**Nanoparticle Loading of Unentangled Polymers Induces Entanglement-Like
Relaxation Modes and a Broad Sol-Gel Transition**

XZ Cao and H Merlitz and MG Forest, JOURNAL OF PHYSICAL CHEMISTRY LETTERS, 10, 4968-4973 (2019).

DOI: 10.1021/acs.jpclett.9b01954

We combine molecular dynamics simulations, imaging and data analysis, and the Green-Kubo summation formula for the relaxation modulus G(t) to elicit the structure and rheology of unentangled polymer-nanoparticle composites distinguished by small NPs and strong NP-monomer attraction, epsilon(NPM )>> k(B) T. A reptation-like plateau emerges in G(t) beyond a terminal relaxation time scale as the volume fraction, c(NP), of NPs increases, coincident with a structure transition. A condensed phase of NP-aggregates forms, tightly interlaced with thin sheets of polymer chains, the remaining phase consisting of free chains void of NPs. Rouse mode analyses are applied to the two individual phases, revealing that long-wavelength Rouse modes in the aggregate phase are the source of reptation-like relaxation. Imaging reveals chain motion confined within the thin sheets between NPs and exhibits a 2D analogue of classical reptation. In the NP-free phase, Rouse modes relax indistinguishable from a neat polymer melt. The Fourier transform of G(t) reveals a sol- gel transition across a broad frequency spectrum, tuned by c(NP) and epsilon(NPM ) above critical thresholds, below which all structure and rheological transitions vanish.

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