erties and Relaxation in Ethylene Carbonate
rd Payne* and Ignatius E. Theodorou Air Force Cambri&e Research Laboratories, L. 6.Hanscbm Field,Redford, Massachusetts 01730 (AseGiz.#d May '$3,
lor@
~
a
/
costs ~aaaisted l bv ~th.e Air~ Force ~ C'anzbridgr: ~ ~ Research ~ ~Laboratories
T h e dielectric properties of ethylene carbonate and propylene carbonate have been studied by a pulse reflection technique and ac measurements in the frequency range 1-9000 R'IHe. Equilibrium dielectric constants Soir i h pure liquids and mixtures with other liquid dielectrics are consistent with the absence of specific intermolecular forces. The dipole relaxation process is described by the Debye equations with relaxation times in the picosecond region at room temperature and the nanosecond region for supercooled propylene carbonate aC - 79". Tho apparent limiting high-frequency dielectric conrjtant in both liquids is approximately 10 suggestiqg thu existence of a second dispersion region at frequencies above 9000 MI-Ez;. The rdaxation times and the viscusity of propylene carbonate are described by an empirical rate equation of the lorin previously applied by 1 3 ajdsun ~ and Cole to their measurements for 1-propanol, propylene glycol, and glycerol.
I ~ t r ~ d ~ ~ ~ t ~ ~ ~ Several stirdies of the dielectric properties of the e y c h c a r ~ ~ o h~aiv~~been ~ e ~reported in the literature.li3 'l?hcy sliow that these compounds have unusually high dielectric constants which in general call be attributed t o Iarge permanent dipole moinents rather than t3 spwific intermolecular association of the type responsible fur the high dielectric constant of, for exen~plo,wawr OI" the N monoalkyk amides.* Wowevep, the eviclenw ifi not entirely unambiguous. For example, the T r . o n . ~ ~constants i~'~ for both ethylene carbonate artd propylene carbonate are significantly higher lhan ,he ukud value for nonassociated liquids. Also the occurreiir:e of doublets in the carbonyl stretching band of 1he ir spectrum has been reporkd in the case of cdhylene carbonate and some closely related compouncls, Bmt not however in propylene carb ~ r a n t e . ~Similar effects in the i r spectra of halogenated esters of acetic acid hav-c been attributed t o rnoleeular assor:iauon6 or rotdionai isornerism? 13ince the latter coulid httrcily ewrpXeiin the phenomenon in the case of ethylene carbonetc Lhe sprctr oscopic: data seem to point to the possibility of association. 1111orlder t G explim ithis problem further, we have investigated the dipole relaxtxalion process in these compounds by exteatlraig the dielectric measurements into the niicrowave f i i i a ~ i ~range. y Accurate mensuremeinls of I h e ats diielectrie constant at 1 NIHz for ethylene eerLonsLc, propy Lcne carbonate, and mixtures 1)lit11 mcitharaol, 4-butyrolactone, arid did e a 1 d~ ~ rqjorted.
A ~ ' ~ / m d~ ~ ~ a ~ ~ ~ ~~ p u o~ jl Xolvents. a t ~~ o ni Pro-~ pylene carbonmde (lalhutheson Coleman and Bell) was ~
The Journal of "hyeaml C%6mistry, V G ~ 78, . No. $0,1979
purified by distillation under reduced pressure on a Podbielniak Semi-Cal (Series 3650) adiabatic fractional distillation column using a reflux ratio of The pressure and temperature a t the head of the colu were maintained at 0.1-0.3 Torr and 55-60', respectively. The kettle ternpera,ture w m kept below 110" .to avoid decomposition. The middle fraction was collected and analyzed by gas c ~ r o ~using ~ a~2- ~ ~ ~ ft copper column packed with ~ r ~ ~ spolyslyrene ~ ~ i ~ k e ~ beads (Pompak &) i n , &Model 5,630 F & J4 cbromat~graph with thcrmal ,conductivity dekeetor. The distillate contained. less than 10 ppm of -waterand no other det,ectabPe low-boiling impurities. Specific conduetanee was in &he range 10-'-lO--s (ohm cui ylene carbonate (l\/Iatheson Coleman and ~ l ~ d dried with 48 molecular sieves then d ~ s ~ twice under reduced pressure on a 40-cm heated $ 1 8 ~column ~ ~ ~ , ~ o packed with glass hel.ices. ~ h r ~ ~analysis of the middle :fraction indicated less than IO ppm of water and one other u.n.identified low-boiling impurity of BQW concc?n%ration. The melting point WBB 36.6" and the specific conductance Y9)-"7-.10-8(ohm cnn) - I * Diethyl carbonate, n&ianoi, arid 4-butyrolactone were likewise Purified by disti1htioi.i. sf'ter d r j h g with molecular sieves. All. solvents were rou.timely analyzed for water and other ianpuri.ties. All mlanipul ation of (I) R. P. Beward and E. C. Vleira, J . P h p . Chem,, 62, 137 (1958). (2) R. Kcmpa and 'VV. 1-1. Lee, d . Chenz., ~ S Q C .1836 ~ (195s) (3) L.Simeral ~ m dR. L.Army, 1.Phus. Chcm,, 7X,, 1448 (1970). (4) C. P. Smyth, "Dielectric Behavior and 8truoturs," MeGraw~
Hill, New York, N Y-, 1955. (5) J. E. Halea, J. 1. Jones, and W. KynaaLon, J7, Chem. Sot:., 618 (1957). (6) E T.McBee and E). L. Christman, J. Avner. Chem. floc.3 T Y , 755 I
~(1955). q
~
(7) LV,Josien and M .
n. Callas, C. E . Acad. Sci.,
248, 1641 (1958).
IELECTRPC PBOPERTfEG8 OF ETHYLENE AND PROPYLENE
nonaqueous solvents was performed in a drybox I,V acuum AtPnosplwefa Model HE-553-2). Ordinary distilled water was redistilled from alkaline pernmnganat e and again distilled under reduced pressure on a 1-111 insulated Pyrex column packed with Raschig rings. The specific conductance of the product ;vas in the rmge 2- 5 ?e IO--' (ohm em) -l. B. ~ e ~ o j Statze s Dielectric u ~ Constant. ~ ~ The ~ etatic dielectric constant was measured a t a fixed freqweney of 3 MKz usirig B cell similar t u that described by Connor, iClarle, and Smyth,* Concentric brass a31ectrodea \verb thl ded onto a Teflon base which also formed pari oi a waier circulation jacket. Banana plugs screw4 into ihv electrodes at the base of the cell enabled the cell bo bc plugged directly into General Radio Type 938 binding posts. Tht cell c a ~ ~was~nieasured ~ t by : a~ substitution ~ ~ ~ method using A Gclneral Radio Type 1606A bridge and Type: 1722N precision variable capacitor. The overall sensitivity of the arrangement was 0.05 pf or 0.01% for !he Rater-filled. ceil. 'The accuracy oC the '1722N cal~aciturwas improved from the nominal value of =k0.3pf to bei,ter 1,han :LO. i pl'by edibration against a General tkadio T y p ~I615A tramformer ratio-arm bridge at 1 l&z* The cell eonstaats were determined from measurements rmde witlt air, water, and methanol in the cell using slandard dielectric constant values a t 25" of 78.JO for wa,tesqand 32.63 for methanol.I0 The capacdance of the air-fillcd cell measured on a HewlettPsckard Type 250A RX bridge a t 1 R'IHz was 8.26 pf. The. capacitance oi the cell filled with a liquid of dielectric constari t C. is given by
G --
CY0e
4-C'
2893
@$RBONATES
(1)
where Co is the geometric capacitance of the air-filled space and @' is the invariant capacitance associated with the Teflon-spaced portion of the electrode area and the terminah. The values of Co and C' mere established as 5.890 and 2.37 pf, respectively. A small change in Co was observed over a long period of time. In arriving at the cell constants (and in subsequent measurements) due consideration was given to the efects of solvent conductance and residual inductance of both the precision condenser and the cell. The 1606h bridge measures the equivalent series RC combination. It wat8 necessary therefore to transform the cell iinpedance t o the equivalent parallel combination in cases where the effcct of solvent conductance was measurable. However, the difference between the series Capacitance and equivalent parallel capacitance was usualiy negligible and amounted to less than 1% in the %.orstcase (?,.e., i n the ease of water). The correction for inductance from all sources was usually less than 10.lyo. The temperature of the cell was controlled to zt0.03" by circulating water through the jacket from a thermo-
stat bath. The water temperature v-as measured in the jacket using NBS calibrated ASTM thermometers with a precision of 0.02'. Partial immersion errors were shown to be negligible under the e ~ ~ e r ~ ~ n e n t a ~ conditions. The variation with temperature of C'o, the air capacitance of the cell, was calculated from consideration of the thermal expansion of the electrodes. This a more accurate procedure than ~ was~considered ~ measuring the cell constant at different t e ~ ~ ~ p e r ~ ~ , ~ r e 3 using R standard calibration liquiri such 8s water. This waB however also done routinely as a check on [he procedure using the accurate water data of Melmberg and ,\Zar,yott.9 The total caleulatelW variai,ion of (To betweeii 0 and 70" was 0.13Ojr, which W V H~~ o ~ ~ ~ mithin experimental error by the rnew [uremenis C. Measurement of Dielectric Cor.~&.rni and Loss at 1-860 ~ ~ M N z . RZeasurements a i frequencies up 1 o 250 RETz viere made with a coaxial displaccm~ntcell similar to the cell. described by Lovell and Chle,'l using a EIewlelt-Packnrd Type 2508 bridge. Irxaproved electrical characteristics were obtained by c ~ ) m b ~ ~ e tthe ing cell from General Radio Typf 900 precisiom rod and tubing using a Type 900 BT precision conxial connector with 5t slightly modified bead bo forin the haw of the cell. For a perfectly fitting plunger the eoinplex dielectric constant of the liquid ( E * ) i s related t o the measured changes in the parallel Capacitance (AC') and conductance (AG') for a given clisplaeeinent ( l ) according to
COZ(L.* -
€8)
=;
AC - 5
c; -
11
(2)
where Co is the geometric capacitance per unit length of the cell, et is the dielectric constant of the plunger material, and w is the angular frequency of the ac signal. By equating real and imaginary parts in eq 2 , the dielectric constant ( E ' ) and loss ( e " ) are shown to be E'
=
€8
+ AC/C,Z
E''= AG/wC&
(3)
(4)
From a prior knowledge of et and the dimensions of the cell the method in principle allows absolute measurement of the complex dielectric constant by measuring the changes of capacitance and conductance with displacement of the plunger. I n practice, however, the cell is imperfect since the plunger does not fit tightly. Also the fringing capacitance at the end of the inner electrode varies at small plunger settings due t o collec(8) W. P. Connor, R. P. Clarke, and C. P. Smyth, J . Amer. Chem. Soc., 64, 1379 (1942). (9) C. G. Malmberg and A. A. Maryott, J. Res. Nut. Bur. Stand., 56, 1 (1956).
(10) R. Parsons, "Handbook of Electrochemical Constants," Butterworths, London, 1959. (11) S. E. Love11 and R. H. Cole, Rev. Sei. Instrum., 30, 361 (1959)
The Journal of Physical Chemistrv, Vol. 7'6,N o . 20r107'3
An a ~ p r o x i ~ ~ mfor t ~E*~ rfrom i eq 5 valid when and C,/C2 c: 0.1 is
]E*/
>3
from which bj, equating real and imaginary parte e' = E t ( 1
-I- C'JCzj, --
The valuc oi &'l/C:,for our cell was 0.08 obtained from measurements on tEe air-filled cell using the exact formula of eq 5 The specified value of Co (0.6667 pf k 0.0'7%) for the G R Type 900 coaxial stock was assumed, The vscliae o f €7 was taken as 2.08. As a check of the correctiiess of the cell constants, calibration measurements 11ere made at li MI-lz with air, methanol, and dime thy1 c:ulfoxiide which gave dielectric constanis in B ~ ~ ~ s a fg rae e~~ ~ ~with oe ~~iestablished t~ values. The coiidii loris for the ~ t ~ ~ ~ ~ o x involved ~ m a t ~ in o neq 7-9 were met for d l t h e liquids studied. The last terms in eq 8 arid 9 \Cere aegligibly small. under all experi. meatal corditions rncouurlered. The problem of the impedance transforming properties of the in: m~.dtrammission line connecting the bridge t o the xidge Lerrninal at high frequencies was solved by ieoKating [he cell from the bridge by a X/2 section. For measurements on nonconducting liquids below 20 R'IEIIz the cell could be mounted directly on the bridge using a G k Type 900-QNP adaptor. The effect of the sei*iasinductance of the internal line (0.019 ~ 1 3 )a,t 20 I!I/83-'s; ealouiated from the lead correction The Journal
of
Phgsicul Chemistry, VoE. Y6,No. 10,1971
(12) H. H. Slrilling, "Electric Transmission Lines," McGsa,w-PHiEl, New Yorb, N.Y . , 1951, (13) 8 . Roberts and A. Von I-Iippel, J . A p p l . Phys., 17, 610 (1946). (14) R. Pnyne arid I. E. Theodorou, Rez.. Sci. Instrum., 42, 218 (1971).
(15) H. Feliner-Feldegg, J. Phys. Chem., 73> 616 (1969). (18) €1. Fellner-Feidegg and E. F. Barnett, ibid.,'74, I962 (1970)
CELECTRIC ~
~
~
~ OF ~ETHYLENE , R TAND~PROPYLENE ~ s CARBONATES
previously. A ~ r ~ ~ s m ~ s line s i o nof approximately 250-em electrical length was constructed from 40-em lengths of Gcrrerd Radio Type 874 50-ohm air line. 'The (*ellconsisted of a General Radio Type 900 LZ30 reference air line terminated with a Type 900 WNC short circuit, to give a dielectric-filled length of 30 em. . ~ ~ e w ~ ~ tpulse t - Pgenerators a ~ ~ ~ Type ~ ~ ~215A (1 nsec rise tnme) and 2B3B (15 psec rise time) supplied the mq uare puises. 'The pulse and reflections were ob-. wwrd on thP lina a$,the generator end by means of a rnazix BP1 conxiai tcr and P6034 or P6035 passive c ~ n ~ Lo~ ae Tekttronix c ~ ~ ~Type 661 sampling scope wrl ki 'b'ype 4S2 sampling unit. The srgnal w:ts usually r.er:nrded directly on a Moseley 1351\.2 X Y ~ ~ ~ o 'rho ~ ~overall e r . rise time of this system js ap-
2895
90 c
CI
+ VI
8 85 .-c0 L
0 W .0
80
40
I
I
I
50
60
70
Temperature ["C1
a0
Figure 1. Static dielectric constant as a function of temperature for ethylene carbonate.
Low-Frequency Measurements. Equilibrium dielcxtric constants were measured a t 1 ;\/fHsfor ethylene ~ ~ ~ ~ bfrom o n 40 ~ ttoe 70" and for propylene carbonate from 0 to 65'. The results given in Table I were corI
70 o
v A
c E
x
0-
E 65 8
'Fable X : Static Dielectric constant (eo) Measured at 1 MBz and Kirlrwood Correlation Factor ( 8 ) for
this work Seward and Vieirafil Kempa and Lee (*) Watanabe and Fuose (26) Simeral and Amey
Ethylene Carbonate and Propylene Carbonate' Liquid
Ethylene carbonate
Propylene ~a:bonate
T,oc
25 40
50 60 70 - 78 0 10 15 20 25 30 35 40 4.5 50 55 60
€0
5.4 89.78 85.81 82.01 78.51 89 71.03 68.64 67.41 66.14 64.92 63.70 62.58 61.42 60.27 59.17 58.05 56.89
0
1.20 (1.10) 1.20 ( I .09) I . 19 (1.08) 1.18 (1.06) 0.73(0.66) 0.99(0.89)
Temperature
Pc)
Figure 2. Static dielectric constant as a function of temperature for propylene carbonate.
1.01 (0.89)
1.02 (0.89)
1.02 (0.88)
a Estimated accuracy of dielectric constant 0.1%. Correlation factor calculated from eq 17.
rected for scale errors and inductance in the standard capacitor and cell inductance, and for the temperature dependence of the cell constant. The dielectric constant> of propylene carbonate was also measured a t - 98" wibh the coaxial displacement cell using a General Radio Type 1615A bridge a t 10 kHz. The uncertainty of the 1-MEXz measurements is estimated a t 0.1%. The results are compared with previous measurements in Figures 1 and 2 . The agreement is generally good.
However, the ethylene carbonate data of Seward and VieiraI are systematically lower than our results by up to 3%. A sample of propylene carbonate rigorously purified by the method of Jasinski and Kirkland,Ie and supplied by them, gave results indistinguishable from those found with our material. Dielectric constants were measured a t 1 A!tHz for mixtures of propylene carbonate with water, diethyl carbonate, and 4-butyrolactone. The results are summarized in Figure 3 in the form of plots of the excess dielectric constant ABdefined by A€ = em
- ( ~ € -+1
2262)
(10)
where em is the measured value for Ihe mixture, el and e2 are the values for the pure components, and 21 and 22 are their respective mole fractions in the mixture. (17) R. Payne, J . Electroanal. Chem., 19, 1 (1968). (18) R. J. Jasinski and 8. Kirkland, Anal. Chem., 39, 1663 (1987).
The Journal of Ph,ysical Chemistrg, Vol. 76, No. 20, 1.972
where Z is tho input impedance of the dielectric-filled line and Zothe c ~ a r a c t e ~ ~~s t ~ c ~ of the trans~ mission line. For a loss-free a t the surface of the liquid i n
~
XIY
(4 2 ) -".."-.-L-2
I
0.2
0'4
I
0.6
I
I
I
0.8
I.o
mnols fraction of PC
Figure 3. Excess dieleot,ric constant as defined by eq 10 for mixtures of pxopjene carbomte with 4-butyrolactone, water, and diethyl c ~ ~ at 25". r ~ o ~ ~ ~ ~
mole fraction of EG
Figure 4. Exlcese dielectric constant as defined by eq 10 for mixLures of ellhyleno cartonate with methanol, water, propylene carbonate, smd benzene at 25' (data of 8eward and Vieirs").
Similar results for ethylene carbonate mixtures calculated from the data of Seward and Vieira' are shown in Figure 4. Jn both cases mixtures of the cyclic carbonate with strongly polar Iiquids (and with each other) produce small deviations from ideal behavior whereas large negative dcvia taons occur in mixtures with lowdielectric conshnt Iiquids. A miscibility gap occurs in the propylene earbonate-water system between approximately 30 and 90 mol % of water a t 25'. . Puke ~ ~Measurements. ~ ~The pulse c reflec-~ technique gi.ves two experimental parameters related to the dielelctric constant of the liquid: the me and the reflection coefficient. For a remains in equilibrium (no dispersion) the ~ ~ o ~ alime g i s~ proportional , ~ i ~ to ~ the ~ ~square root of the dielectxic ~ o n s t m which t can therefore be determined. The Journal of Rhy&al Chemistry, Vol. 76,No. $0,1972
Since Z i s always Iess than go,the reflection coefficient is negative and the rrflected piilse Cor the Bossfree dielectric is an inverted square pulse. Combination of eq 11. and 12 gives
Hence the dielectric constant i s also obtained from the measured reflection coefficient, For the general case of a dielectric with loss the reflection coeBeient varies with time. Bf the relamtion is s10.w eompared to the response of t,he system ihe infinite fscquency dielectric constant is obtained from the height of the ~ a r ~ y reflected pulse a t 1 = 0. ~ ~ ~the~static constant foliows from the height of the pulse 7-0 (the relaxatjoii time). ~ ) e t e ~ ~ of~ the ~ ~relax%n a ~ ~ Q ~ tion time from the time dependence of the r coefficient is diEcult even for thc simple ease of liquid anti requires a full analysis of the spectrum of the input a i d reflected wave forms"'9 A binzplified analysis of this type I V %given ~ recently by ~ ~ e ~ ~ ~ eand r ~ ~ e J ~ Barnett using the Laplace transform method. A typical pulse reflection ~ ~ ~for propylene s ~ ~ ~ carbonate at room temperature in shown ~n Figure 5 . The delay time of the t,rantirnissXon Inme in tlnk case is approximately 10.5 nsec giving a time separation of the incident pulse and the first re ection of 21 nsec. The various features of Figure 5 are identified as follows. The first pulse is the incident tiigarzl sampled as it passes the probe, The second (inverted pulse) is the reflection from the dierectric discontinuity at the liquid surface : it is inverted because the reflection coef3Faclent of the discontinuity "Been" by the line is negative (see eq 11i). The next pulse, also inverted, is the reflection oE the transmitted portion of the signal from the short circuit at the ~ floor ~of the cell. n Subsequent pulses are due to repeated internal reflection with parlial transmission occurring at the dielectric-air inierface and total reflection at the short circuit. Tlre amplitude of the ntk reflected pulse is easily shown t o .Er" --- E,(1 - p " ) ( " - p ) " - ~(- 1y-1 (19)
T.A. Whittingham, S.Phys. Chem., 74,
1524 (1970).
(14
DIELECTRIC ~~~Q~~~~~~~~
OF
2897
ETHYLENE AND PROPYLENE CARBONATES
Figure 5 . Pulse vcflectionw from a 30-cm section of 50-ohm coaxial transmission line terminated by a short circuit and filled with propylene carbonate a t 21'.
according t o eq 13. The subsequent risc i s approximately exponential and is substmtially complete after 5 nsec. This behavior is consistent with the ac measurements. The equilibrium reflection coefficients are also consistent>wil h the static dielectric constant values. The time separation of the first and second reflections in Figure 5 is 16.2 nhec giving a value for P- of 66 in rxccllent agreement with the bridge value. At room temperature ethylene carbonate is a solid. The reflection coefliicient and propagafnon time indicate a dielectxie constant of 2.5 t o 3. C. ITiyh-Frequency Measure"&. stant, and loss measurements were made in the hequency range 10-250 M€Iz for ethylene carbonate at a single temperature (40")) and for propylene carbonate at bix temperatureh ranging from -- 78 l o 70" using the Hewlett -Pacltar d 25OA bridge and the coaxial displacement cell. Dispersion w;25 observcd in this frequemy range for both liquids. The dicieclric constant and loss were determined from plots of the measured parallel capacitance and conductance, recpectively, against plunger disp1ac:ernent using eq 8 and. 9, nc&xting the last term in each ease. The relaxation times given in Table I1 were obtained __
Table I1 : Dielectric Relaxation Times for Ethylene Carbonate ... ._-~..,_.. .. . . . ,.-
..
. .
t- t
and Propylene Carbonate Calculated from Eq 16 T, Liquid
O C
80C
e,
~
Figure 6. Pulse reflections from a 30-cm section of 50-ohm coaxial transmission line terminated by a short circuit and filled with propylene Carbonate a t -78".
for n 2 2 where p is the forward reflection coefficient (Le., air to dielectric). A qualitative examination of Figure 5 shows that the dipole relaxakion process in propylene carbonate at room temperature is extremely rapid. The measurements for ethylene carbonate at 40" are similar and closely resemble the behavior of water (relaxation time a t 25", 8.3 X However, some high-frequency absorption is indicated in Figure 5 by the rounding of later reflections. At -40" the high-frequency attenuat i o n is marked and at, -78" the pulse is completely attenuated after t w o passes through the cell (Figure 6). The ac measurements described below show that the relaxation time at -78" is 1.3 X sec. Some time dependence of the dielectric constant (and hence t,he reflection coefficient) therefore should be apparent at times s,ho\vcvor! coiild ba fit]ted satisfactorily to Debyc
The J O U To j~t'iiusicul ~ Chomiutry, Vol. 76, N o . 20, 1978
Figure 10. Cole-Cole semicircular arc plots for propylenc carbonate at 25 and -78" and ethylene carbon:ttc at 40". Solid lines drawn for Debye parameters given in Figrires 7-9,
observed in the disptmion curves for aliphatic alcohols.21,22This is confirmed by t,hc lo\r-tompcr:Lturt: propylcnc carbonate m(?asurcmcnts which show t,hc second dispersion rcgion (Vigurc I O ) . Norw of t h : results could be fittod to the Colc arid Colv circulitr arc funct,ion,23or t,hc Davidsori arid C h l slw~\.c:cl ~ :Lrc func-
TELECTRIC~
~
0OF ETHYLENE ~ ~ AND ~ PROPYLENE ~ 1 CARBONATES ~ s
tion20 for any value of the empirical argument. The Debye curves in Figur.es 7-9 and the Cole and Cole plots in Figure 10 were calculated from the parameters indicated. 'The rdaxation times are in good agrecment with the bridge values in Table I1 which, however, were aswmed values of E , . obtained with 10.is-e~
A. Static E)ie%ectnk Constants. The possibility of molecular associabion through short-range specific iorces was investigated by calculating the Kirkwood correlation factor ySz4 Kirkwood's extension of the OnsageP equation can be written
where po is the permanent dipole moment, N o is Avogadro's number, V is thc molar volume, and k is Boltzjnann'S constant. Correlation factors were calculated from eq 17 assLimjng dipole monient values of 4.87 for ethylene carbonate and 4.94 for propylene carbonate.e hlolar volumes were calculated from density data given loy Watanabe and FuossZ6(ethylene carbonate) and Simeral and Amey3 (propylene carbonate). em was calcm'lated from published values of the optical refractive ipdex2 assuming as before a 30% increase in the total induced polarizability between optical arid micromavc frequencies. The resultant y values given in Table 1 are close to unity for propylene carbonate as reported by Simcral and Amey3 in the lower temperature range. The ethylene carbonate values are somcwhat higher although still close to unity. Seward and Vieir:xl obtained a vatuc of 1.6 for ethylene carbonate at 40" and hence concluded that some association was present. They evidently used the approximation E, = nain eq 17 which accounts for the discrepancy with our resull,. In view of the sensitivity of the calculation t o the assumed value of e , and the uncertainty of this value no firm conclusion can bc drawn. The g values sh~o.zvnin parentheses in Table I were calculated from a form of eq 17 used by Davidson and Cole20in which E , Is equated t o n7 on the right-hand side and the experimentally measured value for the low-frequency dispersion on the leCt-hand side. I n our experiments this value is close Lo 10. The justification for this procedure is unclear but in any case it has little effect on the results. The sensitivity t o E, arises from the quadratic dependence on the right-hand sidc of eq 17. Calculations of this kind therefore lead to the conclusion that propylene carbonate and probably also ethylene nsager's equation within the limits of uncertainty of the calculation. So me qualitative inferences concerning the possibility of association can be drawn from the excess dielectric consi ant function for various mixtures shown in Figures 3 and 4. Thhyiene carbonate-mater mixtures show surprisingly little deviation from ideal behavior whereas
2899
strong negative deviations might be cxpected due to breakup of the water structure. ~ i ~ behwior ~ ~ aof r the dimethyl sulfoxidewater system has been attributed t o strong interaction of the Lwo components which is supposed to compensate for the disruption of the xvater structure.27 Large negative deviations from ~ ~ npropylene ~ ideality for ethylene c a ~ b o n a t e - b e ~and carbonate-diethyl carbonate nmix%~.arcscould be interpreted as evidence of structure in ihc high dielectric constant components by analogy with the similar effect of dioxane on water, for examples2)25 An alternative interpretation which seems more plausible in view of the earlier discussion is that the low-d~electr~c constant component promotes association of Lhe dipoles of Che or high-dielectric constant ~ ~ ~ m ~ t o form n e ~dimers t larger aggregates o l low moment. Mixtua es with other high-dielectric constant liquids, i.e!, propylene carbonatebutyrolactone and ~ ~ ~ carbonate~ y ~ e ~ e ethylene carbonate show only small d e v k l i o o s from ideality, which seems consistent wiih the gener.al conclusion that, there is little or no specific awmation. IrIowever, it is worth noting that) both 4hylene carbonate and propylene carbonate have TPOLIZOII'S cons tants of approximately 23 which is ~~~~~~~~;~ higher than tlie "normal" value of 2'8 for ;i i7cmnssocl~ded liquid. There is also some evidence of association in chloroethylene carbonate and chlorome caxbonate (chloropropylene carbonate) for which the correlation factors calculated irom the dah. of Keinpa and Lee2 are 31.33 and 1.85, rcsp~otiv modes of association in these compounds e polyanerizalion of the wrboilic acid yleiie glycol and hzghpr & ~ o l , ; of the type dcscribed by Carothers and Van er, these aut-hore also sI,rcss that extensive studies of ethylene c a , ~ b o n ~have t e revealed no evidence of p ~ ~ y ~ e ~ ~inz th6: a t ~five-membered o ~ i ring compounds. . Dielectric Relaxation. As noted earlier., Lhe p i n t reiaxation process in both e Iewre carlionate and ye equations. I n propylene carbonate obeys the propylene carbonate the Debye behaxior 1s also found in the supercooled state at - 7%'. The re'laxrt,tkon times summarized in Table 11 are comparable with values for normal polar liquids of high dielectric coabtant, e.g., dimethylformamide ( T ~= 1.3 X IO-" sec at 37.3°)80. and ~ - ~ u ~ y ~ o ~ a (r0 c t o=n e2.1 sec at Q5).31 (24) J. G . Kirkwood, J . Chem. Phgs., 7, 911 (1939).
Onsagcr, 1.Amer. Chem. Soc., 58, 1486 (1(3:36). (26) M. Watanabe and R. Fuoss, ibid., 78, 527 (1956). (27) J. J. Lindbcrg and J. Kenttamaa, Suo" Renzistilehti B, 33, (25) L.
104 (1960). (28) F. E. Critchfield, J. A. Soc., 75, 1991 (1953).
Gabson, and J. E,. Hall, J. Amer. Chem.
Til. Carothers and F. J. Van Natta, ibid., 52, 314 (1930). (30) 9. J. Bass, W. 1. Nathan, R. i M , Mclghan, and R. a.Cole, J , Phus. Chem., 68, 509 (1964). (31) R. Payloe aiid I. E. Theodorou, unpublished data. (29) W.
The Journal of Phgsical Chemistry, Vol. 76, Xo. 20,1978
RICHARD PAYNE AND TGNATIWB
19 over the ~41~1s: lemperature range with 8 -= 139°K and for the relaxation procem an and 7'150°K fur the viscosaly Iikpntiorr 19 ri;dg previously applied by Ihvidsoai L ~ ~ ~ w - t e ~ p edata r ~ tfor ~ r1e- p r o ~ ~proplyens: ~ n ~ ~ ~ glycol, , and glyceroil where the constania I! m d T V prowed to be the 3ame for viscous fliovk as lor thc ~ ~relam- e tion process. In propylene m t c . hon.evcr, they appesr t o be ~ ~ di t ~ 'The &goxCrance ~ i of T , a e c o P ~ ~ t>o 1 eq ~ 19 i s the reiaxatnorr time t~,rrnd the y.isoo~it~7 become iniinilc w!w 11Y'' Yr 'T his seems physiedly reasonable ~&m suprrcooid pt upylene carbonate hecomes highly viacous at 1 st^^^^ bellow -50" a,ud~ W K M EL glassy sobd iwiclm -~ TOO", 'Ifhe correlalion between the diclce trre rchxation process and 'i,$ae visc10sity miil irc Irirt'iiea cxphre through Debye's ~ ~ ~ naod~i r oF the ~ dipole ~ ~ reo~ientat~on a ~ ~t o which ~ r the~ ~ n ~ relaxation time i s gii7cn by" II-
I
3
I
4
I
5
Figure 11, A,rrlienius phts for dielectric relaxation and viscosity in propylene carbonate. Viscosity data taken from "Propylene e 5 ~ k i O I d W'Technical Bulletin," Jefferson Chemical eo., Biouston, Tex., ISFA.
~
~
~~~~~~~~~~~~~~
which are known t o be associated, e.g., N ormamide and ebbanol, on the other hand generally have ralaxatton times an order of magnitude larger. However, the two examples cited also have correlation factors iu the range 2-5 indicating far more cxt eneive aasociation than is likely to be present in the cyclic c a r ~ ~ ~ The ~ ~ ~relaxation t e s ~ time for supersec) cooled propyjirne carboriaie at -78" (1.3 X i s five orders or" magnitude shorter than the value of 1.89 X lo-$ RCC reported by Davidson and Cole20 for propylene glycd a l -- 7'5' where a distribution of relax* tion times WZLJ also found. The dispersion measurements theref ore sewn consistent with the inference ~ dielectric constant measurements drawn from t l etatic that significant intenmolecular association is absent. The ten~penttduwdepcrrdence of the relaxation time P propylene carbonate in the temperature range -70" can be wltj&dorily represented by the Arrhenius rate equation
A ~x~~[-AH"/RT] (18) setitration (AH*)of 2.1 kcal/mol and
*so z :
with a heat o i sec. Bowprecxponentjal factor ( A ) of 1.23 X ever, AHxcapparently increases ah lower temperatures $s shown by the deviation of the -78" point from the s-lraiglit line plot o C log 70 against l / T in Figure 11. The Asrhenius plot for the viscosity is markedly curved over the wliolc tcniperature range from -54 t o 99" (Figure 11). '"?lie apparent activation energy increases from a value of -3 keaI/mol at 40" t o -7 kcal/mol at -40" T h i d if subst antially higher than the activation energy for I%E relarcation process as usually found.* Both &herel,%xntiontime and the viscosity can be fitted t o an ~mpiriosleapxe,xion of the form I
?%e Journal of Phjisicical Chemistry, V a l . 76,No. 80, 19Y3
7-0
= 4n?Ja"/kT
@Q)
where ?J is the viscosity, a is t moicculnr radius, and k is the Boltzmann constant,. ~ ~ a20tis based ~ o o~n Stokes' calcialidion for motion of a spherical particle in a viscous rviedium and is therefore subject do the well-known uncertainties which s r i when ~ the particle is nonspherieal and of molecular dimensions. A further difficulty is the unknown rela1,ionship between the microscopic relaxation tirnc T~ and tht; r~iea~rired rclaxation time which dqxmh on tvheLhw the 1or:al field acting on the dipole is taken as the Townti?field or the Onsager field On the reasonahlc ns~ianipliorsk a t the latter is more appropriate the value of roin eq 20 can be approximated by the measured re1sxntion time which together with khc ordinary m&er'03coj~ieviscosily leads t o mglecular radii of 1.7 A for ethylcnc ewbonate and 1.8 A for propylene carborrlitc. Thc cl~a111cteaoR Che etliylenc carbonate ring along the direclion of the dtpole estimated from moiiecn~ermodels i s -*.B W ~ h c sFRCK give^ by ecj 20 are Lhoiefore s m d h t h a n expected although surprisingly close in view of the assumptions involved. The assumptim of a Eoreiini i m fndd would reclzilce the value of ro in ey 20 b y B factor itm -i- 2 ) / ( E O -5- 2) ~dilclnwould yield ~ ~ Ionw values ~ ~ of the xnolecmlar radius. In the absence of more detailed ~ e a s ~ r e ~ e at nts frequencies higher than 9 GHz, little diwussion of the high-frcquency dispcrsion is possible. Tlic Xovv-t~niperature m e a s ~ ~ r for e ~ propylene e ~ ~ ~ a r a h n a t e sfem t o indicate a central lrequenog ~~~~r~~~~~~~~~~~ 30 t u " greater than that of the principal dispersion. Roughly 10% of the total dispersion i s ~ c r ~ foro by~ tlie ~ high~ ~ e ~ ~ frequency dispc rsion.
