Volume Properties Of Polymers

Presented byDevansh GuptaM.Sc Polymer

ScienceSemester 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:

• 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.

• 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.

• 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.

• 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.

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.

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.

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"

• 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.

• 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.

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