J. Phys. Chem. 1983, 87,3515-3520
3515
Molecular Relaxation of LiAsF, in 1,P-Dimethoxyethane Herman Farber, Donald E. Irish,' and Sergio Petrucci' Departments of Chemistry and Eiectricai Engineering, Polytechnic Institute of New York, Farmingdate Campus, Farminmle, Long Island. New York 11735 (Received: August 30, 1982; In Final Form: May 12, 1983)
Audiofrequency electrical conductivity, Raman spectra, radiofrequency ultrasonic absorption, and microwave dielectric permittivity of LASF6 in the solvent 1,2-dimethoxyethane(DME) are reported. An analysis of the electrical conductivity data reveals the electrolyte to be associated to ion pairs (KA = 1 X lo5 M-l). Raman spectra of the symmetrical stretching mode of AsF, suggest the ion to be "spectroscopically free", namely, either unpaired or solvent separated from the cation. Ultrasonic relaxation data are interpreted in terms of the equilibrium Li', S,h F 6 - $ L h F 6 , (Sbeing a solvent molecule). The equilibrium appears to be heavily shifted toward solvent-separatedion pain in accord with the information obtained from b a n spectra. In other words, the majority of the electrolyte is associated in the form of a solvent-separated ion pair symbolized by Li+, S, AsF6-. Microwave dielectric relaxation data can be interpreted as due to the diffusion rotation relaxation of ion pairs. The estimate of the charge-to-chargedistance in the ion pairs reinforces the model that the solvent resides between the cation and the anion in the majority of the pairs. The equilibrium is shifted to increase contact pairs, by increasing the electrolyte concentration, in accordance with the law of mass action.
Introduction Progress in battery technology, using lithium electrolytes in ethereal solutions,2 has occurred largely in the last decade. Still many problems persist2 which make further studies of the molecular properties of lithium electrolytes relevant on both theoretical and practical pounds. LiC104 as electrolyte in tetrahydrofuran (THF)3was studied by some of us years ago by ultrasonic relaxation methods. Later, we extended our study to 1,2-dimeth~xyethane~ (DME) because of its ability to chelate alkali ions. We decided then to start a research program along similar lines dealing with the electrolyte LiASF6 which, in preliminary tests, appears more ionized than LiC104 in ethereal solvents. Our aim is to give, by a diversified study using classical and modern methods, a molecular picture of the particular behavior of a given electrolyte such as LiASF6 in a given ether. Hopefully this would give a molecular rationale for the choice of a given electrolyte in battery construction. On the contrary phenomenological information, as low internal resistance, often has been the criterion for the selection of solvents in batteries. Experimental Part The experimental procedures for the conductivity, ultrasonic, and dielectric measurements have been described el~ewhere.~~ Raman spectra were collected at the University of Waterloo, Ontario, Canada, from a Jarrel-Ash 100 Raman spectrometer equipped with an argon-ion laser source tuned at 514.5 nm and interfaced to a Commodore microcomputer. 1,2-Dimethoxyethane was purified as described b e f ~ r e . ~ LiASF6 (Alfa Division, Andover, MA) was redried under vacuum at 60 "C for 1 day. The original product was (1) Department of Chemistry, University of Waterloo, Ontario, Canada. (2) Goldman, J. L.;Mank, R. M.; Young, J. H.; Koch, V. R. J.Electrochem. SOC.1980, 127, 1461. (3) Jagodzinski, P.; Petrucci, S. J. Phys. Chem. 1974, 78, 917. (4) Onishi, S.;Farber, H.; Petrucci, S. J.Phys. Chem. 1980,84, 2922. (5) Farber, H.; Petrucci, S. J. Phys. Chem. 1975, 79, 1221. (6) Saar, D.;Brauner, J.; Farber, H.; Petrucci, S. J.Phys. Chem. 1978, 82. 545. 0022-365416312087-3515$01.50/0
found, by weight loss, to contain about 1% of moisture. Raman spectra of solutions prepared by using the original product revealed a faint OH stretch band at about 3500 cm-l, the same position (3520 cm-l) shown by a 0.4 M aqueous solution in DME prepared and used for comparison's sake. The distilled solvent had no water band by Raman spectra. Repetitive attempts to dry LiASF6 under vacuum at 100-115 "C resulted in the same weight loss as above. However, when the dried product was dissolved in DME, some opalescence and small amounts of precipitate occurred, suggesting some thermal decomposition of the electrolyte. Solutions were prepared by weight for the conductance runs, the molalities being converted to molarities by the use of densities. Other solutions were prepared by weighing the electrolyte directly in volumetric flasks and diluting to the mark with the distilled solvent. All the solutions were used shortly after preparation and kept sealed in large desiccators over Mg(C104)2.Contact with the open air in transferring the solutions to the cells or capillaries was kept within 30-60 9.
Results and Discussion Figure 1A shows the equivalent conductance data (Q-l cm2equiv-l) plotted vs. the concentration c (mol L-' = M) in a log-log plot, for LiAsF, in DME at t = 25.00 "C. In the same plot the corresponding data for LiC104 are reported.4 One may see that there is a dramatic increase of almost 1order of magnitude in the equivalent conductance of LiAsF6 with respect to the one of LiC104 in DME. Figure 1B shows the Fuoss-Kraus7 plot of Ac1l2 vs. c according to the simplified version of the triple-ion theory, neglecting long-range ionic interactions. This simplified theory leads to
with KA and KT the ion-pair and triple-ion formation constants (usingthe symmetrical approximation KT1= Km for the formation constants of the two possible triple ions (7) Fuoss, R. M.; Accascina, F. "Electrolytic Conductance";Interscience: New York, 1959.
0 1983 American Chemical Society
The Journal of Physical Chemistty, Vol. 87, No. 78, 1983
3516
Farber et ai.
Solvent: 1-2 Dimethoxyethane t = 25°C 0 1st Run
1 .0
> f,. The results for A , f,, and B together with the sound velocities U (cm s-') and the calculated maximum excess sound absorption per wave length pm (= ( 1 / 2 ) A f , U )are collected in Table I. From Table I it is apparent that at 25 "C f, is independent of concentration within experimental error (f5%). Further, it is found that pm is linear in c (see below). These observations suggest a first-order or pseudo-first-order process of the type A a B. From the information above we advance the hypothesis that the process of ionic association between Li+ and AsF6-follows the Eigen-type mechanism:
3517
C
10
20
-
50 100 ffMHz)
200
500
Figure 3. (A, C) a / f 2vs. frequency f for LiAsF, in DME at various concentrations at t = 25 O C . (B) a/f2vs. frequency f for LiAsF, (0.3 M) in DME at t = 10 "C.
tion-dependent relaxation frequency contrary to what is observed here. Because of the value of KA= 1 X lo5 M-', we suggest that, at the concentrations of the ultrasonic work, the first step of eq V is complete and few free ions exist. The process then may be written as
(V)
k-1
followed by further steps leading to triple ions. However, we are disregarding these further steps for the treatment of the ultrasonic process. Formation of triple ions would require a t least a second-order process and a concentra(13) Farber, H.; Petrucci, S.J. Phys. Chem. 1981,85, 2987. (14) Begun, G. M.; Rutenberg, A. C. Inorg. Chem. 1967, 6, 2212.
We will denote the free-ion concentrations by c1 and those of the two complex species by c2 and c3, respectively, with the conditions that c zz c1 + c2 + c3 (neglecting other species). This approximation may be justified as follows. Given the scheme7
3518
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983
A+
sf
AB
+
Farber et al.
B $ AB, A
tA,B
we call [AB] = (1- (Y - 3 a ~ ) c c
[A] = [B] = ac [AB21 = [AZBI =
ffTC
where a and CYTare the degrees of dissociation of the ion pair to free and triple ions, respectively. Also
13.0
A
i I
I
3.3
3.4
-23.0r
KT =
'YT ffC(1
c ~ T=
- ff
I
I
3.5 3.6 (1031~)
3.7
Lamb plot for LiAsF6 in 1-2 DME
ffT E -
- 3aT) -
ffc
(KT/KA'/2)~1/z
(VI4
If KT = 28 M-l and KA = 1 X lo5at c = 0.2 M, CYT = 0.03, M. Further, a = 0.01 and CYTC (AB,) = (AzB) = 3 X single ions account only for a few percent of the total concentration of electrolyte (neglecting other species). The collected data of Table I applied to eq VI can be used in the following treatment. Consider the relation15 7-1
= kl
+ kl = k-,(l + K,) = zeAS'-1/Re-AH-i/RT(1 h
+ K,) (VII)
B
d In (~-'/13d(1/13
AH*-, K, R
AHl
l+K1 R
- -spm
- 26,
(AVJ2 KI R T (1 + K1)' C
(XI
I
1
3.6
3.7
(IO~/T)-
,
c
The results are shown in Figure 4A. The solid line has been calculated by linear regressions. The results are as follows: 1.2 = 0.995, intercept = -22.74, and slope = -2510. From the intercept one calculates AS*-, = -2.0 cal mol-' K-l. Equation VI leads also to the relation15
1
3.5
:::L
(VIII)
(k) AS*-, intercept = In - + (h) R
1
3.4
Excess max sound absorption per wavelength vs. concentration for LiAsF6 in 1-2 DME
where k is the Boltzmann constant, other symbols bearing their usual significance. K1 = kl/k_, is the equilibrium constant. 7-1 is the inverse of the relaxation time, and AH*-, and AS*-, are the activation parameters of the reverse process. A plot of In 7-l/T vs. 1/T should be linear with the following slope and intercept: slope =
1 3.3
l
0
o
0.1
0.2 0.3 c x I03(mo1e/cm3)
1
-
0.4
Flgure 4. (A) Eyring plot: In ( r " / T ) vs. 1 / T for 0.3 M LiAsF, in DME. (8) Lamb plot: In ( p m T / U 2 )vs. l/Tfor 0.3 M LiAsF, in DME. (C) km vs. concentration for LiAsF, in DME; t = 25 'C.
The results are shown in Figure 4B. Linear regressions applied to these data give rz = 0.991, intercept = -14.82, and slope = -2517. We are now able to write the system of three equations: l5
where the isoentropic compressibility & = l / ( p V ) and AVs = AVT - (6 / ( p c , ) [ A H , , with 6, the expansivity, p the density, ancfc, the specific heat of the liquid. Equation X implies that a plot of In (pmT/U2)vs. 1/T should give a straight line with slope15 d In ( p m T / V )=--K1 - 1 AH, d(l/T) K,+1 R
(XI)
(neglecting the temperature dependence of p and c,). (15)Chen, C.; Petrucci, S. J.Phys. Chem. 1982, 86,2601.
7-1 g
-eM'-l/Re-mH'-l/RT(l kT + K,) h
with the unknown parameters K,, AH,,AH*-,. Trial and error by changing K1 leads to compatible solutions with K, = 0.01. (K, much smaller than lo-, gives still compatible solutions but it is unreasonable. No ultrasonic
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983 3519
Molecular Relaxation of LiAsF, in 1,2-Dimethoxyethane
t
LiAsFg O.05M in 1-2 DME
-- x V -ru
t =25’C
TABLE 11: Dielectric Relaxation Parameters eo, e,,, e m 2 , frl,fr, and Specific Conductance x of LiAsF, in DME at the Concentrations Investigated at t = 25 “C
v
- 2.5 - 2.0
C,
M
€0
0.10 0.05 0.028
9.8 8.7 8.0
fri,
frz,
c-1
em2
MHz
7.0 7.2 7.2
2.7 2.9 3.0
2.0 2.0 2.0
MHz 35 30 35
X,
51-lcm-l 1.4 X 7.3 X 3.5 X
lo’’
Bottcher’s equation: [ ( € o - 600,)(2€0 1/36,)] vs concentration for LiAsF6 in 1-2 DME t = 25OC
+
f
5
Al
10 f(GHz)-
t
20
50
100
COle-COle plot; LiAsF6 0.05M In 1-2 DME; t =25OC
n
;2.0
+ y b /
,
0.0 0
,
0.05 c x 10J(mole/cm3)
-
0.10
Flgure 6. Bottcher equation for LiAsF, in DME. 01
B3
4
5
6
€
-’
7
t
8
\ , 9
Figure 5. (A) e’ and E“ vs. frequency for 0.05 M LiASF, in DME at t = 25 O C . (B) Cole-Cole plot for 0.05 M LiAsF, in DME at t = 25 OC.
relaxation would be observable if the concentration of one of the two species is too small.) The final results then are > kl 7-’ “=
k-’ = 5.0 X
the intercept through the origin, 1.2 = 0.992, slope = 14.4.) Figure 5A shows t‘ and E’’ - e”, the coefficients of the real and imaginary parts of the complex permittivity E* = E’- J(E”- E”& plotted vs. the frequency f (GHz) for a representative concentration of LiAsF, in DME. The frequency covered is 1-90 GHz. The solid lines are the sum of two single Debye processes according to the functions
-
lo8 s-l
.
AH*-.l= 4.9 kcal mol-’
f/f12
ASs-‘ = -2.0 eu
AHl = 5.1 kcal mol-’ AHs’ = 10.0 kcal mol-’ Finally, combination of ultrasonic and conductance results leads to the correlation K* = 1.0 x 105 = ~ , , + ( iK,) “= K,, as
K1 = ~
3 / ~= 20.01
This implies that c3
