Superdiffusive thermal transport in polymer-grafted spherical nanoparticle melts*

We use a thermal bridge method to measure the thermal conductivity κ in densely packed polymer-grafted spherical nanoparticle (GNP) membranes as a function of the polymer degree of polymerization, N, at fixed grafting density and NP size (radius 8 nm). While κ expectedly increases with NP loading ϕ<0.05 (long grafts) it unexpectedly decreases at higher ϕ’s (short grafts). This pinning behavior is rationalized by a crossover from a homogeneous mixture of NP in interpenetrated long grafts to percolating “hard spheres” of short grafts on NPs. In the latter dry polymer zone, heat transport occurs through stretched grafts. Representation of κ (N) by a modified Maxwell model leads to κ_PMA ~ N^1/2 corroborating the notion of superdiffusive phonon transport in stretched (one-dimensional) short grafts. This structural transition in GNP’s also explains the enhanced elasticity of the same GNP melts for short grafts as revealed by Brillouin light spectroscopy. Utilizing the sound velocities, the increase of κ with N can be attributed to an enhanced phonon mean free path for short grafts. The manifestation of the GNP topology to diverse physical quantities can help to understand the properties of the dry region necessary for quantitative description of the GNP based materials.