Journal of Solution Chemistry, Vol. 28, No. 8, 1999

Temperature-Dependent Dielectric Relaxation of 2-Ethoxyethanol, Ethanol, and 1-Propanol in Dimethylformamide Solution Using the TimeDomain Technique P. W. Khirade,1 Ajay Chaudhari,1 J. B. Shinde,2 S. N. Helambe,2 and S. C. Mehrotra3,* Received July 12, 1998; revised May 11, 1999 Complex reflection coefficients for 2-ethoxyethanol-dimethylformamide (DMF), ethanol-DMF, and 1-propanol-DMF mixtures at several temperatures from 20 to 50° and the frequency range 10 MHz to 10 GHz were determined by timedomain spectroscopy in reflection mode. Fourier transforms and least-squares fitting were used to obtain complex permittivity, static dielectric constant, and relaxation time. The excess dielectric parameters, Kirkwood correlation factors, and thermodynamic properties for the binary mixtures were also determined. The static dielectric constant for the mixtures was fitted well with the modified Bruggeman model. KEY WORDS: Permittivity; time-domain technique; excess dielectric parameters; Kirkwood correlation factor.

1. INTRODUCTION The dielectric relaxation of solute-solvent mixtures gives information about molecular interactions in the system. In the study of dielectric relaxation parameters, the Kirkwood correlation factor of binary mixtures has consider-

Department of Physics, Dr. B.A.M. University, Aurangabad 431 004. G. and Research Centre, Deogiri college, Aurangabad. 3Department of Electronics and Computer Science, Dr. B.A.M. University, Aurangabad 431 004. Email: [email protected]. 1

2 P.

1031 0095-9782/99/0800-1031$16.00/0 C 1999 Plenum Publishing Corporation

Khirade, Chaudharl, Shinde, Helambe, and Mehrotra

1032

Fig. 1. e*(w)spectrum.

able significance in providing valuable information about solute-solvent interaction. In this study, DMF has been used as the solvent and 2-ethoxyethanol, etHanoi, and 1-propanol as solutes. Time-domain reflectometry(1-5) (TDR) was used to obtain the dielectric parameters. With these parameters, the excess dielectric constant, excess inverse relaxation time, Kirkwood correlation factor, and Bruggeman factor may be obtained. A detailed dielectric study of the above systems at temperatures from 20 to 50°C is reported. 2. EXPERIMENTAL DMF (AR grade), ethanol (spectroscopy grade), 1-propanol (AR grade), and 2-ethoxyethanol (Merck grade) were used without further purification. Table I.

Comparison of Data for Pure liquids with Literature Values at 20°C

E0 This work Ethanol 1-Propanol 2-Ethoxyethanol

DMF

25.71 20.05 16.98 41.3

Lit 25.43" 20.45b

— 39.8C (24°C)

p (g-cm -3) This work

0.7894 0.8033 0.9296 0.9489

Lit 0.7893" 0.8035e 0.9297f 0.9487g

"Digest of Literature on Dielectrics (National Academy of Sciences, Washington, DC, 1976). bDigest of Literature on Dielectrics (National Academy of Sciences, Washington, DC, 1976). cSame as reference 19. dR. C. Weast, Ed. Handbook of Chemistry and Physics, (51 Ed., CRC Cleveland, OH 1970-1). eR. C. Weast, Ed. Handbook of Chemistry and Physics, (51 Ed., CRC Cleveland, OH 1970-1). fR. C. Weast, Ed. Handbook of Chemistry and Physics, (51 Ed., CRC Cleveland, OH 1970-1). gR. C. Weast, Ed. Handbook of Chemistry and Physics, (51 Ed., CRC Cleveland, OH 1970-1).

Temperature-Dependent Dielectric Relaxation Table II.

1033

Dielectric Relaxation Parameters for 2-Ethoxyethanol-DMF Mixtures

V

E0

0 10 20 30 40 50 60 70 80 90 100

16.9(1)b 17.9 (7) 21.9(3) 23.8 (6) 26.6 (2) 29.7 (8) 32.2(1) 36.6 (3) 36.9(1) 37.9 (5) 41.3(3)

0 10 20 30 40 50 60 70 80 90 100

15.8 (7) 17.0 (7) 19.1(1) 21.9(8) 24.3 (8) 26.4 (8) 29.7 (5) 31.8(1) 33.6 (9) 35.0 (6) 36.0 (1)

T(ps)

E0

48.1 (6) 52.8 (2) 45.8 (6) 41.3(1) 34.9 (2) 30.5 (3) 28.5 (3) 25.0 (6) 21.1 (3) 17.1 (8) 15.0 (4)

16.4(1) 17.5(1) 20.2(1) 22.6(1) 25.0(1) 27.5 (7) 30.3 (1) 33.6 (5) 37.4 (5) 34.0 (8) 38.2 (3)

36.6 (3) 33.4 (4) 31.4(5) 28.6 (3) 25.1 (2) 23.2 (6) 19.6 (3) 17.2 (4) 14.8 (1) 13.9 (2) 11.2(9)

13.9(4) 16.4 (6) 18.2 (7) 21.4(5) 23.9 (7) 25.7 (6) 27.7 (9) 29.5 (7) 32.3(1) 33.1 (4) 34.5 (2)

20°C

30°C

40°C

a

T(pS)

40.4 (9) 41.8(8) 38.6 (6) 34.2 (5) 30.0 (3) 26.6 (3) 23.2 (2) 20.7 (5) 18.2 (9) 13.0(7) 13.3 (5) 50°C

27.2 (9) 24.3 (3) 27.3 (3) 24.1 (2) 23.1 (2) 20.6(1) 19.1 (2) 15.6 (8) 15.5 (3) 12.7 (3) 10.3 (4)

Volume % DMF. Numbers in brackets indicate uncertainty, e.g., 16.9(1) means 16.9 ±0.1.

b

The solutions were prepared at different volume percentages of 2-ethoxyethanol, ethanol, and 1-propanol in DMF in steps of 10%, at room temperature, assuming ideal mixing behavior. The mole fractions are calculated from the volume-fraction and density data. The complex permittivity spectra were studied using the TDR(6,7) method. A Tektronix 7854 sampling oscilloscope with 7S12 TDR unit was used. A fast-rising step voltage pulse of 25 psec rise time generated by a tunnel diode was propagated through a coaxial line system. The sample was placed at the end of the coaxial line in a standard military application (SMA) coaxial cell of 3.5 mm outer diameter and 1.35 mm effective pin length. All measurements were done under open load conditions. The change in the pulse on reflection from the sample placed in the cell was monitored by the sampling oscilloscope. In this experiment, a time window of 5 ns was used. The reflected pulses without sample R1(t) and with sample Rx(t) were digitized at 1024 points and transferred to a computer through a general-purpose interface bus (GPIB) card.

Khirade, Chaudhari, Shinde, Helambe, and Mehrotra

1034

Table III.

Dielectric Relaxation Parameters for Ethanol-DMF Mixtures

pd

E0

0 10 20 30 40 50 60 70 80 90 100

25.7 (2) 28.5 (3) 30.3 (6) 31.2(8) 33.1 (6) 34.0 (8) 36.4 (4) 37.6 (6) 39.1 (4) 40.0 (3) 41.3(1)

0 10 20 30 40 50 60 70 80 90 100

22.2 26.4 27.9 28.9 30.5 32.1 33.2 35.1 35.9 37.7 36.0

T(ps)

30°C

20°C 130.7(1) 106.7 (2) 82.8 (4) 66.3 (5) 52.1 (2) 44.0 (3) 37.3 (1) 31.7(2) 26.1 (1) 21.5(1) 15.0 (2)

23.4 27.7 28.8 30.8 32.8 33.7 35.1 37.3 36.8 39.1 38.2

90.1 (3) 82.0 (2) 66.6 (2) 55.0(1) 45.6 (1) 37.0 (4) 31.0(1) 26.4 (5) 21.5 (3) 18.3 (9) 13.3(2)

(2) (3) (3) (2) (3) (3) (4) (7) (4) (3) (4)

40°C (2) (5) (3) (4) (2) (3) (4) (4) (6) (8) (3)

T(ps)

E0

50°C 71.7(0) 68.2 (5) 54.9 (1) 45.8 (4) 37.4 (2) 31.4(1) 25.9 (7) 22.5 (6) 18.6 (2) 15.6 (2) 11.2(4)

20.4 (4) 25.2 (6) 26.3 (6) 28.5 (3) 29.6 (5) 31.5(3) 32.5 (4) 33.8 (3) 34.6 (6) 35.8 (8) 34.5 (2)

53.7 (3) 53.3 (4) 46.0 (3) 37.9 (1) 32.0 (2) 27.3 (1) 23.0(1) 20.0(1) 17.0 (2) 14.1 (6) 10.3 (3)

The temperature controller system with a water bath and a thermostat maintained the temperature constant within ± 1°C. The sample cell was surrounded by an insulating container through which the constant temperature water was circulated. 3. DATA ANALYSIS

The time-dependent data were processed to obtain complex reflection coefficient spectra p*(w) over the frequency range 10 MHz to 10 GHz using the Fourier transformation(8,9) where p(w) and q(w) are Fourier transforms of [R 1 (t) — RX(t) and [R 1 (t) + R x (t)], respectively, c is the velocity of light, w is angular frequency, d is the effective pin length, and j = R-1.

Temperature-Dependent Dielectric Relaxation

1035

Table IV. Dielectric Relaxation Parameters for 1-Propanol-DMF Mixtures

pd

E0

0 10 20 30 40 50 60 70 80 90 100

20.0 (2) 23.2 (6) 24.6(1) 26.2 (3) 28.8 (9) 30.5 (1) 33.1(1) 35.9 (4) 36.8 (3) 38.9 (2) 41.3 (2)

0 10 20 30 40 50 60 70 80 90 100

17.3 (3) 20.8(1) 22.4 (3) 24.4 (4) 26.5 (3) 28.5 (3) 31.1 (6) 32.7 (4) 35.0 (5) 36.6 (5) 36.0 (2)

T(pS)

T(ps)

E0

20°C

30°C 267.4 (0) 161.3(4) 1 16.0 (6) 85.4 (6) 64.1 (3) 51.1 (9) 39.4 (4) 32.1 (7) 27.0 (4) 22.3 (8) 15.0(1)

18.9 (3) 22.0 (2) 23.6 (4) 25.3 (3) 27.4 (5) 29.4 (7) 31.8(8) 33.9 (8) 37.2 (5) 39.1 (3) 38.2 (6)

86.6(1) 89.8 (9) 69.3 (3) 52.2 (7) 42.5 (2) 34.4(1) 29.2 (4) 23.6 (7) 18.9 (8) 14.8 (6) 11.2(3)

15.9 (4) 19.4 (3) 21.5(3) 23.9 (3) 26.1 (5) 28.2 (4) 30.3 (5) 31.8(8) 34.3 (3) 36.2 (3) 34.5(1)

40oC

133.85 (2) 108.64 (4) 84.87 (8) 63.65 (6) 49.30 (3) 40.27 (3) 32.56 (6) 25.92 (1) 20.71 (8) 17.35 (1) 13.39 (3) 50°C

79.7 (5) 74.34 (3) 54.98 (6) 42.86 (3) 34.74 (2) 28.56 (9) 23.79 (2) 20.99 (3) 17.57(1) 13.84(2) 10.32 (4)

Complex permittivity spectra e*(w) were obtained from reflection coefficient spectra p*(w) by the bilinear calibration method.(6) Experimental values of e* were fitted with the Debye equation(10-12)

with E0 and T as fitting parameters. A nonlinear least-squares fitting method(13) was used to determine the dielectric parameters. The value of Ei was taken to be 2 for all the systems studied since, for the frequency range considered here, e* is not sensitive to ei. A sample e* spectrum is shown in Fig. 1. 4. RESULTS AND DISCUSSION The measured £0 and density values of the pure liquids used are given in Table I along with literature values. The static dielectric constants and

1036

Khirade, Chaudhari, Shinde, Helambe, and Mehrotra

Fig. 2. (a) Excess permittivity at several temperatures vs. mole fraction DMF in 2-ethoxyethanol. (b) Excess inverse relaxation time vs. mole fraction DMF in 2-ethoxyethanol.

relaxation times obtained by fitting experimental data with the Debye equation are listed in Tables II-IV. The excess parameters,(14) i.e., excess permittivity eE and excess inverse relaxation time (1/T)E, were computed as

where x is the mole fraction and subscripts m, A, and B represent mixture, component A, and component B, respectively, and

where (1/T)E represents the average broadening of the dielectric spectra. The variation of eE and (1/T)E with mole fraction of DMF from 20 to 50°C is shown in Figs. 2-4. The experimental values of both excess parameters were fitted to the Redlich-Kister(15,16) equation

Temperature-Dependent Dielectric Relaxation

1037

Fig. 3. (a) Excess permittivity vs. mole fraction DMF in ethanol. (b) Excess inverse relaxation time vs. mole fraction DMF in ethanol.

where A is either eE or (1/T)E. Values of the coefficients Bj for j = 0, 1, 2, 3 are listed in Table V. With these Bj, AE values were calculated and used to draw the smooth curves in Figs. 2-4. In the systems studied here, eE is positive in the solute-rich region, indicating formation of monomeric or polymeric structures, which increase the total number of dipoles; whereas in the solvent-rich region, eE is negative, indicating formation of dimeric structures, which lead to a decrease of the total number of dipoles in the system. The excess inverse relaxation times of these systems are positive in the solute-rich region. This indicates fast rotation of the dipoles. This may be due to the formation of monomeric structures in this region. In the DMF-rich region these values are negative. This indicates the formation of structures; probably dimeric, which rotate slowly.

1038

Khirade, Chaudhari, Shinde, Helambe, and Mehrotra

Fig. 4. (a) Excess permittivity vs. mole fraction of DMF in 1-propanol. (b) Excess inverse relaxation time vs. mole fraction of DMF in 1-propanol.

The Kirkwood correlation factor(17) g is also a parameter that affords information regarding orientation of electric dipoles in polar liquids. The g for a pure liquid may be obtained with the expression

where u is the dipole moment in the gas phase, p is the density at temperature T (kelvin), M is molecular weight, k is the Boltzmann constant, and N is Avogadro's number. The corresponding equation for the mixtures is not available in the literature. However, for a mixture of two polar liquids, say A and B, Eq. (6) can be modified(18-20) by assuming that geff, defined by

1039

Temperature-Dependent Dielectric Relaxation Table V. Bj Coefficients of the Redlich-Kister Equation Excess permittivity

°C

Bo

B1

20 30 40 50

10.1

-77.3 -80.0 -62.9 -52.4

20 30 40 50

-2.1

20 30 40 50

-1.4

9.5 9.5 10.9

5.9 5.0 9.0

0.6 5.5 9.1

-39.3 -39.1 -32.8 -35.8 -64.0 -55.1 -55.6 -50.1

B2

Excess inv. relaxation time

B3

Bo

2-Ethoxyethanol + DMF -26.7 -272.9 -39.5 -21.2 -227.4 -43.8 -40.7 -13.1 -247. -7.4 -59.9 -260.9 Ethanol-DMF - 185.2 -71.3 19.3 -81.4 -178.3 25.9 - 179.5 -97.4 34.5 -174.2 -104 30.6 1-Propanol-DMF -231.4 -62.6 8.2 26.9 -250.6 -68.5 -91.1 22.3 -228.2 -83.2 -246.4 23.8

B1

B2

-90.9 -97.5 -177 -156

-27.1 34.7 -47.8 -51.2

-645 -794 -677 -655

-114 -130 -155 -161

-39.4 -23.7 -44.8 -53.9

-648 -717 -832.3 -865.9

-145 -154 -155 -174

-52.9 -16.1 -50.1 -76.4

-666.4 -799 -949.5 -991

B3

is the effective Kirkwood correlation factor for a binary mixture with pA and pB the volume fractions of the components. In Eq. (7), the value of geff changes from gA to gB as the concentration of component B increases from 0 to 100%. The calculated values of geff are tabulated in Table VI. These values are approximately equal to unity in pure DMF, indicating no correlation, but the values increase above unity in the solute-rich region, indicating the formation of structures in which intermolecular attraction is significant. The modified Bruggeman equation(21,22)

provides another parameter fB, which may be used as an indicator of solutesolvent interaction. Here a is an adjustable parameter, determined by fitting experimental data with the above equation using least squares. Figures 5a-c show plots of the Bruggeman factor fB vs. volume fraction of solute pB. The thermodynamic parameters14 molar energy of activation DH* and molar entropy of activation AS* were obtained using the equation

and are listed in Table VII.

Khirade, Chaudhari, Shinde, Helambe, and Mehrotra

1040

Table VI. The Kirkwood Correlation Factor geff Temperature (°C)

pd

20

100 90 80 70 60 50 40 30 20 10 0

1.00 1.01 1.09 1.21 1.21 1.30 1.39 1.55 1.89

100 90 80 70 60 50 40 30 20 10 0

2.28 4.30

1.00 1.03 1.08 1.11 1.17 1.18 1.26 1.32 1.44 1.54 1.60

30

40

2-Ethoxyethanol-DMF 1.00 1.00 1.07 0.97

1.20 1.20 1.23 1.30 1.41 1.58 1.87 2.39 4.43

1.14 1.21 1.28 1.32 1.45 1.62 1.86 2.44 4.40

Ethanol-DMF 1.00 1.00 1.11 1.09 1.13 1.09 1.19 1.18 1.21 1.20 1.26 1.25 1.31 1.32 1.37 1.35 1.46 1.41 1.56 1.53 1.49 1.46

Temperature (°C)

50

20

1.00 1.05 1.14 1.17 1.24 1.34 1.49 1.65 1.83

1.00 1.01 1.04 1.11 1.12 1.15 1.22 1.27 1.40 1.59

30

40

50

1-Propanol-DMF

2.41 3.89

1.72

1.00 1.10 1.14 1.13 1.16 1.19 1.25 1.31 1.39 1.59 1.70

1.00 1.09 1.13 1.15 1.20 1.22 1.27 1.33 1.42 1.57 1.59

1.00 1.13 1.16 1.16 1.22 1.25 1.29 1.34 1.39 1.49 1.48

1.00 1.11 1.14 1.19 1.23 1.29 1.32 1.40 1.43 1.54 1.41

5. CONCLUSION Dielectric relaxation parameters, excess parameters, thermodynamic parameters, and Kirkwood correlation factor are reported for 2-ethoxyethanol-DMF, ethanol-DMF and 1-propanol-DMF mixtures for various temperature and concentrations. In these systems, the various dielectric parameters discussed above afford evidence of significant intermolecular interactions in the solute-rich region only. Similar of behavior is observed at 20, 30, 40, and 50°C as the values of all the parameters studied change with increasing temperature in accord with increasing structure-breaking effects. ACKNOWLEDGMENT Financial support from Department of Science and Technology, New Delhi (INDIA) is gratefully acknowledged.

Temperature-Dependent Dielectric Relaxation

1041

Fig. 5. (a) Bruggeman factor vs. volume fraction of 2-ethoxyethanol in DMF. (b) Bruggeman factor vs. volume fraction of ethanol in DMP. (c) Bruggeman factor vs. volume fraction of 1propanol in DMF.

Khirade, Chaudhari, Shinde, Helambe, and Mehrotra

1042

Table VII. Values of Molar Enthalpy of Activation and Molar Entropy of Activation for 2-Ethoxyethanol-DMF, Ethanol-DMF, and 1-Propanol-DMF Mixturesa 2-Ethoxyethanol

a

1-Propanol

Ethanol

pd

DH*

AS*

DH*

AS*

AW*

AS*

0 10 20 30 40 50 60 70 80 90 100

11.5(2) 17.4 (5) 11.2(9) 12.4 (6) 8.6 (9) 7.9 (4) 8.3 (2) 10.0 (1) 7.0 (5) 4.0 (3) 7.7 (9)

0.22 0.24 0.22 0.22 0.21 0.21 0.21 0.22 0.21 0.20 0.21

20.2 (3) 15.2 (7) 12.8 (2) 12.0(2) 10.4 (7) 10.0 (2) 10.2 (7) 9.6 (6) 8.7 (1) 8.5 (6) 7.7 (9)

0.24 0.22 0.22 0.22 0.21 0.21 0.21 0.21 0.21 0.21 0.21

29.7 (6) 17.3 (2) 16.6 (9) 15.3(1) 13.0(3) 12.4 (7) 10.2 (1) 8.2 (3) 8.4 (2) 10.0 (2) 7.7 (9)

0.27 0.23 0.23 0.23 0.22 0.22 0.21 0.21 0.21 0.22 0.21

Units: DH*, kJ-mol -1 ; DS*, J-mol - 1 -K - 1 .

REFERENCES 1. A. C. Kumbharkhane, S. N. Helambe, and S. C. Mehrotra, J. Chem. Phys. 23, 2205 (1993). 2. S. M. Puranik, A. C. Kumbharkhane, and S. C. Mehrotra, J. Chem. Soc. Faraday Trans. 88, 433 (1992). 3. S. M. Puranik, A. C. Kumbharkhane, and S. C. Mehrotra, J. Chem. Soc. Faraday Trans 87, 1569 (1991). 4. A. C. Kumbharkhane, S. M. Puranik, and S. C. Mehrotra, J. Solution Chem. 20, 12 (1991). 5. M. T. Hosamani, R. H. Fattepur, D. K. Deshpande, and S. C. Mehrotra, J. Chem. Soc. Faraday Trans. 91, 623 (1995). 6. R. H. Cole, J. G. Berberian, S. Mashimo, G. Chryssikos, A. Burns, and E. Tombari, J. Appl. Phys. 66, 793 (1989). 7. S. M. Puranik, A. C. Kumbharkhane, and S. C. Mehrotra, J. Microwave Power Electromag. Theory 26, 196(1991). 8. C. E. Shannon, Proc. IRE 37, 10 (1949). 9. H. A. Samulon, Proc. IRE 39, 175 (1951). 10. S. Havriliak and S. Negami, J. Polymer Sci., Polymer Symp. 99 (1966). 11. K. S. Cole and R. H. Cole, J. Chem. Phys. 9, 341 (1941). 12. D. W. Davidson and R. H. Cole, J. Chem. Phys. 18, 1484 (1950). 13. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw Hill, New York, 1969) p. 104. 14. J. B. Hasted, Aqueous Dielectrics. (Chapman and Hall, London, 1973). 15. M. I. Aralaguppi, T. M. Aminabhavi, R. H. Balundgi, and S. S. Joshi, J. Phy. Chem. 95, 5299 (1991). 16. S. F. Al-Azzawl, A. M. Awwad, A. H. Al-Dujaili, and M. K. Al-Noori, J. Chem. Eng. Data 35, 463(1990).

Temperature-Dependent Dielectric Relaxation

17. 18. 19. 20. 21. 22.

1043

H. Frohlich, Theory of Dielectrics (Oxford University Press, London, 1949) A. C. Kumbharkhane, S. M. Puranik, and S. C. Mehrotra, J. Mol. Liquids 51, 261 (1992) A. C. Kumbharkhane, S. M. Puranik, and S. C. Mehrotra,J. Solution Chem. 22, 219(1993) G. MouMouzlas, D. K. Panopoulos, and G. Ritzoulis, J. Chem. Eng. Data 36, 20 (1991). D. A. G. Bruggeman, Ann. Phys. 5, 636 (1935). S. M. Puranik, A. C. Kumbharkhane, and S. C. Mehrotra, J. Mol. Liquids 59, 173 (1994).