Page 106 - Carrahers_Polymer_Chemistry,_Eighth_Edition
P. 106
Molecular Weight of Polymers 69
Polymers added
Time
FIGURE 3.12 Illustration of a size-exclusion experiment. Column separations are given above with the SEC
output given below.
theoretical plate (HETP), which is the reciprocal of the plate count per feet (P). P is directly propor-
tional to the square of the elution volume (V ) and inversely proportional to the height of the column
c
in feet and the square of the baseline (D) as follows:
16 V 2
p = c (3.9)
f D
Conversion of retention volume for a given column to molecular weight can be accomplished using
several approaches, including peak position, universal calibration, broad standard, and actual molecu-
lar weight determination by coupling the SEC to an instrument that gives absolute molecular weight.
In the peak position approach, well-characterized narrow fraction samples of known molecu-
lar weight are used to calibrate the column and retention times determined. A plot of log M versus
retention is made and used for the determination of samples of unknown molecular weight. Unless
properly treated, such molecular weights are subject to error. The best results are obtained when the
structures of the samples used in the calibration and those of the test polymers are the same.
The universal calibration approach is based on the product of the limiting viscosity number
(LVN) and molecular weight being proportional to the hydrodynamic volume. Benoit showed that
for different polymers elution volume plotted again the log LVN times molecular weight gave a
common line. In one approach, molecular weight is determined by constructing a “universal cali-
bration line” through plotting the product of log LVN for polymer fractions with narrow MWD as a
function of the retention of these standard polymer samples for a given column. Molecular weight is
then found from retention time of the polymer sample using the calibration line.
Probably the most accurate approach is to directly connect, couple, the SEC to a device, such as
a light-scattering photometer, that directly measures the molecular weight for each elution fraction.
Here both molecular weight and MWD are accurately determined.
3.6 COLLIGATIVE MOLECULAR WEIGHTS
3.6.1 OSMOMETRY
A measure of any of the colligative properties involves counting solute (polymer) molecules in a
given amount of solvent. The most common technique for polymers is membrane osmometry. The
technique is based on the use of a semipermeable membrane through which solvent molecules
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