34
D.R. Godhani et al. / Journal of Molecular Liquids 168 (2012) 28–35
increased with concentration (C) and decreased with temperature
(T). The concentration and temperature dependence of these data
were tested by least square analysis. Least square means that the overall
solution minimizes the sum of the squares of the errors made in solving
every single equation. The degree of linearity was judged on the basis of
correlation coefficient. A fairly good to excellent correlation between
given parameters and concentration was observed in the studied solvent
systems at three temperatures. The observed correlation between ρ and
C, η and C, and U and C is γ=0.930–0.984, 0.982–0.999 and 0.929–0.983
respectively. The obtained γ values supported a fairly good to excellent
linear dependence of ρ, η and U with C and T. The observed trends for dif-
ferent C and T in ρ, η and U were CF>DMF, DMF>CF and DMF>CF re-
spectively (Figs. 6, 7 and 8). The increased ρ, η and U with C suggest
that the increase of cohesive forces is due to powerful molecular interac-
tions, while the decrease of these parameters with T indicate that cohe-
sive forces decreased. The increasing temperature has two opposite
effects namely increase of molecular interaction (structure formation)
and destruction of structure formed previously. When the thermal ener-
gy is greater than the interaction energy, it causes the destruction of pre-
viously formed structure. Thus, the increase of T favors the increase of
kinetic energy and volume expansion and hence, results in the decrease
of ρ and η. The density and viscosity of medium, pressure, temperature,
etc. affect the velocity. With a view to understand the effect of concentra-
tion, temperature, nature of solvents and the structure of PDI-H on struc-
ture forming or structure-breaking tendency various acoustical
parameters like adiabatic compressibility (κa), intermolecular free path
length (Lf), Rao's molar sound function (Rm), internal pressure (π) and
free volume (Vf) were determined by using the experimental data on ρ,
η and U of PDI-H solutions in CF and DMF at three temperatures according
to standard equations. The concentration and temperature dependence
of acoustical parameters furnish a wealth of information regarding the
strength of molecular interaction occurring in the solutions. Various
acoustical parameters were fitted with concentration by least square
analysis to certain concentration and temperature dependence molecu-
lar interactions in PDI-H solutions and hence, the structure forming or
structure-breaking nature of 1,3,4-oxadiazole derivative (PDI-H) under
investigation.
pressure of a solution is single factor, which plays an important role
in transport properties of solutions. The internal pressure is the resul-
tant of forces of attraction and repulsion between the molecules in so-
lutions. The increase of internal pressure and decrease of free volume
indicates an increase of cohesive forces and vice versa in the solutions
of PDI-H in both solvent systems. This was further supported by free
volume. Free volume (Vf) decreased with C and increased with T for
solutions of PDI-H in CF and DMF (except at 303 K in CF). The increase
in internal pressure and decrease in free volume with concentration in
both systems indicate ordered structural arrangement due to decreasing
entropy of the system. The free volume (Vf) of a solute molecule at a par-
ticular temperature and pressure depends on the internal pressure of a
liquid in which it is dissolved. The decrease in free volume causes internal
pressure to increase or vice versa. However, Tables 3 and 4 show that in-
ternal pressure increased and free volume decreased in CF and DMF
systems. This again confirmed the existence of solute–solute and
solute–solvent interactions in the system studied so far.
The degree of interaction was also measured in terms of solvation
number (Sn). The negative solvation number indicates the structure-
breaking tendency of solute [33]. The decrease in the Sn with C sug-
gested the presence of solute–solute interaction. The resultant value
of the Sn depends upon solvent–solute and solute–solute interactions.
It is clear from Tables 3 and 4 that solvation is powerful in DMF and
minimum in the CF system. The lone pairs and –Cl are electronegative
groups whereas phenyl rings and –CH3 are electropositive groups.
Halogen group forms weak H-bond with electropositive groups and
hence, solvation number was minimum in CF as compared to DMF
system. It is clear from our results that Sn values are positive, which
shows the structure forming tendency in CF and DMF systems. The
variation in Sn with C and T values was also suggesting the presence of
strong dipole–dipole interaction. This is further suggestive that solute–
solute and solute–solvent interactions are present in solution of PDI-H
in CF and DMF.
On the basis of the experimental findings, it is concluded that ρ, η and
U increased with concentration and decreased with temperature in both
systems. Powerful molecular interactions resulted in the structure form-
ing as judged on the basic of positive values of solvation number. Thus,
electronegative (–Cl and lone pairs) and electropositive (–CH3 and phenyl
rings) groups have played an important role on molecular interactions.
Ultrasonic velocity (U) depends on intermolecular free path length
(Lf) inversely. As can seen from Tables 3 and 4 that in CF and DMF systems
both velocity and acoustical impendence (Z) increase with C and decrease
with T of solute. The adiabatic compressibility (κa) and intermolecular
free path length (Lf) are observed to decrease with C and increase with
T suggesting the presence of solvent–solute interactions.
Nomenclature
C
concentration (mol L−1
)
T
absolute temperature (K)
The decrease in κa might be due to aggregation of solvent mole-
cules around solute molecules indicating strong solvent–solute inter-
action. The adiabatic compressibility (κa) of the solutions of PDI-H was
also found to decrease with C and increase with T in both systems.
This phenomenon can be attributed to the solvated molecules that
were fully compressed by the electrical forces of the ions. The com-
pressibility of the solution was mainly due to the free solvent mole-
cules. The presence of compressibility of the solution decreases with
the increase in solute concentration, due to solute–solvent interac-
tions in the system. This was further confirmed by the decrease of Lf
values and the increase in viscosity of PDI-H solutions in CF and DMF.
The linear changes in Rm and b shown in Table 4 and Table 5, (cor-
relation coefficient γ=0.942–0.995), suggest that the absence of any
complex or aggregate formation takes place in both CF and DMF sys-
tems. The internal pressure (π) is the resultant of forces of attraction
and repulsion between the molecules in a solution. The results of adi-
abatic compressibility and intermolecular free path length, which
were found decreased with C and increased with T, while velocity
and viscosity were found increased with C and decreased with T in
CF and DMF system, suggest that solute–solvent interaction is more
predominant. This was confirmed from the results of internal pres-
sure, which found increased (except at 303 K in CF). The internal
pressure (π) increased with C in both solvent systems. Internal
M
M1
M2
W1
W2
R
molecular weight of solutions (kg mol−1
molecular weight of solvent
molecular weight of solute
weight fraction of solvent
)
weight fraction of solute
universal gas constant (J mol−1 K−1
)
b
Van der Waals constant (m3)
m
Pa
s
meter
pascle
second
Greek symbol
ρ
density (kg m−3
)
η
U
Z
κa
Lf
Rm
π
viscosity (m Pa s)
ultrasonic velocity (m s−1
)
specific acoustical impedance (kg m−2 s−1
)
adiabatic compressibility (Pa−1
intermolecular free length (m)
)
Rao's molar sound function (m10/3 s−1/3 mol−1
internal pressure (Pa)
)
Vf
free volume (m3)