We use molecular dynamics simulations to study a semidilute, unentangled polymer solution containing well dispersed, weakly attractive nanoparticles (NP) of size (σN ) smaller than the polymer radius of gyration Rg. We find that if σN is larger than the monomer size the polymers swell, while smaller NPs cause chain contraction. The diffusion coefficient of polymer chains (Dp) and NPs (DN ) decreases if the volume fraction φN is increased. The decrease of Dp can be well described in terms of a dynamic confinement parameter, while DN shows a more complex dependence on σN , which results from an interplay between energetic and entropic effects. When φN exceeds a σN -dependent value, the NPs are no longer well dispersed and DN and Dp increase if φN is increased. arXiv:1804.06993v2 [cond-mat.soft]

Due to their unique structural and mechanical properties, randomly cross-linked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (e.g., chain-length and end-to-end distributions), we generate disordered phantom networks with different cross-linker concentrations C and initial densities ρ init and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for networks with the same C , which determines the number of chains and the chain-length distribution, depends strongly on the preparation protocol of the network, here controlled by ρ init . We rationalize this dependence by employing a generic stress–strain relation for polymer networks that does not rely on the specific form of the polymer end-to-end distance distribution. We find that the shear modulus of the networks is a nonmonotonic function of the density of elastically active strands, and that this behavior has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly cross-linked polymer networks, the knowledge of the exact chain conformation distribution is essential for correctly predicting the elastic properties. Finally, we apply our theoretical approach to literature experimental data, qualitatively confirming our interpretations.