Simplified silica (Zeosil 1165 MP) -SBR (140k carrying silanol end-groups) nanocomposites have been formulated by mixing of a reduced number of ingredients with respect to industrial applications. The thermo-mechanical history of the samples during the mixing process was monitored and adjusted to identical final temperatures. The filler structure on large scales up to microns was studied by transmission electron microscopy (TEM) and very small angle Xray scattering (SAXS). A complete quantitative model extending from the primary silica nanoparticle (of radius 10 nm), to nanoparticle aggregates, up to micron-sized branches with typical lateral dimension of 150 nm is proposed. Image analysis of the TEM-pictures yields the fraction of zones of pure polymer, which extend between the branches of a large-scale filler network. This network is compatible with a fractal of average dimension 2.4 as measured by scattering. On smaller length scales, inside the branches, small silica aggregates are present. Their average radius has been deduced from a Kratky analysis, and it ranges between 35 and 40 nm for all silica fractions investigated here ( si = 8 -21%v).A central piece of our analysis is the description of the inter-aggregate interaction by a simulated structure factor for polydisperse spheres representing aggregates. A polydispersity

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_Although the (n + l)p orbital is unoccupied in transition-metal ground-state configurations which are all ndX(n + I)sY, these (n + l)p functions playa crucial role in the structure of transition metal complexes. As we show here, the usual solution, adding one or more diffuse functions, can be insufficient to create an orbital of the correct energy. The major problem appears to be due to the incorrect placement of the Cn + 1) P orbital's node. Even splitting the most diffuse component of the np orbital and adding a second diffuse function does not completely solve this problem. Although one can usually solve this deficiency by further uncontracting of the np function, here we offer a set of properly optimized (n + 1) P functions that offer a more compact and satisfactory solution to the proper placements of the node. We show an example of the common deficiencies seen in typical basis sets, including standard basis sets in GAUSSIAN94, and show that the new optimized (n + I)p function performs well compared to a fully uncontracted basis set.

An un-cross-linked SBR-system filled with precipitated silica nanoparticles of radius ≈10 nm by mixing is studied as a function of the fraction of graftable matrix chains (140 kg mol–1) varying from 0% to 100%, for a low (ΦSi = 8.5 vol %) and high (16.7 vol %) silica volume fraction. The linear rheology in shear shows a strong impact of the grafting on the terminal flow regime, and a shift to longer relaxation times with increasing grafting. Simultaneously, the plateau modulus stays approximately constant for the low ΦSi, suggesting a link to the silica content. The microstructure of the silica is characterized by using a combination of transmission electron microscopy and small-angle X-ray scattering data. We apply a quantitative model of interacting aggregates, and determine the average aggregation number (decreasing from 160 to 30 with grafting), aggregate size (50 to 30 nm), and compacity (55% to 35%). While the linear rheology seems to be dominated by the matrix composition, both the mixing rheology and the structure display a saturation with increasing grafting fraction. A closer analysis of this effect indicates that a critical amount of grafting is needed to trigger structural evolution. To summarize, a quantitative study of complex nanocomposites with several features of industrial systems demonstrates that the grafting density can be used as a fine-tuning parameter of rheology and microstructure.

We report a complete analysis of model silica/styrene− butadiene rubber (SBR) nanocomposites including a direct and quantitative correlation between the filler structure and the mechanical reinforcement. We compared two different ways of sample processing: a solvent casting route with well-defined colloidal silica and the manufacturing process of internal mixing with industrial silica powder. The multiscale filler dispersion was characterized with a combination of SAXS/TEM in both reciprocal and direct space. The mechanical properties were determined with oscillatory shear measurements. We evaluated the influence of two polymer-filler interfacial additives on the filler dispersion: a coating agent and a coupling agent for different particle concentrations. Using simple analytical functions, we succeed in modeling the filler dispersion. We obtained surprisingly the same general trend whatever the sample processing, solvent casting, or internal mixing. The primary particles form fractal primary aggregates inside the matrix as a result of a diffusion-limited aggregation process driven by the interfacial additive. The coupling agent, which can form covalent bonds with the matrix chains, leads to smaller and denser primary aggregates while the coating one gives rise to larger and more ramified objects. This can be explained by the restriction of nanoparticle diffusion due to covalent bonds. The primary aggregates arrange into a secondary large scale structure, agglomerates, or by a branched network. The spatial correlations between the primary aggregates follow a Percus−Yevick function allowing us to distinguish between more or less interpenetrated networks in a situation of percolation. The viscoelastic behavior of the composites has been analyzed quantitatively with a percolation model. Below the percolation threshold, the reinforcement is mostly driven by the cluster compactness. We highlight a mechanical percolation whose threshold is dependent on the interfacial additive, but not on the material fabrication process, arising at lower filler volume fraction than the structural percolation. Above the percolation threshold, the network modulus varies as the power three of filler network density which is determined from geometrical assumptions. The filler network density, traducing the degree of interpenetration of the aggregates inside the network, is driven by both the interfacial additive and the samples preparation: the coupling agent as well as the internal mixing process gives rise to a denser network with a resulting improved modulus.