 Incorporated composition versus feed composition in EVA

Incorporated composition versus feed composition in EVA distinguishes the monomer mixture available to react from the units actually entering ethylene-vinyl acetate chains. Let $f$ be the mole fraction of vinyl acetate in the reacting monomer mixture, and $F$ its instantaneous fraction among newly incorporated units. Neither quantity is the mass fraction reported on a product datasheet. The copolymer composition equation relates instantaneous composition to the reacting mixture and monomer reactivity ratios; IUPAC explicitly notes that composition generally changes during the reaction.^[ref]

In the terminal model of copolymerization, the identity of the last unit controls addition-rate constants. Define $r_V=k_{VV}/k_{VE}$ and $r_E=k_{EE}/k_{EV}$, where the first subscript identifies the chain end and the second the incoming monomer. IUPAC defines these monomer reactivity ratios as homopropagation-to-cross-propagation rate-constant ratios.^[ref] Steady-state balance between the two chain-end types gives the familiar binary-model expressionFor an original illustration, stipulate $r_V=0.5$, $r_E=2$ and $f=0.2$. The numerator is 0.18 and denominator 1.62, so $F=1/9\approx 0.111$. These illustrative ratios are not measured kinetic constants for a commercial EVA grade. If both ratios were instead one, this model would give $F=f$ at every reacting-mixture composition.

The composition accumulated over a finite reaction interval is different again. Conversion bookkeeping for binary copolymers follows directly from conservation of monomer units. Normalize the initial total to one mole of units, let $X$ be the total molar conversion, and let $f_0$ and $f$ denote initial and remaining vinyl acetate fractions. Assuming no side losses and incorporation of every consumed monomer, the cumulative fraction isFor $f_0=0.20$, $X=0.50$ and remaining $f=0.30$, the polymer has $\overline{F}=0.10$. It is enriched in ethylene-derived units while the unreacted mixture becomes richer in vinyl acetate. At complete conversion, the overall incorporated fraction must return to $f_0$ under these assumptions, even if individual chains or earlier growth intervals differed.

An informative experiment therefore measures reacting-mixture composition, conversion and product composition separately. A low-conversion approximation needs evidence that composition drift is negligible over the actual interval; an initial feed label alone does not establish the chain composition. Convert incorporated mole fractions to mass fractions only after identifying which composition and reaction interval the measurement represents.