Flory–Stockmayer theory

[1] The Flory–Stockmayer theory represents an advancement from the Carothers equation, allowing for the identification of the gel point for polymer synthesis not at stoichiometric balance.

[1] The theory was initially conceptualized by Paul Flory in 1941[1] and then was further developed by Walter Stockmayer in 1944 to include cross-linking with an arbitrary initial size distribution.

The Carothers equation is an effective method for calculating the degree of polymerization for stoichiometrically balanced reactions.

[1] However, the Carothers equation is limited to branched systems, describing the degree of polymerization only at the onset of cross-linking.

The Flory–Stockmayer Theory allows for the prediction of when gelation occurs using percent conversion of initial monomer and is not confined to cases of stoichiometric balance.

Additionally, the Flory–Stockmayer Theory can be used to predict whether gelation is possible through analyzing the limiting reagent of the step-growth polymerization.

[1] In creating the Flory–Stockmayer Theory, Flory made three assumptions that affect the accuracy of this model.

Since steric hindrance effects prevent each functional group from being equally reactive and intramolecular reactions do occur, the gel forms at slightly higher conversion.

[5] Flory postulated that his treatment can also be applied to chain-growth polymerization mechanisms, as the three criteria stated above are satisfied under the assumptions that (1) the probability of chain termination is independent of chain length, and (2) multifunctional co-monomers react randomly with growing polymer chains.

[1] The Flory–Stockmayer Theory predicts the gel point for the system consisting of three types of monomer units[1][5][6][7] The following definitions are used to formally define the system[1][5] The theory states that the gelation occurs only if