J Solution Chem DOI 10.1007/s10953-016-0441-6

Thermodynamic and Molecular Dielectric Relaxation Studies of Polar–Polar Binary Mixtures Using Time Domain Reflectometry Technique A. Mohan1 • M. Malathi1 • S. S. Shaikh2 • A. C. Kumbharkhane2

Received: 11 August 2015 / Accepted: 3 November 2015 Ó Springer Science+Business Media New York 2016

Abstract The complex dielectric spectra of nitrobenzene, 2-butanol and their binary mixtures were measured in the frequency range of 10 MHz–20 GHz at different temperatures using Time Domain Reflectometry. The static permittivities and relaxation times were extracted from the complex dielectric spectra of the pure compounds and binary mixtures by fitting to the Debye model using the least-squares fitting method. The derived static permittivity (e0) and dielectric relaxation time (s0) values were used to calculate various dielectric parameters including the excess dielectric constant, effective Kirkwood correlation factor, excess inverse relaxation time and thermodynamic parameters. Excess dielectric parameters were fitted with the Redlich–Kister type polynomial equation. The result from dielectric analyses confirms the formation of a heterogeneous complex structure by association of unlike molecules. This hetero-molecule interactions produce a electric field in the mixtures and, as a result, the effective dipoles rotate faster. Molecular rotation and dipole reorientation motions in these complex system are discussed in terms of the molar activation entropy and enthalpy. Additionally, the hydrogen bond interaction between solute and solvent were confirmed by FT–IR spectral analysis. Keywords

Molecular relaxation  Dielectric constant  Thermodynamic  Effective dipole

& M. Malathi [email protected] 1

Materials Physics Division, School of Advanced Sciences, VIT University, Vellore, Tamil Nadu 632014, India

2

School of Physical Sciences, Swami Ramanand Teerth Marathwada University, Nanded, Maharashtra 431606, India

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1 Introduction Nitrobenzene (NB) is a well-known parent chemical compound, which is mainly employed for producing aniline, dyes and paracetamol. It is also used as an explosive, shoe polish, leather dressing, paint solvent and odor masking agent in the chemical industry [1, 2]. Liquid phase hydrogenation of NB is one of the chemical processes to achieve high aniline yield. In this process, an alcohol solvent enhances the hydrogen mass transfer and maintains the reaction temperature. These processes have advantages of high volume productivity and high heat transfer coefficient [3–5]. NB has a high dipole moment (4.22 D) due to the presence of a flexible N–O polar bond and highly electronegativity [6, 7]. 2-Butanol has both donor and acceptor groups and forms a network structure through hydrogen bonding. In this aspect, several authors have studied physico-chemical properties of NB with different solvent mixtures [7–11]. In fluid processing industries, solute–solvent interactions play an important role in chemical equilibrium, reaction rate and production yield [12, 13]. Intermolecular forces such as induced dipole, dipole–dipole and hydrogen bonds are responsible for changes of dynamic structure and physical properties in mixtures [14, 15]. Dielectric relaxation spectroscopy is a powerful tool to study the chemical homogeneity and can provide valuable information about liquid dynamics, dipole orientation, charge distribution, molecular rotation and the H-bond connectivity of liquids [16]. In this work, we investigated the dielectric relaxation and thermodynamic behavior of nitrobenzene–2-butanol (NB–2But) binary mixtures at different temperatures. Excess dielectric constant, excess inverse relaxation time, effective Kirkwood correlation factor, enthalpy and entropy were calculated using experimental data. The negative magnitude of excess dielectric permittivity confirms that the effective dipoles were aligned with antiparallel direction and stronger H-bond connectivity developed at 0.3167 mol fraction of NB. Formation of Hydrogen bond connectivity between unlike molecules in binary mixtures was supported by FT–IR spectra analysis.

2 Experimental 2.1 Chemicals and Sample Preparation Nitrobenzene (C99 %, CAS Reg. No: 98-95-3) and 2-butanol (C99 %, CAS Reg. No: 78-92-2) of AR grade were purchased from E-Merck India. The water contents of the compounds used were less than 0.05 % according to the manufacturer’s specification. Both the compounds were used without further treatment. The binary mixtures of NB with 2-butane were prepared at nine different NB mole fractions, gravimetrically, using an electronic digital balance (Adventurer Ohaus AR2140) with accuracy of ±1 9 10-7 kg.

2.2 Measurements The densities of the pure compounds were determined using a DMA 4500 M (Anton Paar) vibrating-tube digital densitometer. The sample cell was calibrated with air and double distilled water before measurements. The accuracy of the measured density and temperature was ±1 9 10-2 kgm-3 and ±0.01 K, respectively. Refractive indices were measured using an Abbe refractometer (SIPCON) with sodium D line light source with an accuracy of ±1 9 10-5. The temperature of the refractometer was controlled by a

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thermostat system (ESCY IC 201) with an accuracy of ±0.5 K. The FT–IR spectra were recorded at 298 K using an IR affinity-1, Shimadzu spectrometer. The complex dielectric spectra were measured using Time Domain Reflectometry (Agilent infiniium DCA-J 86100A with sample oscilloscope HP 54754A). A repetitive fast 39 picoseconds (ps) rising time step voltage pulse was fed through a 50 X impedance semi-rigid slim probe having pin length 0.14 mm. Reflected pulse without sample R1(t) and with sample Rx(t) were recorded in a 2 ns (ns) time window and digitized into 1200 points. The frequency dependent complex spectra were obtained from reflection coefficient spectra. The detailed TDR data analysis procedure was reported previously [17, 18]. The thermostat (ESCY IC 201) was used to maintain constant temperature in the sample cell with an accuracy of ±0.5 K.

3 Results and Discussion The experimental densities, refractive indices and static permittivities for the pure substances along with literature values are given in Table 1. The determined values for the pure liquids differ slightly from the literature values due to the temperature differences. Table 1 Comparison of experimental values of density (q), refractive index (n) and static permittivity (e0) for pure liquids at different temperatures with literature values Compounds

Nitrobenzene

2-Butanol

T (K)

q (kgm-3)

e0

n

Expt.

Lit.

Refs.

Expt.

Lit.

Ref.

278

1215.61

–

–

1.56682

–

–

38.45

–

–

288

1208.80

1208.01

[33]

1.55439

1.55485

[33]

35.82

36.78

[34]

1208.80

[35]

298

1199.52

1198.20

[33]

1.54992

[33]

34.45

1198.12

[9]

1.550042

[9]

1203.10

[11]

308

1189.10

1189.40

[2]

1188.22

[36]

318

1180.01

–

278

818.61

288

298

308

318

810.94

802.82

794.06

785.15

1.54985

Expt.

Lit.

Refs.

34.78

[10]

34.3

[11]

1.549010

[11]

34.8

[36]

1.54369

–

–

33.11

33.13

[10]

33.17

[36]

–

1.53940

–

–

30.86

32.26

[34]

818.03

[37]

1.41838

–

–

19.93

–

–

817.77

[38] 1.39893

1.39951

[39]

18.29

810.25

[37]

810.08

[38]

810.689

[39]

802.19

[37]

802.01

[38]

802.528

[39]

793.75

[37]

793.55

[38]

794.03

[39]

785.117

[39]

784.86

[37]

784.68

[38]

1.39528

1.39052

1.38670

1.3949

[12]

1.39515

[39]

1.3953

[41]

1.3949

[12]

1.39064

[39]

1.3854

[12]

1.38596

[39]

16.41

14.65

13.04

18.45

[40]

18.47

[41]

16.46

[12]

16.58

[40]

16.6

[41]

15.055

[12]

14.93

[40]

14.94

[41]

13.71

[12]

Standard uncertainties are u(q) = ± 2 9 10-2 kgm-3, u(n) = ± 2 9 10-5, and u(e0) = 0.25

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The frequency and concentration dependent complex permittivity spectra of binary mixtures at 298 K are shown in Fig. 1. The real part (e0 ) of the complex permittivity spectrum of NB–2But mixtures was almost independent of frequency below 0.1 GHz. Therefore, static permittivity values were extracted from the low frequency region [19]. There was one single loss peak, for each concentration, in the examined frequency range, which indicated co-operativity in the binary mixtures; the complex permittivity loss peaks were shifted to higher frequencies with increasing of NB concentration, indicating decreasing relaxation times. The various NB concentration complex permittivity spectra of the binary mixtures were fitted to the Debye model, using non-linear least squares, to determine the static dielectric constant and relaxation time. Fitting parameters e0 and s0 (s0 = 1/2pf) were estimated within the corresponding complex permittivity spectrum in which e? was taken as 2.

3.1 Excess Static Permittivity Experimentally obtained static permittivity (e0) values of pure NB, 2But and their binary mixtures at different temperatures are plotted in Fig. 2. The derived static permittivity value varies non-linearly with the solute concentration; this implies that heterogeneous H-bond interactions exist in the mixtures [15]. The addition of NB molecules to the solvent can modify the spherical aggregate into elongated aggregate structures, increasing the static permittivity and altering the dipole packing density in the mixture. Therefore the e0 values continuously increase with increasing of NB concentration. On the other hand, it has been observed that the e0 values decrease when increasing temperature. This decrease tendency reflects a decrease in H-bond strength and size of complex system with increasing temperature [20, 21]. The displacement of electrons from equilibrium positions causes

Fig. 1 The complex dielectric spectra for various NB concentrations of binary mixtures at 298 K

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Fig. 2 Variation of static permittivity versus mole fraction of NB at different temperatures

electronic polarization in molecules; this electron displacement may be affected by H-bond interaction. High frequency dielectric measurements give information about the degree of electronic polarization in binary mixtures [14]. From Fig. 3, it can be seen that the high frequency dielectric permittivities (e?) increase linearly (approximately) with increasing of the NB concentration. This indicates that electronic polarization plays a negligible effect in these binary mixtures.

Fig. 3 Optical frequency dielectric permittivity versus various mole fraction of NB in binary mixtures at different temperatures

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A study of excess static permittivity (e0)E of binary system provided experimental evidence about structural change and H-bond interaction strength in binary mixtures [19]. The plots of (e0)E against mole fraction of NB at different temperature are shown in Fig. 4. The (e0)E values are negative for all NB concentrations, indicating the formation of heteromolecular interactions through H-bonding in the mixtures. In binary mixtures, solute molecules rupture the solvent homo-molecular H-bonds and form multimer structures through unlike molecule H-bonds with a reduction of the effective total number dipoles [15]. The magnitude of (e0)E decreases with increasing temperature, due to the reduction of the effective H-bond strength and dissociation of the H-bonded network structure in the binary mixtures. The stable stoichiometric ratio of NB–2But complex system was evaluated from the largest negative value of the excess dielectric constant. The stable adduct was formed at approximately a 1:2 mol ratio of NB–2But. The excess parameters were expressed mathematically by Redlich–Kister type polynomial equation [22]. The R–K equation is given as follows: yE ¼ XNB ð1  XNB Þ

n X

ai ð1  2XNB Þi

ð1Þ

i¼0

where yE indicates the excess values and ai are the coefficients. The standard deviation has been determined by the following formula: 2P 2 30:5 E E  y y exp cal 7 6 r¼4 5 NP

ð2Þ

where N is number of experimental points and P is number of coefficients. The excess dielectric constant was fitted with Redlich–Kister type polynomial using nonlinear regression to estimate the coefficients and standard deviation. In Fig. 4, the smooth solid lines represents the mathematical calculation of excess permittivity value. The coefficient and standard deviation are given in Table 2.

Fig. 4 Estimated excess dielectric constant for NB–2But mixtures at different temperatures

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J Solution Chem Table 2 Redlich–Kister coefficient and standard deviation values at different temperatures r

Function

Temp. (K)

a0

a1

a2

(e0)E

278

-18.253

-11.560

-19.319

6.736

8.977

0.1229

288

-16.611

-10.139

-27.495

6.875

34.240

0.2087

298

-16.597

-10.011

-27.110

8.894

33.686

0.1992

308

-13.348

-9.344

-25.400

4.398

37.325

0.2086

318

-12.653

-11.222

-14.786

14.749

18.112

0.2057

278

0.039

0.015

-0.019

-0.050

-0.017

5.13 9 10-4

288

0.052

0.015

-0.028

-0.055

-0.009

5.23 9 10-4

298

0.062

0.011

-0.012

-0.034

-0.001

4.12 9 10-4

308

0.067

0.026

-0.059

-0.083

7.47 9 10-4

318

0.091

0.015

-0.009

0.012

9.62 9 10-4

(1/s)E

a3

0.0270 -0.022

a4

3.2 Kirkwood Correlation Factor The Kirkwood–Froehlich equation provides the information about electric dipole orientation in homogeneous system [23, 24]. The Kirkwood correlation factor equation is given as follows: 4pNA q 2 ðe0  e1 Þð2e0 þ e1 Þ gl ¼ 9KTM e0 (e1 + 2)2

ð3Þ

where NA, K, M, T, q, l, e0 and e? are the Avogadro number, Boltzmann constant, molecular weight, temperature in Kelvin, density, dipole moment, static dielectric permittivity and higher frequency static permittivity, respectively. The modified Kirkwood correlation factor gives information about associative polar molecule dipole orientation in heterogeneous systems. The modified equation is given as follows:   4pNA l2NB qNB l2 q ðe0m  e1m Þð2e0m  e1m Þ XNB + But But (1  XNB ) geff ¼ ð4Þ 9KT MNB MBut e0m (e1m + 2)2 where geff is the effective Kirkwood correlation factor, MNB, qNB, XNB represents the molecular weight, density, and mole fraction of nitrobenzene, respectively. lNB is dipole moment of nitrobenzene 4.22D [6]. MBut, qBut represent molecular weight and density of 2-butanol. lBut is the dipole moment of 2-butanol, 1.66D [12]. The e0m, e?m are the dielectric permittivity and high frequency static permittivity of the mixture, respectively. Effective Kirkwood correlation factors geff were calculated using experimental data for the five different temperatures. Figure 5 shows that 2-butanol geff values are greater than unity at all temperatures, which indicates parallel orientation of the electric dipoles. In contrast, the nitrobenzene geff values are less than unity at all temperatures, indicating that the electric dipoles aligned in the anti-parallel direction. In binary mixtures, geff values decrease nonlinearly from that of pure 2But to that of pure NB which indicates that heterogeneous dipole interactions exist in the mixtures [25, 26]. At low concentration of NB, associated 2But molecules act as proton donors which enables dipole interaction with NB molecules. Thus dipole–dipole interactions form multimer structures in the mixture. In

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Fig. 5 Effective Kirkwood correlation factor versus XNB at different temperatures. Inset shows the variation of geff values in the range from 0.4 XNB to 1.0 XNB

the case of high NB concentrations, small amounts of proton donor enabled dipole interaction. As a result the mixture dipoles are aligned anti-parallel and the effective dipole is decreased [20, 27]. This tendency leads to the conclusion that dipole interaction is between the partially negative charged oxygen atom of NB and the partially positive charged hydrogen atom of 2But. The possible dipole–dipole interaction diagram is shown in Fig. 6. Increasing thermal vibration increases the molecular motions and reduces the effective H-bond strength and complex structure size.

3.3 Excess Inverse Relaxation Time Dielectric relaxation dispersion of a molecule depends on the nature of the functional groups, H-bond interaction and molecule size [20, 27]. The experimental relaxation times of NB, 2But and their binary mixtures at five different temperatures are shown in Fig. 7. The solvent molecules have high relaxation times, due to the formation of intra- and inter-molecular hydrogen bonds, which restrict the molecular rotations. In contrast, the solute molecules have low relaxation times compared to the solvent, due to the non-associated nature of NB. As the NB concentration increases, relaxation times of mixtures decrease since the solute molecules counteract the solvent self-association and effectively reduce the complex’s size. This systematic change of relaxation time indicates that the size of the complex structure decreases with increasing of NB concentration [28]. Furthermore, increases in temperature affect the H-bond strength and complex sizes. The increasing thermal agitation increases the effective dipole length and ruptures the H-bond connectivity in mixtures [21, 29]. The change in excess inverse relaxation times was taken into account to explain molecular rotations [20]. The concentrations and temperature dependent excess inverse relaxation time is shown in Fig. 8. As seen from Fig. 8, (1/s0)E is positive for all NB concentrations. This implies that solute–solvent interactions produce an electric field so the effective dipoles rotate rapidly.

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O H O N O H O

Fig. 6 Schematic representation of dipole–dipole interaction of nitrobenzene and 2-butanol molecules

Fig. 7 Plot of relaxation time with the NB mole fraction at different temperatures. The s0 values in the range of 0.4 XNB to 1.0 XNB are shown in inset

3.4 Thermodynamic Parameter The activation parameters (enthalpy DH= and entropy DS=) for the dielectric relaxation process were calculated using the Eyring rate equation [30]:

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Fig. 8 Excess inverse relaxation time versus XNB of the binary mixtures at different temperatures

s¼

h DH 6¼  TDS6¼ exp KT RT

ð5Þ

where s, h, K, T, R are relaxation time, Planck’s constant, Boltzmann constant, temperature in Kelvin and gas constant, respectively. Figure 9 shows the relevant plot of the relaxation times, which is a nearly straight line. The molar activation enthalpy DH= and entropy DS= for pure and nine different binary mixtures were calculated and values are presented in Table 3. The positive values of activation enthalpy DH= confirm that heat was liberated in the molecular reorientation process. As NB is added into 2But the activation energy

Fig. 9 Arrhenius plot of log10 (sT) versus (1000/T) for various concentration of NB

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J Solution Chem Table 3 Thermodynamic parameter of NB–2B mixtures

Numbers in brackets indicates uncertainty in last significant digits. e.g. 26.95 (25) means 26.95 ± 0.25 and 0.025 (10) means 0.025 ± 0.010

XNB

DH= (kJmol-1)

DS= (JK-1mol-1)

0

26.95 (25)

0.025 (10)

0.1052

26.73 (26)

0.034 (10)

0.212

16.39 (51)

0.005 (17)

0.3167

12.98 (22)

-0.003 (23)

0.4146

12.86 (22)

-0.002 (36)

0.4908

11.08 (54)

-0.007 (18)

0.6076

11.61 (72)

-0.005 (24)

0.7106

11.72 (59)

-0.005 (19)

0.8157

11.20 (30)

-0.007 (10)

0.9166

9.65 (44)

-0.013 (14)

1

9.52 (40)

-0.014 (13)

decreases, showing that less energy is required for molecular rotation [27]. The negative entropy values indicate that the system environment is more cooperative for the molecular reorientation process. And the positive entropy indicates that activated system environment is less ordered than for a normal system [24].

3.5 Concentration Dependence FTIR Spectra FT-IR spectroscopy provides important information about functional group interactions between solute and solvent molecules. The FT–IR spectra of pure NB, 2But and binary mixtures in the region 1320–1540 cm-1 are shown in Fig. 10. For nitrobenzene the N–O bond symmetric and asymmetric stretching vibration modes were obtained around 1342

Fig. 10 FT-IR spectra of various NB concentration binary mixtures

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and 1517 cm-1 respectively [31]. Both the N–O bond stretching modes are shifted towards higher wave number with decreasing NB concentration. These blue shifts strongly suggest that the formation of an electrostatic link between the NB oxygen atom and the hydrogen atom of a 2But molecule. From the plot, it may be seen that the peak positions and bandwidths remain unchanged in NB rich mixtures, which indicates weak hydrogen bond interaction. In the case of lower concentrations of NB, both bands are shifted towards higher wave numbers. This suggests that H-bond interaction is stronger when large amounts of associated solvent molecules surround a NB molecule [13, 32].

4 Conclusions The complex permittivity spectra of nitrobenzene in 2-butanol solutions have been studied by TDR spectroscopy in the frequency range of 10 MHz–20 GHz. Formation of heterogeneous complex structures between nitrobenzene and 2-butanol molecules were confirmed by studying various dielectric parameters such as the excess dielectric permittivity, excess inverse relaxation time, effective Kirkwood correlation factor and activation parameters of pure and binary mixtures. The negative excess dielectric permittivity confirmed that effective dipoles were aligned anti-parallel and stronger H-bond connectivity developed at 0.317 mol fraction of nitrobenzene. The increment of thermal vibration disassociates the H-bond interaction and mixture complex size. The FT–IR spectral analysis confirmed H-bond connectivity generated between solute nitro groups with solvent hydroxyl groups in binary mixtures. Acknowledgments The author is thankful to Department of Sciences and Technology—Science and Engineering Research Board (DST-SERB) and Defense Research and Development Organization (DRDO) for providing instrument facility.

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