1. I MPACT OF THE FILLER FRACTION IN NC S G. Baeza et al. Macromolecules 2013 Multi-scale filler structure in simplified industrial nanocomposite systems silica/SBR studied by SAXS and TEM Structural Analysis 1

2. M ULTISCALE S TRUCTURE beadsaggregates network q -2.4 Artist view Tridimensionnal network built up from aggregates made of nanoparticles R bead  10 nm R agg  40 nm  si  (Quantitative Model) -Densification of the silica network -Aggregates remain similar d branch  120 nm

3. analysis G LOBAL V IEW : 3- LEVEL O RGANIZATION High-q : Bead form factor q si  R si (R 0 = 8.55 nm  = 27%) Medium-q : q agg  R agg (35 – 40 nm) Interactions Between Aggregates Low-q : q branch  Network branches (lateral dimension  150 nm), compatible with fractal aggregates (d  2.4). The network becomes denser and denser with  si  Artist view: network built up from Aggregates made of nanoparticles beadaggregatenetwork 3

4. Q UANTITATIVE ANALYSIS : A GGREGATE R ADIUS Subtraction of the fractal law Morphology of an aggregate R agg  si  q agg Kratky Plots allow to extract R agg Distribution Hypothesis q agg 4 d  2.4

5. Q UANTITATIVE MODEL Scattering law linking structure and form (polydisperse case) 1) D ETERMINATION OF N agg distribution Working hypothesis Calculation *Oberdisse, J.; Deme, B. Macromolecules 2002, 35 (11), 4397-4405 * 5 R agg distribution

6. Semi-Empiric law from simulation Hard-Sphere Potential (PY like)  agg  Q UANTITATIVE MODEL Scattering law linking structure and form (polydisperse case) 2) D ETERMINATION OF S inter (q) app  Monte Carlo Simulation of polydisperse aggregates  Estimation of  agg : TEM  fract Same Working hypothesis 6 S app (q) depends on local  si in the branches =  agg inter

7. S ELF C ONSISTENT M ODEL  Final determination of  Results: decreases slightly  constant !  increases slightly  si (nm)   N agg 8.4%v40.20.315153 12.7%v35.90.334043 16.8%36.10.364447 21.1%35.20.384447 7 I(q) is read Experimental I(q) = f(  )  saxs