Theory for enzymatic degradation of semi-crystalline polymer particles

TL;DR

The paper develops a geometric Avrami-like model to describe enzymatic degradation of semi-crystalline polymer particles by treating the degrading amorphous matrix and embedded spherulites as interacting spheres. A novel double Voronoi/Delaunay tessellation-based algorithm computes evolving volumes and interfacial areas, enabling coupled dynamics that predict final degradation yield and kinetic profiles from experimental data on PET textiles and bottles. By mapping parameters from degradation and growth experiments and accounting for non-100% crystallinity inside spherulites, the model accurately reproduces observed yields and timescales, and reveals how initial morphology and particle size govern outcomes. The framework highlights the critical influence of spherulite size, spacing, and crystallization on enzymatic recycling efficacy, offering practical guidance for pretreatment design and waste formulation.

Abstract

In enzymatic recycling or biodegradation of semi-crystalline plastic waste, crystalline spherulites embedded into an amorphous matrix hinder and slow down depolymerisation. When the enzymatic depolymerisation temperature exceeds the glass transition temperature, these spherulites tend to grow. The depolymerisation process is thus controlled by a competition between erosion of the amorphous matrix from the particle surface and the growth of recalcitrant spherulites within the particle bulk and at its surface. We present a geometric model that captures this competition, together with an algorithm to solve the equations numerically. Our algorithm introduces a new extension of Voronoi/Delaunay tessellation in space. We extract the parameters for the model from experimental data on the enzymatic depolymerization by hydrolase LCC-ICCG of PET bottle flakes and textile waste, in order to make a prediction of the observed degradation yield as a function of time. Both the final yield and the degradation kinetics are correctly predicted. Most importantly, the model clarifies how and to which extent nucleating agents, impurities, additives, and/or rapid crystal growth present in the waste can undermine pretreatment efforts aiming to initiate depolymerisation from a material with a low initial crystallinity.

Figures (16)

• Figure 1: Sketches representing the spatial configuration of controlled preparation at two different temperatures (left: high, right: low). They serve as starting points for the degradation process. Spherulites in the right panel are chosen five times smaller and $5^3$ times more numerous (in three dimensions) than in the left panel, but their volume fractions are equal.
• Figure 2: The three different geometric volumes used in the model, at a given time $t$: Degraded volume $V_\text{deg}(t)$ (light green), amorphous volume $V_\text{am}(t)$ (light blue) and spherulite volume $V_\text{sph}(t)$ (light red). The thick solid curves show the interfaces between these volumes.
• Figure 3: Evolution in time of the geometry used in the model: The amorphous volume (blue) is degraded, the spherulites (red) grow (and possibly nucleate) only within the amorphous phase, finally remaining as connected clusters of egg-shaped objects (black curves). The three rows correspond to different growth rates of spherulites with the same degradation rate of the amorphous phase.
• Figure 4: Evolution in time of relative amorphous and of so-far degraded volume, without spherulites, according to equations \ref{['eq:Vtot']} and \ref{['eq:amorph_vol']}. The timescale of degradation, $\tau_h$ is defined in equation \ref{['eq:tauh']}.
• Figure 5: Evolution in time of relative spherulite volume in bulk, according to equation \ref{['eq:avrami_vol']}. The timescale of spherulite growth, $\tau_s$ is defined in equation \ref{['eq:taus']}. Top panels: spatial sketches at chosen times.