The Chain Length Distribution of an Ideal Reversible Deactivation Radical Polymerization

The chain length distribution (CLD) of a reversible deactivation radical polymerization at full conversion is shown to be a negative binomial distribution with parameters that are simple functions of the number-average degree of polymerization and either the chain transfer constant (in the case of polymerizations that incorporate a reversible chain transfer step) or the concentrations of dormant polymer chains and deactivating agent and the rate constants of propagation and deactivation (other types of RDRP). Expressions for the CLD at intermediate conversions are also derived, and shown to be consistent with known expressions for the number-average degree of polymerization and dispersity. It is further demonstrated that these CLDs are well-approximated by negative binomial distributions with appropriate choice of parameters. The negative binomial distribution is thus a useful model for CLDs of reversible deactivation radical polymerizations.