Polymer Viscosity: Polymer Viscosity is mainly defined as Solution viscosity, which is also of prime importance to us.

Solution Viscosity: The solution viscosity depends on concentration and size (i.e., molecular weight) of the dissolved polymer.

For polymers, the solution viscosities that are encountered frequently are relative viscosity, specific viscosity, and reduced specific viscosity. These quantities are defined as follows:

where η is the viscosity of the solution, η_S is that of the solvent and c is the polymer concentration, usually expressed in grams per 100 cm³ or in grams per cm³. Another important quantity in very dilute solutions at vanishing shear rate is the intrinsic viscosity (also called limiting viscosity number) which is defined as:

[η] describes the increase in viscosity of individual polymer chains. Assuming the polymers are spherical impenetrable particles, the increase in viscosity can be calculated with Einstein's viscosity relationship:

where N_p / V is the number of particles per unit volume, _Vh the hydrodynamic volume of a polymer particle and M its molecular weight. The hydrodynamic volume of a particle can be rewritten as follows:

Then the specific viscosity of a very dilute solution reads:

This and similar expressions for other particle geometries can be found in many textbooks. In the case of dissolved, soft polymer particles, Einstein's relation has to be modified. It has been shown that the equation is still applicable to dissolved polymers if the hard sphere radius is replaced by the hydrodynamic radius of the polymer coil. Then the equation can be rewritten in the form:

where α_h = R_h / R_h,0 is the expansion of a polymer coil in a good solvent over that of one in θ-solvent and R_h,0 is the radius of an unperturbed polymer. The equation is known as the Flory-Fox equation. Under θ-conditions it simplifies to

The constant Φ_θ has a value of about 4.2·10²⁴ for rigid spherical particles if [η] is expressed as a function of the radius of gyration.^1,7 If the intrinsic viscosity is measured in both a very dilute θ-solvent and in a "good" solvent, the expansion can be directly estimated.

The values of α_h typically vary between unity for a θ-solvent to about 3 for very good solvents increasing with molecular weight.

Both 〈R_h,0²〉 and αh can be expressed as a function of molecular weight M:

where C₁ and C₂ are constants, M₀ is the molar mass of a monomer and ν is a scaling exponent. The value of ν depends on the solvent-polymer system and its temperature. For example, under θ-conditions the scaling exponent has the value ν = 1/2 and in a good solvent ν = 3/5. With these expressions, the equation for the intrinsic viscosity can be written in the form

This equation is known as the Mark-Howink or Mark-Howink-Staudinger equation where K has the dimensions cm³/g x (g/mol)^a. Mark-Houwink parameters have been tabulated for a large number of polymer-solvent systems in standard references. These parameters are usually determined from a double logaritmic plot of intrinsic viscosity vs. molecular weight:

Similar profiles for different polymers can be obtained. Variations in the Mark-Howink equations can also help us obtain relationships between Melt flow Index/Rate (MFR) and the Intrinsic Viscosity (IV) of certain polymers, such as PET. The Dynisco Rheometers are equipped to relate MFR & IV data for PET. Get in touch with our experts today for more information.