Clément Perrinet

Edwin-Joffrey Courtial

Arthur Colly

Christophe Marquette

René Fulchiron
email: rene.fulchiron@univ-lyon1.fr

Pr * Clément Perrinet

René

Enhancing the Yield Stress in Liquid PDMS to Allow its 3D Printing: Hydrogels as Removable Fillers

Keywords: Additive Manufacturing, Silicone, Hydrogel, Suspensions, Yield Stress Fluid

For manufacturing parts of very soft materials by liquid deposition modeling (e.g., to mimic living soft tissues), formulations of 3D-printable polydimethylsiloxane have been developed, with the aim of increasing the yield stress of the liquid and reducing the final mechanical modulus. In the present work, suspensions of solid-like hydrogel particles, which are easily 3Dprintable, are prepared in order to generate yield stress, and the suspended phase is removed after manufacturing by taking advantage of the thermo-reversibility of the hydrogel behavior, resulting in porosity, which reduces the final rigidity. The reported approach is even more efficient than a previous approach based on emulsion formulations.

Introduction:

Silicone 3D printing has, for several years, been a major challenge in 3D printing technology in the medical devices industry [[ 1] ] . For decades, silicone (composed largely of polydimethylsiloxane, PDMS) has been widely used in the medical devices industry, owing to its biocompatibility due to high chemical stability which prevents interactions with living cells [[ 2] - [ 4] ] , and for its softness, due to its flexible backbone structure composed of alternating silicon and oxygen atoms. This softness is essential for engineering objects which reproduce the mechanical behavior of human tissues [[ 5] - [ 9] ] . The Young's modulus of all human tissues ranges from 10 kPa to 10 MPa [[ 10] ] , with cartilaginous tissues (trachea, esophagus, muscles) above 1 MPa, and very soft tissues below 100 kPa [[ 11] ] . PDMS formulations are often presented as liquid materials which require curing to get a solid and constant shape. Once cured, the silicone is infusible, i.e. un-printable, thus, the process of shaping needs to occur before the curing. 3D printing processing is subject to dynamic innovations, and established categories such as fused deposition modeling (FDM), selective laser sintering and UV curing are becoming less relevant. The printings in this work are conducted with a liquid deposition modeling (LDM) system, derived from FDM. LDM involves a driven syringe depositing the viscous formulation on a tray, without any heating system.

Innovation in processes and material formulations have been recently developed in order to target sophisticated parts made of soft tissues. For example, by dip-coating and leaching techniques, soft materials mimicking soft vascular tissues have been obtained [[ 12] ] ; however, the process is an indirect 3D printing process, since a rigid template must be previously formed.

The printing of liquid PDMS of low viscosity (typically from 0.5-5 Pa s) with LDM technology is a paradoxical challengeliquid PDMS requires high viscosity to keep a given shape, and the cured PDMS needs to be as soft as possible to mimic living tissues. Usually, fillers are added in order to make a liquid more viscous. However, these fillers also confer a high Young's modulus to the cured material [[ 13] ] .

As described in a previous report [[ 14] ] , the main challenge to countering this paradox is enhancing the yield stress behavior of the liquid silicone. Yield stress fluids are characteristic of a biphasic or a bi-component fluid. Examples of yield stress materials include concentrated emulsions, such as cosmetic creams, toothpastes, foams, polymer gels, slurries, and some composites [[ 15] - [ 18] ] . The elastic or solid-like behavior under weak stress is related to interactions between these inclusions in a main phase. The yield stress corresponds to the breakage or modification of such interactions. This may be the breaking of a percolation network continuity or the elastic deformation of a droplet in an emulsion. The viscosity under a sufficient stress decreases, and the system becomes flowable. In addition, for most of these systems, at rest, the microstructure reforms or evolves spontaneously in order to rebuild the network. If the microstructure re-establishes at rest, an increase of apparent yield stress with time is observed [[ 19] ] , revealing the thixotropic character of the material.

For silica/PDMS formulations, adding polyethylene glycol (PEG) [[ 14] ] creates a weak network which changes the behavior of the system at rest. For a low-filled PDMS, it has been proposed that an emulsion can be made which will enhance the yield stress of the system, and allow the printing of such formulations [[ 20] ] . It should be mentioned that emulsion formulations have already been used for 3D printing, but with rigid materials, such as photocurable polycaprolactone [[ 21] ] or acrylate polymer [[ 22] , [ 23] ] . The aim was essentially to obtain a very porous final rigid scaffold.

In this work, which deals with nearly-unfilled PDMS, it is proposed to synthesize suspensions of soft, hydrosoluble inclusions in PDMS, in order to enhance the yield stress before curing and wash off the fillers after curing, creating a porous system with a low Young's modulus, comparable to soft human tissues.

The existence of yield stress in filled polymers is a well-known phenomenon, described in several systems [[ 13] , [ 24] - [ 26] ] . It arises due to the generation of a percolated network of fillers in the polymer matrix. This network is characterized by the attractive forces between fillers, which impact the magnitude of the yield stress. This yield stress is highly dependent on the volume fraction of inclusions [[ 26] ] , up to a maximum close packing which represents the maximum possible fraction that can be inserted in the continuous matrix. This maximum packing value can vary between 0.52 and 0.70, depending on the system [[ 27] ] . The percolation threshold is another characteristic value whose magnitude is highly dependent on the shape of the inclusions and their interactions. For microscopic inclusions, it is usually around 20% v/v, and it can be as low as 1% v/v for nanometric inclusions [[ 13] ] . The percolation threshold may be described as the lowest volume fraction of inclusions at which every inclusion is in contact with at least two other inclusions, creating a continuous network of inclusions in the polymeric matrix. In this work, the fillers are thermo-reversible hydrogels which are very soft solids that are easily breakable or deformable, and which cannot be considered as hard spheres. Thermo-reversible hydrogels can be turned into a liquid when the temperature is increased, or decreased, to a characteristic temperature [[ 28] ] . These hydrogels are not stabilized by crosslinking [[ 29] ] . Only the polymeric conformation in water, arising from soft interactions such as hydrogen bonding, sustains the shape of the system. Thus, the material is a very breakable solid which is also hydrosoluble.

Results and discussion

2.1.Hydrogel

Hydrogels are polymers with hydrophilic functions which enable the trapping of water molecules in their network [[ 28] ] . Hydrogels can be divided into two categories, based on the chemical or physical nature of the cross-link junctions. Permanent bonds are obtained by chemical crosslinking, while temporary bonds constitute physical networks. These bonds can result from polymer chain entanglements, ionic interactions, hydrogen bonds, or hydrophobic interactions

[[ 28] ] .
In this work, only physical hydrogels are of interest, as these gels require solvation with a hydrophilic solvent after processing. The first physical chosen hydrogel was Pluronic F127, provided by BASF, which is of the poloxamer family. Poloxamers are copolymers which combine polyethylene oxide (PEO) and polypropylene oxide (PPO). In water, poloxamers are present as unimers, however, with increasing concentration, a transition to micelle conformation can occur. Moreover, this transition may also occur by increasing temperature. In this work, poloxamer gels were formed by adding 20 wt. % poloxamer to water. This is above the critical micelle concentration (CMC) (18 wt. %). The unimer-micelle transition occurs near 18 °C [[ 30] , [ 31] ] . Accordingly, above 18 °C, poloxamer are in micelle conformation [[ 30] ] , with the hydrophilic parts of polymer structures spread toward the outside, allowing interactions between micelles, leading to gelation [[ 29] ] . Below 18 °C, the gel is destroyed and becomes liquid. Above 70 °C, the poloxamer gel again turns into a liquid. Thus, the gelation of poloxamer in water is possible in a temperature window from 18 °C to 70 °C The second physical hydrogel used is constituted of agar, a well-known natural polymer, usually sold as a pork gelatin substitute. It is a natural polymer of galactane, which has the property to solubilize in hot water and form a gel after cooling. The gel is formed from interactions between polymer chains, owing to helical portions which lead to associations by double-helices. This association is lost at high temperatures, where the agar molecules adopt a random coil conformation, with the transition temperature being approximately 40 °C [[ 32] ] . This type of conformation is predominant in the sol, but can also exist as connecting lengths in the gel structure, imparting some elasticity. Agar gels represent an important hysteresis in the coolingheating process, and the transitional temperature window between the liquid and gel states is large. An applied temperature of 90 °C may be needed to liquefy the system from the gel state, though it must be cooled to 30 °C in order to recover gel consistency.

Rheological behavior

Rheological experiments

The characterization of yield stress could be performed using several methods [[ 33] ] . To get a quantitative measure, the stress growth experiment is a simple method, as it gives an absolute value of the yield stress and measures the impact of the inclusion volume fraction. A more qualitative way is to perform a frequency sweep, which will show a plateau at low frequencies, signifying a percolated network in the system. Figure 1 shows the rheological characterization of the different formulations. It is important to mention that, for these experiments, only one part of the PDMS was used to avoid cross-linking, which would have make experiments impossible due to the relatively short pot-life (20 min) of the RTV 3503 (in the present work, although part B was used, the results are considered similar to those which would have been obtained if part A was used). From these results, it is clear that the higher the amount of hydrogel, the higher the yield stress value. Nevertheless, it should be remembered that the PDMS phase must remain continuous in order to ensure the integrity of the final objectfurthermore, the blend of hydrogel/PDMS must form a co-continuous phase structure. Hence, for the agar gel/PDMS system, a maximum volume fraction of 65 % v/v was obtained. This value is the expected one for most filled formulations [[ 27] , [ 34] , [ 35] ] . This maximum packing value is linked to the maximum yield stress value, which is approximately 240 Pa. In comparison, for the poloxamer gel/PDMS system, a maximum packing value of only 52 % v/v was obtained, which is quite low, according to the literature, but has been previously observed [[ 27] ] . Its maximum yield stress value is 220 Pa, close to the value obtained for agar gel/PDMS. The quality of the percolated network is seen in the frequency sweep test results, which shows that the plateau at low frequency appears at around 20 % v/v for poloxamer gel/PDMS systems, and at 30 % v/v for agar gel/PDMS systems. The important increase of the yield stress value, owing to the creation of a percolated network, should enable the 3D printing of such filled PDMS formulations.

Rheological modeling

The evolution of a suspension's rheological parameters, including the yield stress, often follows a power law of the difference between the inclusion volume fraction (𝛷) and the volume fraction at the percolation threshold (𝛷 𝑝 ) [ For hard filler suspensions, the exponent a is reported to be highly dependent on the interactions between the particles and the suspending liquid. For example, for fumed silica suspensions in PDMS, Paquien et al. observed a decrease in a from 7.2 to 2.8 with increasing number of hydrophobic silica surface treatments [[ 16] ] . Using a similar approach, Auscher et al. [[ 40] ] have shown that, for zirconia particles dispersed in a polyethylene matrix, a hydrophobic treatment of zirconia with stearic acid leads to reducing both the percolation threshold and the exponent a (from 3.6 to 2.1, for the percolation law applied to the yield stress). This variation of the exponent has been explained by considering the weakening of the interactions between particles by the presence of molecules at their surface, which favors interactions with the suspending liquid.

Thus, the contacts between particles become softer, and the global rigidity of the network increases at a lower rate with the contact number (i.e., with the volume fraction of fillers).

The measured yield stress as a function of the inclusion volume fraction was analyzed, with consideration to Equation (1). The first crucial parameter in this equation is the inclusion volume fraction at the percolation threshold (𝛷 𝑝 ). This parameter is usually not easy to determine accurately, and its value can affect determination of the other parameters. In this work, it was simply considered that 𝛷 𝑝 was reached when the yield stress was detectable. In addition, it was verified that the value was consistent with the storage modulus curves, where a marked plateau in the low frequency range is obtained for volume fractions above the threshold 𝛷 𝑝 . The other parameters (m and a) were determined by simple regression.

Figure 2 shows the suitable prediction of the experimental yield stress values by the calculated curves fit to the data. The obtained parameters are given in Table 1, together with the maximum possible hydrogel fractions and the corresponding yield stresses. The relatively low values (<2) obtained for the exponent a compared to those obtained for hard filler suspensions may be explained by the fact that the suspended hydrogels are highly soft, so that the contacts between particles are not punctual and rigid but rather allow the particles to be deformed, leading to a "soft" percolated network.

3D Printing

For the following 3D printing tests, the most interesting formulations (i.e. those with the highest yield stresses) from each system were chosen, namely PDMS + 52% v/v of poloxamer gel (PDMS+52%Plu) and PDMS + 65% v/v of agar gel (PDMS+65%Ag). Figure 3 shows the 3D printing results obtained for the hexagonal shape selected to test the material's properties, with a low surface area sustaining the object and an increasing over-hanging of the hexagon's walls. It must be pointed out that the printed objects shown in Figure 3c and Figure 3d have been washed to remove the hydrogel. This last step will be detailed in the next section. The unmodified PDMS formulation is clearly unsuitable for 3D printing (see Figure 3b), as the liquid PDMS behaves like a low-viscosity liquid with no yield stress, and, consequently, no 3D shape was obtained. For modified formulations with yield stresses of 240 Pa (Figure 3c) and 220

Pa (Figure 3d), objects with height 2.5 cm and medium complexity were printed, with satisfactory fidelity (>92%). Details of the measurements are reported in Supporting Information 1. As discussed in a previous report [[ 14] ] , increasing yield stress enables the printing of more complex structures. The first layers can be printed and withstand the weight of upper layers without collapsing [[ 41] ] . Basically, the higher is the yield stress, the easier is the 3D printing process because it makes the under construction object stronger to support the successive added layers. In the present work, 3D printing tests have not been systematically carried out with different amounts of hydrogels so that it is difficult to determine the minimum yield stress needed for the printing (obviously this can depend on the printed object complexity). However, the yield

a b c d
stress measurement as a function of the hydrogel amount (and its modeling by Equation 1) may evidently be a guide to choose the appropriate formulation and explore the printing possibilities following the criterions that the yield stress, and thus the hydrogel amount, must be high enough.

However, the maximum possible amount of hydrogel must not be exceeded otherwise the phase inversion will ruin the process (the PDMS must remain a continuous phase). Moreover, the evolution of the yield stress and the maximum amount of hydrogel are dependent on the hydrogel nature (see Figure 2). In that regard, the rheological measurements are an essential tool to characterize the suspension.

Moreover, it can be added that the the overall appearance still varies with the formulation. The object made from PDMS+65%Ag has a rugged surface aspect, whereas the object made from PDMS+52%Plu appears smoother. This comes from the difference in the amount of inclusions removed after cleaning and from differences between inclusion sizes, which will be discussed later.

Solvent extraction

A selective extraction was conducted in order to wash the printed objects of their hydrogels.

Solvent selection depends on the hydrogel propertyhydrogels have to be brought to the liquid phase (both gels are thermally reversible), and inclusions need to be accessible to the solvent. A PDMS swelling solvent could therefore be useful.

For poloxamer gel/PDMS systems, the maximum volume ratio is quite low (52% v/v). Although the interconnectivity of hydrogel particles is desired, it must be considered that a (small) fraction of the particles are isolated from the global network (leading to some closed porosity after extraction). Ethanol is a well-known solvent for swelling PDMS, and water is the best solvent for solvating the poloxamer. Thus, a 50:50 mix of both solvents was heated to ebullition, poloxamer gel/PDMS objects were immersed in the co-solvent, and a reflux system was installed. For agar gel/PDMS objects, the agar volume fraction is relatively high, so that the swelling of PDMS by the solvent is less necessary than for polaxamer gel/PDMS objects. Moreover, the agar gel flows at a higher temperature than the poloxamer gel, and the water/ethanol refluxing mix does not reach 90 °C. Thus, boiling water is preferred for agar gel/PDMS objects. The specific extraction solvents applied to both systems each succeeded in extracting gel inclusions from the cured PDMS, verified by thermogravimetric analysis (TGA). These TGA experimental data are available in Supporting Information 2, and show the quasi-total extraction of the hydrogel inclusions (the curves for PDMS and PDMS+Gel washed off are superimposed up to 400°C), apart from 3-4 % of agar molecules, which may remain in the PDMS after washing.

Figure 4 shows SEM pictures obtained for both formulations (PDMS+65%Ag and PDMS+52%Plu), revealing the porosity after solvent extraction. The pores are clearly much larger for the sample formulated with agar gel (typically 200-400 m in diameter) than for the sample formulated with the poloxamer (typically 10-20 m in diameter). From these pictures, it can be concluded that, although the material prepared with the poloxamer shows less porosity due to less hydrogel being incorporated, it may still be of interest due to its very fine porosity. In that respect, it must be pointed out that the porosity structure is governed by first the total amount of hydrogel but also, and above all, by the initial quality of the suspension and the aptitude of the hydrogel to be thinly fragmented during the mixing. It arises that the formulation with the poloxamer leads to much finer dispersion than with the Agar (so fine that a lot of pores may even not be visible by SEM). The material prepared with the agar gel shows much larger pores, likely to the detriment of the mechanical resistance of the material at high deformation.

Young's modulus

As previously mentioned, one of the main goals in this work was to obtain a PDMS material with a very low Young's modulus, in order to mimic soft human tissues under 100 kPa. The mechanical measurement, shown in Figure 5, shows a large decrease in Young's modulus from the initial value of the PDMS material, owing to the protocols used in this work. It is possible to decrease Young's modulus from 250 kPa (PDMS) to 50 kPa for the PDMS+52%Plu washed system, and further to 25 kPa for the PDMS+65%Ag washed system, the porosity in the latter being a more contributing factor. Incidentally, this strong decrease in stiffness clearly indicates that the possible shrinkage of the material after extraction is not very important; otherwise the porosity would have been reduced, thus preventing the stiffness reduction.

Conclusion

The 3D printing of soft PDMS is a challenge for the medical devices industry. The liquid deposition modeling 3D printing system is a cheap, accurate and simple technology which can meet this challenge. It requires an appropriate understanding of the printed materials' rheological properties. With this considered, the yield stress turns out to be a key parameter with which to enlarge the scope of printability of new materials via liquid deposition modeling technology.

Here, a new approach to enhance this yield stress fluid behavior by adding soft hydrogel fillers like poloxamer and agar gels, without hardening the final material, was described. Furthermore, the removal of these fillers after curing of the printed PDMS creates a porous matrix, which is significantly softer than the initial PDMS, contributing to the successful printing of non-trivial sharpened PDMS objects with Young's modulus below 50 kPa. Each technical solution which further enhances the yield stress of the initial liquid PDMS will contribute to the printing of even more complex shapes.

Figure 1 :

 1 Figure 1: Rheological Characterization: a) Stress growth experiments at 1 s -1 for agar gel/PDMS systems, b) Stress growth experiments at 1 s -1 for poloxamer gel/PDMS systems, c) Frequency sweep experiments for agar gel/PDMS systems, d) Frequency sweep experiments for poloxamer gel/PDMS systems. For all experiments, only part B of PDMS was used.

Figure 2 :

 2 Figure 2: Yield stress as a function of the inclusion volume fraction. Symbols: experimental values, solid lines: Percolation laws (Eq. 1)

Figure 3 :

 3 Figure 3: Printing results: a) control object, b) unmodified PDMS object, after curing, c) PDMS+65%Ag) object, after curing and washing, d) PDMS+52%Plu, after curing and washing.

Figure 4 :

 4 Figure 4: SEM observations: a) sample PDMS+65%Ag after extraction of the Agar, b) PDMS+52%Plu, after extraction of the Poloxamer.

Figure 5 :

 5 Figure 5: Compression measurements (repeated 3 times) of unmodified PDMS silicone (dotted lines), PDMS+52%Plu after extraction of the poloxamer (dashed lines) and PDMS+65%Ag after extraction of the agar (solid lines).

  [ 13] , [ 35] -[ 39] ] , as shown in Equation (1):

		a 250							b 250
								PDMS + 30%					PDMS + 20%
								PDMS + 42%					PDMS + 40%
		200					PDMS + 52% PDMS + 58% PDMS + 65%	200			PDMS + 48% PDMS + 52%
	Stress (Pa)	0 50 100 150	0	1000	Strain (%)	2000	3000	Stress (Pa)	0 50 100 150	0	1000 Strain (%)	2000	3000
		10000 c							10000 d
			1000								1000
	Storage Modulus (Pa)	0.1 1 10 100					PDMS PDMS + 30% PDMS + 42% PDMS + 52% PDMS + 58%	Storage modulus (Pa)	1 10 100 0.1			PDMS PDMS + 20% PDMS + 40% PDMS + 48%
								PDMS + 65%						PDMS + 52%
			0.01								0.01
				0.1		1	10	100	1000			0.1	1	10	100	1000
					Angular frequency (rad/s)					Angular frequency (rad/s)
	𝜎 𝑐 = 𝑚 * (𝛷 -𝛷 𝑝 ) 𝑎								(1)

Table 1 : Fitted parameters of Eq. 1 (maximum hydrogel fractions and corresponding yield stresses), for poloxamer gel/PDMS and agar gel/PDMS.

 1

	Suspension	𝛷 𝑝	a	m	𝜎 𝑐 𝑚𝑎𝑥	𝛷 𝑚𝑎𝑥
	Poloxamer-	0.10	1.99	981	223	0.52
	gel/PDMS
	Agar-gel/ PDMS	0.37	1.68	1920	244	0.65

Acknowledgments:

This work was supported by the French government through FASSIL project, selected by FUI (Fonds Unique Interministériel) and by the region Auvergne-Rhône-Alpes. The authors especially thank Jean-Marc Francès and Damien Djian from Elkem Silicones for materials supply and very helpful discussions. The authors also acknowledge the 'Centre Technologique des Microstructures (CT)' of University Lyon 1 for the SEM experiments and especially Pierre Alcouffe of IMP, UMR5223 laboratory.

Methods

Materials:

The PDMS used was Bluesil RTV 3503 from Elkem Silicones. It is provided in two liquid parts:

Part A containing vinyl groups, and part B containing Si-H groups. Equal volumes of each part require mixing for the hydrosilylation reaction to occur, leading to a cross-linked material. The pot-life of the blend at ambient temperature is approximately 20 min. It should be noted that a small amount of silica (4.5% v/v) is included in this PDMS formulation. Hydrogels were synthesized by adding corresponding amounts of polymer powder, polaxomer (20 wt. %) (Pluronic F127, Sigma Aldrich) or agar (5 wt. %) (Sigma Aldrich), and mixing in a measured amount of boiling water, under stirring and reflux of water vapor.

Suspensions preparation:

Suspensions of poloxamer gel/PDMS were prepared by adding a corresponding amount of both materials, premixing by hand with an iron stick followed by high shearing in an Ultra-Turrax T50 Homogenizer (IKA) at 7000 tr min -1 , until the formulation obtains a gel consistency, or otherwise for 5 min, for the lowest levels of hydrogels. Agar gel/PDMS suspensions are, in a liquid state, first placed in an oven at 90°C in a closed recipient, followed by mixing at this temperature as for the poloxamer gel suspensions. Being much harder than the Poloxamer gel, the agar gel's dispersion in the solid state was not possible with an Ultra-Turrax mixer. Hydrogel content values have been selected empirically so that, on the one hand, an obvious effect was detected on the rheological behavior and, on the other hand, the value did not overpass the maximum possible, which would lead to loss of the PDMS phase continuity (leading to a friable final material). The obtained suspensions were stable for at least several days, despite no emulsifier being used.

Rheological tests:

Rheological measurements were conducted using an ARES G2 rheometer (TA Instruments, USA) with a cone-plate geometry of 25 mm diameter and a cone angle of 0.1002 rad. The yield stress measurements were performed in transient mode, carrying out a stress growth experiment at a constant strain rate of 1 s -1 . The stress/strain curve presented a maximum of stress which was taken as the static yield stress value.

3D Printing process:

A liquid deposition modeling (LDM) device with a COSMED 333 Cartesian 3D printer (Tobeca, France) of 10 μm movement precision was used to print the suspensions. Bi-component cartridges of 50 mL (Nordson EFD, USA) were filled with PDMS parts A and B, each being previously blended with the desired amount of hydrogel. It can be mentioned that because of the very low viscosity of the liquid PDMS, no degassing was required; no bubbles were trapped in the blend. The blending of the two parts is ensured at the exit of the cartridge, owing to a static mixer positioned upstream of a 200 µm diameter conical nozzle (Nordson EFD, USA). Extrusion was ensured using a pneumatic system, Equalizer and Ultimus V (Nordson EFD, USA).

Dispensing pressure was adapted for each suspension. 3D printing was controlled via the Repetier Host software (Repetier, V2.0.1, Germany) at a printing speed of 10 mm s -1 . The STL file was a homemade hexagonal model of medium complexity [[ 6] ] , which can be printed without any non-print travel and has a small overhang of 5° (0 being vertical). The file was sliced with the Slic3r software (Slic3r, V3, Italia) using adapted printing parameters. The control sample was printed with Verowhite resin using the Object30 Pro 3D printer (Stratasys, USA). This rigid sample was used as a reference to evaluate the dimensional fidelity of the PDMS samples.

Solvent extraction:

The cross-linked silicone containing the hydrophilic gel was immersed in boiling solvent for 12 h, then dried at 80 °C for 12 h and then at 100 °C for a further 12 h. The solvent was water (b.p. 100 °C) for PDMS+65%Ag sample, and a water/ethanol mixture (50/50) (b.p. approximately 85°C) for PDMS+52%Plu. The sample was previously shaped using a small laboratory press equipped with a cylindrical mold (13 mm diameter, 7 mm thickness), also used for mechanical characterization.

Purification measurements:

The first analysis was conducted by measuring the mass loss after purification. TGA tests were conducted using a Q500 TGA (TA Instruments), with a temperature ramp of 5 °C min -1 , up to 600 °C.

Mechanical characterization:

Compression tests were carried out to determine Young's modulus. Samples of 13 mm diameter and 7 mm thickness were prepared in a small laboratory press (as for solvent extraction experiments). To characterize mechanical behavior, each sample was squeezed between plates (25 mm diameter) on an ARES G2 Rheometer, at 0.01 mm s -1 for 600 s. Nominal stress was calculated by dividing the measured force by the sample section (132.7 mm 2 ). The nominal strain was calculated by dividing the plate displacement by the initial sample thickness. Then, Young's modulus was obtained from the slope of the stress/strain plot for the first 0.1 of strain (the given values are the average of 3 measurements).

SEM observations: The cured systems were observed after hydrogel extraction by SEM. A Merlin electron microscope (from Zeiss) was used to characterize the sample PDMS+52%Plu, using a 2 kV electron beam and a magnification of 190×. For the sample PDMS+65%Ag, a Quanta 250 microscope (FEI) was used, using a 2 kV electron beam and a magnification of 100×.

Conflict of Interest

The authors declare no conflict of interest.

Supporting Information.

Enhancing the Yield Stress in Liquid PDMS to Allow its 3D Printing: Hydrogels as Removable Fillers Clément Perrinet, Edwin-Joffrey Courtial, Arthur Colly, Christophe Marquette, René Fulchiron Supporting Information 1:


Marjorie Marcourt

Philippe Cassagnau

René Fulchiron
email: rene.fulchiron@univ-lyon1.fr

Dimitri Rousseaux

Olivier Lhost

Simon Karam

High Impact Polystyrene / CNT Nanocomposites: application of volume segregation strategy and behavior under extensional deformation

Keywords: Nanocomposites, Extensional Viscoelasticity, Electrical conductivity

The present work focuses on the analysis of two composites: a pure amorphous Polystyrene and a rubber modified Polystyrene (High Impact Polystyrene), both filled with Carbon Nanotubes (CNT) for generating Conductive Polymer Composites (CPC). Recently, CPC has been obtained with very low filler content following a volume segregation strategy which maintains the filler in one continuous phase. This phenomenon enhances the contacts between fillers and consequently gives birth to conductive composites with ultra-low filler concentration. In this work the two composites are analyzed using a specific set-up that gives the possibility to monitor both electrical conductivity evolution and the elongational stress in the melt state. This set-up allows determining the maximal deformation that nanocomposites can undergo before becoming insulating. In addition, the dynamic of the network evolution that is, its destruction and structuring has been analyzed. When the destruction is predominant, the two composites behave the same. However, we have observed a slight disparity when there is a possible competition between destruction and structuring during extensional deformation. This difference has been accounted to the presence of the nodules that might locally prevent the structuring mechanism during extensional deformation.

A. Introduction

Owing to their good mechanical [START_REF] Demczyk | Direct mechanical measurement of the tensile strength and elastic modulus of multiwalled carbon nanotubes[END_REF][START_REF] Walters | Elastic strain of freely suspended single-wall carbon nanotube ropes[END_REF], electrical [START_REF] Yao | High-field electrical transport in single-wall carbon nanotubes[END_REF], and thermal [START_REF] Berber | Unusually high thermal conductivity of carbon nanotubes[END_REF] properties and their specific shape, Carbon Nanotubes (CNTs) are the ideal fillers for the generation of conductive polymer nanocomposites. This specific filler, due to its large aspect ratio, leads to composites with a lower percolation threshold compared to Carbon Black (CB). To push further the boundaries of percolation threshold, a new strategy has emerged. The idea is based on the tailored filler localization in the nanocomposite in order to enhance the formation of the percolated network by confining the fillers. The CNT network architecture design is based on the volume exclusion or on forced segregation.

One strategy is to use immiscible polymer blends in order to force the filler segregation by a privileged affinity between one polymer and the CNTs. The use of immiscible blends for the generation of Conductive Polymer Composites (CPCs) was first investigated by Sumita et al. [START_REF] Sumita | Dispersion of fillers and the electrical conductivity of polymer blends filled with carbon black[END_REF][START_REF] Sumita | Double percolation effect on the electrical conductivity of conductive particles filled polymer blends[END_REF] with CB. The goal is to generate at least one continuous phase in which the fillers will be located. This volume restriction will enhance the formation of a percolated network. Afterward, this strategy has been investigated in a lot for different kind of fillers [START_REF] Gödel | Selective localization and migration of multiwalled carbon nanotubes in blends of polycarbonate and poly(styrene-acrylonitrile)[END_REF][START_REF] Périé | Co-continuous nanostructured nanocomposites by reactive blending of carbon nanotube masterbatches[END_REF][START_REF] Thongruang | Volume-exclusion effects in polyethylene blends filled with carbon black, graphite, or carbon fiber[END_REF][START_REF] Warth | Mechanical properties and electrical conductivity of carbon-nanotube filled polyamide-6 and its blends with acrylonitrile/butadiene/styrene[END_REF][START_REF] Pötschke | Morphology and electrical resistivity of melt mixed blends of polyethylene and carbon nanotube filled polycarbonate[END_REF][START_REF] Göldel | Shape-Dependent Localization of Carbon Nanotubes and Carbon Black in an Immiscible Polymer Blend during Melt Mixing[END_REF][START_REF] Pötschke | A novel strategy to incorporate carbon nanotubes into thermoplastic matrices[END_REF][START_REF] Wu | On the improved properties of injection-molded, carbon nanotube-filled PET/PVDF blends[END_REF][START_REF] Pötschke | Morphology and electrical resistivity of melt mixed blends of polyethylene and carbon nanotube filled polycarbonate[END_REF] Generally, the determination of the filler localization is achieved with only thermodynamic consideration. The minimization of the interfacial energy will drive fillers into the most energetically preferred phase. The localization may be predicted by the calculation of the interfacial energy. Considering a blend made of two polymers P1 and P2 and CNT fillers, the wetting parameter ω12 can be calculated according to Young's equation for the adjustment of wetting angles on an ideal plane [16]. with ϒi-j representing the interfacial tension between the components i and j which are alternatively the filler, the polymer P1 or the polymer P2. The value of ω12 forecasts the filler localization: if ω12 >1 MWCNT will be in the P1 matrix, whereas, if ω12 < -1 they will be in the P2 and finally if -1< ω12 < 1, MWCNT will be found at the interface of the different matrices.

The thermodynamic prediction is enough when considering two polymers with truly different polarities and surface energy [START_REF] Yao | High-field electrical transport in single-wall carbon nanotubes[END_REF][START_REF] Baudouin | Localization of carbon nanotubes at the interface in blends of polyamide and ethylene-acrylate copoly-mer[END_REF][START_REF] Göldel | Shape-dependent localization of carbon nanotubes and carbon black inan immiscible polymer blend during melt mixing[END_REF][START_REF] Göldel | Selective localization andmigration of multiwalled carbon nanotubes in blends of polycarbo-nate and poly(styrene-acrylonitrile)[END_REF][START_REF] Zhang | Morphology and electrical properties of polyamide 6/polypropylene/multiwalled carbon nanotubes composites[END_REF]. However, to be more accurate, the kinetic aspect must be considered by taking into account the processing conditions, the physical properties of the CNTs, the filler dispersion state and the mixture procedure. For instance, some have observed that the addition of nanofillers can refine and even stabilize the continuous microstructure [START_REF] Li | Kinetically trapped cocontinuous polymer morphologies through intraphase gelation of nanoparticles[END_REF][START_REF] Chung | Self-regulated structures in nanocomposites by directed nanoparticle assembly[END_REF]. The best scenario for minimizing the percolation threshold is when the fillers are localized at the interface of the polymer phases. However, this specific case is quite hard to achieve. For instance, Gödel and coworkers have put in the light the impact of the filler shape. Indeed, fillers with a low aspect ratio (such as CB) segregated at the interface of Polycarbonate/SAN blend are more efficient to stabilize the morphology than CNTs [START_REF] Warth | Mechanical properties and electrical conductivity of carbon-nanotube filled polyamide-6 and its blends with acrylonitrile/butadiene/styrene[END_REF].

Nevertheless, the generation of composites with a controlled localization of the filler can be achieved and tuned by the functionalization of the filler to control the chemical affinity with a specific phase, by adapting the polarity [START_REF] Elias | Morphology and rheology of immiscible polymer blends filled with silica nanoparticles[END_REF], or grafting of polymer chains [START_REF] Du | Functionalization of MWCNT with p(mma-co-s) copolymers via ATRP: influence on localization of MWCNT in SAN/PPE 40/60 blends and on rheological and dielectric properties of the composites[END_REF][START_REF] Bose | Fractionated crystallization in PA6/ABS blends: Influence of a reactive compatibilizer and multiwall carbon nanotubes[END_REF] or by kinetic consideration [START_REF] Feng | A method to control the dispersion of carbon black in an immiscible polymer blend[END_REF][START_REF] Persson | Viscosity difference as distributing factor in selective absorption of aluminium borate whiskers in immiscible polymer blends[END_REF][28][START_REF] Stickel | Fluid mechanics and rheology of dense suspensions[END_REF][START_REF] Van Puyvelde | Review on morphology development of immiscible blends in confined shear flow[END_REF][START_REF] Baudouin | Polymer blend emulsion stabilization using carbon nanotubes interfacial[END_REF][START_REF] Baudouin | Interface localization of carbon nanotubes in blends of two copolymers[END_REF].

Leaving apart all experimental conditions, the conductivity of such composites can be tuned by the blend composition (i.e. volume and morphology) of the phase containing the filler. For instance, Xu and coworkers have experienced an increase of five decades in conductivity by varying the blend composition [START_REF] Xu | Enhancement of electrical conductivity by changing phase morphology for composites consisting of polylactide andpoly (ε-caprolactone) filled with acid-oxidized multiwalled carbon nanotubes[END_REF]. Only few works dealt with the co-polymers of Polystyrene (PS). For instance, Moldenaers and coworkers [START_REF] Bharati | Tuning the phase separated morphology and resulting electrical conductivity of carbon nanotube filled PaMSAN/PMMA blends by compatibilization with a random or block copolymer[END_REF][START_REF] Bharati | Enhancing the conductivity of carbon nanotube filled blends by tuning their phase separated morphology with a copolymer[END_REF] achieved to gain four decades in conductivity by playing on the molecular weight Mw and the structure of poly(styrene-random/block-methyl methacrylate) for the generation of PαMSAN/PMMA 40/60 filled with MWCNT. In addition, Mclory et al. [START_REF] Mcclory | Influence of screw speed on electrical and rheological percolation of melt-mixed high-impact polystyrene/MWCNT nanocomposites[END_REF] have dispersed MWCNT in High Impact Polystyrene (HIPS) (melt mixing strategy) and obtained a rather large electrical percolation threshold ( ≈2wt%). By increasing the bead content from 30 to 60 wt% at a constant MWCNTs content of 0.6wt% Shrivastava and coworkers [START_REF] Shrivastava | Influence of selective dispersion of MWCNT on electricalpercolation of in-situ polymerized high-impact polystyrene/MWCNT nanocomposites[END_REF] have obtained an increase of 2 decades of the electrical conductivity.

In addition to the increase of the electrical properties, the aggregates form an elastic network within the matrix. This is characterized by the storage modulus that becomes independent of the frequency in the low frequency range (𝐺 ′ ∝ 𝜔 0 ; 𝐺 ′ = 𝐺𝑒). In the literature the variation of the equilibrium modulus as a function of the filler concentration has been widely investigated [START_REF] Klüppel | Fractal structures in carbon black reinforced rubbers[END_REF][START_REF] Gennes | On a relation between percolation theory and the elasticity of gels[END_REF][START_REF] Majeste | A kinetic model for silica-filled rubber reinforcement[END_REF] and it is well accepted that the value of the storage modulus illustrates the whole response of the local contribution within the network, depending on the network structure and the filler-filler physical connections. More precisely, the filler concentration can be linked to the equilibrium modulus by combining fractal concept for the description of the filler structure and Kantor-Webman model that describes the elasticity of a chain made of particles. The concept of fractal is widely used for composites with filler in the nano to micrometric range [START_REF] Moreira | Aggregation of Carbon Nanotubes in Semidilute Suspension[END_REF][START_REF] Alig | Establishment, morphology and properties of carbon nanotube networks in polymer melts[END_REF][START_REF] Ma | The rheology and modeling of chemically treated carbon nanotubes suspensions[END_REF][START_REF] Jouault | Well-dispersed fractal aggregates as filler in polymer-silica nanocomposites: long-range effects in rheology[END_REF][START_REF] Jouault | Multiscale characterization of filler dispersion and origins of mechanical reinforcement in model nanocomposites[END_REF]. Different models have been exposed. Among them, Heinrich and Klüppel have proposed a Cluster-Cluster Aggregation (CCA) model that differs from the others with the assumption that fillers position can fluctuate around a mean value [START_REF] Klüppel | Structure and properties of reinforcing fractal filler networks in elastomers[END_REF][START_REF] Heinrich | The role of polymer-filler interphase in reinforcement of elastomers[END_REF][START_REF] Klüppel | The role of disorder in filler reinforcement of elastomers on various length scales[END_REF]. This assumption can be applied to CNTs because these fillers in the nanometer range are highly sensitive to the polymer chains mobility. Heinrich et al. have made the assumption that the clusters act as molecular springs with an end-to-end distance ξ, composed of NB backbone units of length d. The backbone can be described as NB with df,B a fractal dimension that describes the backbone connectivity. From the expression of the constant force of the cluster backbone, they have obtained an elastic modulus of the cluster backbone and finally from scaling arguments they have obtained the evolution of the whole elastic modulus (considering three-dimensional case) as:

𝐺 𝑒 ≈ 𝐺 𝐴 𝜙 3+𝑑 𝑓,𝐵 3-𝑑 𝑓 Equation 2
where GA is the elastic modulus of a cluster unit, 𝜙 is the volume fraction, 𝑑 𝑓,𝐵 ≈ 1.3 for the smallest fractal dimension of the CCA-cluster backbone and 𝑑 𝑓 ≈1.8, thereby the exponent (3 + 𝑑 𝑓,𝐵 )/(3 -𝑑 𝑓 ) ≈ 3.6 [START_REF] Klüppel | Fractal structures in carbon black reinforced rubbers[END_REF].

However, the exponents reported in the literature for MWNT dispersed in both thermoplastic and thermoset matrix shows a great discrepancy. For instance, Pötschke et al. have obtained 0.2 and 2.5 for MWCNT dispersed in respectively Polyurethane [START_REF] Pötschke | Thermoplastic polyurethane filled with carbon nanotubes for electrical dissipative and conductive applications[END_REF] and Polycarbonate [START_REF] Pötschke | Rheological and dielectrical characterization of melt mixed polycarbonate-multiwalled carbon nanotube composites[END_REF]. Hobbie and coworkers have observed a power law of 7.1 for MWNT dispersed in Polyisobutylene [START_REF] Hobbie | Nonequilibrium Phase Diagram of Sticky Nanotube Suspensions[END_REF]. In addition, Esteban et al. [START_REF] Ureña-Benavides | Dispersion and Rheology of Multiwalled Carbon Nanotubes in Unsaturated Polyester Resin[END_REF] has observed a power law of 1.7 for MWCNT dispersed in unsaturated polyester resin.

This paper aims at studying the volume segregation effect in HIPS filled with CNT composites. The morphology will be compared to a more simple material: a pure PS matrix filled with CNTs. The percolation threshold, the structure of the filler network, the concentration dependence of the equilibrium modulus and the composites behavior under extensional deformation using a specific set-up will be analyzed. A particular attention will be devoted to the dynamic of the filler network structuring and its destruction during extensional tests.

B. Experimental

1) Materials and blends preparation

The CNTs are the NC7000, supplied by Nanocyl a Belgium company. They are characterized by a diameter d around 9.5nm and a mean length of 1.5µm. The two matrices used are a PS with a melt flow index of 2.4 and a High Impact Polystyrene (HIPS) with a melt flow index of 2.6 were both supplied by Total. In HIPS, nodules of Polybutadiene (PB) are included to improve the impact strength of the material. The composites are melt mixed using a masterbatches dilution strategy and were supplied by Total as pellets. The specimens were compression molded at 200°C.

2) Morphology analysis

The morphologies have been investigated by Scanning Electron Microscopy (SEM) using a device LSM800 from Zeiss. The detection was ensured owing to in-Lens detector which is located inside the beam focusing lens. The observations have been carried out with a distance between the surface and the final condenser lens (the working distance WD) of around 5mm, an aperture size fixed at 30µm and the accelerating voltage ranging from 10 kV to 20 kV. As the in-Lens detector is very sensitive to surface roughness, the sample surface has been cut with a diamond knife to prevent any roughness and promote the contrast between electrically conductor filler and insulating matrix. For the HIPS composite, the sample surface was firstly immerged in Os04 solution for at least four days in order to increase the phase contrast and make easier the specimen preparation by rigidifying the PB nodules. The observation technique will not be detailed in the paper, however the reader can refer to studies on this method [START_REF] Li | The imaging mechanism, imaging depth, and parameters influencing the visibility of carbon nanotubes in a polymer matrix using a SEM[END_REF][START_REF] Li | Imaging of CNTs in a polymer matrix at low accelerating voltages using a SEM[END_REF]. In addition, Transmission Electron Microscopy observations have been carried out in order to complete the morphology characterization. Thin films have been cut at room temperature after the same specimen preparation as for the SEM characterization.

3) Conductivity measurement

Electrical properties analysis has been conducted on compression molded samples that have been additionally submitted to a quiescent treatment at 200°C for about 20 min. This supplementary thermal treatment enables the filler network to recover an equilibrium state in which most of the CNTs take part to the electrical conduction. Indeed, just after the compression molding, this state is not obtained. A colloidal silver paste was applied on the surface sample to ensure a good contact between the electrodes and the specimen surface. Owing to a Keithley 237 power supply, a 10 volt Direct Current (DC) is delivered and the current passing through the sample is measured. The volume conductivity is then deduced using the specimen geometry as:

𝜎 = 𝐿. 𝐼 𝑆. 𝑈 Equation 3
with U the applied voltage, I the measured current, L and S respectively the specimen length and section.

4) Rheological measurements

Dynamic measurements were performed using an Ares rheometer (TA Instruments) equipped with parallel plates of 25 mm diameter under nitrogen atmosphere. The pure matrices where analyzed in the linear viscoelastic domain using the strain-controlled rheometer at different temperatures. Then following the time-temperature superposition principle, master curves have been built for a reference temperature of 200°C. The master curves were then described by a classical Maxwell N modes model [START_REF] Bird | Dynamics of polymeric liquids[END_REF]:

𝐺 ′ (𝜔) = ∑ 𝐺 𝑖 𝜔 2 𝜆 𝑖 2 1 + 𝜔 2 𝜆 𝑖 2 𝑁 𝑖=1 Equation 4 𝐺 ′′ (𝜔) = ∑ 𝐺 𝑖 𝜔𝜆 1 + 𝜔 2 𝜆 𝑖 2 𝑁 𝑖=1 Equation 5
where Gi is the modulus contribution corresponding to the relaxation time λi. For the fitting, the λi were fixed over the range of time constants corresponding to the reverse of the experimental frequency range. Using an iterative non-linear least square regression algorithm applied to the relative difference between calculated and experimental complex moduli G*(), the Gi contributions were deduced. The number of modes was fixed as the best compromise between the fitting quality and physically adequate (non-negative) values of the Gi. The frequency range for the HIPs matrix is chosen in order to characterize the relaxation mechanism attributed to the PS phase (frequency range > 0.1 rad/s). In Figure 1 the master curves are displayed fitted by a 5 modes Maxwell model for the pure PS matrix and by a 6 modes Maxwell model for the HIPS matrix. The weight average relaxation time λw can be calculated from the λi and Gi parameters by:

𝜆 𝑤 = ∑ 𝐺 𝑖 𝜆 𝑖 2 𝑛 𝑖=1 ∑ 𝐺 𝑖 𝜆 𝑖 𝑛 𝑖=1 = 𝜂 0 𝐽 𝑒 0 Equation 6
The build of the master curve gives access to the shift factors aT, that follow the William Landel Ferry equation [START_REF] Ferry | Viscoelastic properties of polymers[END_REF][START_REF] Williams | The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids[END_REF]. Table 1 displays the weight average relaxation times for the two matrices determined from the master curves at a reference temperature of 200°C and calculated at different temperatures using the appropriate shift factors also given in Table 1. In addition, the viscoelastic behavior of the PS-MWCNT and HIPS-MWCNT filled with 0.15; 0.3; 0.6; 0.8; 1; 1.25; 1.5; 2; 3 wt% were analyzed at 200°C at a strain fixed to 1% chosen in the linear viscoelasticity domain. In order to control the aggregation state of the composites, the samples were first annealed for 20 min before the dynamic measurement. In an early study [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF], we have shown that the filler concentration does not impact the dynamic of the polymer chains. In this work, the weight average relaxation time of the pure matrix will be used to calculate the Weissenberg number for the different extensional experiments. Indeed, we consider that the polymer molecular mobility remains unaffected by the CNT network.

5) Extensional deformation combined with conductivity measurement

Extensional experiments were carried out with a commercialized Extensional Viscosity Fixture EVF (TA instruments) mounted on the ARES rheometer (TA instruments). The set-up was modified in order to measure the specimen conductivity during the extensional test. This specific set-up has already been detailed in an earlier work [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF].

C. Results and discussion

1) Morphology

The different morphologies of the composites will be first analyzed. Figure 2 shows a TEM micrograph of the HIPS/MWCNT. With interfacial energy from the literature, the wetting coefficient ωPS-PB can be calculated and it is found equal to 2 at 200°C [START_REF] Barber | Static and dynamic wetting measurements of single carbon nanotubes[END_REF][START_REF] Sun | Effect of ABS Rubber Content on the Localization of MWCNTs in PC/ABS Blends and Electrical Resistivity of the Composites[END_REF]. By considering the thermodynamic prediction (ωPS-PB>1), the MWCNTs have a better affinity with PS than PB. In this work, the CNTs were first melt mixed in a PS matrix for the generation of a highly filled masterbatch and then diluted with rubber-modified PS to obtain composites with a tailored filler concentration. CNTs are not expected to be found in the PS phase inside the PB nodules, because they should have to pass through the PB envelope. This is shown by the TEM micrographs where the CNTs are located in the PS phase outside the nodules.

Figure 3 shows two Scanning Electron Microscopy (SEM) micrographs of both composites filled with ~0.8 vol% of MWCNT. The observation is carried out with SEM with the in-lens detector. This detector gives the possibility to the observation of the CNTs thanks to enhanced contrast between the fillers and the matrix [START_REF] Li | The imaging mechanism, imaging depth, and parameters influencing the visibility of carbon nanotubes in a polymer matrix using a SEM[END_REF][START_REF] Li | Imaging of CNTs in a polymer matrix at low accelerating voltages using a SEM[END_REF]. The bright dots are CNTs. The dark phase is the insulating PS matrix and the grey scaled phases are the PB nodules functionalized with OsO4. In the PS matrix, the CNTs form a well percolated network of aggregates homogeneously distributed (Figure 3a). Figure 3b shows that in the HIPS matrix; the aggregates make a network in the PS rich phase around the nodules. The aggregates seem to be larger in the HIPS/MWCNT composites than in the PS/MWCNT composite. Due to not enough contrast within micrographs this assumption could not be confirmed by image analysis. In addition, the volume of the PB nodules in the HIPS has been estimated to 40 vol% by TEM analysis.

2) Effect of the nodules on the electrical conductivity

The conductivity in Conductive Polymer Composites arises when the fillers form a percolated network within the material [START_REF] Kirkpatrick | Percolation and conduction[END_REF][START_REF] Bauhofer | A review and analysis of electrical percolation in carbon nanotube polymer composites[END_REF]. Classical percolation theory has been applied in order to determine the percolation threshold and the exponent for the two composites.

𝜎 = 𝜎 0 (𝜙 -𝜙 𝑐 ) 𝑡

Equation 7

First of all, one must mention that during the melt mixing the CNT length can be reduced. The length distribution of the CNT after melt processing has been determined in TEM analysis on samples after the matrix has been removed with appropriate solvent. This analysis has only been carried out on the HIPS composite; as the processing conditions are quite comparable one can make the assumption that the length distribution is similar for the two matrices.

Fillers with aspect ratio in the range of 100 can theoretically generate composites with a percolation threshold a few lower than 0.1 vol% [START_REF] Balberg | Percolation thresholds in the 3-dimensional sticks system[END_REF]. From the measured conductivities, the percolation law parameters, 0 and t, were determined from simple linear regressions on the logarithmic form of Equation 7 by adjusting the percolation threshold 𝜙 𝑐 (maximizing the determination coefficient r 2 of the linear regressions). The obtained exponent is 1.74 with a percolation threshold at 0.33 vol% of CNT for the PS/CNT composite and respectively 2.24 and 0.16 vol% for the HIPS/MWCNT composite. Hence, the two composites lead to slightly larger percolation thresholds than expected. The exponents illustrate the formation of a 3D network according to the percolation theory. As expected, due to the segregation of the fillers [START_REF] Sumita | Dispersion of fillers and the electrical conductivity of polymer blends filled with carbon black[END_REF][START_REF] Sumita | Double percolation effect on the electrical conductivity of conductive particles filled polymer blends[END_REF][START_REF] Gödel | Selective localization and migration of multiwalled carbon nanotubes in blends of polycarbonate and poly(styrene-acrylonitrile)[END_REF][START_REF] Thongruang | Volume-exclusion effects in polyethylene blends filled with carbon black, graphite, or carbon fiber[END_REF] the HIPS matrix generates composites with a lower percolation threshold than the PS matrix. In order to explain the difference between the two composites, the effective concentration of the CNT in the PS phase outside the nodules has been calculated with Equation 8:

𝜙 (𝑣𝑜𝑙%) = 𝑉 𝐶𝑁𝑇 𝑉 𝐶𝑁𝑇 + 𝑉 𝑃𝑆 × 100 Equation 8
where VCNT is the volume occupied by CNT aggregates and VPS is the volume occupied by PS. Taking into account the PS phase accessible to the fillers gives the possibility to explain the different percolation thresholds obtained. Figure 4 shows the conductivity evolution as a function of the nominal CNT concentration for both PS and HIPS matrices. The corresponding percolations laws are also plotted. Moreover, the conductivity variation for the HIPS matrix is also plotted versus the CNT volume fraction in the accessible PS phase calculated with Equation 8. The conductivity evolutions as a function of this corrected concentration for the two different matrices superimpose very well showing the efficiency of the volume segregation resulting from the presence of PB nodules.

Hence, taking into account the effective volume concentration of the fillers in the PS phase for the HIPS composite, the matrices lead to similar percolation threshold. The nodules are randomly dispersed in the continuous PS phase. Thus, the conductivity of the material is preserved. Last, but not the least, the presence of the nodules which occupy around 40 % of the total volume gives the possibility to decrease the global CNT weight concentration of nearly 50 %. It must be mentioned that, everywhere in the following of this work, the considered volume concentration of CNT will be the corrected concentration in the PS phase considering the restricted volume. However, it can be noticed in Figure 4, that the HIPS conductivity (after correction) may appear slightly lower than the PS composite conductivity. This is certainly due to the effective section of electrical pattern which are smaller in the HIPS composite than in the pure PS.

3) Effect of the volume segregation on the filler network structure

The percolation theory applied to composites made of insulating matrix filled with electrically conductor particles gives the possibility to characterize the insulating/conductor transition. However, this concept does not give further details on the network structure. That is why, in addition to volume conductivity measurements, dynamic rheology measurements have been carried out on both composites in order to investigate the network formation and its evolution as a function of the CNTs concentration. It must be pointed out that attention has been paid on the modulus measurement since CNTs networks are very sensitive to the experimental conditions and especially to the melt history [START_REF] Rahatekar | Length-Dependent Mechanics of Carbon-Nanotube Networks[END_REF][START_REF] Alig | Destruction and formation of a carbon nanotube network in polymer melts: Rheology and conductivity spectroscopy[END_REF]. The aggregation state must be controlled in order to characterize a well-structured network. That is why in this work, the storage modulus has been measured after an annealing treatment of around 20 min for the two composites. The experimental curves of G' as a function of the angular frequency are shown for different CNTs concentrations in Figure 5 for the PS composites and in Figure 6 for the HIPS composites. Like the evolution of the conductivity, the increase of the equilibrium storage modulus Ge that is, the plateau modulus appearing in the low frequency region for percolated structures, can be described with a percolation law:

𝐺 𝑒 ≈ 𝐺 0 (𝜙 -𝜙 𝑐 ) 𝑡 Equation 9
The determination of the percolation threshold 𝜙 𝑐 has been achieved again by the maximization of the determination coefficient r 2 of the logarithmic form of Equation 9, giving the other parameters G0 and t at the same time. A value of 𝜙 𝑐 equal to 0.22% was obtained for the PS matrix and of 0.24% for the HIPS matrix. These values are very close to each other consistently with the consideration of the CNT fraction only in the PS phase for the HIPS as it was shown for the conductivity. Nevertheless, it must be conceded that this percolation threshold is slightly lower than this obtained for the conductivity with the PS matrix (0.33%) but it must be kept in mind that the comparison between percolation thresholds coming from mechanical and electrical techniques can be somewhat questionable. Particularly, in the present case, the matrix (PS or HIPS) is in the melt state for the rheological measurements while it was solidified for the conductivity.

Figure 7 shows the evolution of the equilibrium modulus as a function of the filler concentration in the PS. The equilibrium moduli of the HIPS composites are larger than these of the PS composites, evidently due to the presence of the PB nodules which leads to a higher modulus of the sole matrix itself. The curves given by the percolation laws are also displayed in Figure 7. For the composites with the PS matrix, the obtained exponent is 2.76 close to the value of 2.5 reported by Pötschke et al. for CNT in polycarbonate [START_REF] Pötschke | Rheological and dielectrical characterization of melt mixed polycarbonate-multiwalled carbon nanotube composites[END_REF]. However, the HIPS composites materials exhibit a lower exponent of 1.84. This difference compared to the pure PS matrix may be due to a different structure of the network in the HIPS composites.

4) Analysis of the filler network under extensional deformation

The extensional viscosity of the materials have been measured at different temperatures in the range of 140°C to 210°C and different elongation rates between 0.01 s -1 to 0.1 s -1 . In Figure 8 is plotted the ratio between the composites extensional viscosity at 180°C and 0.1 s -1 and the zero shear viscosity of the unfilled material. For concentrations up to 1 vol% the obtained ratio is around 3 as expected for the classical Trouton's ratio. Thus, the presence of a percolated network does not influence the extensional viscosity. However, for the HIPS based composites at filler volume concentrations above 1 vol%, a large deviation is observed, whereas this deviation is not observed for the PS based composites. This deviation can be accounted for the segregation that enhances the formation of connections between the aggregates in the HIPS. It has been observed that the deviation from the Trouton's ratio of 3 occurs at a lower CNT content when using CNT with larger aspect ratio or highly filled suspension [START_REF] Weinberger | Extensional flow behavior of polymer solutions and particle suspensions in a spinning motion[END_REF][START_REF] Krishnamoorti | Shear response of layered silicate nanocomposites[END_REF]. In addition, the analysis of the linear viscoelastic behavior has shown that the network strength is higher in the HIPS than in the PS. This denser filler network has a crucial impact on the material flow ability. Concomitantly, with this large deviation, a smaller strain-at-break is observed for the HIPS based composites. In the literature, the PS strain-at-break is larger than for HIPS or even blend of PS and HIPS matrices [START_REF] Barroso | Unusual extensional behavior of a polystyrene/HIPS blend[END_REF]. Even if the filler content is quite low the generated interface volume is very large. The polymer chains embedded within the filler network do not have exactly the same behavior than in pure matrix. Their mobility is strongly reduces and the break appears at lower strains.

At large filler concentration, the flow ability of the HIPS composite is dramatically impacted. From a pragmatic point of view, the use of nanofillers with large aspect ratio is motivated by their potential in the generation of conductive composites with low amount of fillers. Nevertheless, the small effect of the CNT on the measured extensional stress is not enough to provide valuable information on the filler network evolutions.

The composites have been analyzed using a specific set-up of combined conductivity and extensional viscosity measurements. This set-up gives the possibility to measure the electrical conductivity variation of the melt specimen which experiences an extensional deformation at a constant strain rate. Figure 9 shows the conductivity variation of two composites filled with about 0.8 vol% of CNT in the PS phase at 160°C and an extensional rate fixed at 0.01 s -1 . The slight concentration difference between the two composites and the fact that at a Hencky deformation ε equal to 0, the two specimens are not at their equilibrium state have no strong impact on the following results. For the two specimens, the conductivity decreases during the extensional experiment. As explained in our previous work [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF], the conductivity decrease results from the progressive destruction of the filler network during the extensional test. The connections between the aggregates break due to the deformation of the sample. The two curves follow the same variation except that the HIPS composite shows a slightly faster decrease. Notwithstanding, this small difference is not enough significant to conclude.

The morphology of the two specimens after a Hencky deformation of 1 has been characterized. The two SEM micrographs are presented in Figure 10 where the white arrows illustrate the deformation direction. The structure of the PS composite (see Figure 10a) is made of aggregates stretched and oriented in the deformation direction. However; the structure of the HIPS morphology (see Figure 10b) is somewhat more difficult to characterize due to the presence of the PB nodules. First, the aggregates are stretched like in the pure PS matrix, but their orientation is less pronounced. Moreover, due to the PB nodules, the extensional rate is not homogeneous in the material and this can locally orient the aggregates in different directions than the whole deformation direction. In the following, the recovery mechanism and the competition between structuring and destruction mechanisms during the extensional deformation will be investigated more precisely. The conductivity recovery is a phenomenon largely addressed in the literature [START_REF] Alig | Conductivity spectroscopy on melt processed polypropylene-multiwalled carbon nanotube composites: recovery after shear and crystallization[END_REF][START_REF] Alig | Electrical conductivity recovery in carbon nanotube polymer composites after transient shear[END_REF][START_REF] Alig | Destruction and formation of a conductive carbon nanotube network in polymer melts: in-line experiments[END_REF][START_REF] Alig | Dynamic percolation of carbon nanotube agglomerates in a polymer matrix: comparison of different model approaches[END_REF][START_REF] Alig | Destruction and formation of a carbon nanotube network in polymer melts: rheology and conductivity spectroscopy[END_REF]. In our previous work carried out on PS filled with MWCNTs [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF], we have shown that the polymer dynamics plays a major role in this mechanism. Indeed, the polymer chains govern the recovery mechanism as it gives sufficient mobility for isolated CNT or highly disentangled bundle of CNTs for the formation and reinforcement of the network. Here, the conductivity recovery has been analyzed for the HIPS composite following the same methodology. Specimens filled with about 0.80 vol% have been deformed in order to investigate the following conductivity recovery under quiescent conditions. This experience has been carried out at different temperatures. Like for the PS matrix composites [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF], the conductivity recovery of the HIPS/CNT material fulfills a time-temperature superposition principle. A master curve of the conductivity recovery can be built and one obtains Williams Landel Ferry coefficients close to those obtained from rheological measurements (when using the same reference temperature). Figure 11 displays WLF plots of the aT shift factors obtained respectively from the dynamic rheology of the pure matrices and from conductivity recovery experiments of both matrices filled with about 0.8 vol%. The reference temperature is 180°C. For the PS composites, the data from the dynamic rheology and conductivity recovery are very close. However, for the HIPS composite a slight difference can be observed between the aT from the conductivity recovery and those from the dynamic rheology at high temperatures. The possible explanation of this result is that the shift factors obtained from rheology can be blurred because of the presence of the PB nodules which bring some uncertainty in the build of the master curve. Conversely, for the conductivity measurements, the PB nodules do not act in the CNT mobility. Thus, the network structuring is due to the mobility given by the polymer chains. Figure 12 shows the conductivity recovery of the two composites after a Hencky deformation of 1 at 170°C and at 0.01 s -1 . The recovery of the two composites superimposes very well. The same results have been observed at higher and lower temperatures (not shown here).

a) b)

Figure 11 : WLF plot for the aT shift factor from the build of the master curve of the pure matrices and from the build of the master curve of conductivity recovery. The reference temperature (T0) is 180°C

Figure 12 : Conductivity recovery under quiescent condition at 170°C of PS filled 0.79 vol% CNT and HIPS filled with 0.82 vol% CNT after a Hencky deformation of 1 at 170°C and 0.01 s -1

The filler reinforcement is driven by the same mechanism for the two composites. Disentangled and isolated CNT can diffuse and the attractive filler-filler interaction forces trigger the generation of inter-particles connections.

Under extensional deformation, a competition between destruction and restructuring of the network can occur. The use of the Weissenberg number (𝜆 𝑤 𝜀) is useful for the determination of which mechanism is predominant. The contribution of the polymer chain mobility is taken into account thanks to the use of the weight average relaxation time of the pure matrix. Figure 13 illustrates the conductivity variations for the two composites under different experimental conditions that cover a wide range of Wi. It can be pointed out that they show different conductivity values at the beginning of the extensional test. This is due to the fact that the specimens are not fully aggregated and depending on the working temperature, they will tend to reach their equilibrium state (i.e. state where all the CNTs take part to the conductivity) with more or less rapidity. At large Wi, all the measured conductivity curves merge to the same one. It is worth noting that the two materials exhibit the same limiting deformation (ε=1) before becoming insulating (under 10 -6 S/cm). Under those conditions, the relaxation mechanisms are too slow compared to the extensional rate. By changing the experimental conditions (playing on temperature and on extensional rate), the Wi can be reduced. In this specific case, a competition between restructuring and destruction can be theoretically observed and Figure 13 shows that the specimens can undergo larger deformation before becoming insulating. This shift to larger deformation observed for the two composites illustrates this competition. In addition, a large range of CNT concentrations have been analyzed. From all the conductivity measurements (not shown here), a specific value of the strain εσ was noted. This is the strain for which the sample conductivity dropped to the arbitrarily chosen value of 10 -6 S/cm. In Figure 14 and Figure 15, this strain is plotted as a function of the filler volume fraction for different extensional conditions that cover low and large Wi values. For the HIPS materials, only the results for specimens with filler concentrations lower than 2.1 vol% have been plotted. Indeed, the specimens filled with larger CNT concentrations were broken very early, that is, for deformations where the conductivity was still high. At low temperature, composites based on both matrices present close conductivity variations and the obtained εσ superimposed remarkably. However, with the increase of the temperature, the composites with the PS matrix show very slightly larger εσ than with the HIPS matrix. Even if λw is larger for the pure PS than for the PS in the HIPS matrix (see Table 1), the restructuring phenomena appears more pronounced in the pure PS matrix.

The presence of the nodules and the difference in the aggregates size in the HIPS matrix can influence the network destruction under extensional deformation. Indeed, the deformation rate is not really homogeneous within the sample. Because of the nodules which are less deformed, the deformation rate is larger in some locations of the PS phase. In addition, the presence of the nodules might strongly prevent the formation of connections between aggregates, especially in the deformation direction and consequently, enhances the destruction of the network. Finally, the difference in the filler dispersion state must be kept in mind as only isolated CNTs and disentangled group of CNTs can acquire sufficient mobility of the matrix. The concentration of this population may be different for the two matrices and may impact the restructuring mechanisms.

D. Conclusion

In this work, two polymer matrices: a pure PS and a rubber-modified PS filled with Carbon Nanotubes have been analyzed in order to put in the light the influence of the restricted volume for the fillers. Indeed, it has been observed that the forces segregation of the filler in the PS continuous phase of the HIPS leads to the achievement of composites with a very lower percolation threshold. Indeed, the HIPS material which contains about 40 volume percent of nodules gives the possibility to decrease by a factor of about 2 the weight fraction of CNTs, while preserving the same conductivity compared to the pure PS matrix. The resulting elastic networks in the two composites are slightly different and this has been attributed to the difference in the dispersion state and more precisely the difference in the size and density of agglomerates that constitute the filler network.

The dynamics of the structuring and destruction of the filler network have been investigated in quiescent conditions and under extensional deformation. Like in the PS/CNT materials, the polymer dynamics in the rubber-modified matrix governs the structuring mechanism. The competition between structuring and destruction of the network can be weighted thanks to the Weissenberg number defined as the product of the deformation rate and the weight average relaxation time of the matrix. When the restructuring is negligible during the deformation, the two composites have the same limiting deformation before becoming electrically insulating. However, at low Wi, when the restructuring mechanism can compete with the destruction induced by the deformation, the PS/CNT composite shows larger limiting deformation than the rubber-modified composite. Indeed, the restructuring phenomenon is limited for the HIPS/CNT specimens, even if the relaxation time is lower. This has been attributed to the presence of the nodules that can prevent locally the formation of connections between aggregates and induces non homogeneous deformation rate within the specimen.

In addition, a strong deviation from the Trouton's ratio of 3 combined with small strain at break has been observed for the HIPS/CNT specimens when the filler concentration is larger than 1. %. The amount of CNTs impacts the polymer chains mobility and consequently decreases the material properties.

List of Figures and Tables

Figure 1 :

 1 Figure 1 : Master curve of PS (filled symbols) and HIPS (open symbols) matrices built for a reference temperature of 200°C. Symbols: E xperimental data G' and G", Solid lines: Discrete Maxwell model.

Figure 2 :

 2 Figure 2 : TEM micrograph of HIPS filled with 0.82 vol% CNT

Figure 3

 3 Figure 3 SEM micrographs of PS filled with 0.79 vol% MWCNT (left) and HIPS filled with 0.82 vol% MWCNT (right), magnification = x2000, WD 5mm 20kV and in-lens detector.

Figure 4 :

 4 Figure 4 : Evolution of the conductivity as a function of the volume fraction of MWCNT. Empty circles and filled squares: raw data. Solid and dashed lines: percolation laws respectively for the PS and HIPS matrices. Filled circles: conductivity measured in the HIPS matrix and plotted versus the volume fraction of CNT in PS Phase (see Eq. 8). .

Figure 5 :

 5 Figure 5 : Storage moduli versus angular frequency at 200°C for PS composites.

Figure 6 :

 6 Figure 6 : Storage moduli versus angular frequency at 200°C for HIPS composites (indicated volume concentrations are concentrations in the PS phase).

Figure 7 :

 7 Figure 7 : Variation of the equilibrium modulus as a function of the CNT volume fraction in PS continuous phase. Symbols: Experimental data. Lines: Percolation laws.

Figure 8 :

 8 Figure 8 : Ratio between extensional viscosity at 0.1 s -1 of the composites and the shear viscosity of the matrices at 180°C

Figure 9 :

 9 Figure 9 : Conductivity evolution under extensional deformation at 180°C for an extensional rate of 0.01 s -1

Figure 10 :

 10 Figure 10 : SEM micrographs of the two composites after a Hencky deformation of 1 at 160°C and 0.01 s -1 a) PS filled with 0.79 vol% CNT, b) HIPS filled with 0.82 vol% CNT in the PS phase and the conductivity is around 8.10 -5 S/cm for the two specimens. The scale bar is 2µm.

Figure 13 :

 13 Figure 13 : Conductivity variation for PS filled with 0.79 vol% CNT (a) and HIPS filled with 0.82 vol% CNT (b) under extensional conditions that lead to large and low Wi for the two composites.

Figure 14 :Figure 15

 1415 Figure14: Evolution of the Hencky strain value when the composites conductivity reaches 10 -6 S/cm as a function of the filler volume fraction for the two types of matrix for specimen under extensional rate fixed at 0.1 s -1 at 160°C a) and at 180°C b)

Figure

  Figure 1: Master curve of PS (filled symbols) and HIPS (open symbols) matrices built for a reference temperature of 200°C. Symbols: Experimental data G' and G", Solid lines: Discrete Maxwell model.

1 :

 1 Figure 1: Master curve of PS (filled symbols) and HIPS (open symbols) matrices built for a reference temperature of 200°C. Symbols: Experimental data G' and G", Solid lines: Discrete Maxwell model.

Figure 2 :

 2 Figure 2: TEM micrograph of HIPS filled with 0.82 vol% CNT.

Figure 3

 3 Figure 3 SEM micrographs of PS filled with 0.79 vol% MWCNT (left) and HIPS filled with 0.82 vol% MWCNT (right), magnification = x2000, WD 5mm 20kV and in-lens detector.

Figure 4 :

 4 Figure 4: Evolution of the conductivity as a function of the volume fraction of MWCNT. Empty circles and filled squares: raw data. Solid and dashed lines: percolation laws respectively for the PS and HIPS matrices. Filled circles: conductivity measured in the HIPS matrix and plotted versus the volume fraction of CNT in PS Phase (see Eq. 8).

Figure 5 :

 5 Figure 5: Storage moduli versus angular frequency at 200°C for PS composites.

Figure 6 :

 6 Figure 6: Storage moduli versus angular frequency at 200°C for HIPS composites (indicated volume concentrations are concentrations in the PS phase).

Figure 7 :

 7 Figure 7: Variation of the equilibrium modulus as a function of the CNT volume fraction in PS continuous phase.

Figure 8 :

 8 Figure 8: Ratio between extensional viscosity at 0.1 s -1 of the composites and the shear viscosity of the matrices at 180°C.

Figure 9 :

 9 Figure 9: Conductivity evolution under extensional deformation at 180°C for an extensional rate of 0.01 s -1 .

Figure 10 :

 10 Figure 10: SEM micrographs of the two composites after a Hencky deformation of 1 at 160°C and 0.01 s -1 a) PS filled with 0.79 vol% CNT, b) HIPS filled with 0.82 vol% CNT in the PS phase and the conductivity is around 8.10 -5 S.cm -1 for the two specimens. The scale bar is 2µm.

Figure 11 :

 11 Figure 11: WLF plot for the aT shift factor from the build of the master curve of the pure matrices and from the build of the master curve of conductivity recovery. The reference temperature (T0) is 180°C.

Figure 12 :

 12 Figure 12: Conductivity recovery under quiescent condition at 170°C of PS filled 0.79 vol% CNT and HIPS filled with 0.82 vol% CNT after a Hencky deformation of 1 at 170°C and 0.01 s -1 .

Figure 13 :

 13 Figure 13: Conductivity variation for PS filled with 0.79 vol% CNT (a) and HIPS filled with 0.82 vol% CNT (b) under extensional conditions that lead to large and low Wi for the two composites.

Figure 14 :

 14 Figure14: Evolution of the Hencky strain value when the composites conductivity reaches 10 -6 S/cm as a function of the filler volume fraction for the two types of matrix for specimen under extensional rate fixed at 0.1 s -1 at 160°C a) and at 180°C b).

Figure 15 :

 15 Figure 15: Evolution of the Hencky strain value when the composites conductivity reaches 10 -6 S/cm as a function of the filler volume fraction for the two types of matrix for specimen under extensional rate fixed at 0.1 s -1 at 200°C a) and at 210°C b).

Table 1 :

 1 Shift factors aT and weight average relaxation times for the two matrices calculated for different temperatures

		aT (PS)	λw for the pure	aT (HIPS)	λw of the PS in the
	T°C		PS matrix (s)		HIPS matrix(s)
	210	0.506	2.1	0.553	1.7
	200	1	4.2	1	3.2
	180	6.24	26	4.49	14
	160	115	483	38.6	124

Table 1 :

 1 Shift factors aT and weight average relaxation times for the two matrices calculated for different temperatures

Acknowledgments

This work was funded by the ANRT and Total. The authors kindly thank engineers P. Alcouffe, X. Jaurand and C. Cuccuzzela for significantly help in Scanning Electronic Imaging technics, doctor G. Seytre and technician L. Cavetier for helping setting-up the home made EVF system and engineer and laboratory technician Eddi Scandino for the generation of the different composites.