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# Degree of Polymerization

The number of repeating units (n) in a polymer chain is known as the degree of polymerization. It is represented by the following relationship.
Degree of polymerization (n) = Molecular weight of the polymeric network / Molecular weight of the repeating unit. (2m)

The degree of polymerization, or DP, is usually defined as the number of monomeric units in a macromolecule or polymer or oligomer molecule.

For a homopolymer, there is only one type of monomeric unit and the number-average degree of polymerization is given by $DP_n\equiv X_n=\frac{M_n}{M_0} - degree of polymerization$, where Mn is the number-average molecular weight and M0 is the molecular weight of the monomer unit. For most industrial purposes, degrees of polymerization in the thousands or tens of thousands are desired.

Some authors, however, define DP as the number of repeat units, where for copolymers the repeat unit may not be identical to the monomeric unit. For example, in nylon-6,6, the repeat unit contains the two monomeric units —NH(CH2)6NH— and —OC(CH2)4CO—, so that a chain of 1000 monomeric units corresponds to 500 repeat units. The degree of polymerization or chain length is then 1000 by the first (IUPAC) definition, but 500 by the second.

In step-growth polymerization, in order to achieve a high degree of polymerization (and hence molecular weight), Xn, a high fractional monomer conversion, p, is required, as per Carothers’ equation: Xn = 1/(1−p). A monomer conversion of p = 99% would be required to achieve Xn = 100. For chain-growth polymerization, however, this is not generally true and long chains are formed for much lower monomer conversions.

##### Projection of Cone

Projection of Cone Sample Problem1: Draw the projection of  cone , base 30 mm diameter and axis 50 mm long...

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