In this work, we develop and validate a semi-analytical, physics-based predictive model to describe the photo-oxidative degradation kinetics of Low-Density Polyethylene (LDPE), resolving a critical kinetic anomaly observed in the nanometric regime. While classical Diffusion-Limited Oxidation (DLO) theories successfully predict degradation profiles for thick components governed by oxygen starvation, they implicitly assume kinetic homogeneity for specimens significantly thinner than the critical oxidation depth. However, recent experiments on nanometric LDPE films (146-200 nm) reveal a counter-intuitive, non-linear inverse dependency of mass loss on thickness that explicitly contradicts standard Fickian predictions. Demonstrating that oxygen starvation is physically untenable at this scale due to negligible diffusion timescales, we attribute this behavior to a novel Volatile Trapping Mechanism. We posit that the rate-limiting step governing the macroscopic weight change is not the ingress of oxygen, but the diffusive egress of volatile oxidative by-products. These low-molecular-weight fragments, generated by chain scission, do not evaporate instantaneously but accumulate within the polymer matrix, effectively inhibiting the forward reaction kinetics through a local saturation effect. The proposed computational framework treats degradation as a coupled reaction-diffusion problem derived from first principles of mass transport. Unlike purely empirical approaches that rely on unconstrained curve fitting, the formulation links the production rate of volatiles to their thickness-dependent diffusion characteristic time, adapting autocatalytic degradation logic to account for the transient retention of volatile species. Model predictions were validated against experimental datasets obtained from nanometric LDPE films. The framework accurately reproduces the observed thickness-dependent mass loss rates, capturing the transition from bulk-like behavior to the inhibited kinetics of thicker films without the need for ad-hoc empirical factors. Overall, this physics-based framework establishes a robust methodology for predicting polymer lifetime at the nanoscale, unveiling how diffusive product egress, rather than oxygen ingress, acts as the governing kinetic constraint in confined geometries.