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AIP Conference Proceedings 2220, 080001 (2020); https://doi.org/10.1063/5.0001107 2220, 080001
© 2020 Author(s).
Study of excess acoustical and thermo-
dynamical parameters of binary solutions of
polypropylene glycol-400 and n-alkanols at
303 K
Cite as: AIP Conference Proceedings 2220, 080001 (2020); https://doi.org/10.1063/5.0001107
Published Online: 05 May 2020
Monika Dhiman, Kuljeet Singh, D. P. Gupta, D. P. Singh, and Arun Upmanyu
Study of Excess Acoustical and Thermo-dynamical
Parameters of Binary Solutions of Polypropylene Glycol-400
and n-Alkanols at 303 K
Monika Dhiman1, Kuljeet Singh2, D.P. Gupta1,D.P.Singh3 and Arun Upmanyu1,a)
1Department of Applied Sciences, Chitkara Institute of Engineering and Technology, Chitkara University, Rajpura
140401, Punjab, India.
2Department of Physics, SGGS College, Sector-26, Chandigarh 160019, India.
3Acoustics Research Centre, 4-215, Mississauga Valley Blvd., Mississauga, ON, L5A 1Y7, Canada
a)Corresponding author: arunupmanyu@gmail.com
Abstract. The study of the acoustical and thermodynamic properties of binary mixtures helps to obtain information on
various molecular features of the mixtures. As polypropylene glycol (PPG) is an industrially important polymer and the
alcohols are excellent solvents for many polymers, this fact has tingled our interest to study the molecular interactions in
the solutions of PPG and alcohols. In the present investigation, using ultrasonic velocity and density data, taken from
literature, several excess parameters e.g. excess ultrasonic velocity (UE), excess acoustic impedance (ZE), excess isentropic
compressibility ( KsE), excess intermolecular free length ( LFE ), excess internal pressure (
iE) and excess free volume (VFE)
for binary solutions of polypropylene glycol-400 with ethanol, 1-propanol and 1-butanol have been determined at 303 K.
The behavior of polymeric solutions is discussed in terms of molecular interactions among different molecules. The
negative values of KsE, LFE, and VFE over the entire range of mole fraction indicate the presence of strong associative
interactions and suggest the possibility of hydrogen bonding between the different molecules, clathrate formation and
likelihood of complex formation in the systems under study. The effect of the increasing size of the alkyl group of alkanols,
on the intermolecular interactions has also been discussed.
INTRODUCTION
The thermodynamic properties of a liquid mixture are very useful to provide insightful knowledge of molecular
interactions existing in the system and help to improve the design of industrial process [1-2]. Excess parameters are
relatively more insightful to the molecular interactions than the thermodynamic properties of the mixture. The excess
thermodynamic properties [3-4] have been found to provide useful information concerning mass transport and fluid
flow [5]. Polypropylene glycol (PPG) is widely used in the formulation of polyurethanes. It also finds applications as
a rheology modifier, in automobile seats, in foams, and membranes. It is a prime ingredient in the manufacture of
paintballs. PPG being an industrially important polymer, thermodynamic studies of its binary mixtures in various
alkanols are of considerable interest owing to their multiple applications.
Many researchers have reported about the ultrasonic investigations of molecular interactions in PPG [6-10].
Zafarani-Moattar et al. [6] have studied the aqueous solutions of PPG in the temperature range 283.15 K-313.15 K.
They have reported the presence of polymer-solvent and polymer-polymer interactions in the system. The study also
indicated the weakening of hydrogen bond interactions at higher temperatures, leading to a decrease in the molecular
order in the system. Yasmin et al. [7] described the nature of polymer solutions by computing acoustical parameters
for the binary mixtures of PEG-400 + methanol, PEG -400 + ethanol, and PPG-400 + 2-propanol systems at 298.15
K. Venkatramanan et al. [8] have reported the studies of molecular interactions in the blend of PPG-400 with PPG-
3000 at 303 K. Using interferometric technique, Gayathri et al. [9] have measured ultrasound velocity, in binary
mixtures of PPG and toluene at 303 K. Recently, several acoustical parameters of PPG-400 have been reported by
3rd International Conference on Condensed Matter and Applied Physics (ICC-2019)
AIP Conf. Proc. 2220, 080001-1–080001-6; https://doi.org/10.1063/5.0001107
Published by AIP Publishing. 978-0-7354-1976-6/$30.00
080001-1
Raju et al. [10]. A review of the literature [6-10] has revealed that only a limited study is available for PPG-400 and
alkanols binary mixtures, using excess parameters methodology, to understand the nature, type and strength of
molecular interactions present in these systems.
In the present study, excess ultrasonic velocity (UE), excess acoustic impedance (ZE), excess isentropic
compressibility (KsE), excess intermolecular free length (LFE), excess internal pressure (
iE) and excess free volume
(VFE) for polymeric solutions of PPG-400 + ethanol, PPG-400 + 1-propanol and PPG-400 + 1-butanol have been
determined, for various compositions of the mixtures, at 303 K. The variations of these parameters with change in
mole fraction of PPG-400 have been discussed in terms of molecular interactions prevalent in the systems under study.
THEORY
i (=internal pressure) for the liquid state is given by following relation
P
K
TP
T
P
T
V
E
T
p
i
(1)
Where
p (=coefficient of expansion) and KT (=isothermal compressibility) of the polymer solution. Generally in
case of liquids, the product of absolute temperature and thermal pressure coefficient, i.e
T
p
K
T
is very high in
comparison to external pressure P [11] therefore can be ignored in eq. 1 in the present calculation. Thus eq. 1 can be
written as
T
p
iK
T
(2)
In the present system
p and KT are calculated using standard relation [12-13]
41
0191.0 Tp K
(3)
342943
1071.1 dUTKT
(4)
Where U in m/s, d in gm/cm3 and T in K.
The VF of the mixture are calculated from the relation [14-15]
i
FP
RT
V
(5)
Since P <<
i, therefore can be ignored in eq. 5.
Acoustic Impedance (Z) and Adiabatic compressibility (Ks) are computed using standard relation[16]
UdZ
(6)
1
2dU
Ks
(7)
Intermolecular Free length ( LF )defined by Jacobson [17]
,
s
FKkL
(8)
constant k is temperature dependent which is given as [93.875 + (0.375 T)]×108 and T(in K) is
Excess parameters viz; UE, ZE KsE, LFE,
iE and VFE of the binary solution of polypropylene glycol-400 and n-alkanols
have been calculated using the relation given below
2211 XAXAAAExcess
(9)
Where A represents a parameter e.g. U, Z, Ks, LF,
i, VF and subscripts 1 and 2 refers to pure PPG-400 and n-alkanol.
X1 and X2 are the mole fraction of PPG-400 and n-alkanols in the solution. In the calculation for excess parameters U,
080001-2
Z, Ks, LF are taken from the literature [10] and
i and VF have been determined theoretically using equations 2 & 3
respectively.
RESULT AND DISCUSSION
Theoretically evaluated internal pressure (
i) and free volume (VF ) values with the change in mole fraction of
PPG-400 at 303 K are presented in Table 1. The variation of UE, ZE KsE, LFE,
iE and with the change in mole fraction
of PPG-400 are reported in Figures 1-6. All the reported results are in SI units. A perusal of the Table 1 indicates that
i
shows a regular increase and VF reports a regular decrease with addition of macromolecules of polypropylene glycol
in each binary system. A similar effect is observed with addition of higher alkanols.
TABLE 1: The variation of internal pressure (
i) and free volume (VF ) with change in mole fraction (X1) of PPG in
polymeric solution of PPG-400 and n-alkanols at 303 K.
X1
i x107
[ Pa]
X1
VF x10-6
[mol m-3]
PPG-400
+
Ethanol
PPG-400
+
1-Propanol
PPG-400
+
1-Butanol
PPG-400
+
Ethanol
PPG-400
+
1-Propanol
PPG-400
+
1-Butanol
0.0
27.57
29.39
30.97
0.0
9.14
8.57
8.13
0.1
33.70
39.26
41.32
0.1
7.48
6.42
6.10
0.2
37.46
40.76
41.84
0.2
6.72
6.18
6.02
0.3
39.63
42.23
42.49
0.3
6.36
5.96
5.93
0.4
41.51
42.81
42.99
0.4
6.07
5.88
5.86
0.5
42.00
43.11
43.45
0.5
6.00
5.84
5.80
0.6
42.78
43.54
43.83
0.6
5.89
5.79
5.75
0.7
43.36
43.91
44.22
0.7
5.81
5.74
5.70
0.8
43.64
44.23
44.39
0.8
5.77
5.70
5.67
0.9
43.97
44.47
44.54
0.9
5.73
5.67
5.66
1.0
44.62
44.62
44.62
1.0
5.65
5.65
5.65
These observed trends of variation of
i and VF are closely related to dipole-dipole interactions, hydrogen bonding,
as well as size/steric effect of the interacting molecules. The mixing of the PPG molecules with alkanols would
dissociates the intra hydrogen bonding present in pure liquids with subsequent formation of (new) hydrogen bond
between the oxygen atom of PPG and hydrogen atom of hydroxyl group of alkanol molecules. Also, the addition of
large sized PPG molecules tends to decrease in free space in the system due to clathrate formation. The preponderance
of associative interactions counter balance the steric effect of PPG and lead to an increase the internal pressure in each
system. The magnitude of
i follow the sequence PPG-400+ ethanol < PPG-400+1-Propanol < PPG-400+1-butanol
and supplement the fact that strength of hydrogen bonding between PPG-400 and n-alkanols increase with increase
in carbon - carbon chain [18]. The bulkiness of PPG is than the different alcohols allow to accommodate alcohol
molecules in the voids which leads to more closing packing of the molecules and hence results in decrease in the
magnitude of free volume There is a likelihood clathrate formation due to the adjustment of small sized alkanol
molecules at the interstitial site of the macromolecules of PPG.
The variation in excess isentropic compressibility (KsE) with mole fraction of the binary mixtures of PPG-400 with
ethanol, 1-propanol, and 1-butanol are displayed in Figure 1. The KsE curves for the mixtures show negative deviation
over the entire composition range. In general, KsE depends upon various types of interactions between solute and
solvent of solution [19-21]: (1) weak dipole-dipole interaction or dispersion forces results positive contribution and
hence results the contraction in the compressibility and volume of solution. (2) complex forming, charge transfer
interactions and H-bond formation gives negative contribution (3) the constituent molecules of the binary liquid
accommodate with each other due to variable size/shape which results the structural modification and leads a negative
contribution.
080001-3
The KsE is the resultant of strong interactions like dipole-dipole (d-d) interactions, dipole induced dipole (d-i-d),
charge transfer, and orientation ordering and interstitial accommodation which are responsible for more compact
structure making KsE negative and breakup of the solvent structures make KsE positive [22,23]. In general, relative
molecular size of the components of solution decides the magnitudes of the various contributions. The negative values
of KsE for all the systems studied here signify increasing dipole-dipole interactions effects among the constituents of
the binary systems. Up to X1=0.135, the increase in negative values of KsE is due to increasing proton donating ability
with increasing chain length of alkan-1-ols. For values of X1> 0.135, the preponderance of macromolecule of PPG-
400's size/steric effect, takes over this effect. The negative KsE values also suggest the presence of strongly associative
hydrogen bonding due to dipolar interaction between solute and alkanols.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-25
-20
-15
-10
-5
0
K
E
s
(PPG - 400 + Ethanol)
K
E
s
(PPG - 400 + 1- Propanol)
K
E
s
(PPG - 400 + 1- Butanol)
Excess isotronic compressibility (
K
E
s
) x 10-11
mole fraction (X1) of PPG-400
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-8
-6
-4
-2
0
L
E
F
(PPG - 400 + Ethanol)
L
E
F
(PPG - 400 + 1- Propanol)
L
E
F
(PPG - 400 + 1- Butanol)
Excess intermolecular free lenght (L
E
F
) x 10-12
mole fraction (X1) of PPG-400
FIGURE 1. The variation of excess isentropic
compressibility (KsE) as a function of mole fraction of PPG-
400
FIGURE 2. The variation of excess intermolecular free
length (LFE) as a function of mole fraction of PPG-400
The variation of excess intermolecular free length (LFE), as a function of mole fraction of PPG-400 is reported in
Figures 2. As reported [24], the sign of excess thermodynamic properties plays a substantial effect to assess the
molecular structure and the strength of molecular interactions in the liquid mixture via various interactions such as
charge transfer, d-i-d, and d-d interactions, interstitial accommodation and orientation ordering. From the perusal of
Fig. 2, it is observed that LFE curves for the mixtures show negative deviation over the entire composition range. This
trend of variation of LFE is as expected and is in close agreement with the observed trends of variations of internal
pressure, free volume and KsE for the systems under study. In general, LFE values varies with (a) increase in
intermolecular free length, due to breaking of hydrogen bond, loss of dipolar interactions and difference in size/shapes
of the constituent molecules [25-26] and (b) decrease in intermolecular free length as a result of hydrogen bonding,
complex formation, interstitial accommodation and dipole-dipole interactions between the component molecules [27].
The first effect would result in negative deviation in ultrasonic velocity and positive deviation in adiabatic
compressibility and second effect supports the opposite behavior of first one. The negative value of KsE and LFE
indicate the presence of strong interactions between solute and solvent molecules which may result in complex
formation [28] due to intermolecular H-bonding between the two components [ (PPG-400) = 3.5 D, (Ethanol)= 1.66D, (1-
Proponal) = 1.68D, (1-Butanol) = 1.66 D]. The likelihood of the formation of such a complex is at X1= 0.2 to 0.4 in
PPG-400+ethanol mixture where as such a possibility is at X1=0.13 t0 0.15 for other two binary systems studied here.
As reported above, the positive deviations in UE [Fig. 3] and ZE [Fig. 4] further support the strong association
between the different molecules.
080001-4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
10
20
30
40
50
60
70
80
90
100
110 UE (PPG - 400 + Ethanol)
UE (PPG - 400 +1-Propanol)
UE (PPG - 400 + 1-Butanol)
xcess ultrasonic velocity UE )
mole fraction (X1) of PPG-400
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
3
6
9
12
15
18
21
24 ZE (PPG - 400 + Ethanol)
ZE (PPG - 400 + 1-Propanol)
ZE (PPG - 400 + 1-Butanol)
xcess acoustic imedance ZE ) x 104
mole fraction (X1) of PPG-400
FIGURE 3.The variation of excsess ultrasonic velocity ( UE
) as a function of mole fraction of PPG-400
FIGURE 4.The variation of excess acoustic impedance ( ZE )
as a function of mole fraction of PPG-400
The observed negative deviation of VFE [Fig 5] for all the three systems also supplements the formation of H-
bonding [29-30] between unlike molecules and strong dipole-dipole interactions.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-2
-1
0
V
E
F (PPG - 400 + Ethanol)
V
E
F (PPG - 400 + 1- Propanol)
V
E
F (PPG - 400 + 1- Butanol)
Excess free volume (VE
F ) X10-6
mole fraction (X1) of PPG-400
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
1
2
3
4
5
6
7
8
9
10
E
i (PPG - 400 + Ethanol)
E
i (PPG - 400 + 1-Propanol)
E
i (PPG - 400 + 1-Butanol)
xcess internal pressure
E
i)x 107
mole fraction (X1) of PPG-400
FIGURE 5. The variation of excess free volume (VFE) as a
function of mole fraction of PPG-400
FIGURE 6. The variation of excess internal pressure
(iE) as a function of mole fraction of PPG-400
The magnitude of VFE values is observed as [PPG-400 + Ethanol] < [PPG-400 + 1-propanol] < [PPG-400 +
1-butanol] indicate that the magnitude of H-bonds formed by the alkanols increase with increase in the carbon-carbon
chain [29,31]. It is confirmed by corresponding increase in internal pressure (
i) values and decrease in free volume
(VF) values (Table 1). The variation of excess free volume (VFE) and excess internal pressure (
iE) as a function of
mole fraction of PPG-400 are shown in Fig. 5 and Fig.6 respectively. The trends of variation of these parameters, with
rise in mole fraction of PPG-400 in the binary mixtures, are as expected. As the behavior of internal pressure is
inverse of free volume, therefore the trend of
iE [Fig 6] and VFE [Fig 5] are opposite with change in X1, for all the
systems. This is in agreement with above discussion and conclusions arrived at.
CONCLUSIONS
On the basis of acoustical and thermo-dynamical investigations, for three binary solutions: (I) PPG-400+
ethanol, (II) PPG-400 + 1-propanol and (III) PPG-400 +1-butanol at 303 K, it is concluded that, apart from polymer-
solvent interactions, a possibility of clathrate formations exists in these binary mixtures. Even the possibility of
080001-5
complex formation at the PPG-400 mole fraction X1 = 0.2 to 0.4 for System I and X1 = 0.13 to 0.15 for System II and
System III cannot be ruled out. The trends of variations of internal pressure, free volume, and excess parameters, such
as KsE, LFE, VFE , UE , ZE and
iE for these systems supplement these conclusions. The success of excess parameters, to
depict the nature and type of molecular interactions going on in the bulk of binary mixtures, under study, is confirmed.
The increase in chain length of the n-alkanols, in these binary systems, leads to stronger associative interactions in the
systems.
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