Ultrasonic study of molecular dynamics in some binary mixtures

Abstract

The study of propagation of ultrasonic waves in liquids and liquid mixtures in very much useful for examining the nature of intermolecular interactions in chemical systems. Ultrasonic velocity is an important physical parameter which mainly depends on the structure of molecules. In the present investigation, ultrasonic velocities have been measured in binary mixtures of (i) Methanol-Chlorobenzene, (ii) Ethanol-Chlorobenzene and (iii) 1-Propanol-Chlorobenzene to understand the molecular interactions. Various models have been employed to calculate the acoustical parameters in order to substantiate these interactions. The various acoustic parameters such as adiabatic compressibility, free length, acoustic impedance, relaxation time, free volume, available volume and internal pressure were also measured to substantiate these interactions. Many interesting features were observed and they are carefully discussed.

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Journal of Chemical and Pharmaceutical Research
__________________________________________________
ISSN No: 0975-7384
CODEN(USA): JCPRC5
J. Chem. Pharm. Res., 2011, 3(5):348-358
348
Ultrasonic study of molecular dynamics in some binary mixtures
K. Rajathi
1
*, S. J. Askar Ali
2
and A. Rajendran
3
1
Department of Chemistry, Govt. Arts College, Thiruvannamalai, Tamil Nadu, India
2
P.G and Research Dept. of Chemistry, The New College (Autonomous), Chennai, Tamil Nadu, India
3
Department of Chemistry, Sir Theagaraya College, Chennai, Tamil Nadu, India
______________________________________________________________________________
ABSTRACT
The study of propagation of ultrasonic waves in liquids and liquid mixtures in very much useful
for examining the nature of intermolecular interactions in chemical systems. Ultrasonic velocity
is an important physical parameter which mainly depends on the structure of molecules. In the
present investigation, ultrasonic velocities have been measured in binary mixtures of (i)
Methanol - Chlorobenzene, (ii) Ethanol - Chlorobenzene and (iii) 1-Propanol - Chlorobenzene
to understand the molecular interactions. Various models have been employed to calculate the
acoustical parameters in order to substantiate these interactions. The various acoustic
parameters such as adiabatic compressibility, free length, acoustic impedance, relaxation time,
free volume, available volume and internal pressure were also measured to substantiate these
interactions. Many interesting features were observed and they are carefully discussed.
Key Words: Ultrasonic study, Molecular dynamics, Binary mixture, Acoustic parameter,
Acoustic impedance.
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INTRODUCTION
Ultrasonic is a branch of acoustics dealing with sound above the audible range, and in many
respects analogues to microwave physics in the field of electromagnetism. Both are characterized
by special instrumentation and measuring techniques. Ultrasonic’s frequencies are higher than
20,000 Hz and their wavelengths are small. The sound waves of frequency lower than the
audible limit are called infrasonic. Supersonics refers to the velocities higher than the velocity of
sound. Ultrasonic velocity is an important physical parameter having structural dependence [1-
5]. The study of propagation of ultrasonic waves in liquids and liquid mixtures is very much

K. Rajathi
et al J. Chem. Pharm. Res., 2011, 3(5):348-358
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349
useful for examining the nature of intermolecular and intramolecular interactions in these
systems. Phsyico-chemical properties can be understand among the interacting components from
ultrasonic velocity measurements and it can be coupled with other experimental data such as
density and viscosity to calculate various acoustical parameters such as adiabatic compressibility,
free length, acoustic impedance, relaxation time, free volume, available volume and internal
pressure, which are useful in understanding the molecular interactions in binary mixtures [6-8].
In the present investigation, ultrasonic velocities have been measured in binary mixtures to
understand the molecular interactions. Various models have been employed to calculate the
acoustical parameters in order to substantiate these interactions. Ultrasonic studies were carried
out in the following binary mixtures containing chlorobenzene as one of the components. (i).
Methanol - Chlorobenzene, (ii). Ethanol - Chlorobenzene and (iii).1-Propanol – Chlorobenzene.
The acoustical parameters have been calculated for these three binary mixtures at different
concentrations of Chlorobenzene at 303K.
EXPERIMENTAL SECTION
Reagents
All the chemicals used in this study are of AR grade. Methanol, Ethanol and 1-Propanol were
refluxed and distilled before use. The spectral grade Chlorobenzene of BDH make was used after
simple distillations.
Preparation of binary mixtures
Jobs continuous variation method was used to prepare the binary mixtures of required
proportions [9-13]. The binary liquid mixtures were preserved in well stoppered conical flasks.
After mixing the liquids thoroughly, the flasks were left undisturbed to attain thermal
equilibrium.
Measurement of Ultrasonic Velocity
The different methods that can be employed for the detection of the ultrasonic velocity are, (i)
Optical method, (ii) Pulse technique and (iii) Interferometric method. In this investigation the
interferometric method has been employed for the determination of ultrasonic velocity. In the
interferometer a standing wave is set up between the generating quartz crystal and a reflector.
The wavelength is measured by moving the reflector or by using the standing wave as a grating
for diffraction of light. In this way velocity could be measured with an accuracy better 1 part in
10
5
. The principle used is the measurement of wavelength in the medium. Density was
determined by the specific gravity method. Viscosity was measured by Ostwald’s viscometer
method. Measurement of Ultrasonic velocity (U), Viscosity (η) and Density (ρ) of liquids are
useful to determine the thermodynamic and acoustic parameters of the binary mixtures. These
acoustical and the thermodynamic properties help us understand the characteristics of the liquid.
The nature of the molecular interaction in the liquid can be proved by making use of the
parameters such as Adiabatic compressibility (β), free length (L
f
), Acoustic impedance (Z) and
Relaxation time (τ), free volume (V
f
), available volume (V
a
) and internal pressure (π
i
). These
parameters were measured by the standard procedures available in the literatures.

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350
RESULTS AND DISCUSSION
The acoustic parameters were calculated for various compositions of Methanol, Ethanol, 1-
Propanol with Chlorobenzene binary mixtures from ultrasonic velocities and the results are given
in Tables 1-6. These data are discussed in the light of molecular interaction between the
components.
.Ultrasonic velocity (U)
The ultrasonic velocity increases with increase in the mole fraction of Chlorobenzene in all the
three systems investigated (Table 1-3). This suggests that there are molecular interactions
between the components of binary mixtures. The ultrasonic velocity for a given composition of
1-Propanol – Chlorobenzene mixture is greater than that of similar composition of Ethanol –
Chlorobenzene and Methanol-Chlorobenzene mixtures. Ultrasonic velocity increases with
increase in chain length of alcohol (Table 1-3). The plot of ultrasonic velocity against mole
fraction of Chlorobenzene for the three systems is given in fig.1.
TABLE 1: Ultrasonic Velocity (U), Density (ρ) and Viscosity (η) values for the binary mixture of Methanol -
Chlorobenzene at 303K
Mole fraction of
Chlorobenzene Ultrasonic
velocity(U),ms
-1
Density ((ρ),Kgm-3 Viscosity
(η)×10
-3
,Nm
-2
s
0.0000
0.0424
0.0906
0.1459
0.2098
0.2849
0.3741
0.4818
0.6144
0.7819
1.0000
1089.8
1105.0
1119.2
1124.0
1140.0
1150.0
1161.2
1182.4
1198.4
1212.0
1241.5
780.2
811.2
847.4
870.9
907.9
932.8
967.6
1001.6
1030.6
1068.9
1093.2
0.5984
0.6907
0.7105
0.7189
0.7377
0.7458
0.7673
0.7878
0.8039
0.7782
0.8882
TABLE 2: Ultrasonic Velocity (U), Density (ρ) and Viscosity (η) values for the binary mixture of Ethanol -
Chlorobenzene at 303K
Mole fraction of
Chlorobenzene Ultrasonic
velocity(U),ms
-1
Density
((ρ),Kgm-3 Viscosity
(η)×10
-3
,Nm
-2
s
0.0000
0.0598
0.1250
0.1968
0.2759
0.3637
0.4611
0.5715
0.6957
0.8372
1.0000
1130.3
1146.4
1157.0
1165.7
1172.8
1182.4
1190.2
1197.4
1209.0
1222.4
1241.5
782.9
822.1
846.3
876.4
907.9
936.4
969.5
997.4
1028.9
1057.2
1093.2
1.0178
1.2184
1.1662
1.0368
1.0386
0.9860
0.9327
0.9206
0.8962
0.8796
0.8882
TABLE 3: Ultrasonic Velocity (U), Density (ρ) and Viscosity (η) values for the binary mixture of 1-Propanol -
Chlorobenzene at 303K
Mole fraction of
Chlorobenzene Ultrasonic
velocity(U),ms
-1
Density ((ρ),
Kgm-3 Viscosity
(η)×10
-3
,Nm
-2
s
0.0000
0.0753
0.1551
0.2394
1185.9
1192.4
1197.1
1200.4
794.7
826.5
852.8
889.3
1.9423
1.8158
1.5743
1.3295

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351
Mole fraction of Chlorobe
nzene
0.3249
0.4234
0.5242
0.6315
0.7461
0.8686
1.00000
1203.5
1206.7
1209.2
1216.4
1219.1
1226.8
1241.5
912.1
943.3
971.6
1005.7
1024.1
1055.9
1093.2
1.2450
1.1281
1.0736
0.9413
0.9186
0.9060
0.8882
Fig.1 Variation of ultrasonic velocity
[Series-1=1-Propanol; series-3=Ethanol; series-5=Methanol]
Density (ρ)
In all the three systems, the density increases with increase in concentration of Chlorobenzene
due to increase in the presence of ions or particles. As the number of particles increases, the
electrostriction and density increases. Table (1-3) shows the increase in density with the increase
in concentration. It is also observed that density for 1-Propanol-Chlorobenzene is greater than
that for other two systems. Density increases with increase in chain length of alcohol (Table 1-3).
Ultrasonic
V
elocity, ms
-
1

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TABLE 4: Acoustical parameters for Methanol -Chlorobenzene Binary Mixture at 303K
Mole fraction of
Chlorobenzene Adiabatic compressibility,
β×10
-10
, Kg
-1
ms
2
Free length, L
f
, Ǻ Acoustic
impedance,Z×10
6
Kgm
-
2
s
-1
Relaxation time,
τ×10
-9
,s
Free
volume,V
f
×10
-
7
,mL
Available
volume, Va×10
-
2
,m
3
Internal
pressure Π
1,
Atm
0.0000
0.0424
0.0906
0.1459
0.2098
0.2849
0.3741
0.4818
0.6144
0.7819
0.0000
10.7919
10.0959
9.4210
9.0886
8.4752
8.1062
7.6646
7.1413
6.7563
6.3688
5.9348
0.6570
0.6355
0.6139
0.6029
0.5822
0.5694
0.5537
0.5345
0.5199
0.5047
0.4872
0.8503
0.8964
0.9484
0.9789
1.0350
1.0727
1.1236
1.1843
1.2351
1.2955
1.3572
0.8610
0.9297
0.8925
0.8712
0.8336
0.8061
0.7841
0.7501
0.7242
0.6608
0.7028
0.50
0.48
0.55
0.64
0.74
0.88
1.10
1.24
1.51
2.07
2.23
2.8
3.0
3.2
3.5
3.8
4.2
4.9
5.2
5.9
6.8
8.0
86772
84416
80526
69960
63544
56530
48075
44694
38797
32079
33343
TABLE 5: Acoustical parameters for Ethanol - Chlorobenzene Binary Mixture at 303K
Mole fraction of
Chlorobenzene
Adiabatic
compressibility, β×10
-10
,
Kg
-1
ms
2
Free
length
,L
f
,
Ǻ
Acoustic
impedance,Z×10
6
Kgm
-2
s
-1
Relaxation time, τ×10
-
9
,s
Free
volume,V
f
×10
-
7
,mL
Available volume,
Va×10
-2
,m
3
Internal pressure
Π
1,
Atm
0.0000
0.0598
0.1250
0.1968
0.2759
0.3637
0.4611
0.5715
0.6957
0.8372
1.0000
9.9978
9.2556
8.8269
8.3970
8.0078
7.6385
7.2814
6.9928
6.6493
6.3302
5.9348
0.6324
0.6085
0.5942
0.5796
0.5660
0.5528
0.5397
0.5289
0.5157
0.5032
0.4872
0.8849
0.9245
0.9792
1.0216
1.0648
1.1072
1.1539
1.1943
1.2439
1.2923
0.7028
0.8610
0.9297
0.8925
0.8712
0.8336
0.8061
0.7841
0.7501
0.7242
0.6608
0.7028
0.41
0.36
0.45
0.61
0.70
0.87
1.09
1.29
1.57
1.90
2.23
4.2
4.4
4.6
4.9
5.2
5.5
5.9
6.3
6.8
7.3
8.0
72803
74183
66861
58275
53894
48003
43194
39192
35221
31547
33343
TABLE 6: Acoustical parameters for 1-Propanol - Chlorobenzene Binary Mixture at 303K
Mole fraction of
Chlorobenzene
Adiabatic compressibility,
β×10
-10
, Kg
-1
ms
2
Free length, L
f
, Ǻ Acoustic impedance,Z×10
6
Kgm
-2
s
-1
Relaxation time,
τ×10
-9
,s
Free
volume,V
f
×10
-
7
,mL
Available
volume, Va×10
-
2
,m
3
Internal pressure
Π
1,
Atm
0.0000
0.0753
0.1551
0.2394
0.3249
0.4234
0.5242
0.6315
0.7461
0.8686
0.0000
8.9468
8.5097
8.1832
7.8035
7.5699
7.2806
7.0391
6.7201
6.5706
6.2926
5.9348
0.5982
0.5834
0.5721
0.5587
0.5503
0.5397
0.5306
0.5185
0.5127
0.5017
0.4872
0.9425
0.9855
1.0209
1.0675
1.0977
1.1382
1.1749
1.2233
1.2484
1.2954
1.3572
2.3170
2.0602
1.7177
1.3833
1.2566
1.0951
1.0076
0.8434
0.8048
0.7601
0.7028
0.25
0.31
0.42
0.60
0.73
0.93
1.12
1.49
1.71
1.93
2.23
5.6
5.8
6.0
6.1
6.4
6.6
6.8
7.0
7.4
7.7
8.0
72725
66830
58901
51657
47345
42676
39393
35044
32536
30558
33343

K. Rajathi
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353
Adiabatic compressibility (β)
The adiabatic compressibility values for various compositions of the three binary mixtures have
been calculated from the measured ultrasonic velocities (Table 4 - 6). The plots of adiabatic
compressibility against mole fraction of Chlorobenzene for the three systems are given in fig.2. It
may be noted that in all the three cases adiabatic compressibility decreases with increase in
concentration of Chlorobenzene indicating relatively stronger Hydrogen bonding over wide
range of concentration. According to Fort and Moore, Hydrogen bonding between unlike
components makes a negative contribution to compressibility [14]. The compressibility data also
shows that dipole induced dipole attraction are stronger in Methanol-Chlorobenzene binary
mixture than in Ethanol-Chlorobenzene and in 1-Propanol – Chlorobenzene binary mixtures.
Adiabatic compressibility decreases with increase in chain length of Alcohol (Table 4 - 6).
Linear free length (L
f
)
Intermolecular free length is related to ultrasonic velocity. As the ultrasonic velocity increases
due to the increase in concentration, the intermolecular free length has to decrease and vice versa
[15]. Increase in concentration leads to decrease in gap between two species and which is
referred by intermolecular free length. It may be noted that in all the three cases linear free length
decreases with increase with increase in concentration of Chlorobenzene (Table 4 - 6). This
shows that dipole induced dipole attraction increases with the concentration of Chlorobenzene.
The linear free length for a given composition for Methanol – Chlorobenzene binary mixture is
greater than that for similar compositions in other two systems. Linear free length decreases with
increase in chain length of alcohol (Table 4-6). The plots of linear free length against mole
fraction of Chlorobenzene for the three systems are given in fig.3.
Fig.2 Variation of Adiabatic compressibility
[Series-1=1-Propanol; series-3=Ethanol; series-5=Methanol]
Adiabatic compressibility,Kg
-
1
ms
2
Mole fraction of Chlorobenzene

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Fig.3 Variation of linear free length
[Series-1=1-Propanol; series-3=Ethanol; series-5=Methanol]
Fig.4 Variation of Acoustic impedance
[Series-1=1-Propanol; series-3=Ethanol; series-5=Methanol]
Linear free length
Ǻ
Mole fraction of Chlorobenzene
Mole fraction of Chlorobenzene
Acoustic impedance, Kg
-
2
S
-
1

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Acoustic impedance (Z)
The acoustic impedance increases with increase in concentration of Chlorobenzene in all the
three systems studied. The increase in acoustic impedance with the concentration can be
explained on the basis of lyophobic interaction between solute and solvent molecules [16, 17]
which increases the intermolecular distance, making relatively wider gap between the molecules.
It is also observed that acoustic impedance for 1-Propanol-Chlorobenzene binary mixture is
greater than that for the other two systems. The plots of acoustic impedance verses mole fraction
of Chlorobenzene for the three systems are given in fig.4. Acoustic impedance increases with
increase in chain length of alcohol (Table 4-6).
Relaxation time (τ)
The relaxation time increases at lower concentration and decreases at higher concentration of
Chlorobenzene for all the three systems (Table 4 – 6). This shows that molecular interaction is
strong at lower concentration of Chlorobenzene and relatively weak at higher concentration. It is
also observed that relaxation time for 1-Propanol – Chlorobenzene binary mixture is greater than
that for other two systems. The plots of relaxation time versus mole fraction of Chlorobenzene
for the three systems are given in fig.5. Relaxation time increases with increase in chain length of
alcohol (Table 4 - 6).
Fig.5 Variation of Relaxation time
[Series-1=1-Propanol; series-3=Ethanol; series-5=Methanol]
Available volume (V
a
)
For all the three systems, available volume increases with increase in concentration of
Chlorobenzene (Table 4-6). It is also observed that available volume for 1-Propanol –
Chlorobenzene binary mixture is greater than that for other two systems. Available volume
increases with increase in chain length of alcohol (Table 4-6) (fig. 6).
Mole fraction of Chlorobenzene
Relaxation time, s

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Fig.6 Variation of free volume
[Series-1=1-Propanol; series-3=Ethanol; series-5=Methanol]
Fig.7 Variation of Internal pressure
[Series-1=1-Propanol; series-3=Ethanol; series-5=Methanol]
Mole fraction of Chlorobenzene
Internal pressure, atm
Mole fraction of Chlorobenzene
Free volume, ml

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Internal pressure (π
i
)
The internal pressure in a binary liquid mixture is a measure of cohesive forces between the
components. The internal pressure values for the three binary mixtures at different compositions
are given in (Table 4-6). These values indicate that the internal pressure changes with
composition of the alcohols and hence cohesive forces changes with the concentration of
Chlorobenzene. The internal pressure is maximum when the concentration of Chlorobenzene is
the lowest. It is also interesting to observe that the free volume of the binary liquid mixtures
increases as internal pressure decreases. The variations of internal pressure with respect to the
mole fraction of the chlorobenzene for the three systems are given in fig.7. It is also observed
that internal pressure for methanol- chlorobenzene binary mixture is greater than that for the
other two systems. Internal pressure decreases with increase in chain length of alcohol
(Table 4-6). CONCLUSION
The various acoustic parameters such as adiabatic compressibility, free length, acoustic
impedance, relaxation time free volume, available volume and internal pressure have been
evaluated from ultrasonic velocity, density and viscosity for the binary liquid mixture of
Methanol – Chlorobenzene, Ethanol – Chlorobenzene and 1- Propanol - Chlorobenzene systems
at 303K. In the present investigation, it could be inferred that there are inter molecular
interactions among the components of the binary mixtures, leading to the possible hydrogen
bond formation of the type Cl…H-O between unlike molecules. Molecular interaction increases
with increase in the concentration of Chlorobenzene in all the three systems. It is also observed
that molecular interaction increases with increase in chain length of alcohol in the order 1-
Propanol > Ethanol >Methanol.
Acknowledgement
The authors thank the Principal and the Management of The New College, Chennai-14, Govt.
Arts College, Thiruvannamalai and Sir Theagaraya College, Chennai-21 for the constant support
and the encouragement given.
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