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6.1.2.
Intrinsic viscosity: Definition and determination
The specific viscosity depends on the concentration of dissolved molecules,
but the limiting value of
η
sp
/c as c approaches zero is a characteristic property
of the polymer/solvent system. Mathematically:
η
[ ]
=
lim
c
→
0
η
sp
c
Note that the intrinsic viscosity has the brackets
[]
as part of the symbol. It has
further dimensions ‘inverse concentration’ such as ml/g, indicating it
represents a volume per gram of polymer. In fact, it expresses the effective
hydrodynamic volume, which is determined both by the physical volume of the
macromolecule and its shape in solution.
Since the viscosity may depend on the shear rate (non-Newtonian behaviour),
also
[η]
will depend on the shear rate in such cases. For studies of
macromolecular shape it is important to perform measurements at sufficiently
low shear rate, i.e. in the Newtonian range. For this reason the symbol
[η]
γ→
0
is used. In practise, measurements can be obtained at different shear rates,
and results can be extrapolated to zero shear rate.
Finding the intrinsic viscosity (experimental data)
Huggins’ equation is the basis for determining the intrinsic viscosity from
experimental data. It describes how the specific viscosity (of a dilute solution)
depends on the concentration:
η
sp
c
=
η
[ ]
+
k
'
η
[ ]
2
c
Experimental data consist of a data matrix of the following type (flow-through-
times for different concentrations):