J . Phys. Chem. 1985, 89, 2313-2316
2373
Kinetlcs of Complexation of the Macrocyclic Ethers 18C6 and 12C4 with LiAsF, in 1,2-Dimethoxyethane at 25 C Helmut Richman,* Yoshifumi Harada,I Edward M. Eyring,: and Sergio Petrucci*+ Departments of Chemistry, Polytechnic Institute of New York, Long Island Center, Farmingdale, New York 1 1 735, and University of Utah, Salt Lake City, Utah 841 12 (Received: November 19, 1984)
Ultrasonic relaxation spectra of the systems LiAsF, added to the macrocyclic ethers 18-crown-6(18C6) or 12-crown-4 (12C4), in molar ratio R sz 1, in the solvent 1,2-dimethoxyethane(DME) at t = 25 OC, are reported. The concentration range covered was 0.05-0.25 M for 18C6 and 0.1-0.3 M for 12C4. Ancillary electrical conductance data for the same systems in the concentration range lo4 to -0.05 M at 25.00 OC reveal that the lithium-macrocycle interaction is weak, the conductance data being the same up to M, within experimental error of the data for the electrolyte alone in DME. Based on previous work revealing the presence of an outer sphere-inner sphere equilibrium LiSAsF6 * LiAsF6, where S denotes solvent, the present data are interpreted by a mechanism envisaging competition between the above reaction and the complexation scheme LiSAsF6 + c + Lic, AsF6 + s, where c is the crown ether. The results for LiASF6 + 18C6 are compared with previous results for the system LiC104 + 18C6 in DME.
-
Introduction In previous it has been found that LiAsF6 in the solvent 1,2-DME is the strongest electrolyte system so far investigated which, in principle, could be used for construction of secondary lithium batteries. It was of interest to see whether one could further enhance the electrical conductivity of this system by adding to Li+ such complexing agents as crown ethers. It was also of interest to determine the rate constants of formation and dissociation of the crown ether with the cation, since a too stable complex is unsuitable for the electrochemical reactions at the electrode surface. These practical interests paralleled more theoretical concerns such as the extent of interaction of crown ethers with a cation already solvated by DME which (by structure and chelating 18C6 in ability) mimics a part of a crown ether. As LiC10, DME had already3 been investigated, a comparison with LiAsF6 18C6 in D M E would offer an insight into the role (if any) of the anion in the complexation mechanism. This research in a strongly competing solvent for the first coordination sphere around Li+ is a prelude to work in solvents of less competitive nature but more in use for battery construction. To the above end, two experimental methods, audio-frequency electrical conductivity in the electrolyte concentration range lo-"-5 X M and ultrasonic relaxation spectrometry in the frequency range 1-400 MHz and electrolyte concentration range 0.05-0.3 M, have been used.
+
+
Experimental Section The equipment and procedure for the conductance4 and ultrasonic workZ have been described elsewhere. The materials LiAsF6,' 1,2-DME,3 and 18C63were purified as previously reported. 12C4 (Aldrich) was vacuum distilled. Solutions were prepared by weight burets directly in the conductance cell, kept at t = 25.00 f 5 X as monitored by a calibrated Pt thermometer and Mueller bridge.4 The conductance room was airconditioned at 71 f 1 O F . For the ultrasonic work, solutions were prepared in volumetric flasks, kept in desiccators, and used shortly after preparation. Contact of the solutions with the atmosphere was kept to a maximum of 20-30 s during the filling time of the cells. Results Figure 1A reports the equivalent conductance vs. concentration in the form of log A vs. log c for LiASF6 18C6 in molar ratio
+
'Polytechnic Institute of New York. *University of Utah. 8 On leave from the Max-Planck Institute for Biophysical Chemistry, Goettingen-Nikolausberg, West Germany. On sabbatical leave from Fukui University, Fukui, Japan.
0022-3654/85/2089-2373$01.50/0
TABLE I: Equivalent Conductance and Concentration at t = 25.00 OC for LiAsFr, LiAsFn + 18C6. and LiAsFr + 12C4 in DME" LiAsF, LiAsF, + 18C6b LiAsF, + 12C4c A, R-' A, R-' A, R-' cm2 cm2 cm2 104c,M equiv-' 104c, M equiv-I 10-4c,M equiv-' 1.8051 31.910 4.1943 26.551 3.2186 26.835 10.115 19.570 6.8613 20.138 3.0538 26.781 6.4551 20.722 18.812 14.895 22.092 15.451 44.237 13.020 43.990 12.271 14.514 15.864 85.738 11.802 86.408 11.377 40.036 11.920 153.52 11.621 205.94 11.654 70.421 10.715 270.25 12.202 446.47 13.163 136.94 10.162
"At least one significant figure in excess of the sensitivity of the method is reported in order to avoid round-off errors in future calculations carried out by others. The cell constant is K, = 0.1156 cm-I, as calibrated by KC1 solutions in water at t = 25.00 'C. *Mole ratio R = 0.975. c R = 1.004.
R = [18C6]/[LiAsF6] = 0.958 at 25 "c. In the same plot the data for LiAsF6 in DME' are also reported. The two sets of data overlap within experimental error, indicating a weak or nondetectable interaction between LiAsF6 and 18C6. Figure 1B reports the equivalent conductance vs. concentration (log A vs. log c) for LiAsF6 + 12C4 in DME at 25 "C. Two runs at molar ratios R = 0.974 and 1.004 have been made. As for the case of 18C6, no difference, within experimental error, is visible compared with the data for the electrolyte LiAsF, in DME except M. This again indicates weak interaction between for c > Lif and 12C4 in DME, which is vital information for the interpretation of the ultrasonic data. Notice that LiClO, + 18C6 in DME shows the same behavior in c o n d ~ c t a n c eexcept ,~ for data M where a difference starts showing up when the at c > crown ether is present. Table I reports the equivalent conductance and concentration for some of the systems investigated. Figure 2 reports the ultrasonic spectrum vs. frequency f in the form of the excess sound absorption per wavelength 1 for a representative concentration of LiASF6 added to 18C6 in DME at where a is the absorption 25 OC. In the above 1 = (a- E')u/f, coefficient of sound ( N p cm-') at the frequency f , E is the background sound absorption, a, at f >> the relaxation frequencies fI andfI, (see below), u / f is the wavelength, and u is the sound
-
(1) Farber, H.; Irish, D. E.; Petrucci, S. J . Phys. Chem. 1983, 87, 3515. (2) Delsignore, M.; Maaser, H.; Petrucci, S. J . Phys. Chem. 1984, 88, 2405. (3) Farber, H.; Petrucci, S. J . Phys. Chem. 1981, 85, 1396. (4) Petrucci, S.; Hemmes, P.; Battistini, M. J . Am. Chem. SOC.1967, 89, 5552. (5) Chen, C.; Wallace, W.; Eyring, E. M.; Petrucci, S. J . Phys. Chem. 1984, 88, 5445.
0 1985 American Chemical Societv
2374 The Journal of Physical Chemistry, Vol. 89, No. 11, 1985
Richman et al.
,t
A 20
0 20M t 1 2 C 4 0.20M
LlASF6
0 x a
in DME
,
1
25OC
t
500
t5
400
-%
n"
300
1 0
200
05
100
0
bolt
B
VS 100
1
lor LIAIF +12C4
0
10
2
5
10
20
50
Figure 3. p vs. /for LiASF6 (0.20 M) = 25 OC.
h DME, 1'25.OO0C
20
100
zoo
500
f
(MHz)-
+ 12C4 (0.20 M) in DME at f
LiA*Fe+ 1 x 4
n , A LIA8fe
h DUE
15
f 42
; 1 .o
5 . -2
-3
l0PlOC
-
f i 9
-1
0
Figure 1. (A) 1QgA vs. log c for LiAsF6 + 18C6 in DME at t = 25 OC. The triangles refer to LiASF6 in DME (ref 1). (B) log A vs. log c for LiASF6 + 12C4 in DME at t = 25 "C. The triangles refer to LiAsF, in DME (ref 1).
-f I z
LlAsFB
TABLE II: Ultrasonic Relaxation Parameters' gI, f,, pII, fII,and B and Sound Velocity u for LASF, + 18C6 and LiASF6 + 12C4 in DME at 25 O C for the Concentrations Investigated cLiAsFa* c10C6, fit fiI, 10178, io-su, M M 105rr MHz 105p,1 MHz cm-I s2 cm s-I 0.25 0.25 500 100 400 14 48 1.195 0.20 0.20 400 350 12 100 47 1.194 0.20 0.20 450 110 400 11 48 1.194 0.15 0.15 350 70 330 10 47 1.194 0.10 0.10 280 7 40 320 90 1.190 0.052 0.053 200 290 90 4.5 35 1.187 CLihF6, C12C4r fiI, 1017~, M M 105ul MHz 1OSurl MHz cm-' s2 cm s-I 0.30 0.29 550 100 140 3 50 1.300 0.25 0.25 570 85 100 2 49 1.190 0.20 0.20 450 80 80 2 48 1.196 0.175 0.175 370 90 85 1.7 44 1.180 0.10 0.10 220 90 70 1.7 42 1.174
"The calculated relaxation parameters are affected by an average error of &5%, except the parameter B which carries an error of *1 X 1O-I' (cm-' s2). The sound velocity u is measured with a n average error of *2%.
0 2 0 M f 1 8 C 8 0.20M
in DME , 1-25'C
may be possible including a distribution of relaxation times. The present one is the simplest possible interpretation of the spectrum. Figure 3 shows a representative plot of the ultrasonic spectrum vs. frequencyf, in the f o q of h, for a representative concentration of LiAsF6 added to 12C4 in DME a t 25 OC. The solid line in Figure 3 is the calculated sum of two Debye relaxation processes of excess maximum sound absorption per wavelength hI and pII centered at the relaxation frequencies fr and fir. Table I1 reports all the calculated ultrasonic relaxation parameters together with the sound velocity u at concentrations investigated in DME at 25 O C .
500
400
300
200
100
__-e'
o
----is 1
2
Discussion
.-. -.- - _ _ 5
10
20
50
100
200
500
f(MHz)--
Figure 2. Excess sound absorption per wavelength p vs. frequencyffor LiASF6 (0.20 M) + 18C6 (0.20 M) in DME at t = 25 O C .
velocity. The solid line in Figure 2 is the calculated sum of two Debye single-relaxation processes used to interpret the spectrum
where fr and fr, are the relaxation frequencies of two Debye processes. wI and hII are the respective maximum sound absorptions per wavelength. It should be pointed out that other mathematical solutions for interpretation of the sound spectrum
Electrical Conductance. In order to have a quantitative evaluation of the apparent weak interaction of both macrocycles with LiAsF6 in DME, we have applied the Fuoss-Kraus triple-ion theory6 to the conductance data for LiAsF, + 18C6 and LiASF6 12C4, respectively, in DME and have compared the results with those for the electrolyte LiASF6 in DME. In this evaluation we have purposely ignored the presence of the macrocycle and applied the Fuoss-Kraus equation, as done before.' We then have
+
( 6 ) Fuoss, R. M.; Accascina, F. "Electrolytic Conductance"; Interscience: New York, 1959.
18C6 and 12C4 with LiAsF, in 1,2-Dimethoxyethane
The Journal of Physical Chemistry, Vol. 89, No. 11, I985 2375 TABLE III: Calculated Parameters K A and KT in DME, with A. = 138 fl-' cm2 equiv-I and AoT = (2/3)A0, according to the Fuoss-Kraus Triple-Ion Theory and the Function
Fuoss-Kraus T W ions theory LiOsFg in DME 1.25%:.
1
I
Data horn J.Phy1. J.Phyi. Chem. ( 1 8 8 3 ) . 87. 3 5 1 5 with hO- 1 3 8 n - 1 cm2 gq- 1
R=
system LiASF6 LiAsF, + 18C6 LiASF6 + 12C4 LiASF6 + 12C4
0.4 o
0. Fuosr-Kr8us Triple ions theory LtOsFs + l a c 6 in DME
B
[macrocycle] [LiASF,]
IO-~K,,K ~ , M-I 0.91 1.09
M-I
0 0.9575
9 int slope 0.98 0.4578 7.325 0.97 0.4175 10.861
1.004
0.90 0.4098 9.134
1.13
33
0.974
0.95 0.4428 11.501
0.97
39
24 39
9
LiAsF +1OCe
and LIAS$+
12C4 In DME
0.2
0.3
R - (18C6)/(LiOs F g ) = 0 . @ 5 8 t = 25%
I
0.
u "
