J . Phys. Chem. 1989, 93, 989-997 required before we can definitely say that the difference is due to the mobility of the cation in the film. We are currenly repeating the current-pulse experiment using Bu4NBF4as the supporting electrolyte. The apparent diffusion coefficients obtained from the finite diffusion regime are consistently larger than the Dapp)sfrom the semiinfinite regime (Table 11). Rubinstein et al. applied the method described here to an electrode coated with a redox polymer film and noted a similar discrepancy; however, in their case Dapp,F was a factor of 3 less than Rubinstein et al. account for this observation by postulating the existence of two uncoupled diffusion pathways within the polymer film.20a This explanation could, in principle, account for the trend in the data observed here. Electron micrographs of electrochemically synthesized polypyrrole clearly show that the polypyrrole surface is not If the surface topological features are significant relative to the average film thickness, the film will clearly not be of uniform thickness. Furthermore, because the profilometer stylus is too large to fit into the crevices between surface topological features, the thickness measured is prcbably the maximum thickness (i.e,, the locus of points most distant from the substrate Pt electrode surface). Because is proportional to p, this overestimated spuriously large. film thickness could make Dapp,F Finally, it seems likely that a gradient in film density, as discussed in our previous paper, might also account for the discrepancy between the finite and semiinfinite diffusion data.14 We are currently attempting to ascertain which, if any, of these proposed explanations is correct. In addition to the disparity between Daqp,land Dapp,?there is a second similarity between the data obtained by Rubinstein et al.20aand the data reported here; in both cases, the experimental transition between the semiinfinite and finite diffusion regimes is more gradual than the theoretically predicted transition (Figure 3). These gradual experimental transitions could result from either multiple diffusion pathways or nonuniform film thicknesses;2oa again, we are currently attempting to ascertain which explanation is correct. While the experimental and simulated Nyquist plots diverge somewhat in the transition region, the agreement in both the (31) (a) Diaz, A. F.; Lee.,W.-Y.; Logan, A.; Green, D. C. J. Electroanal. Chem. 1980, 108, 377. (b) Diaz, A. F. Chem. Scr. 1981, 17, 145.
989
semiinfinite (high frequency) and finite (low frequency) regimes is excellent. Indeed, the agreement between simulated and experimental Nyquist data shown in Figure 3 is as good as, or better than, that obtained for any other system to which this theoretical model has been applied.18.” Thus, the Huggins model is clearly applicable to reduce polypyrrole.
Conclusions In this and our previous paper on electrochemical investigations of electronically conductive polymers, we assumed that an electrochemical cell incorporating the reduced form of polypyrrole could be approximated by a Randles-type equivalent circuit.I4 The agreement between the experimental data and the predictions of the theoretical models based on this equivalent circuit indicate that this assumption is justified. Clearly, this equivalent circuit is not applicable to the oxidized form of polypyrrole. We are currently conducting ac impedance experiments on the oxidized polymer. A finite transmission line equivalent circuit,32developed by Keiser et al.33awill be used to interpret these data. The Keiser model has been employed recently by Candy et al.33bto characterize the structure of thin, porous metal films using ac impedance. We have now used two independent electrochemical methods to evaluate Dapp)sassociated with the oxidation of electronically conductive polymers. While the data obtained are qualitatively consistent, quantitative comparisons are not yet possible; we are currently generating the requisite data. In addition, we are currently using these two methods to evaluate the effects of various molecular and supermolecular factors of the polymer on the rate of charge transport in electronically conductive polymers. We will report the results of these investigations soon. Acknowledgment. This work was supported by the Air Force Office of Scientific Research, the Office of Naval Research, and the Robert A. Welch Foundation. We acknowledge N. A. Greco for valuable consultation. Registry No. Bu4NBF4,429-42-5;CH,CN, 75-05-8; Pt, 7440-06-4; polypyrrole, 30604-81-0;pyrrole, 109-97-7. (32) De Levie, R. Advances in Electrochemistry and Electrochemical Engineering Wiley: New York, 1967; Chapter 6. (33) (a) Keiser, H.; Beccu, K. D.; Gutjahr, M. A. Electrochim. Acta 1976, 21, 539. (b) Candy, J.-P.; Fouilloux, P.; Keddam, M.;Takenouti, H. Electrochim. Acta 1981, 26, 1029.
Molecular Structure and Dynamics of LICIO, -k 18-Crown-6 Macrocyclic Complexes in Dimethyl Carbonate at 25 OC Meizhen Xu, Nadia Obeid,? Edward M. Eyring, and Sergio Petrucci* Weber Research Institute, Polytechnic University, Route I 1 0, Farmingdale, New York I 1 735, and Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 (Received: February 16, 1988) Electrical conductance in the concentration range 3 X lo-” to -0.05 M, infrared spectra (of the v4 band of the C104- ion) in the concentration range 0.025-0.20 M, and microwave dielectric relaxation spectra in the concentration range 0.05-0.19 M for LiC10, added to the macrocycle 18-crown-6(18C6), in molar rate R z 1, all in the solvent dimethyl carbonate (DMC), are reported. The conductance data are interpreted by the Chen equation and by the Fuoss-Hsia equation. The infrared spectra of LiC104 in DMC reveal a concentration distribution of contact and solvent-separatedpairs (‘spectroscopically free” C104-). When 18C6 is added, the proportion of spectroscopically free C104- increases. The microwave dielectric spectra for LiC104 + 18C6 in DMC reveal a Debye relaxation for the solute very similar in amplitude and relaxation frequency to that of the electrolyte LiC104 in DMC previously reported.
Introduction The structure and mechanism of migration of electrolytes complexed by macrocycles in solvents of very low permittivity is New York Academy of Sciences sponsored summer student. *To whom correspondence should be sent at Weber Research Institute.
0022-3654/89/2093-0989$01.50/0
a problem of continuing interest to researchers in fields as different as biology and electrochemistrY. For instance, it is important to know whether in media mimicking biological membranes an electrolyte complexed by macrocycles such as valinomycin is still in the form of ion pairs. Similarly, it is relevant for electrochemists involved in the con0 1989 American Chemical Society
Xu et al.
990 The Journal of Physical Chemistry, Vol. 93, No. 2, 1989
0
LiC104 in DMC
A LiClOq +lac6 (R =
0.985)
in DMC
\
\
\ \ \ \ \
I
I
-3
-2
10g,oc
-
I
-1
I
0
Figure 1. Plot of log A vs log c, with A the molar conductance (S cm2 mol-') and c the concentration (mol/dm') for LiC10, and LiC104 + 18C6 in the solvent DMC at 25 OC.
struction of secondary lithium batteries to find ways to ionize the electrolyte dissolved in the low-permittivity medium, to decrease the internal resistance of the battery. To answer as many of the above questions as possible with a model system, electrical conductivity, infrared spectra, and microwave dielectric spectra of the electrolyte LiC10, with the macrocycle 18C6 (18-crown-6) dissolved in the solvent DMC (dimethyl carbonate) have been reported here and compared (the conductances and dielectric data) to results reported previously for LiC104 alone in DMC.
Experimental Part The instrumentation and the experimental methods for the conductivity,' infrared,2 and microwave measurements3 have been described before. LiC104 (Aldrich ACS) was redried at 70 O C overnight in vacuo. Dimethyl carbonate was distilled repeatedly over 3-A molecular sieves until the presence of the water band at -3550 cm-' was no longer detectable with the infrared spectrometer scale set a t 0.1 absorbance units full scale. 18C6 (Aldrich) was recrystallized from Aldrich Gold Label acetonitrile. The solvent adduct was decomposed by subjecting the crown ether to vacuum overnight at room temperature. Solutions were prepared by weight in volumetric flasks and used within a few hours of preparation. Contact with the open atmosphere was limited to at most 30-60 s during preparation and filling of the measuring cells. Results and Calculations Electrical Conductance. Figure 1 reports a plot of log A vs log c for both LiC104 and LiC10, + 18C6 in molar ratio R = 1 in DMC at 25 OC. An increase of the total molar conductance (1) Petrucci, S.; Hemmes, P.; Battistini, M. J. Am. Chem. Soc. 1967, 89, 5552. (2) Saar, D.; Petrucci, S . J . Phys. Chem. 1986, 90, 3326. (3) Delsignore, M.; Farber, H.; Petrucci, S. J . Phys. Chem. 1985,89,4968,
and literature cited therein.
A at each concentration c with respect to LiC104 in DMC is noticed. Table I (supplementary material; see the paragraph at the end of the paper) reports the values of A and c. The data for the electrolyte LiClO, in the solvent DMC have been reported before3 and interpreted by the Fuoss-Kraus triple-ion theory4 modified by the use of the permittivity of the solution (instead of that of the solvent). We have, however, shown for LiC10, in 2-methyitetrahydrofuran (2-MeTHF),' LiASF6 in 2-MeTHF,6 and LiC104 in 1,3dioxolane' that introduction of triple-ion equilibria does not appear to be necessary if one allows the ion-pair equilibrium constant K , to vary with concentration, namely, with the permittivity of the solution. The underlying idea is that as the system becomes a mixture of solvent and solute dipoles (the ion pairs) the latter species increase the polarization of the solution and hence the permittivity. These changes in the solvent dielectric properties affect the dissociation equilibrium, thus causing K, to change. In other words, the deviation of the A vs c plot from the Ostwald mass law prediction and the appearance of a minimum would be attributable to the shift in the ion-pair equilibrium rather than to the formation of triple ions8 We have applied the Cavell and Knight proposal8 to the data of LiC10, in DMC using the full Fuoss-Hsia equationg A = A, - S(ca)'/'
+ E(CCY)In ( c a ) + J , ( c a ) - J ~ ( c a ) ~-/ * K p ( c 4 Af*z (1)
(4) Fuoss, R. M. J . Am. Chem. Soc. 1934,56,1031,1127; 1936,58, 982. Fuoss, R. M.; Kraus, C. A. J . Am. Chem. Soc. 1935,57, 1; 1933,55,3614. (5) Maaser, H.; Xu, M.; Hemmes, P.; Petrucci, S.J . Phys. Chem. 1987, 91, 3047. (6) Inoue, N.; Xu, M.; Petrucci, S. J . Phys. Chem. 1987, 91, 4628. (7) Xu,M.; Inoue, N.; Eyring, E. M.; Petrucci, S. J. Phys. Chem. 1988, 92, 2781. (8) Cavell, E. A. S.; Knight, P. C. Z . Physik. Chem. (New Folge) 1968, 57, 3. (9) Fuoss, R. M.; Hsia, K. L. Proc. Natl. Acud. Sci., US.1966,57, 1550.
LiC10,
+ 18-Crown-6 in DMC at 25 OC
The Journal of Physical Chemistry, Vol. 93, No. 2, 1989 991
TABLE II: Results of the Fuoss-Hsia Analysis of the Conductance Data for the Systems Studied in DMC at 25 O C Q 104c,M A, S cm2 mol-l Kp, M-l KF,M-' 108dF,C m System:* LiC104in DMC c = 3.12 + 7.833~ 47.229- 125.61~' 3.5683 0.002530 3 6.01 X loi2 5.95 X 10l2 5.97 10.720 0.0015583 5.31 X 10l2 5.38 X 10l2 5.98 20.323 0.001328 2 3.88 X 10l2 3.83 X 10l2 6.04 1.89 X 10l2 1.85 X 10l2 6.17 42.937 0.001318 1 78.760 0.001488 5 8.23 X 10" 8.34X lo1[ 6.30 159.87 0.002148 1 2.03 X loL1 2.05 X 10" 6.51 412.97 0.0058785 1.18 X loio 1.18 X 1OIo 6.80 696.65 0.013938 1.44 X lo9 1.44 X lo9 6.82 5.32 X lo* 5.31 X lo8 6.77 863.82 0.021501 1060 0.041264 1.36 X lo8 1.36 X lo8 6.82 1417 0.084089 2.83 X lo7 2.80 X lo7 6.66
+
Systemb LiC104+ 18C6 in DMC;R = 0.987 (=[18C6]/[LiC104]) t = 3.104 13.625~ - 10.8173- 22.1093
+
3.9521 11.536 25.594 51.937 79.593 166.42 291.70 424.75 508.85
0.0039020 0.0031208 0.0028160 0.0028348 0.0030858 0.0044126 0.0073935 0.012204 0.016560
2.29 X 1.25 X 7.00 X 3.51 X 1.95 X 4.81 X 1.05 X 2.90 X 1.39 X
10l2
loLz 10"
10" 10" lolo 1O'O
lo9 lo9
2.29 X 10l2 1.27 X 10l2 6.95 X loL1 3.53 X loL1 1.93 X loL' 4.87 X 1O'O 1.06 X 1Olo 2.90 X lo9 1.38 X lo9
6.22 6.34 6.45 6.55 6.63 6.77 6.89 6.97 7.02
Fit of the K values by the Fuoss relation (eq 111) with the distance parameter dP !Ao = 116 S cm2 mo1-I (assumed). Here the permittivity of the solutions is expressed by nonlinear regression applied' to the original data as t
= 3.12
+ 7 . 8 3 ~+ 4 7 . 2 2 ~- ~125.61~'
and the Debye-Huckel expression for the mean activity coefficient is
fi
-In f* = S,-(C~)'/~/( 1 + Aq(ca)1/2)
(11)
In eq I1 as well as in eq I the minimum Bjerrum distance of approach between free ions q (q = e2/2ekT) has been imposed for f*,Jl(q), and J2(q). A digital computer has been set up to calculate by sucoessive approximations the degree of dissociation
mol-' the value of Kpat c = 3.568 X lo4 M is Kp = 4.86 X 10l2 M-', which can be reproduced by the Fuoss function with dF = 6.015 X cm (KF= 4.86 X 10l2 M-l). At c = 159.87 M, Kp = 1.64 X 10" and dF = 6.57 X (KF = 1.66 X 10" M-'). Similarly for A. = 128 (S cm2 mol-') a t the same two concentrations Kp = 7.31 X 10l2M-I, dF = 5.925 X lo-* cm (KF = 7.30 X 10l2 M-l), K = 2.46 X 10" M-l, dF= 6.46 X cm (KF = 2.47 X 10" M-p), respectively. It appears therefore that changes in permittivity with concentration are not quite sufficient to account for the change of A with concentration in a solvent of so low a permittivity as DMC. The need to change dF could be attributable to the contribution of other conducting species (such as triplets as postulated before) or to inadequacies of eq I. Fuoss questioned" the tactic of setting J1= Jl(q) and J2 = J2(q)as being inconsistent with hydrodynamic conditions requiring the radial component of the hydrodynamic velocity of ions to vanish for a distance equal to the hydrodynamic radius R . In the original theory R = a with a equal to the minimum approach distance between ions. By setting R = q, in solvents of low permittivity one introduces the problem that q is much larger than any reasonable collision distance in a boundary hydrodynamic condition. Indeed in DMC q corresponds to -90 X cm! We have therefore repeated the calculation using J l ( a ) and J2(a)with a = 6 X cm, namely, setting the collision diameter a = d,, as calculated above. The results for Kp and dF are extremely close to those calculated with J l ( q ) and J2(q),and hence the trend of dFwith concentration, as shown in Table 11, persists. The conclusion drawn from the above analysis is that the introduction o f t = t(c) into the conductance equation (I) for LiClO, in DMC is not quite adequate to accommodate the description of the electrolyte by the simple dissociation equilibrium LiC104 s Li+ C104-. Notice that a change of 1 A in the distance parameter dF is not trivial at these permittivities, the formation constant KF being a very sensitive function of dF. We have, in fact, checked the above by reevaluating the molar conductance A, imposing KF = KF (d = 5.97 A), namely, the distance parameter that fits Kp at the lowest concentration (Table 11). The values of the degree of dissociation a and of the activity coefficientfhave been calculated at each concentration by combining Ostwald's law and the Debye-Hiickel activity coefficient f:
+
1-a
KF = -
a:
Cfi2ff2
h a=-= Arrce
A A. - S ( C ~ ) ' /Eca ~ In (ea) J l c a - J2(ca)'l2
+
+
From a,Kp is evaluated by using the relation 1-a Kp = Cfi2.2
up to the convergence of Kp,forcing A = Ld from eq I and thus expressing Kp as the final result of the fit. Table I1 reports the results for Kp and the fit of these data to the Fuoss expressionlo
?!?!
KF = 3000 exp(
ST)
where dFis a distance parameter and e = t(c). It is apparent that the fit can be achieved at the cost of changing dF by about 1 A throughout the concentration range explored. As dF increases, forcing KF to decrease to fit Kp,one could surmise that the changes in permittivity to t with c are not sufficient to rationalize the changes in Kp' As the changes occur from very low concentrations, where eq I ought to be valid, these changes in dF may reflect exaggerated decreases of Kp attempting to mask some contribution to the total conductivity by other species such as possibly triplets. Changes of A. by &lo% from the value A. = 116 S cm2 mol-' predicted by the Walden rule do not help. For A. = 104 S cm2 (10) Fuoss,
R.M.J. Am. Chem.Sac. 1958,80, 5059.
fi
= e ~ p ( - 2 . 3 0 3 S ~ ( c a ) ' / ~ /+ (l X q d 2 ) )
and evaluating A from eq I setting Kp = K~(5.97).Increasingly large systematic differences with concentration between hd and Aerptl are recorded from these calculations. It would appear, therefore, that at least for the present system, there is a need to postulate some ionic contribution other than the one deriving from the ion-pair equilibrium. Either eq I is inadequate a t these low permittivities, as in DMC, or other ionic species make additional contributions to the total conductivity as assumed before by Delsignore et al.' Notice, in fact, that the stability of postulated species such as triple ions increases with decreasingpermittivity. If these species are present, their effect on the total conductivity should be more evident in solvents of lower permittivity such as DMC. The system LiC10, 18C6 has been treated by the approach of Chen et al.,12viewing the system as dominated by the equilibria
+
Li+ + C104-
+ C F! Liclo, + C a LiC+ + C104-
(Iv)
where C denotes crown ether and [ L P ] = ac, [LiC+] = a&, [C104-] = (a + a$, [LiClO,] = (1 - a - a&, [C] = (1 - a&. Taking a
