Innocent BOUDIMBOU Véronique Collin

Edith Peuvrel-Disdier

New insights in dispersion mechanisms of carbon black in a polymer matrix under shear by rheooptics

Keywords: carbon black, fracture, elastomer, shear, rheo-optics

The dispersion behaviour of different carbon black grades was investigated in a common elastomer matrix under shear using a transparent plate-and-plate counter-rotating shear cell coupled with an optical microscope. The objective was to investigate the effect of carbon black intrinsic characteristics (specific area and structure) on dispersion mechanisms. Shear conditions were selected in order to study independently erosion and rupture mechanisms.

The independent study of rupture and erosion mechanisms brings new findings on the respective effect of the filler intrinsic parameters on each mechanism:

-Rupture is a sudden mechanism occurring above a critical shear stress which depends on the pellet size. The rupture criterion appears not to depend on the carbon black specific area or the structure, -Erosion proceeds via the detachment of a fixed eroded volume per strain unit and is driven by the applied shear stress and strain. Erosion is a local mechanism. The erosion rate depends on the carbon black characteristics. Faster erosion was measured for a carbon black with a higher structure at equivalent specific area or a lower specific area at equivalent structure. This in-situ characterisation of dispersion mechanisms highlights that the effect of the carbon black characteristics on the two main dispersion mechanisms (rupture and erosion) is completely different.

Introduction

The degree of carbon black dispersion during mixing strongly affects the physical and mechanical properties of filled rubber parts. An effective reinforcement of the rubber matrix by the filler implies a good dispersion and distribution of the filler in the matrix. Classical reinforcing filler for rubber are carbon black and silica. They are introduced as pellets (agglomerates). Pellets are agglomerated objects with a multiscale structure. They consist of aggregates, themselves constituted by fused elementary particles. The dispersion process corresponds to the filler size reduction during the mixing operation. The minimum size which can be reached is the aggregate size. Dispersion and distribution of the filler in the polymer matrix is performed during the mixing operation in an internal mixer for example. Dispersion is possible as soon as the hydrodynamic stress induced by the flow exceeds some cohesive stress of the agglomerates. Two main mechanisms of dispersion occur during mixing, denoted as rupture and erosion. These two mechanisms are distinguished by the size of resulting fragments, the kinetics of the process and the needed energy input. Rupture is characterised by the sudden fracture of the pellet into a few fragments. Erosion is a progressive mechanism where small fragments are continuously detached from the periphery of the parent pellet. These mechanisms were first deduced from dispersion experiments performed in an internal mixer [1][2]. The use of rheo-optical techniques allows one to observe in-situ during shear the dispersion mechanisms of agglomerates [3][4][START_REF] Feke | Handbook of Powder Technology in Volume 11 Granulation[END_REF][START_REF] Collin | [END_REF][START_REF] Collin | European Rubber Research -Practical Improvements of the Mixing Process[END_REF]. The role of different parameters on dispersion was investigated: cohesion strength of the filler, hydrodynamic parameters, affinity between the filler and the matrix, level of infiltration of the matrix inside the agglomerate, viscosity of the matrix [4]. Most studies were conducted on model systems (agglomerates obtained by compression of fluffy powders, with a millimetre diameter range, suspended in a low viscosity Newtonian fluid). Due to the low viscosity of the matrix, the infiltration level plays a key role on the dispersion kinetics.

Dispersion processes being very sensitive to the filler/matrix system, the prediction of the dispersion step for a given system cannot be extrapolated from the knowledge of the behaviour of a model filler/matrix system or another system. In order to better understand the dispersion step in tire processing, the dispersion of commercial materials used in the tire formulation (the carbon black grade N234 and a styrene butadiene copolymer matrix) was previously investigated [START_REF] Collin | [END_REF][START_REF] Collin | European Rubber Research -Practical Improvements of the Mixing Process[END_REF]. In this case, carbon black is received directly from the supplier in the shape of pellets (radius from 20 to 120 µm investigated in this study). The pelletizing step is performed by the supplier. Pellets were thus used as received. The styrene butadiene copolymer is very viscous and highly viscoleastic. Shear conditions were defined such that erosion and rupture mechanisms could be investigated independently which is not possible in an internal mixer. The rupture mechanism characterized by the sudden breakup of the pellet into a few large fragments was observed in-situ during shear for the first time in a highly viscoelastic polymer. This study confirmed that rupture happens above a critical shear stress.

However it more particularly showed that the critical stress for rupture depends on the pellet initial size (inverse proportionality). Measurements of erosion kinetics evidenced that erosion occurs beyond a critical shear stress via the continuous detachment of constant small fragment size. This means that erosion kinetics plotted as the agglomerate size reduction versus time depends on the pellet initial size (erosion is faster for a smaller pellet size). However erosion kinetics plotted as the eroded volume versus time do superimpose whatever the pellet initial size is. The mechanism is governed by the shear stress and the strain subjected to the pellet.

Dispersion criteria and kinetics were used to define a mathematical model which was then used to model dispersion in an internal mixer [START_REF] Collin | ANTEC 2006 Proceedings of the 64th Annual Conference[END_REF]. Results were obtained on a single filler/matrix couple and stressed the role of hydrodynamic parameters on dispersion mechanisms of carbon black in this polymer matrix. However these results did not consider the role of the carbon black intrinsic properties (specific area and/or structure) on dispersion mechanisms. Dispersion studies performed in internal mixers with typical materials for the tire industry showed that the filler intrinsic characteristics affect dispersion kinetics: a carbon black with a larger structure or a lower specific area appears to be easier to disperse [START_REF] Dizon | [END_REF][10][11][START_REF] Leblanc | In Rhéologie des élastomères et leur mise en forme[END_REF].

Using rheo-optics and a model system (agglomerates obtained by compression of fluffy powder, with a millimeter diameter range, suspended in a low viscosity Newtonian fluid), [START_REF] Li | [END_REF] [START_REF] Li | [END_REF] found a different result. In their case, they compared the behaviour of agglomerates with different structures but at equivalent densities and same elementary particle size. They found that high structure carbon black agglomerates were found more difficult to erode than agglomerates of low structure carbon black at equivalent tensile strength. The different result is explained by the authors by the fact that they worked at fixed density, whereas a pelletized high structure carbon black for rubber industry has a lower density than a pelletized low structure one which could explain the easier dispersibility of the pelletized high structure black in the case of carbon black supplied for rubber industry. We would like to address this point in the present paper via direct and independent observations of both dispersion mechanisms. This paper is devoted to the determination of the role of the filler intrinsic parameters such as the specific area and the structure on dispersion mechanisms in the case of commercial products used in the tire industry. This was done by comparing the dispersion behaviour of different grades of carbon black characterized by different specific areas and structures. A rheo-optical approach was used in this work. Shear conditions were chosen to study independently rupture and erosion mechanisms and thus to determine the role of the filler intrinsic parameters on each mechanism. We will show that rupture and erosion mechanisms are affected differently by the filler intrinsic characteristics.

Experimental section

Materials

The polymer used is this study is a styrene-co-butadiene rubber (SBR, 25E produced by Michelin), grade used in tire industry. Two SBR matrices were used. They corresponded to the same grade but came from two different batches and referred to SBR1 and SBR2 in the following. The rheological behaviour of the SBR matrices was measured by oscillatory experiments using a RMS800 Rheometrics rheometer (25mm-diameter plates). Measurements were performed in the linear regime either at 110 or 140°C depending on the SBR batch. The rheological behaviour of both matrices is shown in Figure 1.

Figure 1

The two batches were characterized by a different rheological behaviour. The first batch SBR1 was more viscous and more elastic than SBR2. This explains that dispersion measurements were performed at 140°C in SBR1 and at 110°C in SBR2. In these thermal conditions, the two batches had similar rheological behaviours.

A polybutadiene rubber matrix (BR, Neocis-BR40 from Enichem) was also used for some erosion measurements in order to probe the effect of the infiltration of the matrix into the filler on the erosion kinetics. This matrix was chosen for its very close rheological behaviour at 140°C with SBR1 but its faster infiltration ability into silica relatively to SBR (see Figure 6 in the following).

The dispersion behaviour of different carbon black grades was investigated. The filler characteristics are summarized in Table 1.

Table 1

These carbon blacks differ in their relative specific area and structure. The specific area is determined by the adsorption of specific molecules (for example cetyltrimethyl ammonium bromide, CTAB). This measurement is related to the reverse of the size of elementary particles constituting the aggregate. The structure is representative of the way the elementary particles are arranged inside the aggregate. It is classically estimated by the measurement of the volume of oil or dibutyl phthalate (DBP) absorbed by 100 g of filler. A low structure carbon black is characterized by a compact arrangement whereas a high structure carbon black by a branched arrangement. The concept of structure and specific area relatively to the aggregate arrangement is illustrated in Figure 2. Five of the carbon grades were selected for their similar specific area but different structure and vice versa in order to investigate independently the effect of the specific area or the structure on the dispersion mechanisms.

N326 and N347 have similar specific areas but different structures and were used to determine any effect of structure on dispersion mechanisms. On the other side N234, N327 and N160 have similar structures and different specific areas. The last two carbon black grades (N134 and N772) were chosen for their different intrinsic parameters and used in the last part of this paper to probe the relationship proposed between the erosion efficiency and the intrinsic properties of the carbon black.

All carbon grades were received in the shape of pellets of various sizes. The pelletizing step is part of the carbon black production process. In the present study, carbon black pellets were used as received from the supplier and not submitted to any particular mechanical nor thermal treatment before their use.

One silica grade (Micropearl Zeosil Z1115MP from Rhodia) was also used to probe the infiltration ability of SBR and BR matrices into the pellet. This silica grade was chosen for its similar specific area (CTAB) as compared to carbon black N234 (see Table 1).

Experimental set-up

Experiments were conducted on the transparent counter-rotating shear cell and following the procedure described in our previous work [START_REF] Collin | [END_REF][START_REF] Collin | European Rubber Research -Practical Improvements of the Mixing Process[END_REF][START_REF] Boudimbou | [END_REF].

The transparent counter-rotating shear cell coupled with an optical microscope was used to observe the carbon black dispersion mechanisms while the pellet was suspended in the polymer matrix and submitted to a shear flow. The apparatus consists of two transparent parallel glass plates rotating in opposite directions (Figure 3). The advantage of this geometry is that the relative velocities of the two plates can be adjusted so that the velocity of the suspended particle can be set to zero in the reference framework of the laboratory. This allows us to observe using an optical microscope the behaviour of the same particle suspended in a matrix under shear for a long period of time. The apparatus is equipped with ovens in order to be able to work from room temperature up to 180°C. Observations are performed in the plane containing the vorticity axis and the flow direction at 110 or 140°C depending on the SBR matrix used.

A stainless steel ring was fixed on the lower plate in order to confine the polymer flow inside the parallel plate geometry. This ring aims at extending the shear rate range where observations under shear can be performed. The ring avoids the matrix ejection and pushes the development of elastic instabilities which disturb the flow to higher shear rates [START_REF] Boudimbou | [END_REF]. Shear rates up to 150 s -1 can be investigated.

Procedures

Dispersion tests

Samples consisted of a sandwich of two thin films of SBR with a few pellets of carbon black randomly set in between.

Attention was paid to obtaining reproducible results and thus to all factors which may affect the hydrodynamic stress or the cohesion stress. This includes not only the mechanical settings of the shear cell (glass plate parallelism, colinearity of the axes of rotation, concentricity of the outer ring with both plates, zero gap and rotation speed of the plate calibrations) which are necessary to define a correct shear rate, but also the following parameters:

• the pellet diameter relatively to the gap dimension: the vicinity of the shear cell walls may affect the normal stress submitted to the agglomerate and consequently its dispersion rate. This was evidenced experimentally by Ponchaitaward et al. via the determination of different dispersion rates for two sizes of agglomerate subjected to the same macroscopic shear stress [START_REF] Ponchaitaward | [END_REF]. The numerical simulation of the flow around a solid particle allowed us to define the condition under which there is no wall effect on the particle. If the R/h < 0.2 (where R is the radius of the pellet and h is the distance between the center of the particle and the closest glass plate), the pellet is only subjected to the applied macroscopic shear stress and not to additional stresses due to the vicinity of the shear cell walls [17],

• the pellet shape: only pellets with a shape as spherical as possible were characterized,

• the contact time between the filler and the matrix before the dispersion test: the pellet being porous, the matrix may infiltrate into the agglomerate and modify its cohesion and the way the stress is transmitted through the agglomerate and induce changes in the kinetics of dispersion [START_REF] Feke | Handbook of Powder Technology in Volume 11 Granulation[END_REF]18]. Most experiments were conducted with the same contact time between the filler and the matrix prior to any shear application: after insertion of the sample in the shear cell and setting the gap, the sample was left at rest for 45 minutes in order to have a homogeneous temperature. A given shear history was then submitted to the sample, conditions in which the dispersion mechanisms was characterized. The potential effect of the matrix infiltration inside the pellet is discussed in the following for each dispersion mechanism,

• the pre-shear history submitted to the pellet before the dispersion characterisation: In order to have reproducible results, critical conditions for rupture, for example, were always determined on "fresh samples", which are pellets directly observed after the sample preparation and not submitted to any previous shear histories.

As described in our previous paper [START_REF] Collin | [END_REF], different shear histories were applied in order to study rupture or erosion mechanisms independently:

• Rupture was obtained by gradually increasing the shear rate until the rupture mechanism was observed. The shear rate at which the rupture occurs is considered as the critical shear rate ( R C γ  ). The critical shear stress for rupture ( Rupture C τ ) corresponds to the shear rate multiplied by the viscosity of the SBR at this shear rate for the given temperature ( ( )

T , R C γ η  ): ( ) T , . R C R C Rupture C γ η γ = τ   (1)
• Erosion kinetics was measured by following the gradual and continuous size reduction of the carbon black agglomerate as a function of time for a given shear rate. Following the data on the rupture mechanism, the shear rate of investigation was chosen in a range where due to the pellet size, rupture was not possible for the applied shear rate.

According to our previous results found on erosion, erosion data were represented as the eroded volume versus time or strain unit ( t .

γ γ  = ): ( ) ( ) γ = - f R t R 3 0 3 (2)
where 0 R is the intitial pellet size and R is the pellet time at time t.

Infiltration tests

Infiltration kinetics of the SBR1 and BR matrices were measured into silica agglomerates at 140°C. Porous silica agglomerates present the particularity to appear as black objects when observed by transmission optical microscopy if they contain air and become transparent as soon as a liquid penetrates inside. The silica Zeosil Z1115MP was chosen for its similar specific area as N234 carbon black grade. Measurements were performed in the counterrotating shear cell but at rest. The same protocol as for dispersion experiments was thus used for the sample preparation. Practical details for the infiltration kinetics determination can be found in reference 19.

Results

Rupture mechanisms

Rupture criterion

An example of the rupture mechanism of a N234 carbon pellet under shear is shown on Figure 4.

Figure 4

The rupture condition is experimentally determined as the critical shear rate at which the rupture mechanism is observed. This measurement is performed for different pellet sizes in order to know the rupture condition variation with the pellet size. As dispersion is assumed to occur if the hydrodynamic shear stress is larger than the cohesion strength of the pellet, the rupture criterion is expressed as the critical shear stress (using eq. 1). We found in our previous study that the critical shear stress for rupture was inversely proportional to the pellet size in the case of N234 carbon black in a SBR matrix [START_REF] Collin | [END_REF]. However, as it is depicted in Figure 5, variations of the critical shear rate for rupture with the pellet size and of the critical shear stress respectively show similar tendencies. The rupture condition determined on a single filler type in a single matrix does not allow us to discriminate on whether the rupture criterion should be based on the applied shear rate or the applied shear stress.

Figure 5

For this purpose, measurements were performed in this work on the same carbon black (N234) in two different SBR matrices. Since the two SBR matrices only differ in their rheological behaviour (same chemical composition and thus affinity with carbon black), similar criteria for rupture should be found for the two matrices. Results are reported in Figure 5 where critical conditions for rupture are reported as the critical shear rate versus the initial pellet size (Fig. 5.a) and secondly as the critical shear stress (Fig. 5.b).

These measurements show that if the critical shear rates for rupture for the same pellet size are different in the two matrices, rupture data do superimpose when they are represented as the applied shear stress. These measurements prove that the applied shear stress is one of the hydrodynamic key parameters for the rupture mechanism. Dispersion data are in the following expressed in terms of shear stress and do not indicate in which SBR matrix the experiments were performed.

Potential infiltration of SBR

The pellets being porous, they can be infiltrated by the matrix. This is true even if the matrix is very viscous (case of SBR in this study) [19]. The level of infiltration depends on the contact time between the filler and the matrix [20]. This infiltration and more specifically the infiltration level modifies the cohesion strength of the agglomerate and the way the stress is transmitted through the agglomerate. This induces changes in the kinetics of dispersion [START_REF] Feke | Handbook of Powder Technology in Volume 11 Granulation[END_REF]18]. However, in the present case, the matrix being very viscous, the infiltration time can be very long and needs to be compared to the time for the dispersion experiment.

Figure 6 shows the infiltration kinetics of the SBR1 matrix into silica at 140°C. This figure

shows that in the case of SBR1, no infiltrated layer could be detected by optical microscopy before 1000 minutes of contact time between the matrix and the filler. The infiltration of a 50 µm radius micropearl was not total after 3000 minutes. Such a long infiltration in two steps was already reported by Astruc et al. for elastomer matrices [19]. The affinity of SBR towards carbon black is higher than for silica, which means that the infiltration into carbon black pellet must be quicker. However due to the huge time necessary for the SBR infiltration into silica and regarding the large size of the pellets considered during rupture experiments, we assumed that rupture measurements were performed on dry (not infiltrated) pellets. This was confirmed by the fact that variations of the contact time (around the 45 minutes defined in the protocol)

did not change the critical stress for rupture for a given pellet size.

Figure 6

Effect of carbon black characteristics on rupture

The dispersion behavior of N160, N326 and N347 carbon black grades was investigated using the same protocol as for the N234 grade. The rupture mechanism observed for the different grades showed similar features as the ones observed for the N234 grade:

• rupture occurs beyond a critical shear stress,

• the critical stress depends on the initial pellet size. The larger the initial pellet size is and the easier it is to disperse the agglomerate by rupture.

The exact dependence of the critical stress for rupture with the initial pellet size is reported in Figure 7 for the different carbon black grades.

Figure 7

This figure shows that the critical stresses for rupture for the different carbon black grades measured for similar pellet sizes are the same within experimental errors. The specific area or structure of the carbon black (at least for the investigated carbon blacks) does not seem to affect the critical condition for rupture. The criterion for rupture is found to depend on the pellet size but not on the carbon intrinsic characteristics. The log-log plot of the rupture criterion shows that the critical macroscopic shear stress is proportional to X 0 R -:

X Rupture C R - ∝ 0 τ (3)
where X varies between 0.75 and 0.8.

We previously reported an inverse proportionality for the N234 grade in SBR [START_REF] Collin | [END_REF] however complementary measurements performed in this study allows a better determination of the power law exponent.

Interpretation of the non dependence of the rupture criterion on the carbon black characteristics:

The non-dependence of the critical stress for rupture is not an intuitive phenomenon. This condition can be estimated either by considering the balance between the hydrodynamic stress and the cohesion stress or by considering an energetic balance. The two approaches are considered successively in the following.

The critical shear stress for rupture can be seen as the stress necessary to separate the agglomerate into two fragments (not necessarily of equal dimensions). Horwatt et al. [21] related the cohesion strength of a fragment relatively to the agglomerate parent to the number of bonds between the fragment to the agglomerate parent (N b ), the mean interparticle force (H) and the size of the fragment to be detached (R):

2 b Cohesion R H N π = σ (4)
The mean interparticle force can be considered as constant for the different carbon black grades of this study. The exponent of the power law dependence of the critical stress for rupture with the agglomerate size is only predicted by this model if we assume that severed fragments have a size close to the agglomerate size

( 0 R R =
) and the number of connecting bonds to be fractured is proportional to the agglomerate initial size:

X b R N - ∝ 2 0 (5)
This corresponds to an intermediary case of agglomerate between a dense one where the number of bonds to be severed is proportional to the surface area of fracture [21] and a sparse one where the number of bonds is small and does not depend on the agglomerate size [22]. If this relationship is valid, the cohesion strength does not depend anymore on parameters characterizing the aggregate level but only on the agglomerate size. This would explain that the critical shear stress for rupture does not depend on the carbon black characteristics.

The second approach considers the energy balance for the crack development. According to Griffith's fracture criterion, the fracture grows if the strain energy supplied by the hydrodynamic stress is greater than the energy required for the crack growth. Based on this energy balance and considering the fractal dimension of the aggregate, Zaccone et al. [23] developed a fracture model for dense aggregates with high fractal dimension (case of the present carbon black grades [START_REF] Donnet | In Carbon black: Science and technology[END_REF]). They established a power law dependence between the critical stress for rupture and the agglomerate size where the exponent depends on the fractal dimension but not on the size of the elementary particles thus not on the specific area. The fact that, the fractal dimension is very similar for carbon blacks of different grades [START_REF] Donnet | In Carbon black: Science and technology[END_REF] could explain that the rupture criterion does not depend on the carbon black grade.

The two interpretations of the rupture criterion do not have the same physical meanings. The approach based on a stress balance considers the number of bonds to be severed and this model should apply if we assume that the fragment size is close to the agglomerate size and the number of bonds is nearly proportional to the agglomerate size. The energetic approach is based on the energy required for a crack to propagate. This approach is quite attractive since it follows the classical approach of rupture mechanics with the initiation of a crack and the crack propagation. The result of this work is that the condition for the crack propagation is the same for the investigated carbon black grades. This does not mean that the way the pellet breaks (crack propagation paths) is similar. The crack propagation paths must correspond to the weakest points (defects in the pellet) [START_REF] Kendall | [END_REF]. The way the three carbon grades fractured under shear (number and size of fragments) looked similar however no systematic measurement of the fragment size distribution was performed.

Erosion mechanism:

Erosion kinetics

An example of the pellet size reduction due to the erosion process under shear is shown in Figure 8.

Figure 8

Our previous work on erosion of N234 grade in the SBR matrix showed that erosion is possible if the shear stress is larger than a critical value, proceeding via the detachment of a constant volume per strain unit, and that the eroded volume depends on the applied shear stress and the quantity of strain units [START_REF] Collin | [END_REF]. This means that the pellet size reduction is slow for large pellets and becomes faster when the pellet size decreases (Figure 8.b). The erosion process was found to be well described by a single erosion law:

( ) t R R Erosion C 3 t 3 0 γ τ - τ α = -  (6)
where

3 t 3 0 R R -
is the eroded volume with 0 R the initial pellet size and t R its size at time t, α is the erosion efficiency, τ is the applied shear stress, Erosion c τ is the critical shear stress for erosion, γ  is the applied shear rate and t is the shearing time.

This law takes into account the initial agglomerate size, the applied shear stress and the quantity of strain. It involves two parameters characteristic of the filler/matrix system: the erosion efficiency and the critical shear stress for initiating erosion.

Effect of infiltration

As for rupture, erosion in the SBR matrix was assumed to occur on dry (not infiltrated) pellets. In order to probe the effect of an infiltrated layer on the erosion process, erosion kinetics was measured in the BR matrix. This matrix was chosen for its much faster infiltration into silica (see Figure 6). Four different contact times were probed between 15 and 60 minutes. The time zero corresponded to the moment when the temperature control indicated the set temperature. Once the contact time was reached, a constant shear rate was applied and the resulted erosion process was measured. Figure 9 compares erosion kinetics of the N234 carbon black grade (same pellet size, R 0 = 34 µm) at the same shear rate (5 s -1 ).

Figure 9

These measurements show that the erosion rate (defined as the slope of the eroded volume per strain unit) is faster as the contact time and thus the infiltrated layer is increased. The faster erosion for a thin infiltrated layer is explained by Yamada et al. [START_REF] Boudimbou | [END_REF] by the detachment of the infiltrated layer. As the contact time is increased, the infiltrated layer should be larger which is in agreement with a higher erosion rate.

The fact that the erosion rate varies with the contact time (infiltration depth) in the BR matrix confirms that infiltration does not play any role in the case of the SBR matrix. If infiltration would play a role, for the same contact time, the infiltration depth should be larger for smaller pellet sizes [20]. In this case, for the same shear rate, the erosion rate should vary with the pellet size (via the difference in infiltrated depth) at least during the first step of erosion. This is not what is observed in the case of the SBR matrix. As shown in our previous paper, erosion data for different initial pellet sizes at a constant shear rate superimpose when plotted as the eroded volume versus time (Figure 8 in reference 6). This means that the erosion rate at fixed shear rate is constant whatever the pellet initial size and that measurements were performed on dry pellets.

Effect of carbon black characteristics

The dispersion behaviour of the different grades of carbon black was compared using the protocol designed for erosion experiments. The continuous detachment of small fragments from the outer surface of the parent agglomerate was observed for all the carbon grades under the application of a constant shear rate. Erosion kinetics was more specifically measured for the N234, N326 and N347 carbon grades. A comparison of erosion kinetics measured on the three types of carbon black at the same shear stress of 120 kPa (corresponding to a 10 s -1 shear rate) is depicted in Figure 10. This shear stress value was selected so that the only possible dispersion mechanism is erosion for the considered pellet sizes. Measurements were performed on pellets with similar initial sizes. Following eq. 6, kinetics is plotted as the eroded volume versus the applied strain (Figure 10.a).

Figure 10

This figure shows that the erosion mechanism although induced by the same shear stress proceeds at different erosion rates for the three carbon black grades. The comparison of the behaviour of N234 and N347 grades (different specific areas but similar structures) indicates faster erosion for the N347 grade characterized by a lower specific area. The comparison of the behavior of N347 and N326 grades (different structures but similar specific areas) depicts faster erosion for the carbon black N347 with a larger structure. This shows that the erosion process depends on the carbon black intrinsic properties.

In order to determine the parameters of the erosion law (critical shear stress for erosion and the erosion efficiency in equation 6), erosion kinetics were measured at different shear stresses for each carbon black grade. The variation of the erosion rate with the applied shear stress for the three carbon black grades is shown in Figure 10.b.

The erosion process for the grades N326 and N347 shows similar features as for the N234 grade :

• erosion proceeds via the detachment of a constant volume of matter per strain unit,

• this erosion rate k varies linearly with the applied shear stress and depends on the carbon black grade,

• there is a critical shear stress for initiating erosion in all cases.

The slope of the erosion rate versus stress curve corresponds to the erosion efficiency ( α ) and the intercept of the curve with the X-axis to the critical shear stress for erosion ( Erosion C τ ) (Eq. 6). Erosion efficiencies and critical stresses for erosion values are reported in Table 2.

Table 2

The critical stresses for erosion for the three carbon black grades are in the same order of magnitude. The order of magnitude of the critical stress for erosion is only important to know whether erosion is possible or not and to be compared with the critical shear stress for rupture.

The comparison with critical shear stress for rupture values shows that erosion and rupture can happen simultaneously for pellets larger than 70 µm in radius. For this order of magnitude of pellet size, although both mechanisms do happen, the size reduction due to erosion is negligible relatively to the one due to rupture.

The main information for the dispersion process is the erosion efficiency and its variation with the carbon black characteristics. The effect of the carbon black grade on the erosion efficiency is more obvious. The two to two comparison of the erosion efficiencies for different grades shows that the erosion kinetics is larger for carbon black grades with the lower specific area (carbon black N347, when grades of similar structures N347 and N326 are compared) and the larger structure (carbon black N347, when grades of similar specific areas N234 and N347 are compared). A quicker dispersion for a carbon black with a lower specific area or a larger structure is a classical result for industrial carbon black grades dispersed in an internal mixer [START_REF] Dizon | [END_REF][10][11]. Relatively to these studies, this work allows us to differentiate the effect of the filler characteristics on each dispersion mechanism. The present measurements demonstrate that the carbon characteristics do not affect these mechanisms in the same way:

no effect on the condition for rupture but an effect on erosion.

Explanation of the dependence of the erosion efficiency on the carbon black characteristics:

The present result is different from the results of Li et al. based on rheo-optical dispersion experiments on compressed carbon black agglomerates suspended in a low viscosity matrix [START_REF] Li | [END_REF]. However Li et al. compared two carbon black agglomerates characterized by a different structure but with equivalent density and same specific area (same elementary particles). Donnet et al. [START_REF] Donnet | In Carbon black: Science and technology[END_REF] proposed to use the porous volume determined by the DBP adsorption to calculate the apparent density of carbon black. Since the porous volume (determined per 100g of silica) via the DBP adsorption includes inter-aggregate voids and voids between agglomerates, the IS2 index based on mercury porosimetry (considering voids with a radius lower than 4 µm) is preferred to estimate the porous volume inside the pellet and calculate the apparent density of the pellets:

1 CB app 1 100 2 IS -         ρ + = ρ (7)
where IS2 in cm 3 /100 g, CB ρ is the specific density of carbon black, CB ρ = 1.95 g/cm 3 .

The apparent pellet densities of the three carbon black grades used in this study were calculated using the IS2 index. Values are reported in table 1. Based on this calculation, the two carbon black grades with similar structure (N234 and N347grades) indeed have similar density. Their difference in terms of erosion efficiency is well explained by their different specific area and thus the size of their elementary particles constituting the aggregates. The erosion efficiency parameter corresponds to the effect of the applied stress on the erosion rate that is the quantity of eroded volume which is removed per strain unit (for a fixed shear rate).

If we assume that the fragment to be detached is the aggregate, the size of the elementary particles and their arrangement inside the aggregate (that is the structure) determines the volume to be detached. The volume detached during one pellet revolution is greater for a lower specific area carbon and explains the faster erosion. At equivalent specific area (N326 and N347 grades), the two carbon blacks have a different structure and a different density which explains their different behaviour in erosion. For a fixed size of elementary particles, a higher structure corresponds to a more complex arrangement and thus a less dense aggregate occupying a larger volume which also leads to faster erosion. The result found by Li et al.

concerns a different case where agglomerates with similar density, same specific area but different structures are compared. According to the authors high structure agglomerates formed by compression may result in more interlocked structures than by pelletization which explains the more difficult erosion in their case of a high structure carbon black.

For all carbon black agglomerates (pelletized or compressed agglomerates), the erosion rate depends on the applied shear stress and the quantity of strain units.

3.2.4

Relationship between the erosion kinetics and the carbon black intrinsic parameters Different attempts were already made to define empirical laws relating parameters characterizing the dispersion rate to the carbon black characteristics [10][11]. Based on our measurements and existing laws, we propose an empirical law expressing the variation of the erosion efficiency α versus the structure (defined by the DBP value) and the specific area (defined by the CTAB value). Our data were found to obey the following empirical relationship:

CTAB DBP B CTAB A + = α (8)
where A and B are proportionality constants determined for the erosion efficiency parameter α expressed in µm 3 /kPa.strain unit, CTAB in m 2 /g and DBP in ml/100g. In this case, A=2.7 10 -7 and B=1. 3 10 -6 . The dimension of the constants was not indicated for sake of simplicity.

Based on this equation, the variation of the erosion efficiency with the structure (DBP) is represented in Figure 11 for different values of specific area (noted S in this figure).

Figure 11

The validity of this relationship was checked for two other carbon black grades N772 and N134. Estimating the erosion efficiency of these two carbon blacks is interesting since the specific area and the structure play an opposite effect on erosion. The N772 grade is assumed to be easy to disperse due its low specific area but difficult if one considers its low structure. This is the contrary for the N134 with its high specific area and its high structure. Erosion efficiencies were measured for these two carbon blacks. Table 3 reports the erosion efficiency parameters measured experimentally and estimated using Eq. 8. There is a good agreement between the erosion efficiency calculated by the empirical law and the experimental values. It also shows that although the N134 and N772 carbon black grades are very different, they present similar erosion efficiencies.

Table 3

Application to a mixing operation

Although measured on isolated pellets, the determined criteria and laws for dispersion bring some information on what happens in an internal mixer as far as dispersion is concerned:

-The dependence of the critical shear stress for rupture with the cluster size is consistent with what happens during a mixing operation. If a constant critical shear stress for rupture is assumed (as predicted by the planar rupture model [26][27]), this means that, for a given shear stress larger than the condition, all pellets (whatever their size) would be ruptured and would break down to the level of the smallest entity that is the aggregate size. Dispersion should thus be very rapid. This is of course not consistent with what is observed in practice [2,[START_REF] Leblanc | In Rhéologie des élastomères et leur mise en forme[END_REF]. This is due to the higher resistance to rupture of the small pellets. This size dependence of the critical condition for rupture thus seems to be in line with the industrial experience.

-It is obvious that rupture is more efficient to decrease the pellet size than erosion. However, the rupture mechanism is only active at the beginning of the mixing process down to a critical agglomerate size (defined by the applied shear stress). Below this size erosion is the only possible dispersion mechanism to reduce the agglomerate size.

-Although not discussed in this way in this paper, the erosion process is governed by the energy supplied to the mix. The shear stress multiplied by the strain corresponds to an energy per volume unit. The final dispersion state thus depends on the mixing energy which includes the effect of the mixing time.

-The present study highlights that the condition for the first dispersion step (dominated by the rupture mechanism) is not affected by the carbon black characteristics whereas the second step dominated by the erosion mechanism is.

Conclusions

The effect of the carbon black intrinsic characteristics on dispersion mechanisms and criteria was investigated by direct observation of isolated clusters suspended in a SBR matrix under shear using a transparent counter-rotating shear cell coupled with an optical microscope. It was the first time that the effect of intrinsic parameters could be probed independently on rupture and erosion mechanisms. The observation and determination of dispersion criteria and laws allow us to show that the variation of the carbon black intrinsic properties does not affect in the same way the two dispersion mechanisms:

-The critical shear stress for initiating rupture mechanism varies inversely with the pellet size. This condition for rupture was found not to be affected by the carbon black intrinsic parameters.

-On the contrary, erosion which is a more local mechanism is affected by the specific surface and the structure of the carbon black pellets. Its kinetics does depend on the carbon black intrinsic properties. Erosion is faster for a low specific area carbon black at equivalent structure and a high structure carbon black at equivalent specific area. This dependence is in agreement with results obtained from internal mixer studies, where dispersion results from both mechanisms at the same time [START_REF] Dizon | [END_REF][10][11].

This type of data brings some insights on:

the physics of the dispersion mechanisms which is linked to the internal structure of the pellet, and the dispersion process during a mixing operation. This work provides a set of pertinent and workable dispersion criterion and laws that could be incorporated in a complete modelling of the flow in an internal mixer in the case of industrial products [START_REF] Collin | ANTEC 2006 Proceedings of the 64th Annual Conference[END_REF].

CAPTIONS FOR THE TABLES: Table 1:

Characteristics of the carbon black and silica grades used in this study. Data were determined by Michelin.

Table 2:

Erosion parameters of the carbon black grades N234, N326 and N347 in SBR.

α is the erosion efficiency and Erosion C τ is the critical stress for erosion.

Table 3:

Erosion efficiencies of the carbon black grades N134 and N772 in SBR:

comparison of the measured and calculated (Eq. 6) parameters. Representation adapted from [START_REF] Melson | In Basic rubber testing : selecting mecthods for a rubber test program[END_REF].

CAPTIONS FOR THE FIGURES:

Figure 2

 2 Figure 2

Figure 3

 3 Figure 3

Figure 1 :

 1 Figure 1: Complex viscosity * η (a.) and storage modulus G' (b.) against pulsation curves for the two SBR matrices. Empty symbols represent the rheological behaviour of SBR1 measured at 140°C and solid symbols the behaviour of SBR2 measured at 110°C.

Figure 2 :

 2 Figure 2:Schematic representation of the concept of the specific area and the structure on the arrangement of elementary particles inside the aggregate.

Figure 3 :

 3 Figure 3:Counter-rotating shear cell. The diameter of the upper glass plate is 40 mm.

Figure 4 :

 4 Figure 4:Example of rupture sequence of a N234 carbon black pellet (R 0 =50µm) in SBR1 at 140°C under shear (

Figure 5 :

 5 Figure 5: Rupture criteria of the N234 carbon black grade in both SBR matrices represented as: a. the critical shear rate versus the pellet size, b. the critical shear stress versus the pellet size.

Figure 6 :

 6 Figure 6: a. Example of infiltration of SBR1 into silica, R 0 = 44 µm at 140°C. b. Comparison of infiltration kinetics of SBR1 and BR in Z1115MP micropearls (R 0 = 44 µm in SBR1, R 0 = 38 µm in BR) at 140°C. Infiltration kinetics are plotted as the radius of the non-infiltrated part normalized by the micropearl radius versus time.

Figure 7 :

 7 Figure 7:Log-log representation of the critical shear stress for rupture versus the pellet size of the N234, N326, N347 carbon black grades in SBR.

Figure 8 :

 8 Figure 8:Sequence of erosion of a N234 carbon black cluster in SBR1: R 0 =22µm, 1 s 6 γ -

Figure 9 :

 9 Figure 9:Erosion kinetics measured in the BR matrix at 140°C for different contact times between the pellets of carbon black N234 for the same pellet size, R 0 = 34 µm, and the same shear rate 5 s -1

Figure 10 :

 10 Figure 10: Erosion kinetics data of the N234, N326, N347 carbon black grades in the SBR matrix for an applied shear stress of 117 kPa. Kinetics plotted as: a. the eroded volume versus strain, b. the erosion rate versus the applied shear stress.

Figure 11 :

 11 Figure 11:Variation of the erosion efficiency with the carbon black structure (DBP) and specific area (S) in SBR following Eq. 7.

Figure 1 Collin 2 Figure 3 4

 1234 Figure 1

Figure 5 Collin 6 7 8 9

 56789 Figure 5

Acknowledgments

This work gathers results from different PhD studies. The PhD of Véronique Collin was part of a larger project supported by the European Community in the framework of the "Competitive and Sustainable Growth" program. The PhD of Innocent Boudimbou is granted and supported via the International Competitiveness Cluster Lyon & Rhône-Alpes Chemicals/Environnement (AXELERA). The authors wish to thank partners of both projects amoung which MFP Michelin, Rhodia, Snecma Propulsion Solide, ThyssenKrupp Elastomertechnik, Optigrade-TechPro, Polyflow, Cesame (U.C. Louvain), LPMG of Mines de Saint Etienne, LRMP from Saint-Etienne university and LTDS of E.N.S. Lyon and T.U. Lodz for their fruitful collaboration. Michelin is acknowledged for supplying the products and the characterization of the fillers. The authors wish to thank B. Cantaloube and P. Navard for stimulating discussions during this work.


Trystan Domenech

Edith Peuvrel-Disdier

Bruno Vergnes
email: bruno.vergnes@mines-paristech.fr

The importance of specific mechanical energy during twin screw extrusion of organoclay based polypropylene nanocomposites

Keywords: A. Nanocomposites, A. Polymer-matrix composites (PMCs), D. Rheology, E. Extrusion, Dispersion

This study demonstrates how the specific mechanical energy (SME) can be used to describe the influence of extrusion parameters such as screw rotation speed, feed rate and barrel temperature on clay dispersion in organoclay (OMMT) based polypropylene nanocomposites. These materials were prepared by a melt mixing masterbatch process via twin screw extrusion with a wide range of processing conditions. Maleated polypropylene (PP-g-MA) was used as a compatibilizer to allow clay exfoliation.

Characterization of the morphological evolution along the extrusion profile revealed that microscale dispersion primarily happens in the melting zone, whereas continuous exfoliation is observed all along the kneading zones, up to the die exit. The results indicate that exfoliation in the kneading zones is mainly issued from clay tactoids and small aggregates with characteristic size inferior to 10 µm, emphasizing the crucial role of primary microscale dispersion on the final structure and properties of the nanocomposites. Relevant quantitative prediction of the multiscale dispersion state along the extrusion profile was obtained using the melt state SME as unique parameter.

Introduction

Reinforcement of polymer matrix by the addition of nanoclay particles is an efficient strategy to extend polymers' range of applications by enhancing their mechanical [START_REF] Kojima | Mechanical properties of nylon 6-clay hybrid[END_REF][START_REF] Cho | Nylon 6 nanocomposites by melt compounding[END_REF], thermal [START_REF] Giannelis | Polymer layered silicate nanocomposites[END_REF][START_REF] Zanetti | Fire retardant halogenantimony-clay synergism in polypropylene layered silicate nanocomposites[END_REF] and barrier properties [START_REF] Messersmith | Synthesis and barrier properties of poly(ε-caprolactone)-layered silicate nanocomposites[END_REF][START_REF] Sherman | Nanocomposites: A little goes a long way[END_REF]. Nanostructuring of these hybrid materials is obtained by intercalation or exfoliation of the native stacked clay platelets by the macromolecules [START_REF] Giannelis | Polymer layered silicate nanocomposites[END_REF][START_REF] Vaia | Synthesis and properties of two-dimensional nanostructures by direct intercalation of polymer melts in layered silicates[END_REF][START_REF] Vaia | Kinetics of polymer melt intercalation[END_REF]. Melt processing has revealed to be a very suitable route for nanocomposites production as it benefits flexible processability of continuous mixing processes and does not require the use of solvents, which is advantageous from an environmental and economical point of view.

In the case of widely used polyolefin matrices such as polypropylene, the grafting of polar groups such as maleic anhydride along polypropylene backbone turns out an effective approach to improve polymer-clay affinity and allows the formation of intercalated/exfoliated polypropylene based nanocomposites [START_REF] Kawasumi | Preparation and mechanical properties of polypropylene-clay hybrids[END_REF][START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF][START_REF] Kim | Structure and properties of polypropylene-based nanocomposites: Effect of PP-g-MA to organoclay ratio[END_REF].

Besides compatibilization concern, it is important to understand how processing conditions affect the structure of nanocomposites during melt mixing step in order to establish processing strategies which could lead to highly exfoliated PP based nanocomposites. Out of the massive literature dealing with nanocomposites, few references discuss the influence of processing conditions on the resulting nanocomposites' structure [START_REF] Cho | Nylon 6 nanocomposites by melt compounding[END_REF][START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF][START_REF] Dennis | Effect of melt processing conditions on the extent of exfoliation in organoclay-based nanocomposites[END_REF][START_REF] Shah | Nylon 6 nanocomposites prepared by a melt mixing masterbatch process[END_REF][START_REF] Zhu | Effects of process conditions and mixing protocols on structure of extruded polypropylene nanocomposites[END_REF][START_REF] Lertwimolnun | Effect of processing conditions on the formation of polypropylene/organoclay nanocomposites in a twin screw extruder[END_REF][START_REF] Lertwimolnun | Influence of screw profile and extrusion conditions on the microstructure of polypropylene/organoclay nanocomposites[END_REF][START_REF] Treece | Twin-screw extrusion of polypropylene-clay nanocomposites: Influence of masterbatch processing, screw rotation mode, and sequence[END_REF][START_REF] Médéric | Structural and rheological properties as a function of mixing energy for polymer/layered silicate nanocomposites[END_REF]. An important aspect of the melt processing approach is to fulfill a dispersive mixing, i.e. to break the native organoclay agglomerates down to individual layers. Several studies revealed that the state of dispersion of the nanocomposites is sensitive to both shear intensity and residence time [START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF][START_REF] Dennis | Effect of melt processing conditions on the extent of exfoliation in organoclay-based nanocomposites[END_REF][START_REF] Lertwimolnun | Effect of processing conditions on the formation of polypropylene/organoclay nanocomposites in a twin screw extruder[END_REF][START_REF] Lertwimolnun | Influence of screw profile and extrusion conditions on the microstructure of polypropylene/organoclay nanocomposites[END_REF][START_REF] Treece | Twin-screw extrusion of polypropylene-clay nanocomposites: Influence of masterbatch processing, screw rotation mode, and sequence[END_REF][START_REF] Médéric | Structural and rheological properties as a function of mixing energy for polymer/layered silicate nanocomposites[END_REF][START_REF] Fornes | Nylon 6 nanocomposites: the effect of matrix molecular weight[END_REF]. Furthermore, quantitative characterization of the overall dispersion state is quite challenging as nanocomposites can be highly polydisperse systems. X-ray diffraction (XRD) and transmission electron microscopy (TEM) are widely used to describe nanoscale organization. However, these characterization techniques provide a local insight and cannot be representative of the whole range of the dispersion state [START_REF] Morgan | Characterization of polymer-layered silicate (clay) nanocomposites by transmission electron microscopy and X-ray diffraction: A comparative study[END_REF][START_REF] Schaefer | How nano are nanocomposites?[END_REF]. On the other hand, melt rheology is very sensitive to the nanostructure [START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF][START_REF] Krishnamoorti | Rheology of end-tethered polymer layered silicate nanocomposites[END_REF][START_REF] Ren | Linear viscoelasticity of disordered polystyrene-polyisoprene block copolymer based layered silicate nanocomposite[END_REF][START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF][START_REF] Aubry | Rheological investigation of the melt state elastic and yield properties of a polyamide-12 layered silicate nanocomposite[END_REF][START_REF] Vermant | Quantifying dispersion of layered nanocomposites via melt rheology[END_REF][START_REF] Cassagnau | Melt rheology of organoclay and fumed silica nanocomposites[END_REF][START_REF] Vergnes | The use of apparent yield stress to characterize exfoliation in polymer nanocomposites[END_REF][START_REF] Zouari | Time evolution of the structure of organoclay/polypropylene nanocomposites and application of the time-temperature superposition principle[END_REF] and has the advantage to probe macroscopic volume properties of the nanocomposites samples.

Beyond of fundamental interest, it is also crucial to understand the mechanisms of clay dispersion from its natural agglomerate form to exfoliated nanostructure during the extrusion process. Modularity of twin screw extruders enables the use of numerous types of elements (conveying screw, back flowing screw, mixers, kneaders, etc) which can be combined with countless possibilities. The design of screw profile will affect flow properties within the extruder and local parameters like filling ratio, shear rate, temperature and residence time. Consequently, it will also influence distribution and dispersion of the clay within the matrix. In a previous study [START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF], we showed how the influence of processing conditions on the final structure of extruded nanocomposites can be described by a single parameter, using the specific mechanical energy (SME).

The latter represents the level of energy per mass unit that is transferred to the material by mechanical input during extrusion. In the present article, we emphasize on the evolution of dispersion state along the extrusion profile by investigating the role of local SME contribution and dispersion mechanisms of the organoclay filler, using identical nanocomposite formulation [START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF]. For this purpose, dead-stop experiments were carried out after reaching stationary conditions in order to sample materials from various zones along the extrusion profile. However, the lack of information about local extrusion parameters during melt processing raises a problem in the establishment of processingstructure relationships along the screw profile. To overcome this limitation, we used a flow simulation software (Ludovic ® ) to calculate local extrusion parameters along the screw profile [START_REF] Vergnes | A global computer software for polymer flows in corotating twin screw extruders[END_REF] and confront experimental results with empiric laws based on SME.

Materials and methods

Materials

The polypropylene (PP) used in this study was a semi-crystalline injection grade isotactic homopolymer produced by LyondellBasell under the reference Moplen HP400R. It had a density of 0.905 g/cm 3 (25°C), a melting temperature of 165°C and a 25 g/10 min melt flow index (230°C, 2.16 kg). A montmorillonite based organoclay (OMMT, Dellite ® 67G) in powder form with a density of 1.7 g/cm 3 was kindly provided by Laviosa Chimica Mineraria. This grade of organoclay featured 48 wt% of dimethyldehydrogenated-tallow quaternary ammonium as organic modifier and a cation exchange capacity of 115 meq/100 g. Polypropylene grafted with maleic anhydride (PPg-MA, Eastman TM G-3015) was purchased from Eastman Chemical Company and used as a compatibilizer. This grade had a maleic anhydride content of 3.1 wt%, a density of 0.913 g/cm 3 and a melting temperature of 162°C.

Compounding of organoclay based PP nanocomposites

Nanocomposites were prepared via a masterbatch process [START_REF] Shah | Nylon 6 nanocomposites prepared by a melt mixing masterbatch process[END_REF][START_REF] Treece | Twin-screw extrusion of polypropylene-clay nanocomposites: Influence of masterbatch processing, screw rotation mode, and sequence[END_REF]. A masterbatch with a PP-g-MA to OMMT ratio of 2:1 was compounded at the Danish Technological Institute, as described elsewhere [START_REF] Drozdov | Viscoelasticity, viscoplasticity, and creep failure of polypropylene/clay nanocomposites[END_REF], with following formulation: 40 wt% PP, 40 wt% PP-g-MA and 20 wt% OMMT. In a second step, the masterbatch was diluted into the PP matrix to produce PP/PP-g-MA/OMMT nanocomposites with respective weight fractions of 85/10/5 using a ThermoFisher Rheomex PTW24 co-rotating twin screw extruder with laboratory scale modular screw profile design (diameter D = 24 mm, length to diameter ratio L/D = 40). The screw configuration is described in Fig. 1. The temperature was set identically for all barrel elements, except for the first one which was regulated at 80°C. An appropriate mixture of PP and masterbatch pellets was tumbled mixed and then fed into the hopper using a gravimetric feeder. Once extrusion conditions have reached steady state, extruded strands were pelletized. Nanocomposites were prepared for a wide range of processing conditions, depending on screw rotation speed N, feed rate Q and regulated barrel temperature T reg , as listed in Table 1. Each of these three parameters was varied individually to assess its effect on the resulting state of dispersion and properties of the nanocomposites. For each extrusion condition, the drive motor torque τ was recorded. The specific mechanical energy (SME, in kWh/t) was then calculated using Eq. (1) which involves motor power (P motor = 11 000 W) and maximum values of drive motor torque (τ max = 180 Nm) and screw rotation speed (N max = 1000 rpm):

Q N N P SME motor ⋅ ⋅ ⋅ = τ τ max max (1)
Extruded nanocomposites pellets were collected and dried in a vacuum oven at 80°C during 15 h, prior to be formed into disk-shaped samples [START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF] for further material characterization.

Dead-stop experiments

The Rheomex extruder is equipped with a clam-shell barrel system which can be opened to allow access to the screw profile. Dead-stop experiments were carried out by suddenly stopping the extruder once stationary conditions were reached (typically after 10 minutes). Then, barrel was cooled down to 100°C by internal water flow in approximately 15 minutes, before opening the barrel. Few quantities of materials (between 2 and 4 g) were collected in the material-filled zones of the screw profile, i.e. in the kneading elements. These sampling zones were indexed from A to J, as indicated on Fig. 1. This sampling was carried out for screw rotation speeds of 100, 300 and 500 rpm at constant feed rate and barrel temperature of 3 kg/h and 180°C, respectively.

Characterization

In order to estimate the efficiency of dispersive mixing during extrusion, multi-scale morphological characterization was performed on each sample. The presence of undispersed clay agglomerates was detected using a Philips XL30 scanning electron microscope (SEM) as described elsewhere [START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF]. Particle analysis was carried out from the SEM pictures using Visilog image analysis software. This step allowed to quantify microscale dispersion through the area ratio A r (%) defined by Eq. ( 2), where A MMT is the area occupied by residual clay agglomerates and A 0 is the analyzed section area (equals to 17.2 mm 2 ). Clay particles with equivalent diameter inferior to 10 μm were not taken into account. The quality of microscale dispersion is thus augmented when A r decreases.

0 100 A A A MMT r ∑ ⋅ = (2)
Local nanoscale organization was observed from ultra-thin sections using a Philips CM12 transmission electron microscope (TEM) [START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF]. The mean basal spacing d 001 of the samples was measured using a Philips Xpert' Pro X-ray diffractometer (XRD) in order to assess the extent of intercalation [START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF].

Rheological measurements were used to quantify the extent of exfoliation. Small amplitude oscillatory shear (SAOS) measurements were performed on a straincontrolled ARES rheometer (TA Instruments). Parallel plate geometry with 25 mm diameter and 1 mm gap was used. All rheological tests were conducted in the molten state with a fixed temperature of 180°C under nitrogen environment, using compressed disk samples. Prior to frequency sweep tests, samples were equilibrated after loading in the rheometer at 180°C for one-half hour, similarly to protocols previously proposed by other authors [START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF][START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF]. Frequency sweep tests were carried out from 10 2 to 10 -2 rad/s in angular frequency. Shear strain did not exceed 1 % to ensure these tests were conducted within the linear viscoelastic range and a new sample was used for each rheological test.

Above their percolation threshold, nanocomposites were reported to display a nonterminal low frequency response which is indicative of a solid-like behavior, with the appearance of a storage modulus (G') plateau and a significant increase of the complex viscosity (|η*|) in the low frequency regime [START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF][START_REF] Krishnamoorti | Rheology of end-tethered polymer layered silicate nanocomposites[END_REF][START_REF] Ren | Linear viscoelasticity of disordered polystyrene-polyisoprene block copolymer based layered silicate nanocomposite[END_REF][START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF]. This solid-like behavior of nanocomposites has been attributed to the existence of a three-dimensional percolation network formed by anisotropic clay platelets within the matrix [START_REF] Krishnamoorti | Rheology of end-tethered polymer layered silicate nanocomposites[END_REF][START_REF] Ren | Linear viscoelasticity of disordered polystyrene-polyisoprene block copolymer based layered silicate nanocomposite[END_REF][START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF].

Lertwimolnun and Vergnes [START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF] proposed using a Carreau-Yasuda model combined with a yield stress term (Eq. 3) to describe the frequency dependence of nanocomposites' complex viscosity |η * |, where ω is the angular frequency, σ 0 is the melt yield stress, η 0 is the zero-shear viscosity, λ is characteristic relaxation time, a is the Yasuda parameter and m is the shear-thinning index:

( ) ( ) [ ] ( ) a m a 1 0 0 1 - * ⋅ + ⋅ + = ω λ η ω σ ω η (3)
Moreover, σ 0 has been shown to efficiently characterize the level of exfoliation [START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF][START_REF] Lertwimolnun | Effect of processing conditions on the formation of polypropylene/organoclay nanocomposites in a twin screw extruder[END_REF][START_REF] Lertwimolnun | Influence of screw profile and extrusion conditions on the microstructure of polypropylene/organoclay nanocomposites[END_REF][START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF].

Flow modeling

Simulations of flow conditions along the co-rotating twin screw extruder were performed using Ludovic © software, which enables the calculation of the main local flow variables like shear rate, filling ratio, melt temperature, pressure, residence time and dissipated energy, from melting zone to die exit [START_REF] Vergnes | A global computer software for polymer flows in corotating twin screw extruders[END_REF]. Numerous experimental validations in compounding (filler dispersion, reactive extrusion), optimization and scale-up applications have shown that Ludovic © offers consistent description of the flow conditions in twin screw extrusion processes [START_REF] Carneiro | Experimental and theoretical study of the twin screw extrusion of polypropylene[END_REF][START_REF] Vergnes | Modelling of flow and chemistry in twin screw extruders[END_REF]. These simulations were carried out to establish relationships between nanocomposites structure and processing parameters along the screw profile, where local physical values cannot be precisely measured (or measured at all) during processing. Rheological data (flow curves) of the PP/PP-g-MA matrix were used for those calculations. Indeed, for the range of shear rates encountered in extrusion (10-100 s -1 ), there is quite no difference in viscosity between matrix and nanocomposite.

Results and discussion

Morphology of native OMMT and masterbatch

Dellite © 67G is an off-white powder, composed of agglomerated layered silicate with characteristic size comprised between 10 and 40 µm [START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF]. These bundles of stacked OMMT layers present van-der-Waals interactions leading to important cohesive forces, which must be overcome by the applied shear stresses during melt mixing process in order to reach nanoscale dispersion. Basal spacing d 001 of the Dellite © 67G was found to be 3.37 nm by XRD measurements.

SEM study of the masterbatch revealed the existence of OMMT agglomerates within the matrix, with equivalent diameter ranging from 10 to 170 µm (Fig. 2a), leading to an area ratio A r of 12.8 %. The presence of OMMT bundles exceeding 40 µm in equivalent diameter indicates that agglomeration of the OMMT powder occurred during the masterbatch compounding step. TEM observations showed the presence of tactoids containing 3 to 5 stacked layers, as well as individualized platelets which is a sign of partial exfoliation (Fig. 2b). XRD experiments provided a basal spacing d 001 of 3.44 nm, denoting a partial intercalation of the tactoids present within the masterbatch.

Influence of processing conditions on melt state SME and resulting structure

The mechanical energy transferred to the material during the extrusion process depends on various physical parameters such as shear intensity, residence time and melt temperature. It is therefore important to understand how processing parameters like screw rotation speed, feed rate and barrel temperature affect the SME prior to the establishment of relationships between the SME and the dispersion state. Since the mixing process takes place in the melt state, it seems appropriate to consider that the energy consumed by the solid conveying and the melting on the first part of the screw profile (Fig. 1) does not contribute to the OMMT dispersion. Ludovic © simulations allow to calculate the SME dissipated in the melt state (SME melt ) which strongly depends on processing conditions. The increase of screw rotation speed induces torque reduction due to shear thinning behavior of the polymeric matrix, as well as a lower filling ratio of the extruder and important viscous heating. Despite torque decrease, screw speed augmentation results in a linear increase of SME melt . On the other hand, feed rate augmentation simultaneously leads to torque increase (as expected from higher filling ratio) and residence time reduction, giving rise to SME melt decrease. Furthermore, SME melt is found to lessen linearly with barrel temperature. This trend is related to torque reduction caused by the decrease of the matrix viscosity.

Here, we show that SME melt is a key descriptor of processing influence on OMMT multiscale dispersion, similarly to the total SME defined by (Eq. 1) [START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF]. Plot of the area ratio as a function of SME melt is represented on Fig. 3a. Variations of processing conditions through the settings of screw speed, feed rate and barrel temperature lead to a mastercurve that underlies the predominance of SME melt on microscale dispersion. The increase of SME melt from its lowest to its highest value in the investigated range leads to a reduction of the area ratio by a factor of seven, linked to a significant decrease in number and size range of OMMT agglomerates. Microscale dispersion is thus enhanced when processing conditions are set to maximize SME melt , at least in the studied range.

The area ratio was found to scale with SME melt as a decreasing power law. Similar correlation has been recently found by Villmow et al. [START_REF] Villmow | Influence of screw configuration, residence time, and specific mechanical energy in twin-screw extrusion of polycaprolactone/multi-walled carbon nanotube composites[END_REF], using the experimentally measured SME, in the case of polycaprolactone/multi-walled carbon nanotube composites, where the nanotubes were also introduced into the extruder as agglomerated powder.

The effect of SME melt on the exfoliation level is illustrated on Fig. 3b. As said before, rheological analysis allows to determine the yield stress σ 0 which is used as a quantitative measurement of the extent of exfoliation. Fig. 3b shows that a mastercurve is built when the yield stress is represented as a function of SME melt , whatever the processing conditions. At first, the yield stress grows linearly with SME melt up to a value close to 360 kWh/t. Above this critical SME melt value, the yield stress stabilizes at a plateau value, suggesting that no further exfoliation seems to occur. Médéric et al. [START_REF] Médéric | Structural and rheological properties as a function of mixing energy for polymer/layered silicate nanocomposites[END_REF] found a similar result with polyamide 12/OMMT nanocomposites processed in an internal mixer, with much lower critical SME value (around 140 kWh/t in experimental value). This may suggest that the critical SME depends on the polymer-clay affinity since exfoliation is known to be much easier in a polar PA matrix rather than in PP [START_REF] Kawasumi | Preparation and mechanical properties of polypropylene-clay hybrids[END_REF][START_REF] Dennis | Effect of melt processing conditions on the extent of exfoliation in organoclay-based nanocomposites[END_REF]. The saturation of the extent of exfoliation reveals a certain limit of the influence of processing conditions on nanoscale dispersion. This phenomenon is observed for the highest screw rotation speeds, where important shear thinning and high melt temperature can soften the shear stresses and thus limit layer delamination. Moreover, XRD measurements indicate a partial collapse of the interlayer spacing when screw rotation speed exceeds 500 rpm (Table 1), what also might inhibit exfoliation.

Considering the temperature range (210-260 °C) and the mean residence times (90-110 s), this could be due to thermal degradation of the surfactant, as often evoked in the literature, but desorption of the surfactant molecules from the interlayer spacing could also be a possible mechanism.

TEM observations shown in Fig. 3b highlight the simultaneous presence of partially oriented tactoids and single layers. Augmentation of the yield stress corresponds to a reduction in tactoids thickness, as well as an increase in individual layers number and a shortening of interparticle distances, indicating an enhancement of nanoscale dispersion which confirms the trend depicted by rheological measurements. We recently showed that this raise in exfoliation level led to higher stiffness of the nanocomposites in the semicrystalline state [START_REF] Domenech | Influence of twin-screw processing conditions on structure and properties of polypropylene -organoclay nanocomposites[END_REF].

Morphological evolution along the extrusion profile

Multiscale observations

The progress of OMMT dispersion during extrusion processing was investigated by following the structural features of the hybrid material along the extrusion profile. This analysis was carried out for screw rotation speeds of 100, 300 and 500 rpm at constant feed rate (3 kg/h) and barrel temperature (180°C). Fig. 4a shows typical SEM pictures of the samples collected along the screw profile after processing (N = 500 rpm, Q = 3 kg/h, T reg = 180°C). A significant reduction in size of the OMMT agglomerates is observed from zone A to B, i.e. the melting zone. In fact, even the frontier between PP and masterbatch pellets can be distinguished on the zone A sample as the melting of polymers is incomplete at this stage of the extrusion process. Afterwards, no meaningful evolution of the microscale dispersion of the OMMT can be observed from zone B to the die exit. These observations point out that microscale dispersion mainly happens in the melting zone, since most of the OMMT agglomerates present afterwards remained undispersed within the matrix.

Evolution of nanoscale dispersion along the extrusion profile was also monitored using TEM, as illustrated in Fig. 4b for the same processing conditions. The increase in tactoids and single platelets number together with the reduction of tactoids thickness indicates an enhancement of the exfoliation level along the extrusion profile. One can note that the orientation of clay particles (tactoids and platelets) becomes more pronounced as the material flows towards the die exit, which could be attributed to a progressive flow induced alignment of anisotropic clay particles [START_REF] Pujari | X-ray scattering measurements of particle orientation in a sheared polymer/clay dispersion[END_REF][START_REF] Dykes | Shear-induced orientation in well-exfoliated polystyrene/clay nanocomposites[END_REF].

Rheological analysis

Linear viscoelastic behavior of PP/PP-g-MA matrix and nanocomposites samples from various zones of the extrusion profile is represented in Fig. 5. The matrix exhibits a classical Carreau-Yasuda behavior, whereas nanocomposites show a low frequency G' plateau and yield stress behavior. Rheological data were fitted using the Carreau-Yasuda with yield stress model (Eq. ( 3)) by adjustment of the five parameters. As shown on Fig. 5b, an excellent agreement is observed between experimental data and fitted curves, confirming that Eq. ( 3) provides a very accurate description of the nanocomposites rheological behavior. The increase of the exfoliation level intensifies the solid-like behavior of the nanocomposites and leads to a yield stress augmentation, which can thus be used as a quantitative parameter to measure the extent of exfoliation at fixed clay content [START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF][START_REF] Vergnes | The use of apparent yield stress to characterize exfoliation in polymer nanocomposites[END_REF]. Here, the low frequency G' plateau becomes increasingly marked and reaches higher values as material progresses towards the die exit, suggesting the development of a long scale network formed by anisotropic clay platelets through progressive exfoliation along the screw profile, in accordance with local TEM observations. Augmentation of screw speed results in a substantial acceleration of nanoscale morphological development along the extrusion profile, as shown on Fig. 6b.

Correlation between dispersion progress and local SME

In order to explore the influence of processing on the progressive nanocomposite formation along the screw profile, flow parameters of the twin-screw extrusion process were calculated using Ludovic © software. Excellent agreement between experimental measurements and Ludovic © results was found in terms of residence time, melt temperature at the die exit, die pressure and SME, confirming the relevance of these simulations. Fig. 7 shows the evolution of SME melt along the screw profile for several screw rotation speeds. It clearly appears that energy is mainly dissipated in the zones containing blocks of kneading discs, whereas conveying elements show insignificant dissipation. The rise in screw rotation speed magnifies the increase of SME melt along the screw profile, in accordance with the results presented in section 3.2. In this selected range of processing conditions, the area ratio and melt yield stress of the samples collected at the die exit can be described as a function of SME melt using Eq. ( 4) and ( 5), respectively, where α = 47.14 kWh n /t n , β = 4.78 Pa.t/kWh and n = 0,7321:

n melt r SME A - ⋅ = α (4) melt SME ⋅ = β σ 0 (5)
These results correspond to the trends shown in Figs. 4 and5 for the same range of processing conditions.

Based on calculations of local SME melt values via Ludovic © simulations, Eq. ( 4) and

(5) were used to calculate the area ratio and melt yields stress along the screw profile.

Comparisons of calculated values (dashed lines) with experimental values (symbols) are presented in Fig. 6. A fair agreement is obtained, despite some deviations can be noted concerning the variations of the area ratio in zones A through C, where agglomerate dispersion was found to be more drastic. Nevertheless, these calculations lead to a satisfactory description of the multiscale OMMT dispersion state development along the extrusion profile, without any adjustment parameter.

These results confirm that microscale dispersion of OMMT principally takes place in the melting zone, whereas nanoscale dispersion appears to follow a progressive development along the screw profile. The dispersion efficiency at both micro and nanoscale is clearly favored by the increase of screw rotation speed, at least up to 500 rpm, in accordance with the results presented in section 3.2.

Dispersion mechanisms

Understanding of OMMT dispersion mechanisms involved during extrusion is a key step towards melt processing optimization. Plot of the melt yield stress as a function of the area ratio presented in Fig. 8a illustrates the dispersion regimes. For extrusion zones A and B (white region in Fig. 8a), a significant reduction of the area ratio occurs while the melt yield stress is almost unaffected. This indicates the preponderance of OMMT agglomerate fragmentation into smaller particles with characteristic size inferior to 10 µm, as illustrated in Fig. 8b. Furthermore, the influence of shear stress on microscale dispersion suggests a rupture mechanism [START_REF] Collin | New insights in dispersion mechanisms of carbon black in a polymer matrix under shear by rheo-optics[END_REF][START_REF] Kasaliwal | Analysis of agglomerate dispersion mechanisms of multiwalled carbon nanotubes during melt mixing in polycarbonate[END_REF], which could explain why the dispersion of OMMT agglomerates primarily occurs in the melting zone since shear stresses are maximum in this part of the extrusion profile. The influence of feed rate on the area ratio (Fig. 3a) reveals the sensitivity of microscale dispersion to residence time which could be the signature of an erosion-like mechanism, previously observed in shear flows for other fillers like carbon black [START_REF] Collin | New insights in dispersion mechanisms of carbon black in a polymer matrix under shear by rheo-optics[END_REF], silica [START_REF] Scurati | Analysis of the kinetics of agglomerate erosion in simple shear flows[END_REF] and carbon nanotubes [START_REF] Kasaliwal | Analysis of agglomerate dispersion mechanisms of multiwalled carbon nanotubes during melt mixing in polycarbonate[END_REF].

A change of dispersion regime is observed after the melting zone (grey region in Fig. 8a), where a substantial rise of the melt yield stress is accompanied by a slight decrease of the area ratio from zone B to the die exit, highlighting the preponderance of OMMT exfoliation. Since the area ratio is nearly unchanged after the melting zone, exfoliation of the layers must come from clay particles with characteristic size less than 10 µm, i.e. aggregates and tactoids. The TEM micrograph presented on Fig. 8c supports this hypothesis and reveals that OMMT platelets seem to be peeled off from the surface of aggregated stacks. Similar observation of peel apart mechanism was reported by Dennis et al. [START_REF] Dennis | Effect of melt processing conditions on the extent of exfoliation in organoclay-based nanocomposites[END_REF] in the case of melt processed organoclay based nylon 6 nanocomposites. Thereby, OMMT dispersion by melt mixing in twin screw extrusion can be described as a two-step process. First, microscale dispersion takes place in the melting zone by the fragmentation of agglomerates into smaller tactoids and aggregates.

However, this step results in a certain amount of undispersed agglomerates whose number and size depend on processing conditions. The second step is a progressive delamination of the montmorillonite layers, which takes place in the kneading zones up to the die exit. The latter strongly depends on processing conditions and may only be possible in the case of intercalation of the PP-g-MA compatibilizer between stacked layers [START_REF] Kawasumi | Preparation and mechanical properties of polypropylene-clay hybrids[END_REF][START_REF] Lertwimolnun | Influence of compatibilizer and processing conditions on the dispersion of nanoclay in a polypropylene matrix[END_REF].

Summary and conclusions

This article offers in-depth discussion about the relationships between processing and multiscale structure of PP/PP-g-MA/OMMT nanocomposites prepared by twin screw extrusion via a masterbatch dilution method. Melt processed nanocomposites revealed to be highly polydisperse systems, exposing the concomitant presence of OMMT individual layers, tactoids and agglomerates. The microscale feature of nanocomposites is rarely probed in the structural analysis that can be found in the literature, where the focus is mainly set on local nanoscale organization through XRD and TEM analysis. Nonetheless, this aspect is crucial since the presence of agglomerates might act as structural defects which could be related to the failure of mechanical properties enhancement predictions.

Development of the multiscale dispersion state of the nanocomposites during melt processing was determined thanks to samples collection along the screw profile.

Numerical simulations using Ludovic © software allowed a quantitative description of the dispersion state development along the extrusion profile based on melt state SME calculations. The melting zone revealed to be crucial regarding microscale dispersion, as reduction in number and size of the OMMT agglomerates mainly takes place in this part of the screw profile. The presence of residual agglomerates after the melting zone underlies the importance of microscale structural characterization of the extruded materials. A progressive increase of the extent of exfoliation was found to arise from the SME contribution of kneading elements on the rest of the screw profile. Additionally, this work gives an insight of the OMMT dispersion mechanisms involved during extrusion. In a first step, agglomerates are sharply broken down into smaller aggregates and tactoids by the mean of rupture and erosion mechanisms. These smaller clay particles are then exfoliated through a peel-like mechanism which is favored by the rise of shear intensity up to a certain limit.

Ultimately, SME appears to be a key parameter of melt processing with regard to the structure and properties of nanocomposites, even though it might not be the only influential parameter since the effect of screw profile design was not reported here. In terms of applications, results have shown that structuring of nanocomposites using twin screw extrusion can be optimized by working under high SME conditions until a critical limit beyond which exfoliation can no longer be enhanced by the processing conditions.

Existence of critical phenomenon concerning the extent of exfoliation may indicate a limited effect of shear intensity on layer individualization. As a consequence, use of elongational strain type of elements in the kneading zone of the screw configuration might be a solution to extend the processing limits highlighted in this study.

Table 1

Twin screw extrusion processing conditions and associated material parameters, where t mean stands for mean residence time and T melt for melt temperature at the die exit.

N

Figures and Captions Fig. 1 .

 Captions1 Figures and Captions

Fig. 2 .

 2 Fig. 2. (a) SEM and (b) TEM pictures of the OMMT masterbatch.

Fig. 3 .

 3 Fig. 3. Evolution of (a) the area ratio and (b) the melt yield stress as a function of SME melt for nanocomposites prepared over a wide range of processing conditions, with corresponding SEM and TEM pictures.

Fig. 4 .Fig. 5 .

 45 Fig. 4. (a) SEM and (b) TEM pictures of the samples collected along the screw profile after processing at N = 500 rpm, Q = 3 kg/h and T reg = 180°C.

Fig. 6 .

 6 Fig. 6. Evolution of dispersion parameters along the screw profile: (a) area ratio, (b) melt yield stress. Symbols represent experimental data, dashed lines represent simulation results based on Eq. (4) and[START_REF] Messersmith | Synthesis and barrier properties of poly(ε-caprolactone)-layered silicate nanocomposites[END_REF].

Fig. 7 .

 7 Fig. 7. Evolution of SME melt along the screw profile for several screw speeds, obtained from Ludovic © calculations.

Fig. 8 .

 8 Fig. 8. (a) Dispersion regimes of twin-screw extrusion process, (b) SEM illustration of OMMT agglomerates breakup, (c) TEM illustration of OMMT exfoliation by tactoid peel-off mechanism.

Acknowledgement

Authors thank Stephanie Bonny, Thierry Colin, Walid Bahloul, Nathalie Bozzolo and Gabriel Monge (CEMEF, France) for their precious contributions to this work, as well as Aleksey Drozdov (DTI, Denmark) for gently providing the masterbatch.

Financial support by the European Commission through FP7 project Nanotough-213436 is gratefully acknowledged.