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
INDIAN J PURE & APPL PHYS, VOL 51, JUNE 2013
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
NADH et al.: ACOUSTICAL AND COMPUTATIONAL STUDIES OF BINARY MIXTURES
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
INDIAN J PURE & APPL PHYS, VOL 51, JUNE 2013
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
NADH et al.: ACOUSTICAL AND COMPUTATIONAL STUDIES OF BINARY MIXTURES
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
INDIAN J PURE & APPL PHYS, VOL 51, JUNE 2013
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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