1

IMPACT OF THE FILLER FRACTION IN NCS

G. Baeza et al. Macromolecules 2013

Multi-scale filler structure in simplified industrial nanocomposite systems silica/SBR studied by SAXS and TEM

Structural Analysis

MULTISCALE STRUCTURE

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10-3 10-2 10-1

q (Å-1)

I(q)

/

si

(cm

-1) q

branch

qsi

qagg

8.4%v

beadsaggregatesnetwork

q-2.4

Artist viewTridimensionnal network built up from aggregates made of nanoparticles

Rbead10 nm

Ragg40 nm

si (Quantitative Model)-Densification of the silica network-Aggregates remain similar

dbranch120 nm

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10-3 10-2 10-1

21.1%v16.8%v12.1%v

q (Å-1)

I(q)

/

si

(cm

-1)

si

3

analysis

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10-3 10-2 10-1

21.1%v16.8%v12.1%v8.4%v

q (Å-1)

I(q)

/

si

(cm

-1)

si

qbranch

qsi

qagg

GLOBAL VIEW: 3-LEVEL ORGANIZATION

High-q : Bead form factorqsi Rsi (R0= 8.55 nm = 27%)

Medium-q : qagg Ragg (35 – 40 nm) Interactions Between Aggregates

Low-q : qbranch Network branches (lateral dimension 150 nm), compatible with fractal aggregates (d2.4).

The network becomes denser and denser with si

Artist view:network built up from Aggregates made of nanoparticles

beadaggregatenetwork

QUANTITATIVE ANALYSIS: AGGREGATE RADIUS

Subtraction of the fractal law

Morphology of an aggregate

Ragg

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2 10-3 4 10-3 10-2 2 10-2

q (Å-1)

I(q)

/

si

(cm

-1)

si

qagg

Kratky Plots allow to extract <Ragg>

Ragg Distribution Hypothesis

0.5

1

2

3

4

2 10-3 4 10-3 10-2 5 10-2

0.1

1

10-3 10-2 10-1

21.1%v16.8%v12.7%v8.4%v

q (Å-1)

q2 I(q

) /

si

(Å-2

cm

-1)

qagg

4

agg

aggin si

V

Vκ

q

πR

aggagg

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10-3 10-2 10-1

q (Å-1)

I(q)

/

si

(cm

-1)

d 2.4

5

QUANTITATIVE MODEL

0

0.02

0.04

0 100 200

G[R

agg(N

agg)]

Nagg

<Nagg

>

<Nagg

2>1/2

Nagg

max

si

3aggagg V

κR π

3

4N

5

R*qexp

N

N*qP

2G

2

agg

2agg

agg

qP qS VΔρΦ

qIagg

appintersi

2

si

Scattering law linking structure and form (polydisperse case)

1) DETERMINATION OF <Pagg>

Nagg distribution

Working hypothesis

Calculation 6

agg

8

agg2G

R

RR

*Oberdisse, J.; Deme, B. Macromolecules 2002, 35 (11), 4397-4405

*

Ragg distribution

6

2agg

4agg

PYαΦ 21

αΦ-1 = 0)(qS

Semi-Empiric law from simulation

Hard-Sphere Potential (PY like)

qP qS VΔρΦ

qIagg

appintersi

2

si

agg

QUANTITATIVE MODELScattering law linking structure and form (polydisperse case)

2) DETERMINATION OF Sinter(q)app

Monte Carlo Simulation of polydisperse aggregates

Estimation of agg : TEM

κΦ

ΦΦ

fract

siagg

fract Same Working hypothesis

Sapp (q) depends on local si in the branches = agg inter

7

SELF CONSISTENT MODEL

q,P q,S VΔρΦ

q,Iagg

appintersi

2

si

Final determination of

Results:<Ragg> decreases slightly

<Nagg> constant !

increases slightly

si <Ragg> (nm) <Nagg> Nagg

8.4%v 40.2 0.31 51 53

12.7%v 35.9 0.33 40 43

16.8% 36.1 0.36 44 47

21.1% 35.2 0.38 44 47

I(q) is readExperimental

I(q) = f()saxs

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2 10-3 4 10-3 10-2 2 10-2

q (Å-1)

I(q)

/

si

(cm

-1)