Determination of Molar Masses of Polymers I

During polymerization, monomers join together to form long polymer chains. But these chains do not all reach the same length.

As a result, a polymer sample contains molecules with different molar masses.

So, we use average molar masses to describe the distribution of chain sizes in the sample.

First is the number-average molar mass, written as M̅_n. It equals the summation of n_i times M_i, divided by the summation of n_i.

Here, n_i is the number of molecules with a specific molar mass, and M_i is their molar mass. This average treats each molecule equally.

Next is the weight-average molar mass, written as M̅_w. It equals the summation of n_i times M_i squared, divided by the summation of n_i times M_i.

Since the contribution of molar mass is greater, larger polymer chains with higher molar mass contribute more to this average.

The ratio of these two averages defines dispersity, written as Đ.

A value of one means all polymer chains have the same length. However, most polymers have dispersity greater than one, indicating chains of different sizes.