End Curvature-Mediated Entropy Effects on Transport of Nanorods in Polymer Networks

While spherical nanoparticles have been extensively investigated, yielding well-established foundational insights into their diffusion dynamics in polymer matrices, the transport behaviors of rod-like nanoparticles (nanorods, RNPs) remain far less characterized, and especially the regulatory role of end curvature remains inadequately studied. This limits the rational design of RNP–polymer composite systems for targeted applications. By employing coarse-grained molecular dynamics simulations, we found that the transport behaviors of RNPs in cross-linked polymer networks are not solely dictated by size but are finely tuned by end curvature. RNPs with capped ends (capsule-like structure) with lengths equal to half-integer multiples of the network mesh size exhibited significantly faster diffusion than those with lengths equal to integer multiples. In contrast, RNPs with flat ends (cylindrical structure) showed the opposite trend: integer multiples resulted in faster diffusion than half-integer multiples. Further free energy analysis revealed that capped RNPs with half-integer mesh lengths exhibit an entropy–energy compensation mechanism, reducing the free energy barrier and promoting diffusion. By contrast, flat RNPs with both integer and half-integer multiples of mesh lengths exhibit entropy–energy reinforcement effects, leading to higher free energy barriers than those of capped RNPs. These mechanism differences explain the observed alternation in diffusivity and establish the end curvature as a critical parameter to regulate RNP transport behaviors. These findings enhance our fundamental understanding of nonspherical nanoparticle transport in confined polymer environments and offer actionable guidelines for the rational design of nanodrug carriers, nanoscale rheology, and polymer nanocomposites.