Chain Conformations and Bound-Layer Correlations in Polymer Nanocomposites

Small angle neutron scattering studies on polystyrene loaded with spherical silica nanoparticles under contrast-matched conditions unequivocally show that chain conformations follow unperturbed Gaussian statistics independent of chain molecular weight and filler composition. Liquid state theory calculations are consistent with this conclusion and also predict filler-induced modification of interchain polymer correlations which have a distinctive scattering signature that is in nearly quantitative agreement with our observations.

Figure 1

(a) TEM micrographs of nanocomposites formed from PS of molecular weight $250\mathrm{kg}/\mathrm{mol}$ indicating vol % loading of silica in each sample. (b) Ratio of the radii of gyration of polymers in the presence of particles to the corresponding pure blend for PS $90\mathrm{kg}/\mathrm{mol}$ (green squares), PS $250\mathrm{kg}/\mathrm{mol}$ (blue circles), and PS $620\mathrm{kg}/\mathrm{mol}$ (red triangles) as functions of silica volume fraction. Inset: Plots of “raw” SANS intensities $I_{\mathrm{expt}}(q)$ in absolute units as a function of $q$ for the PS $250\mathrm{kg}/\mathrm{mol}$ nanocomposites. The black squares, purple circles, green triangles, blue inverse triangles, dark cyan “left” triangles, and red “right” triangles correspond to a particle vol % of 0, 2.9, 6.0, 9.1, 15.9, and 27.4, respectively. The yellow line show fits to the 27.4 vol % data as discussed in the text.

Figure 2

(a) Experimental Kratky plots (symbols same as in the inset in Fig. 1) of the PS $250\mathrm{kg}/\mathrm{mol}$ systems using intensity values defined as $I(q)=I_{\mathrm{expt}}(q)/{\varphi }_p-I_{\mathrm{incoherent}}$. (b) Kratky plots from PRISM theory with $D/d=26.4$, ${\epsilon }_{\mathrm{pc}}=1$, and $\alpha =0.5$. The black, green, blue, dark cyan, and red lines correspond to filler vol % of 0, 1, 5, 10, and 20, respectively. (c) Plots of peak intensity from Kratky plots as a function of filler volume fraction. Lines are guides to the eye. Theoretical results used $D/d=26.4$ (upper red line) and $D/d=14$ (lower red line), respectively. For $D/d=26.4$, along with ${\epsilon }_{\mathrm{pc}}=1$ and $\alpha =0.5$ (black squares), four other combinations are represented—${\epsilon }_{\mathrm{pc}}=1.5$ and $\alpha =0.5$ (green triangles), ${\epsilon }_{\mathrm{pc}}=2.5$ and $\alpha =0.5$ (blue squares), ${\epsilon }_{\mathrm{pc}}=1$ and $\alpha =0.75$ (dark cyan crosses), and ${\epsilon }_{\mathrm{pc}}=1.5$ and $\alpha =1$ (purple plusses), respectively. For $D/d=14$, ${\epsilon }_{\mathrm{pc}}=1$ and $\alpha =0.5$ (open black squares). The blue circles and lines are the results from the experiments. (d) Peak locations and peak widths corresponding to experiments (symbols) and theory (lines), respectively.