There are two major classes of polymerization processes and the average molar mass of the product varies with time in distinctive ways. In stepwise polymerization any two monomers present in the reaction mixture can link together at any time and growth of the polymer is not confined to chains that are already forming. As a result, monomers are consumed early in the reaction and the average molar mass of the product grows linearly with time. In chain polymerization an activated monomer, M, attacks another monomer, links to it, then that unit attacks another monomer, and so on. The monomer is used up as it becomes linked to the growing chains. High-molar-mass polymers (‘high polymers’) are formed rapidly and only the yield, not the average molar mass, of the polymer is increased by allowing long reaction times.
Stepwise polymerization commonly proceeds by a condensation reaction, in which a small molecule (typically H2O) is eliminated in each step. Stepwise polymerization is the mechanism of production of polyamides, as in the formation of nylon-66:
H2N(CH2)6NH2 + HOOC(CH2)4COOH → H2N(CH2)6NHCO(CH2)4COOH + H2O
\(\underrightarrow {\mathrm {continuing\;to}}\) H–[HN(CH2)6NHCO(CH2)4CO]n–OH
Polyesters and polyurethanes are formed similarly (the latter without elimination). A polyester, for example, can be regarded as the outcome of the stepwise condensation of a hydroxyacid HO–R–COOH.
The degree of polymerization, \(\langle N \rangle\) is the average number of monomer residues per polymer molecule: in terms of the polymerization rate constant kr,1
\(\langle N \rangle\) = \(1+ k_{\mathrm r}t[A]_{0}\)
The average length grows linearly with time. Therefore, the longer a stepwise polymerization proceeds, the higher the average molar mass of the product.
Chain polymerization occurs by addition of monomers to a growing polymer, often by a radical chain process. It results in the rapid growth of an individual polymer chain for each activated monomer. Examples include the addition polymerizations of ethene, methyl methacrylate, and styrene, as in
–CH2CH2X· + CH2=CHX → –CH2CHXCH2CHX·
and subsequent reactions. The central feature of the kinetic analysis is that the rate of polymerization is proportional to the square root of the initiator, In, concentration:
\(v= k_{\mathrm r} [\mathrm {In}]^{1/2}[\mathrm M]\)
For a polymer produced by a chain mechanism with mutual termination, the average number of monomers in a polymer molecule, <N>, produced by the reaction is the sum of the numbers in the two combining polymer chains and
\(\langle N \rangle\) = \(2k_{\mathrm r}[\mathrm M][\mathrm {In}]^{-1/2}\)
We see that, the slower the initiation of the chain (the smaller the initiator concentration and the smaller the initiation rate constant), the greater is the kinetic chain length, and therefore the higher is the average molar mass of the polymer.
1 Full details of the derivation of this and the following equations in terms of rate laws are given in our Physical chemistry: Thermodynamics, structure, and change (2014).