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Theoretical
investigations of effective Debye temperature, pseudo-Grüneisen parameters and
Bayer’s nonlinear parameter for four industrially important polymers viz.
polyacrylonitrile (PAN), polyvinylpyrrolidone (PVP), polyvinyl chloride (PVC),
polymethyl methacrylate (PMMA), using dimethylformamide (DMF) as solvent, have
been done at 303.15K. The composition dependence of these parameters for three
polymer blends viz; PAN/PVP, PAN/PVC and PAN/PMMA using DMF as solvent, have
also been studied at 303.15K. The variation of these parameters, with change in
concentration of the polymer solution, is explained in terms of nature,
strength and type of intermolecular interactions, harmonicity and structural
changes occurring in the bulk of these polymeric solutions.
Keywords: Intermolecular interactions, Harmonicity,
Structural changes
BACKGROUND
Most of
the polyacrylonitrile (PAN) produced is employed in acrylic fibers, which
contain nearly 85 percent or more of it. PAN being almost insoluble in organic
solvents and extremely difficult to dyeing, very little fiber is manufactured
having PAN alone. However, a copolymer (like vinyl acetate) containing PAN can
easily be spun into fibers, which are soft enough to allow the penetration of
dyes. Another polymer, polyvinylpyrrolidone
(PVP) has been used as a plasma volume expander for trauma victims since 1950s. In addition, it is used in medical products, hair care products and cosmetics. Its variant,
PVP-I, a compound of PVP and iodine, is commonly used as an antibacterial agent
and antiseptic. The polymer polyvinyl chloride (PVC) is
extensively used in the construction sector. Having the properties of rigidity
and low flammability, PVC is used in manufacture of pipes, conduits, sidings,
door and window frames. Its blends with plasticizers are used in floor tiles, garden
hoses, imitation leather upholstery and shower curtains. Another polymer,
polymethyl methacrylate (PMMA) is employed in domed skylights, luminous
ceilings, swimming pool enclosures, instrument panels and aircraft canopies. It
is also injection-moulded into headlights, taillights and lighting-fixture
covers [1].
Polymer
blends are physical or mechanical mixtures of two or more polymers, which show
large potential for the construction and development of novel surfaces with
extraordinary properties. For the production of novel surfaces using polymer
blends, numerous parameters have to be considered (e.g. nature of blend,
solvent etc.) which permit us to transform and mold the final desired structure
[2]. Polymer blends have assumed a very important status scientifically and
technologically in recent years. Because of their extensive applicability, we
report in this paper a comparative study of the various thermo-dynamic
parameters for four polymers PAN, PVP, PVC, PMMA and their blends in dimethyl
formamide (DMF). The aim of this study is to understand the polymer-solvent
interactions and polymer-polymer compatibility through their thermodynamic
properties.
During the past
few decades, many researchers [3-5] have
The Bayer’s nonlinear parameter (B/A)
has a major role in non-linear acoustics. Its knowledge is immensely useful in
the fields of underwater acoustics, medicines and biomaterials [10-12]. It
provides information about internal pressure, structural behavior and acoustic
scattering. Several researchers have done experimental and theoretical studies
related to non-linearity of the liquid systems, using Bayer’s nonlinear
parameter. The anharmonicity and molecular order of Van der Waals bonds
prevalent in the liquid mixtures can be assessed by measuring lattice Gruneisen
parameter [12-14].
In the present
study, effective Debye temperature (θD),
pseudo-Gruneisen parameter (G) and non-linearity parameter (B/A) are determined for solutions of
pure polymers viz. PAN, PVP, PVC, PMMA and their blends viz. PAN/PVP, PAN/PVC
and PAN/PMMA, in DMF. The polymer blends, prepared by mixing the two polymers
in equal (50/50) proportions, were dissolved in DMF, which acted as a solvent.
The investigation of intermolecular interactions for these polymeric solutions
have been done at various concentrations, and at a constant temperature of
303.15 K.
THEORETICAL BACKGROUND
Since PAN and other polymers, PVP, PVC, PMMA, chosen
for current study, readily dissolve in DMF to produce solutions of low
viscosity, so these solutions are useful to characterize the molecular
interactions between the constituents of the solutions. The standard relations,
as reported in literature [13-15] are used to determine effective Debye
temperature (θD),
pseudo-Grüneisen parameter (G) and
Bayer’s number (B/A). The
experimental data for ultrasonic velocity (u), density (d), effective mass (M)
and temperature (T) required for computation of θD, G and B/A are taken from literature [16].
The effective Debye
temperature (θD) for solids can be
calculated using following expressions:
where βa can be calculated from the thermodynamic relation
βa
= (ρmix u2mix)-1
and γ is defined as
ϒ = βT /
βa
The parameter C1 in
terms of the linear thermal expansion coefficient (a) as
C1
= (13/3) + (1/ αT) + (4 αT/3) (2)
Bayer’s nonlinearity and Lattice Gruneisen parameters in terms of C1
are given by
G= C1 - 1
RESULTS AND DISCUSSIONS
The computed values
of θD, G, and B/A of pure polymers PAN, PVP, PVC,
PMMA dissolved in DMF and the polymer blends PAN/PVP, PAN/PVC, PAN/PMMA
dissolved in DMF as function of concentrations, at 303.15 K, are reported in
the (Tables 1-3). All the
parameters are reported in SI system expect stated otherwise.
Most of the physical properties of the polymers and their variation with
change in concentrations of the polymer solutions have been co-related with the
dynamics of polymer chain. The change in θD, G, and B/A parameters with concentration of polymers are found to be important in
studying the structural changes associated with the polymers in solution and
makes way to identify the molecular interactions between the polymer and
solvent. A perusal of
Table 1 reveals that the values of θD, G,
and B/A fluctuate within a small range (For PAN+DMF, θD=45.3K-51.0K, G=7.35-7.55,
B/A=6.85-7.05, and for PVP+DMF, θD=45K-50.5K, G=7.34-7.50,
B/A=6.84-6.99), with rise in the polymers (PAN and PVP) concentrations in the binary solution.
In case of blend, PAN/PVP (50/50), the values θD (45.69-47.44)
is intermediate whereas the values of G
(7.354-7.409) and B/A (6.854-6.909) is less than
their pure counterparts with respect to the change in concentration in the
solution. The consequence of addition of polymers is in the disruption of the
structure of the pure components and restriction of their rotational motion.
Interstitial accommodation and orientational order led to a more compact
structure and to an observed decrease in the effective Debye temperature.
The lattice Gruneisen
parameter is governed by the molecular order and structure. The Bayer’s
nonlinearity parameter (B/A) is
strongly sensitive [17,18] and provides the information relating to internal
pressure, clustering, intermolecular spacing. The decrease in θD, B/A and G values with rise in concentration of each solute
indicates increase in intermolecular modes of vibration and harmonicity in the
liquid state. This accounts for the associating nature in polymer solutions due
to weak intermolecular attractive forces [12,19,20].
A perusal of Table 2 reveals that the
values of θD, G and B/A fluctuate within a
small range (For PAN+DMF, θD=45.3-51.0,
G=7.35-7.55, B/A=6.85-7.05
and for PVC+DMF, θD=46.5-60.7, G=7.39-7.90,
B/A=6.89-7.40), with
rise in the polymers (PAN and PVP) concentrations in the binary solution. In
case of blend, PAN/PVC, the
variation in the value of θD (51.66-47.74)
is intermediate whereas the values of G (7.456-7.561) and B/A
(6.956-7.049) is less than their pure counterparts with respect to
change in concentration in the solution. These pure and blend polymers again
exhibit similar behavior as reported for other polymers in Table 1.
Consequently, the behavior of θD, G, and B/A parameters again
indicate the increase in intermolecular modes of vibration and
harmonicity in the liquid state and associating nature in polymer solutions due
to weak intermolecular attractive forces [12,19,20].
A perusal of Table 3 reveals that the
values of θD, G, and B/A fluctuate within
a small range (For PAN+DMF, θD=45.3-51.0K,
G=7.35-7.55, B/A=6.85-7.05
and for PAMMA+DMF, θD=48.9K-51.1K,
G=7.47-7.55, B/A=6.97-7.05)
with rise in the
polymers (PAN and PMMA) concentrations in the binary solution. It is
interesting to notice that unlike other polymer blends (PAN/PVP and PAN/PVC)
variation in the value of θD (42.02 -59.67)
is greater than their pure counterparts with respect to change in
concentration in the solution whereas the variation in the values of G
(7.229-7.819) and B/A (6.729-7.319) are less than that of pure
polymers solutions. The higher values of θD indicate that the
addition of polymers results in the disruption of the structure of the pure
polymers and restriction of their rotational motion. The interstitial accommodation
and orientational order led to a less compact structure and to an observed
increase in the range of θD. The decrease in θD, B/A and G values with rise in concentration of each solute
indicates fluctuating behaviour in intermolecular modes of vibration and
harmonicity in the liquid state. This accounts for the changes in associating
nature of the polymer solutions due to weak intermolecular forces [12,19,20].
For a better understanding of molecular
interactions prevalent in the polymer solutions, having DMF as a solvent, and
solutes such as pure polymers e.g. PAN, PVC, PVP, PMMA, and polymer blends e.g.
PAN/PVP, PAN/ PVC and PAN/PMMA, the average value (A.V.) of θD, G
and B/A respectively have also been reported (Tables 1-3). The
average magnitude of θD for polymer blends +DMF solutions
follow the order; PAN/ PMMA >PAN/ PVC > PAN/ PVP. The order of the
average values for G and B/A also follow a
similar trend as reported for θD. Whereas, in case of pure
polymers solutions the A.V. of θD, G,
B/A of polymer solutions of PMMA lie between PVC and PVP. These trends
indicate that PAN/PMMA+DMF is having more structural changes, higher intermolecular
modes of vibration and harmonicity as compared to PAN/PVC+DMF and PAN/PVP+DMF whereas in case
of pure polymer solutions PVC is found to have the highest values of θD,
G, B/A.
The miscibility study of polymer blends
PAN/PVP, PAN/ PVC and PAN/ PMMA are already reported in literature [2,13]. The previous reports indicate that PAN/PMMA
blend is highly immiscible and PAN/PVP is completely miscible when polymers mix
together in equal (50/50) proportions for preparation for blends with. Our
study indicates that immiscible blends make more compact structure and having
more intermolecular modes of vibration and harmonicity than miscible blends.
CONCLUSION
The variation of θD, G,
B/A values, with rise in concentration of polymers in DMF, indicate
considerable changes in intermolecular forces existing in the bulk of the
solution. The present study helps in investigation of the miscibility
characteristics of polymer blends, PAN/PVP, PAN/PVC and PAN/PMMA in DMF. The
intermolecular interactions prevalent in the polymer solutions of four pure
polymers and three polymer blends in a DMF solvent, have been explained in
terms of θD, G, B/A. The reported average
values of θD, G, B/A for polymer blends
solutions under study reveal that immiscible blends (PAN/PMMA) exhibit more
compact structure and higher intermolecular modes of vibration and
harmonicity than miscible blends (PAN/ PVP and PAN/ PVC) in DMF solvent.
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