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

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

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

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

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), * 5 R agg distribution

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

S ELF C ONSISTENT M ODEL  Final determination of  Results: decreases slightly  constant !  increases slightly  si (nm)   N agg 8.4%v %v % % I(q) is read Experimental I(q) = f(  )  saxs