The Role of the Topological Constraints in the Chain Dynamics in All Polymer Nanocomposites

We investigate all-polymer nanocomposites, formed by linear chains and single-chain polymer nanoparticles (SCNPs), by means of large-scale simulations. To distinguish the role of the soft penetrable character of the SCNPs in the topological constraints from other specific contributions present in experiments, the simulations for different compositions of the mixture are performed at constant density and with identical segmental mobility and monomer excluded volume for the SCNPs and linear chains. Every composition leads to a well-dispersed nanocomposite with fully penetrated nanofillers. Hence, unlike in the case of hard nanofillers, the SCNPs do not exert confinement effects on the linear chains and only contribute to the topological constraints. We discuss the intramolecular dynamics of the linear chains in terms of the tube model. We determine the entanglement length of the linear chains by analyzing their isoconfigurational mean paths (IMP) and the primitive paths (PP) as a function of the concentration and topology of the SCNPs. In the analysis we use different estimators proposed in the literature. The IMP and PP analysis in the nanocomposites with sparse SCNPs yields values of the entanglement length smaller and larger, respectively, than in the reference pure linear melt, though small variations are observed. A more consistent trend is found in the nanocomposites with globular SCNPs, where both the IMP and PP analysis unambiguously reveal that the linear chains are more entangled than in the pure linear melt. Such differences between the effects of SCNPs with different topologies are presumably related to the much higher fraction of threadable loops in the globular SCNPs, with respect to their sparse counterparts, which effectively lead to more topological constraints.