Beyond the Kuhn segment: Conformational substructures and relaxation dynamics in flexible chains

Abstract

The statistical, “monomer-based” segment length b and the Kuhn length lk 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 reexamine these foundational quantities. By 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 (≈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 β ≈ 0.5, whereas RCS and CE relax faster with β ≈ 0.7. 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 β reflects the dimensionality and cooperativity of conformational rearrangements at the Kuhn-segment scale.