For most
chain-growth polymerizations, the propagation steps are much faster than the initiation steps, so that each growing chain is formed in a short time compared to the overall polymerization reaction. During the formation of a single chain, the reactant concentrations and therefore the propagation rate remain effectively constant. Under these conditions, the ratio of the number of propagation steps to the number of initiation steps is just the ratio of
reaction rates: \nu = \frac{R_p}{R_i} = \frac{R_p}{R_t} where is the
rate of
propagation, is the rate of
initiation of polymerization, and is the rate of
termination of the polymer chain. The second form of the equation is valid at
steady-state polymerization, as the chains are being initiated at the same rate they are being terminated (). An exception is the class of
living polymerizations, in which propagation is much
slower than initiation, and chain termination does not occur until a quenching agent is added. In such reactions the reactant monomer is slowly consumed and the propagation rate varies and is not used to obtain the kinetic chain length. Instead the length at a given time is usually written as: \nu = \frac{[\ce{M}]_0-[\ce{M}]}{[\ce{I}]_0} where represents the number of monomer units consumed, and the number of radicals that initiate polymerization. When the reaction goes to completion, , and then the kinetic chain length is equal to the number average degree of polymerization of the polymer. In both cases kinetic chain length is an average quantity, as not all polymer chains in a given reaction are identical in length. The value of ν depends on the nature and concentration of both the monomer and initiator involved. ==Kinetic chain length and degree of polymerization==