Universal Viscosity Behavior of Polymer Nanocomposites

Nonequilibrium molecular dynamics simulations are used to show that the shear viscosity of a polymer melt can be significantly reduced when filled with small energetically neutral nanoparticles, apparently independent of the polymer’s chain length. Analogous to solvent molecules, small nanoparticles act akin to plasticizers and reduce the viscosity of a polymer melt. This effect, which persists for particles whose sizes are as large as the chain size or the entanglement mesh size, whichever is smaller, can be overcome by making the chain-nanoparticle interactions significantly attractive. Our simulations allow us to systematically organize the viscosity data of filled polymer melts, and thus provide a strong basis from which to predict the flow behavior of these commercially important class of materials.

Figure 1

Reduced shear viscosity ${\eta }^{*}=\frac{\eta {\sigma }^3}{\epsilon \tau }$ versus reduced strain rate ${\dot{\gamma }}^{*}=\dot{\gamma }\tau$. Neat and NP-filled melts are represented by open and closed symbols, respectively, at a fixed ${\varphi }_{\mathrm{NP}}=0.11$ for $N=40$ (▪), $N=100$ (▾), $N=200$ (◆), and $N=400$ (●). (a) ${\sigma }_{\mathrm{NP}}=1\sigma$, (b) ${\sigma }_{\mathrm{NP}}=10\sigma$. Insets show the ratio of the filled to neat melt viscosity as a function of ${\dot{\gamma }}^{*}$.

Figure 2

Effect of NP size and type of interaction between the NP and polymer on shear viscosity for (a) $N=40$, ${\dot{\gamma }}^{*}\to 0$, (b) $N=400$, ${\dot{\gamma }}^{*}={10}^{-5}$ for ${\varphi }_{\mathrm{NP}}=0.11$. Dependence of viscosity on loading of neutral NP for (c) $N=40$ with (${\sigma }_{\mathrm{NP}}=10\sigma$ and $1\sigma$) as ${\dot{\gamma }}^{*}\to 0$, and (d) $N=100$ with (${\sigma }_{\mathrm{NP}}=8$ and $10\sigma$) as ${\dot{\gamma }}^{*}\to 0$ and $N=400$ with (${\sigma }_{\mathrm{NP}}=10\sigma$) at ${\dot{\gamma }}^{*}={10}^{-5}$. In all the plots the closed symbols correspond to rough NP, while the open symbols correspond to smooth NP. In (c) and (d) we show the Einstein and Batchelor predictions.

Figure 3

(a) Effect of ${\sigma }_{\mathrm{NP}}$ on $N_e$ for $N=400$ melts filled with smooth NPs with $A_{np}=100\epsilon$ and ${\varphi }_{\mathrm{NP}}=0.11$. (b) Net packing fraction (NPF) as a function of smooth NP size for ${\varphi }_{\mathrm{NP}}=0.11$. The lines represent the pure melts. (c) Effect of NP-polymer bead interaction strength on NPF for $N=400$ melts and rough NPs; ${\varphi }_{\mathrm{NP}}=0.11$. Line represents the pure melt. (d) Dependence of $\eta$ on NPF for the $N=40$ melt with neutral ${\sigma }_{\mathrm{NP}}=1\sigma$ NPs. Line is the pure melt.

Figure 4

Polymer radius of gyration versus NP diameter. The experimental data correspond to (▪) $\eta /{\eta }_p<1$, (◆) $\eta /{\eta }_p>1$, (●) $\eta /{\eta }_p\approx 1$ at low NP loading, and (▴) is where $\eta$ shows an initial increase of viscosity with NP loading followed by a decrease. (a) Experimental data for athermal systems is from 4, 5. Systems above the solid orange line should be miscible. The black “viscosity” line is extrapolated from our simulations. (b) Corresponding plot for “thermal” NP-polymer systems. Only the viscosity line is shown. Data are from 6, 7, 8, 9, 10, 11, 12.