PET Nucleation as a Thermodynamic Mirror of Black Hole: An Analogy

We investigate solvent-mediated nucleation and crystallization of poly(ethylene terephthalate) (PET) from trifluoroacetic acid (TFA) solutions upon gradual addition of water, a poor solvent for PET. The system undergoes liquid–liquid phase separation, formation of PET-rich domains, and growth of nanoparticles, interpreted within classical nucleation theory and polymer solution thermodynamics, where solvent composition controls the balance between bulk free-energy gain and interfacial free-energy cost. On this conventional basis, we introduce a strictly heuristic analogy between surface-energy-dominated PET nucleation and entropy–area concepts from black-hole thermodynamics. In this view, increasing water content drives the system from a homogeneous, high-entropy solution to an aggregated state and the PET–solution interface is used metaphorically as a “soft-matter event horizon” beyond which individual chain conformations become experimentally inaccessible. Inspired by Bekenstein’s area law, we explore a simple toy model in which an effective entropy-like measure is postulated to scale with aggregate surface area, without claiming experimental verification of entropy–area scaling in PET or literal applicability of gravitational bounds. Thus, the work provides an experimentally grounded study of PET nucleation, augmented by a cross-disciplinary, metaphorical framework for discussing boundary-dominated thermodynamics.