J. Phys. Chem. 1987,91, 3047-3055 and essentially act as inhibitors. The structures of compounds such as 1,l-diphenylethylene which make up the CCs are similar to radical scavengers and inhibitors such as ptert-butylcatechol. Absolute values for their efficiencies as radical scavengers cannot be reasonably estimated until there is better knowledge of the amounts of the various compounds present in the CCs.
Conclusions The two reactions observed here, darkening and normal polymerization, are the result of radicals formed in the fragmentation of styrene on the collapse of cavitation bubbles. At higher collapse temperatures,,the fragments are similar to those found in pyrolysis and give rise to colored compounds. Thus, the overall mechanism is quite complex. It is possible that it involves two reactions that compete for the products of an initial fragmentation reaction, but it is also possibly due to the inhibiting of the polymerization through radical scavenging by the polyaromatic colored compounds formed. The initial step must involve some bimolecular atom transfer, as the activation energies obtained are too low for a simple bond
3047
cleavage reaction expected in unimolecular gas-phase decomposition. When hydrocarbons are added to the styrene, their main influence on the reaction is not primarily chemical in nature but rather arises mainly from their influence on the vapor pressure. Results obtained in these styrene studies are consistent with previous results on the polymerization of methyl methacrylate and the darkening of nitrobenzene and other aromatic compounds. Acknowledgment. The authors thank Dr. S . Bywater of the National Research Council and Dr. K. Taymaz of Consumer and Corporate Affairs, Canada, for providing gel permeation data, Dr. G. Buchanan and Mr. K. Bourque of Carleton University for N M R data, Dow Chemical Canada Inc. for a supply of styrene monmer, and Dr. M. Goldenberg of CIBA-GEIGY Corp. for the suggestion of using chromatography to remove inhibitors from the monomer. The project was supported financially by the Natural Sciences and Engineering Council of Canada through a grant. Registry No. C6H5CH=CH2, 100-42-5; polystyrene, 9003-53-6.
Molecular Relaxation Dynamics and Structure of LiCiO, Solutions in 2-Methyltetrahydrofuran Heidrun Maaser: Meizhen Xu, Paul Hem",$
and Sergio Petrucci*
Weber Research Institute and Department of Chemistry, Long Island Center, Polytechnic University, Farmingdale, New York I 1 735 (Received: July 1, 1986; In Final Form: October 3, 1986)
Electrical conductance data in the temperature range +25 to -43 O C are reported and interpreted by the Fuoss-Kraus triple-ion theory. Theoretical expressions for the thermodynamicparameters for triple ions A W T and SoT have been derived. Comparison is made between the experimental figures of AW and ASoand the correspondingvalues calculated from the Bjerrum theory of ion pair formation. Comparison is also made between the experimental M O T and SoT and the values now calculated from theory. Both these tests give reasonable estimates of the ion pair separation distance d and of the ion to dipole separation distances a (in the triple ion.) Infrared spectra of the (infrared-active) 8, band of the perchlorate anion in the wavenumber band 550-700 cm-' reveal a complex spectral envelope which can be deconvoluted into three Gaussian-Lorentzian bands. One of them, centered at -625 cm-I, is assigned to the "spectroscopically free" ClO,- ion (that is, to the solvent-separated Li'S, CI04- and/or to the solvent-separated dimer (Li'S, C104--LifS, Clod-) where S is a solvent molecule), the perchlorate ion having Td symmetry. The other bands centered at 639 and 654 cm-' are presumed to be due to contact species, the C104having lower symmetry. The maximum band absorbances have been correlated to the electrolyte concentration by polynomial functions. Ultrasonic relaxation spectra in the concentration range 0.05-0.4M and frequency range 0.5-400 MHz are described by a single Debye relaxation function. Independence of the relaxation frequency on electrolyte concentration for c > 0.1 M and linearity of the maximum excess absorption coefficient of sound per wavelength p,,, on concentration identify the ultrasonic relaxation process as due to a first-order or pseudo-first-order process. The ultrasonic spectra are interpreted by the second step of the dimerization equilibrium 2M Me-M s M2, namely, by the scheme M-M M2 ( I C ~ , - ~ where ) M is the monomeric ion pair, M-M a solvent-separateddimer or quadrupole, and M2 a contact dimer. Temperature dependence of the ultrasonic relaxation spectra allows for estimation of activation and thermodynamicparameters of the observed equilibrium. Microwave dielectricrelaxation spectra in the frequency range -0.8-90 GHz and concentration range 0.05-0.3M are interpreted by two Debye relaxation processes at 1.8 and 35 GHz, respectively. The one at lower frequency is attributed to the presence of the solute. Bottcher plots of the lower relaxation strength 4(t) vs. total concentration of electrolyte show a marked concave down curvature, revealing that not all of the electrolyte exists in dipolar form. Since K A E lo* M-I and the concentration of triple ions is small, no appreciable extent of free ions exists in solution as to cause the curvature of the Bottcher plot. The observed phenomenon is interpreted as evidence of the presence of dimer ion pairs or quadrupoles. M-M, the solvent-separated dimers, are the predominant species in solution, and previous theoretical work predicts that the ion pair components can rotate independently of each other. In fact, by approximating (Me-M) E c/2 and plotting the Bottcher relaxation strength function @(e) vs. c/2, one observes an approximately linear correlation.
(1) Delsignore, M.; Maaser, H. E.; Petrucci, S.J . Phys. Chem. 1984,88,
Colgate Palmolive, Piscataway, NJ 08854. *Miles Laboratories, Elkhart, IN 46514.
2405.
(2) Farber, H.; Irish, D. E.; Petrucci, S. J . Phys. Chem. 1983, 87,3515.
0022-3654/87/2091-3047$01.50/0 0 1987 American Chemical Society
3048 The Journal of Physical Chemistry, Vol, 91, No. 11, 1987 TABLE I: Equivalent Conductanee A (SI-' cm2 equiv-') and Concentration E (mol/dm3) for LiCI04 in 2MeTHF c X lo4 A c X IO4 A c X lo4 t = 25.00 "C 0.1784 0.1476 0.1294 0.1230
A
2.1329 4.9423 10.683 27.842
0.7462 0.5113 0.3582 0.2357
56.573 101.64 179.08 257.16
830.59 1097.3 2591.1
0.1952 0.2200 0.3227
7.9115 24.568 60.889
0.4620 0.3006 0.2147
t = 5.00 OC 134.81 0.1703 28: 96 0.1468 537.50 0.1433
1177.74
0.1746
6.1472 13.818 56.736
0.7019 0.5093 0.2897
t = -15 O C 147.31 0.2103 298.79 0.1763 668.83 0.1604
1175.9 1580.95
0.1802 0.2079
9.7009 24.149 54.723
0.7675 0.5239 0.3791
t = -35 o c 156.65 0.2519 307.81 0.2059 660.51 0.1678
1296.05 1983.9
0.1825 0.2226
5.3754 12.990 36.006
0.9582 0.7124 0.4756
t = -43 oc 94.881 0.3274 211.08 0.2464 454.59 0.1871
799.14 964.67
0.1654 0.1655
investigated the conductance of LiC104 in 2MeTHF down to -43 OC,namely, to temperatures comparable to subarctic or stratospheric conditions. This hopefully will give information relevant to the solution behavior of batteries subjected to the same conditions. Theoretically, we have used these data to evaluate the thermodynamic parameters for triple-ion formation which were compared with the corresponding theoretical quantities derived below. We have also performed infrared spectra on LiC104 solutions in 2MeTHF, which have proven to be useful in giving structural information in a concentration range where conductance theory fails. The above background has been useful in the subsequent work on the dynamics of the solute species in solution performed by ultrasonic relaxation kinetics and by microwave dielectric spectrometry. Experimental Section The equipment and procedure for the cond~ctance,~ IR spectra,4 and ultrasonicS and microwave dielectric spectra' have been described before. LiC10, (Johnson Matthew Inc., Seabrook, NH) was redried at 70 OC in vacuo overnight. 2MeTHF (Aldrich) was distilled over metal sodium and benzophene under reduced pressure. Solutions were prepared by weight for the conductance work; with volumetric flasks for the IR and ultrasonic and dielectric work (adding solvent to weighed LiC104 predried directly in the same flasks), contact with the atmosphere of the solution in all cases was limited to 30-60 s, namely, to the time necessary to fill the IR and ultrasonic cells. For the conductance work at low temperatures, addition of the weighed portions of stock solution, from weighing burets, to the solution of the conductance cell was performed outside the thermostat, after the conductance cell had returned to room temperature. This was done in order to avoid condensation of atmospheric humidity because of temperature gradients. Results and Calculations EZectrical Conductance. Figure 1 reports representative plots of the log of the equivalent conductivity A for LiCIO, vs. the log of the concentration c, at various temperatures. Table I reports
Maaser et al. TABLE II: Static Permittivity e, Viscosity IJ of 2MeTHF, Calculated Limiting Equivalent Conductance A,, (Walden's Rule), and Values of K , and KT for LiC104 in 2MeTHF at the Temperature Investigated T, K
e
IJ, P
A,,, n-' cm2 equiv-'
298.15 278.15 258.15 238.15 230.15
6.24 6.77 7.38 8.10 8.42
0.0047 0.0057 0.0072, 0.00968 0.0110
144 119 93 70 61
KT~
K A , M-' M-' 1.S2 X lo8 33 3.5, X 3.1 X 1.05 X 7.2 X
lo7 20., lo7 lo7 ll., lo6 6.6
%"a
lo4, M 179.08 285.96 298.79 307.81 211.08
TABLE III: Experimental Association Constants KA, Calculated Values of KF (Eq 111) and KBj(Eq IV), and Corresponding Distance Parameters dFand dBjfor LiCI04 in 2MeTHF at the Various Temperatures Investigated dF X lo8, dBi X lo8, T, K KA, M-' K F , M-' cm KBj, M-l cm 298.15 1.S2 X lo8 278.15 3.55 X lo7 258.15 3.1 X lo7 238.15 1.0, X lo7 230.15 7.2 X lo6
1.82 3.57 3.06 1.03 7.26
X lo8 X lo7 X
lo7
X lo7 X lo6
4.36 4.74 4.72 5.00 5.10
1.86 X 3.58 X 3.08 X 1.04 X 7.17 X
lo8 lo7 lo7 lo7 lo6
3.95 4.28 4.26 4.50 4.59
the corresponding values of A and c at all the temperatures investigated. The data have been interpreted by the Fuoss-Kraus triple-ion theory6 in the form
where
( 1 - L(cA)'/2)(l A ~ ~ /
~ -
i-"'
is a term lumping all the interionic terms together.6 In particular, p' = 1.8247 X l 0 6 / ( ~ T ) is ~ /the ~ Debye-Hiickel term of the activity coefficientf= e~p[(-2.303/A~~/~)p'(cA)'/~] and S = [0.8204 X
106/(eT)3/2]Ao + 82.501/q(eT)1/2is the Onsager coefficient of / ~ the . above the conductance equation A = do- S ( C A / A ~ ) ~ In the values of the permittivity t and of the viscosity coefficient q have been taken from the work of Szwarc et aL7 both at T = 298 K and at the other temperatures. At T = 298.15 K the value of Ao(LiC104) = 26.75 R-l cm2 equiv-' in propylene carbonate8 of viscosity q = 0.0253 P has been retained, giving A,,q = 0.671. Then from assumed consistency of the Walden rule, one calculates do = 144 R-l cm2 equiv-I in 2MTHF of q = 0.0047 P. Figure 2 shows a plot of eq 1, namely, Ag(c)c'/2 vs. (1 - A/Ao)c at t = 25 "C. The solid line calculated by linear regression up to c = 179 X lo4 M gives 9 = 0.993, intercept = 0.01068, and slope = 0.2353, from which one evaluates K A = 1.83 X lo8 M-l and KT = 35 M-l having arbitrarily retained the position ATo = 2/3Ao = 96 R-' cm2 equiv-' as done before.2 Table I1 reports the values of A, (from Walden's rule), e, q, K A , and KT at all the temperatures investigated. Table I1 also reports the maximum concentration for each case used in applying eq I. Thermodynamic Parameters. In this section we shall try to extract information of thermodynamic nature from the above data. We start by matching the values of K A with the Fuoss association formation constant9
where L is Avogadro's number, dF is the minimum distance in
(3) Petrucci, S.; Hemmes, P.; Battistini, M. J . Am. Chem. SOC.1967, 89,
5552. (4) Saar, D . ; Petrucci, S. J . Phys. Chem. 1986, 90, 3326. (5) Petrucci, S . J. Phys. Chem. 1967, 71, 1174. Petrucci, S.; Battistini, M. J. Phys. Chem. 1967, 71, 1181. Onishi, S.; Farber, H.; Petrucci, S . J. Phys. Chem. 1980, 84, 2922. Reference 1. Petrucci, S.; Adamic, R. J.;
Eyring, E. M. J. Phys. Chem. 1986, 90, 1677.
(6) Fuoss, R. M.; Kraus, C. A. J. Am. Chem. SOC.1933,55,416. Fuoss, R. M.; Accascina, F. Elecrrolytic Conductance; Interscience: New York, 1959. (7) Nicolls, N.; Sutphan, C.; Szwarc, M. J . Phys. Chem. 1968, 72, 1021. (8) Salomon, M.; Plichta, E. J. Electrochim. Acra 1984, 29, 731. (9) Fuoss, R. M. J. Am. Chem. SOC.1958, 80, 5059.
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987 3049
LiC104 Solutions in 2-Methyltetrahydrofuran
d
I t
64
0
100 ~l-AlAo~x104-+
t
i 150
I
200
Figure 2. Fuoss-Kraus plot of (Ag(c)c'12) vs. (1 - A/A& for LiC104 in 2MeTHF at t = 25 OC. Van? Hoff prOt for brrpak fametion s y s t m LiCIO, h 2Mew
0
20-
log,
c
-
Figure 1. Representative plot of log A vs. log c at various temperatures for LiCIOI in 2MeTHF. The arrow indicates the approximate position of the minimum in A.
the ion pair, and c is the permittivity, with other symbols having their usual significance. Table I11 reports the calculated KF, the experimental KA, and the corresponding Va= !l of dFused for the fit (within iO.01 A). The d 0.1 M suggest that the observed ultrasonic relaxation corresponds to first-order or a pseudo-first-order process.
(19) Maaser, H. E. Doctoral Dissertation, Rutgers University, 1982.
LiC104 Solutions in 2-Methyltetrahydrofuran
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987 3053
with
TABLE VII: Collected Kinetic and Thermodynamic Parameters for the Observed Eauilibrium in Solutions of LiCIOI in 2MeTHF k2N 7-1 = 1.5 x 108 s-I MZ= 3.60 kcal/mol A L 2 * = -14.9 cal/(K mol) AHz*= 5.45 kcal/mol AILz* = 1.85 kcal/mol
Then
TABLE V I E Dielectric Relaxation Parameters ee e,], c,~, fl, fz, and Experimental Electrical Conductivity x for LiClO, in 2MeTHF at f=25OC C, M €0 fi, GHz f2,GHz x , Q-’ cm-’
and since
c = 2(MJ
+ 2(M,M) + (M) 5T
”
AVZ2
4p, RT
2(M2)
0.30 0.207 0.106 0.0468
+ 2(M,M)
K2 (1 + K2)2c
= 2af, = k2
+ k-2
7.2
6.1
2.5 2.5 2.5 2.5
6.2
6.2 6.2
1.8
35
1.8 1.8
35
1.29 X lo4
35
1.8
35
3.59 x 10-5 1.03 x 10-5
D7-
e-
t
(XXI)
6: i1
where 7 is the relaxation time of the observed process. The infrared spectra, above, seem to indicate, however, that solventseparated species are preponderant. This would imply that the equilibrium constant
a-
0.1
and that
u
0,s
1
k-2 = TehS-2* /R e-Aff-2’ IRT h
(XXII)
where the symbols have their usual significance. Equation XXII leads to
s
2
RPb)
7-l
2.23 X lo4
D-
predicting an approximate linearity between pn and c, as observed (Figure 7). For c > 0.1 M, where presumably (M)
