Figure 1

Storage (solid) and loss (open) modulus of PS in xylene with $M_w=1\times {10}^6\mathrm{g}/\mathrm{mol}$ and $\varphi =0.3$ containing a dilute concentration of Au nanoparticles at $T=-5°\mathrm{C}$ (circles) and $50°\mathrm{C}$ (triangles). The dashed line indicates the plateau modulus.Reuse & Permissions

Figure 2

XPCS intensity autocorrelation function for PS solution with $M_w=1\times {10}^6\mathrm{g}/\mathrm{mol}$ and $\varphi =0.30$ containing a dilute concentration of Au nanoparticles at $T=-20°\mathrm{C}$ and $Q=0.09{\mathrm{nm}}^{-1}$. The line is the result of a fit to a stretched-exponential form, Eq. (1), with exponent $\alpha =0.45\pm 0.05$ characterizing the subdiffusive nanoparticle motion. The inset shows $\alpha$ for different solutions as a function of the number of entanglements per chain, $N=M_w{\varphi }^{-1.3}/M_e(1)$, where $M_e(1)=17000\mathrm{g}/\mathrm{mol}$ is the entanglement molecular weight of PS melt [10].Reuse & Permissions

Figure 3

Mean XPCS relaxation times normalized by solution viscosity as a function of wave vector for solutions with $M_w=1\times {10}^6\mathrm{g}/\mathrm{mol}$ and $\varphi =0.3$ at $T=-20°\mathrm{C}$ (red circles), $\varphi =0.3$ at $T=-5°\mathrm{C}$ (black $\times$s), $\varphi =0.3$ at $T=10°\mathrm{C}$ (green squares), $\varphi =0.3$ at $T=25°\mathrm{C}$ (blue inverted triangles), $\varphi =0.3$ at $T=50°\mathrm{C}$ (red stars), and $\varphi =0.2$ at $T=25°\mathrm{C}$ (black diamonds). The dashed line displays the relation $\tau \sim Q^{-4}$.Reuse & Permissions

Figure 4

Average time $t_L$ for nanoparticles to move the entanglement spacing $L$ as a function of $t_{\mathrm{rep}}/N$, where $t_{\mathrm{rep}}$ is the reptation time obtained from rheology and $N$ is the entanglements per chain. Included are data for all solutions and $T$ for which both $t_L$ and $t_{\mathrm{rep}}$ are determined accurately: $M_w=3\times {10}^5\mathrm{g}/\mathrm{mol}$ and $\varphi =0.3$ (stars), $1\times {10}^6\mathrm{g}/\mathrm{mol}$ and 0.2 (pluses), $1\times {10}^6\mathrm{g}/\mathrm{mol}$ and 0.3 (squares), $3\times {10}^6\mathrm{g}/\mathrm{mol}$ and 0.1 ($\times \mathrm{s}$), $3\times {10}^6\mathrm{g}/\mathrm{mol}$ and 0.2 (diamonds), $3\times {10}^6\mathrm{g}/\mathrm{mol}$ and 0.3 (circles), $3\times {10}^6\mathrm{g}/\mathrm{mol}$ and 0.4 (triangles), and $9\times {10}^6\mathrm{g}/\mathrm{mol}$ and 0.3 (inverted triangles). The line shows the relation $t_L=t_{\mathrm{rep}}/N$. Inset: mean XPCS relaxation time at $25°\mathrm{C}$ and $Q=0.09{\mathrm{nm}}^{-1}$ versus PS molecular weight for solutions with $\varphi =0.3$ (squares) and 0.2 (circles) along with the results of power-law fits $\tau \sim M_W^{2.4\pm 0.1}$ (solid lines). Also in the inset are the reptation times ($\times$s) for $\varphi =0.3$ at $50°\mathrm{C}$ along with the result of a power-law fit, $t_{\mathrm{rep}}\sim M_w^{3.2\pm 0.2}$ (dashed line).Reuse & Permissions