Molecular Weight Averages and Distribution

Abstract

Since a synthetic polymer is an assembly of molecules having different molecular weights (MW), the MW value has to be expressed as an average, and several different MW averages are defined (see Chap. 1). These MW averages are measured by different chemical and physical methods and are also calculated statistically in SEC by different equations. Consider a mixture of ten molecules with MW 100 and five molecules with MW 1000, then the average values can be calculated as follows. The arithmetic mean is the sum of the MW of all the molecules divided by the number of molecules as

$${M_n} = \frac{{100 + 100 + ... + 100 + 1000 + ... + 1000}}{{10 + 5}} = \frac{{10 \times 100 + 5 \times 1000}}{{15}}400$$

The weighted mean is the sum of the weight times the MW of all the molecules divided by the total weight of the mixture as

$${M_w} = \frac{{100 \times 100 + 100 \times 100 + ... + 100 \times 100 + 1000 \times 1000 + ... + 1000 \times 1000}}{{100 + 100 + ... + 100 + 1000 + .... + 1000}} = \frac{{10(100 \times 100) + 5(1000 \times 1000)}}{{10 \times 100 + 5 \times 1000}} = 850$$

The former corresponds to the number-average MW, M _n, and the latter is defined as the weight-average MW, M. There are five MW averages defined as the weight-average MW, M _w.