Physically-motivated primitive path analysis of entangled polymer networks

Physical entanglements between polymer chains enhance the moduli, strength, and toughness of elastomers and gels, yet relating entanglement micromechanics to macroscopic mechanical benefits remains difficult. Experimentally investigating entanglements is challenging due to their nanoscale sizes, subsurface locations, and chemical indistinguishability from their surroundings. Computationally mapping structure-property relations is costly when using physics-based models that enable direct entanglement observation, such as coarse-grained molecular dynamics (CGMD). Entanglements are also transient, configuration-dependent features without clear quantitative definitions. To address this ambiguity, we introduce an approach that quantitatively defines local entanglements along simulated polymer backbones using the Gaussian Linking Number, and introduce a geometric center of entanglement verified to represent the position through which entropic chain forces are transmitted via Kremer-Grest CGMD simulations. Unlike existing approaches, which output a single linking number for chain pairs, our method identifies the multitude of load-transmitting inter- and intra-chain entanglements along a polymer's backbone. To bridge scales, we introduce a topological distillation algorithm that converts entangled CGMD networks into representative discrete network models (DNMs), representing entanglements as vertices and primitive paths as load-transmitting edges. Our DNMs reproduce small-strain virial stress predictions of the Kremer-Grest model with a 97% reduction in computational cost, verifying both physical accuracy and computational efficiency. This distillation procedure will facilitate physics-based, predictive modeling of entangled network mechanics, from polymers to architected metamaterials.