# Degree of polymerization

The degree of polymerization, or DP, is usually defined as the number of monomeric units in a macromolecule or polymer or oligomer molecule.[1][2][3]

For a homopolymer, there is only one type of monomeric unit and the number-average degree of polymerization is given by $DP_n\equiv X_n=\frac{M_n}{M_0}$, 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.[4][5] 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.

IUPAC definition

The number of monomeric units in a macromolecule an oligomer molecule, a block, or a chain.[6]

## Correlation with physical properties

Relationship between degree of polymerization and melting temperature for polyethylene. Data from Flory (1963).

Polymers with identical composition but different total molecular weights may exhibit different physical properties. In general, increasing degree of polymerization correlates with higher melting temperature [7] and higher mechanical strength.

## Kinds of degree of polymerization

Mainly, there are two types used to measure the degree of polymerization, number average degree of polymerization and weight average degree of polymerization. Number Average degree of polymerization is found by finding the Weighted mean of mole fraction o. While the weight average degree of polymerization is found by finding the weighted mean of weight fraction .[8]

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