Handbook of Size Exclusion Chromatography and Related ...

which is ameasure of the increase in viscosity caused by the addition of the
polymer to the solvent. The reduced viscosity h r=c, where cis the polymer
concentration, is ameasure of the specific capacity of the polymer to increase the
solutionrelativeviscosity.Inthelimitof infinitedilutionthisquantityisknownas
the intrinsic viscosity:
[h] ¼ h sp
c c!0
The reduced viscosity has aconcentration dependence in dilute solutions
described by the Huggins equation,
(3)
h sp
c ¼[h]þk0 [h] 2 c (4)
wherek 0 istheHugginsconstant.InSECtheconcentrationofthesoluteisusually
low,sothattheassumptionof infinitedilutionisgenerallyvalidandtheconditions
for Eq. (3) hold. Thus, the intrinsic viscosity of an eluting polymer can be
determined from measurements of the specific viscosity and concentration of the
eluting polymer solution at each elution volume.
The intrinsic viscosity of apolymer solution is related to its molecular
weight by the empirical relation known as the Mark–Houwink equation:
[h] ¼KM a
whereKandaaretheMark–Houwinkcoefficients,whichdependonthepolymer,
solvent, and temperature.
Measurementofthespecificviscosityrequiresthatboththesolutionandthe
solvent viscosity be measured at the same flow rate. This can be achieved by
measuring the solvent viscosity baseline before and after the polymer peak elutes
or by measuring the solution viscosity as the peak elutes using a reference
capillary.Anexampleofsuchaflow-referencedviscometerisshowninFig.1(6).
This is afluid analog of the electrical circuit known as aWheatstone bridge. With
onlysolutionflowingthroughtheviscometer,theflowresistancesR1,R2,R3,and
R4 are balanced and the differential pressure transducer signal is zero. When a
polymer solution enters the viscometer, it fills capillaries R1, R2, and R3, but the
reservoir prevents it from reaching the fourth capillary,R4, which still contains
flowing solvent. A pressure transducer measures the resultant difference in
pressure between the two sides of the bridge. The specific viscosity h sp is
calculatedfromtheratioofthisdifferentialpressuretothepressuredropacrossthe
bridge. Other types of viscometers include single-capillary (7) and referenced
dual-capillary (8) designs. Alisting of commercial instrumentation is givenin the
appendix.
Figure 2shows the viscometer and refractometer tracings as afunction of
elution volume for a mixture of equal amounts of three nearly monodisperse
© 2004 by Marcel Dekker, Inc.
(5)