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Filler-ller interactions and viscoelastic behavior of
polymer nanocomposites
Emmanuelle Chabert, Michel Bornert, Elodie Bourgeat-Lami, Jean-Yves
Cavaillé, Remy Dendievel, Catherine Gauthier, Jean-Luc Putaux, André Zaoui
To cite this version:
Emmanuelle Chabert, Michel Bornert, Elodie Bourgeat-Lami, Jean-Yves Cavaillé, Remy Dendievel,
et al.. Filler-ller interactions and viscoelastic behavior of polymer nanocomposites. Materials Sci-
ence and Engineering: A, Elsevier, 2004, 381 (1-2), pp.320-330. �10.1016/j.msea.2004.04.064�. �hal-
00111433�
Filler–filler interactions and viscoelastic behavior
of polymer nanocomposites
E. Chabert
a,b,∗
, M. Bornert
b
, E. Bourgeat-Lami
c
, J.-Y. Cavaillé
a
,
R. Dendievel
d
, C. Gauthier
a
, J.L. Putaux
e
, A. Zaoui
b
a
GEMPPM, UMR 5510 INSA/CNRS, 69621 Villeurbanne cedex, France
b
LMS, UMR 7649 École Polytechnique/CNRS, 91128 Palaiseau cedex, France
c
LCPP, UMR 140 CPE/CNRS, 69616 Villeurbanne cedex, France
d
GPM2, UMR 5010 INPG/CNRS, BP 46, 38042 St Martin d’Hères cedex, France
e
CERMAV, UPR 5301 CNRS, BP 53, 38041 Grenoble cedex 9, France
This work presents the main results obtained within a project on
mechanical properties of polymer
based
nanocomposites. The
specific
point
was how to analyze and model the filler–filler interactions in the description of the viscoelastic behavior of these materials. This paper
aims at presenting the general strategy used by the different partners to address this question, together with original experimental results and
micro-mechanical modeling. Different nanocomposite materials were fabricated using the latex route, leading to random dispersions of rigid
submicronic particles (PS = polystyrene, silica) in a flexible polybutylacrylate matrix at various volume fractions. In addition, encapsulated
silica particles in a styrene–acrylate copolymer were produced, leading, after film formation, to a limited number of contacts between silica
fillers. The processing route of these encapsulated particles was optimized and the resulting morphology was analyzed by TEM experiments.
In the case of random mixtures, a strong effect of reinforcement appears in the rubbery field of the soft phase when the filler content is above a
critical fraction (percolation threshold). The reinforcement in the rubbery plateau can be still exacerbated in the case of the PS particles if the
material undergoes a heat treatment above the main relaxation of the PS phase. These experimental results illustrate the difference between
geometrical percolation (when particles are just in contact) and mechanical percolation (with strong interactions between the fillers). The
comparison of the results for PS and silica fillers shows once more that the strength of the interactions plays an important role. To account for
the whole set of experimental data, two ways of modeling were explored: (i) homogenization methods based on generalized self-consistent
schemes and (ii) a discrete model of spheres assembly which explicitly describes the ability of the contacts to transmit efforts.
Keywords: Nanocomposites; Mechanical properties; Percolation; Discrete modeling approach; Self-consistent modeling; Cryo TEM
1. Introduction
Among the several reasons to incorporate fillers into poly-
mers (cost reduction, improvement of some physical proper-
ties such as flame retardancy or barrier properties) mechan-
ical reinforcement is expected [1]. Traditional fillers display
average characteristic sizes in the range of several microns.
However, due to the development of nanosized fillers, the
specific influence of the nanometric size in the reinforce-
ment mechanisms has to be addressed. Composite materials
∗
Corresponding author. Tel: +33 169333318; fax:+33 169333026.
E-mail address: chabert@lms.polytechnique.fr (E. Chabert).
based on nano-sized fillers, the so-called nanocomposites,
are presently studied especially because they may have un-
usual combinations of properties [2–6]. These unusual prop-
erties may be a consequence of the extremely large specific
interfacial area (hundreds of m
2
/g). They may be also related
to the very short distances between the reinforcing fillers
(about 10
−8
m), that may become close to the characteristic
size of the macromolecular coils. In addition, some years
ago, we showed that drastic reinforcing effects may be ob-
served at very low volume fractions for fillers with very large
aspect ratio, when the percolation of the fillers occurs [7].
However, the processing of composite materials that only
differ by the size of the fillers (keeping constant the disper-
sion state and surface properties) is not a simple task. In or-
1
der to by-pass this difficulty, experimental data may be com-
pared to theoretical predictions that are developed to account
for the mechanical behavior of heterogeneous materials. Pa-
rameters which play a role for the mechanical properties of a
filled polymer (elastic modulus for instance) are the follow-
ing: (i) the (visco)elastic properties of its constitutive phases,
(ii) the volume fraction of filler, (iii) the morphology (i.e.,
shape, aspect ratio, and distribution of the filler within the
polymeric matrix) and (iv) the interactions between fillers
and between filler and matrix. Various models have been
proposed in the literature to understand the complex inter-
play between these parameters and to display a prediction
of the elastic moduli of polymer composites. Moreover, it
is generally accepted that these elastic calculations can be
extended to the description of the viscoelasticity of filled
polymers through the correspondence principle of Hashin
[8]. In fact, the classical models, at least in their former de-
velopments, ignore direct interactions between fillers: fillers
are considered as a homogeneous phase which interacts with
the matrix or, at most, with the effective medium, and thus
these models may be unefficient when the interactions be-
tween the fillers themselves rule the mechanical response
of the composite. Moreover, they cannot simply account for
the percolation of rigid fillers within a soft matrix.
The work presented in the following has been performed
in the framework of a collaboration between several labo-
ratories. The general strategy was first to elaborate model
nanocomposites with controlled morphologies, to character-
ize their mechanical behavior in the linear domain and to
develop mechanical models adapted to describe their behav-
iors. The first part of the paper presents the fabrication route
to process polymers filled with spherical particles with di-
ameters in the nanometer range. In order to understand re-
inforcement mechanisms depending on connectivity or on
the aggregation state, we have focused on spherical fillers
to avoid orientation effects. Materials were produced with
different dispersion states: nanocomposites obtained from
a mixture of hard/soft latex particles and nanocomposites
made of encapsulated hard particles surrounded by a soft
polymer shell. In the first part (Section 2), we provide de-
tails on sample preparation and characterization of the ob-
tained materials. In a second part (Section 3), the viscoelastic
behavior of the nanocomposites, characterized by dynamic
mechanical measurements, is described. These experimen-
tal data illustrate the influence of filler–filler interactions on
the linear mechanical behavior of these materials. At last
(Section 4), different routes to model the (visco)elastic re-
sponses are discussed.
2. Processing of nanocomposite systems
A convenient way to process nanocomposite materials
is based on the mixture of various aqueous suspensions
(colloids) [9–12]. Emulsion polymerization is well known
to provide in a simple way polymer colloidal suspensions
with typical particle size in the range of ten to a few hun-
dred nanometers. When both colloids are film forming, a
co-continuous material can be expected, provided that the
fraction of each component is large enough. Blending of
hard and soft particles would lead, after film formation, to a
random distribution of hard particles in the continuous soft
matrix, with a certain probability to form aggregates de-
pending on the volume fraction of filler. On the contrary, if
the particles are structured, with a stiff core and a soft shell,
then the material should consist, after shell coalescence, of a
soft matrix with regularly dispersed stiff spherical domains,
without contact between each other.
2.1. Nanocomposites obtained from PS–PBA and
silica–PBA latex blends
Different composites, based on the mixture of a film form-
ing latex (matrix) with aqueous suspension of fillers in re-
quired proportions, were prepared. Choice was made of a
poly(butyl acrylate) matrix (PBA, glass transition tempera-
ture T
g
around −47
◦
C) filled with spherical particles of ei-
ther polystyrene (PS, T
g
around 97
◦
C) or silica. Homopoly-
mer latexes of PS or PBA were obtained through batch emul-
sion polymerization process. A typical recipe was as fol-
lows: deionized water = 900 g, monomer = 90 g, NaHCO
3
= 0.75g,initiator = 0.75 g (K
2
S
2
O
8
for PS and (NH
4
)
2
S
2
O
8
for PBA), emulsifier = 2.91 phm of NC12(3-(dimethyl do-
decylammonium)propane-1-sulfonate) for PS, and 0.33 phm
of sodium dodecyl sulfate for PBA. The temperature of
polymerization = 70
◦
C. Latexes were cleaned using ion
exchange resins removing most of the surfactant, in order
to avoid a possible effect on film forming process, film
microstructure or film properties. They were cleaned in a
non-diluted state (around 10 wt.% solid content) until con-
ductivity remains constant. Particle sizes were around 110
nm for PS and 135 nm for the PBA latex (as measured by
dynamic light scattering, Malvern Autosizer Lo-C instru-
ment). Silica nanoparticles have been synthesized according
to the Stöber process [13]. In a typical procedure, absolute
ethanol (1555 g, Acros Organics), de-ionized water (24.9 g)
and ammonia (12.75 M, 96.6 g, Laurylab) were filled into a
5L polypropylene flask. The mixture was stirred at 160 rpm
to be homogenized and tetraethoxysilane (91.65 g, Fluka)
was introduced at once. Reaction occurred at room temper-
ature under continuous stirring for 2 weeks. The alcoholic
silica suspension was dialyzed against water before use. Par-
ticle size was determined to be 125 nm by dynamic light
scattering (DLS). The solid content of the resulting suspen-
sion was determined gravimetrically.
After blending different amounts of filler (PS or silica)
(from 15 to 45vol.%) and PBA latexes, films were made
by evaporation under controlled atmosphere during a de-
lay long enough to achieve a complete maturation, i.e., 2
weeks at 35
◦
C and 90% relative humidity. Although PBA
matrix is transparent after maturation, highly filled com-
posite films were rather opaque, suggesting aggregation of
2
(CH
3
O)
3
Si
O
O
Fig. 1. Chemical formula of the 3-trimethoxysilyl propyl methacrylate
silane coupling agent used in the silica encapsulation reaction.
the hard phase [14], as it has been previously observed on
similar PS/PBA systems by small angle neutron scattering
[15]. Films were tested after the film formation process (and
called “as-dried films”) or after a thermal treatment at 140
◦
C
for 4 h.
2.2. Nanocomposites obtained from encapsulated silica in
P(S–BA) copolymer
The second nanocomposite system was based on encap-
sulated silica in a P(S–BA) copolymer. The choice of this
copolymer (with glass transition close to 0
◦
C was moti-
vated by the possibility to test the mechanical behavior. As
a matter of fact, we tried first with films issued from latex of
encapsulated silica in PBA, but these films were very diffi-
cult to handle. One reason could be the formation of a high
degree of crosslinking in these systems due to both chain
transfer to polymer and bimolecular termination by recom-
bination [16]. Such a mechanism is expected to significantly
affect film formation and mechanical properties.
Since silica is initially hydrophilic, its surface needs to be
modified to make possible anchoring and polymerization of
the hydrophobic butyl acrylate and styrene (co)monomers
through an emulsion polymerization process. This was
achieved by the chemical grafting of an alkoxysilane bear-
ing a polymerizable methacryloyl end group (see Fig. 1).
The grafting was performed as described previously by
direct addition of 3-trimethoxysilyl propyl methacrylate
(MPS, Acros Organics) to an aqueous silica suspension
[17]. The silica sol (30N50), with a mean hydrodynamic
diameter of 68nm as determined by DLS and 32 wt.% solid
content, was kindly supplied by Clariant S.A. (France) and
diluted in de-ionized water before use. A fixed amount
of MPS (corresponding to 16 mol/m
2
silica surface) was
introduced in the diluted silica sol (10g L
−1
) containing
0.25g L
−1
sodium docedyl sulfate surfactant (SDS, Acros
Organics). The reaction was conducted at room tempera-
ture for 1 week. The suspension was concentrated using an
evaporating rotator before use.
The grafted silica particles were further engaged in a
free radical polymerization process to make the polymer
grow from their surface. The emulsion polymerization re-
action was performed in batch at 70
◦
C in a 250 mL double
wall glass reactor fitted with a condenser. The reactor was
charged with 100g of the aqueous suspension containing the
grafted silica beads (37g L
−1
) and the surfactant (a mixture
of SDS : 1.25g L
−1
and poly(oxyethylene) isooctyl cyclo-
hexyl ether : TX-405, 0.75g L
−1
, Aldrich). After degassing,
the monomers from Aldrich (styrene : 36 g L
−1
and butyl
Fig. 2. Cryo-TEM image of grafted silica particles (dark) encapsulated
with P(S-BA) through emulsion polymerization.
acrylate : 63 g L
−1
) and the initiator (potassium persulfate
: KPS, 0.5 g L
−1
, Acros Organics) were successively intro-
duced at 70
◦
C under stirring to start polymerization. The
monomer to polymer conversion was of 86% as determined
gravimetrically.
The morphology of the composite particles was char-
acterized using cryo-transmission electron microscopy
(cryo-TEM). Using the method described elsewhere [18,19],
thin liquid films of the particle suspension were formed on
carbon membranes and rapidly frozen into liquid ethane.
The particles were then observed at low temperature em-
bedded in a preserving film of vitreous ice, using a Philips
CM200 ‘Cryo’ microscope operated at an accelerating volt-
age of 80 kV. The TEM image in Fig. 2 clearly attests for a
successful encapsulation of the nanometric silica particles
by the P(S–BA) copolymer. Although the silica beads ap-
pear to be uncentered in the polymer shell, they are expected
to be homogeneously distributed in the coalesced latex film.
However, a limited number of silica/silica contacts may be
present.
For comparison purpose, blends of silica and P(S–BA)
copolymer latexes were prepared by mixing together the sil-
ica sol and a latex of P(S–BA). This copolymer latex was
obtained from the previous latex of encapsulated silica in
P(S–BA), after having eliminated the grafted silica by cen-
trifugation. Silica/P(S–BA) nanocomposites were obtained
after maturation of latex blends or encapsulated latex during
2 weeks at 35
◦
C and 90% relative humidity.
3. Viscoelastic behavior
The dynamic shear moduli (G
, G
) of various nanocom-
posites were measured as a function of temperature with
a homemade inverted pendulum working in helium atmo-
sphere [20]. Experiments were performed in the temperature
3
0,00001
0,0001
0,001
0,01
0,1
1
-100 -50 0 50 100 150
T (˚C)
G' (GPa)
PBA
15% PS
20% PS
25% PS
35% PS
45% PS
PS
0,01
0,1
1
10
-100 -50 0 50 100 150
T (˚C)
tan d
PBA
15% PS
20% PS
25% PS
35% PS
45% PS
PS
Fig. 3. Real shear modulus and loss factor vs. temperature for “as dried” PS–PBA nanocomposites with different filler amounts (1 Hz).
range [−170 to 150
◦
C] with a heating rate of 1
◦
C/min and
at a fixed frequency of 0.1 or 1 Hz.
3.1. PS–PBA nanocomposites
The dynamic mechanical responses of PBA and PS/PBA
“as-dried systems” (i.e., just after PBA maturation) are
shown in Fig. 3. The properties of a film of pure PS (ob-
tained by freeze-drying/hot pressing) are also reported. A
significant reinforcement of the shear modulus is observed
in between PS and PBA main (or α) relaxations (−32
◦
C
≤ T ≤ 118
◦
C). One can notice that this reinforcement is
not linear: the faster increase is observed around 20 vol.%,
i.e., near the geometric percolation threshold. In the same
temperature range, the height and the width of the tan δ
peak (associated with the PBA glass transition) decrease,
with a slight shift of the relaxation to lower temperature.
Nevertheless, differential scanning calorimetry measure-
0,01
0,1
1
10
-100 0 100
T (˚C)
after annealing
before annealing
after annealing
before annealing
0,0001
0,001
0,01
0,1
1
-100 0 100
T (˚C)
G' (GPa)
tan d
Fig. 4. Real shear modulus and loss factor for PBA samples filled with 35% PS, before and after thermal treatment (1 Hz).
ments performed on these systems showed that the PBA
glass transition temperature remains constant and equal to
−47
◦
C (for a heating rate of 10
◦
C/min) whatever the filler
content. Hence, the shift of T
α
to lower temperature as the
filler content increases is probably due to a mechanical
coupling effect. In addition to a higher level of the relaxed
modulus, the temperature dependence of composite mod-
uli differs from that observed for the pure matrix and for
the filler phase. For the composite materials, the relaxed
modulus first decreases until 70
◦
C and then increases be-
fore falling again above the PS main relaxation. These two
counteracting phenomena lead to the presence of a bump
in the the tan δ curves, located between the peaks associ-
ated with the PBA and PS main relaxations. As discussed
in [21], these two phenomena are a consequence of the
evolution of filler–filler interactions with temperature: in
the low temperature range (T ≤ 70
◦
C), the decrease of
relaxed composite moduli can be attributed to a decrease of
4
