# Question fe368

Mar 10, 2015

The average molecular weight or molar mass average of a polymer is the average molar mass of the polymer chains.

In polymers, the individual polymer chains rarely have exactly the same chain length and molar mass. There is always a distribution of molar masses.

There are two common types of molar mass average.

Number Average Molar Mass (${M}_{n}$).

M_n = (∑N_i M_i)/(∑N_i),

where $i$ are the chains of a given polymer length, $M$ are their molar masses, and $N$ are numbers of each type of chain.

"Weight" Average Molar Mass (${M}_{w}$)

M_w = (∑N_i M_i^2)/(∑N_i M_i),

The molar mass distribution of a polymer is measured by its dispersity, Đ (pronounced D stroke).

Đ = M_w/M_n#

If the molecules all have the same mass, the distribution is uniform. If they have different masses, the distribution is nonuniform.

Biological polymers are often uniform. They may have Đ ≈ 1, indicating that all the polymers are about the same length.

For typical addition polymers, Đ often ranges from 10 to 20.

With some synthetic polymers, you can control the reaction conditions such as temperature, initiation rate, reactant ratios; limit termination steps, etc. so that the chains are similar in length.

You can often get dispersities close to 1.

The video below shows how to calculate ${M}_{n}$, ${M}_{w}$, and Đ for a polymer.