J. Phys. Chem. 1988, 92, 2789-2798
1Olo M-’ s-I at T = 298.2 K. This rate constant is larger by a factor of 2 and by an order of magnitude, respectively, than the k , values reported in Table V for LiAsF6 reacting with 18C6 and with 15C5. If we allow for the uncertainty in u, this seems to imply an energy of activation for the first forward step of (5) slightly larger than diffusion controlled. This in turn might involve some ligand rearrangement in the first step of complexation ( 5 ) .
For the more flexible 18C6 macrocycle reacting with LiASF6 in DXL, a ligand rearrangement, separated from the encounter, is evidenced by the lower relaxation process reported in this work. However, if the rate-determining step of the entrance of the cation into the cavity is ligand dependent, one would expect 12C4 and 15C5 (being more rigid than 18C6) to react slower than 18C6 in the final step of cation inclusion. Evidence that 12C4 shows a slower relaxation process cfII = 1.7-3.0 MHz) when reacting with LiASF6 in DME solvent when compared to 18C6 cfII = 7-12 MHz), in the concentration range 0.1-0.3 M at 25 OC, already exists in the literature.I2 From Table V it is evident that the k-* values for both 15C5 and 12C4 LiASF6 are about 1 order of magnitude smaller than for 18C6 + LiAsF6. Similarly, the available k2 for LiAsF, 15C5 is 1 order of magnitude smaller than the corresponding k2 for LiAsF6 18C6, reflecting the above observations.’* The existing data lend themselves to a further observation. If one calculates the diffusion-controlled rate constant between neutral particles in dioxolane following Smoluchowsky, namely, kD = 8RT130007, with 11 = 0.00589 P,’ one obtains kD = 1.1 X
+
2789
Acknowledgment. We thank the Army Office of Scientific Research, Triangle Park, N C (ARO Grant No. DAA G-29-85KO05 l ) , and the National Science Foundation (Grant No. CHE-85-13266) for their generous support of various aspects of this work. Registry No. DXL, 646-06-0; 1,2-DME, 110-71-4;12C4, 294-93-9; 18C6, 17455-13-9;15C5, 33100-27-5;LiAsF,, 29935-35-1.
+
+
Supplementary Material Available: Infrared digitized spectrum (P, region) of 0.409 M LiASF6 in DXL-DME mixtures (XDMB = 0.195) and plots of normalized absorbances Ao,/l versus electrolyte concentration C for the three solute bands of the deconvoluted infrared spectra for LiAsF, in DXL-DME mixtures (XDME = 0.195) (1 page). Ordering information is given on any current masthead page.
(12) Richmann, H.; Harada, Y.; Eyring, E. M.; Petrucci, S . J . Phys.
Chem. 1985, 89, 2313.
Structure and Molecular Relaxation Dynamics of LiC104 1,3-Dloxolane at 25 O C
+ Macrocycle Solutions in
Meizhen Xu,+ Naoki Inoue,*Edward M. Eyring, and Sergio Petrucci*,§ Department of Chemistry, Polytechnic University, Farmingdale, New York 1 1 735, and Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 (Received: July 8, 1987; In Final Form: October 29, 1987)
Infrared spectra of the ij4region of ClO,- for LiC104 in 1,3-dioxolane(DXL) reveal the presence of two solute bands centered at D N 624 cm-’ and at 8 = 639 cm-’, which are attributed to spectroscopically free C104- and to LiC104 contact species, respectively. Upon addition at molar ratio R = 1 of crown ethers 18-crown-6 (18C6) or 15-crown-5 (1 5C5), the band at D = 639 cm-I disappears. However, upon addition of crown ether 12-crown-4 (12C4) the band at D = 639 cm-’ persists partially. Electrical conductance of LiC104 added to any one of the macrocycles 18C6, 15C5, and 12C4, in the molar ratio R N 1, in DXL reveals an increase of the total conductivity with respect to that of LiC10, in DXL at t = 25.00 OC. The highest molar conductance is shown by the macrocycle 15C5 + LiC104system. Microwave dielectric relaxation results of the complex permittivity e* = c’ - A’’in the frequency range 0.65-90 GHz at 25 OC are reported for the systems LiC104 + 18C6, LiC10, + 15C5, and LiC104 + 12C4 in molar ratio R = 1 The data are interpreted by the sum of two Debye relaxation processes, one attributed to the solvent and one to the solute. Ultrasonic relaxation spectra for the system LiC104 + 12C4 at R N 1 in the frequency range 0.6--400 MHz and concentration range 0.05-0.34 M at 25 OC are describable by the sum of two Debye relaxation processes and are interpreted by means of the Eigen-Winkler mechanism. For the system LiC104 + 15C5 at R E 1 the ultrasonic spectra in a comparable concentration and frequency range are described by a single Debye relaxation process whose relaxation frequency is comparable in position and concentration dependence to the faster relaxation of the system LiC10, + 12C4. I
Introduction It is well-known from the literature of electrolyte solutions’ that in media of permittivity less than 10 free ions are in a minority in most cases and that dipolar ion pairs are the dominant substrate species, which are sources of either ionic dissociation or further complexation to dimers and higher species. Naturally, when macrocycles are added to these electrolyte solutions, the starting point of the molecular interaction has to be conceived as a relatively long-range dipole-dipole interaction ‘On leave from the Department of Chemistry, University of Peking, Pekin , China. !On leave from the Department of Physics, Ehime University, Ehime, Japan. ‘Polytechnic University.
0022-365418812092-2789$01.50/0
(between the ion pair and the macrocycle) followed by possible desolvation of the cation with concomitant encapsulation in the cavity of the macrocycle. In the process, the anion may be excluded from the first coordination shell of the cation, thus producing a “crown ether separated” ion pair. To our knowledge, a structural-dynamical investigation of the effect of the size of the macrocycle cavity with the same cation in media of low permittivity and of the role of the anion in the above processes has not been carried out. Such a study should suggest guidelines for the best system to choose for maximum ionizing capabilities of the macrocycle. This type of information (1) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 2nd ed.; Reinhold: New York, 1950. Robinson, R. A,; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworth: London, 1959.
0 1988 American Chemical Society
2790
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988
may have applications in battery construction. The same study could offer a comparative view of the function of cavity size in the transport of ions through membranes by macrocyclic antibiotics. With these ends in view, we have chosen to reexamine2 LiC104 in DXL as the substrate electrolyte solution. The crown ethers 18-crown-6 (18C6), 15-crown-5 (1 5C5), and 12-crown-4 (12C4) were chosen because of their substantial differences in cavity sizes. The study can be roughly divided into a structural part carried out with infrared spectroscopy and electrical conductance and a dynamic part carried out by microwave dielectric and ultrasonic relaxation spectrometry. For the sake of clarity, after the Experimental Section, the results and calculations will be presented as subsections depending on the experimental method of attack.
Experimental Section The equipment for the infrared,3 c o n d ~ c t a n c e ,microwave ~ d i e l e ~ t r i c ,and ~ ultrasonic measurements6 has been described previously. The material LiC104 was redried at 70 "C in vacuo for a week. 1,3-Dioxolane (99+%, Aldrich Gold Label) was distilled over sodium at reduced pressure and then kept for 2 weeks over molecular sieves. Absence of water was verified by highresolution (0.1 absorbance units full scale) infrared spectroscopy by checking for the unobservability of the broad absorption band of water at -3600 cm-I. No band of water was discernible within the resolution of the Perkin-Elmer 9 8 3 6 spectrometer (fO.OO1 absorbance unit or 0.004% of H 2 0 based on a calibration plot). 18C6 (Aldrich) was recrystallized from distilled acetonitrile and subjected to vacuum for a day. 15C5 and 12C4 were kept over 3- and 5-A molecular sieves for 2 weeks (minimum) and checked for absence of water before use. Solutions for the infrared, dielectric, and ultrasonic work were prepared by weighing the salt and the macrocycle in volumetric flasks and diluting to the mark with the solvent after the homogenized solution was prepared by ultrasonic stirring of the components. Solutions for the conductance work were prepared by weight by adding them to the solvent in the conductance cell by weight burets. Contact of the solutions with the open atmosphere was kept to a minimum (30-60 s overall) for each run. Solutions were used immediately after preparation for the infrared, dielectric, and ultrasonic work and within 8-10 h (the time lapse of an experimental run) for the conductance work. Results and Discussion Infrared Spectrometry. The various bands of the infrared spectrum of the perchlorate ions have been reviewed in a recent paper.' As was done previously,' we have chosen for the present work the p4 mode of C104-as a probe to investigate the structure of LiC104 in DXL and of LiC104 macrocycles in DXL. Figure 1A shows a differential digitized infrared spectrum of LiC104 in DXL. The spectral envelope can be deconvoluted into two bands described by Gaussian-Lorentzian product functions of the type
+
where Aoj is the maximum absorbance of the corresponding band centered at BO,, ;a is the variance, with a, = (Au,)lj2/1.46, and ( A U , ) ~is/ the ~ width of the band at Aoj/2. The two bands are centered at DO626 = 625.5 cm-I and PO639 = 639 cm-' (with A0626 = 0.33, ( A Y ~ ~= ~14.6 ) ~cm-', / ~ = 0.09, (Au639)1/2 = 14.5 cm-l). The optical path length of the cells was ( 2 ) Onishi, S.; Farber, H.; Petrucci, S.J . Phys. Chem. 1980, 84, 2922. ( 3 ) Saar, D.; Petrucci, S.J . Phys. Chem. 1986, 90, 3326. (4)Petruai, S.; Hemmes, P.; Baltistini, M. J . A m . Chem. SOC.1967, 89, 5552. ( 5 ) Xu,M.; Eyring, E. M.; Petrucci, S. J . Phys. Chem. 1986, 90,6125 and references therein. (6)Delsignore, M.; Farber, H.; Petrucci, S.J . Phys. Chem. 1986, 90, 66. Delsignore, M.; Maaser, H.; Petrucci, S. J . Phys. Chem. 1984, 88, 2405. (7) Maaser, H.; Xu,M.; Hemmes, P.; Petrucci, S. J . Phys. Chem. 1987, 91, 3047.
Xu et al. F--v4 envelope L ~ C I O0~49M 05-
1
in DXL
1
G~ envelope.
L~CIO, 0 419M+
1 12C4 o 4 1 8 in~ DXL
a
0 4-
0 4-
I I
0.21
0
680
660
640
620
600
' r4
,15C5
I
05-
580
envelope, LiClO, 0445M + 0444M in DXL
1
-V
(cm-')
08 06!
v, envelope, LiCIO, 0492M+ 1iC6 0 495M II DXL
I
R
05 04-
I031
C
680
660
640
620
600
-?(cm-')
580
0 680
660
640
-v
620 (cm-')
600
580
Figure 1. (A) Differential infrared spectrum of the v4 envelope of the C104- ion; 0.49 M LiCIO, in DXL. (B) Differential infrared spectrum of the e, envelope of the Clod-ion; 0.419 M LiCIO, + 0.418 M 12C4 in DXL. (C) Differential infrared spectrum of the v4 envelope of the CIOL ion; 0.445 M LiCIO, + 0.444 M 15C5 in DXL. (D) Differential infrared spectrum of the v4 envelope of the C10,- ion; 0.492 M LiCIO, + 0.495 M 18C6 in DXL.
0.005 cm with both cells being of the Perkin-Elmer, sealed, demountable type with NaCl windows. The reference cell contained DXL solvent. Figure 1 parts B-D, reports corresponding differential spectra for LiC104 added to 12C4, 15C5, and 18C6 crown ethers, respectively, in molar ratios as indicated. The digitized spectra can be interpreted by a single Gaussian-Lorentzian band at no = 624 18C6 and LiC10, + 15C5 but by a small cm-l for LiC10, residual additional band at tro = 639 cm-I for LiCIO, + 12C4. Omission of this band results in a poor reproduction of the spectrum profile in the 630-650-cm-' region as also evidenced in Figure 1B. It is well-known that accurate quantitative infrared spectra are difficult to obtain by differential spectroscopy because of a multitude of possible errors including mismatch of cell path length, effects of the solute on the absorbance of adjacent solvent bands, and different molar concentrations of solvent in the two cells, affecting the absorbance of adjacent solvent bands. For these reasons we opted to work with only one cell and to include the solvent bands in the deconvolution analysis by Gaussian--Lorentzian functions. Figure 2A depicts the digitized infrared spectrum of DXL solvent in the wavenumber range 600-750 m-'.Figure 2B depicts a representative digitized infrared spectrum of LiC10, in DXL. The spectral envelope has been deconvoluted into four band components, two belonging to the solvent and two to the solute. Table I reports the results of the above analysis in terms of the parameters AoJ,voJ, and AD,)^,^ in addition to the length of the cells 1. Figure 2C reports the normalized AoJ/l quantities versus concentration. The solid lines were calculated by nonlinear regression fitting of a cubic polynomial to the Ao,/l data:
+
A o J / l=
CY
+ PC + y d + 6C3
(2)
The quantities a , /3, y, and 6 are reported in Table 11. Figure 3 for LiC104 + 12C4 in DXL, Figure 4 for LiC104 + 15C5, and
+ Macrocycle Solutions in 1,3-Dioxolane
LiC10,
Digitized infrared spectrum
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 2791
Of 1,3-Dioxolane in the
0
wavenumber region 600-750 cm-’
Digitized Infrared Spectrum LiC104 0429+12C4 0 430 M in DXL
01
i
I
I
I 01
o,5
0.4
t
4
I1
Digitized infrared spectrum LiC104 0.503M in DXL
I
750
Normalized absorbances of the bands of the V4 - envelope LiC104 +12C4 in DXL
A06241G
@
i
t
031 0.2i 0.1
1
-0
1
100
I 750
700
650
Normalized aEorbances of the deconvoluted bands of the v4 envelope for LiC104 in DXL
n ,
600
0.1
0.2
-
0.3 0.4 C(M)
3 I
A0639’G
0.5
I
0.6
I
Digitized infrared spectrum
t 0,41
4
0 3-
C(M)
-
0 2-
(A) Digitized infrared spectrum of 1,3-dioxolane in the wavenumber region 600-750 cm-’. (B) Digitized infrared spectrum of 0.503 M LiClO, in DXL. (C) Normalized absorbance of the deconvo-
Figure 2.
01
luted bands of the p4 envelope for LiCIO, in DXL.
+
0
Figure 5 for LiC104 18C6 as well as Table I1 report corresponding spectra and numerical analyses for the LiC10, macrocycles solutions in DXL. We now interpret the above spectra. The band at 624 cm-’, which persists upon addition of 18C6 or 15C5, is attributed as before7 to “spectroscopically free” C104-, namely, to free ions and/or to solvent-separated (or crown-separated) complex species. Because the ion pair association constant for LiC10, in DXL at t = 25 OC is quite large* ( K A N lo7 M-I), it appears that the free ion concentration is minimal, and the band at 624 cm-’ is due mainly to solvent-separated species. In contrast with LiC104 in the solvent 2-methyltetrahydrofuran (2MeTHF)7 no band at PO = 658 cm-l is visible, and furthermore, at variance with the case of LiC104 in 2MeTHF solutions7 no ultrasonic relaxation for LiCIO, is observable in DXLS2 In 2MeTHF the observed ultrasonic relaxation for LiClO, solution was attributed’ to :dimerization of the LiClO, ion pair to form (LiClO&. The above facts may be correlated by inferring that the band at DO = 659 cm-’ in 2MeTHF is due to contact dimers that are not present in DXL. This would not preclude the possibility that the band at 624 cm-I in DXL is due to solvent-separated dimers in addition to the solvent-separated ion pairs. The band at PO = 639 cm-l is probably due to contact species with the cation pertubing the 8, vibrational mode of “free” C104-. Contact ion pairs are the most probable cause of this band. Addition of the macrocycles
+
Ao6,,/G
Normalized absorbance of the F4=624cm-’band. ~ i C 1 0 ~ + 1 5 Cin5DXL
100
0
5
@
0.1
0.2
0.3
0.4
0.5 C(M) --t
Figure 4. (A) Digitized infrared spectrum of 0.453 M LiCIO, + 0.453 M 15C5 in DXL. (B) Normalized absorbance of the 1, band for LiCIO, + 15C5 in DXL.
18C6 or 15C5 in molar ratio R E 1 wipes out this band at PO = 639 cm-’ by segregating the cation into the macrocycle cage. For the case of 12C4 a residual small band at i j o = 639 cm-’ persists, as was pointed out for the differential spectrum (Figure 1B). It
2792 The Journal of Physical Chemistry, Vol. 92, No. 10, 1988
Xu et al.
TABLE I: Cell Lengths and Infrared Parameters for the Deconvoluted Envelope of LiCI04 and of LiClO,
+ Macrocycles in DXL
LiC104 in DXL
I , cm
CLicI04, M 0.109 0.204 0.305 0.355 0.401 0.503
0.005 07 0.004 92 0.005 02 0.005 45 0.002 33 0.005 00
cm-'
A0639
0.029 0.053 0.073 0.030 0.0966
639 639 639 639 639
cLiCI04, 0.0504 0.103 0.160 0.204 0.255 0.314 0.404 0.429 0.509
0.005 03 0.005 28 0.005 19 0.004 87 0.004 94 0.004 85 0.004 85 0.005 02 0.004 99
C12C4r
0.0504 0.101 0.158 0.202 0.255 0.314 0.404 0.430 0.507
A0639
IO6393
cm-'
CLIC104,M 0.0507 0.108 0.152 0.231 0.311 0.402 0.453
0.005 63 0.005 07 0.005 56 0.005 55 0.005 57 0.005 42 0.005 15
11 11 11 11 10 8 10
a
P
Y
C18C6r
0.0639 0.102 0.151 0.223 0.284 0.355 0.409 0.504
6
0.04 -0.009
624 639
0.25 0.024
624
LiC104 + 15C5 in DXL 0.68 267.0
0.999
LiC104 + 18C6 in DXL 256.5
0.996
624
-0.81
34.81 -4.78
r2
626 639
LiC10, + 12C4 in DXL -228.0 200.6 144.4 302.6 -403.8 -31.26
(A?624)1/21 cm-' 18 15 14.8 14.8 14.5 14.3
ii0624, cm-I
(A.8624)1/23cm-' 11.2 11.2 11.2 11.2 11.2 11.2 10.8 10.5
624 624 624 624 624 624 624 624 624
11
cm-I 624 624 624 624 624 624 624
(AD624)1/2?cm-' 11 10.5 11 11 11 11 11
1'624, cm-' 624 624 624 624 624 624 624 624
(Ap624)1/21 cm-' 11 10 10 10 9.9 I1 11
+ 18C6 in DXL
+ pc + -yC + ac3
LiC104 in DXL 122.1 16.87 25.68 26.73
A0624 0.067 0.124 0.180 0.229 0.269 0.323 0.421 0.524 0.532
1'624,
0.0858 0.155 0.245 0.361 0.470 0.570 0.623
TABLE II: Coefficients of tbe Cubic Polynomials' Used To Describe the Concentration Dependence of the Normalized Absorbances A O,// for the Deconvoluted Bands of the I, Envelope for LiCIOp and for LiCIO, + Macrocycles in DXL
I, cm-'
D0626, cm-' 626 626 626 626 626 626
+ 15C5 in DXL
0.0508 0.108 0.151 0.231 0 310 0.403 0.453
CL,C1O4?M 0.065 1 0.106 0.152 0.223 0.285 0.355 0.408 0.504
Ag/l= a
(A2639)1/2r cm-'
c15C53
LiC104
I , cm 0.004 93 0.004 97 0.004 92 0.005 46 0.005 12 0.005 56 0.002 88 0.005 58
14.5 14.5 14.5 14.5 14.5
639 639 639 639 639 639 639
0.010 0.015 0.021 0.032 0.047 0.062 0.043
LiC104
I , cm
A0626
0.071 0.132 0.185 0.260 0.130 0.348
+ 12C4 in DXL
LiC104
I , cm
(A%39)1/2?cm-'
0.998 0.992
0.080 0.119 0.170 0.303 0.334 0.501 0.318 0.721
the C104- ions suggests a large complexation constant K, between cation and macrocycle. This is testified to in the next section. Electrical Conductivity. Figure 6 reports the molar conductivities A (S cm2 mol-') of LiC10, in DXL at t = 25.00 OC, taken from the literature,2and of the systems LiC104 + 18C6, LiC104 + 15C5, and LiC104 + 12C4 in DXL at 25 OC in molar ratio R = 1.0 in the form of log A versus log C. Table I11 reports the measured values of A at the corresponding concentrations C (mol/dm3 = M). Chen et aL8 have interpreted the conductance of NaC104 added to 18C6 in 1,2-dimethoxyethane (DME) as due to the dissociation of the two species Na+,C14- F? Na+
0.995 0.972
"The nonlinear regression has been carried out by giving 50% statistical weight to the origin. The same holds for the linear regression. A simpler quadratic function Ao,/l = a, + b,C + c,C? can also fit the data although, on the average, with a lower determination coefficient 9. Also, the reported significant figures for the coefficients of the polynomials are in excess of the precision of the data to avoid round off errors in calculations.
appears likely that the less bulky macrocycle 12C4 cannot shield the cation completely from contact with C104- even after the cation has entered the macrocycle cavity. At least for the cases of 18C6 or 15C5 added to LiC104in molar ratio R = 1, the complete exclusion of the cation from contacting
11
+ C10;
NaC+,C104- e NaC'
+ C10;
where C denotes the crown ether complexing the cation. This leads to the expression
where Kp = [NaC1O41/ [Na'] [CIO4-lf,* [NaC+][C104-lf,2 KA =
[NaC1041[Cl The quantity g(C) lumps together all the electrostatic terms: (8) Chen, C.; Wallace, W.; Eyring, E. M.; Petrucci, S. J . Phys. Chem. 1984, 88, 5445.
LiC104
+ Macrocycle Solutions in 1,3-Dioxolane
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 2793
fi
Digitized Infrared Spectrum
dc)= 1 - (S/Ao3/2)(CA)’/2
8
LiC104 0.504Mt18C6 0.504M in DXL
In the above equationsf, is the Debye-Hiickel activity coefficient: 1.8247 X 106(eT)-3/2Ao-’12( CA)’/2
hfi =
1 + (2.9 127 / e l2)a0(CA / Ao) I2
and S is the Onsager conductance coefficient: 0.8204 X lo6 82.501
S=
A0
(eZ9312
+11(e T )I / 2
where the quantities e = 7.0, 7 = 0.005 888 P,9and the collision distance d = 5 A, the latter as a reasonable parameter, have been used. Also A. = 104 S cm2 mol-’ from the Walden rule Aoq = 0.614 has been used for LiC104 in DXL at t = 25 O C , as was done Equation 3 has been applied to the present data at C I M for LiC104 + macrocycles in DXL at 25 OC. Linear plots result from the functions. Table IV reports the results of linear regression giving determination coefficients 9,intercepts, slopes, the calculated Kp and K , values, and finally the cation-crown ether complexation constant K, = K#* = [LiC+]/([Li+][C]), where fi2. In using the K, values, one should assume it is assumed fi2 them to be correct to an order of magnitude at best. Equation 3 contains assumptions such as A, = A,, namely, equality of the limiting conductances of LiC104 and of LiCC104 and of the corresponding activity coefficients. The above approximations limit eq 3 to legitimate application only in media for which t C 10 and at quite low concentrations. Nevertheless, the values of K, will be useful in the analysis of the ultrasonic data. They also confirm the infrared data suggesting that the complexation constants K , >> 1. Microwave Dielectric Relaxation. Figure 7 representative plots of the coefficient e’ of the real part and of the coefficient E ” ~= e” - E’’~ of the imaginary part of the complex permittivity t * = d - Jd’ for LiC104 macrocycles ( R = 1) 12C4,15C5, and 18C6, respectively, in the solvent DXL at t = 25 OC. In the above, = 1.8 X 101zx/f is the conductance contribution to the loss coefficient e”. The solid lines are the sum of two Debye relaxation processes according to the functions:
+
Normalized absorbance of the band. L;CI04+15C5 in DXL
c4=624cm-’
A~6,,,/
gf
a
C(M)
-
+
Figure 5. (A) Digitized infrared spectrum of 0.504M LiC10, 0.504 M 18C6 in DXL. (B)Normalized absorbance of the i~~ band for LiC10,
+ 18C6 in DXL.
I
i
Log,oA ys. logloC for LiCIO, and for LiC104+ macrocycles in DXL; t=25.00°C
The parameters 6 tml,tm2,fi,a n d h and the specific conductances are collected in Table V. For the interpretation of the data, the relaxation process at high frequency is attributed to the solvent because of the similarity of the relaxation parameters to the ones for the solvent DXL.9 The relaxation at low frequency, which is absent for the pure solvent, is attributed to the rotational relaxation of solute dipole pairs. In particular, the infrared and conductivity results indicate that Li+ is heavily complexed by the macrocycles and that the conductance of the macrocycle solutions is rather low. This suggests that the great majority of the solute species exists in the form of ion pairs LiC+,C104-, namely, as a cation embedded in the cavity of the macrocycle but still paired to the anion through the macrocycle (except perhaps for the case of 12C4, which shows a residual infrared band at 639 cm-I). It is the diffusional rotational relaxation of this crown ether complex ion pair that is thought to be the source of the lowfrequency dielectric relaxation. Figure 8 shows Bottcher plots of the function
Figure 6. log A versus log C for LiC1O4 and LiC104 + macrocycles in DXL; t = 25.00 OC.
( 9 ) Saar, D.; Braumer, J.; Farber, H.; Petrucci, S.Adv. Mol. Relax. Inter. Processes 1980, 16, 263.
plotted versus the concentration C. Linear regression (giving 50% statistical weight to the origin) gives the results collected in Table VI, from which by neglecting the polarizability reaction field factor product (uf with respect to unity, as was done previously,2 one recovers the apparent dipole moments p (Table VI). By retaining
\
-1.01
I
-4
\
\
,
I
-3
-2
log,&
-1
2794
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988
Xu et al.
TABLE 111: Molar Conductance A and Concentration for LiC104 in DXLz and for UCIOA+ Macrocvcles in DXL at t = 25.00 OC LiC104 LiC104 + 12C4 104C, M A. S cm2 mol-' 104C, M A, S cm2 mol-' 1st Run 1.6164 2.8210 1.9068 2.3832 4.7632 2.1627 1.0577 6.5265 0.78141 11.972 9.1524 2.1338 0.57960 27.958 1.8829 18.496 0.46075 63.619 1.7648 31.911 0.39 196 147.92 1.8714 48.656 0.31854 293.34 2.3027 90.253 0.29200 532.07 3.1 147 194.45 0.27433 296.94
loL
0.29688 0.4699 0.99169
481.8 595.3 889.4 2142
LiC104 + 15C5 104C, M A, S cm2 mol-'
f
:x
890.3 1132.6 2217
9.5903 7.8973 6.4504 5.0964 4.5273 4.4663 5.2691 6.8101 8.0627 9.0171 12.123
W
*. 0.5
? intercept 0.992 5.75 X lo4 0.985 35.10 X lo4 0.980 22.96 X lo4
10
8
t6
-w 4
+
3.3462 7.3682 16.0917 34.129 6 1.823 97.709 187.08 400.86
K+
M1936 547 737
a rigid dipole model I.C = a,,e, where e is the charge of the electron, one may calculate the a,, values reported in Table VI. These values of a,, are reasonable and larger than the value calculated for LiC104 in DXL at t = 25 0C,2as would be expected if the crown TABLE V Dielectric Relaxation Parameters for LiCI04 + Macrocycles in Electrical Conductivity x of the Solutions CLicIoq M C12C4r €0 e001 0.05 14 0.051 1 8.25 6.90 0.101 9.20 6.95 0.103 9.40 6.95 0.150 0.150 10.50 6.95 0.204 0.204 M 0.0257 0.0500 0.103 0.151
CLiclod*M 0.0265 0.0502 0.104 0.151
C18C6r
0.0268 0.0502 0.102 0.15
5.0
50 100
F(GHz)--
,
,
LiClOd 0 . 1 0 4 M * l 8 C 6 0 102M ~n DXL: I - 2 5 ' C
7.8764 10.5679
slope Kp, M-l K.4 1.110 1.70 X lo7 1.14 X lo4 1.924 1.60 X lo6 3.42 X lo4 1.692 2.78 X IO6 2.65 X lo4
CISCS*
0.5
6.2137 5.5826 4.81 11 4.1595 3.8107 3.6830 3.7920 4.5828
2nd Run 1079.2 1886.0
CLicIod, M 0.0257 0.0503 0.104 0.151
50 100
LiCIO, 18C6 104C, M A, S cm2 mol-l
K, =
12C4 15C5 18C6
5.0 F(GHz)--
2.8322 3.2070 4.0993 6.9839
TABLE Iv: R d b of the Conductance Analysis According to Eq 3 Applied to the Data of LiCI04 + Macrocycles in DXL at t = 25.00 O C
macrocycle
W 1
;u 4
1st Run 5.0666 8.6881 16.376 38.032 73.284 154.30 341.67 649.79
i h
2nd Run 680.40 1180.4 2250.0
O .llO 0 OllM Miinn D DXL. X L , t - 2255''CC
0.5
5.0
50 100
F(GHz)--
+
Figure 7. (A) e' and e / versus frequency f for 0.103 M LiC104 0.101 M 12C4 in DXL; t = 25 OC. (B) e' and q" versus frequency f for 0.15 1 M LiC10, + 0.151 M 15C5 in DXL; t = 25 OC. (C) d and e< versus frequency f for 0.104 M LiC10, + 0.102 M 18C6 in DXL; r = 25 OC.
ether is partially interposed between the ionic partners of the ion pairs. Furthermore, the values of the lower relaxation frequency f l give the decay time of the polarization of the solute in the solution T~ = (27rfJ'. Neglecting differences between T, and the microscopic relaxation time (of the rotation of the complexes) and equating the T~ values to the Debye relation T~
= 47~a,~q/(kT)
the quantities a, have been calculated and are reported in Table VI. In this calculation the viscosity has been approximated to DXL at t = 25 OC According to Two Debye Relaxation Functions. 6002
fi,
3.4 3.4 3.4 3.4
€0
€001
cw2
7.90 8.66 10.00 10.85
6.95 6.95 6.95 6.95
3.4 3.4 3.4 3.4
€0
e001
coo2
8.0 8.5 9.8 10.8
6.95 6.95 6.95 6.95
3.4 3.4 3.4 3.4
GHz
h,GHz
1.5 1.5 1.5 1.5 fi,
GHz
34 34 34 34 f2,
1.3 1.3 1.3 1.3 fi, GHz 1.1 1.1 1.1 1.1
GHz 34 34 34 34
f2,
GHz 34 34 34 34
x,S cm-I 1.52 X 4.17 x 10-4 8.24 x 10-4 1.31 x 10-3 x,S cm-' 1.31 x 10-4 3.36 x 10-4 8.59 x 10-4 1.57 x 10-3 x. S cm-' 1.09 x 10-4 2.5, x 10-4 7.44 x 10-4 1.27 x 10-3
LiC104
+ Macrocycle Solutions in 1,3-Dioxolane
!,
3
-
Bottcher plot: LiC104 + 1 2 C 4 in
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 2795
8
700 LiC104 0.3%M+12C4 0 . 3 3 & 4 in
600- t=25OC 500
t (,g
Bottcher plot: LiC104 + 15C5 in DXL; t = 2 5 ' C ~
-Y ili
1
p,=720~10-~ fI =200MHz pn=50 x 10-5 f1=2.7MHz B = 1 0 6 ~ 1 0 - 'cm-ls2 ~ u =1.366x105 cm s-'
-
400-
3003. 200
-
100-
c
--I---)
0.5
0
LiC10,
!, ui
? c5
3/
Bottcher plot: LiClO4 + 18C6 in DXL: t = 2 5 C
/Q
2
5
10
20
I
I
I
50 100 200
500
50 1 0 0 2 0 0
500
0.049M+ 12C4 0.049M in DXL;
1z
2oo
@
~
i
/
1
I
B=149~10-~~cm s2- ~
100
u =1.352x105 cm s-l
v
0.05
0
0.10 0.15 0.20 C(moUdm3) -c
Figure 8. (A) Bottcher plot for LiCI04 + 12C4 in DXL; t = 25 "C. (B) Bottcher plot for LiCIO, + 15C5 in DXL; t = 25 'C. (C) Bottcher plot for LiC104 + 18C6 in DXL; t = 25 "C.
1
2
5 10 2 0 f(MHz) --+
Figure 9. (A) p versusffor 0.336 M LiCIO, + 0.336 M 12C4 in DXL; t = 25 'C. (B) p versusffor 0.049 M LiCIO, + 0.049 M 12C4 in DXL; t = 25 'C.
TABLE VI: Results from the Bottcher Plot (eo - eool)(2eo + 1)/(3ef) versus Cand from the Debye Relation T = 4ua:q/(kT) for LiCIOl and for LiCIO., + Macrocycles in DXL at t = 25 'C 1 OlSp, 1 OSU,, 1 OSU,, system r2 intercept slope esu cm cm cm LiC1042 0.998 0.106 6.289 10.1 2.1 3.60 LiC10, + 12C4 0.973 0.07 12.155 14.08 2.9, 3.89 LiC104 + 15C5 0.986 0.07 18.713 17.47 3.64 4.08 LiC10, + 18'26 0.989 0.06 18.114 17.18 3.58 4.32
be that of the solvent 9 = 0.005 888 P at t = 25 "C. Again the values follow a trend, namely, the larger the macrocycle the longer the resulting rotational relaxation time. The differences between the a, and the a, values may reflect their significance, namely, an intercharge distance versus the radius of the solvated rotating pair. Ultrasonic Relaxation. Figures 9 reports representative ultrasonic spectra of LiC10, + 12C4 in DXL at 25 OC. Notice that neither LiClO, alone in DXL nor 12C4 alone in DXL shows a relaxation spectrum. The spectra must then result from interaction between electrolyte and macrocycle. Figure 9 depicts the quantity p = a,,X = ( a - B p ) u versus f, namely, the excess sound absorption per wavelength versus frequency$ In the above, B is the background sound absorption ratio alf at frequencies much above the relaxation frequencies fI andf,,. A = u / f is the wavelength of sound, and u is the sound velocity. The solid lines in Figure 9 are the sum of two Debye relaxation processes centered at the frequencies fr and fir,respectively:
0.5
500 -
pm=400x10-5 f, =18OMHz
t
LiC104 0.05M+15C5 0.05M in DXL; t=25"C
p m= 230x 1O+ 2,301
f,
=150MHz B = 137 x IO-'
0
cm-' s*
u = 1 . 3 5 6 x 1 0 5 cm s''
X
3.
0
1
2
5
10
f(MHz)
Here *I and pIIare the maximum excess sound absorptions per wavelength at the relaxation frequenciesf, and AI, respectively.
20
1
1
,
50 1 0 0 2 0 0
,
500
Figure 10. (A) p versusffor 0.198 M LiClO, + 0.198 M 15'25 in DXL; t = 25 "C. (B) ,u versusffor 0.05 M LiCIO, + 0.05 M 15C5 in DXL; t = 25 'C.
2796 The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 TABLE VII: Ultrasonic Relaxation Parameters and Sound Velocities for LiC104 + Macrocycles in DXL at 25 OC CLicIoI, M 0.336 0.202 0.150 0.102 0.049
Macrocycle: 12C4 CIZC~, fr,, M 10Spi MHz 10Spil MHz 0.336 720 200 50 2.7 0.202 480 160 40 2.2 0.150 340 150 40 2.0 0.102 240 140 30 1.7 0.049 140 140 25 1.5 f r 9
10178, 1osu, cm-' s2 cm s-l 106 120 129 131 149
1.366 1.352 1.350 1.345 1.352
Macrocycle: 15C5
0.198 0.10 0.05 0.025
0.198 0.10 0.05 0.025
400 280 230 70
180 160 150 100
119 126 137 155
1.368 1.365 1.356 1.345
Figure 10 reports corresponding representative spectra for the system LiC104 + 15C5 in DXL at 25 OC. A single Debye relaxation suffices to interpret within experimental error the ultrasonic spectra of the two solutions of Figure 10. Table VI1 reports the ultrasonic relaxation parameters pI,f,,F , ~fI1, , and B and the sound velocity u for all the systems investigated. The ultrasonic spectra for the systems LiCIO, + 12C4 in DXL have been interpreted by the two-step Eigen-Winkler mechanism: LiC104 + C
kl k-I
kl
LiC104. .C c=LiCC104 k-2
where K, = K x = (1 - a)/(u2C), with the activity coefficients neglected and with u the overall degree of dissociation. For u ,' K2 = C3/C2,and C = C I C2 C3,where C, denotes LiCC104 concentration. Linear regression of pI versus rC1gives 9 = 0.996, intercept = 0, slope = 2103 = (n/(2/3s))(AV12/(Rr)), where the C values are in mol/cm3. From this AV, = 41.3 cm3/mol. Also from the relation"
+ +
(7)
where C is the crown ether, LiC104.. -C is an intermediate with the Li+ end of the LiC104 dipole pair still sitting outside the cavity of the macrocycle, and LiCC104 symbolizes the dipole pair with Li+ sitting inside the macrocycle ring. The reaction scheme (7) predicts two relaxation times, and for two loosely coupled processes it yields
k29
Xu et al.
(1 1)
I',yl has been calculated. Linear regression of pIIversus I']> Cs'. The relaxation processes (judging from the independenceof the relaxation frequency of the total cryptate concentration and the linearity of the maximum excess absorptions per wavelength with concentration) correspond to first-order or pseudo-first-order rate processes. The relaxation processes are interpreted as due to intramolecular rearrangements of the cryptates according to the scheme A, P A2 P A,; probably involved is a rotation of the two nitrogen atoms of the cryptand that coordinate the metal cation (with the cation always bound to the cryptand). The process with the lower relaxation frequency is thought to correspond to an endc-exo P endo-endo configuration change of the cryptand with concomitant entrance of the cation into the ring structure. As the cation diameter exceeds the cavity size the process becomes more difficult resulting in a decreased relaxation frequency. Kinetic and thermodynamic parameters have also been calculated for the above processes.
Introduction Recently we reported an investigation of the isomeric relaxation of cryptand 222 in various solvents.] The observed p r ~ were s ~ attributed to the rotational relaxation of the lone electron uairs (1) Eggers, F.; Funck, T.;Richmann, K. H.; Schneider, H.; Eyring, E. M.; Petrucci, S . J . Phys. Chem. 1987, 91, 1961.
0022-3654/88/2092-2798$01.50/0
of the two nitrogen atoms of the cryptand, in accord with the scheme endwendo a endo-exo exo-exo. The relative PPUlation of the three species, hence the appearance of one or two relaxation Processes, appeared dependent on the nature of the solvent or more specifically on the ability of the solvent to interact with one or both nitrogen ends of the cryptand. In aprotic solvents such as propylene carbonate only one relaxation process was 0 1988 American Chemical Society
