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

Krishna, T. Vijaya; Sastry, S. Sreehari; Ha, Sie Tiong; Murthy, V. R. K.

doi:https://doi.org/10.1155/2013/425893

Journal of Chemistry

On this page

Abstract Introduction Experimental Results and Discussion Conclusion Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2013 | Article ID 425893 | https://doi.org/10.1155/2013/425893

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

T. Vijaya Krishna,¹S. Sreehari Sastry,²Sie Tiong Ha,³and V. R. K. Murthy⁴

Academic Editor: Karin Larsson

Received18 Jan 2012

Revised25 Jun 2012

Accepted02 Jul 2012

Published29 Aug 2012

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.

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 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 , 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 and imaginary parts of the complex dielectric permittivity are determined with microwave bench (X-Band-8.60 GHz) using Plunger technique [19] for the above temperatures. The high frequency dielectric permittivity 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 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. 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]. where is molecular weight of solute,, and are, respectively, the slopes of and with respect to the weight fraction of the solute, is density of solvent, and is the static dielectric permittivity of solvent (Benzene).

The excess dipole moments of the systems are determined [12, 21, 22] by (2) as follows: where is the dipole moment of NMA, is the dipole moment of either 1PN or IPA, and is the dipole moment of the equimolar solute mixtures NMA + 1PN or NMA + IPA.

The excess Helmholtz free energy 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 represents the excess dipolar energy due to long range electrostatic interaction, represents the excess dipolar energy due to the short range interaction between identical molecules, and represents the excess free energy due to short-range interaction between dissimilar molecules.

The above terms are given in detail in (4) as where, , , , is the molar volume of the components, and , 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 . The excess permittivity, , which provides qualitative information about formation of multimers in the mixture, can be computed as [24] where 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.

indicates that there is no interaction between the components in the mixture.

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.

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 which gives information regarding the dynamics of solute-solvent interaction and represents the average broadening of dielectric spectra can be defined [25] as

The thermodynamic parameters excess Gibb’s energy of activation , excess molar enthalpy of activation , and excess molar entropy of activation at different mole fractions can be determined by fitting 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 Modified Neglect of Differential Overlap (MNDO) converged geometry optimization procedure using PC Spartan and ArgusLab modeling softwares. Ab initio calculations 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 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.

The 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 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.

The excess dipole moment 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 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 [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 and its constituent parameters , , [32].

The value of represents the long-range interaction between the dipoles in the mixture. In system 1 and system 2, the positive values of indicate the existence of attractive forces between the dipoles and larger separation between the interacting molecules. Negative values of indicate the repulsive force between dipoles and interacting molecules are at closer distance. In both systems, values of are positive up to equimolar concentration and negative for remaining concentrations. The values of are decreasing for all the mole fractions, in both systems, as the temperature is increasing and are given in Table 3.

This shows that the strength of dipole-dipole interaction depends on the concentration and temperature of the mixture. The values of 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 of predict the information on the short range interaction between similar molecules. In both systems the values of 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 for system 1 are greater than system 2 predicting the strong short range interaction between the components of similar molecules.

The values of predict the information on the strength of interaction between unlike molecules. In both systems, the values of 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.

Finally the high positive values of 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].

The decrement in the internal energy of molecule leads to the increment in the excess free energy value. The negative values of 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 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. 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 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.

The calculated values of excess inverse relaxation time , for both systems, are negative and are presented in Figures 3 and 4 for the systems 1 and 2, respectively.

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 values, with mole fraction and temperature, for system 1 and system 2 are shown in Figures 5 and 6, respectively.

The values of are positive, in both systems, which indicates the presence of interaction between the molecules of the mixtures. The magnitude of 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 in few binary liquid mixtures to hydrogen bond formation between unlike molecules, which supports the present investigation. Further, it is observed that values of system 1 are greater than that of system 2 indicating a stronger bond formation in system 1. The excess molar enthalpy and excess molar entropy values are shown in Figures 7 and 8, respectively. The negative values of , 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].

The hydrogen bonding energy or the interaction energy values are calculated, for both systems, using Hamiltonian quantum mechanical calculations and are given in Table 7.

The 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.

(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 of , 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 . 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.

Acknowledgments

The authors gratefully acknowledge the Project no. 34-12/2008 (SR), dated 30-12-2008 of UGC, and UGC DRS lEVEL III program no. F.530/1/DRS/2009 (SAP-I), dated 09-02-2009 New Delhi, to the Department of Physics for providing financial assistance.

References

J. Crossley, “Dielectric relaxation and hydrogen bonding in liquids,” Advances in Molecular Relaxation Processes, vol. 2, no. 1, pp. 69–99, 1970.
View at: Google Scholar
U. Kaatze, “Dielectric spectroscopy of aqueous solutions. Hydration phenomena and hydrogen-bonded networks,” Journal of Molecular Liquids, vol. 56, p. 95, 1993.
View at: Publisher Site | Google Scholar
J. N. Murrell and A. D. Jenkins, Properties of Liquids and Solutions, Wiley, New York, NY, USA, 1994.
J. W. Wijnen, J. B. F. N. Engberts, and M. J. Blandmer, “Analysis of the kinetics of solvolysis of p-nitrophenylsulfonylmethyl perchlorate in binary alcoholic mixtures in terms of the thermodynamic properties of the solvent mixturesJournal of the Chemical Society,” vol. 2, p. 363, 1993.
View at: Google Scholar
G. Nath, S. Sahu, and R. Paikaray, “Study of acoustic parameters of binary mixtures of a nonpolar liquid with polar liquid at different frequencies,” Indian Journal of Physics, vol. 83, no. 4, pp. 429–436, 2009.
View at: Google Scholar
R. J. Sengwa, V. Khatri, and S. Sankhla, “Static dielectric constants and kirkwood correlation factor of the binary mixtures of N-methylformamide with formamide, N,N-dimethylformamide and N,N-dimethylacetamide,” Journal of Solution Chemistry, vol. 38, no. 6, pp. 763–769, 2009.
View at: Publisher Site | Google Scholar
J. Whysner, L. Vera, and G. M. Williams, “Benzidine mechanistic data and risk assessment: species- and organ-specific metabolic activation,” Pharmacology & Therapeutics, vol. 71, p. 107, 1996.
View at: Publisher Site | Google Scholar
P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,” Physical Review, vol. 136, no. 3B, pp. B864–B871, 1964.
View at: Publisher Site | Google Scholar
A. J. George, An Introduction To Hydrogen Bonding, Oxford University Press, London, UK, 1997.
T. Vishwam, V. Subramanian, D. V. Subbaiah, and V. R. K. Murthy, “Conformational and microwave dielectric relaxation studies of hydrogen bonded polar binary mixtures of propionaldehyde with isopropyl amine,” Molecular Physics, vol. 106, no. 1, pp. 95–101, 2008.
View at: Publisher Site | Google Scholar
K. A. Higasi, Y. Koga, and M. Nakamura, “Dielectric relaxation and molecular structure. V. Application of the single frequency method to systems with two debye dispersions,” Bulletin of the Chemical Society of Japan, vol. 44, p. 988, 1971.
View at: Publisher Site | Google Scholar
T. Madhu Mohan, S. Sreehari Sastry, and V. R. K. Murthy, “Investigations on Binary Mixtures of Propan-2-ol with Methyl Benzoate and Ethyl Benzoate,” Journal of Solution Chemistry, vol. 40, no. 11, pp. 1847–1862, 2011.
View at: Google Scholar
G. Parthipan, G. Arivazhagan, and T. Thenappan, “Dielectric and thermodynamic studies on a binary mixture of anisole with butyric or caprylic acid,” Philosophical Magazine Letters, vol. 88, no. 2, pp. 125–136, 2008.
View at: Publisher Site | Google Scholar
K. Dharmalingam, K. Ramachandran, P. Sivagurunathan, B. Prabhakar Undre, P. W. Khirade, and S. C. Mehrotra, “Dielectric relaxation of butyl acrylate-alcohol mixtures using time domain reflectometry,” Chemical Papers, vol. 61, no. 4, pp. 300–307, 2007.
View at: Publisher Site | Google Scholar
M. Chitra, B. Subramanyam, and V. R. K. Murthy, “Conformational and dielectric analysis of hydrogen bonded polar binary mixtures of methyl benzoate with anilin,” Indian Journal of Pure and Applied Physics, vol. 39, pp. 461–466, 2001.
View at: Google Scholar
N. Sathyan, V. Santhanam, V. Madhurima, and J. Sobhanadri, “Conformational study on the binary mixture acetone-methanol involving H-bonding,” Journal of Molecular Structure, vol. 342, no. C, pp. 187–192, 1995.
View at: Google Scholar
Spartan Version 5. 1. 1, Wave function Inc., 18401 Von Kaman Ave., Suite 370, Irvine, Calif, USA, 1999.
Argus Lab 4. 0. 1, M.A. Thompson, Planaria Software LLC, Seattle, Wash, USA.
N. E. Hill, W. E. Vaughan, A. H. Price, and M. Davies, Dielectric Properties and Molecular Behavior, Northland Reinhold Company, London, UK, 1968.
D. Lide, CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, Fla, USA, 78th edition, 1971.
A. N. Prajapathi, V. A. Rana, and A. D. Vyas, “Microwave absorption and relaxation studies of binary mixtures of fluoro substituted anilines with some primary alcohols in benzene solutions,” Indian Journal of Pure and Applied Physics, vol. 44, p. 620, 2006.
View at: Google Scholar
T. M. Mohan, S. S. Sastry, and V. R. K. Murthy, “Correlations among dielectric and thermodynamic parameters in hydrogen bonded binary mixtures of alcohol and alkyl benzoates,” Journal of Molecular Liquids, vol. 159, no. 3, pp. 173–179, 2011.
View at: Publisher Site | Google Scholar
K. K. Gupta, A. K. Bnashal, P. J. Singh, and K. S. Sharma, “Temperature dependence of dielectric relaxation of rigid polar molecules acetophenone, pyridine and their mixtures in dilute solutions of benzene,” Indian Journal of Pure and Applied Physics, vol. 41, no. 1, pp. 57–63, 2003.
View at: Google Scholar
A. C. Kumbharkhane, S. M. Puranic, and S. C. Mehrotra, “Dielectric relaxation studies of aqueous N,N-dimethylformamide using a picosecond time domain technique,” Journal of Solution Chemistry, vol. 22, pp. 219–229, 1993.
View at: Publisher Site | Google Scholar
A. Chaudhari, C. S. Patil, A. Shankarwar, B. R. Garbad, and S. C. Mehrotra, “Temperature Dependent Dielectric Relaxation Study of Aniline in Dimethylsulphoxide and Dimethylformamide Using Time Domain Technique,” Journal of the Korean Chemical Society, vol. 45, no. 3, pp. 201–206, 2001.
View at: Google Scholar
F. Cernuschi and H. Eyring, “An elementary theory of condensation,” The Journal of Chemical Physics, vol. 7, no. 7, pp. 547–551, 1939.
View at: Google Scholar
J. Lou, A. K. Paravastu, P. E. Laibinis, and T. A. Hatton, “Effect of temperature on the dielectric relaxation in solvent mixtures at microwave frequencies,” Journal of Physical Chemistry A, vol. 101, no. 51, pp. 9892–9899, 1997.
View at: Google Scholar
T. Vijaya Krishna, S. Sreehari Sastry, and V. R. K. Murthy, “Dielectric relaxation, thermodynamic and theoretical studies on hydrogen bonded polar binary mixtures of N-methyl aniline with propan-1-ol and isopropyl alcohol,” Indian Journal of Physics, vol. 85, pp. 379–390, 2011.
View at: Publisher Site | Google Scholar
T. Vishwam, M. Chitra, V. Subramanian, and V. R. K. Murthy, “Conformational and dielectric analysis of hydrogen bonded polar binary mixtures of propan-1-ol with propionaldehyde,” Molecular Physics, vol. 105, no. 17-18, pp. 2411–2417, 2007.
View at: Publisher Site | Google Scholar
M. Chitra, B. Subramanyam, and V. R. K. Murthy, “Conformational and dielectric analysis of hydrogen bonded polar binary mixtures of methyl benzoate with N-methylaniline,” Molecular Physics, vol. 99, no. 18, pp. 1569–1573, 2001.
View at: Publisher Site | Google Scholar
J. Sobhanadri, V. Satheesh, and M. Jayaraj, “Dielectric studies of allyl alcohol with (i) Pyridine, (ii)1,4-Dioxane and (iii)Phenol hydrogen bonded complexes,” Journal of Molecular Liquids, vol. 64, p. 247, 1995.
View at: Publisher Site | Google Scholar
R. Varadarajan and A. Rajgopal, “Dipolar excess thermodynamic parameters and Kirkwood-Frohlich correlation factor of monoalcohols,” Indian Journal of Pure and Applied Physics, vol. 36, pp. 119–124, 1998.
View at: Google Scholar
B. B. Swain, “Excess thermodynamic functions of mixing in binary mixtures of alcohols and tolune,” Current Science, vol. 54, p. 504, 1998.
View at: Google Scholar
V. A. Rana, A. D. Vyas, and S. C. Mehrotra, “Dielectric relaxation study of mixtures of 1-propanol with aniline, 2-chloroaniline and 3-chloroaniline at different temperatures using time domain reflectometry,” Journal of Molecular Liquids, vol. l02, pp. 379–391, 2002.
View at: Google Scholar
A. Chaudhari, A. Das, G. Raju et al., “Complex permittivity spectra of binary mixture of ethanol with nitrobenzene and nitrotoluene using time domain technique,” Proceedings of the National Science Council A, vol. 25, p. 205, 2001.
View at: Google Scholar
J. Sengwa, Madhvi, S. Sankhla, and S. Sharma, “Characterization of heterogeneous interaction behavior in ternary mixtures by a dielectric analysis: equi-molar H–bonded binary polar mixtures in aqueous solutions,” Journal of Solution Chemistry, vol. 35, pp. 1037–1055, 2006.
View at: Publisher Site | Google Scholar
T. M. Reed and T. E. Taylor, “Viscosities of liquid mixtures,” The Journal of Physical Chemistry, vol. 63, pp. 58–67, 1959.
View at: Publisher Site | Google Scholar
A. Ali and A. K. Nain, “Intermolecular interactions in ternary liquid mixtures by ultrasonic velocity measurements,” Indian Journal of Physics, vol. 74, pp. 63–67, 2000.
View at: Google Scholar
B. S. Bjola, M. A. Siddiqi, U. Fornefeld-Schwarz, and P. Svejda, “Molar excess volumes and molar excess enthalpies of binary liquid mixtures of norbornadiene + benzene, + cyclohexane, + decane, and + carbon tetrachloride,” Journal of Chemical and Engineering Data, vol. 47, no. 2, pp. 250–253, 2002.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2013 T. Vijaya Krishna et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies