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Frederick M. Lewis, with Frank R. Mayo, coauthored the 1944 paper establishing a quantitative basis for comparing monomers in copolymerization, with styrene and methyl methacrylate as its named chemical system.^[ref] The published name is retained without expanding the middle initial or assigning individual experimental steps to either coauthor.

The scientific problem is that incorporated composition can differ from the reacting-mixture composition. In the terminal model of copolymerization, two monomer reactivity ratios describe relative self-addition and cross-addition preferences. Inferring both ratios requires observations that distinguish their effects, rather than one measurement that happens to match the feed.

An original identifiability example uses the copolymer composition equation at equimolar feed. It reduces toAn observation $F_1=1/2$ establishes $r_1=r_2$ within this model, but leaves their common value unknown. Pairs $(0.2,0.2)$, $(1,1)$ and $(2,2)$ all satisfy it. They need not predict the same sequence correlations or behavior at another feed.

At a second feed $f_1=0.20$, the three candidate pairs instead predict $F_1\approx 0.3684$, $0.2000$ and $0.1429$, respectively. This invented comparison explains the information gained by varying the monomer mixture. It is not a reconstruction of the original authors' measured constants.

Modern IUPAC recommendations likewise use several starting compositions together with conversion and product-composition observations.^[ref] Lewis's verified contribution belongs to the experimental and theoretical development of that comparison problem. Composition data test the kinetic model and its parameters; they do not acquire a unique interpretation merely because one fitted curve passes through one point.

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.