The model predicts that enzymatic degradation of PET can leave behind a dominant, fluffy cluster of residual material as well as many much smaller particles. It places around 90% of the spherulites in that dominant cluster, whose high surface-to-volume ratio is characteristic of a fluffy, loosely connected structure.
That is the central question of the study: what clusters remain after the first stage of degradation, and what do those remnants look like? The analysis follows their morphology and connectivity, then uses a release-time calculation for a dominant remaining cluster.
The geometry of what remains
The model uses spherical geometry for both the degrading particle and the growing spherulites, rounded structures represented in the calculation.
To work out how those structures are arranged and connected, the numerical workflow uses adapted Delaunay/Voronoi tessellation calculations, a geometric way to analyze spherulite shape and connectivity.
Three patterns emerge
In illustrative cases, the predicted remnants fall into three broad patterns: the dilute case has small clusters; the diverse case combines smaller clusters with a larger one; and the dense case forms one big cluster.
Across the three examples, the reported cluster counts are 3,700, 738 and one cluster.
The diverse case is especially surface-rich. Its total surface-to-volume ratio is 8.2, while the dominant cluster’s ratio is 7.2, a combination the analysis describes as high excess surface, including a high-ratio dominant cluster.
PET splits the leftovers
For the PET application, the model uses data from two waste sources treated at different temperatures. It predicts a dominant cluster containing around 90% of the spherulites, alongside very small clusters.
The dominant PET cluster has a high or very high surface-to-volume ratio, which is characteristic of a fluffy, loosely connected structure. In other words, most of the modeled spherulites sit in one open-looking remnant while much smaller clusters remain alongside it.
Across the PET examples, the small residual particles measure 3 to 30 micrometres, and the number of small clusters ranges from 267 to 2,429.
The initial particle in the PET example is around 160 micrometres, so the predicted small remnants are far smaller than the particle at the start of the calculation.
One PET-bottle scenario shows the scale of the smaller population. At 65°C, the remaining particles are 34% of their initial volume; around 4.1 million additional small particles are produced, and they represent 3% of the initial volume.
Release is scenario-specific
To estimate when the dominant remnant is released, the paper develops a reduced effective model for its release time.
Across the listed bottle and textile cases, final-release times are 11.1, 9.2, 5.3, 9.9 and 4.0 hours. The corresponding normalized release values are 1, 1, 1, 1 and 0.7. These figures describe scenario-specific outcomes rather than one timetable for every PET particle.
A built-in constraint
The results are shaped by a deliberate model choice: spherulite depolymerization is neglected because it is treated as slower than depolymerization of the amorphous matrix. The study is therefore focused on clusters remaining after the first stage, rather than on degradation of the spherulites themselves.
The supplied document is an arXiv preprint. Its front matter says the submitted manuscript was subsequently accepted for publication, while the supplied front matter lists an institutional affiliation but does not report funding.
Paper data and sources
Original title: Residual semi-crystalline particles released during enzymatic degradation of plastics
Authors: Michael Schindler, Ludwik Leibler
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text