Biodegradable polyesters (PLA, PGA, PCL, PLGA) degrade mainly by hydrolysis: water diffuses into the bulk and cleaves ester bonds (–CO–O–) in the backbone at random, independent of position — this is random chain scission, not end-nibbling erosion.
Each intact ester bond has a constant per-step probability of cleaving. With N₀ bonds surviving to time t, the bond survival kinetics are first-order (analogous to radioactive decay):
dN/dt = −k(t)·N
N(t) = N₀ · e^(−∫k dt)
The number-average degree of polymerization Xn (monomer units per surviving chain fragment) follows directly from bonds broken per original chain:
Xn(t) = Xn(0) / (1 + Xn(0)·p(t))
p(t) = fraction of ester bonds hydrolyzed
Mn(t) ∝ Xn(t) (number-average molecular weight)
Crucially, mass loss lags Mn decay: cleaving a 200-mer into two 100-mers has almost no effect on solid mass — fragments are still solid and insoluble. Only once fragments fall below a critical oligomer length do they diffuse out as soluble products, so mass loss stays near zero for a long induction period, then falls steeply — the classic PLA "bulk erosion" curve.
Real hydrolysis is also autocatalytic: the carboxylic-acid end groups created by each scission event lower the local pH and accelerate further hydrolysis nearby — especially in thick bulk samples where acidic degradation products can't diffuse out fast enough. The "Autocatalysis strength" control scales k(t) by the fraction of bonds already broken, reproducing the accelerating (sigmoidal) degradation seen experimentally in PLGA implants and sutures.
- Rate constant k — baseline per-step hydrolysis probability per intact bond (water availability / temperature / pH).
- Autocatalysis strength — how much accumulated scission accelerates further scission (self-catalyzed acid buildup).
- Chain length — initial monomers per polymer chain, i.e. initial degree of polymerization Xn(0).