Directional Entropy Bands for Surface Characterization of Polymer Crystallization

Molecular dynamics (MD) simulations provide atomistic insights into nucleation and crystallization in polymers, yet interpreting their complex spatiotemporal data remains a challenge. Existing order parameters face limitations, such as failing to account for directional alignment or lacking sufficient spatial resolution, preventing them from accurately capturing the anisotropic and heterogeneous characteristics of nucleation or the surface phenomena of polymer crystallization. We introduce a novel set of local order parameters-namely, <i>directional entropy bands</i>- that extend scalar entropy-based descriptors by capturing first-order angular moments of the local entropy field around each particle. We compare these against conventional metrics (entropy, the crystallinity index, and smooth overlap of atomic positions (SOAP) descriptors) in equilibrium MD simulations of polymer crystallization. We show that (i) scalar entropy bands demonstrate advantages compared to SOAP in polymer phase separation at single-snapshot resolution and (ii) directional extensions (dipole projections and gradient estimates) robustly highlight the evolving crystal-melt interface, enabling earlier nucleation detection and quantitative surface profiling. UMAP embeddings of these 24-30D feature vectors reveal a continuous melt-surface-core manifold, as confirmed by supervised boundary classification. Our approach is efficient and directly interpretable, offering a practical framework for studying polymer crystallization kinetics and surface growth phenomena.