Molecular Weight Growth and Carothers Equation

Carothers was mainly interested in polyesterifications, and later in polyamidations, of compounds with the structures AXA and BYB, or sometimes AXB, in which X and y are inert chemical moieties whereas A and B are the active carboxyl and hydroxyl or amine groups, giving rise to a cormecting ester or amide group 7. and splitting off a by-product (water) W [Eq. (1)]. 

If reacting groups A and B do not belong to the same molecule, and thus do not create a ring, this reaction leads to a decrease of one polymer molecule (comprising the starting monomers). 

With two monomers, on introduction of the initial stoichiometric ratio r = [B]o/[A]o between mole concentrations of groups A and B, a similar reasoning leads to Eq. (3). 

The effect of ring formation on M of open chain molecules can be taken into account by introducing pc, the conversion of end groups yielding rings, in Eqs. (2) and (3). For instance, when there are two monomers AXA and BYB, Eq. (4) is obtained. 

Stockmayer [7] has obtained the distribution for the fractions of the initial monomer units present in each finite polymer molecules (Eq. (5), where is the set of isomers with x repeating units X). 

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