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274932 Density-Functional Theory and Small Angle X-Ray Scattering Experiments for the Structure Factor of Solvent-Free Nanoparticle-Organic Hybrid Materials

Nanoparticle-organic hybrid materials (NOHMs) contain inorganic nanocores surface functionalized by oligomeric chains in the absence of unattached solvent molecules [1]. In this talk, we present a density-functional theory and small angle X-ray scattering (SAXS) experiments to characterize the static structure factor of NOHMs. The structure factor of NOHMs is qualitatively different from that of hard-sphere suspensions. In monodisperse NOHMs, the fact that each particle along with its tethered oligomers occupies the same volume implies that the static structure factor approaches zero at zero wave number. This behavior has been predicted by a density-functional theory [2] and confirmed by molecular dynamics simulations [3]. Our experimental results show that the structure factor in NOHMs with small core particle volume fraction is much smaller than that in hard spheres. However, we observe a nonzero structure factor at small wave number and this might be attributed to unavoidable polydispersity.

Here, we synthesize NOHMs that consist of silica nanoparticles surface-grafted with polyisoprene corona. Some systems are synthesized to be approximately monodisperse while others consist of blended bidisperse mixtures. The density-functional theory considers a bidisperse suspension of oligomer-tethered particles with different core radii and/or oligomer grafting densities. These variations yield variations in the tethered fluid volume per particle and distort the bulk structure at large length scales such that the structure factor exhibits a nonzero value at zero wave number. The theory predicts a much larger effect of bidispersity in grafting density than bidispersity in core radius on the structure factor at zero wave number. The bidispersity of core radius with a fixed grafting density has a relatively small effect on the structure factor at small wave number because the volume of the particle grows as *a*^{3} and the volume of the tethered fluid grows at a somewhat similar rate, as the O(*a*^{2}) surface area, where *a*is the particle radius. Our results also suggest that scattering experiments could be used to evaluate the uniformity of the oligomer grafting achieved in the synthesis procedures.

[1] P. Agarwal, H. Qi, and L. A. Archer, *Nano Lett.* **10**, 111 (2010).

[2] H.-Y. Yu and D. L. Koch, *Langmuir* **26**, 16801 (2010).

[3] A. Chremos, A. Z. Panagiotopoulos, H.-Y. Yu, and D. L. Koch, *J. Chem. Phys.* **135**, 114901 (2011).

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