Explain the molecular mass with respect to polymers.

Question

During the formation of polymers, different macromolecules have different degree of polymerisation i.e. they have varied chain lengths. Thus, the molecular masses of the individual macromolecules in a particular sample of the polymer are different. Hence, an average value of the molecular mass is taken. There are two kinds of average molecular masses of polymers.

    
1. Number-average molecular mass   
    
2. Mass-average molecular mass   

The two types of molecular masses are defined and calculated as follows:
    
1. Number-average molecular mass

When the total mass of all the molecules of a sample is divided by the total number of molecules, the result obtained is called the number-average molecular mass. For example, suppose in a particular sample

N₁ molecules have molecular mass M₁ each.

N₂ molecules have molecular mass M₂ each.

N₃ molecules have molecular mass M₃ each and so on. Then, we have

Total mass of all the N₁ molecules = N₁M₁.

Total mass of all the N₂ molecules = N₂M₂.

Total mass of all the N₃ molecules = N₃M₃ and so on.

∴ Total mass of all the molecules = N₁M₁ + N₂M₂ + N3M₃ + .....

= ΣN_iM_i

Total number of all the molecules = N₁ + N₂ + N₃ + ....

= ΣN_i

Hence the number-average molecular mass will be given by
 


 is generally determined by osmotic pressure measurement.
    
2. Mass-Average molecular mass

When the total mass of groups of molecules having different molecular masses are multiplied with their respective molecular masses, the products are added and the sum is divided by the total mass of all the molecules, the result obtained is called the mass-average molecular mass. Supposing, as before that N₁, N₂, N₃, etc, molecules have molecular mass M₁, M₂, M₃ etc. correspondingly.

Total mass of N₁ molecules = N₁M₁.

Total mass of N₂ molecules = N₂M₂.

Total mass of N₃ molecules = N₃M₃ and so on.

The products with their respective molecular masses will be (N₁M₁ × M₁), (N₂M₂ × M₂), (N₃M₃ × M₃), etc. i.e. N₁M₁², N₂M₂², N₃M₃², etc.

Sum of the products = N₁M₁² + N₂M₂² + N₃M₃² + ......

= ΣN_iM_i²

Hence the mass-average molecular mass is given by
 


 is generally determined by technique like ultra centrifugation of sedimentation.