Copolymer Composition

Predict instantaneous copolymer composition from feed ratio and reactivity ratios (Mayo–Lewis equation)

How this works

When two monomers copolymerize, the growing chain end usually doesn't add each monomer at the same rate it appears in the feed. The Mayo–Lewis equation predicts the instantaneous mole fraction of monomer 1 in the copolymer, F1, from the feed mole fraction f1 and the two reactivity ratios r1 and r2 (how much each chain end prefers its own monomer over the other one).

F1 = (r1f1² + f1f2) ÷ (r1f1² + 2f1f2 + r2f2²)    where f2 = 1 − f1

r1 > 1 means a monomer 1 chain end prefers adding another monomer 1 (the copolymer runs rich in monomer 1 relative to the feed); r1 < 1 means it prefers crossing over to monomer 2. When both ratios are below 1, the system tends toward alternation; when both are above 1, it tends toward blockiness. If an azeotropic composition exists (F1 = f1), the copolymer composition stays constant as conversion proceeds even though the composition would otherwise drift as the faster comonomer is consumed first.

Composition calculator

Autofills names and reactivity ratios below; edit freely afterward
0 to 1; mole fraction, not mass or volume fraction

The dashed diagonal is where copolymer composition equals feed composition. The solid curve is F1 predicted across the whole feed range; the accent dot marks your current feed. If the curve crosses the diagonal, that crossing (marked in red) is the azeotrope.

Reference reactivity ratios

Typical literature values, usually from bulk or solution free radical copolymerization near 60 °C. Reactivity ratios are sensitive to temperature, solvent, and the method used to measure them, so treat these as starting points and verify against a primary source for real formulation work.

Monomer 1Monomer 2r₁r₂Tendency