Every lactic-acid monomer starts as a free sphere on the left. Whenever two free chain-ends drift close enough, they have a chance to condense into a bond each frame — the reaction rate follows the Arrhenius equation, so hotter melt and an active catalyst both speed up growth, while unreacted ends become scarcer as the melt converts. On the right, the same monomer count starts pre-polymerized into one long petroleum-derived chain.
k_p = A_p · exp(−E_p / R·T) · (catalyst ? 8 : 1)
X̄n = N_monomers / N_chains (Carothers, degree of polymerization)
k_deg = A_d · (RH/100)^1.5 · exp(−E_d / R·T_compost)
bonds(t) = bonds₀ · e^(−k_deg·t) (first-order chain scission)
- Melt temperature — raises the polymerization rate constant k_p exponentially (Arrhenius); above ~170 °C monomers convert fast.
- Catalyst — a tin/lactide catalyst (as used industrially for PLA) multiplies k_p roughly eight-fold without changing the activation energy.
- Humidity & compost temperature — drive hydrolytic chain scission: water attacks ester bonds faster when both are high, snapping the bioplastic chain back into oligomers and monomers.
- Petroleum reference — its C–C backbone has no hydrolyzable ester linkages, so the same compost conditions barely touch it; its scission rate constant is fixed ~1000× lower and ignores the sliders.
Real-world relevance: this is why a PLA cup breaks down in an industrial compost (55 °C, high humidity) in months, while an ordinary plastic cup in the same bin looks almost unchanged for decades.