Degree of Polymerization, Dp The degree of polymerization, or DP, is usually defined as the number of monomeric units in polymer molecule.

CAROTHERS THEORY where: No  number of molecules present initially Carothers developed a simple method of analysis for predicting the molar mass of polymer prepared by polycondensation He recognized that the number average degree of polymerization with respect to monomer unit. Equation 1 where: No  number of molecules present initially N  number of molecules remaining after a time (t) of polymerization

ASSUMPTION FOR CAROTHERS THEORY There are equal numbers of functional groups, Xn can be related to the extent of reaction P at time t. Number of functional groups that have reacted P = _________________________________________________________ Number of functional groups present initially Probability of functional group present initially has reacted.

Therefore the total number of molecules decreases by one for each pair-wise reaction between functional groups. Equation 2

Combining equation (1) and (2) gives the Carothers equation. This equation is applicable to RA2 + RB2 , ARB and RA2 polymerization’s in which there is an exact stoiciometric balance in the number of mutually reactive functional groups.