Each sample loses mass by first-order decay: the fraction remaining falls exponentially at a rate k set by the material, then scaled by temperature and moisture. PHA, natural fibre and conventional plastic follow a mild Q10 rule (roughly a fixed multiplier in rate per 10°C rise). PLA is different: microbial hydrolysis barely starts below its glass-transition range, so its rate is gated by a steep logistic threshold centred near 50°C — it stays almost inert in a home bin and only breaks down fast once the pile is genuinely hot, which is why PLA packaging is labelled "industrially compostable" rather than just "compostable".
mass(t+dt) = mass(t) · exp(-k_eff · dt)
k_eff = k0 · Q10^((T-25)/10) · moist(m) [PHA, fibre, plastic]
k_eff = k0 · gate(T) · moist(m) [PLA]
gate(T) = 1 / (1 + exp(-(T-50)/2.5))
moist(m) = exp(-((m-opt)/width)²)
- Temperature — industrial composting holds 50–60°C; this is the only regime where PLA's hydrolysis gate opens and its curve breaks away from flat.
- Moisture — each material has its own optimum; too dry starves the microbes, too wet crowds out oxygen and slows aerobic breakdown for all four.
- Time speed — simulated days per real second, so multi-month decomposition plays out in seconds without changing the underlying rates.
- Conventional plastic (PE/PP) is shown for contrast — its rate constant is orders of magnitude smaller, so under any of these conditions it stays visually almost unchanged, matching its real centuries-scale persistence.
Bubbles rising off each bed represent CO&sub2; released as aerobic microbes respire the breaking polymer — their rate is drawn directly from each material's instantaneous decay rate, so a faster-shrinking bed visibly off-gasses more.