J. Phys. Chem. 1991, 95, 7055-7061
7055
Infrared and Mlcrowave Dielectric Relaxation of Benzonltriie, Acetonitrile, and Their Mixtures with Carbon Tetrachlorlde at 25 O C P. Firman, A. Marcbetti: M. Xu, Edward M. Eying, and S. Petrucci* Weber Research Institute, Polytechnic University, Farmingdale, New York I 1 735, and Department of Chemistry, University of Utah, Salt Lake City, Utah 841 12 (Received: July 19, 1990; In Final Form: April 10, 1991)
Infrared refractive indices at B N 300 cm-I (f = 9OOO GHz) and P N 400 cm-I (f = 12OOO GHz) and complex permitthities e* = t' - Jd' at 3 = 300 cm-' and Y Y 400 cm-I for acetonitrileand acetonitrile-carbon tetrachloride as well as benzonitrile and benzonitrile-carbon tetrachloride mixtures at B N 125 cm-' (3750 GHz) at 25 OC are reported. Microwave complex permittivities e*, in the frequency range -0.4-90 GHz for the same systems at 25 O C , are also reported. Visible refractive indices at X = 589.3 nm (the sodium D line) for benzonitrile and benzonitrile-xrbon tetrachloride mixtures and for acetonitrile and acetonitrile-carbontetrachloride mixtures and static dielectric permittivities for the same systems at 25 OC are reported. The observed dielectric relaxation processes at microwave frequencies up to 13.8 GHz for pure benzonitrile and up to 80 GHz for acetonitrilecan be described by a single Debye relaxation function, using a parameter e,. This value is larger than the figure for nIR2at P = 125 cm-I for pure benzonitrile. For pure benzonitrile, an almost complete profile of d = d w wavenumber 3 has been determined up to the visible. For the mixtures, a single Debye relaxation function can describe the microwave dielectric data by using a parameter e,. The latter becomes practically equal to nn2, within experimental error, I0.05, respectively. Potential applicationsof t, (or nIR2)data in for mixtures of composition XwsN I 0.10 and XCH,CN evaluating the longitudinal relaxation times rL and the short-range structural relaxation time rG in f e m t o s e c o n d - p i c d molecular dynamics studies of solvation and the need for a better understanding of the dielectric properties of mixed liquids in the development of supercapacitors are both noted.
I~tdUCtiOa
Microwave techniques for determiniig the complex permittivity e* = d - Je" of liquids and liquid mixtures have been developed mainly since World War I1 with results reported in monographs.' It has been evident since at least 1955, as reported by Poley,2 that the Debye theory of a single rdaxation process (for the decay of the polarization) gives reasonable fits to e' vs frequency data, only up to frequencies of -40 GHz. Above 60-70 GHz, for many liquids such as chlorobenzene,' tails of the main relaxation process appear. Moreover, it has been shown that the value of e, (the extrap olated figure for d at frequencies high with respect to the Debye relaxation frequencyf,) is generally larger than nlR2and larger than n$, the squared far-infrared and the squared visible refractive index at A = 589.3 nm, corresponding to the Na doublet in the visible. In fact, for water d goes from a reported' 4.55 at 30 cm-' corresponding to t, extrapolated from microwave data to nIR2= 1.76 at 400 cm-', which is close to nD2= 1.777 (at 16969 cm-').' For rigid molecular liquids such as C6H5-X, Hill5 proposed a libration resonant-relaxation theory which would add to the rotational Debye process a new type of process (a partial rotation between neighbor potential wells) distinct from the Debye full rotational one. Also, first Lorentz6 and later Van Vleck and Weisskopf proposed a theory of damped m n a n t absorptions for the atomic and electronic polarizations that would affect the permittivity n2 at infrared (IR) and optical frequencies. These processes would lead to the progressive decay of the atomic polarization at 1R frequencies and to the electronic polarization at visible and UV frequencies. The numerical interpretation of the dielectric spectra requires a knowledge of e , and/or of nlR2to be used and further requires adequate theoretical criteria for the choice. As recently as 1989, it was remarked that the understanding of this region of the dielectric spectra of liquids is limited.' There has been, however, intense activity in recent years aimed at elucidating the dielectric properties at both microwave and far-infrared frequencies by considering the relaxation dynamics of permanent and induced dipoles. These studies have focused*' on methyl cyanide (acetonitrile) as a model molecule. Experimental studies by Yarwood and co-workersEbhave followed using benzonitrile as the model 'On leave of absence from the University of Modena, Modena, Italy. 0022-3654/91/2095-7055S02.50/0
system. For this liquid the dielectric microwave relaxation time reported at -38 ps is slow with respect to the far-infrared a b sorption spectrum attributed to librational motion of the permanent dipoles with a peak at -55 cm-'(-0.1 ps). In the latter study," however, the focus was on the attenuation coefficient a;no data on the wavelength of the liquid, namely, on the refractive index at infrared frequencies, or on the real part e' of the complex permittivity e* = t' - Jt'' were reported. In addition to the dielectric problem, a knowledge of the numerical value of e, for liquids is essential to calculations of both the solvent rearrangement times of a liquid around a solute (either rL, the long-range longitudinal relaxation time, or 70, the short-range structural relaxation time)9 explored by femtoaecond-picosecond spectroscopy. Also, development of a high-charge storage capacitor for high-frequency circuitry has been advct cated.l0 Such capacitors require liquids and liquid mixtures of relatively high permittivity to fill the capacitor and to hold the charge. Thus mixtures of apolar-polar components are needed for which there is adequate knowledge of their dielectric properties and of the relations between chemical structure of the polar component and the dielectric properties. With these goals in mind, we have undertaken a research program to provide reliable ex~~
~
~
(1) Hill, N. Dielectric Behavior and Molecular Struetun; Van Nootrand London, 1969. Smyth, C. P. Dielectric Behaulor and Structw, McGraw Hill: New York, 1958. (2) Poley, J. P. Appl. Sei. Res. B. 1955, I , 337. (3) Davics, M.; Pardoe, G. W. F.; Chamberlain, J. E.; Gebbie, H. A. Tram. Faraday SOC.1968,64847. Gcbbie, H. A.; Stone, B. N. W.; Findlay, F. D.; Pyatt, E. C. Nature (London) 1965, 205, 377. Chamberlain, J. E.; Werner, E. B. C.; Gebbie, H. A.; Slough, W. Trans. Faraday SOC. 1%7,63, 2605. (4) Chantry, C. W.; Gebbie, H. A. Nature (Lodon) 1966, 208, 378. (5) Hill, N. E. Proc. Phys. Soc. 1963,82,723. (6) Lorenu, H. A. The Theory of Electrom; Dourr: New York, 1915. (7) Van Vleck, J. H.; Wehkopf, V. F. Rev. Mod. Phys. 1945, 17. 227. (8) Cole, R. H. Annu. Rnr. Phys. Chem. 1989,40,1. (a) Edwards, D. M. F.; Madden, P. A. Mol. Phys. 1984, Sf, 1163. Edwards, D. M. F.; Meddcn, P. A.; McDonald, I. R. Mol. Phys. 1W, 51, 1141. Ses dro: Madden, P. A.; Kivelron, D. In Adwrvvs in Chemical Physics; Prigogim, I., Rice,S.A., Ed.;J. Wiley and Sons: New York, 1984; Vol. LVI,p 543. (b) Ouillaume, F.; Yanvood, J.; Price, A. H. Mol. Phys. IN?, 62, 1307. (9) Wolyncs, P. G. 1. Chem. Phys. 1!J87,86, 5133. (IO) U.S.Army Workshop on Capacitors for Pulw Power Application; Ashbury Park, NJ, Nov 17-19, 1987.
Q 1991 American Chemical Society
Firman et al.
7056 The Journal of Physical Chemistry, Vol. 95, No. 18, 1991
!
0.1 mm call wllh slllcon wlndowa.
slllcon wlndows.
madlum: CH,CN; 1=25*C
360 -
7
340
-
300
-
3
0.20
10
12
14
16
18
AtxNI'(cm)
20
22
+
24
26
-
20
30
32
34
Figure 2. Absorbance vs pathlength increments at 3 300 cm-I for acetonitrile at 25 O C . The variable path cell had K R S S windows.
Number of lnlarfaranca lrlnga
+
Number
Of
Inbrf*r*nc* f r l n v
--$
Figure 1. (A) Wavenumber vs interference fringe number for the
optical path length silicon standing wave pattern of an empty 0.1." window infrared cell. (B) Wavenumber vs interference fringe number for the standing wave pattern of a cell filled with CH,CN of 0.1-mm thickness and with silicon windows. perimental e* = C' - Je'' data at both microwave and infrared frequencies in liquids. Benzonitrile2and acetonitrile" were studied in the past in a limited frequency range. For acetonitrilecarbon tetrachloride mixtures infrared refractive indices at I 200 cm-I were reported.11We decided to start from these systems, seeking adequate data above 36 GHz for benzonitrile2 and above 18 GHz for aCetonitrile.'l Mixtures of acetonitrile and benzonitrile with carbon tetrachloride have also been investigated,since they also give clues to the self-association of the polar component of the mixture. For CH$N the self-association phenomenon has already been studied quantitatively by NMR techniques.12 Also data for refractive indices at P = 125 cm-1 for benzonitriltCC1, and at P Y 300 cm-'cf= 9000 GHz) and P H 400 cm-' cf = 12000 GHz) for all the systems are reported. Static dielectric permittivities eo and visible refractive indices nD for the two solvents and their mixtures with CCI, are also reported at 25 OC.
-
Experimentrl Section The refractive indices at infrared frequencies of -300 cm-I have been determined by scanning the frequency between 180 and -400 cm-' with a dispersive Perkin-Elmer 983 G spectrometer, computer assisted for digitizing and recording of transmittances. A 0.1-mm optical path length, silicon windowed, sealed, 1400 series cell (provided by Specac, U.K., and distributed by NSG Precision Cells Inc., Farmingdale, NY, who sealed the windows) was used. The refractive indices at -400 cm-'were determined by scanning the same instrument between 300 and 500 cm-'but using a sealed Perkin-Elmer cell (0.1-mm optical path) with KRSS windows. The sealed cells were thcrmostated at 25.0 OC by liquid circulating in a jacket holding the cell. The temperature was monitored by a thermistor attached to the sample cell jacket, and the thermostat was re lated by a proportional thermoregulator with a sensitivity of l o - R c . The frequency was scanned in a double-beam mode with the cell first empty and then filled with the liquid under study. A minimumof 15 min was required for the cell to acquire mechanical stability with temperature, even when empty. This was determined by scanning at various times and determining the empty cell thickness by the fringe method. Only after 15 min did the cell thickness remain constant.
-
(1 1) Arnold, K.E.;Yanuood, J.; Price,A. H.Mol. Phys. 1983,44451. (12) Boss, P.A. Maier; Popov, A. 1. J . Am. Chrm. Soe. 1985, 107,6168.
The fringe method was then used with the cell filled with the thermostated liquid under study after thermal equilibration. Fringes were digitized and recorded by the spectrometer and the apparent lengths of the cell empty, 4, and full, 4,were calculated by linear regression of 'peak" wave number vs peak number. Representative plots of the record 'peaks" for both the empty cell and the cell filled with acetonitrile are reported in Figure 1, parts A and B. The refractive index is the ratio (see Appendix, supplementary material)
n = C/Co (1) and is the average value at I I !300 cm-I for the 180-400-cm-1 range and at I H 400 cm-l for the 300-500Cm-1range. The peak at I H 378 cm-I is one of the resonance bands of acetonitrile or benzonitrile, and it has been, of course, avoided in the 'peak" counting by the fringe method. For the attenuation constant CY (Np cm-I), a variable path length cell (Janos, Townsend, VT) with a minimum fiduciary mark division of 5 pm and KRS5 windows has been used at I Y 300 cm-I. Some measurements were performed with a variable path cell (Specac, U.K.) with minimum fiduciary mark divisions of 5 pm and silicon windows. The absorbance A vs path length increment AI was recorded. Figure 2 reports one of the plots of A vs AC (with 0 marked as the beginning of the values read) for acetonitrile at 25 OC and 5 N 300 cm-' (f= 9000 GHz). We recall that A = log 1 / T = log Po/P (2) where T is the transmittance and Po and P are the power at distances 0 and 4,respectively. Further, because of the Lambert-Beer law I =Iopc with
p = pOe-2ac
(3)
12 = P, the squared intensity equal to the power, and CY = (2.30 103/ 2) ( A/ C) (4)
Therefore a plot of A vs C at the wavenumber I, as depicted in Figure 2, gives CY from the slope of the plot. The wavelength X is calculated from n = b/X,hence e' and e" can be calculated from the relations C' = (h/A)'[l - (cYA/~w)~] (5) c''
= (AO/X)'(CYA/T)
Here X,denotes the free space wavelength. Numerically, for the present systems at 3 H 300 cm-I, C' = n2 within experimental error since the term [ l - ( c r h / 2 ~ ) ~is] practically equal to 1. An alternate method used was to set the two windows of the variable path length cell so close together that fringes of interference resulted. This is because the refractive index of KRS5 (n H 2.38) and of silicon (n Y 3.4) are high compared to those of liquids (n H 1.5). Standing waves are created between the wave returning from the cell window far from the IR source and the incoming wave in the liquid (from the window close to the IR source). A damped wave is observed by changing the distance between the windows until no power returns from the
Infrared and Microwave Dielectric Relaxation of Nitriles receding window. However, the precision of the "peak" positions determined by this method is inferior to the precision obtained above with a fixed path length cell, scanning the frequency around the desired value (300 and 400 cm-I, respectively). A Bruker FTIR spectrometer (Model IFS88) was used for the far-IR measurements at I H 125 cm-I. The instrument as constructed requires many hours of prepurging of its atmosphere as recommended by the manufacturer. It also fails to hold against air leakage in any adequate way. We have found that purging times were reduced to 1 h by using a homemade purging system with air prechilled at -30 OC (passad through a chilled trap) followed by passage over molecular sieve columns before the compressor stage. Dried air compressed at -30 p i was again passed through columns (Cole-Parmer, holding up to 100 p i ) filled with Drierite and molecular sieves and filtered through a Balston 0.1-pm filter, before reaching the gears and the optical m i o n of the instrument. The spectrometer was encased in a homemade Lucite drybox with gloves, allowing cell manipulation for optical path length changes with no opening of the box. The same fringe method was employed in the wavenumber range 150-90 cm-' where benzonitrile has a wide transparent window. Absorbance vs distance measurements were made at P = 125 cm-'. Temperature was monitored as for the PE-983G instrument by measuring the temperature of a Jack-thermostat4 holder for the silicon-windowed variable path length cell (Specac, U.K.). The spectrometer with its computer graphics system provides either digital or graphic data for absorbance vs wavenumber, as desired. (We are indebted to MR. Paul Dalili of Bruker Inc., Bellarica, MA, for patient instructions on the instrumental details.) The UHF and microwave instrumentation for work up to 90 GHz has been described e1~ewhere.l~For pure acetonitrile, at f = 50 GHz, a traveling wave technique has been used to determine the attenuation constant OL (Np cm-'),13 whereas the power reflection method13has been used to determine X/2, where X is the wavelength in the liquid. Use of this hybrid method allows for increased precision at f = 50 GHz in the value of a for highly dielectrically glossy liquids. In this case, the reflection technique allows detection of only two to three interference peaks before the wave returning from the metal reflector is completely abs0rbed.l) From a and A the values of d and d' are calculated by use of eq 5 with the modification that for d
d = (xo/X)2(1
- (W2*)2) + ( x o / U 2
The Journal of Physical Chemistry, Vol. 95. No. 18, 1991 lo51
10
t w
5
0
ni
E' +
nR (300)
Figure 3. ColtCole plot of e" vs c' for benzonitrile at 25 O C . Solid line corresponds to the Debye function with e,, = 25.1, c, = 4.5, and/, = 4.5
GHz. 47B*nzonltril*, lr25'C
0.02
650
0.04
0.10
0.08
0.06
l(inch) -+
-
( I 3) Farkr. H.;Petrucci, S.The Chemical Physics of Solvation; Dogonadze, R.R.. et al., Eds.; Elsevier: Amsterdam, 1986; Vol. B, Chapter 8.
*
A
and -tn(-)
-tn(,-)
(6) where X, = 26 is the cutoff wavelength of the rectangular wave guide of large dimension 6. The refractive indices in the visible at the sodium line X = 589.3 nm, for acetonitrile, benzonitrile, and their mixtures with carbon tetrachloride at 25.0 OC, have been measured with an Abbe precision refractometer with calibration charts (Bellingham and Stanley Ltd., London, U.K., distributed by Ercona Corp., Patchogue, NY). Table I (supplementary material) reports the results of these measurements. Values of the static permittivity for acetonitrile, benzonitrile, and their mixtures with carbon tetrachloride have been determined at 25 OC and f = 1.1 MHz by using a resonator technique and a cell of capacity C,, = 0.566 pF for the pure solvents and a cell of capacity Co = 5.20 pF for the CCll mixtures rich in CCl,. Benzonitrile (Aldrich, Gold Label) was kept over molecular sieves (predried in vacuo at 110 "C) for 1 week and then distilled in vacuo in an all-Pyrex column with no grease on the joints. Acetonitrile (Aldrich, Gold Label) was purified in two ways. A portion was distilled Over Pz05. Another portion was kept over molecular sieves for 1 week and then distilled in the same column used for the benzonitrile except for the in vacuo conditions. The same results were obtained with the two distilled products. These results agreed with experimental results obtained in other laboratories, as shown below. Carbon tetrachloride (Aldrich, Gold Label) was distilled in a column similar to those used for the nitriles after exposure over molecular sieves or P205.
VI.
tho number 01 A14 lrom tho window lor C ~ H ~ C N f = BOQHz ( Y = 2.93 cm-')
t
t=25'C
l
A 1
l
2
I
I
I
3
4
5
I
N+
Attenuation At (dB) vs distance C (in.) of the reflector from the window separating liquid from air for benzonitrile at the frequencyf= 88 GHz and 25 OC. (9)Linear plot of the indicated functions vs number of maxima and minima from the window giving ah/2 from Figure 4. (A)
the slope.
The mixtures were prepared by weight on an analytical balance ( 104-g sensitivity) in volumetric flasks. Exposure to the atmo-
sphere was limited during preparation of mixtures and filling the cells to 20-30 s overall. Reclults and Discussion (a) Pure Liquids. Figure 3 reports the ColtCole plot of P vs c' for benzonitrile at 25 OC. Previous literature dataZat 21 1 OC and frequencies up to 36 GHz were interpreted by a single
Firman et al.
7058 The Journal of Physical Chemistry, Vol. 95, No. 18, 1991 ((Tnl)
0.03
I
I
0.09
0.30
3.0
0.90
30
9.0
300
I
Acrtonitr; a=(2.303/2)(AIl)
I
l
l
,
,
5
10
20
50
100
I
m
I
l
l
5001Ooozooo
I
woo
I
loo00
1
D(cm.')+
t t
Figure 6. Microwave d and squared refractive index I# at far-infrared and visible (D doublet) frequencies vs wavenumber I for C&CN at 25.0 O C . The dashed line has no theoretical significance.
701
c -
40
10
c
II t1
I
I
350
400
320
G mi'\ Figwe 5. (A) Digitized absorption coefficient a (cm-I) for benzonitrile at wavenumb encompascing the band C entered at I = 378 cm-l. Cell thickness C = 0.0212 cm. (e) Digitized absorption coefficient a (cm-I) for acetonitrile at wavenumbers encompassing the band centered at 3 = 378 cm-l. Cell thickness = 0.0210 cm.
Debye relaxation function with eo = 25.6,f, = 4.2 GHz, and c, = 3.85. The present data extend to 88 GHz. The power reflected from a metal reflector vs distance from the mica window separating liquid and air is depicted in Figure 4A as attenuation (dB) vs distance I (in.), The position of the maxima and minima after ordinate correction for deviations from the crystal linear square law gives the voltage reflection coefficient l' = I" exp(0.11512(At - At,)) where At, is the asymptotic value of the attenuation and (1 - X/&)2 + (aX/21)2 r-2 = (7) (1 + (aA/2~)~ r, is obtained by successive approximation^.'^ Figure 4B reports the quantities -In [(I" - r,)/(l - rr,)] vs odd N values and -In [(I'. F)/(l IT,)] vs even N values for the maxima and minima, respectively, giving aX/2 from the slope of the solid line, which was calculated by linear regression. The above details are reported to document the reliability of e' and e" atf = 88 GHz. The solid line in Figure 3 is the fit according to a single Debye function with parameters to = 25.l,f, = 4.5 GHz, and e, = 4.5 in fair accord with literature parameters2at 21 f 1 OC. The data above/= 13.8 GHz diverge from the Debye fit in a tail probably reflecting librational processes at higher resonant frequencies. Additional reflecting the decay of the atomic polarization and of resonant character indeed exist at frequencies above the microwave region. A maximum in the attenuation constant a was observed4at I = 55 cm-I (f= 1650 GHz) for benzonitrile. Our data also show evidence of an additional resonant process at D H
+
*
378 cm-' for benzonitrile. Figure SA reports the value of the digitized attenuation constant a (cm-') for a cell of thickness C = 0.0212 cm according to eq 4 for benzonitrile at wavenumbers encompassing the band centered at I H 378 cm-'. Notice that (see Table I (supplementary material)) the refractive index of benzonitrile at I H 300 cm-l is nMo = 1.609 at 25 OC, a figure somewhat higher than the value obtained at B 400 cm-I, nm = 1.579 at 25 O C , and closer to the value of the refractive index in the visible at the D doublet of sodium, IID = 1.525, at 25 OC. This would seem to imply that the above band, also common to acetonitrile, may be related to a distortion of the C+N group common to both benzonitrile and acetonitrile. Figure 5B reports the attenuation coefficient a around I N 378 cm-I for acetonitrile. From Table I it is evident that the value of nm = 1.414 at I N 300 cm-l is higher than the value nm = 1.348 at B N 400 cm-l, which is close to nD = 1.3415 at 25 OC. Experimental evidence of a decrease of the refractive index from microwave frequencies through far-IR frequencies up to the visible is shown in Figure 6. Here the quantity e' for microwave frequencies up to 90 GHz and the quantity n2 c' for far-IR wavenumbers of 125,300, and 400 cm-' (3.75,9.00, and 12.0 THz where 1 THz = 10l2 Hz) are reported vs both wavenumber B (cm-I) and frequency f (THz) for benzonitrile at 25 O C . It is evident that there is a decay of n2 tending to level off at visible frequencies. A theoretical explanation based on rigid molecules for the differences between e, and nlR2 above each resonant relaxation has been offered by HiLs Poley2had noticed that the difference e, - nR2 was proportional to p2, the squared dipole moment of the molecule in the gas phase, for several benzene-substituted (C6Hs-X) liquids. HillSderived an expression based on a librational resonant relaxation with molecules partially rotating over small energy barriers between shallow traps. Use of the Hill expression
-
(f,
- n1R2)/(eo - nlR2) = kT/(1/2)Zw2
(8)
gave I = w/2uc = 23 cm-l, which is a factor of -2 smaller than the value B = 55 cm-l reported for benzonitrile by Gebbie et al.' In the above, I denotes the moment of inertia and w is the angular velocity. The above is recalled to indicate that according to Hill's theory the value of e, = 3.85 at 21 OC had to be retained from the Debye theory, and the value" of nIR2= 2.34, at 70 cm-I a h the librational relaxation process, had to be used in order to calculate the frequency of the latter process, to be distinguished for rigid molecules from the fully rotational one of Debye nature. Later theories, reviewed by Madden and Kivelson,8' based on libration and dipole-induced relaxation have been proposed. These theories give an overly sharp resonant-relaxation profile to the (14) Cartwright, C.
H.;Errera, J. Proc. R.Soc. 1936, Af54, 138.
Infrared and Microwave Dielectric Relaxation of Nitriles
The Journal of Physical Chemistry, Vol. 95, No. 18, 1991 7059 Acetonitrile,t=25OC
-
Debye fuflctlofl
30
t
.I
o
Barthel et al
.This
work
-w 20
Figure 7. ColtCole plot of c“ vs e’ for acetonitrileat 25 OC. Solid line corresponds to the Debye function with eo = 35.8, e, = 5, andf, = 45 GHz. 5.0
decay of nlR and to the profile of the attenuation coefficient a with wavenumber P for liquid CHC13 at 296 K. The authors? in their review article, concluded that the deficiencies of presently available theories of molecular reorientation in dense liquids arise from an inability to describe the dynamics of intermolecular torques and not from inadequate descriptions of inertial motion. Now let us consider the results for acetonitrile for comparison with those of benzonitrile. Figure 7 reports the Cole-Cole plot of P vs d for acetonitrile at 25 OC. The data up to f = 80.5 GHz (from f = 0.38 GHz) can be described well by a single Debye relaxation function with parameters Q = 35.8, t, = 5.0, andf, = 45 GHz. Parts A and B of Figure 8 show the coefficients t’ and t”, respectively, vs the frequencyf with the calculated values according to the Debye function expressed by a solid line. Notice that any objection based on the reliability of the data presented here for benzonitrile and acetonitrile is unfounded. We have close agreement with the data of PoleyZin benzonitrile at 21 f 1 OC and agreement within experimental mor with the data by BarthelI5 for acetonitrile, indicated on Figure 8A,B from 2.50 to 39.0 GHz. These datal5 are of excellent internal precision and were obtained by traveling wave interferometry, in contrast with our data, which were obtained by standing wave reflectometry with the exception of the data at f = 51.7 GHz. As for benzonitrile, other processes of resonant nature exist for acetonitrile at frequencies above the microwave region. Arnold et al.” reported the existence of an absorption band centered at -97 cm-I (2910 GHz). We have noticed a band at 378 cm-’ (1 1 340 GHz). The value of nIRz= 1.82 reported below for P = 400 cm-I clearly encompasses the 97-cm-’ band and the one at 378 cm-’. On the other hand, nZ5D = 1.3415 acetonitrile. Hence, (nZ5D)’ = 1.80. This implies that the permittivity of acetonitrile at B = 400 cm-I is only 1% higher than the visible value at 589.3 nm (P = 16969 cm-I), where presumably the atomic polarization has already decayed. It is unfortunate that the existence of a broad resonant band centered at 97 cm-’ negates the applicability of the methods described above for the determination of the complex permittivity t* = e’ - Jt” for acetonitrile at wavenumbers much below 300 cm-I. However, both refractive index and attenuation coefficient data for acetonitrile obtained by FTR techniques in the wavenumber range 20-1 50 cm-’ at 20 f 1 OC have been reported.16 (b) Mixtuns with CCl,. The motivation of the present work in terms of investigating both CH3CN and C6H5CNmixed with CCI, has been stressed in the Introduction. In the present and following sections the results for the mixtures are presented and discussed. Figure 9A (supplementary material) reports the squared refractive index at D Y 300 cm-’ and P Y 400 cm-’ vs the concentration of C6H5CNC (mol/dm3) for the mixtures C6HSCNCCI4 investigated at 25 OC. Table I (supplementary material) reports the refractive indices P Y 125 cm-’, P Y 300 cm-’, and P Y 400 cm-’ and at A = 589.3 nm for benzonitrile-carbon
1 10 20 0.5
f(GHz)
500
200
2000 10 1000 5000
+ Acetonitrile, t=25’C Debye function
18
pt f(GHz)
o
Barthel et al
.This
work
+
Figure 8. (A) c‘ vs f for acetonitrile at 25 OC. (B)8’vsffor acetonitrile at 25
OC.
tetrachloride mixtures at 25 OC. The data can be represented by the linear regression nlR2 =
2.21
+ 6.65 X lO-’CQHgN; 9 = 0.84 at P = 125 cm-I
nIR2
= 2.382
+ 2.34 x 10-’CCflICN; 9 = 0.93 at P = 300 cm-*
nlRZ
2.379 + 1-31’ X ~O-’CQH,CN;
9 = 0.80 at P = 400 cm-’ nD2 =
2.127
+ 2.151 x 1o-’CCfl6CN; 9 = 0.99 at P = 16 969 cm-I
with 9 the determination coefficient. Figure 10A (supplementary material) displays the values of the attenuation coefficient a (cm-I) vs the concentration of benzonitrile (expressed in mol/dm3) at P H 300 cm-’ (f=9O00 GHz) and at P Y 400 cm-’ (f = 12 000 GHz) at 25 OC. Table I (supplementary material) reports the same data together with further data at P = 125 cm-I. From the values of a and the interpolated values of n, the values of the wavelength A have been calculated. Then the values of c’ and 6’’ at B = 125 cm-I, B N 300 cm-I, and B = 400 cm-’ have been calculated and reported in Table I. Table I reports also the values of the refractive indices at the sodium line (A = 589.3 nm, P = 16 969 cm-I) for the benzonitrildC1, mixtures at 25 OC. Figure 9A reports the refractive index nD of the above mixtures CC&CN.
(IS) hrthel, J.; Bachhukr, K.; Buchner. R.;Gill, J. B.;Kleebauer, M. Chem. Phys. Lett. 1990, 167,62. (16) Birch, J. R.; Ping, K. F.; Humin, S. K.; Yarwood, J.; Catlow, B. Chem. Phy& Lett. 1985, 117, 197.
100
50
5
Figure 9B (supplementary material) reports the squared refractive index at P Y 300 cm-’ and P = 400 cm-’for the mixtures CH3CN-CC14 investigated at 25 OC vs the concentration of CH3CN (mol/dm3). Table I reports the refractive index at D Y 300 cm-I and at P Y 400 cm-’ for acetonitrile and acetonitrile-
7060 The Journal of Physical Chemistry, Vol. 95, No. 18, 1991
Firman et al. C&CN-CC14
I? I
C=8.50M
A ~~toraturm data 0 Exporimontal data
0
S W
0.1 0.2
+51
5-
2
5
20
t
-
if
10 20 50 100200 500 f( GHz) +
C(moI/dm')-b
,
qwM =0.SS8
t Io'W
0.5 1
mixturmm at 21%
-
Stallc pormittlvity va. molar comontratlon lor CH/N-CC14 M X ~ Wat O26% O
C=8.55M
Dobye
i 5
4
30 t
-
Extrapdalad lrom mlcrow8vo data
A ~ ~ t o r a t udata o 0 Exporlnmntai data
3
2 'w
0.1 0.2
0.5 1
2
5
10 20
50 100200 500
t(GHz) +
Figure 11. (A) Plot of t' and of t'' vs f for the C6H,CN-cCII mixtures of composition X w = 0.866 (C = 8.50 mol dm-9 at 25 OC. The solid line is the Debye Gction with the parameters reported in Table I1 (supplementary material). (B) Plot of e' and oft" vsffor the CH,CNCCI, mixture of composition XCH = 0.598 (C = 8.55 mol dm-') at 25 OC. The solid line is the Debye Kction with the parameters reported in Table I1 (supplementary material).
carbon tetrachloride mixtures at 25 "C. The data can be represented by the linear regressions nIR2
2.296 - 0.017CCH3CNat I = 300 ; '"I
9 = 0.93
n~~ = 2-12, - 1.741 X 10-2C~~3CN at = 16969 cm-l;
r2 = 0.998 with 9 the determination coefficient. In the same figure for CH3CN the value of ID^ = 1 .BO is reported, as well as the data for the CH3CN-CCI4mixture. By retaining the figure" nlRZ= 2.49 at B 200 cm-I at face value for pure acetonitrile, it follows that starting from c, = 5 (extrapolated from the microwave data ending at I = 2.7 cm-',f= 81 GHz), the value of nlR2has dropped to 2.49 at I N 200 cm-I and to 1.82 at B N 400 cm-I, quite close to the solid line value of no2 = 1 -80. Hence at 3 = 400 cm-I the atomic polarization of acetonitrile has already decayed. Figure 109 (supplementarymaterial) reports the values of the attenuation (expressed coefficient CY vs the concentration of acetonitrile CCHFN in mol/dm3) at I = 300 cm-I (f = 9OOO GHz) and I H 400 cm-' (f= 12000 GHz) at 25 "C (Table I). From the values of a and n (Table I), the values of c' and c" at v N 300 cm-I and I N 400 cm-' for pure acetonitrile is affected by the resonant band at I = 378 cm-I. It is therefore not reported. Table 1 reports the value of the refractive indices at the sodium line (A = 589.3 nm, D = 16969 cm-') for the acetonitrile-CC1,
C(mOi/dm')+
M p e 12. (A) Experimental e,, values and q, values extrapolated from
microwave spectra for C ~ H J C N ~ CatI ,the compositions investigated at 25 OC. (B) Experimental q, values and co values extrapolated from microwave spectra for CH3CNCC14at the compositions investigated at 25 O C .
mixtures at 25 "C. These nD data are reported in Figure 9B vs CCH,C~. Figure 11A reports the representative plots of 'E and C" vs the frequencyfof one of the C6HSCN-CC1, mixtures investigated by dielectric spectrometry at 25 "C. A single Debye relaxation function is adequate to represent the data of the C6HSCN-CC14mixtures. Figure 11B presents representative plots of c' and E'' vs the frequencyfand of e'' vs c' for one of the CH$N-CCI, mixtures investigated by dielectric spectrometry at 25 "C. The concentrations of benzonitrile or of acetonitrile in the mixtures range from the diluted range to the more concentrated range up to X C ~ H ~=C0.87 N and XCH,CN = 0.60. It may be seen that as far as the dielectric data are concerned a single Debye relaxation function is capable of describing the data within experimental error. Table I1 (supplementary material) reports the parameters obtained by the Debye fit of the dielectric microwave data. To check on the reliability of the extrapolated Q values obtained from microwave data by the Debye function, measurements of the static permittivity a t f = 1 .I MHz for benzonitrile, acetonitrile, and their mixtures with CCI, at 25 OC have been made by the dielectric resonator technique. Parts A and B of Figure 12 report the experimental data for to together with the extrapolated values from microwave frequencies at the compositions investigated at 25 "C. Table I reports
The Journal of Physical Chemistry, Vol. 95, NO.18, 1991 7061
Infrared and Microwave Dielectric Relaxation of Nitriles
Figure 13A reports the Bbttcher plot of #(e) vs C for benzonitrile dissolved in CC14 up to C = 1.50 mol/dm3. The solid straight line has been calculated by linear regression giving 50% statistical weight to zero intercept. The calculation gives 9 = 0.999 and a slope of 1.431 from which the apparent dipole moment p = 4.g3 X 1W18esu cm has been calculated. This figure is in fair accord with the value of p = 4.1 X lo-'* esu cm from the gas phase.2 Figure 13B reports the Bijttcher plot of #(e) vs C for acetonitrile dissolved in CC14 up to C = 10.5 mol/dm3. A clear curvature of the plot suggests that some of the polar solutels exists in an apolar form. Application of the dimerization equilibrium18
C,H,CN h CCC, t
= 25.0.C
2CH3CN s (CH3CN)Z
(1 1)
2M s D
r
C ~ in C N C!, I-25'C, Kd4.35
tI
1
i
0.4 0.3 0.5
0.1 -
0.2
W
0.0
I
I
I
I
I
0.1
0.2
0.3
0.4
0.5
I
C:,,Jmol/dd-
Fipn 13. (A)Bbttcher plot of d(e) = (eo - 4 ( 2 % + 1)/3% ~8 the total concentration of knzonitrile for the C6H,CNCC14mixtures of concentration CGH N I 1.5 M at 25 'C. (B)Bdttcher plot of c$(c) = (eo - c.) (2% 1)/$~vs the total concentration of acetonitrile CCH,CNo and vs the concentration ( M ) of undimerized acetonitrile (with a dimerization
+
constant Kd = 0.35) for CH3CNCC14mixtures at 25 OC. The arrows indicate the coordinates of the adjacent line in each case. The scale for the two abscissas is the same.
the numerical values of the measured eo values for benzonitrile and acetonitrile mixtures. (e) C&CN md CH,CN at Low Concentration in CCI,. A Dielectric Study of the Dimerization of CH3CN. The BBttcher quation'' correlates the concentration C of a dipolar species of apparent dipole moment p to the relaxation strength Ae = eo e, for that species eo
- em = 4
r x ~ 10-3 -p2 3e0 3kT 260 1C (1 -
+
(9)
where L is Avogadro's number, a! is the polarizability, and f is the reaction field factor. The above expression can be rewritten, neglecting the polarizability a!, and neglecting the reaction field factor f term [( 1 - (m2Y 0.91 with respect to unity, as
(17) BMtcher, C . J . F. Theory o/Dielecirlc Polarhiion; Elsevier: Amsterdam, 1973.
with the dimerization constant Kd = [D]/[MIz and the conservation equation Co= [MI + 2[D] with C, the total concentration of CH3CN, leads to the relation [MI = (-1 + (1 + 8KdC0)'/*)/4Kd. Figure 13B presents the function #(e) vs [MI, using the minimum value of Kd that linearizes the plot, namely, & = 0.35. This figure is valid only as an order of magnitude given the relative insensitivity of the linearization of the plot. It is significant, however, that Kd = 0.35 is within the range of the standard error of the value Kd = 0.56 f 0.27 obtained by PopovL2 by NMR techniques for the dimerization of CH3CN in CCI,. Equation 10 has been used successfully in a comparable concentration range for rather strongly interactive systems such as dipolar ion pairs in ~olution.'~*'~ The correspondence with Kd obtained by NMR techniquesI2lends credence to the interpretation of the curvature of Figure 13B as arising from dimerization of acetonitrile. The present approach based on the NMR evidence of the dimerization of acetonitrile is an alternative to the use of the Kirkwood aggregation parameter' g expressing phenomenologically a similar concept.
Conclusion The observed dielectric relaxation at 25 OC and at microwave frequencies for pure benzonitrile V; = 4.5 GHz, Td = ( 2 4 ) - ' = 35 ps] and pure acetonitrile V; = 45 GHz, 7d = (2rj3-l = 3.5 ps] can be described by a single Debye relaxation function up to 13.8 and 80.5 GHz, respectively, by use of a parameter em (e, = 4.5 for benzonitrile and e, = 5 for acetonitrile) that is larger than the squared refractive index nD2 in the visible at the sodium D doublet. For benzonitrile values of the infrared nIR2at 3 = 125, 300, and 400 cm-1 are reported, giving a qualitative indication of the decay profile of the atomic polarization with wavenumber 1. For acetonitrile only data at P = 300 cm-' and 3 = 400 cm-' are reported. In addition to the reported resonant processes at 55 cm-I for benzonitrile' and at P = 97 cm-', a common resonant process at P = 378 cm-I for both liquids has been recorded. Data for e, and e, for the benzonitrile-CC14 mixtures give a reasonable value of the apparent dipole movement of C6H5CN. The corresponding data for acetonitrilecarbon tetrachloride reveal acetonitrile to be associated, giving a dimerization constant comparable to literature values" obtained by NMR techniques. Acknowledgment. We acknowledge support from the Army Research Office, Durham, NC, through Grant DAAL03-89-K0148. Supplementary Material Available: Tables of IR refractive indices, attenuation coefficients, and dielectric coefficients for CH3CN-CCl, and C6HSCN
