The degree of polymerization, or DP, is 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, 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. This number does not reflect the variation in molecule size of the polymer that typically occurs, it only represents the mean number of monomeric units. 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 —NH6NH— and —OC4CO—, 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 definition, but 500 by the second.
In step-growth polymerization, in order to achieve a high degree of polymerization, Xn, a high fractional monomer conversion, p, is required, according to Carothers' equation For example, a monomer conversion of p = 99% would be required to achieve Xn = 100. For chain-growth free radical polymerization, however, Carothers' equation does not apply. Instead long chains are formed from the beginning of the reaction. Long reaction times increase the polymer yield, but have little effect on the average molecular weight. The degree of polymerization is related to the kinetic chain length, which is the average number of monomer molecules polymerized per chain initiated. However it often differs from the kinetic chain length for several reasons:
Synthetic polymers invariably consist of a mixture of macromolecular species with different degrees of polymerization and therefore of different molecular weights. There are different types of average polymer molecular weight, which can be measured in different experiments. The two most important are the number average and the weight average. The number-average degree of polymerization is a weighted mean of the degrees of polymerization of polymer species, weighted by the mole fractions of the species. It is typically determined by measurements of the osmotic pressure of the polymer. The weight-average degree of polymerization is a weighted mean of the degrees of polymerization, weighted by the weight fractions of the species. It is typically determined by measurements of Rayleigh light scattering by the polymer.
