Figure 2: Effect of NPs on dynamic viscosity and glass transition temperature of polymers.

(a) Plot of complex viscosity (η*) versus shifted frequency (a_t ω) for neat PMMA and for PNCs SiO₂–PEG_2k/PMMA_55k, SiO₂–PEG_2k/PMMA_165k and SiO₂–PEG_2k/PMMA_280k with φ =2% at T =190 °C. Similar behaviour was observed in steady shear measurements (Supplementary Fig. 4). Inset shows the relative viscosity (η_r=η_PNC/η_neat) for SiO₂–PEG_2k/PMMA_55k (triangles) from steady shear measurements at ∼0.02 s⁻¹ at T=180 °C, for SiO₂–PEG_2k/PMMA_165k (circles) at ∼0.02 s⁻¹ at T=190 °C and for SiO₂–PEG_2k/PMMA_280k (diamonds) at ∼0.001 s⁻¹ at T=170 °C. The dashed line is the predicted relative viscosity from the Einstein–Batchelor equation^9,10. Error bars smaller than symbol size are not shown. (b,c) T_g values obtained using DSC for SiO₂–PEG_2k/PMMA_55k and SiO₂–PEG_2k/PMMA_280k, respectively. Closed symbols correspond to PNCs and open symbols correspond to corresponding particle-free neat blends. Dashed lines represent the data computed using the mixing rule predicted by the Fox equation . DSC measurements are performed at different scan rates (2, 5, 10, 15 and 20 K min⁻¹) and obtained T_g values showed no dependence on scan rates (Supplementary Figs 5 and 6). Results for SiO₂–PEG_2k/PMMA_165k are shown in Supplementary Fig. 7.