# Dielectric, Thermodynamic, and Computational Studies of Hydrogen Bonded Binary Mixtures of N-Methylaniline with Propan-1-ol and Isopropyl Alcohol

Authors: T. Vijaya Krishna; S. Sreehari Sastry; Sie Tiong Ha; V. R. K. Murthy
Journal: Journal of Chemistry
 (2013)

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## Abstract

The molecular interactions between the polar systems N-methylaniline with alcohols, propan-1-ol, and isopropyl alcohol for various mole fractions at different temperatures are studied by determining the dielectric permittivity using LF impedance analyzer, microwave bench, and Abbe's refractometer in radio, microwave, and optic frequency regions, respectively. Dipole moment, excess dipole moment, excess Helmholtz free energy, excess permittivity, excess inverse relaxation time, and excess thermodynamical values are calculated using experimental data. Hamiltonian quantum mechanical calculations are performed using PC Spartan and ArgusLab modeling softwares for both pure and equimolar binary systems of N-methyl aniline with alcohols.


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## Body

## 1. Introduction

Dielectric relaxation spectroscopy is a powerful tool for examining the underlying physics of solvent systems [1, 2] and for exploring the molecular dynamics of liquids, which are characterized by inter- and intramolecular structures that vary rapidly with time. Historically, such studies have focused separately on long-range and short-range molecular forces [3]. At one extreme, long-range, nonspecific dispersion forces produce weakly bonded van der Waals complexes, while at the other, short-range, highly directional hydrogen bonding generates molecular networks. In reactions, where the solvent is directly involved in the process (as in solvolytic reactions), the reaction rate can be markedly sensitive to the solvent structure and dynamics [4]. In chemical processing applications, the availability of quantitative data on dielectric properties of solvent systems or methods for their prediction are essential for the design and implementation of microwave heated processes.There is an increased interest in the study of liquid mixtures leading to formation of hydrogen bonding in the system due to solute-solvent interactions during the recent times [5]. Hydrogen bonding is complex in liquid state because of the uncertainty in identifying the particular bonds and the number of molecules involved. The presence of hydrogen bond brings a considerable change in the dielectric properties of liquid mixtures [6]. The component liquids taken in course of this investigation are amines and alcohols. Aromatic amines, which are nonassociative, are very important in biology, in the production of dyes, pesticides, and antioxidants [7, 8]. Alcohols are industrially and scientifically important organic compounds and their physical and chemical properties are largely determined by the –OH group. Alcohols are strongly associated in solution because of dipole-dipole interaction and hydrogen bonding. The nature of interaction between –NH and –OH groups plays an important role in biological systems and drug synthesis [9, 10].The present work aims at studying the dielectric behavior of pure and binary mixtures of N-methylaniline with propan-1-ol (system 1) and N-methylaniline with isopropyl alcohol (system 2) in different frequency ranges for various mole fractions at different temperatures. From the experimental data, the dielectric parameters dipole moment, excess dipole moment, excess Helmholtz free energy, excess permittivity, excess inverse relaxation time, and excess thermo dynamical values are calculated for the pure and binary mixtures [11–14]. Hamiltonian quantum mechanical calculations [15, 16] such as semiempirical and ab initio calculations are performed by optimized converged geometry operation using PC Spartan and ArgusLab modeling softwares [17, 18]. The obtained theoretical values are further compared with the experimental values.


## 2. Experimental

The compounds N-methylaniline (NMA), propan-1-ol (1PN), and isopropyl alcohol (IPA) of AR grade are purchased from E. Merck, Germany, and are purified by standard methods. The binary mixtures are prepared for different mole fractions, that is, mole fraction(X2) of N-methylaniline is varied from 0 to 1 in alcohols 1PN and IPA (with a step increment of 0.1). The temperature controller system with a water bath, supplied by M/s Sakti scientific instruments company, India, has been used to maintain the constant temperature within the accuracy limit of ±1 K. Densities at different temperatures are measured by using a 10 ml specific gravity bottle and METTLER TOLEDO balance (Model no: AB135-S/FACT) whose accuracy is 0.01 mg.The static permittivity values at the spot frequencies 1 kHz(εstatic), 10 kHz, 100 kHz, 1 MHz, and 10 MHz for the above systems are measured using HP-LF impedance analyzer (Model no: 4192 A) at different temperatures. The real (ε′) and imaginary (ε′′)  parts of the complex dielectric permittivity (ε*=ε′-jε′′) are determined with microwave bench (X-Band-8.60 GHz) using Plunger technique [19] for the above temperatures. The high frequency dielectric permittivity (ε∞=n2) is obtained from the refractometer measurements using M/s ASCO make Abbe’s refractometer with sodium D light as source at different temperatures. The error in the estimation of  εstatic,ε′,ε∞ and density is 1% and the error in the estimation of  ε′′,τ  is 2%. Dipole moments of the liquids in gaseous state are taken from literature [20].


### 2.1. Theory

The dipole moments for the pure and equimolar systems (system 1 and 2) are measured experimentally, by diluting them in nonpolar solvent benzene, using Higasi’s method [11]. 								(1)μ2=27kTM2(a0-a∞)4πNd1(ε1+2)2,
where M2 is molecular weight of solute,a0, and a∞  are, respectively, the slopes of  εstatic and ε∞  with respect to the weight fraction of the solute, d1 is density of solvent, and ε1 is the static dielectric permittivity of solvent (Benzene).The excess dipole moments(Δμ) of the systems are determined [12, 21, 22] by  (2) as follows:
(2)Δμ=μ12-μ1-μ2,
where μ1 is the dipole moment of NMA,  μ2 is the dipole moment of either 1PN or IPA, and μ12 is the dipole moment of the equimolar solute mixtures NMA + 1PN or NMA + IPA.The excess Helmholtz free energy(ΔFE) is a good dielectric parameter to evaluate the interaction between the components in the mixture through breaking mechanism of hydrogen bond and is expressed [23] as
(3)ΔFE=ΔForE+ΔFrrE+ΔF12E,
where ΔForE  represents the excess dipolar energy due to long range electrostatic interaction, ΔFrrE represents the excess dipolar energy due to the short range interaction between identical molecules, and ΔF12E represents the excess free energy due to short-range interaction between dissimilar molecules.The above terms are given in detail in (4) as
(4)ΔFE=-NA2{∑r=1,2xr2μr2[Rfr-Rfr0]-NA2+∑r=1,2xr2μr2[grr-1][Rfr-Rfr0]-NA2+x1x2μ1μ2[Rf1+Rf2-Rf10-Rf20]∑r=1,2xr2μr2[Rfr-Rfr0]},
where,  Rfr0=(8πNA/9Vr)((εr-1)(ε∞r+2)/(2εr+ε∞r)),    Rfr=(8πNA/9Vr)((εm-1)(ε∞r+2)/(2εm+ε∞r)),      g12=gf,     Vr is the molar volume of the components, and εr, ε∞r are the dielectric permittivity values at static and optic frequencies of the pure liquids, respectively. The error in the estimation of excess Helmholtz free energy is 0.001 J-mol−1.The contribution of hydrogen bonds to the dielectric properties of the mixtures can be studied in terms of excess permittivity(εE). The excess permittivity, εE, which provides qualitative information about formation of multimers in the mixture, can be computed as [24]
(5)εE=(εm-ε∞m)-[(ε1-ε∞m)x1+(ε2-ε∞m)x2],
where x is mole fraction and suffix 1, 2, and m represents liquid 1, liquid 2, and mixture, respectively.The qualitative information provided by excess permittivity about the mixtures is as follows.ε
E
=
0 indicates that there is no interaction between the components in the mixture.ε
E
<
0 indicates that the components in the mixture interact in such a way that the effective dipolar polarization gets reduced and the components may form multimers leading to less effective dipoles.ε
E
>
0 indicates that the components in the mixture interact in such a way that the effective dipolar polarization gets increased and the components may form multimers leading to more effective dipoles.The excess inverse relaxation time(1/τ)E which gives information regarding the dynamics of solute-solvent interaction and represents the average broadening of dielectric spectra can be defined [25] as
(6)(1τ)E=(1τ)m-[(1τ)1x1+(1τ)2x2].The thermodynamic parameters excess Gibb’s energy of activation(ΔG*)E, excess molar enthalpy of activation (ΔH*)E, and excess molar entropy of activation (ΔS*)E  at different mole fractions can be determined by fitting the Eyring rate equation [26, 27] as
(7)τ=hkTexp(ΔG*RT)=hkTexp(ΔH*-TΔS*RT),
where h is the Planck’s constant, k is the Boltzmann constant, T is the temperature in Kelvin, and R is the gas constant.Minimum energy structures of the monomers NMA, 1PN, IPA, and the equimolar hydrogen bonded complexes are obtained from semiempirical Hamiltonian quantum mechanical calculations such as Austin Model 1 (AM1), Parameterized Model number 3 (PM3), and Modified Neglect of Differential Overlap (MNDO) converged geometry optimization procedure using PC Spartan and ArgusLab modeling softwares.Ab initiocalculations have been carried out using PC Spartan modeling software and the geometry optimizations are done at the Hartree-Fock (HF) level using 6-31G* basis set.


## 2.1. Theory

The dipole moments for the pure and equimolar systems (system 1 and 2) are measured experimentally, by diluting them in nonpolar solvent benzene, using Higasi’s method [11]. 								(1)μ2=27kTM2(a0-a∞)4πNd1(ε1+2)2,
where M2 is molecular weight of solute,a0, and a∞  are, respectively, the slopes of  εstatic and ε∞  with respect to the weight fraction of the solute, d1 is density of solvent, and ε1 is the static dielectric permittivity of solvent (Benzene).The excess dipole moments(Δμ) of the systems are determined [12, 21, 22] by  (2) as follows:
(2)Δμ=μ12-μ1-μ2,
where μ1 is the dipole moment of NMA,  μ2 is the dipole moment of either 1PN or IPA, and μ12 is the dipole moment of the equimolar solute mixtures NMA + 1PN or NMA + IPA.The excess Helmholtz free energy(ΔFE) is a good dielectric parameter to evaluate the interaction between the components in the mixture through breaking mechanism of hydrogen bond and is expressed [23] as
(3)ΔFE=ΔForE+ΔFrrE+ΔF12E,
where ΔForE  represents the excess dipolar energy due to long range electrostatic interaction, ΔFrrE represents the excess dipolar energy due to the short range interaction between identical molecules, and ΔF12E represents the excess free energy due to short-range interaction between dissimilar molecules.The above terms are given in detail in (4) as
(4)ΔFE=-NA2{∑r=1,2xr2μr2[Rfr-Rfr0]-NA2+∑r=1,2xr2μr2[grr-1][Rfr-Rfr0]-NA2+x1x2μ1μ2[Rf1+Rf2-Rf10-Rf20]∑r=1,2xr2μr2[Rfr-Rfr0]},
where,  Rfr0=(8πNA/9Vr)((εr-1)(ε∞r+2)/(2εr+ε∞r)),    Rfr=(8πNA/9Vr)((εm-1)(ε∞r+2)/(2εm+ε∞r)),      g12=gf,     Vr is the molar volume of the components, and εr, ε∞r are the dielectric permittivity values at static and optic frequencies of the pure liquids, respectively. The error in the estimation of excess Helmholtz free energy is 0.001 J-mol−1.The contribution of hydrogen bonds to the dielectric properties of the mixtures can be studied in terms of excess permittivity(εE). The excess permittivity, εE, which provides qualitative information about formation of multimers in the mixture, can be computed as [24]
(5)εE=(εm-ε∞m)-[(ε1-ε∞m)x1+(ε2-ε∞m)x2],
where x is mole fraction and suffix 1, 2, and m represents liquid 1, liquid 2, and mixture, respectively.The qualitative information provided by excess permittivity about the mixtures is as follows.ε
E
=
0 indicates that there is no interaction between the components in the mixture.ε
E
<
0 indicates that the components in the mixture interact in such a way that the effective dipolar polarization gets reduced and the components may form multimers leading to less effective dipoles.ε
E
>
0 indicates that the components in the mixture interact in such a way that the effective dipolar polarization gets increased and the components may form multimers leading to more effective dipoles.The excess inverse relaxation time(1/τ)E which gives information regarding the dynamics of solute-solvent interaction and represents the average broadening of dielectric spectra can be defined [25] as
(6)(1τ)E=(1τ)m-[(1τ)1x1+(1τ)2x2].The thermodynamic parameters excess Gibb’s energy of activation(ΔG*)E, excess molar enthalpy of activation (ΔH*)E, and excess molar entropy of activation (ΔS*)E  at different mole fractions can be determined by fitting the Eyring rate equation [26, 27] as
(7)τ=hkTexp(ΔG*RT)=hkTexp(ΔH*-TΔS*RT),
where h is the Planck’s constant, k is the Boltzmann constant, T is the temperature in Kelvin, and R is the gas constant.Minimum energy structures of the monomers NMA, 1PN, IPA, and the equimolar hydrogen bonded complexes are obtained from semiempirical Hamiltonian quantum mechanical calculations such as Austin Model 1 (AM1), Parameterized Model number 3 (PM3), and Modified Neglect of Differential Overlap (MNDO) converged geometry optimization procedure using PC Spartan and ArgusLab modeling softwares.Ab initiocalculations have been carried out using PC Spartan modeling software and the geometry optimizations are done at the Hartree-Fock (HF) level using 6-31G* basis set.


## 3. Results and Discussion

We studied the temperature dependence on dielectric relaxation in pure and binary mixtures of N-methylaniline (NMA), propan-1-ol (1PN), and isopropyl alcohol (IPA) at different frequencies to understand the nature of molecular orientation processes [28]. The dielectric data is used to calculate Kirkwood effective correlation factor, corrective Kirkwood correlation factor, Bruggeman parameter, relaxation time and the thermodynamic parameters-Gibb’s energy of activation, molar enthalpy, and molar entropy of activation. Conformational analysis of the formation of hydrogen bond between equimolar mixtures of propan-1-ol with benzoates is studied from FT-IR spectra. The theoretical vibrational frequencies of the pure and equimolar hydrogen bonded systems are obtained from Hamiltonian quantum mechanical calculations using Spartan modeling software. The same data is used to study excess dielectric parameters and reporting in this communication.The dipole moment(μ) values for pure and equimolar systems (system 1 and system 2) at room temperature are determined experimentally with Higasi’s method and theoretically with Hamiltonian quantum mechanical calculations (ab initioand semiempirical) and the corresponding values are given in Table 1.Table 1
Experimental and theoretical dipole moment (μ) and excess dipole moment (Δμ) values in Debye for pure systems—NMA, 1PN, IPA, and equimolar systems—NMA + 1PN, NMA + IPA at room temperature (PCS: PC Spartan, AGS: ArgusLab).
Theoretical
Compound
Experimental
HF 6-31G*PCS
AM1
PM3
MNDO
PCS
AGS
PCS
AGS
PCS
AGS
μ
Δμ
μ
Δμ
μ
Δμ
μ
Δμ
μ
Δμ
μ
Δμ
μ
Δμ
μ
Δμ
NMA
1.87
—
1.48
—
1.48
—
1.48
—
1.24
—
1.24
—
1.11
—
1.13
—
1PN
1.57
—
1.67
—
1.47
—
1.54
—
1.40
—
1.43
—
1.35
—
1.39
—
IPA
1.63
—
1.71
—
1.61
—
1.62
—
1.52
—
1.53
—
1.43
—
1.44
—
NMA + 1PN
3.12
−0.32
3.02
−0.13
2.55
−0.40
2.75
−0.27
2.39
−0.25
2.02
−0.65
2.24
−0.22
2.27
−0.25
NMA + IPA
3.21
−0.29
3.10
−0.09
2.75
−0.34
2.38
−0.72
2.52
−0.24
2.12
−0.65
1.96
−0.58
1.93
−0.64The dipole moments for these systems are measured experimentally by diluting them in nonpolar solvent benzene. It is very clear from the experimental dipole moment values that there is an increase in the dipole moment of equimolar mixture when compared to the individual systems. This may be due to the formation of hydrogen bonding between the mixture systems [29]. The theoretical dipole moment values, mainly Hartree-Fock calculations, are in good agreement with the experimental values. The small deviation between the theoretical and experimental values may be due to the model dependency in theoretical case and due to the π electron cloud of nonpolar solvent benzene affecting the dipole moment value of the solute systems in experimental case [30]. The dipole moment values, measured for the pure and equimolar systems, are significantly affected by the variation in temperature as shown in Table 2.Table 2
Experimental dipole moment (μ) and excess dipole moment (Δμ) values in Debye for pure systems—NMA, 1PN, IPA, and equimolar systems—NMA + 1PN, NMA + IPA at different temperatures.
Temperature/K
NMA (μ)
1PN (μ)
IPA (μ)
NMA + 1PN
NMA + IPA
(μ)
(Δμ)
(μ)
(Δμ)
303
1.87
1.57
1.63
3.12
−0.32
3.21
−0.29
308
1.83
1.59
1.69
3.17
−0.25
3.28
−0.24
313
1.89
1.60
1.68
3.31
−0.18
3.34
−0.23
318
1.88
1.58
1.69
3.25
−0.21
3.27
−0.30
323
1.91
1.62
1.74
3.43
−0.10
3.38
−0.27The excess dipole moment(Δμ) values obtained theoretically and experimentally (at different temperatures) are given in Tables 1 and 2. It is observed that in all cases the values of Δμ are negative which indicates the absence of any contribution from ionic structure of the binary system to the total dipole moment since the formation of an ionic structure involves a very high positive value for Δμ [31]. The excess dipole moment value is a qualitative index for the presence of hydrogen bonding in system 1 and system 2.The long-range and short-range interactions between dipoles can be studied from the thermodynamical parameter excess Helmholtz free energy(ΔFE) and its constituent parameters ΔForE, ΔFrrE, ΔF12E [32].The value ofΔForE represents the long-range interaction between the dipoles in the mixture. In system 1 and system 2, the positive values of ΔForE indicate the existence of attractive forces between the dipoles and larger separation between the interacting molecules. Negative values of  ΔForE indicate the repulsive force between dipoles and interacting molecules are at closer distance. In both systems, values of  ΔForE are positive up to equimolar concentration and negative for remaining concentrations. The values of   ΔForE are decreasing for all the mole fractions, in both systems, as the temperature is increasing and are given in Table 3.Table 3
Variation ofΔForE with mole fraction (x2) of NMA in 1PN and IPA at different temperatures.
X
2
T
=
303
K
T
=
308
K
T
=
313
K
T
=
318
K
T
=
323
K
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
0
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
0.1
32.2230
27.7058
34.6322
26.8023
34.6322
21.0805
35.2345
17.4667
25.5977
19.2736
0.2
44.2690
43.3656
46.9794
40.6552
42.4621
36.7403
44.8713
32.8253
39.4506
29.5127
0.3
36.4391
29.5127
39.7518
26.2000
36.4391
24.2460
36.7403
14.7563
39.1495
12.3471
0.4
07.2276
−02.7103
06.0230
−06.3241
−01.8069
−13.2506
−2.7103
−18.9724
−01.8069
−15.6598
0.5
−32.8253
−32.5242
−36.7403
−40.3541
−46.0759
−48.7863
−42.4621
−49.9909
−39.4506
−47.2805
0.6
−69.2645
−65.6507
−73.1794
−78.9013
−86.7312
−85.8277
−80.7082
−81.3105
−78.6001
−75.8898
0.7
−98.7772
−91.2484
−106.3059
−109.6186
−116.5450
−117.4485
−106.3059
−115.6416
−108.7151
−108.414
0.8
−101.7887
−92.1519
−113.8347
−103.5956
−126.483
−99.6806
−111.1243
−96.0668
−106.6071
−99.0783
0.9
−77.9978
−55.7127
−85.8277
−71.3725
−78.6001
−76.4921
−75.8898
−73.1794
−76.4921
−71.3725
1
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000This shows that the strength of dipole-dipole interaction depends on the concentration and temperature of the mixture. The values ofΔForE for system 1 are greater than system 2. This may be due to the interaction of the compounds in the mixture which produces structural changes.The values ofΔFrrE  predict the information on the short range interaction between similar molecules. In both systems the values of ΔFrrE  are highly positive at all mole fractions, as shown in Table 4, indicating the existence of short range interaction through hydrogen bonding. The values of ΔFrrE for system 1 are greater than system 2 predicting the strong short range interaction between the components of similar molecules.Table 4
Variation ofΔFrrE with mole fraction (x2) of NMA in 1PN and IPA at different temperatures.
X
2
T
=
303
K
T
=
308
K
T
=
313
K
T
=
318
K
T
=
323
K
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
0
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
0.1
93.2360
72.5771
98.1749
69.2645
96.3680
56.0139
95.7657
46.0759
72.2760
48.4851
0.2
166.3552
143.6485
173.4624
136.1198
162.0187
125.8807
163.5244
113.2324
148.7681
104.1979
0.3
210.3231
169.2463
220.7429
162.9221
215.0211
151.7796
210.805
136.1198
205.8050
128.5910
0.4
215.1415
168.6440
220.4418
166.5359
213.2142
158.7060
206.2877
143.6485
203.7820
144.5520
0.5
198.0061
166.5359
203.2762
164.1267
201.4693
160.2118
200.5659
151.4784
201.4693
151.4784
0.6
171.8361
146.0577
180.0877
145.7566
180.9911
147.8646
179.7865
143.3474
180.9911
144.2508
0.7
132.4758
114.1358
140.6370
117.7496
147.2623
123.1703
145.7566
118.9542
145.7566
118.9542
0.8
85.8578
74.0829
93.6576
80.4070
102.3910
84.3220
98.1749
80.4070
98.1749
82.2139
0.9
38.3062
29.5127
43.9679
36.138
44.8713
40.6552
43.6667
38.8483
44.8713
39.1495
1
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000The values ofΔF12E predict the information on the strength of interaction between unlike molecules. In both  systems, the values of ΔF12E have appreciable change with respect to concentration and temperature. This reveals that hetero association involves between the compounds varying with concentration and temperatures as shown in Table 5.Table 5
Variation ofΔF12E with mole fraction (x2) of NMA in 1PN and IPA at different temperatures.
X
2
T
=
303
K
T
=
308
K
T
=
313
K
T
=
318
K
T
=
323
K
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
0
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
0.1
04.5660
03.5571
04.7283
03.3878
04.5556
02.2125
04.5433
01.4001
02.6182
01.6316
0.2
12.7254
11.1322
13.1707
10.5485
12.4053
09.5581
12.3508
08.2157
10.8613
07.2089
0.3
17.9897
15.0014
18.7276
14.9589
19.1441
14.0558
18.5466
12.3544
18.1683
11.1860
0.4
15.8424
13.7909
16.6357
14.0691
17.5316
13.8111
16.9762
12.0862
16.5832
12.0029
0.5
09.3078
08.0868
10.1822
09.2444
11.7528
09.9796
10.9800
09.3189
10.2016
09.0461
0.6
−00.7338
−00.4287
−0.4216
02.0523
02.4032
02.9171
01.0159
02.1709
00.3387
01.3464
0.7
−10.4347
−08.6805
−9.6881
−04.9768
−08.3641
−04.0990
−10.9610
−03.8869
−10.2385
−05.1880
0.8
−16.4193
−13.5920
−14.8587
−08.5288
−13.5373
−14.4807
−16.9548
−14.4175
−18.1462
−12.9819
0.9
−10.8746
−10.4485
−10.0267
−09.1445
−12.5144
−09.1620
−12.3988
−09.0969
−12.0188
−09.1149
1
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000Finally the high positive values ofΔFE for system 1 and system 2, Table 6, indicate the formation of β-clusters with antiparallel alignment [12]. Due to the formation of these β-clusters, the effective dipole moment will be decreased when compared to the sum of individual systems and thereby it destructs the angular correlation between nonideal molecules which may decrease its internal energy [33].Table 6
Variation ofΔFE with mole fraction (x2) of NMA in 1PN and IPA at different temperatures.
X
2
T
=
303
K
T
=
308
K
T
=
313
K
T
=
318
K
T
=
323
K
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
NMA + 1PN
NMA + IPA
0
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
0.1
130.0250
103.8400
137.5354
99.4546
135.5558
79.3069
135.5435
64.9427
100.4919
69.3903
0.2
223.3496
198.1463
233.6125
187.3235
216.8861
172.1791
220.7465
154.2734
199.0800
140.9195
0.3
264.7519
213.7604
279.2223
204.0810
270.6043
204.1814
266.0919
163.2305
263.1228
152.1241
0.4
238.2115
179.7246
243.4016
174.2809
228.9389
159.2665
220.5536
136.7623
218.5583
140.8951
0.5
174.4886
142.0985
176.7181
133.0170
167.1462
121.4051
169.0838
110.8064
172.2203
113.2440
0.6
101.8378
79.9783
106.4867
68.9076
96.6631
64.9540
100.0942
64.2078
102.7297
69.7074
0.7
23.2639
14.2069
24.6430
03.1542
22.3532
01.6228
28.4897
−00.5743
26.8030
05.3522
0.8
−32.3502
−31.6610
−35.0358
−31.7174
−37.6293
−29.8393
−29.9042
−30.0773
−26.5784
−29.8463
0.9
−50.5662
−36.6485
−51.8865
−44.3790
−46.2432
−44.9989
−44.6219
−43.4280
−43.6396
−41.3379
1
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000
00.0000The decrement in the internal energy of molecule leads to the increment in the excess free energy value. The negative values ofΔFE indicate the formation of α-clusters. Due to the formation of these  α-clusters, the effective dipole moment will be increased which increases the internal energy.The excess permittivity(εE) is another dielectric parameter, which gives information about the interaction between the components of the mixture. Rana et al.  [34] had pointed out that the change in the value of  εE with concentration is due to the interaction between dissimilar molecules which may produce structural changes. In system 1 and system 2, negative values of  εE are obtained for all concentrations at different temperatures as shown in Figures 1 and 2, respectively. These negative values indicate that the molecules in the mixture form multimers through hydrogen bonding in such a way that the effective dipole moment gets reduced [35, 36]. The more negative deviations in  εE values of system 1 compared to system 2 indicate that the strength of hydrogen bond formation is more in system 1 than in system 2.Figure 1
Plot of excess permittivity(εE)  with mole fraction (X2) of NMA in IPA at different temperatures.Figure 2
Plot of excess permittivity(εE) with mole fraction (X2) of NMA in 1PN at different temperatures.The calculated values of excess inverse relaxation time(1/τ)E, for both  systems, are negative and are presented in Figures 3 and 4 for the systems 1 and 2, respectively.Figure 3
Plot of excess inverse relaxation time((1/τ)E) with mole fraction (X2)  of NMA in 1PN at different temperatures.Figure 4
Plot of excess inverse relaxation time((1/τ)E) with mole fraction (X2)  of NMA in IPA at different temperatures.These negative values indicate the slower rotation of dipoles due to the formation of hydrogen-bonded structures producing a field, which hinders the effective dipole rotation [14, 25]. Further, it is observed that the negative deviations are more in case of system 1 than in system 2 which shows greater strength of intermolecular hetero interaction in system 1.The variation of excess Gibb’s energy of activation(ΔG*)E  values, with mole fraction and temperature, for system 1 and system 2 are shown in Figures 5 and 6, respectively.Figure 5
Variation of excess Gibb’s energy of  activation(ΔG*)E with mole fraction (X2)  of NMA in   1PN at  different temperatures.Figure 6
Variation of excess Gibb’s energy of activation(ΔG*)E with mole fraction (X2)  of NMA in IPA  at different temperatures.The values of(ΔG*)E are positive, in both  systems, which indicates the presence of interaction between the molecules of the mixtures. The magnitude of (ΔG*)E  is an excellent indicator of the strength of interaction between unlike molecules in liquid mixtures [37]. Ali and Nain [38] attributed the increasing positive values of (ΔG*)E  in few binary liquid mixtures to hydrogen bond formation between unlike molecules, which supports the present investigation. Further, it is observed that (ΔG*)E values of system 1 are greater than that of system 2 indicating a stronger bond formation in system 1. The excess molar enthalpy (ΔH*)E  and excess molar entropy (ΔS*)E   values are shown in Figures 7 and 8, respectively. The negative values of (ΔH*)E, for both the systems, show that strong attractive interactions are present between unlike molecules of the mixtures [39]. The formation of hydrogen bonding between the components in system 1 and system 2 is also justified by the negative values of excess molar entropy [14].Figure 7
Variation of excess molar enthalpy(ΔH*)E with mole fraction (X2)  of NMA in 1PN and IPA.Figure 8
Variation of excess molar entropy(ΔS*)E   with mole fraction (X2) of NMA in 1PN and IPA.The hydrogen bonding energy or the interaction energy(ΔE) values are calculated, for both  systems, using Hamiltonian quantum mechanical calculations and are given in Table 7.Table 7
Heat of formation (E) and hydrogen bonding energy (ΔE) values in kcal mol−1 (PCS: PC Spartan, AGS: ArgusLab).
AM1
PM3
MNDO
Compound
PCS
AGS
PCS
AGS
PCS
AGS
E
Δ
E
E
Δ
E
E
Δ
E
E
Δ
E
E
Δ
E
E
Δ
E
NMA
24.21
—
25.43
—
20.67
—
21.44
—
24.26
—
25.46
—
1PN
–68.92
—
–68.15
—
–61.57
—
–61.44
—
–67.71
—
–65.68
—
IPA
–68.03
—
–66.59
—
–63.94
—
–63.20
—
–65.41
—
–63.68
—
NMA + 1PN
–49.35
–4.64
–45.32
–2.60
–46.11
–5.21
–46.07
–6.07
–43.51
–0.06
–40.25
–0.03
NMA + IPA
–48.19
–4.37
–44.07
–2.91
–45.93
–2.66
–46.65
–4.89
–48.20
–7.06
–38.40
–0.19The interaction energy between the components of a mixture should be negative if that mixture is stabilized by the presence of hydrogen bonds. Moreover, the magnitude of the interaction energy would be a measure of the hydrogen-bonding stabilization. The hydrogen bonding energies in the present study are found to be negative in both the binary complexes, in all theoretical models, indicating the formation of hydrogen bonding [30]. The optimized converged geometrical structures of hydrogen bonded systems 1 and 2, which are obtained from Hamiltonian quantum mechanical calculations, are shown in Figures 9(a) and 9(b), respectively.Optimized converged geometrical structures of hydrogen bonded (a) NMA AND 1PN            and                (b) NMA AND IPA (red: oxygen, blue: nitrogen, black: carbon, white: hydrogen).
(a)
(b)Studying the variations in the above dielectric and thermodynamical parameters, one can observe some sort of correlation among them leading to structural changes in mixture. For instance, the high positive values ofΔFE, for the present systems, indicate the formation of β-clusters with antiparallel alignment. Due to this, the effective dipole moment will be decreased when compared to the sum of individual systems, which gives negative values of excess dipole moment and excess permittivity. Further, the formation of β-clusters destructs the angular correlation between nonideal molecules which may decrease the internal energy and thus giving negative values of interaction energy (ΔE). Another observation in the present study is that the relaxation time decreases as the temperature increases, which gives negative values of excess inverse relaxation time. This may be due to the decreasing viscosity of medium. With increase in the temperature, the thermal agitation increases and the dipole requires more energy in order to attain the equilibrium with the applied field and results in negative excess molar entropy values. This indicates that the activated state is more ordered than the normal state, which is true because in the activated state the dipoles try to align with the applied field. Thus the parameters determined in the paper correlate one another and at the same time each parameter supports the formation of hydrogen bonding between the mixture systems.


## 4.  Conclusion

The dielectric and thermodynamic parameters, dipole moment, excess dipole moment, excess Helmholtz free energy, excess permittivity, excess inverse relaxation, and excess thermodynamical values, are computed for the pure and binary mixtures of the systems N-methylaniline with propan-1-ol (system 1) and N-methylaniline with isopropyl alcohol (system 2) for various mole fractions at different temperatures. The formation of hydrogen bonding between the mixture systems is identified by studying the variations in the parameters determined. Using quantum mechanical calculations, the values of dipole moment and excess dipole moment are determined theoretically and they are in good agreement with the experimental values.



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*Source: 425893-2012-08-29.xml*