Acoustical and computational studies on hydrogen

Indian Journal of Pure & Applied Physics Vol. 51, June 2013, pp. 406-412

Acoustical and computational studies on hydrogen bonded binary mixtures of N,N-dimethylacetamide with alcohols M Lakshmi Nadha, T Madhu Mohanb*, T Vijaya Krishnab & Ch Ravi Shankar Kumarc a

Department of Physics, Malla Reddy College of Engineering for Women, Hyderabad 500 055

b

*Department of Physics, Vasireddy Venkatadri Institute of Technology, Nambur 522 508, India c

Department of Physics, Institute of Science, GITAM University, Visakhapatnam, India *E-mail: [email protected] Received 20 June 2012; revised 10 January 2013; accepted 12 March 2013

Ultrasonic velocity, density and viscosity measurements have been carried out in the polar binary mixtures of N,N-dimethylacetamide with alcohol (propan-1-ol/propan-2-ol) for various mole fractions at 303.15 K. The experimental data has been used to calculate the parameters-adiabatic compressibility, intermolecular free length, internal pressure, acoustic relaxation time, Wada’s constant, Rao’s constant and excess values. The optimized geometry, harmonic vibrational wave numbers and dipole moments of pure and equimolar binary mixtures have been calculated by ab-initio Hartree-Fock (HF) and Density Functional Theory (DFT-B3LYP) methods with 6-31+G* and 6-311+G** basis sets using Spartan 08 modeling software. Vibrational frequencies during the formation of hydrogen bond in the equimolar binary mixture systems of N,N-dimethylacetamide with alcohol (propan-1-ol/propan-2-ol) are supported by experimental FT-IR spectra. The calculated wave numbers are found to agree well with the experimental wave numbers. Keywords:

Adiabatic compressibility, FT-IR spectra, Hartree-Fock, Density functional theory

1 Introduction The ultrasonic and thermodynamic studies of molecular interactions have got significant importance in industry and engineering applications1,2. The measurement of ultrasonic velocity has been adequately employed in understanding the nature of molecular interactions in pure liquids and liquid mixtures. The ultrasonic velocity measurements are highly sensitive to molecular interactions and can be used to provide qualitative information about the physical nature and strength of molecular interaction in the liquid mixtures3-5. The relaxation studies of polar molecules in polar solvents have been widely used to study the molecular structures including the molecular interactions in liquid mixtures6,7. Alcohols play an important role in many chemical reactions due to their ability to undergo selfassociation with manifold internal structures. Alcohols are used in the manufacturing of perfumes, paint removers and antiseptic agents. N,N-dimethylacetamide belongs to the amide group and is used as solvent in chemical and biological processes. It is also used in blood pressure and respiration studies. The applications of these compounds motivated the authors to perform experimental studies on the binary mixtures of N,N-dimethylacetamide and alcohols in

order to understand the molecular association and also the related properties. The ultrasonic investigations of pure and binary mixtures of N,N-dimethylacetamide with propan-1-ol (system 1) and N,N-dimethylacetamide with propan2-ol (system 2) for various mole fractions at 303.15 K, have been studied. Using the experimental data, the ultrasonic parameters-adiabatic compressibility, intermolecular free length, internal pressure, acoustic relaxation time, Wada’s constant, Rao’s constant and excess values are determined8-11. The vibrational frequencies of the pure and equi molar hydrogen bonded systems are calculated by the Hartree-fock self-consistent field method and Density Functional Theory (DFT-B3LYP) methods with 6-31+G* and 6-311+G** basis sets using Spartan 08 modeling software12. The vibrational frequencies during the formation of hydrogen bond in the equimolar binary mixture systems of N,N-dimethylacetamide with propan-1-ol/propan-2-ol are supported by experimental FT-IR spectra. The obtained theoretical values are compared with the experimental values. 2 Experimental Details The compounds N,N-dimethylacetamide (DMA), propan-1-ol (1PN) and propan-2-ol (IPA) of AR grade

NADH et al.: ACOUSTICAL AND COMPUTATIONAL STUDIES OF BINARY MIXTURES

( 99%) are procured from E Merck, Germany. All the compounds are further purified by standard procedure13. Job’s method of continuous variation is used to prepare the mixtures of required proportions. The mixed liquid binary systems are preserved in well-stoppered conical flasks. After mixing the liquids thoroughly, the flasks are left undisturbed to allow them to attain thermal equilibrium. The densities of pure liquids and liquid mixtures are measured by using a specific gravity bottle. The accuracy in the measurement of density with the specific gravity method is ± 0.5%. The mass measurements are performed on a digital electronic balance (Mettler Toledo AB 135, Switzerland) with an uncertainty of ± 0.00001 g. Viscosities are determined using Ostwald’s glass capillary viscometer, which is calibrated with benzene and doubly distilled water at 303.15 K. The values are accurate to ± 0.001 mPa.s. Ultrasonic velocities are determined using single crystal ultrasonic pulse echo interferometer (model F-80, Mittal Enterprises, India) working at 2 MHz and the ultrasonic velocity has an accuracy of ±0.5 m/s. The FT-IR-spectra of pure and equi molar binary mixture systems are recorded in the region 400-4000 cm−1 on Perkin-Elmer (spectrum bX) series. 3 Theory Using the experimentally measured values of ultrasonic velocity (U), density (ρ) and viscosity (η) the following acoustic and thermodynamic parameters can be evaluated. The adiabatic compressibility (βad) has been determined from the ultrasonic velocity (U) and density (ρ) of the medium using the formula,

β ad =

1 U 2ρ

… (1)

The intermolecular free length (Lf) of a binary liquid mixtures at a given mole fraction is given by:

L f = K j βad

… (2)

where Kj is the Jacobson’s constant and it is temperature dependent constant. Its value is 2.0755×10−6 at 303.15 K. On the basis of statistical thermodynamics, the internal Pressure (πi) can be determined using the relation:

1/2

§ Kη · π i = bRT ¨ ¸ © U ¹

ρ 2/3 M eff7/6

407

… (3)

where b is the cubic packing which is assumed to be 2 for all liquids and solutions, R is gas constant, T is temperature in kelvin, K is a temperature independent constant which is equal to 4.28 × 109 for all liquids and η is viscosity in Nsm-2. Meff is the effective molecular weight (Meff=Σmixi, in which mi and xi are molecular weight and mole fraction of the individual constituents, respectively). Molar sound velocity or Rao’s constant (R). R=

M eff

ρ

(U )1/3

… (4)

Wada’s constant (W)

W=

M eff

1

ρ ( β ad )1/7

… (5)

Acoustic relaxation time (τ)

τ=

4η 3ρU 2

… (6)

The excess values (AE) can be determined using the relation,

AE = Aexp − ( A1 x1 + A2 x2 )

… (7)

where A1, A2 are any acoustical or thermodynamical values of pure liquids and x1, x2 are the mole fractions of the liquid 1and liquid 2, respectively. The excess dipole moments (∆µ) of the equimolar systems are determined by the equation14:

∆µ = µ12 − µ1 − µ 2

…(8)

where µ1 is the dipole moment of DMA, µ2 is the dipole moment of either 1PN or IPA and µ12 is the dipole moment of the equimolar solute mixtures DMA + 1PN or DMA + IPA.

The minimum energy structures of the monomers of N, N-dimethylacetamide, propan-1-ol, propan-2-ol and the equimolar hydrogen bonded complexes are obtained from ab-initio Hartree-Fock (HF) and Density Functional Theory (DFT-B3LYP) methods

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408

Fig. 1 — Plots of (a) ultrasonic velocity, (b) density and (c) viscosity with mole fraction ( x2 ) of N,N-dimethylacetamide in system 1 and system 2 at 303.15 K Table 1 — Values of adiabatic compressibility (βad), intermolecular free length (Lf), internal pressure (τι), acoustic relaxation Time (τ) and Wada’s constant of system 1 and system 2 at 303.15 K (x2)

0 0.1213 0.1888 0.3467 0.4516 0.5535 0.6501 0.7529 0.8319 0.9181 1

(βad)×1010 (m2/N) System 1 System 2 5.0528 5.2683 5.4328 5.8811 6.2248 6.5535 6.9158 7.3799 7.7818 8.2231 8.7124

5.0528 5.4399 5.6408 6.2237 6.6218 7.0962 7.6676 8.3081 8.8183 9.4289 10.1034

Lf × 1011 (m) System 1 System 2 4.6653 4.7638 4.8376 5.0332 5.1782 5.3132 5.4581 5.6382 5.7897 5.9516 6.1262

4.6653 4.8408 4.9293 5.1778 5.3408 5.5288 5.7471 5.9823 6.1633 6.3731 6.5970

(πι) 10−8 (Pa) System 1 System 2 4.2114 5.0763 5.3250 5.8456 6.2063 6.6252 7.0926 7.7312 8.2678 8.9557 9.7131

with 6-31+G* and 6-311+G** basis sets, using Spartan 08 modeling software to determine the vibrational frequencies and dipole moments.

4 Results and Discussion The experimentally determined values of ultrasonic velocity (U), density (ρ) and viscosity (η) of the two systems (system 1 and system 2) at 303.15 K are shown in Figs 1(a,b and c), respectively.Ultrasonic velocity is an acoustical parameter which can give good information regarding the molecular interactions between liquid mixtures. The non-linear variation of U with respect to the mole fraction indicates the existence of interaction between the components of the liquid mixtures15. In the present study, in both the systems (system 1 and system 2) the ultrasonic velocity is decreasing and varying non-linearly with

4.2114 4.9212 5.1190 5.6549 6.0340 6.4717 6.9535 7.6455 8.1795 8.9586 9.9471

τ (pico sec) System 1 System 2 0.5767 0.8079 0.8754 1.0138 1.1141 1.2315 1.3720 1.5826 1.7714 2.0188 2.3080

0.5767 0.7836 0.8388 1.0004 1.0931 1.2591 1.4383 1.7087 1.9172 2.1495 2.3081

Wada’s constant W × 103(m19/7.N1/7) System 1 System 2 1.9618 1.9215 1.8812 1.8073 1.7586 1.7104 1.6636 1.6111 1.5715 1.5269 1.4822

1.9618 1.9013 1.889 1.8171 1.7711 1.7183 1.6707 1.6188 1.576 1.5321 1.4921

respect to the mole fraction of alcohol (1PN/ IPA) indicating the existence of molecular interaction between the components of the liquid mixtures as shown in Fig. 1(a). The values of adiabatic compressibility (βad), intermolecular free length (Lf), internal pressure (πi) acoustic relaxation time (τ) and Wada’s constant (W) of system 1 and system 2 are evaluated and given in Table 1. While the ultrasonic velocities of both the systems decrease with increasing mole fraction of alcohol (1PN/ IPA), the adiabatic compressibility (βad) and intermolecular free length (Lf) show the reverse trend i.e., both the parameters are found to increase with mole fraction of alcohol (1PN/IPA) in the mixture. The increase in adiabatic compressibility and intermolecular free length with increasing mole fraction of alcohol indicates significant interactions


between DMA and alcohol molecules forming hydrogen bonding through dipole-dipole interactions16. The variation of ultrasonic velocity in a solution depends upon the increase or decrease of intermolecular free length after mixing the compounds. On the basis of the model proposed by Eyring and Kincaid17 for sound propagation, the ultrasonic velocity decreases if the intermolecular free length increases and vice-versa. This phenomenon is observed in the present investigation for both the systems. The molecules of alcohol are self-associated in pure state through intra molecular hydrogen bonding and DMA is a non-aqueous solvent since it has no hydrogen bonding in pure state. Therefore, DMA acts as an aprotic protophilic medium with high dielectric constant and it is considered as a dissociating solvent. Thus, the addition of DMA in the mixture causes dissociation of hydrogen bonded structures. In the present investigation, the addition of alcohol (1PN/ IPA) with DMA causes dissociation of hydrogen bonded structure of alcohol (1PN/IPA) and subsequent formation of new hydrogen bond (–C=O….HO−) between proton acceptor oxygen atom (with lone pair of electrons) of –C=O in DMA group and hydrogen of HO– in alcohol (1PN/IPA) group. The internal pressure, in both the systems, is observed to be increasing with increase in the concentration of alcohol (1PN/IPA). The increase in internal pressure generally indicates the association of molecules through hydrogen bonding and thereby, it supports the present investigation8. The acoustic relaxation time (τ) is found to increase in both the systems, with increase in the concentration of alcohol (1PN/IPA) in the mixture. This increment in the acoustic relaxation time suggests that the interaction between the molecules of the components is stronger than the attractive forces between the molecules of each component. In the present

409

investigation, the relaxation times are of the order of 10−12 s since the structural relaxation process is showing the presence of molecular interaction18. Further, it is observed that relaxation time of pure DMA is less compared to alcohol (1PN/IPA) due to the lack of self-associated groups. The relaxation time of pure alcohol (1PN/IPA) is high due to the formation of intra molecular hydrogen bonding between one alcohol molecule and another (R−OH….OH−R), which leads to the formation of self-associated groups. The increase in the number of self-associated groups causes the system to absorb more electromagnetic energy. Due to this, the molecules relax very slowly leading to higher relaxation times. The relaxation time is found to increase as the concentration of alcohol (1PN/IPA) increases in DMA indicating the increasing associative nature of the mixture, which supports the formation of hydrogen bonding between the –C=O of DMA group and HO– group of alcohol (1PN/ IPA) molecules restricting the free internal rotation of the molecules of the mixture. The decrement in the Wada’s constant values with increasing mole fraction of alcohol (1PN/ IPA) indicates the attraction between the dissimilar molecules of the liquid mixture. The dipole moment (µ) values for pure and equimolar liquid mixtures, at room temperature, are determined theoretically from ab-initio Hartree-Fock (HF) and Density Functional Theory (DFT-B3LYP) methods19 with 6-31+G* and 6-311+G** basis sets using Spartan 08 modeling software and the corresponding values are given in Table 2. The theoretical dipole moment values of the individual systems agree well with the reported standard values20. It is observed that the formation of hydrogen bond between the two individual compounds causes an increment in the resultant dipole moment value. The excess dipole moment (∆µ) values which indicate the presence of a hydrogen bonding between the

Table 2 — Theoretical dipole moment (µ) and excess dipole moment (∆µ) values in Debye for pure N,N-dimethylacetamide (DMA), propan-1-ol (1PN), propan-2-ol (IPA) and equimolar binary mixture systems at room temperature Theoretical

Compound

µ DMA 1PN IPA System 1 (DMA+1PN) System 2 (DMA+IPA)

Hartree – Fock (HF) 6-31+G* 6-311+G** ∆µ µ ∆µ

Density Functional Theory (DFT-B3LYP) 6-31+G* 6-311+G** µ ∆µ µ ∆µ

3.90 1.99 1.85

-------

4.11 1.95 1.82

-------

4.29 1.84 1.85

-------

4.04 1.66 1.77

-------

5.18

-0.71

5.11

-0.95

5.47

-0.66

5.25

-0.45

5.02

-0.73

5.71

-0.22

5.17

-0.97

5.35

-0.46

410


compounds are given in Table 2. It is observed that, in all the cases ∆µ values are negative indicating the absence of any contribution from ionic structure of the binary mixture system to the total dipole moment, because the formation of any ionic structure21 involves a very high positive value for ∆µ. The variation of Rao’s constant (R) with mole fraction of alcohol (1PN/IPA) is shown in Fig 2. The linear variation in the Rao’s constant value with concentration variation suggests that the interactions are concentration dependent. In both the systems, Rao’s constant values are decreasing with increase in the concentration of the alcohol (1PN/ IPA) in the mixture. Thus, the dipole induced dipole attraction 22 increases with increase in the concentration of associative alcohol (1PN/ IPA). In order to have a much more clear picture about the strength of molecular interactions between the components of the liquid mixtures, it is of interest to discuss the parameters in terms of excess values. Nonideal liquid mixtures show considerable deviation from linearity in their physical behaviour with respect to concentration and this deviation has been attributed to the presence of strong or weak interactions. The magnitude of deviation depends upon the nature of the constituents and composition of the mixtures. In the present work, the variations of excess adiabatic compressibility, excess intermolecular free length and excess internal pressure are studied with concentration variation of alcohol (1PN/ IPA) and their respective plots are shown in Figs 3-5. The excess adiabatic compressibility values, for both systems, are negative over the entire composition range of mixtures (Fig. 3). The negative values of

Fig. 2 — Plot of Rao’s constant with mole fraction (x2) of N,Ndimethylacetamide in system 1 and system 2 at 303.15 K

Fig. 3 — Plot of excess adiabatic compressibility with mole fraction (x2) of N,N-dimethylacetamide in system 1 and system 2 at 303.15 K

Fig. 4 — Plot of excess intermolecular free length with mole fraction (x2) of N, N-dimethylacetamide in system 1and system 2 at 303.15 K

Fig. 5 — Plot of excess internal pressure with mole fraction (x2) of N,N-dimethylacetamide in system 1and system 2 at 303.15 K


excess adiabatic compressibility show that the liquid mixture is less compressible than the pure liquids indicating that the solution and molecules in the mixture are more tightly bound in the liquid mixture than in pure liquids. According to Fort and Moore23, a negative excess adiabatic compressibility is an indication of strong heteromolecular interaction in the liquid mixture and is attributed to charge transfer, dipole-dipole, dipole-induced dipole interactions and hydrogen bonding between unlike components. Further, it is observed that the excess adiabatic compressibility values are more negative in case of system 2 compared to system 1 indicating that the strength of bond formation in system 2 is more compared to system 1. The excess intermolecular free length values in both the systems, are negative over the entire range of composition exhibiting a minimum as shown in Fig. 4. This indicates structural readjustments in the liquid mixtures towards a less compressible phase of fluid and closer packing of molecules24. Thus, the negative values of excess intermolecular free length

411

indicate the strengthening of hydrogen bonding between DMA and alcohol (1PN/IPA) molecules. In the present study, it is observed that the excess intermolecular free length values are more negative in case of system 2 compared to that of system 1 indicating that the strength of intermolecular interaction in system 2 is greater than that of system 1. The negative values of excess internal pressure suggest that only dispersion and dipolar forces are operating with complete absence of complex formation25,26. Further, the high negative values of excess internal pressure in system 2 indicate the high strength of bond formation compared to system 1 (Fig. 5). Observing the experimental FT-IR spectra (Table 3) for the equimolar binary mixture of system 1(DMA+1PN), there is a shift of 16 cm−1 wave number in the position of –C=O and 25 cm−1 wave number in the position of –OH for the mixture compared with the pure spectrums of DMA and 1PN, respectively. Similarly, the FT-IR spectra for the equimolar binary mixture of system 2 (DMA+IPA),

Table 3 — Experimental and theoretical FT-IR analysis of the pure N,N-dimethylacetamide (DMA), propan-1-ol (1PN), propan-2-ol (IPA) and equi molar binary mixture systems at room temperature Compound

Band

Experimental ν (cm−1)

∆ν (cm−1)

C=O OH OH

1685 3346 3550

System 1 (DMA+1PN)

CO--HO

System 2 (DMA+IPA)

CO--HO

DMA 1PN IPA

Hartree-Fock (HF) 6-31+G* 6-311+G**

Theoretical Density Functional Theory (DFT-B3LYP) 6-31+G* 6-311+G**

-------

ν (cm−1) 1732 3387 3588

∆ν (cm−1) -------

ν (cm−1) 1722 3379 3581

∆ν (cm−1) -------

ν (cm−1) 1692 3364 3548

∆ν (cm−1) -------

ν (cm−1) 1682 3369 3524

∆ν (cm−1)) -------

1669 3321

16-(CO) 25-(HO)

1703 3355

29-(CO) 32-(HO)

1694 3345

28-(CO) 34-(HO)

1666 3334

26-(CO) 30-(HO)

1664 3327

18-(CO) 42-(HO)

1672 3512

13-(CO) 38-(HO)

1708 3552

24-(CO) 36-(HO)

1696 3544

26-(CO) 37-(HO)

1674 3509

18-(CO) 39-(HO)

1661 3478

21-(CO) 46-(HO)

Fig. 6 — Optimized converged geometrical structure of hydrogen bonded from DFT (B3LYP) with 6-311+G** basis set (a) N,N-dimethylacetamide and propan-1-ol (b) N,N-dimethylacetamide and propan-2-ol (Red: oxygen, Black: carbon, White: hydrogen, Blue: nitrogen)

412


there is a shift of 13 cm−1 wave number in the position of –C=O and 38 cm−1 wave number in the position of –OH for the mixture compared with the pure spectrums of DMA and IPA, respectively. These shifts are caused by the strong interaction between the high electro-negative charge of oxygen in DMA and hydrogen of the alcohol. Thus, the IR analysis convinces intermolecular hydrogen bonding of the equimolar binary mixtures in system 1 and system 2 effectively with proportionate variations in stretching frequencies of –C=O and –OH as compared to their respective pure systems27. The comparison of experimental and the scaled down theoretical FT-IR values28 is provided in Table 3 and the obtained vibrational frequencies values are found to be in reasonable agreement with the experimental values29,30. The optimized geometrical structures representing the formation of hydrogen bonding in system 1 and system 2, which are obtained from Density Functional Theory (DFT-B3LYP) method with 6-311+G** basis set calculation using Spartan 08 modeling software,are shown in Figs 6(a and b).

5 Conclusions The ultrasonic parameters-adiabatic compressibility, intermolecular free length, internal pressure, acoustic relaxation time, Wada’s constant, Rao’s constant and excess values are computed for the pure and binary mixtures of N,N-dimethyl-acetamide with propan-1-ol (system 1) and N,N-dimethylacetamide with propan-2-ol (system 2) for various mole fractions at 303.15 K. The formation of hydrogen bond between the mixture systems is identified by studying the variations in the parameters determined. The existence of hydrogen bond between of –C=O group of N,N-dimethylacetamide with –OH group of propan-1-ol and propan-2-ol is confirmed through FT-IR spectra. The theoretical FT-IR values determined using Hartree-Fock (HF) and Density Functional Theory (DFT-B3LYP) methods with 6-31+G* and 6-311+G** basis sets calculations are in reasonable agreement with the experimental values. Further, the excess values are useful to compare the strength of bond formation in the two systems. Acknowledgement The authors are thankful to the Management of Vasireddy Venkatadri Institute of Technology, Nambur, for encouragement and providing research facilities.

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