| In this thesis a series of theoretical models for the overall viscoelastic properties of a class of polymer nanocomposites is presented. The composite medium under investigation consists of spherical nanoparticles at low volume fractions (<10%), which are homogeneously dispersed in a liquid matrix of linear monodisperse homopolymers. The filler diameter and their average wall-to-wall distance are comparable with the average size of the host polymer macromolecule. The goal is (1) to identify the relevant physics on the molecular and sub-molecular scales, and (2) capture that physics to develop molecularly informed constitutive models to reproduce the peculiar features of viscometric functions of these materials, observed in experiments. Such constitutive equations that incorporate parameters representing the state and the dynamics on smaller scales are desirable since they allow material performance optimization based on designing material structure at the nanoscale.; Three classes of models are defined based on the relative molecular weight of the chains M, and the polymers overlapping threshold Mc: (1) unentangled case M < Mc, (2) close to overlap concentration M ≈ Mc, and (3) entangled systems M > Mc. The effect of the polymer-particle energetic affinity on the system behavior is also studied. Different theoretical models corresponding to these regimes are proposed. It is shown that the material viscoelastic properties, to a great extend, is controlled by the energetic interactions between polymer chains and nanoparticles. |
