The polymer chains are long if the termination rate kT is much slower than the propagation rate. If kP and kT are equal, the chain lengths will be very short. A measure of the polymer chain length is the kinetic chain length l, defined by
l = rate of propagation / rate of initiation.
l = { k p / (2 k T kI )1/ 2 } [ M ]1/ 2 / [ I ] 1/ 2
(30.18)
This implies that lower the initiation rate and [ I ], higher the chain length.
The above polymerization scheme was based on addition reactions. In another scheme, during each step when a monomer is added, a small molecule such as water is eliminated, as exemplified in the example of nylon given below.
H2 N - (CH2)6 - NH2 + HOOC - (CH2)4 - COOH H - M - OH + H2O
................ H - [M] n OH + H2O
where M = - NH - (CH2)6 - NH - CO - (CH2)4 - CO -
(30.19)
In each step an amide linkage (- CO - NH -) is formed by eliminating a water molecule. The chain lengths generally increase until a significant monomer fraction remains in solution. The polymerization process can be controlled either by sudden cooling, addition of scavengers (which reduce the radical/ion concentrations) or by removing the polymeric material from the reaction mixture.
H - M - OH + H2O 
