Polymer diffusion in a polymer nanocomposite: effect of nanoparticle size and polydispersity

Abstract

The tracer diffusion of deuterated polystyrene (dPS) is measured in a polystyrene nanocomposite containing silica nanoparticles (NPs), with number average diameters d_n of 28.8 nm and 12.8 nm, using elastic recoil detection. The volume fractions of the large and small NPs (ϕ_NP) range from 0 to 0.5, and 0 to 0.1, respectively. At the same volume fraction of NPs, the tracer diffusion of dPS is reduced as NP size decreases because the interparticle distance between NPs (ID) decreases. The reduced diffusion coefficient, defined as the tracer diffusion coefficient in the nanocomposite relative to pure PS (D/D₀), plotted against the confinement parameter, namely ID(d_n) relative to tracer size, ID(d_n)/2R_g, nearly collapses onto a master curve, although D/D₀ is slightly greater for the more polydisperse, smaller NPs. Using a log normal distribution of NP size from SAXS, the average ID of the smaller NPs is shown to increase by 25% at ϕ_NP = 0.1 as polydispersity (σ) increases from 1 to 1.39. By accounting for polydispersity, the confinement parameter better represents the effect of NP spacing on polymer diffusion. These experiments demonstrate that polymer tracer diffusion in polymer nanocomposites is empirically captured by the confinement parameter and that an increase in the average ID due to NP polydispersity has a secondary effect on model NP systems with a narrow distribution of sizes. However, for commercial systems, where polydispersity can be quite large, the effect of size distribution can significantly increase ID which in turn will influence polymer dynamics.