Physical Properties of Polymers

Muhammad Zafar Iqbal

Date: 22-04-2008

Today

• Plastic Flow in Polymers• Viscosity of simple liquids• Viscosity of Polymers• Factors affecting the viscosity: Temperature and

Molecular Weight• Measurement of Viscosity

Plastic Flow in Polymers• 3 types of deformation• Plastic flow or irreversible flow• Newton’s law of viscosity• Types of fluid based on the above law

Simple methods to measure the viscosity of simple liquids include (but not limited to):

1- Rate of efflux of the liquid from a tube under known pressure head.2- From the force necessary to rotate a cylinder in another cylinder of liquid3- From rate of fall of a ball through a fluid

Temperature dependence of viscosity is normally determined through Arrhenius equation as:

Note: It is found that deviations of viscosity are reduced at high temperatures for simple viscous liquids but not for polymers

Eyring’s Theory of Viscosity• This theory is based on quasi-crystalline lattice consisting of

holes and occupied sites.• When a liquid moves in a direction, the individual molecules

in the structure move in the flow direction.• This can occur only by changing the places with holes in the

structure. i.e. by jumping from one occupied site to the next vacant one.

• In the absence of any applied stress, the jumps from all the directions are equally probable and the holes move at random through the structure and so the liquid does not change its shape.

• The movement of a molecule from A to B can be treated as a rate process, involving passage from an energy barrier “E”.

• In the absence of any stress, A & B are equivalent positions at the same energy level and the rate of interchange of molecules is given by:

• E may be regarded to be related to the energy required to separate two molecules completely.i.e. to the latent heat of vaporization. (From analogy)

For mathematical model for viscosity:

Net rate from A to B :Since,The rate at which the layers of liquid move is proportional to

shear rate and shear stress is proportional to applied stress.Then from Newton’s Law of viscosity:

From mathematics, for x<<1, sinhx ~ x, and

Here the viscosity coefficient is independent of shear rate: Newtonian

Viscosity of Polymers• The energy of activation is expected to be related to the latent heat of

vaporization of the liquid, since the removal of a molecule from the surroundings of its neighbor forms a part of both processes. Such a relationship is indeed found and is taken as evidence that the particle that moves from site to site is probably a single molecule.

• As chain length is increased in a homologous series of liquid up to a polymer range, the activation energy of flow does not increase proportionally with the heat of vaporization but levels off at a value which is independent of molecular size (the size of the chain).

• It means that in long chain, the unit of flow is considerably smaller that the complete molecule.

• It may be a segment of molecule that may contain 5-50 C-atoms.

• Viscous flow occurs by successive jumps of the segments untill the whole chain is shifted.

But mind that, the chain segments of viscous flow are not necessarily the Same as the chain segment of high elasticity. The size of network segment is however larger than that of viscousSegment.

Effect of Molecular Weight of Viscosity• From the last discussion, it is clear the energy of activation is

activation for viscous flow is independent of molecular weight of the polymer chain.

• Latent heat is, of course, the function of molecular weight

From Arrhenius equation of viscosity,

And it is found from experimentation that,

Experimental Measurements

• Rotational Rheometer

• Capillary Rheometer