## Molecular Mass of Polymers Preparation and Properties

→ The properites of polymers are related to their molecular weight, shape and structure. The number of monomer units present in a polymer is called Degree of Polymerisation. Also number of monomer units determines the size of polymers.

→ The molecular mass of organic compounds (it can be a monomer) is fixed whether it is formed by any method.

For example, molecular weight of Ethylene molecule is 28 but when it is polymerised, it can be represented as:

→ Here, value of n is different for different polymer molecules. Therefore, molecular weight of all the polymers present in polymer sample will be different. The reason for this is that degree of polymerisation of different polymers is different i.e., their chain length is different. Thus, the molecular weight of polymers is not fixed because their degree of polymerisation is different.

These are therefore expressed as average molecular mass in two forms :

- Number average molecular weight
- Weight average molecular weight

→ Number average molecular weight : It is represented as (M_{n}) The sum of molecular weight of all the polymers present in a polymer sample when divided by total number of polymers present gives average molecular weight of polymers.

→ If in any sample, total number of molecules is n and molecular weight of n_{1} molecules is m_{1}, n_{2} is m_{2} and similarly molecular weight of n_{i} is m_{i} then

Total molecular mass of all molecules

Number average molecular weight is determined by osmotic pressure method.

Weight Average Molecular Mass : It is represented as M_{w}.

→ In a polymer sample, number of molecules of different weights are multiplied by their molecular weight and the product obtained is divided by total number of molecules. This gives the weight average molecular mass.

→ If in any sample, total number of molecules is n and molecular weight of n_{1} molecules is m_{1}, n_{1} is m_{2} and similarly molecular weight of n_{i }– is m_{i} then

Total mass of n_{1} molecules = n_{1}m_{1}

Total mass of no molecules n_{2}m_{2}

Similarly, total mass of n_{i} molecules = n_{i}m_{i} and the their product with their will be as follows :

It can be determined by Light Scattering, sedimentation and Fast centrifugation methods.

## Polydispersity Index

→ In a chemical compounds, the molecular weight of all the molecules is different. Thus these are monodisperse. But in polymers, mass of molecules is different. Therefore, these are polydisperse. Some naturally occurring polymers like Protein are monodisperse.

It is the ratio of the mass average molecular mass of the number average molecular mass.

→ For natural polymers, PDI is usually equal to one which means that they are monodisperse. In other words, such polymers are more homogeneous. On the contrary, synthetic polymers generally have PDI > 1 which means that they are less homogeneous.

## Numericals of Molecular Mass of Polymers

→ A polymer sample contains the molecular weight of 20 molecules is 20,000, the molecular weight of 40 molecules is 30,000 and molecular weight of another 20 molecules as 40,000. Then calculate

M_{n} and M_{w}.

Solution : Calculation of number average molecular