Local Density Field as a Physical Order Parameter for Conductivity Prediction in Block Copolymer/Carbon Nanotube Nanocomposites via a Voxel-Based Graph Attention Network

The electrical conductivity of block copolymer nanocomposites is governed by a complex interplay between nanofiller organization and block copolymer morphology. However, establishing a quantitative, predictive link between the molecular-scale structure and macroscopic properties remains a fundamental challenge. Here, we demonstrate that the local particle density field serves as a pivotal order parameter controlling the conductive network. By integrating hybrid particle-field molecular dynamics simulations with a graph learning framework, we transform continuous molecular coordinates into a discrete density representation that explicitly encodes this key physical parameter. Our model achieves accurate conductivity predictions across three archetypal carbon nanotube (CNT)-diblock copolymer nanocomposite configurations: randomly mixed, template-free systems (BRCR), CNTs embedded within preassembled lamellar polymer templates (BTCR), and CNTs selectively confined and aligned within self-assembled lamellar domains (BTCO), over a CNT concentration range of 1.0–8.0 vol %. More importantly, the model’s interpretability decodes the distinct conduction mechanisms operative in each morphology: from stochastic network formation in disordered composites, through directed pathway integration in confined templates, to thermodynamics-driven refinement in compatibilized systems. Our analysis of topological network metrics and attention scores quantitatively links these emergent conductive behaviors to the underlying polymer-mediated filler organization. This work establishes local density encoding as a generalizable strategy for elucidating structure–property relationships in complex polymer composites, offering a new paradigm for the data-driven design of functional nanomaterials.