Ethylene-vinyl acetate

Ethylene-vinyl acetate, abbreviated EVA, is a copolymer made from the monomers Ethylene and vinyl acetate. Its chain contains ethylene-derived units $-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}{\mathrm{H}}_2-$ and vinyl-acetate-derived units $-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}(\mathrm{OCOC}{\mathrm{H}}_3)-$. The polymerization joins the carbon skeletons while retaining the acetate side group. Consequently ethylene-vinyl acetate denotes a family of compositions and chain lengths, rather than one small molecule with a unique molar mass.^[ref][ref]

A useful distinction is between the mole fraction of incorporated vinyl acetate units and their mass fraction. Write $x=N_{\mathrm{VA}}/(N_{\mathrm{VA}}+N_{\mathrm{E}})$. Ignoring the contribution of chain ends for sufficiently long chains, the unit molar masses are $M_{\mathrm{E}}=28.05\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ and $M_{\mathrm{VA}}=86.09\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. ThusA chain population with 20% of its units derived from vinyl acetate has about 43.4% of its mass in those units. Conversely, 20% by mass corresponds to only about 7.53% of the units. The difference comes from the roughly threefold unit-mass ratio. Here $x$ describes the incorporated chain composition; incorporated composition versus feed composition in EVA is a separate issue from this arithmetic conversion.^[ref]

The manufacturer's EVA 2018 datasheet illustrates actual reporting practice: its typical vinyl acetate content is 18.2% by mass. That value characterizes the named product and does not define every ethylene-vinyl acetate material.^[ref]

A particularly revealing application is laser capture microdissection. The 1996 report placed a transparent thermoplastic ethylene-vinyl acetate film on a histological section. A carbon dioxide laser pulse activated a chosen region of the film, whose local adhesion transferred selected cells for subsequent analysis. This connects a polymer processing response to spatially selective sampling of tissue; the report's film is not identified with the commercial grade cited above.^[ref]

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.

Conversion bookkeeping for binary copolymers uses conserved component amounts to distinguish initial feed, residual feed and cumulative incorporated composition. It is an accounting constraint on a closed batch, separate from the kinetic prediction supplied by the copolymer composition equation.

Normalize initial total monomer amount to one mole. Let $f_0$ be its type-1 mole fraction, $X$ total molar conversion and $f$ the type-1 fraction in the remaining pool. Assume no additional feed, side losses or consumption outside the material being counted. The incorporated amounts areTheir sum is $X$, so the cumulative type-1 fraction isThis is a molar-unit balance; conversion by mass requires the corresponding component molar masses. The IUPAC terminology distinguishes instantaneous composition from integrated conversion/composition relationships.^[ref]

For an original example, choose $f_0=0.20$, $X=0.50$ and residual $f=0.30$. The incorporated amounts are 0.05 and 0.45 mol, giving ${\overline{F}}_1=0.10$. Individual monomer conversions are $0.05/0.20=25\%$ and $0.45/0.80=56.25\%$. The residual mixture becomes richer in the less-consumed component even though the polymer contains less of it than the initial feed.

Nonnegative incorporated and remaining amounts impose, for $0\le X<1$,For $f_0=0.20$ and $X=0.10$, a reported residual fraction of 0.50 is impossible under the assumptions: it would leave $0.90(0.50)=0.45$ mol of type 1 when only 0.20 mol was present initially.

For a differentiable conversion trajectory, the instantaneous fraction is $F_1=d(X{\overline{F}}_1)/dX=f-(1-X)df/dX$. Equivalently, $(1-X)df/dX=f-F_1$. This is the bridge between conservation and kinetic composition drift. At complete conversion there is no residual mixture to assign an $f$ value; the total incorporated composition nevertheless equals $f_0$ under the closed-batch assumptions. The IUPAC experimental recommendation measures conversion and composition separately rather than replacing both by an initial feed label.^[ref]