Kinetic chain length

In polymer chemistry the kinetic chain length of a polymer, ν, is the average number of units called monomers added to a growing chain during chain-growth polymerization. During this process, a polymer chain is formed when monomers are bonded together to form long chains known as polymers. Kinetic chain length is defined as the average number of monomers that react with an active center such as a radical from initiation to termination.

This definition is a special case of the concept of chain length in chemical kinetics. For any chemical chain reaction, the chain length is defined as the average number of times that the closed cycle of chain propagation steps is repeated. It is equal to the rate of the overall reaction divided by the rate of the initiation step in which the chain carriers are formed. For example, the decomposition of ozone in water is a chain reaction which has been described in terms of its chain length.

In chain-growth polymerization the propagation step is the addition of a monomer to the growing chain. The word kinetic is added to chain length in order to distinguish the number of reaction steps in the kinetic chain from the number of monomers in the final macromolecule, a quantity named the degree of polymerization. In fact the kinetic chain length is one factor which influences the average degree of polymerization, but there are other factors as described below. The kinetic chain length and therefore the degree of polymerization can influence certain physical properties of the polymer, including chain mobility, glass-transition temperature, and modulus of elasticity.

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:

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