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related to IV [inherent viscosity, c 2 1
0 )]. The magnitudes of these param-
eters depend primarily on the choices of concentration and solvent and to some
extent on the solution temperature. There is no general agreement on these experi-
mental conditions, and comparison of such data from different manufacturers is
not always straightforward.
ln(
η/η
3.3.7 Copolymers and Branched Polymers
The relationships used to this point assume implicitly that the hydrodynamic
radius of a polymer molecule is a single-valued function of the size of the macro-
molecule. This is not true if copolymer composition or molecular shape is also
changing. Branched polymers, for example, are more compact than their linear
analogs at given molecular weight. They will therefore exhibit lower intrinsic vis-
cosities. The change in solution viscosity depends on the frequency and nature of
the branching. The extent of solvation may similarly vary with the chemical com-
position of a copolymer. For these reasons, MHS relations are not readily estab-
lished for polymers like low-density polyethylene, where branching varies with
polymerization conditions or for styrene-butadiene copolymers in which the
copolymer composition can be varied widely.
3.4 Size Exclusion Chromatography
Size exclusion chromatography (SEC) is a column fractionation method in which
solvated polymer molecules are separated according to their sizes. The technique
is also known as gel permeation chromatography (GPC). The separation occurs as
the solute molecules in a flowing liquid move through a stationary bed of porous
particles. Solute molecules of a given size are sterically excluded from some of
the pores of the column packing, which itself has a distribution of pore sizes.
Larger solute molecules can permeate a smaller proportion of the pores and thus
elute from the column earlier than smaller molecules.
Size exclusion chromatography provides the distribution of molecular sizes
from which average molecular weights can be calculated with the formulas sum-
marized in Chapter 2. SEC is not a primary method as usually practiced; it
requires calibration in order to convert raw experimental data into molecular
weight distribution.
SEC can be used for analytical purposes or as a method to produce fractions
with narrower molecular weight distributions than those of the starting polymer.
We confine ourselves here to the former application.
3.4.1 Experimental Arrangement
In SEC analyses, a liquid is pumped continually through columns packed with
porous gels which are wetted by the fluid. A variety of such packings can be
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