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

TL;DR

This study redefines the minimal statistical segment length in polymers, revealing conformational heterogeneity and distinct relaxation behaviors at the Kuhn scale through atomistic simulations of polyethylene.

Contribution

It identifies the true minimal size for a statistical segment and uncovers conformational substructures with unique relaxation dynamics in flexible chains.

Findings

A single Kuhn segment (~11 bonds) is the smallest uncorrelated unit but non-Gaussian.

True Gaussianity appears only in larger blocks containing multiple Kuhn segments.

Distinct substructures (ACS, RCS, CE) exhibit different relaxation signatures.

Abstract

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 truly statistical segment - Gaussian, uncorrelated, and valid as an entropic spring - is not rigorously established. Using atomistic simulations of entangled polyethylene, we re-evaluate these foundational quantities. By fitting end-to-end distance distributions of C--C bond blocks and validating with higher-moment analyses, we identify for the first time the minimal sizes corresponding to a statistical segment and an entropic spring. A single Kuhn segment (approximately 11 bonds) is the smallest statistically uncorrelated unit, but its distance distribution is strongly non-Gaussian, while the monomer-based segment $b$, used in rheology and classical tube-theory formulations, is not statistical at all. True Gaussianity emerges only for blocks containing multiple Kuhn segments. At the Kuhn scale, we uncover a previously unresolved conformational heterogeneity. Each segment samples a broad range of conformations, from coiled (approximately 4~\AA) to extended (approximately 14~\AA), giving rise to three distinct substructures: aligned chain segments (ACS), random conformational sequences (RCS), and chain ends (CE). These exhibit distinct dynamical signatures. ACS relax with a stretched-exponential exponent $\beta \approx 0.5$, consistent with quasi-one-dimensional, defect-mediated localized modes, whereas RCS and CE relax with $\beta \approx 0.7$. By connecting these results to localized-mode theory and continuous-time random-walk models, we provide a molecular interpretation of stretched-exponential relaxation in polymer melts.