Editing Living polymerization (section)

==Fast rate of initiation: low polydispersity==
[[File:Nonlivingpolymanimation.gif|thumb|300px|right| Figure 1: Rate of initiation is slower than the rate of propagation, leading to the formation of active species at different points in time during the polymerization.]]
[[File:living polymerization animation.gif|thumb|300px|right|Figure 2: Rate of initiation is instantaneous in comparison to the rate of propagation, causing all the active species to form simultaneously, and chain growth to occur at the same rate.]]
One of the key characteristics of a living polymerization is that the chain termination and transfer reactions are essentially eliminated from the four elementary reactions of [[chain-growth polymerization]] leaving only [[Initiation (chemistry)|initiation]] and (chain) propagation reactions.

A key characteristic of living polymerization is that the rate of initiation (meaning the dormant chemical species generates the active chain propagating species) is much faster than the rate of chain propagation. Thus all of the chains grow at the same rate (the rate of propagation).

The high rate of initiation (together with absence of termination) results in low (or narrow) polydispersity index (PDI), an indication of the broadness in the distribution of polymer chains.<ref>{{cite web |title=Living polymer |publisher=[[International Union of Pure and Applied Chemistry ]] |work=Gold Book |doi=10.1351/goldbook.LT07156 |url=http://goldbook.iupac.org/LT07156.html |access-date=January 4, 2023}}</ref> The extended lifetime of the propagating chain allowing for co-block polymer formation and end group functionalization to be performed on the living chain.  These factors also allow predictable molecular weights, expressed as the number average molecular weight (M<sub>n</sub>). For an ideal living system, assuming efficiency for generating active species is 100%, where each initiator generates only one active species the [[Kinetic chain length]] (average number of monomers the active species reacts with during its lifetime) at a given time can be estimated by knowing the concentration of monomer remaining. The number average molecular weight, [[Molar mass distribution#number average molecular mass|M<sub>n</sub>]], increases linearly with percent conversion during a living polymerization  
:<math>\ v = \frac{[M]_0-[M]}{[I]_0}</math><ref name=Principles />