Question #fe368

1 Answer
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.