Eiji lkada and 'Teizo Watanabe
1078
a1 in the place of the molecule. The g factor is the best indicator of which &ucture is present. The two values found are near 2,0048 (see Table I) and match those of HNjC02- (2.00425) and the other amido radicals (2.0044-2.0053)22 much more closely than the value of 2.00325 for I-fC(0- p N . * The amido form seems more likely, therefore. The identification, as given, implies that the pK of thci, NW proton in the ester form is several units lower than in HNCOZ-. Conclusio1n Study of the radicals present under conditions of OH attack on cyanate has allowed identification of the initial product as 1 be adduct HNC02- . A secondary radical -02CNHNC02- is, ascribed to H abstraction from the dimer of the primary radical. The primary reaction is similar to that observed with CN- and HCN in that reaction at the carbon occurs. It seems unlikely that reaction of OW with thiocyanate follows a similar path as conversion of the intermediate NCSOH- to (SCN)2- would then be difficult. No radicals resulting from q,q- reaction with cyanate were found. efcrences airad Notes (1) Supported in part by the U.S. Atomic Energy Commission (2) D. Behar,J. Phys. Chem.. 76, 2517 (1972).
(3) D. Behar, P. L. T. Bevan, and G . Scholes. J. Phys. Chem., 76, 1537 (1972). (4) D. Behar and R. W. Fessenden,J. Phys. Chern., 36,3945 (1972). (5) I. S. Ginns and M. C. R. Symons, J. Chem. Soc.. Daiton Trans.. 185 (1972). (6) I. S . Ginns and M. C. R . Syrnons, J. Chern. SOC..Dalton Trans.. 3 (1973). (7) D. Behar and R. W. Fessenden, J. Phys. Chem.. 76, 1706 (1972). (8) F. Owens, R . A . Breslow, and 0.R. Gillian, J. Chem. Phys., 54, 833 (1971). (9) W. C. Easley and W. Weltner, J. Chem. Phys., 52, 197 (1970). (10) W. S ,Metcalf, J. Chem. Soc., 148 (1942). (11) K. Eiben and R . W. Fessenden. J. Phys. Chem., 75, '1186 (1971) (12) D. Beharand R. W. Fessenden, J. Phys. Chem.! 36, 1710 (1972). (13) The OH proton splitting assigned to HC(OH)=N is 0.89 6.4 (14) N. V. Sidgwick, "The Chemical Elements and Their Compounds," Vol. I, Oxford, 1950, p 673. (15) H. Zeldes and R. Livingston, J. Amer. Chern. Soc.. 90, 4540 (1988). (16) P. Neta, private communication. (17) M . Anbar and E. J. Hart, as reported by M . Anbar and P. Neta, Int. J. Appl. Radiaf. Isofopes. 18, 493 (1967). (18) R . W. Fessenden and P.Neta, J. Phys. Chem.. 76, 2857 (1972). (19) R. Livingston and H. Zeldes, J. Chem. Phys.. 47, 4173 (1967). (20) E. L. Cochran, F. J. Adrian, and V . A. Bowers, J. Chem. Phys.. 51, 2759 (1969). (21) For instance, the value of a N for (CI.13)2h in aqueous solution is 15.65 G." (In nonpolar solvents the value is slightly higher, W. 6. Danen and T. 1.Kensler, J. Amer. Chem. Soc.. 92,5235 (1970)). (22) W. C. Danen and R. W. Gellert. J. Arner. Chern. SOC.. 94, 6853 (1972). (23) R. Fantechi and G. A. Welcke. J. Chem. Soc.. Faraday Trans. 2. 68,942 (1972). (24) D. E. Wood, C. A. Wood, and W. A , Lathan, J. Amer. Chem. Soc.. 94, 9278 (1972). (25) V . Malatesta and K. V. Ingold, J. Amef. Chem. S o c . 95, 6110 (1973).
New Asynimelric Dielectric Relaxations in Two Liquid Triacetates Eiji lkada" and Teizo Watanabe Faculty of Engineering, Kobe University, Nada. Kobe, 657. Japan (Received Augusf 7, 7973)
The dielectric properties of liquid glyceryltriacetate and 1,2,6-hexanetriacetatewere studied. The dielectric constants and losses were measured over the frequency range from 23 Hz to 3 MHz and at temperatures from -60 to 60". The measured values of the static dielectric constants of the two triacetates were between 6 and 10 a t the experimental temperatures and are much smaller than those of the corresponding hydroxyl-substituted compounds. The two triacetates showed asymmetric dielectric relaxations a t low temperatures, The loci of the Cole-Cole plots did not fit those of the Davidson-Cole-type relaxations, - ~was ~]fl. but could be expressed by the Havriliak-Negami equation E* - E , = (€0 - c m ) / [ l + ( j u ~ ~ ) ~ It fourtd that the values of the distribution parameters (1 - a ) and /3 for glyceryltriacetate, 1,2,6-hexanetriacetate, and poly(viny1 acetate) were approximately equal. It was concluded that the asymmetric dielectric relaxations were apt to appear in chain molecules containing multiple polar groups. The relaxation mechanism of these triacetates was discussed in contrast with those of the polyhydroxyl compounds, which showed the Davidson-Cole-type relaxations.
Introduction It is well known that liquid or supercooled polyhydroxyl compounds such diols and triols exhibit DavidsonCole-type asymnretiric dielectric r e l a x a t i o n ~ l -which ~ can be expressed by the chquations 60 - e c * - &l = (1) (1 P T " Y where E* is the complex dielectric constant, € 0 and E , are
+
The Journal of P h i c k a i Chemistry. Voi. 78. No. 1 1 . 1974
the limiting low- and high-frequency dielectric constant, respectively, j is the imaginary unit, w is the angular frequency, T O is the mean relaxation time, and (3 is the distribution parameter of the relaxation times. On the other hand, the Cole-Cole plots of the principal relaxations of polar polymers in the glass-rubber transition region (so-called " a relaxation") generally show another asymmetric curve4s5 which is in most cases flatter than those for the polyhydroxyl compounds.
Asyrnrnetric Dielectric Relaxations in Two Liquid Triacetates
1099
TABLE I: Physical Constants of the TWQ Triacetates Temp, "C
30.0 10.0 20.0 30.0
1,2,6-Hexanetriacetate 1.1045 1.0958 I.0861
20.0 L 4 -
40
35
45
50 55 60 65 70 Dielectric Constant, E'
75
80
85
90
Cole-Cole plot for PVAc. €'and e'' of this plot were measured by Ishida, el a/. (Y. Ishida, M. Matsuo, and K. Yamai u j i , Kolioid-Z. 2. Pdym., 180, 108 (1961).): 0,experimental points; @, calcuiated points obtained by using the HavriliakNegarni equation. (1 a ) and 6 were determined by the method described in Appei-~dix. Numbers beside data points denote frequency in H2 Figure 1.
I -
Havriliak an.d Negami4 suggested a new empirical equation to fit asymmetric cy relaxations showing this wider distribution of irelaxation times
where each parameter has the same physical meaning as described above, and (1 - a ) is another distribution parameter of the relaxation times. Apparently this equation is comprised of both the Cole-Cole6 and the DavidsonCole equations. Therefore, for (1 - a ) = 1, the HavriliakNegami equation corresponds to the Davidson-Cole equation, and the Davide,on-Cole-type relaxation may be considered as a limiting case of the Havriliak-Negami-type relaxation As most Elavidson-Cole-type relaxations have been generally observed for polyhydroxyl compounds, it was a t first concluded that such relaxations were characteristic for polyhydroxyl compourds which formed molecular clusters uia intermolecular hydrogen bonds. The same type of relaxation was, however, also observed in non-hydrogenbonded liquids such as isoalkyl halides7,8 and alkanethiols,g therefore, this, conclusion was partly denied. On the other hand, a relaxations of poly(viny1 acetate) (PVAc) have been studied by many workerslOJ1 and it has been reported that the Cole-Cole loci of PVAc closely resembled those of the Davidson-Cole-type asymmetric relaxation seen in Figure 1. The apparent similarity in the shape of Cole-Cole curves for the polyhydroxyl compounds and for PVAc is very interesting to us. The purpose of this work is to study the relationship between the two asymmetric relaxations, i.e., the Davidson-Cole and the Havriliak-Negami-type relaxations. The two triacetates were selected as low-molecular weight model compounds of PVbc, and the dielectric properties of these two triacetates were compared with those of the polyhydroxyl compounds which showed Davidson-Coletype relaxation. ~
E x ~ ~ ~Section i ~ e n ~ ~ ~ Materials. 1.,2,6-Hexanetriol (1 mol) was acetylated with 1..5 mol of acetic anhydride and 4.5 mol of pyridine a t 100" for 3 hr. The product was distilled twice under reduced pressure t~ reiiiove pyridine and acetic anhydride. Residual unreacted hydroxyl groups were checked by infrared absorption of the OH stretching vibration and it was found that the quantity of the residual hydroxyl groups was negligibly small. Commercial glyceryltriacetate of the specified grade was used without purification. Density and refractive index were determined by the Lyp-
Refractive indices, nD
Glyeeryltriacetate 1.1698 1.1597 1.1489
10.0
3Q
Densities, g/ml
1.431.3
I.4272 1.4339 1.4352
kin-type pycnometer and by the Pulfrich refractometer, respectively. The physical constants of the two triacetates are collected in Table I. Dielectric Measurement. Dielectric constants and losses were measured by a ratio arm transformer bridge (Ando Electric Go., type TR-1BK) over the frequency range from 23 Hz to 3 MHz. The dielectric cell was a concentric platinum glass cell having a geometrical capacity of 13.0 pF. Temperature measurement of the cell was determined using a Au-Co us. Cu thermocouple and a standard thermometer. The glass cell was immersed in a well-stirred alcohol bath at the lower temperatures and in a water bath at the higher temperatures.
Results and Discussion Static Dielectric Constant. Temperature dependences as expressed by plots of the static dielectric constants against the reciprocal of absolute temperature are well represented by straight lines as shown in Figure 2. The values of the static dielectric constants of both triacetates vary between 6 and 10 in the experimental temperature range. These values are much smaller than those of glyeeroll and 1,2,6-he~anetriol,~ which are equal to ca. 60, because the substitution of the hydroxyl groups in the triols by the acetoxyl group leads to the absence of formation of molecular clusters by intermolecular hydrogen bonding OH. .O. The dipole moments of glyceryltriacetate and 1,2,6-hexanetriacetate were calculated from the static dielectric constants by means of the Onsager equation12
-
(3) where to and t , are the limiting low- and high-frequency dielectric constants, respectively, NO is the number of molecules per cubic centimeter, fro is the dipole moment in vacuo, and hT is the thermal energy. The calculated values of the dipole moment vary from 2.44 do 2.57 D as the temperature increases from -60 to -7.4" for 1,2,6hexanetriacetate and from 2.33 to 2.49 D as the temperature increases from -58.1 to 40" for glyceryltriacetate. Dielectric Relaxation. Both 1,2,6-hexanetriacetate and glyceryltriacetate showed dielectric dispersion and absorption over the experimental frequency and temperature ranges. The plots of frequency dependence of dielectric loss for the two triacetates are broad and asymmetric as often seen in the curves for the diol and the hriol, but the shapes of the curves do not change markedly at different measuring temperatures. The Cole-Cole plots of 1,2,6hexanetriacetate and glyceryltriacetate are shown in Figures 3 and 4, respectively. Apparently, these arcs closely resemble those expressed by the Bavidson-Cole equation, but do not coincide with the arc calculated according to this equation, as is shown in Figure 5 . Tlavidson and Cole The Journal of Physical Chemistry. Voi. 78. No 1 I . 1974
Eiji Ikadn. and "rei20 Watanabe
Dielectric Constant, d'
Comparison of the calculated locus of t h e [>avidsonCole-type relaxation with t h e experimental locus: 0 ,experimental points at each experimental frequency. Dotted line shows the calculated locus of the Davidson-Cole-type relaxation The distribution parameter of the calculated locus IS 0 422 Figure 5.
3.0
-.--+'
'
" 4.0 ' .
"
45 '
.
*
' 5.0
.i,IO3
T
Figure 2. Temperature dependence of the static dielectric stants: 0 , glyceryltriacetate; @, 1,2,6-hexanetriacetate.
con1
f-------.-
Dielectric Constant, C'
Typical Cola-Cole plot for 1 ,Z,Fj-hexanetriacetate: 0 , experimental pcints; Figure 3.
Frequency, Hr
Figure 6. Log
tan [p-' tan-'
t"/(ti
- e r n ) ] vs. log frequency,
Dielectric Constant. E'
. Typical Cole-Cole plot for glyceryltriacetate. In this figure agreement between the calculated points and the experimental poinis is so good as to render them indistinguishable. The calculated ~iointswere therefore omitted from this figurs. reported that the plot of log tanl0-l tan-llt"/(c' - e m ) ] ] against log frequency gives a straight line having a slope of 112 rf the observed u c fits the Davidson-Cole-type relaxati0n.l This rriethod was applied for the observed arcs of these triacetates arid various values for t, and were tried. No plot, however, gave a straight line. Typical plots are shown in Figure 6. It can be concluded from this result that the asyrmietric dielectric relaxations of the triacetates cannot oe represented by the Davidson-Cole equation although the shapes of the Cole-Cole arcs closely resemble those of the Davidson-Cole-type relaxation. The new empirical equation suggested by Havriliak and Negamt to describe the asymmetric dielectric relaxation was examined to ascert,iin its applicability for these experimental loci. Iltada and Watanabe reported that the asymmetric a relaxations of the various kinds of acrylonitrilebutadiene copolymers could be well represented by the ~ a ~ r i ~ i e ta~ u~a t i-o n~. ~ e ~ ~ ~ ~ The real zinc: imaginary parts of eq 2 are given by E' -t =- (to - e=)r-d ' COS ptI (4a) c''
==
(eo --
6,Jr-j
' sin
pO
The Journal of Physical Ck?misrry. Voi. 78. No. 7 1 . 7974
(4b)
Determination of the five numerical constants (1 - a ) , 60: e m , @,and 7 0 was carried out by the same method described in Appendix. The calculated 6 ' and e ' ' at each measuring frequency f were obtained by introducing the five numerical constants and o ( = 2n-f) into eq 4a-d. The experimental values of EO, e,, (1 - a ) , %, are collected in Table 11. Coniparison of the calculated values for 1,2,6hexanetriacetate at -50.7" with the experimental points is shown in Figure 3. The experimental points for glyceryltriacetate a t -53.7" agreed almost completely with the calculated values. Other experimental arcs for both triacetates a t different temperatures also agreed well with calculated arcs. The Havriliak-Negami eqwt,ion is therefore considered to be a good representation of the dielectric relaxation of these t,wo triacetates. Although most of the dielectric relaxations of the polar !OW molecules have been treated by the Debye,13 the C~l.e--Cole,~ and the Davidson-Cole equations, some exceptional relaxations could not be expressed by the above three equations. Recently, the dielectric relaxations of c ~ , ~ - d ~ b r o ~ such o a ~as~ ~ ~ e s l,.l-dibromobutane, 1.,6-dibrornohexane, 1,8-dibromooctane, and 1,lO-dibromodecane were studied by Garg and coworker^.^^ The shapes of their experimental Cole-Cole arcs also resemble those of the Davidson-Cole-type relaxation, but the observed arcs deviate from the arcs calcu-
Asymmetric Dieiectric Relaxations in Two Liquid Triacetates 11: R
ion Parameters o f Two
ates a
-58.1 -53.7 -49.5 -43.5 -39.1
-6Q.5 -55.4 -50.7 .-441.9
-37.7 70.0
9.20 9.03
13.89
8.73 8.66
Glyceryltriacetate 3.49 0.915 0.523 3 . 5 3 0.964 0.497 3.55 0,967 0.494 3.53 0.954 0.483 3.65 0.982 0.484
1,2:,6-Hexanetriacetate 3.55 0.945 0.525 8.73 3.53 0.888 0 . 5 3 3 8.53 3.50 0.939 0.473 8 . 3 3 3,50 0.934 0.489 8.13 3 5 3 0.936 0.487 t3.88
8.65
Pcly(vinyl aeetate)a 3 20 0.902 0 . 5 5 6
2.65 X 10-8 3.32 x 10-4 6.50 X 8.38
x
1.33 X
10-6
5.69 x 10-4 2.59 X 6.93 X 1.52 X
3.12 x 10-7 2.24 X
Calculated hy w L n gthe experimental data of Ishida, et al.
lated for the Dlavidson-Cole-type relaxation. A similar result is seen in the measured Cole-Cole arcs of n-octyl iodide.15 Chain molecules which contain more than two polar groups are likely Lo show asymmetric dielectric relaxations such as the Davidson-Cole or the Havriliak-Ne.gami-type relaxation. This deduction holds not only for the dielectric relaxations of polyhydroxyl compounds such as diols and triols, but also for those of the triacetates, polar polymers, anti a,w-dibromoalkanes. All of these compounds contain .multiple polar groups in a molecule. On tihe other hand, polar molecules which contain one polar group do not generally show asymmetric relaxation, but show Debye or Cole-Cole-type relaxation, with the exception of sonic a k a n e halides. Hence it is considered that the interrelation of the motion of each polar group may be associated with the asymmetric dielectric relaxations. I t is reported that glyceroli and 1,2,6-hexanetrio13 show Davidson-Cole-type relaxations. I t is apparent that the significant difference between the triol and the triacetate can be ascribed to whether the hydrogen bond exists in the liquid structure or not. The polyhydroxyl molecules, where breaking; and re-forming of the hydrogen bond must occur on relax.ation, exhibit Davidson--Cobtype relaxation. Triacei;atev which do not contain the hydrogen bond show Ilavriliak-Negami-type relaxation which has the two kinds of' distribulioc. of relaxation times. This behavior coincides with the fact that the 'hydrogen-bonding normal alcohols show the siingle Debye-type behavior,16 and the non-hydrogen-~)ontl-ngmono-substituted alkanes such as n-alkyl bromides show a distribution of the relaxation times as seen in the Cole-Cole-type relaxation.17 At the same time, it was found that two kinds of the distribution parameters ( 1 - a ) and 6 seemed to be associated wit,h the acetate molecules. The three acetate molecules PVAc, glyceryltriacetate, and 1,2,6-hexanetriace"sate show nearly the same values for (1 - a ) and /3 which are ca. 0.9 and 0.5. respectively, as is shown in Table TI. Therefore, these values of the two distribution parameters are eharacteriscic 3 f the acetoxyl-substituted chain molecules. It i s interesting that long-chain PVAc and shortchain triacetatses exhibit the same distribution of relaxation times.
