Page 102 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Molecular Weight of Polymers 65

M n
M v M w
Fraction of polymer chains with a given molecular weight M z

Molecular weight

FIGURE 3.9 Molecular weight distributions.

Typical techniques for determining molecular weight are given in Table 3.3. The most popular

techniques will be considered briefly. All classical molecular weight techniques require dilute solu-
tions, generally 0.01 g/mL or 1% (1 g/100 mL) solutions. To further minimize solute interactions,
extrapolation of the measurements to infinite dilution is normal practice.

For polydisperse polymer samples, measurements that lead directly to the determination of the
molecular weight, such as light-scattering photometry and membrane osmometry, are referred to as
“absolute molecular weight” methods. Techniques such as viscometry are not absolute molecular
weight methods because they require calibration using an absolute molecular weight technique.

3.4 FRACTIONATION OF POLYDISPERSE SYSTEMS

The data plotted in Figure 3.9 was obtained by the fractionation of a polydisperse polymer sample.
Polydisperse polymers can be fractionated by a number of techniques. The most widely used tech-
nique is chromatography. Other methods include addition of a nonsolvent to a polymer solution, cool-
ing a polymer solution, solvent evaporation, extraction, diffusion, or centrifugation. The molecular
weight of the fractions may be determined using any of the classic techniques given in Table 3.3.
Fractional precipitation is dependent on the slight change in the solubility with molecular weight.
When a small amount of miscible nonsolvent is added to a polymer solution the product with the
highest molecular weight precipitates first. The procedure is repeated after the precipitate is removed.

Molecular weights are run for each fraction and a curve developed that is similar to Figure 3.9.

3.5 CHROMATOGRAPHY
As noted before, certain techniques such as colligative methods, light-scattering photometry, spe-
cial mass spectral (MS) techniques, and ultracentrifugation allow the calculation of specifi c or
absolute molecular weights. Under certain conditions, some of these also allow the calculation of
the MWD.
There are a wide variety of chromatography techniques, including paper and column techniques.
Chromatographic techniques involve passing a solution containing the to-be-tested sample through

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