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Dielectric behaviour and intermolecular forces in some dipolar mixtures
Dielectric Behaviour and lntermolecular Forces in Some Dipolar Mixtures* T. J. B H A T T A C H A R Y Y A , T. V. G O P A L A N AND P. K. K A D A B A * * Department o f Electrical Engineering, University o/Kentucky, Lexington, Ky. (U.S.A.) (Received August 30, 1966)
S UMMA R Y The dielectric relaxation of chloroform and benzophenone & n-heptane and of binary mixtures of chlorobenzene and bromobenzene in a viscous solvent "Nujol" have been studied in detail. The complex dielectric constants of these mixtures at various concentrations have been measured at 10, 3, 2 and 1.3 cm.
Also measured are the individual dispersions of the polar constituents of the ternary mixture in solution in n-heptane at the same relative concentrations and the static dielectric constants of the above mixtures. The results are explained in terms of hindering forces influencing dipole rotation.
RESUME Le phOnom~ne de relaxation diOlectrique a Ot~ dtudi~ de fagon dOtaill~e dans le cas du chloroforme et du benzophOnone en solution dans r heptane normal ainsi que de m~lanoes binaires de chlorobenz~ne et de bromobenzOne dissous dans un solvant visqueux, le "Nujol". La constante diOlectrique complexe (parties r~elle et imaginaire) de ces m~langes a ~t~ mesur~e, pour diff&entes concentrations en compos~s polaires, ?l raide de microondes de 10, 3, 2 et 1.3 em. Les constantes di~leetriques statiques ont ~galement Ot~
mesurOes. Dans le eas des mOlanges ternaires, oit deux constituents polaires ~taient dissous dans r heptane normal, les mOmes proportions relatives que dans les m~langes ne contenant qu'un seul composO polaire ont Otd utilis~es; la contribution ?t la dispersion des ondes de chacun des constituents polaires a ainsi pu ~tre mesurOe et comparOe gt celle du m~me compos~ agissant seul. Les r~sultats obtenus sont interprOtks ~ raide de forces de friction qui s'opposent h la rotation des dipoles.
Z USA M M E N F A S S UNG Die dielektrische Relaxation yon Chloroform und Benzophenon in n-Heptan und yon biniiren L6sungen yon Chlorbenzol und Brombenzol in einem viskosen L6sunosmittel "Nujol" wurden ausffihrlich untersucht. Die komplexen dielektrischen Konstanten dieser L6sunoen wurden Jfir versehiedene Konzentrationen bei 10, 3, 2 und 1.3 cm gemessen. Ferner
wurden die individuellen Dispersionen der polaren Bestandteile der terngiren LOsun9 in n-Heptan bei der oleichen relativen Konzentration und statischen Dielektrizitiitskonstante wie bei den obigen L6sungen 9emessen. Die Ergebnisse werden auf Kr~fte zurfick9effihrt, welche die Dipolrotation erschweren.
* Part of the investigation reported in this paper was presented at the 8th European Congress on Molecular Spectroscopy held at Copenhagen, Denmark, August 14-20, 1965.
** Present address: Herff School of Engineering, Memphis State University, Memphis, Tenn., U.S.A.
Materials Science and Engineering - Elsevier Publishing Company, Amsterdam - Printed in the Netherlands
258
T . J . BHATTACHARYYA, T. V. GOPALAN, P. K. KADABA INTRODUCTION
The theories of Debye, Kauzmann 1 and others assume that, in the phenomenon of dielectric relaxation, the molecules retain their identity. The considerable amount of experimental evidence reported by various workers in the literature on dilute solutions of single polar liquids in non-polar solvents 2 supports such a view. Schallamach 3, in his studies on the binary mixtures of polar liquids of a somewhat complex nature at radio frequencies, was, on the other hand, led to believe that the dielectric relaxation mechanism cannot be directly connected with individual molecules, but is a disturbance of an appreciable region in the liquid, involving a volume nearly large enough to be representative in its composition of the bulk concentration. On this basis, any liquid, even if a mixture of two polar components, should have only one relaxation time. A study made in the kilocycle region4 of an equimolar mixture ofisobutyl bromide and isobutyl chloride at temperatures close to and below the melting point of the individual components seems to indicate a single dispersion region. Mixtures of several simple rigid polar molecules in various concentrations in non-polar solvents in the temperature range 0 to 100°C have been studied at a single frequency in the microwave region 5. The polar constituents were non-associated liquids. The measurements tend to indicate the persistence of two dispersion regions for these mixtures even at relatively high concentrations. Further results at the same frequency on the loss factor-temperature measurements of the mixtures, both associated and non-associated liquids, are reported in a recent paper 6. These results also show two dispersion regions in all the mixtures studied. Variable temperature curves are more difficult to interpret than variable frequency ones, especially if the change of relaxation time with temperature is small, as is the case with the above investigation. Measurements with variable frequency have the advantage that the static permitivity of the polar constituents is not varied during a set of measurements at one concentration. The present investigation is primarily concerned with the dielectric relaxation of benzophenone and chloroform in a neutral solvent. The effect of hindering forces on dipole rotation is discussed. The polar constituents have sufficiently different relaxation times and their individual dispersion curves are well established in the literature. The measurements have
been made at various concentrations over a range of frequencies at a single temperature. Complex dielectric constants of other mixtures such as nitro compounds, nitriles, halobenzenes and others are being measured at various frequencies and the dielectric relaxation of these mixtures will be discussed in subsequent papers. EXPERIMENTAL
The real and imaginary parts of the dielectric constants of the various mixtures reported in this investigation have been measured at 10, 3, 2 and 1 cm. In the case of the mixtures in the medium loss range, a reflection method developed by Surber 7 was found most suitable and this method was used. This method is based on observing the variation of the reflection coefficient as the depth of the liquid is varied by a movable micrometer-driven shortcircuit plunger. One advantage of this method is the direct determination of 2d, the wavelength in the dielectric. A slight modification of the experimental set-up involved the use of two slide-screw tuners, one to match the klystron to the line and the other to match the reflection from the right-angle bend. This insured a voltage standing-wave ratio of 1.02 + 0.01 with the liquid cell empty. For very low loss dielectrics the wave-guide losses begin to approach the same order of magnitude as the dielectric loss. In such liquids, the effect of the system losses can be eliminated by using several lengths of the dielectric column and by plotting the reciprocal of the standing-wave ratio against the length of the dielectric. The details are described in the ONR contract report 8. The accuracy in the determination of e', the real part of the dielectric constant, was 1% and in the determination of e", the imaginary part, was 3~o. Also measured were the static dielectric constants of the various mixtures at a frequency of 100 kc using a 716-C General Radio capacitance bridge. RESULTS AND DISCUSSION
The e' vs. concentration curves for the ternary mixtures ofbenzophenone and chloroform in n-heptane are shown in Fig. 1. It can be seen that when the data are extrapolated to infinite dilution, all the curves approach a value of 1.9 for e'. This is the value of e' for n-heptane. The e" vs. concentration curves are shown in Fig. 2. These curves are also not linear. While the 3 cm curve is almost a straight line, the 1.2 and 10 cm graphs deviate from linearity. Mater. Sci. Eno., 1 (1966/67} 257-262
259
DIELECTRIC BEHAVIOUR AND INTERMOLECULAR FORCES IN DIPOLAR MIXTURES
53 o
O~A.= 3.0xlOScn O--,Ao= 10.1 c m
49
o~,=
•
4.5
3.30 cm
a-~;k.= 199 c m A--~;ko= 1.30 c m
4.1
3.7
33
An analysis of the data in the concentration range from 0.1 to 0.3 mole fraction of the polar components of the ternary mixtures by a method suggested in the literature a ~ leads to two relaxation times. One of the relaxation times, z~, was found to lie between 3 x 10 -t2 and 4.2x 10 -x2 sec while the other, z2, varies from 9.7 x 10 -~2 to 37.4 x 10 -~2 sec with increase in concentration of the polar components from 0.1 to 0.3. The data for the ternary mixture in the concentration range below 0.1 mole fraction, on the other hand, do not lend themselves to accurate analysis. The data on binary mixtures of benzophenone in n-heptane as shown in Fig. 3 give
2.5
0.6
2.1 j i ~ i #
0.4
f
0
0.1
0.2 03 C in molefraction
04
Q5 ~,
Fig. 1. Variation of the real part of the dielectric constant e' vs. concentration C, of solution in n-heptane of benzophenone and chloroform. Temperature of measurement, 45 ___1°C. 20 = wavelength of measurement.
A plausible explanation of the deviations is as follows: The literature value of the critical wavelength of pure benzophenone 9 is 15.4 cm at 50°C and that of pure chloroform ~° is 1.4 cm at 25°C. If one assumes that molecular identity is preserved, then the rapid rise of the 10 cm graph at higher concentrations could be attributed to the effect of benzophenone being more predominant. Likewise, the effect of chloroform becomes more and more significant as we approach the 1 cm region.
2C 1.6
0,..~%,
=10 cm 0"-'~ ~%= 3 cm 0-~7%= 2 cm A--~,.= 1 cm
0.8
o
n
o .,
0(3
0.04
0.08
0:12
0:16
020
0.24
0.28
/
Q32
C in molefraction
Fig. 2. Variation o f the loss factor e" vs. concentration C, o f solution in n-heptane of benzophenone and chloroform. Temperature of measurement, 45 ___1 °C. 2o = wavelength of measurement.
2.0
2A
26
3.2
Fig. 3. Cole-Cole plots o f solution in n-heptane o f benzophenone at various concentrations. Temperature: 45 _+ 1 °C.
very good Cole-plots, almost approaching the Debye-circle, and lead to a relaxation time of about 1 0 - i t sec for all the concentrations studied. This is in very good agreement with the value of 10-x x sec found in the literature 9 for a dilute solution of benzophenone in n-heptane at. 40°C. A similar analysis of the data for the binary mixtures of chloroform in n-heptane leads to a relaxation time which lies between 2.89 x 10 -x2 and 3.74 x 10 -~2 sec when the chloroform concentration in the mixture reduces from 0.32 to 0.08. The literature value for the relaxation time of chloroform a2 in dilute solution in n-heptane is 3.1 x 10-~2 sec at 40°C. So by comparing the relaxation times of the single component mixtures with the resolved relaxation times, za and z2, for the ternary mixture, it would be reasonable to attribute zx to chloroform and z2 to benzophenone. The resolved relaxation times, ~x and z2, for the ternary mixture would be different from the corresponding values for the single component mixtures because of the difference in molecular environment. It can be noted that the resolved relaxation times, z2, are much larger when compared with the relaxation times for the corresponding single component mixture. This would mean that the benzophenone molecules experience less rotational and Mater. Sci. Eng., 1 (1966/67) 257-262
260
T . J . BHATTACHARYYA, T. V. GOPALAN, P. K. KADABA
translational freedom of motion in the ternary mixture for the concentration range studied. The relaxation time v s . concentration curve for the above ternary mixture is shown in Fig. 4. The results thus seem to indicate that the polar components preserve their molecular identity in mixtures. This is in conformity with the theories of Debye, Kauzmann 1 and others. It is, however, interesting to note that there is a critical concentration roughly about 0.1 mole fraction at which both the relaxation times increase with the decrease of concentration below this critical concentration. Above the critical concentration, the relaxation times show the expected behaviour, that is, increase with increase in concentration of the polar components, which incidentally increases the viscosity of the mixture.
35.0
0-~ TI,CHCL 3 • "->'~,C13H100
310
27.0 23.0 19.0 ,%1
~) 15.0 x
7.O 3.0
0
"0"0-0.0.0_______. 0 __----~ 0 ~
0.10
Q20 (230 C in rnolefcaction
0.40
QSO D
Fig. 4. Variation of the relaxation times zl and z= vs. concentration C, of solution in n-heptane of benzophenone and chloroform. Temperature 45 + I°C.
As an explanation, it is suggested that dipoledipole interaction produces a hindering effect on the rotation of the individual molecules and self-association in one of the polar components, possibly chloroform, inhibits the hindering effect at higher concentration. With increase in dilution, more and more chloroform molecules would become free as
a result of the breaking of the hydrogen bonds. This would increase the hindering effect due to dipoledipole interaction and in turn the relaxation time of the polar components. It can be noticed that the viscosity data shown in Table 1, below 0.1 mole fraction, which is the critical concentration according to Fig. 4, do not show any appreciable change with concentration and differ very slightly from the viscosity of the solvent. TABLE 1:
VISCOSITIES r/ FOR MIXTURE OF B E N Z O P H E N O N E AND CHLOROFORM IN n - H E P T A N E AT
45°C
Solute concentration in mole fraction: 0.3 0.2 0.1 0.08 0.06 0.04 0.02 (Pure heptane) Viscosity (11) in centipoises : 0.74 0.59 0.39 0.37 0.35
0.34 0.34 0.34
Thus the effect, if any, of viscosity in trying to reduce the relaxation times with increase in dilution would not be significant and the effect of the hindering forces would be the predominant factor in the process. Above the critical concentration the increase is rather rapid and the effect of viscosity would thus be the more predominant factor in determining the loss. At the critical concentration, the hindering effect and the effect of viscosity tend to balance each other. The loss curves of benzophenone in n-heptane show a normal behaviour typical of a non-associated polar compound in a non-polar solvent. The behaviour of chloroform in n-heptane, however, is interesting. The relaxation v s . concentration for this binary mixture is shown in Fig. 5. It can be seen from the Figure that there is a tendency for the relaxation time to increase with increase in dilution. This can be taken as an indication that the chloroform molecules form some associated groups through hydrogen bonding and the mutual hindering effect of the chloroform molecules seems to predominate over the effect of viscosity. This is similar to the effect observed for the above ternary mixture. However, contrary to our experience with the ternary mixtures, we do not find any critical concentration in this case. The viscosity of chloroform is 0.424 cP at 50°C. and that of heptane is 0.34 cP at 45°C. Hence the mixture is not expected to differ much from the solvent heptane. Evidence of self-association in chloroform is also available through infrared studies of dilute solutions of chloroform in carbon tetrachloridela-*s Mater. Sci. Eng., 1 (1966/67) 257-262
261
DIELECTRIC BEHAVIOUR AND INTERMOLECULAR FORCES IN DIPOLAR MIXTURES
&8
relaxation time in both these cases. A trend towards a maximum in the relaxation time has been reported in an earlier investigation 16 for binary mixtures of chlorobenzene and bromobenzene in 4.55~ mixture of cyclohexane in paraffin. The measurements were, however, restricted to only two frequencies and relatively few concentrations.
N
c.,
3.6
T 3.4 ~ 3.2 3.0
22
O 2C
2.8
0.40
&2
d34
o.•6
C in molefraction Fig. 5. Variation of relaxation time • vs. concentration C, of chloroform in solution in n-heptane at 45 + I°C.
118 9x 16
o/
14
\:
[]
In order to investigate further the influence of hindering forces on dipole rotation, the relaxation of chlorobenzene and bromobenzene which are both non-associated liquids were studied in a viscous non-polar solvent "Nujol". The highly viscous solvent was chosen for the following reason. If our assumption concerning the influence of hindering effect on dipole rotation is true, we may expect the hindering effect and consequently the relaxation time to decrease with increase in dilution of the polar component. This would be as a result of decrease in dipole density with dilution. With a highly viscous solvent, the mixture viscosity would increase with decrease in concentration of the polar component. This would have the effect of increasing the relaxation time. One would then expect a maximum in the relaxation time at a certain critical concentration. With a solvent of low viscosity such as n-heptane or cyclohexane, the change in relaxation time with change in the viscosity of the mixture would be in the same direction as the change in the relaxation time due to the hindering effect. The relaxation time v s . concentration curves for the binary mixtures of chlorobenzene and bromobenzene in Nujol are shown in Fig. 6. It can be seen that the relaxation time for both the halobenzenes reaches a peak when the percentage of Nujol is in excess of 5 0 ~ in the case of bromobenzene-Nujol mixture and in excess of 4 0 ~ in the case of chlorobenzene-Nujol mixture. As stated above, the opposing influences of viscosity and hindering effect on dipole rotation would explain the peak in the
12
10
2C)
3~0
4~0
50
60
Percentage by volume of the polar component
70
Fig. 6. Variation of relaxation time T vs. concentration of chlorobenzene and bromobenzene in solution in Nujol at 26 + I°C. O, bromobenzene in Nujol; El, chlorobenzene in Nujol.
ACKNOWLEDGEMENT
This investigation was supported partly by a contract with the U. S. Atomic Energy Commission and partly by a grant from the National Science Foundation, U.S.A. REFERENCES 1 (a) P. DEBYE, Polar Molecules, Chemical Catalogue Co., Inc., New York, 1929. (b) W. KAUZMANN, Rev. Mod. Phys., 14 (1942) 1. 2 J. G. POWLKSAND C. P. SMGH, Physical Methods of Organic Chemistry, Chapter XXXV, Part III, Vol. 1, Interscience, New York, 2nd edn., 1954. 3 A. SCnALLAMACH, Trans. Faraday Soc., 42A (1946) 180. 4 D. J. DENr{EY, J. Chem. Phys., 30 (1959) 1019. 5 P. K. KADABA,J. Phys. Chem., 62 (1958) 887. 6 S. K. GARGANDP. K. KADABA,J. Phys. Chem., 69 (1965) 674. 7 W. H. StrRBER, JR., J. Appl. Phys., 19 (1948) 514. 8 Methods of measurements of the dielectric constants of liquids at microwave frequencies, Techn. Rept. No. 1 ; ONR Contract N6-Ori-105, Task order IV; 1948. 9 G. B. RATm~tAN, A. J. CURTIS, P. L. McGEER AND C. P. SMVTH, J. Chem. Phys., 25 (1956) 412. 10 W. P. CONNERAND C. P. SMVTIa,J. Am. Chem. Soc., 65 (1943) 382.
Mater. Sci. Eng., 1 (1966/67) 257-262
262
T . J . BHATTACHARYYA, T. V. GOPALAN, P. K. KADABA
11 K. BEROMANNAND C. P. SMYTrt, J. Phys. Chem., 64 (1960) 665. 12 D. H. WHIFFENAND H. W. THOMPSON, Trans. Faraday Soc., 42A (1946) 122. 13 R. B. BERNSTEINAND M. TAMERS,J. Chem. Phys., 23 (1955) 2201.
14 U. LIDEL AND E. D. BECKER, J. Chem. Phys., 25 (1956) 173. 15 E. D. BECKER, Spectrochim. Acta, 15 (1959) 743. 16 D. H. WHIFFEN AND H. W. THOMPSON, Trans. Faraday Soc., 42A (1946) 114.
Mater. Sci. Eng., 1 (1966/67) 257-262
S UMMA R Y The dielectric relaxation of chloroform and benzophenone & n-heptane and of binary mixtures of chlorobenzene and bromobenzene in a viscous solvent "Nujol" have been studied in detail. The complex dielectric constants of these mixtures at various concentrations have been measured at 10, 3, 2 and 1.3 cm.
Also measured are the individual dispersions of the polar constituents of the ternary mixture in solution in n-heptane at the same relative concentrations and the static dielectric constants of the above mixtures. The results are explained in terms of hindering forces influencing dipole rotation.
RESUME Le phOnom~ne de relaxation diOlectrique a Ot~ dtudi~ de fagon dOtaill~e dans le cas du chloroforme et du benzophOnone en solution dans r heptane normal ainsi que de m~lanoes binaires de chlorobenz~ne et de bromobenzOne dissous dans un solvant visqueux, le "Nujol". La constante diOlectrique complexe (parties r~elle et imaginaire) de ces m~langes a ~t~ mesur~e, pour diff&entes concentrations en compos~s polaires, ?l raide de microondes de 10, 3, 2 et 1.3 em. Les constantes di~leetriques statiques ont ~galement Ot~
mesurOes. Dans le eas des mOlanges ternaires, oit deux constituents polaires ~taient dissous dans r heptane normal, les mOmes proportions relatives que dans les m~langes ne contenant qu'un seul composO polaire ont Otd utilis~es; la contribution ?t la dispersion des ondes de chacun des constituents polaires a ainsi pu ~tre mesurOe et comparOe gt celle du m~me compos~ agissant seul. Les r~sultats obtenus sont interprOtks ~ raide de forces de friction qui s'opposent h la rotation des dipoles.
Z USA M M E N F A S S UNG Die dielektrische Relaxation yon Chloroform und Benzophenon in n-Heptan und yon biniiren L6sungen yon Chlorbenzol und Brombenzol in einem viskosen L6sunosmittel "Nujol" wurden ausffihrlich untersucht. Die komplexen dielektrischen Konstanten dieser L6sunoen wurden Jfir versehiedene Konzentrationen bei 10, 3, 2 und 1.3 cm gemessen. Ferner
wurden die individuellen Dispersionen der polaren Bestandteile der terngiren LOsun9 in n-Heptan bei der oleichen relativen Konzentration und statischen Dielektrizitiitskonstante wie bei den obigen L6sungen 9emessen. Die Ergebnisse werden auf Kr~fte zurfick9effihrt, welche die Dipolrotation erschweren.
* Part of the investigation reported in this paper was presented at the 8th European Congress on Molecular Spectroscopy held at Copenhagen, Denmark, August 14-20, 1965.
** Present address: Herff School of Engineering, Memphis State University, Memphis, Tenn., U.S.A.
Materials Science and Engineering - Elsevier Publishing Company, Amsterdam - Printed in the Netherlands
258
T . J . BHATTACHARYYA, T. V. GOPALAN, P. K. KADABA INTRODUCTION
The theories of Debye, Kauzmann 1 and others assume that, in the phenomenon of dielectric relaxation, the molecules retain their identity. The considerable amount of experimental evidence reported by various workers in the literature on dilute solutions of single polar liquids in non-polar solvents 2 supports such a view. Schallamach 3, in his studies on the binary mixtures of polar liquids of a somewhat complex nature at radio frequencies, was, on the other hand, led to believe that the dielectric relaxation mechanism cannot be directly connected with individual molecules, but is a disturbance of an appreciable region in the liquid, involving a volume nearly large enough to be representative in its composition of the bulk concentration. On this basis, any liquid, even if a mixture of two polar components, should have only one relaxation time. A study made in the kilocycle region4 of an equimolar mixture ofisobutyl bromide and isobutyl chloride at temperatures close to and below the melting point of the individual components seems to indicate a single dispersion region. Mixtures of several simple rigid polar molecules in various concentrations in non-polar solvents in the temperature range 0 to 100°C have been studied at a single frequency in the microwave region 5. The polar constituents were non-associated liquids. The measurements tend to indicate the persistence of two dispersion regions for these mixtures even at relatively high concentrations. Further results at the same frequency on the loss factor-temperature measurements of the mixtures, both associated and non-associated liquids, are reported in a recent paper 6. These results also show two dispersion regions in all the mixtures studied. Variable temperature curves are more difficult to interpret than variable frequency ones, especially if the change of relaxation time with temperature is small, as is the case with the above investigation. Measurements with variable frequency have the advantage that the static permitivity of the polar constituents is not varied during a set of measurements at one concentration. The present investigation is primarily concerned with the dielectric relaxation of benzophenone and chloroform in a neutral solvent. The effect of hindering forces on dipole rotation is discussed. The polar constituents have sufficiently different relaxation times and their individual dispersion curves are well established in the literature. The measurements have
been made at various concentrations over a range of frequencies at a single temperature. Complex dielectric constants of other mixtures such as nitro compounds, nitriles, halobenzenes and others are being measured at various frequencies and the dielectric relaxation of these mixtures will be discussed in subsequent papers. EXPERIMENTAL
The real and imaginary parts of the dielectric constants of the various mixtures reported in this investigation have been measured at 10, 3, 2 and 1 cm. In the case of the mixtures in the medium loss range, a reflection method developed by Surber 7 was found most suitable and this method was used. This method is based on observing the variation of the reflection coefficient as the depth of the liquid is varied by a movable micrometer-driven shortcircuit plunger. One advantage of this method is the direct determination of 2d, the wavelength in the dielectric. A slight modification of the experimental set-up involved the use of two slide-screw tuners, one to match the klystron to the line and the other to match the reflection from the right-angle bend. This insured a voltage standing-wave ratio of 1.02 + 0.01 with the liquid cell empty. For very low loss dielectrics the wave-guide losses begin to approach the same order of magnitude as the dielectric loss. In such liquids, the effect of the system losses can be eliminated by using several lengths of the dielectric column and by plotting the reciprocal of the standing-wave ratio against the length of the dielectric. The details are described in the ONR contract report 8. The accuracy in the determination of e', the real part of the dielectric constant, was 1% and in the determination of e", the imaginary part, was 3~o. Also measured were the static dielectric constants of the various mixtures at a frequency of 100 kc using a 716-C General Radio capacitance bridge. RESULTS AND DISCUSSION
The e' vs. concentration curves for the ternary mixtures ofbenzophenone and chloroform in n-heptane are shown in Fig. 1. It can be seen that when the data are extrapolated to infinite dilution, all the curves approach a value of 1.9 for e'. This is the value of e' for n-heptane. The e" vs. concentration curves are shown in Fig. 2. These curves are also not linear. While the 3 cm curve is almost a straight line, the 1.2 and 10 cm graphs deviate from linearity. Mater. Sci. Eno., 1 (1966/67} 257-262
259
DIELECTRIC BEHAVIOUR AND INTERMOLECULAR FORCES IN DIPOLAR MIXTURES
53 o
O~A.= 3.0xlOScn O--,Ao= 10.1 c m
49
o~,=
•
4.5
3.30 cm
a-~;k.= 199 c m A--~;ko= 1.30 c m
4.1
3.7
33
An analysis of the data in the concentration range from 0.1 to 0.3 mole fraction of the polar components of the ternary mixtures by a method suggested in the literature a ~ leads to two relaxation times. One of the relaxation times, z~, was found to lie between 3 x 10 -t2 and 4.2x 10 -x2 sec while the other, z2, varies from 9.7 x 10 -~2 to 37.4 x 10 -~2 sec with increase in concentration of the polar components from 0.1 to 0.3. The data for the ternary mixture in the concentration range below 0.1 mole fraction, on the other hand, do not lend themselves to accurate analysis. The data on binary mixtures of benzophenone in n-heptane as shown in Fig. 3 give
2.5
0.6
2.1 j i ~ i #
0.4
f
0
0.1
0.2 03 C in molefraction
04
Q5 ~,
Fig. 1. Variation of the real part of the dielectric constant e' vs. concentration C, of solution in n-heptane of benzophenone and chloroform. Temperature of measurement, 45 ___1°C. 20 = wavelength of measurement.
A plausible explanation of the deviations is as follows: The literature value of the critical wavelength of pure benzophenone 9 is 15.4 cm at 50°C and that of pure chloroform ~° is 1.4 cm at 25°C. If one assumes that molecular identity is preserved, then the rapid rise of the 10 cm graph at higher concentrations could be attributed to the effect of benzophenone being more predominant. Likewise, the effect of chloroform becomes more and more significant as we approach the 1 cm region.
2C 1.6
0,..~%,
=10 cm 0"-'~ ~%= 3 cm 0-~7%= 2 cm A--~,.= 1 cm
0.8
o
n
o .,
0(3
0.04
0.08
0:12
0:16
020
0.24
0.28
/
Q32
C in molefraction
Fig. 2. Variation o f the loss factor e" vs. concentration C, o f solution in n-heptane of benzophenone and chloroform. Temperature of measurement, 45 ___1 °C. 2o = wavelength of measurement.
2.0
2A
26
3.2
Fig. 3. Cole-Cole plots o f solution in n-heptane o f benzophenone at various concentrations. Temperature: 45 _+ 1 °C.
very good Cole-plots, almost approaching the Debye-circle, and lead to a relaxation time of about 1 0 - i t sec for all the concentrations studied. This is in very good agreement with the value of 10-x x sec found in the literature 9 for a dilute solution of benzophenone in n-heptane at. 40°C. A similar analysis of the data for the binary mixtures of chloroform in n-heptane leads to a relaxation time which lies between 2.89 x 10 -x2 and 3.74 x 10 -~2 sec when the chloroform concentration in the mixture reduces from 0.32 to 0.08. The literature value for the relaxation time of chloroform a2 in dilute solution in n-heptane is 3.1 x 10-~2 sec at 40°C. So by comparing the relaxation times of the single component mixtures with the resolved relaxation times, za and z2, for the ternary mixture, it would be reasonable to attribute zx to chloroform and z2 to benzophenone. The resolved relaxation times, ~x and z2, for the ternary mixture would be different from the corresponding values for the single component mixtures because of the difference in molecular environment. It can be noted that the resolved relaxation times, z2, are much larger when compared with the relaxation times for the corresponding single component mixture. This would mean that the benzophenone molecules experience less rotational and Mater. Sci. Eng., 1 (1966/67) 257-262
260
T . J . BHATTACHARYYA, T. V. GOPALAN, P. K. KADABA
translational freedom of motion in the ternary mixture for the concentration range studied. The relaxation time v s . concentration curve for the above ternary mixture is shown in Fig. 4. The results thus seem to indicate that the polar components preserve their molecular identity in mixtures. This is in conformity with the theories of Debye, Kauzmann 1 and others. It is, however, interesting to note that there is a critical concentration roughly about 0.1 mole fraction at which both the relaxation times increase with the decrease of concentration below this critical concentration. Above the critical concentration, the relaxation times show the expected behaviour, that is, increase with increase in concentration of the polar components, which incidentally increases the viscosity of the mixture.
35.0
0-~ TI,CHCL 3 • "->'~,C13H100
310
27.0 23.0 19.0 ,%1
~) 15.0 x
7.O 3.0
0
"0"0-0.0.0_______. 0 __----~ 0 ~
0.10
Q20 (230 C in rnolefcaction
0.40
QSO D
Fig. 4. Variation of the relaxation times zl and z= vs. concentration C, of solution in n-heptane of benzophenone and chloroform. Temperature 45 + I°C.
As an explanation, it is suggested that dipoledipole interaction produces a hindering effect on the rotation of the individual molecules and self-association in one of the polar components, possibly chloroform, inhibits the hindering effect at higher concentration. With increase in dilution, more and more chloroform molecules would become free as
a result of the breaking of the hydrogen bonds. This would increase the hindering effect due to dipoledipole interaction and in turn the relaxation time of the polar components. It can be noticed that the viscosity data shown in Table 1, below 0.1 mole fraction, which is the critical concentration according to Fig. 4, do not show any appreciable change with concentration and differ very slightly from the viscosity of the solvent. TABLE 1:
VISCOSITIES r/ FOR MIXTURE OF B E N Z O P H E N O N E AND CHLOROFORM IN n - H E P T A N E AT
45°C
Solute concentration in mole fraction: 0.3 0.2 0.1 0.08 0.06 0.04 0.02 (Pure heptane) Viscosity (11) in centipoises : 0.74 0.59 0.39 0.37 0.35
0.34 0.34 0.34
Thus the effect, if any, of viscosity in trying to reduce the relaxation times with increase in dilution would not be significant and the effect of the hindering forces would be the predominant factor in the process. Above the critical concentration the increase is rather rapid and the effect of viscosity would thus be the more predominant factor in determining the loss. At the critical concentration, the hindering effect and the effect of viscosity tend to balance each other. The loss curves of benzophenone in n-heptane show a normal behaviour typical of a non-associated polar compound in a non-polar solvent. The behaviour of chloroform in n-heptane, however, is interesting. The relaxation v s . concentration for this binary mixture is shown in Fig. 5. It can be seen from the Figure that there is a tendency for the relaxation time to increase with increase in dilution. This can be taken as an indication that the chloroform molecules form some associated groups through hydrogen bonding and the mutual hindering effect of the chloroform molecules seems to predominate over the effect of viscosity. This is similar to the effect observed for the above ternary mixture. However, contrary to our experience with the ternary mixtures, we do not find any critical concentration in this case. The viscosity of chloroform is 0.424 cP at 50°C. and that of heptane is 0.34 cP at 45°C. Hence the mixture is not expected to differ much from the solvent heptane. Evidence of self-association in chloroform is also available through infrared studies of dilute solutions of chloroform in carbon tetrachloridela-*s Mater. Sci. Eng., 1 (1966/67) 257-262
261
DIELECTRIC BEHAVIOUR AND INTERMOLECULAR FORCES IN DIPOLAR MIXTURES
&8
relaxation time in both these cases. A trend towards a maximum in the relaxation time has been reported in an earlier investigation 16 for binary mixtures of chlorobenzene and bromobenzene in 4.55~ mixture of cyclohexane in paraffin. The measurements were, however, restricted to only two frequencies and relatively few concentrations.
N
c.,
3.6
T 3.4 ~ 3.2 3.0
22
O 2C
2.8
0.40
&2
d34
o.•6
C in molefraction Fig. 5. Variation of relaxation time • vs. concentration C, of chloroform in solution in n-heptane at 45 + I°C.
118 9x 16
o/
14
\:
[]
In order to investigate further the influence of hindering forces on dipole rotation, the relaxation of chlorobenzene and bromobenzene which are both non-associated liquids were studied in a viscous non-polar solvent "Nujol". The highly viscous solvent was chosen for the following reason. If our assumption concerning the influence of hindering effect on dipole rotation is true, we may expect the hindering effect and consequently the relaxation time to decrease with increase in dilution of the polar component. This would be as a result of decrease in dipole density with dilution. With a highly viscous solvent, the mixture viscosity would increase with decrease in concentration of the polar component. This would have the effect of increasing the relaxation time. One would then expect a maximum in the relaxation time at a certain critical concentration. With a solvent of low viscosity such as n-heptane or cyclohexane, the change in relaxation time with change in the viscosity of the mixture would be in the same direction as the change in the relaxation time due to the hindering effect. The relaxation time v s . concentration curves for the binary mixtures of chlorobenzene and bromobenzene in Nujol are shown in Fig. 6. It can be seen that the relaxation time for both the halobenzenes reaches a peak when the percentage of Nujol is in excess of 5 0 ~ in the case of bromobenzene-Nujol mixture and in excess of 4 0 ~ in the case of chlorobenzene-Nujol mixture. As stated above, the opposing influences of viscosity and hindering effect on dipole rotation would explain the peak in the
12
10
2C)
3~0
4~0
50
60
Percentage by volume of the polar component
70
Fig. 6. Variation of relaxation time T vs. concentration of chlorobenzene and bromobenzene in solution in Nujol at 26 + I°C. O, bromobenzene in Nujol; El, chlorobenzene in Nujol.
ACKNOWLEDGEMENT
This investigation was supported partly by a contract with the U. S. Atomic Energy Commission and partly by a grant from the National Science Foundation, U.S.A. REFERENCES 1 (a) P. DEBYE, Polar Molecules, Chemical Catalogue Co., Inc., New York, 1929. (b) W. KAUZMANN, Rev. Mod. Phys., 14 (1942) 1. 2 J. G. POWLKSAND C. P. SMGH, Physical Methods of Organic Chemistry, Chapter XXXV, Part III, Vol. 1, Interscience, New York, 2nd edn., 1954. 3 A. SCnALLAMACH, Trans. Faraday Soc., 42A (1946) 180. 4 D. J. DENr{EY, J. Chem. Phys., 30 (1959) 1019. 5 P. K. KADABA,J. Phys. Chem., 62 (1958) 887. 6 S. K. GARGANDP. K. KADABA,J. Phys. Chem., 69 (1965) 674. 7 W. H. StrRBER, JR., J. Appl. Phys., 19 (1948) 514. 8 Methods of measurements of the dielectric constants of liquids at microwave frequencies, Techn. Rept. No. 1 ; ONR Contract N6-Ori-105, Task order IV; 1948. 9 G. B. RATm~tAN, A. J. CURTIS, P. L. McGEER AND C. P. SMVTH, J. Chem. Phys., 25 (1956) 412. 10 W. P. CONNERAND C. P. SMVTIa,J. Am. Chem. Soc., 65 (1943) 382.
Mater. Sci. Eng., 1 (1966/67) 257-262
262
T . J . BHATTACHARYYA, T. V. GOPALAN, P. K. KADABA
11 K. BEROMANNAND C. P. SMYTrt, J. Phys. Chem., 64 (1960) 665. 12 D. H. WHIFFENAND H. W. THOMPSON, Trans. Faraday Soc., 42A (1946) 122. 13 R. B. BERNSTEINAND M. TAMERS,J. Chem. Phys., 23 (1955) 2201.
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Mater. Sci. Eng., 1 (1966/67) 257-262