.; Berthier, C.; Gorecki, W. J . Phys. 1984,45, 739. (b) Berthier, C.; Gorecki, W.; Minier, M.; Armand, M. B.; Chabagno, J. M.; Rigaud, P.Solid State Ionics 1983, 1 1 , 91. (12) Shoup, D.; Szabo, A. J . Electroanab Chem. 1982, 140, 237.
23
"C
Figure 1. Microelectrode (25-km-diameterdisk) cyclic voltammetry of 10 mM Cp,Fe-N+PFC dissolved in network PEO/LiCIO4(Li/O = 0.02) at various temperatures. u = 5 mV s-'.
Model 175 programmer for potential control, in a Faraday cage, and at temperatures controlled by an electric heater surrounding the microcell glass container. The equilibrium temperature was monitored by an OMEGA T or J type thermocouple. Diffusion coefficients of the electroactive solutes were determined either from slow potential sweep (usually 5 mV s-') voltammetric limiting currents or from the slopes of Cottrell plots (current vs t-1/2)of potential step chronoamperometric responses (1 s < t C 100 s). The isothermal measurements as a function of the solute and salt concentrations in Figures 2-4 were repeated at least three times. Results Diffusion coefficients (Dapp)of electroactive solutes are smaller in polymer electrolytes than in fluid electrolytes by several orders of magnitude and furthermore can exhibit a strong dependence on experimental conditions. Figure 1 shows, for example, the 25-fold change in Cp2Fe-N+PF6- cyclic voltammetric currents that occurs over a 50 O C temperature range. The voltammograms change in shape as well as in magnitude over this temperature range. The shape change has a geometrical basis and occurs because the diffusional range (ca. (2D,ppt)1/2)of ferrocene in the network polymer has dimensions comparable to the electrode radius, r. Roughly speaking, (2Da,pt)'/2 > r a t the higher temperatures so that the voltammograms exhibit steady-state limiting currents characteristic of radially dominated diff~sion.~ At lower temperatures, the slower diffusion causes partial reversion to semiinfinite linear diffusion conditions and the voltammograms exhibit the corresponding transient current peaks and diffusion tails. These features are important because they signal necessary choices between microdisk electrode diffusion relations and techniques for accurate determination of the experimental diffusion coefficient Dapp. Detailed procedures for measuring diffusion rates in polymer solvents are given elsewhere," but briefly, the techniques we employ are (slow potential sweep) steady-state cyclic voltammetry, when Dappis large, and (potential step) chronoamperometry, when Dappis small. The chronoamperometric current (i) at a microdisk electrode according to Shoup and Szabo isI2 i/4nFDapprC= 0.7854 + 0 . 8 8 6 2 ~ - ~+/ 0.2146 ~ exp(-0.7823i--li2) (1) where i-
= 4DapPt/r2
and C is concentration of electroactive solute, r is microdisk radius, and t, n, and F have their standard meanings. Equation 1 gives two limiting regimes of i, depending on the value of the dimensionless parameter T (the ratio of the diffusion layer depth to the electrode radius). When T >> 1 , eq 1 reduces to a steady-state (13) Longmire, M. L.; Watanabe, M.; Zhang, H.; Wooster, T. T.; Murray, R. W. Anal. Chem., in press.
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
2616
I
-6i-
Watanabe et al.
-7,
Concentration / M 01 02
-T----
I
0
-7 0
I
03
I
I
f
f
i
4
i
I
41
P
1
I
-9 0
1
5
I
I
20
10 15 Concentration / mM
-8 0
Figure 2. Experimentally obtained diffusion coefficients (Dapp)of ferrocene derivatives at 65 "C as a function of their concentrations in network PEO/LiC104 electrolytes (Li/O = 0.02): 0 , Cp2Fe-COOH; A, Cp2Fe-COO-Na+; 0, Cp2Fe-N+PF6-;A,
Cp2Fe;0, C P * ~ F ~ .
TABLE I: Experimentally Obtained Diffusion Coefficients (D,w) of Ferrocene Derivatives (5 m M ) in Network PEO/LiCIO, Electrolytes (Li/O = 0.02) at 65 OC no. of data solute D ~cm2 ~ s-I~ , points
Cp2Fe-COOH Cp,Fe-COO-Na+ Cp2Fe-N+PF6Cp2Fe CP*~F~
2.8 ( f 0 . 2 2 )
x 10-7
3 6 4 3 10
7.4 ( h 2 . 3 ) X 7.5 (h0.85) X 3.8 (f0.34) X 2.2 (h0.49) X IO-*
0
0 05
01
Wf
Figure 3. Dappfor Cp2Fe-N+PFc at 65 OC as a function of its concentration and weight fraction ( w J in network PEO/LiC104 electrolyte (Li/O = 0.02): 0,experimentally obtained diffusion coefficient (Dapp); -, the best fit of Dappto eq 5 (see Table I1 for the parameters); ---, calculated physical diffusion coefficient (Dphya)(see text for details).
.-.
current which is the same as obtained in a slow potential sweep voltammogram under radial diffusion conditions ilim= 4nFDapprC
(3)
When T CpzFe > C P * ~ F ~The .
paPp
,
I
0.1 0
I
015
Wf
Figure 4. Experimentally obtained diffusion coefficients (0.p) of 5 mM Cp2Fe-N+PF~(0) and C P * ~ (A) F ~ as a function of L d 0 4 concentration (Li/O) and weight fraction (wf) in network PEO/LiCIO, electrolytes at 65 OC. The best fits of Daw values to eq 5 are shown by solid lines (see Table I1 for the parameters). Ionic conductivity ( u ) of the solute-free electrolytes (0)at 65 "C is cited from ref 10a for a com-
parison. ferrocene solubilities in network PEO polymer are not very large, except for Cp2Fe-N+PF6-, which dissolved up to ca. 0.3 M. Solubilities of Cp2Fe-COOH, Cp,Fe-COO-Na+, and C P * ~ are F~ ca. 40, 7.5, and 15 mM, respectively. (The decrease of Dappfor Cp*,Fe at 20 mM is due to a solubility limit and consequent precipitation of the solute as small crystallites in the network polymer electrolyte which could be observed microscopically.) Cp2Fe was used only at 5 mM concentration out of concern for sublimation loss in the course of sample preparation (see Experimental Section), and we view the Cp2Fe result as less reliable on this account. Dappcould be investigated over a much wider concentration range for Cp2Fe-N+PF6- and, as seen in Figure 3, decreases
TABLE 11: Best Fit of Figures 3 and 4; Electroactive Solute Diffusion Coefficients in Network PEO/LiCIO, Electrolytes at 65 O C to Eq 5 solute solute
concn, mM
Cp,Fe-N+PF,-
5-300
LiC104concn, Li/O 0.02
C pzFe-N +PF6-
5
0.005-0.1
Cp*,Fe
5
0.01-0.1
w{ range of variable 1.94 X 10-3-1.04 X lo-' 1.06 X 10-2-1.77 X lo-' 2.10 X 10-'-1.76 X lo-'
D(O), cm2 s-I ( 7 . 3 x 10-8)b 7 . 3 x 10-8c 1.5
x 10-7d
3.4 x 10-*d
P (1 0.9)b 15.7c*c 10.9d-/
15.3dJ
Weight fraction of electroactive solute or LiCIO,. bThe best fit is shown in Figure 3 by solid line. CThebest fit of physical diffusion data (dashed line in Figure 3), after exclusion of contribution of electron hopping. See text. dThe best fits are shown in Figure 4 by solid lines. CTheexperimental identity of eqs 5 and 8 means P = re ti*/(^^")^, where e and ti* are the main variables. In the context of these equations, the difference in p (15.7 vs 10.9) is caused by a change in e for Cp2Fe-N+PF,- and LiCIO,: u* is the same because the diffusing molecule is the same. /In the context of eqs 5 and 8 the difference i n P ( 1 0.9 vs 15.3) is caused by a change in L%* with diffusing molecule.
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2617
Ferrocene Diffusion Dynamics in Network PEO
-
5
/
-
increasing amount of sorbed acetonitrile, followed an equation similar to eq 5, with wf referring to acetonitrile, but with a positive rather than a negative sign in the exponential term. The present isothermal transport data are analyzed in terms of free volume theoryI5 as a convenient vehicle and in order to make a contrast with the plasticization data.9 We assume that the free volume (uf) of the network polymer system decreases in proportion to the weight fraction (wf) of the ferrocene electroactive solute or that of the electrolyte salt
3
c c
'U E cn b
.
v
Uf
OI
0
1
-101
I
26
28
I
I
30 32 1 0 0 0 K IT
' I'-8 34
Figure 5. Temperaturedependences of experimentallyobtained diffusion coefficient ( Dapp)for ferrocene derivatives in network PEO/LiCIO, electrolytes: A,,Cp2Fe-NtPFc ( 5 mM) at Li/O = 0.02; V, Cp2FeN+PFc (10 mM) at Li/O = 0.02; A, Cp2Fe-N+PF6-( 5 mM) at Li/O = 0.10 0,Cp*,Fe ( 5 mM) at Li/O = 0.01; 0 , C P * ~ (F5 ~mM) at Li/O = 0.IO. Temperaturedependences of ionic conductivity of the solute-free electrolytes are cited from ref 10a for a comparison: W, Li/O = 0.01; 0,Li/O = 0.02; 0, Li/O = 0.10.
substantially at high concentrations. The change follows a relation of the form Dapp = D ( 0 ) exP(-bwf)
(5)
where wf is the weight fraction of the electroactive Cp2Fe-N+PF[, D ( 0 ) is Dappat wf = 0, and /3 is a constant. These parameters for the best fit of eq 5 to Figure 3 are shown in Table 11. The experimental diffusion rate Dspp also depends on the concentration of the LiCIO, electrolyte in the network polymer as shown in Figure 4 for 5 mM Cp*2Fe (A)and Cp2Fe-N+PF6(0)at 65 OC. The change in Dappagain follows a relation of the form of eq 5, where wf is weight fraction of LiCIO, instead of ferrocene. The eq 5 fitting parameters for Figure 4 are shown in Table 11. Dappof Cp*2Fe is, throughout, lower than that of Cp2Fe-N+PF{ and decreases more strongly wih increasing LiCIO, concentration. Figure 5 displays the temperature dependency of Dappfor low concentrations of Cp*,Fe and Cp2Fe-N+PF6- at high and at low LiC104 electrolyte concentration. Dapp.is at all temperatures depressed by higher electrolyte concentration. Figure 5 also shows the ionic cond~ctivityl~ of three different concentrations of LiCIO, in network PEO in the absence of ferrocene solute. Like D,,, ionic conductivity decreases at higher electrolyte concentration and gives positively curved Arrhenius plots. Such non-Arrhenius temperature dependency is observed for diffusive phenomena in polymers above their glass transition temperatures ( T J . We will (vide infra) attach some significance to the qualitative similarities in the behaviors of Dappand ionic conductivity.
=
UfO
-
(6)
tWf
here vf" is the free volume in the absence of ferrocene or electrolyte and t is a constant which represents the effectiveness of an electroactive solute or an electrolyte to cause a decrease of free volume upon dissolution in the polymer. This assumption is opposite to that taken for plasticization of a polymer by organic vapor sorption,I6 where uf is assumed to increase in proportion to the volume fraction of the sorbed vapor. According to free volume theory, the diffusion coefficient of a small molecule (in the present case, an electroactive solute) is given byI5 D = Do exp(-yu*/uf)
(7)
where Do is constant at a given temperature, u* is the minimum free volume size for the diffusive displacement of the molecule, and y is a numerical constant expressing an extent of overlap of free volume. Combining eqs 6 and 7, and recognizing that D = D ( 0 ) when wf= 0, gives 1 = -Of0 -In [ D ( w f ) / D ( 0 ) ] yu*
(ufo)z
wflto*
(8)
where D ( w f )is the diffusion coefficient of the electroactive solute at a given weight fraction (alternatively, concentration) of eleciroactive solute or of electrolyte (Le., Dapp).Using the (Table 11) D ( 0 ) and D ( w f ) values derived from eq 5, plots of l/ln [D( w f ) / D ( 0 )vs ] l/wf are linear with intercepts close to zero for all of the results in Figures 3 and 4. That is, eqs 5 and 8 have the same form for low values of wf of electroactive solute and of electrolyte. This analysis shows that the changes in Dapppresented in Figures 3 and 4 can be satisfactorily modeled in terms of simple free volume theory, upon assumption of eq 6. The meaning of eq 6 should be considered. We have previously observedloa that Tg of network PEO polymer increases with increase of wf of LiC10, electrolyte dissolved in the polymer. The change in T g with wf could be expressed as Tg ("C) = -53.2
+ 217wf
(9)
The free volume of the network polymer can be expressed by
Discussion Dependency of Do,, on Ferrocene and on Electrolyte Concentrations. The results of Figures 2-4 show that Dappin network PEO is relatively constant at low ferrocene concentrations, but at high concentrations of ferrocene, and of electrolyte, Dappundergoes a substantial decrease, in a manner represented by eq 5 . This decrease in diffusion rate of the electroactive solute is in sharp contrast to the increase of D, of [ O ~ ( p h e n ) ~ (phen ] ~ + = phenanthr~line)~ and of ferrocene' tkat occurs in linear PEO/LiCF3S03 polymer electrolyte upon sorption of small molecules like acetonitrile into the polymer solution. Those increases in Dapp,with
where ug and fg are the specific volume and free volume fraction at T respectively, and cy is the free volume thermal expansion coeftcient above Tg. Combining eqs 9 and 10 gives an equation with the same form as eq 6. Now the factors that cause dissolution of electroactive solute like Cp,Fe-N+PF; and of electrolytes like LiCIO, in network PEO are undoubtedly interactions between the polymer chain and solute or electrolyte. It is well-known that polyethers like PEO strongly solvate ions by dipolar or coordinating interactions, especially cation^.^ Such interaction may reduce the chain segmental mobility by amounts related to the solute or electrolyte concentrations (wf). Decreases in segmental mobility are typically reflected by increases in Tgof the polymer matrix, as mentioned above. In the present case, decrease in the segmental mobility also leads to decrease in the diffusion rate (Dapp)of the ferrocene electroactive solute, since the redistribution of free volume by which diffusive displacement occurs is concurrent with chain segmental motions. For the ferrocene solutes, the effect
(14) The ionic conductivity was calculated from the WLF equation: log [ u ( T j / u ( T ) ]= C , ( T - T ) / [ C 2 + (T- TJ], whereu(T) isionicconductivity at T,and the values of C,, u(T& and TB, cited in ref loa.
(15) Cohen, M. H.; Turnbull, D. J . Chem. Phys. 1959, 31, 1164. (16) (a) Fujita, H. Fortschr. Hochpo1ym.-Forsch. 1961, 3, 1. (b) Fujita, H.; Kishimoto, A.; Mastumoto, K. Trans. Furuduy SOC.1960, 56, 424.
e,,
2618
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
on segmental mobility was noticeable only when wfwas appreciable (Figure 3); the small concentrations (wf = 10-3-10-z) of ferrocenes used in Figure 2 produced negligible changes in Dapp. We next consider the important point that transport of electrochemical charge to and from electrodes can occur not only by physical diffusion of the oxidized and reduced forms of the electroactive species but also by electrons hopping between them (Le., electron self-exchange between ferrocene and ferrocenium). That this effect can be important when diffusion constants are small was noted by Buttry and Anson and othersI7 and by ourselves in the case of solid-state transport in PEO polymer solvents.Ic The relevant Dahms-Rufft8 equation is Dapp = Dphys
+ (7/4)ka~p6~C
(11)
where DphFis the physical diffusion coefficient of the electroactive solute, 6 is the solute intersite distance at electron transfer, and C is the solute concentration. kapp,the apparent electron selfexchange rate constant, is related to the self-exchange rate constant (kcx) and the collision-limited rate constant (kd) by 1/kapp
= l/kd +
l/kex
(12)
and kd and Dphys, for equal radii and DphFof oxidized and reduced species, by19 kd = 4i?N~S(2Dphys)/ lo3
(13)
where N A is Avogadro's number. Equation 1 1 indicates that electron hopping contributes most to transport rates when Dphysis small and concentration is large. Contrary to this expectation, Figure 3 shows that Dappdecreases rather than increasing at increased concentrations of electroactive ferrocenes. Considering that the effect predicted by the right-hand side of eq 1 1 might be superimposed upon even larger and opposing free volume changes in DPhF(vide supra), causing the net diffusion rate to decrease, the magnitude of the electron hopping term was estimated. We assumed a Iiterature20J1value (acetonitrile solvent) for ferrocene, k,, = 1.4 X lo7 M-Is-l (65 "C) and 6 = 7.6 X cm for the Cp2Fe-N+PF6- species in the network PEO polymer to give from eqs 11-1 3 estimates of the real Dphysvalues as shown in Figure 3. The comparison shows that the experimental Dapp and the estimated Dphysdo not differ significantly at low concentrations (Le., those in Figure 2). At higher concentrations Dapp exceeds Dphysby as much as 35% owing to electron hopping, provided k,, in the polymer is as large as in acetonitrile solution. Figure 3 thus may modestly underestimate the decrease in free volume caused by the CpzFe-N+PF6- solute. It should be mentioned that the highest concentrations of Cp2FeN+PF; in Figure 3 may also incur some error in D,, from electrostatic migration effects, since those concentrations are comparable to that (ca. 0.4 M) of the LiC104 electrolyte at the Li/O = 0.02 concentration used. It is evident that experiments with an uncharged electroactive solute which exhibits a small electron self-exchange rate constant would, in principle, lead to the most accurate representation of the effect of solute concentration on polymer solvent free volume. (17) (a) Buttry, D. A.; Anson, F. C. J . Am. Chem. SOC.1983, 105,685. (b) Guadalupe, A. R.; Usiter, D. A.; Potts, K. T.; Hurrell, H. C.; Mogstad, A.-E.; Abruna, H. D. J . Am. Chem. SOC.1988, 110, 3462. (c) Ohsaka, T.; Seto, K.; Matsuda, H.; Oyama, N . J . Elecrrochem. SOC.1985, 132, 1871. (d) Oyama, N . ; Ohsaka, T.; Yamamoto, H.; Kaneko, M. J . Phys. Chem. 1986, 90, 3850. (e) Morishima, Y.; Akihara, I.; Lim, H. S.; Nozakura, S. Macromolecules 1987, 20, 978. (18) (a) Dahms, H. J . Phys. Chem. 1968,72, 362. (b) Ruff, I.; Friedrich, V. J. J . Phys. Chem. 1971, 75, 3297. (c) Ruff, I.; Friedrich, V. J.; Demeter, K.; Csaillag, K. J . Phys. Chem. 1971, 75, 3303. (d) Ruff, I.; Korosi-Odor, I . Inorg. Chem. 1970, 9, 186. (e) Ruff, I. Electrochim. Acta 1970, 15, 1059. (19) von Smoluchowski, M. Phys. Z. 1916, 17, 557, 585. (20) (a) Nielson, R. M.; Golvin, M. N . ; McManis, G.E.; Weaver, M. J . J. Am. Chem. Soc. 1988, 110, 1745. (b) Nielson, R. M.; McManis, G. E.; Golvin, M. N.; Weaver, M. J. J . Phys. Chem. 1988, 92, 3441. (c) Nielson, R. M.; McManis, G.E.; Safford, L. K.; Weaver, M. J. J . Phys. Chem. 1989, 93, 2152. (21) The k,, value for Cp,Fe+/" couple at 65 OC was calculated from the equation k,, = A,, exp(-AH*,,/RT), where A,, = 2.5 X I O i o M-' s-' and AH*ex = 5.0 kcal mol" in acetonitrile.20b
Watanabe et al. Physical Diffusion of Small Molecules and Ions in Rubbery Polymers. The rates of physical diffusion of small molecules (Le., simple gases, volatile and nonvolatile organics) and ions in polymers above their T i s vary enormously, possibly from to cmz s-I or lower.22-24 Diffusion of simple gases and of volatile organics has been vigorously studied in polymersz2 and appears to be generally faster and have differing dependency on diffusant concentration than the less studied nonvolatile organic, organometallic (like the ferrocenes studied here), and inorganic ion23*24 solutes in polymers. The diffusion coefficients of simple gases such as H2 and He in polymers are quite large (typically 104-10-5 cm2 at 25 OC, in some cases cmz s-l even at T,) and additionally exhibit Arrhenius temperature dependency (normally E, < 10 kcal mol-]) down to and in some cases even below Tg.2zThe diffusion rates of simple gas molecules and sorbed volatile organic molecules in polymers are also frequently enhanced by their own sorption (plasticization).16*22In contrast, diffusion coefficients of small ions (Li', Na+, CF3S03-, C104-, SCN-) in linear PEO and poly(propy1ene oxide), determined by pulsedfield-gradient NMR23and radiotracer methods,24are both much smaller (ca. 10-9-10-s cm2 s-l at 65 0C23924)and furthermore decrease with increasing electrolyte c o n ~ e n t r a t i o n . The ~ ~ ~cation ,~ also diffuses more slowly than the The literature thus indicates that diffusivity of solutes in polymers above their T,'s is greatly affected by interactions between the polymer and the diffusing substance (as well as its size). Small gas molecules that interact weakly with the polymer diffuse rapidly and independently of the polymer segmental motion dynamics, whereas, although of comparable size, strongly interacting ions like Li+ and Na+ diffuse slowly as their motions are coupled to the rates of segmental motions. Within the framework of free volume theory (eqs 6 and 7), these two cases can be considered as extremes of diffusion of small substances, in which interactions between the polymer and diffusing substance change not only of (via the magnitude and sign (negative or positive) of e, eq 6) but also u*. The free volume required for diffusion, u * , of a simple gas reflects its own molecular size and is comparable to uf of the system, whereas u* for ionic diffusion becomes very large (>>uf) due to the strong interaction between the ion and the polymer chain (as well as uf becoming small according to eq 6) and corresponds to the size involved in the segmental motion. The point of the preceding discussion is that diffusion of the electroactive ferrocenes studied here in network PEO, with respect to Dsppbeing small, decreasing with solute concentration (Figure 3) and exhibiting non-Arrhenius behavior (Figure 5), appears to be more similar to that of ions that interact strongly with the polymer matrix than that of simple noninteracting molecules. Considering next the variation among the diffusion rates of the five ferrocenes examined (Table I), with the exception of Cp,Fe,Z5 we see that Dapp appears to decrease (Cp2Fe-COOH26 > Cp,Fe-COO-Na+ i= Cp2Fe-N+PF, > Cp*,Fe) with increasing size (Cp2Fe-COOH < Cp2Fe-COO-Na+ < Cp2Fe-N+PF6- < Cp*,Fe) of the diffusing electroactive molecule. Other correlative effects seem to be absent: (i) The cationic Cp,Fe-N+ and the anionic Cp2Fe-COO- exhibit nearly identical diffusion rates, whereas in electrolytes like LiC104 dissolved in PEO polymers, the anion is typically faster.23 (ii) The neutral Cp*zFe might (22) (a) Crank, J.; Park, G. S., Eds. Diffusion in Polymers; Academic: London, 1968; Chapters 2 and 3. (b) Stern, S. A,; Frisch, H. L. Annu. Rev. Mater. Sci. 1981, 11, 523. (23) (a) Bhattacharja, S.; Smoot, S. W.; Whitmore, D. H. Solid State Ionics 1986,18/19,306. (b) Gorecki, W.; Andeani, R.; Berthier, C.; Armand, M. B.; Mali, M.; Roos, J.; Brinkmann, D.Solid Srare Ionics 1986, 18/19, 295. (c) Lidsey, S. E.; Whitmore, D. H.; Halperin, W. P.; Torkelson, J. M. Polym. Prepr. (Am. Chem. Soc. Diu. Polym. Chem.) 1989, 30, 442. (24) (a) Chadwick, A. V.; Worboys, M. R.; Strange, J. H. Solid State Ionics, 1983, 9/10, 1155. (b) Chadwick, A. V.; Worboys, M. R. In ref 5a, Chapter 9. (c) Bridges, C.; Chadwick, A. V.; Worboys, M. R. Br. Polym. J. 1988, 20, 207. (25) Recall that there may have been sublimation loss of Cp,Fe during cross-linking which would bias Damlow. (26) The network PEO electrolytes containing Cp2F&OOH might have a lower cross-linking density compared with the others, due to the possible reaction between isocyanate and carboxylic groups in the sample preparation.
J . Phys. Chem. 1990, 94, 2619-2623 exhibit less dipolar interaction with the network PEO matrix than the ionic ferrocenes, yet in fact it diffuses more slowly. We surmise that all of the ferrocenes have sufficiently large molecular size (>>vr)and/or reasonably strong interactions with the PEO matrix (hence their slow, non-Arrhenius diffusion), so that the free volume requirements for diffusive displacement are, within the group of ferrocenes, influenced more by molecular size than by variation in dipolar or nonpolar interactions. Relation of Ferrocene Do,, Values to the Ionic Conductivity of Network PEO. We finally consider the comparison in Figures 4 and 5 of the ionic conductivity of network PEO polymer electrolyte with ferrocene Dappvalues measured at low concentrations (where there is negligible electron hopping) as a way to better understand ionic diffusivity in this polymer. Ionic conductivity in polymer/electrolyte solutions is thought to be determined by the product of carrier ion population and ion diffusivity. Plots of ionic conductivity vs electrolyte concentration typically exhibit maxima5.lh (see Figure 4,top curve) which have been interpreted as two opposing contributions at increasing electrolyte concentration: an increase of carrier ion population and a decrease of the ionic diffusivity. There have been few r e p ~ r t ~ however, , ~ ~ ~ ,of~actual - ~ ~detection ~ of a decrease of ion diffusivity. In the ferrocene diffusion measurements, the (electron) carrier population is given without ambiguity by the total ferrocene concentration, since the impetus for transport in the measurement is a concentration and not a voltage gradient and ion pairing should be of little account. The decrease in Dappshown in Figure 4 and expressible by eq 5, accordingly a clear decrease in ferrocene diffusivity with increasing electrolyte concentration, is thus of interest since it supports the parallel proposal of decleasing ionic diffusivity with increasing electrolyte concentration.
2619
Continuously curved Arrhenius plots for ionic conductivity, as shown in Figure 5, are also widely observed in amorphous polymer electrolytes5 and have been fit to the Vogel-Tamman-Fulcher (VTF)27and Williams-Landel-Ferry equations.28 Both equations represent how diffusivity changes with temperature but leave unanswered questions such as whether the non-Arrhenius profile of ionic conductivity (a) represents how ion diffusion coefficients change with temperature or instead (b) represents a temperature dependence of ion pair and multiplet dissociations that control the actual number of ionic carriers present. We take it as significant, then, that Dappand ionic conductivity in the network PEO polymer exhibit quite similar (Figure 5) non-Arrhenius temperature dependencies in both magnitude and extent of curvature. These similarities can be taken to mean that the temperature dependence of ionic conductivity reflects the temperature dependence of ion diffusivity. This suggestion agrees with experimental comparisons of ionic diffusion coefficient and ionic conductivity in linear PEO electrolytes.2k Acknowledgment. This research was supported in part by grants from the Department of Energy (DE-FG05-87ER13675) and the National Science Foundation. M.W. acknowledges a sabbatical leave from Sophia University. (27) (a) Vogel, H. Phys. 2. 1921, 22,645. (b) Tamman, G.;Hesse, W. 2. Anorg. Allg. Chem. 1926,156,245. (c) Fulcher, G.S. J . Am. Ceram. SOC. 1925,8, 339. (d) The VTF equation of the form of a(T) = ( A / T ' / * )exp[ - B / ( T - T o ) ] where , To is ideal glass transition temperature and A and B are constants, is generally used for the expression of the temperature dependence. (28) (a) Williams, M. L.; Landel, R. F.; Ferry, J. D. J . Am. Chem. SOC. 1955, 77, 3701. (b) Reference 14.
Multlfrequency Electron Spin-Echo Envelope Modulation Spectroscopy of m-Dinltrobenzene Adsorbed on Alumina Sarah A. Cosgrove and David J. Singel* Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138 (Received: July 31, 1989)
We report electron spin-echo spectroscopy of a radical species formed upon the adsorption of m-DNB (m-dinitrobenzene) from benzene solution on activated y-alumina. Two- and three-pulse echo modulation patterns were obtained at sample temperatures of 110 K and electron spin excitation frequencies of 6.2,7.4,8.2,9.1, 10.3, and 11.8 GHz. Modulation frequencies are assigned to 27Al,I4N,and 'Hnuclei, on the basis of suppression effects, the values of the modulation frequencies, and, particularly, the dependence of the modulation frequencies on external field strength. Aluminum modulations indicate that the radical species formed by interfacial electron transfer is bound to the alumina surface. Through frequency-tracking experiments, we assign the I4Nmodulation componentsas double-quantum frequenciesand determine hyperfine and quadrupole coupling constants of the observed I4N. The values of these parameters indicate that the adsorbed radical is an ion-pair complex.
-
Introduction Radicals generated by interfacial electron transfer on dispersed metal oxides have recently been studied via ESEEM (electron spin-echo envelope modulation) and CW-ENDOR (electron nuclear double resonance) techniques.' The measurement of nuclear spin interactions via such techniques provides a means toward the elucidation of chemical, structural, and dynamical characteristics of the adsorbed species-information important for advancing the understanding of the electron-transfer process. Electron-nuclear
magnetic resonance techniques are of special utility in the study of complex systems because the nuclear spins in the vicinity of the paramagnetic center are selectively probed. Accordingly, they enable the investigation of specific sites and of specific chemical processes-an important advantage in the study of dispersed, catalytic materials. EPR (electron paramagnetic resonance) has long been used to monitor the formation of organic radicals on metal oxide surf a c e ~ . ~These - ~ studies have been particularly fruitful in estab-
(1) Snetsinger, P. A.; Cornelius, J. B.; Clarkson, R. B.; Bowman, M. K.; Belford, R. L. J . Phys. Chem. 1988, 92, 3696. Clarkson, R. B.; Belford, R. L.: Rothenberger, K . S.; Crookham, H . C. J . C a r d 1987, 106, 500. Rothenberger, K. S.; Crookham, H. C.; Belford, R. L.; Clarkson, R. B. J . Carol. 1989, 115, 430.
(2) Flockhart, B. D.; Leith, I. R.; Pink, R. C. Trans. Faraday SOC.1969, 65, 542. Muha, G. M. J . Catal. 1979, 58, 470. (3) Flockhart, B. D.; Scott, J. N. A,; Pink, R. C. Trans. Faraday SOC. 1966, 62, 730. (4) Flockhart, B. D.; Leith, I. R.; Pink, R. C. Trans. Faraday SOC.1970, 66, 469.
0022-3654/90/2094-2619$02.50/0
0 1990 American Chemical Society
