= Monomer reactivity ratio
{title2=$r_i=k_{ii}/k_{ij}$}
A \b[<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 $i$,
$$
r_1=\frac{k_{11}}{k_{12}},\qquad r_2=\frac{k_{22}}{k_{21}}.
$$
These are homopropagation-to-cross-propagation ratios, as defined in the IUPAC terminology.<IUPAC Compendium of Chemical Terminology, fifth edition (Gold Book)>[Monomer reactivity ratios, entry 15410, definition]{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> gives
$$
p_{11}=\frac{r_1f_1}{r_1f_1+f_2},\qquad p_{12}=1-p_{11}.
$$
For 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 $r_1r_2=1$, 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.<Radical Copolymerization Reactivity Ratios by IUPAC>[Official announcement, three-or-more-reaction measurement design]{ref} One measured copolymer composition at one feed generally cannot identify two unknown ratios. Joint uncertainty and possible composition drift belong to the interpretation.
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