https://doi.org/10.1351/goldbook.15388
In a binary copolymerization, the ratio of two rate constants defining the relative activity of an active center on a given type of terminal unit of a chain carrier toward one type of monomer, in the two cases where the penultimate unit of the chain carrier is identical to and different from the terminal unit.
Notes:
- The reactions involved are defined in accordance with the penultimate-unit effect, namely, \[\begin{array}{l} ...-{\rm{m}}_{11}^{\ast} + {\rm{M}}_{1}\ce{->[\textit{k}_{111}]} ...-{\rm{m}}_{11}^{\ast} \\ ...-{\rm{m}}_{21}^{\ast} + {\rm{M}}_{1}\ce{->[\textit{k}_{211}]} ...-{\rm{m}}_{11}^{\ast} \\ ...-{\rm{m}}_{11}^{\ast} + {\rm{M}}_{2}\ce{->[\textit{k}_{112}]} ...-{\rm{m}}_{12}^{\ast} \\ ...-{\rm{m}}_{21}^{\ast} + {\rm{M}}_{2}\ce{->[\textit{k}_{212}]} ...-{\rm{m}}_{12}^{\ast} \\ ...-{\rm{m}}_{12}^{\ast} + {\rm{M}}_{1}\ce{->[\textit{k}_{121}]} ...-{\rm{m}}_{21}^{\ast} \\ ...-{\rm{m}}_{22}^{\ast} + {\rm{M}}_{1}\ce{->[\textit{k}_{221}]} ...-{\rm{m}}_{21}^{\ast} \\ ...-{\rm{m}}_{12}^{\ast} + {\rm{M}}_{2}\ce{->[\textit{k}_{122}]} ...-{\rm{m}}_{22}^{\ast} \\ ...-{\rm{m}}_{22}^{\ast} + {\rm{M}}_{2}\ce{->[\textit{k}_{222}]} ...-{\rm{m}}_{22}^{\ast}, \end{array}\] where \({\rm{M}}_{1}\) and \({\rm{M}}_{2}\) are the two monomers involved in the binary copolymerization and \(-{\rm{m}}_{ij}^{\ast} (i,j = 1,2)\) denotes a chain carrier having an active site on its terminal monomer unit of type \({\rm{M}}_{j}\) and having the adjacent, penultimate monomer unit of type \({\rm{M}}_{i}\) (see chain carrier).
- The chain-end reactivity ratios are expressed mathematically by the equations \[s_{1} = k_{211}/k_{111};\ s_{2} = k_{122}/k_{222}\].
- The monomer reactivity ratios, defined in accordance with the penultimate-unit effect, are \[r_{112} = k_{111}/k_{112};\ r_{212} = k_{211}/k_{212};\ r_{221} = k_{222}/k_{221};\ r_{121} = k_{122}/k_{121}\]. The symbols for the monomer reactivity ratios are often abbreviated to \(r_{1}\), \(r_{1}^{\prime}\), \(r_{2}\), \(r_{2}^{\prime}\), respectively (see monomer reactivity ratios for the definitions of \(r_{1}\) and \(r_{2}\) ignoring the penultimate-unit effect).