Carothers Equation - Linear Polymers: Two Monomers in Equimolar Quantities

Linear Polymers: Two Monomers in Equimolar Quantities

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 _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

• X_n is the number-average value of the degree of polymerization, equal to the average number of monomer units in a polymer molecule.
  For the example of nylon-6,6 X_n = 2n (n diamine units and n diacid units).
• p is the extent of reaction (or conversion to polymer), defined by

• p = (N₀-N)/N₀, where:
• N₀ is the number of molecules present initially
• N is the number of unreacted molecules at time t

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 X_n = 50, and p = 99% is required for X_n = 100.