Carothers' equation

In step-growth polymerization, the Carothers equation (or Carothers' equation) gives the degree of polymerization, X_n, for a given fractional monomer conversion, p.

There are several versions of this equation, proposed by Wallace Carothers who invented nylon in 1935.

The simplest case refers to the formation of a strictly linear polymer by the reaction (usually by condensation) of two monomers in equimolar quantities. An example is the synthesis of nylon-6,6 whose formula is [-NH-(CH₂)₆-NH-CO-(CH₂)₄-CO-]_n from one mole of hexamethylenediamine, H₂N(CH₂)₆NH₂, and one mole of adipic acid, HOOC-(CH₂)₄-COOH. For this case

In this equation

This equation shows that a high monomer conversion is required to achieve a high degree of polymerization. For example, a monomer conversion, p, of 98% is required for ${\displaystyle {\bar {X}}_{n}=50}$, and p = 99% is required for ${\displaystyle {\bar {X}}_{n}=100}$.

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