#### 1.3 Intrinsic Viscosity Determination

We can either use the Huggins equation, which is derived from a virial expansion of the specific viscosity in powers of
the intrinsic viscosity, or the Kraemer equation, which results from an expansion of the inherent viscosity, to
determine the intrinsic viscosity.

##### 1.3.1 Huggins Equation

The specific viscosity is related to the intrinsic viscosity by a power series of the form

where k_{0},k_{1},k_{2}... are dimensionless constants, and k_{0} = 1.

Dividing by concentration, and truncating to only the second term, we form the Huggins equation
as

| (6) |

The constant k_{H} is termed the Huggins constant and has values ranging from 0.3 in good solvents to 0.5 in poor
solvents. It contains information about hydrodynamic and thermodynamic interactions between coils
in solution. A plot of the reduced viscosity, extrapolated to zero concentration yields the intrinsic
viscosity.

##### 1.3.2 Kraemer Equation

We may construct another expansion based on the relative viscosity, in dilute solutions where the specific viscosity is
much less than 1.

Using the expression for the specific viscosity in the Huggins equation above, Eq. 6, provides Equation 7, the
Kraemer equation.

A plot of the inherent viscosity, extrapolated to zero concentration, yields the intrinsic viscosity. Viscometry yield
a viscosity average molecular weight, _{ν} where

where n_{i} is the number density of chains of molar mass M_{i}.