Measurement of Molecular Weight Averages

All synthetic polymers and many natural polymers have a molecular weight distribution and it is usual to calculate average molecular weights from these distributions. Although there are a considerable number of averages that have previously been used, the most common are the number average, Mn, weight average, Mw, and the z-average, Mz. These are defined as follows:

where N is the number of molecules of molecular weight M .

The molecular weight is generally calculated from the normalized chromatograms by dividing the chromatogram into slices. The area of each slice (h.) is measured and the molecular weight (M.) determined from the calibration curve. The molecular weight averages are then calculated as follows:

In practice, the weight average molecular weight generally corresponds to a molecular weight near the maximum of the chromatogram and the repeatability of the measurement from SEC is normally better than for the other averages. The number average molecular weight is sensitive to minor variations at the low molecular weight end of the distribution while the z-average is more influenced by differences at the high end of the distribution.

The term 'polydispersity' is often used as a measure of the width of a molecular weight distribution and is usually the ratio of the weight average to number average molecular weights (Mw/Mn).

Figure 3 shows an overlay of the chromatograms for four solutions containing a total of ten individual, narrow molecular weight distribution polystyrene calibrants and Figure 4 shows the log (molecular weight) versus retention volume calibration derived from these chromatograms.

Figure 5 shows an overlay of one of the chromato-grams for one of the above calibrant solutions and a broad molecular weight distribution polymer of unknown molecular weight and Figure 6 shows the calculated molecular weight averages and molecular distribution obtained from applying the calibration to the molecular weight computation with this chromatogram.

In Figure 6, the frequency is expressed as weight fraction per unit of log (molecular weight), Wn(log M).

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