Volume Properties including molar volume, density, coefficient of volumetric thermal expansion, coefficient of linear thermal expansion etc

1. Volume Properties OfPolymers
Presentedby
Devansh Gupta
M.ScPolymerScience
Semester2

2. • The volumetric properties are extremely important for nearly every
phenomenon or process. The space occupied by one mole of a
material at a given temperature and pressure is known as the
molar volume of that material, which is denoted by V. One mole of
a polymer contains Avogadro's Number NA (6.022×1023) of repeating
units of the monomer.
• It is sometimes more useful to consider the specific volume ν,
defined as the ratio of the substance's volume to its mass, which is
the reciprocal term of the density ρ, defined as the mass per unit
volume.
• Now, If M denotes the molecular weight of one mole of repeating
units of the polymer and V denotes the volume occupied by one
mole of material, then the specific volume v and the density ρ are
defined as follows in terms of V and M:

3. • The molar volume is a function of the temperature T, normally
increases with increasing temperature as a result of the
increasing internal atomic motions. This is not always happen.
Exceptions to this rule also exist. For example, when ice melts at
the melting temperature the liquid water occupies less space than
the ice because of the highly directional hydrogen bonds frozen
into a crystalline lattice of ice.
• Thermal expansion is, therefore, not a fundamental law of nature,
but merely the most commonly observed net result of the
combined effects of the many fundamental physical processes
which take place when the temperature is increased.

4. • The coefficient of volumetric thermal expansion (a) is defined as
the fractional rate of change of V(T) as a function of T, and can be
best estimated from the dependence of V on T if the functional
form of V(T) is known-
• In Above Equation ∂ denotes a partial derivation. Here V is also a
function of pressure. The pressure dependence of V is usually
taken into account by using a "thermodynamic equation of state"
which describes the behavior of V as a function of the
temperature and the pressure simultaneously.

5. • The coefficient of linear thermal expansion (β) is another useful
quantity that is commonly quoted in the literature. It simply
equals one third of the coefficient of volumetric thermal
expansion (α) for an unoriented material.
• The value of β may differ significantly among the three principal
axis directions of an oriented polymer. Some highly oriented
specimens, such as certain fibers, may even retract (means a
negative β) instead of expanding in the direction of chain
alignment with increasing temperature. The reason for this
behavior is that the additional thermal energy allows increased
chain segment mobility while the entropic driving force causes
these segmental motions to induce chain retraction towards the
entropically favored random coil configuration.

6. • It is important to note, however, that for oriented specimens of a
given polymer, at a given temperature, the β values in the three
principal axis directions still add up to a so that the overall
volumetric effect of a small temperature increase don’t change
orientation but merely distributed differently in different
directions within the specimen.
• The molar volume V of a material is the sum of these
components:
1. Van Der Waals Volume (Vw) defined as the Space truly occupied
by atoms. More formally, Vw is defined as the space actually
occupied by the molecule, which is impenetrable to other
molecules with normal thermal energies corresponding to
ordinary temperatures.

7. 2. The packing volume defined as the amount of additional
"empty" space, taken up due to packing constraints imposed
by the sizes and shapes of the atoms or molecules which
constitute the material. The packing volume is equal to the
difference between the molar volume at absolute zero
temperature and the van der Waals volume.
3. The expansion volume results from thermal motions of atoms
and is the difference between the molar volumes at the
temperature of interest and at absolute zero temperature.
Now, According to classical thermodynamics, the degrees of
motion causing thermal expansion are all frozen at absolute zero
temperature. They gradually become available with increasing T,
so that a increases slowly with T.

8. Three factors generally become increasingly important with
increasing temperature.
(a)Hard sphere defined as a repulsion which prevent atoms from
occupying the same space, while atoms can move arbitrarily far
away from each other.
(b)Frozen-in & dynamic components of the entropy. According to
the third law of thermodynamics, the entropy of a perfect crystal at
absolute zero temperature equals zero. On the other hand, because
of the disordered arrangement of the atoms, some entropy
(disorder) is "frozen into" an amorphous material even at T=OK.
Atomic motions increase with increasing temperature, and the
entropy increases as a result of these motions.
(c) Secondary relaxations, These relaxations signal the inception of
certain relatively localized motions of chain segments or of side
groups, resulting from an increase of the thermal energy sufficient
to overcome the activation energies for such motions.

9. 4. The amount of free volume, Free volume can be inserted into a
material as a result of the slowing down of molecular-level
relaxation processes. In addition, free volume increases with
increasing T because of thermal expansion. The free volume
can therefore play a role in thermal expansion processes both
at low and at high temperatures.
5. In a semicrystalline polymer, the molar volume V (and hence
also the density ρ), may changes at the melting temperature
Tm of the crystalline phase. The enthalpy and entropy also
typically changes at Tm. Such changes observed at Tm in the
first derivatives of the Gibbs free energy signify that melting is a
"first-order phase transition"

10. • The temperature dependence of the specific volume of an
amorphous material is illustrated schematically in the figure
below. The coefficient of thermal expansion increases from its
value for the "glassy" polymer to its typically much larger value for
the "rubbery" polymer when the temperature increases from below
to above Tg. The rate of decrease of the density with increasing
temperature then becomes much faster above Tg.

11. • The extrapolation of the line shown for the equilibrium liquid to
below Tg can be viewed as representing the behavior of a
crystalline material or of the crystalline phase of a semicrystalline
material. It can be seen that, for a given chemical structure, the
crystalline phase of a semicrystalline polymer will have a lower
specific volume (a higher density) than the amorphous phase for
the vast majority of polymers.

12. Source
• Prediction Of Polymer Properties, 3rd Edition By Jozef Bieerano