Ultrasonic Absorption Study of Liquid Dialkyl Carbonates
The Journal of Physical Chemistty, Vol. 82, No. 23, 1978 2531
Ultrasonic and Microwave Dielectric Relaxation of Liquid Dialkyl Carbonates David Saar, Joseph Brauner, Herman Farber, and Sergio Petrucci" Depaflment of Chemistry and Nectrical Engineering, Brooklyn and Farmingdale Campuses, Polytechnic Institute of New York, New York, New York 11201 (Received May 4, 1978)
Ultrasonic absorption data for pure dimethyl, diethyl, dipropyl, dibutyl, and propylene carbonates in the frequency range 3-300 MHz and in the temperature range 25-55 "C are reported. An ultrasonic relaxation process of the Debye type with a relaxation frequency f R = 8.5-10 MHz at 25 "C, which is largely independent of the length of the alkyl chain in the alkoxy group, has been found for the noncyclic carbonates. No such process has been observed for the cyclic propylene carbonate and for dimethoxymethane which lacks the carbonyl group. The observed relaxation process is interpreted as being due to a cis-trans isomerization of the alkoxy groups. By using theories for thermal relaxation processes both the activation parameters AH: and AS,' for the reverse step of the equilibrium and the thermodynamic parameters AH" and K for the equilibrium have been determined. Complex dielectric permittivities in the microwave frequency range 0.6-67 GHz for the above noncyclic carbonates at 25 "C are also reported. The data can be described over almost all the frequency range studied by a single Debye relaxation process. The high end of the frequency range shows some positive deviations of the loss in accord with literature data. The dielectric relaxation process is interpreted as due to a segmental motion of the molecule under the influence of the electric field. The different nature of the relaxation mechanisms for the ultrasonic and dielectric processes is attributed to the different type of perturbing function inherent in the two methods.
Introduction Mechanical waves of ultrasonic radio frequencies have been used in the past to investigate the dynamics of molecular relaxation in pure 1iquids.l Similarly, electromagnetic waves a t microwave frequencies have been employed to study the decay of polarization in these same substances due to the relaxation of the orientation of dipolar molecular groups.2 Very rarely have both types of waves been employed by the same research group to investigate the molecular dynamics of organic liquids, the most common situation being mutual ignorance of the information obtainable by the alternate tool. Because of the different natures of the perturbing waves complementary information of great value can be obtained by the use of both techniques. The compressions and rarefactions caused by the mechanical waves can disturb a pressure sensitive equilibrium which has a AV, (= AVT - OAH/pC ) # 0 as indicated by the well-known relation (a In K/ap?, = -AV,/RT.3'4 Thus, the concentration of a molecular form which is small relative to some other form at low pressure may be substantially increased at high pressure if its molar volume is smaller or its enthalpy is higher than that of the other form. An applied electric field, for example, in the form of an electromagnetic wave, may also cause a shift in the equilibrium between two molecular forms. If the two forms have a different dipole moment the equilibrium constant relating them can be changed according to the relation (a In K/aE) = aM/RT, where AM is the change in the dipole moment per Alternatively, if a given molecular form with a non-zero dipole moment (because of the presence of one or more polar groups) always predominates, a dielectric relaxation process associated with the orientations (following the alternating field) of one or more of these polar groups will be present. In this latter case the dielectric relaxation process (associated with the dipolar orientation of the predominant species) may not be related to the ultrasonic relaxation process. 0022-365417812082-2531$01.OO/O
Dialkyl carbonates were chosen because of their relation to esters which contain one of the two alkoxy groups present in the carbonates and because of the possibility that these molecules might be considered model monomers for the corresponding polycarbonate polymers.
Experimental Section (a) Apparatus. The ultrasonic equipment and procedures have been described el~ewhere.~A linear leastsquares method was applied to all the absorption (db) data vs. distance at each frequency. The dielectric equipment and procedures have been described elsewheree6 Cannon viscometers no. 0 and 1 (Cannon, University Park, Pa.) with manufacturer calibration certificates were used. Two 50-mL pycnometers calibrated with distilled water at 25.0 "C were also used. Thermostatting of the ultrasonic and dielectric cells and of the viscometers and pycnometers was within h0.05 "C. (b) Materials. Diethyl, dipropyl, and dibutyl carbonates (Eastman Kodak) were vacuum distilled in an all-glass apparatus and used sh%ortly thereafter. Dimethoxymethane (lab stock) was distilled at atmospheric pressure. Propylene carbonate (Eastman Kodak) was used without further purification, the result being only of a qualitative nature. Results and Calculations (a) Ultrasonic Relaxation. Figure 1 shows the results expressed as a/f" vs. the frequency f (MHz) for dimethyl carbonate and diethyl carbonate at the various temperatures investigated. a is the sound absorption coefficient (Np cm-l). The solid lines represent values given by a Debye type function for a single relaxation p r o c e ~ s : ~ ~ ~ a/P = ( A / 1 +
(f/fd2) +B
(1)
Figure 2 shows similar plots for the other two carbonates investigated. Table I collects the quantities A , B, and f R for these systems. The sound velocities are linear functions 0 1978 American Chemical Society
2132
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978
Petrucci et al.
TABLE I : Ultrasonic Parameters A, B (cm-" s2), and f~ (MHz) According to Eq I for the Liquid Carbonates Investigated at 25, 40, and 55 "C
Dielhilrorbonota f
-25'C
1017~ liquid dimethyl carbonate diethvl carbonate dipropyl carbonate dibutyl carbonate propylene carbonate dimethoxymethane
t, cm-"
"C
25 40 55 25 40 55 25 40 55 25 40 55 25 25
s2
101'B cm-I sz
4500 56 2930 70 2230 70 2357 43 1570 30 1100 50 1600 50 1140 60 850 60 1540 60 1100 70 750 60 47.3 i 0.9 36 I 2
f ~ ,
MHz 8.5 15 22 9.5 17 30 10 15 24 8.5 12 20
of temperature expressable by the equations calculated by linear regression: dimethyl carbonate u = 1196 - 3.67(t - 25) m/s r2 = 0.996 diethyl carbonate u = 1179 - 3.47(t - 25) m/s rz = 0.985 dipropyl carbonate u = 1122 - 4.23(t - 25) m/s
rz = 0.995
dibutyl carbonate u = 1253 - 3.20(t - 25) m/s
r2 = 0.988
where r is the correlation coefficient. For propylene carbonate which has its alkoxy groups held in a ring structure, no relaxation is visible at 25 "C, whereas for all the other liquids at 25 " C a relaxation process centered around 8.5-10 MHz is apparent (Table 1). Ultrasonic data expressed as a/fLvs. f were obtained at 25 "C for dimethoxymethane. This last molecule has no carbonyl group but rather a methylene group to which the alkoxy groups are bound, and again no relaxation process is evident for this molecule (Table I). (b) Dielectric Relaxation. Figure 3 displays the quantities E' and E", the real and imaginary parts of the complex permittivity, plotted vs. f (GHz) for liquid diethyl, dipropyl, and dibutyl carbonates at 25 "C. The data for dimethyl carbonate (shown here for comparison) have been reported previously.6 Figure 4 gives the Cole-Cole plots of E" vs. E' for the investigated liquids. The solid lines represent the values given by Debye type functions for a single relaxation process' 6' = E m + (€0 - E m ) / ( l + cf/fR)2) (11) 6'' = (€0 - E m ) ( f / f R ) / ( l + (f/fd2) In Figure 4 the data for diethyl carbonate show a deviation
2000
5
2
1'
20
IC
50
100
200
2000n L,
i0c0
1'
t
t
k
i0
20
IO
IbO 200
f(NHsl
-
Figure 1. Ultrasonic relaxation of dimethyl carbonate and diethyl carbonate at 25,40, and 55 "C: ordinate, a l p 10'' cm-' s2; abscissa, frequency f(MHz). The solid lines are the calculated values according to a single Debye relaxation function.
1'
2
5
I0
20
50
IW 2W
1'
2
5
IO
20
50
100 200
2
5
10
20
50
IO0
eo0
400
'1
200
flMHz)
Flgure 2. Ultrasonic relaxation of dipropyl carbonate and dibutyl carbonate at 25, 40, and 55 "C. The solid llnes are the calculated values according to a single Debye relaxation function.
TABLE 11: Apparent Relaxation Parameters e,, e,, and f ~Microscopic , Relaxation Time T ~ Shear , Viscosity I), Density p , Molar Volume V, and Molecular Volume u for the Dialkyl Carbonates Studied in This Work at t = 25 "C liquid carbonate E,, EfR, GHZ 10127, s 11, CP p? g / c m ~ V , cm3/mol 102zu c m ~ / m o l dimethylb 3.12 2.35 22 6.64 0.585 1.0630 84.739 1.408 diethyl 2.84 2.31 16 9.33 0.7 50 0.9689 121.92 2.02~ dipropyl 2.73 2.29 10 15.06 1.243 0.9366 156.0, 2.593 dibutyl 2.60 2.25 8 19.00 1.717 0.9195 189.49 3.148 The dependence of density on temperature for the last three liquids, in the temperature range 25-55 "C, can be expressed by the relations determined by the following linear regressions: (diethyl carbonate) p = 0.9969 - 1.11 X l O - V , "C r z = 0.999; (dipropyl carbonate) p = 0.9586 - 0.907 X l O - V , "C r z = 0.993; (dibutyl carbonate) p = 0.9439 0.975 X 1 0 - 3 t ,"C r 2 = 0.999. Reference 6.
The Journal of Physical Chemistv, Vol. 82, No.
Ultrasonic Absorption Study of Liquid Dialkyl Carbonates
:I
23, 1978 2533
tl Dimethylcarbonate ( R e f 61
35
1
=2YC
D I p ropy I co r bono l e
W
t =
t
30-
”
25°C
A -
W
0
25-
1.6
2 0-
)4
15-
)2
10-
t
8
flGHz)--
f(MHz)-
t
D i butylcorbonote
t
W
35
t W
30
06
25
t =25”C
” 30-
t
- ”
n A
25-
.-.
W
U
f(GHz1
-
f (GHz)
f
Flgure 3. Real part e’ and coefficient of the imaginary part E” of the complex permittivity plotted vs. the frequency f (GHz) for dimethyl, diethyl, dlpropyl, and dibutyl carbonates at 25 OC. The solid lines are calculated functions according to a single Debye relaxation function.
from a simple Debye process a t high frequencies (>35 GHz). Recent literature data* for dimethyl carbonate and diethyl carbonate show positive deviations from the Cole-Cole locus at high frequencies. This deviation has been attributed to a non-Debye absorption process in the far IR a t millimeter wavelengths. By non-Debye is meant not associated with dipolar orientational relaxation. We will purposely neglect this contribution to the total loss E”; thus the extrapolated quantity E , retains the formal significance of the real part of the complex permittivity just after the dipolar orientation polarization has relaxed. Apparent relaxation times were thus calculated from the one-term Debye-type relaxation functions (eq 11)and will be compared among themselves for the liquids investigated. Table II presents the values of eo, E,, and f R for these liquids.
Discussion (a) Ultrasonic Relaxation. Of the liquid carbonates investigated only propylene carbonate has its alkoxy groups largely immobilized by a ring structure; only for this carbonate is a relaxation process absent. Therefore the hypothesis is advanced that the molecular mechanism of the ultrasonic relaxation process involves a cis-trans isomerization of the alkoxy groups. Specifically,we propose an equilibrium between the two possible structures R
8 = O
R
cis-cis
0.40.3-
0.1 -
0.2
Oipropylcorbonate
0.3,on
Eo = 2 . 7 3 E, 2.29 f, = I O G H z
I
i
Di butylcarbonote Eo = 2 . 6 0 E, f,
2.2
2.4
2.6
2.8
=2.25 3 8.OGHz
3.0
3.2
Figure 4. Cole-Cole plots of the quantity e” vs e’ for dimethyl, diethyl, dipropyl, and dibutyl carbonates at 25 OC.
0‘
e 2
I
Cole-Cole plot for d i - a l k y l c a r b o n a t e s
E’ ---c
R
/
I
t = O
cis-trans
which is similar to that postulated by previous workersg for the case of the alkyl esters where one of the alkoxy groups of the carbonates is replaced by an alkyl group. (A concerted type of mechanism involving a cis-cis *
trans-trans equilibrium is not ruled out.) The existence of a t least two forms for dimethyl carbonate has been reported recently by Katon and CohenlO based on IR spectra. They obtained a AH = 2.6 0.5 kcal/mol for the isomerization equilibrium. From Table I it may be seen that the relaxation frequencies a t 25 OC are of the same order of magnitude for
*
2534
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978
TABLE 111: Activation Parameters AS,*, 4H,*,and Thermodynamic Parameters AH" and Equilibrium Constant K for the Isomeric Equilibria in Liquid Dialkyl Carbonate Studied by Ultrasonic Relaxation AH,+, AS,*, cal/ kcal/
liquid carbonate
(mol deg)
dimethyl diethyl dipropyl dibutyl
-4.6 -0.11 - 6.0 -6.8
mol 5.5
81.
fraction units [A] + [B] = 1 by introducing K = [B]/[A], one hasg
AH', kcal/ mol
5.0
2.85 3.72 3.02
4.8
2.01
6.8
Petrucci et
103K
8.1 1.9
6.1 33.8
the nonring carbonates investigated. This means that, if the equilibrium proposed above is correct, the major contribution to the energy barrier of the isomerization process comes from the rotation about the C-0 bond (and not from the hydrodynamicresistance to the motion of the alkyl group which goes from one to four carbon atoms in length). This at least seems to be true over the variation in the length of the alkyl chain studied. Another check on the validity of this argument was made by studying dimethoxymethane. Here the C=O group is replaced by a CH2 group (probably causing the C-0 bonds to become true single bonds). This should cause more molecular flexibility and permit free rotation of the alkoxy groups; indeed at 25 "C no ultrasonic relaxation process was visible over the entire frequency range investigated (10-270 MHz). Given the molecular process
It is now assumed that AVT = O9 for an isomerization reaction so that AV, s -OAH"/pC,. Substituting this approximation for AV, and 0, = l/pu2 into eq V one obtains
where again for an isomerization reaction it hasg been assumed that AS" = 0 so that AG = AHo. Modifying eq VI slightly one arrives at
+
The function x2e-X/(1 e-x)2,with x = AH"/RT, has a maximum at x = 2.4. This means that for x > 2.4 or AH" > 2.4RT, the quantity w,,/Tu2 will increase by decreasing x or, in other words, by increasing T. This behavior has been verified for all the carbonates investigated which implies that AHo > 1.42 kcal/mol at T = 298.15 K. Now, in eq VI onegmay approximate (1 e-mo/RT)2= 1and, taking the natural log of both sides of the equation, one may write
+
k
A&B kr
with K = kf/k, one can write the following e q ~ a t i o n : ~ 7-l = 2 ~ = f k f ~t k, = k r ( l 4- K) =
(eAsi*lR)(e-m:IRT)(1t K) (1111 h where the symbols used have their usual meanings. Rearranging1' we recover
A plot of In (r-l/T) vs. 1 / T yields a straight line with slope =
d In (r-l/T) = -d(l/T) R
and showing intercept = [In
(a)
-KAHo (Iv) K t 1 R
t
%]
Plots of the quantity In r-l vs. 1 / T were linear with squared correlation coefficients r2 = 0.991,0.999,0.994,and 0.976 for dimethyl, diethyl, dipropyl, and dibutyl carbonate, respectively. The calculated values of AS: are given in Table 111. To calculate AHr*one needs to know AH" as is obvious from eq IV. This latter parameter is calculable from the maximum excess sound absorption per wavelength, pmax= (A/2)ufR. The values appearing on the right-hand side of the above equation have been tabulated in Table I. For the process A ;=I B one hasg
Neglectinggthe temperature dependence of the first term on the right, one would expect a plot of In (Tpmax/u2)vs. 1 / T to be linear with a slope of -AHo/R. This seems to be the case for the system investigated (squared correlation coefficients r2 = 0.999,0.993,0.958,and 0.952 for dimethyl, diethyl, dipropyl, and dibutyl carbonate, respectively). The values of AH" obtained are presented in Table 111. For dimethyl carbonate AHo = 2.85 kcal/mol which agrees within the experimental error with the value of 2.6 f 0.5 kcal/mol obtained by infrared spectra.1° The agreement is fairly remarkable considering the approximations involved in eq VIII. Table I11 also reports the values of K - e-mo/RT.It may be seen that K
