Beyond the Kuhn Segment: Conformational Substructures and Relaxation Dynamics in Flexible Chains

The statistical, ``monomer-based' segment length $b$ and the Kuhn length $l_k$ are central to polymer physics, yet the minimal size required for a segment to be truly statistical-Gaussian, uncorrelated, and valid as an entropic spring-has not been rigorously established. Using atomistic simulations of entangled polyethylene, we re-examine these foundational quantities. y fitting end-to-end distance distributions of C--C bond blocks to Gaussian forms and validating them with higher-moment analyses, we identify the minimal sizes corresponding to a statistical segment and an entropic spring. A single Kuhn segment ($\approx$11 bonds) is the smallest statistically uncorrelated unit, but its distribution is strongly non-Gaussian, while the widely used monomer-based length $b$ is not statistical. Gaussian statistics emerge only for blocks containing multiple Kuhn segments. At the Kuhn scale, we identify a heterogeneous organization into aligned chain segments (ACS), random conformational sequences (RCS), and chain ends (CE), each with distinct dynamical signatures. ACS exhibit strongly stretched relaxation with $\beta\approx0.5$, whereas RCS and CE relax faster with $\beta\approx0.7$. All segments display subdiffusive translational motion on the Kuhn scale. These results provide a molecular interpretation of stretched-exponential relaxation in polymer melts, in which the exponent $\beta$ reflects the dimensionality and cooperativity of conformational rearrangements at the Kuhn-segment scale.