Poly-Dispersity Index Of Polymers

First of all we should know what are polymers and how they are defined????

"A polymers is defined as a large molecule (or macromolecule), formed by joining together thousands of smaller molecule units by chemical bonds (or covalent bonds)". These smaller molecules that interact with each other to form a larger molecule are called "Monomers".

 

To understand how the molecular weight is distributed within polymers, we study about the poly-dispersity index. "The polydispersity index measures the distribution of molecular mass in a given polymer sample". The molecular weight of a polymer is defined as the sum of the atomic weights of each atom in the molecules, which is present in the polymer. Due to the different chain lengths of polymers, we cannot directly measure the molecular weight of the polymer. So we calculate the average molecular weight of the polymer on two basis- "Number average molecular weight" and "Mass average molecular weight".

       

The number average molecular weight of polymers is related to "Mole fractions" whereas the weight average molecular weight of Polymers are related to "Weight fraction". The mass average molecular weight is always greater than the number average molecular weight. It is sometimes equal to but not less than the number average molecular weight.

        Mₙ＝ ∑x¡M¡ & Mw＝ ∑w¡M¡

 Here,

        x¡ denotes mole fraction

        w¡ denotes weight fraction

Poly-dispersity Index

PDI means poly-dispersity index. This is sometimes called the molecular weight distribution. "The polydispersity index is defined as the ratio of weight average molecular weight to the number average molecular weight of a polymer". It is denoted by a symbol " Đ /PDI".

Case-1; 

When, PDI or Đ＝1 then the polymer is "Mono-disperse". In this case, both the number average molecular weight and the weight average molecular weight are the same.  

          ➩ { Mₙ＝ Mw }

    Nearly all the "Natural polymers" are mono-disperse or uniform.

Case-2;

When, PDI or Đ ≻1 then the polymer is "Poly-disperse". In this case, weight average molecular weight is higher than the number average molecular weight. Polymers are of various chain-lengths.

          ➩ { Mₙ ≻ Mw }

Nearly all the "Synthetic or man-made polymers" are poly-disperse.

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