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

e molecular interactions between the polar systems N-methylaniline with alcohols, propan-1-ol, and isopropyl alcohol for variousmole 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 quantummechanical calculations are performed using PC Spartan and ArgusLab modeling sowares for both pure and equimolar binary systems of N-methyl aniline with alcohols.


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, nonspeci�c 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.
ere 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.e presence of hydrogen bond brings a considerable change in the dielectric properties of liquid mixtures [6].e 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 scienti�cally 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.e nature of interaction between -NH and -OH groups plays an important role in biological systems and drug synthesis [9,10].
e 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][12][13][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 sowares [17,18].e obtained theoretical values are further compared with the experimental values.

Experimental
e compounds N-methylaniline (NMA), propan-1-ol (1PN), and isopropyl alcohol (IPA) of AR grade are purchased from �. Merck, Germany, and are puri�ed by standard methods.e binary mixtures are prepared for different mole fractions, that is, mole fraction ( 2 ) of Nmethylaniline is varied from 0 to 1 in alcohols 1PN and IPA (with a step increment of 0.1).e temperature controller system with a water bath, supplied by M/s Sakti scienti�c 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 speci�c gravity bottle and M�TTL�R TOL�DO balance (Model no: AB135-S/FACT) whose accuracy is 0.01 mg.
e static permittivity values at the spot frequencies 1 kHz ( static ), 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.e real () and imaginary () parts of the complex dielectric permittivity ( * =  � −  �� ) are determined with microwave bench (X-Band-8.60GHz) using Plunger technique [19] for the above temperatures.e high frequency dielectric permittivity ( ∞ =  2 ) is obtained from the refractometer measurements using M/s ASCO make Abbe's refractometer with sodium D light as source at different temperatures.e error in the estimation of  static ,  � ,  ∞ and density is 1% and the error in the estimation of  �� ,  is 2%.Dipole moments of the liquids in gaseous state are taken from literature [20].
2.1.eory.e 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].
where  2 is molecular weight of solute,  0 , and  ∞ are, respectively, the slopes of  static and  ∞ with respect to the weight fraction of the solute,  1 is density of solvent, and  1 is the static dielectric permittivity of solvent (Benzene).
e excess dipole moments (Δ) of the systems are determined [12,21,22] by (2) as follows: where  1 is the dipole moment of NMA,  2 is the dipole moment of either 1PN or IPA, and  12 is the dipole moment of the equimolar solute mixtures NMA + 1PN or NMA + IPA.e excess Helmholtz free energy (Δ  ) 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 where Δ   represents the excess dipolar energy due to long range electrostatic interaction, Δ   represents the excess dipolar energy due to the short range interaction between identical molecules, and Δ   12 represents the excess free energy due to short-range interaction between dissimilar molecules.
e contribution of hydrogen bonds to the dielectric properties of the mixtures can be studied in terms of excess permittivity (  ).e excess permittivity,   , which provides qualitative information about formation of multimers in the mixture, can be computed as [24]   =   −  ∞  −  1 −  ∞   1 +  2 −  ∞   2  , (5) where  is mole fraction and suffix 1, 2, and m represents liquid 1, liquid 2, and mixture, respectively.e qualitative information provided by excess permittivity about the mixtures is as follows.
= 0 indicates that there is no interaction between the components in the mixture.
< 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.
> 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.
e excess inverse relaxation time (1/  which gives information regarding the dynamics of solute-solvent interaction and represents the average broadening of dielectric spectra can be de�ned [25] as e thermodynamic parameters excess Gibb's energy of activation (Δ *   , excess molar enthalpy of activation (Δ *   , and excess molar entropy of activation (Δ *   at different mole fractions can be determined by �tting the Eyring rate equation [26,27] as 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 Modi�ed Neglect of Differential Overlap (MNDO) converged geometry optimization procedure using PC Spartan and ArgusLab modeling sowares.Ab initio calculations have been carried out using PC Spartan modeling soware and the geometry optimizations are done at the Hartree-Fock (HF) level using 6-31G * basis set.

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].e 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.e theoretical vibrational frequencies of the pure and equimolar hydrogen bonded systems are obtained from Hamiltonian quantum mechanical calculations using Spartan modeling soware.e same data is used to study excess dielectric parameters and reporting in this communication.
e dipole moment ( 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 initio and semiempirical) and the corresponding values are given in Table 1.e 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.is may be due to the formation of hydrogen bonding between the mixture systems [29].e theoretical dipole moment values, mainly Hartree-Fock calculations, are in good agreement with the experimental values.e small deviation between the theoretical and experimental values may be due to the model dependency in theoretical case and due to the  electron cloud of nonpolar solvent benzene affecting the dipole moment value of the solute systems in experimental case [30].e dipole moment values, measured for the pure and equimolar systems, are signi�cantly affected by the variation in temperature as shown in Table 2.
e excess dipole moment (Δ 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 Δ 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 Δ [31].e excess dipole moment value is a qualitative index for the presence of hydrogen bonding in system 1 and system 2.
is shows that the strength of dipole-dipole interaction depends on the concentration and temperature of the mixture.e values of Δ   for system 1 are greater than system 2. is may be due to the interaction of the compounds in the mixture which produces structural changes.
e values of Δ   predict the information on the short range interaction between similar molecules.In both systems the values of Δ   are highly positive at all mole fractions, as shown in Table 4, indicating the existence of short range interaction through hydrogen bonding.e values of Δ   for system 1 are greater than system 2 predicting the strong short range interaction between the components of similar molecules.
e values of Δ  12 predict the information on the strength of interaction between unlike molecules.In both systems, the values of Δ   12 have appreciable change with respect to concentration and temperature.is reveals that hetero association involves between the compounds varying with concentration and temperatures as shown in Table 5.
Finally the high positive values of Δ  for system 1 and system 2, Table 6, indicate the formation of -clusters with antiparallel alignment [12].Due to the formation of these 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].
e long-range and short-range interactions between dipoles can be studied from the thermodynamical parameter excess Helmholtz free energy (Δ   and its constituent parameters Δ   , Δ   , Δ  12 [32].e value of Δ   represents the long-range interaction between the dipoles in the mixture.In system 1 and system 2,    are decreasing for all the mole fractions, in both systems, as the temperature is increasing and are given in Table 3.
e decrement in the internal energy of molecule leads to the increment in the excess free energy value.e negative values of Δ  indicate the formation of -clusters.Due to the formation of these -clusters, the effective dipole moment will be increased which increases the internal energy.e excess permittivity (  ) 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   with concentration is due to the interaction between dissimilar molecules which may produce structural changes.In system 1 and system 2, negative values of   are obtained for all concentrations at different temperatures as shown in Figures 1 and 2, respectively.ese 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].e more negative deviations in   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. e calculated values of excess inverse relaxation time (1/  , for both systems, are negative and are presented in Figures 3 and 4 for the systems 1 and 2, respectively.ese negative values indicate the slower rotation of dipoles due to the formation of hydrogen-bonded structures producing a �eld, 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.e variation of excess Gibb's energy of activation (Δ *   values, with mole fraction and temperature, for system 1 and system 2 are shown in Figures 5 and 6, respectively.e values of (Δ *   are positive, in both systems, which indicates the presence of interaction between the molecules of the mixtures.e magnitude of (Δ *   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 (Δ *   in few binary liquid mixtures to hydrogen bond formation between  7 and 8, respectively.e negative values of (Δ * )  , for both the systems, show that strong attractive interactions are present between unlike molecules of the mixtures [39].e formation of hydrogen bonding between the components in system 1 and system 2 is also justi�ed by the negative values of excess molar entropy [14].e hydrogen bonding energy or the interaction energy (Δ values are calculated, for both systems, using Hamiltonian quantum mechanical calculations and are given in Table 7.
e 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 hydrogenbonding stabilization.e 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].e 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 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 of Δ  , for the present systems, indicate the formation of -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 -clusters destructs the angular correlation between nonideal molecules which may decrease the internal energy and thus giving negative values of interaction energy (Δ.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.is 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 �eld and results in negative excess molar entropy values.is 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 �eld.us 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.

Conclusion
e 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.e formation of hydrogen bonding between the mixture systems is identi�ed 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.

F 1 :
Plot of excess permittivity (  ) with mole fraction ( 2 ) of NMA in IPA at different temperatures.the positive values of Δ   indicate the existence of attractive forces between the dipoles and larger separation between the interacting molecules.Negative values of Δ   indicate the repulsive force between dipoles and interacting molecules are at closer distance.In both systems, values of Δ   are positive up to equimolar concentration and negative for remaining concentrations.e values of Δ

F 2 :
Plot of excess permittivity (  ) with mole fraction ( 2 ) of NMA in 1PN at different temperatures.

F 3 :F 4 :
Plot of excess inverse relaxation time ((1/   with mole fraction ( 2  of NMA in 1PN at different temperatures.Plot of excess inverse relaxation time ((1/   with mole fraction ( 2  of NMA in IPA at different temperatures.
T 3: Variation of Δ   with mole fraction ( 2 ) of NMA in 1PN and IPA at different temperatures.
Variation of excess Gibb's energy of activation (Δ *   with mole fraction ( 2  of NMA in IPA at different temperatures. T 7: Heat of formation () and hydrogen bonding energy (Δ) values in kcal mol − (PCS: PC Spartan, AGS: ArgusLab).
and excess molar entropy (Δ * ) values are shown in Figures