Monomer reactivity ratio ($r_i=k_{ii}/k_{ij}$)

A monomer reactivity ratio compares two propagation rate constants for the same terminal chain type in a binary copolymerization. With $k_{ij}$ denoting addition of monomer $j$ to an end of type $i$,These are homopropagation-to-cross-propagation ratios, as defined in the IUPAC terminology.^[ref] Each is dimensionless when numerator and denominator use matching rate conventions. Neither is simply the ratio of the two monomers' total consumption rates.

A chain-end addition probability depends on available concentrations as well as on the rate constants. For a type-1 end at fixed mixture mole fractions, the terminal model of copolymerization givesFor stipulated $r_1=0.5$, an equimolar mixture gives $p_{11}=1/3$. At $f_1=0.8$ it gives $p_{11}=2/3$, whereas at $f_1=0.2$ it gives $p_{11}=1/9$. Even though $k_{11}<k_{12}$ in each case, sufficient abundance of monomer 1 can make self-addition more frequent. These are illustrative kinetic parameters, not measured constants for a named commercial polymer.

The pair $(r_1,r_2)$ determines both rows of the fixed-feed transition matrix. When $r_1{r}_2=1$, its two rows coincide for nonzero feed fractions, giving independent additions within the idealized fixed-feed model. That does not require the incorporated fraction to equal the feed fraction. For example, $r_1=2$, $r_2=1/2$ and $f_1=1/2$ give probability $2/3$ of adding type 1 from either end.

Experimentally, a ratio is associated with the specified monomer pair, reaction conditions and kinetic model. It is not a universal index belonging to an isolated monomer. The IUPAC recommendation uses several starting compositions together with conversion and incorporated-composition measurements to estimate the two ratios.^[ref] One measured copolymer composition at one feed generally cannot identify two unknown ratios. Joint uncertainty and possible composition drift belong to the interpretation.