Superdiffusive Thermal Transport in Polymer-Grafted Nanoparticle Melts

In contrast to normal diffusion processes, thermal conduction in one-dimensional systems is anomalous. The thermal conductivity is found to vary with the length as κ∼L^{α}(α>0), but there is a long-standing debate on the value α. Here, we present a canonical example of this behavior in polymer-grafted spherical nanoparticle (GNP) melts at fixed grafting density and nanoparticle radius. For long chains (chain length N≥945), the experimental κ(N) of GNP melts decreases with N, i.e., polymer concentration. For N<945, however, κ(N) unexpectedly increases with N with a maximum near N∼945. For these systems, the extensional free energy per polymer chain is predicted to be maximized near N_{max}≈940 for σ≈0.47  chains/nm^{2}, which indicates the dominance of extended conformations at short N and Gaussian-like conformation for longer N. In the former regime, the thermal conductivity of extended polymer chains increases with N and follows κ_{p}∼N_{dry}^{0.46±0.02}, which provides experimental evidence of a novel class of superdiffusive thermal transport with α=1/2.