Handbook of Size Exclusion Chromatography and Related ...

for branched polymers or copolymers, for which there is no single calibration
curve relating elution volume to molecular weight (1).
An additional potential source of error is the sensitivity of the calibration
curve to alterations in the experimental conditions. Anything that alters the elution
time of a given molecular weight species, such as changes or fluctuations in flow
rate, column degradation, or enthalpic interactions with the column packing, can
lead to serious errors in the measurement of molecular weight.
Because of these limitations, it is clearly desirable to measure the molecular
weight, or some property related to molecular weight, directly as the sample elutes
from the columns. This is generally done by connecting either a light-scattering
detector or a viscometer to the SEC system. The eluting polymer flows through
the detector cell as it leaves the column and before it reaches the concentration
detector. In a light-scattering detector, the excess light scattered by the eluting
polymer is proportional to molecular weight. For an on-line viscometer, the
specific viscosity can be used to calculate the molecular weight either in
conjunction with the Mark–Houwink coefficients of the polymer solution or by
using the method of universal calibration.
This chapter reviews the principles and methodology of molecular weight
determination by light scattering and viscometry in conjunction with SEC. The
emphasis is on those aspects of molecular weight measurement relevant to SEC
analysis; more detailed general treatments of light scattering, viscometry, and
polymer solutions are available elsewhere (2–10). Applications of both methods are
discussed with particular emphasis on molecular weight determination of polymers
that are heterogeneous in composition or architecture; it is in these areas that molecular
weight sensitive detectors offer the greatest advantage over conventional SEC.
2 PRINCIPLES
2.1 Viscometry
At a constant flow rate, the pressure drop across a capillary tube P is proportional
to the viscosity of the liquid flowing through the tube. For a polymer solution, the
ratio of this pressure to the pressure for the pure solvent P0 is equal to the relative
viscosity hr of the solution,
P
P0
¼ h
¼ hr h0 where h is the solution viscosity and h 0 is the solvent viscosity. The specific
viscosity is defined as
© 2004 by Marcel Dekker, Inc.
h sp ¼ h h 0
h 0
(1)
¼ h r 1 (2)