Christine Frances
email: christine.frances@ensiacet.fr

Nadine Le Bolay

Christine Frances⁎

come

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible Any correspondence concerning this service should be sent to the repository administrator: tech-oatao@listes-diff.inp-toulouse.fr Editorial Special issue on innovative processes and materials drug in order to improve its bioavailability [START_REF] Subra-Paternault | Preparation of naproxen-excipient formulations by CO 2 precipitation on a slurry[END_REF]. Wet nanogrinding process, as a route to produce nanoparticles in dense suspensions using a stirred media mill, is then described in the next paper [START_REF] Ouattara | Grinding of calcite suspensions in a stirred media mill: Effect of operational parameters on the product quality and the specific energy[END_REF]. Then, papers [START_REF] Page Mostefa | A purification route of bio-acrylic acid by melt crystallization respectful of environmental constraints[END_REF] and [START_REF] Gerard | Effect of calcium based additives on the sodium bicarbonate crystallization in a MSMPR reactor[END_REF] both concern crystallization processes but with two different strategies. Melt crystallization as a purification route respectful of environmental constraints is examined in reference [START_REF] Page Mostefa | A purification route of bio-acrylic acid by melt crystallization respectful of environmental constraints[END_REF] and a crystallization process performed in a continuous reactor for synthesis purpose is presented in paper [START_REF] Gerard | Effect of calcium based additives on the sodium bicarbonate crystallization in a MSMPR reactor[END_REF]. Spray-drying is the process used in both papers [START_REF] Turchiuli | Use of different supports for oil encapsulation in powder by spray drying[END_REF] and [START_REF] Da Costaneto | Preparation and evaluation of chitosan-hydrophobic silica composite microspheres: Role of hydrophobic silica in modifying their properties[END_REF] but for two different purposes.

In reference [START_REF] Turchiuli | Use of different supports for oil encapsulation in powder by spray drying[END_REF], the spray drying of oil-in water emulsions, containing hydrophilic carriers, is used to encapsulate lipophilic compounds into powders while in paper [START_REF] Da Costaneto | Preparation and evaluation of chitosan-hydrophobic silica composite microspheres: Role of hydrophobic silica in modifying their properties[END_REF], spray drying is performed to produce chitosan-hydrophobic silica composite microspheres. A complementary analysis is reported on a pneumatic drying process [START_REF] Aubin | Modeling and simulation of drying operations in PVC powder production line: Experimental and theoretical study of drying kinetics on particle scale[END_REF].

Moreover, the development of new processes and materials may have an impact on societal and environmental issues and these potential drawbacks must be properly evaluated and solutions must be developed to overcome them. The last two papers of this special issue concern the emission of fine or ultrafine particles in air [START_REF] Saleh | Dust generation from powders: A characterization test based on stirred fluidization[END_REF] or water [START_REF] Liu | Nanoparticles in wastewaters: Hazards, fate and remediation[END_REF]. In paper [START_REF] Saleh | Dust generation from powders: A characterization test based on stirred fluidization[END_REF], a characterization test of dust generation is developed, whereas the last paper presents a review of the risks associated to the release of nanoparticles into the aquatic environment and lists some techniques for remediation.

Obviously, new developments in particulate processes are only possible thanks to innovative characterization methods and methodologies. Thus, the reported works in this special issue are mainly based on the use of recent characterization techniques such as NMR, X-Ray diffraction, Transmission Electron Microscopy, FTIR spectroscopy and Raman spectroscopy or include the development of specific methodologies based on rheological characterization or dynamic vapor sorption measurements.

We would like to thank the editor-in-chief of Powder Technology, Prof. Jonathan Seville, for his support in publishing this special issue and the editorial office of Powder technology for their help and guidance. As the guest editors, we also would like to thank the authors for their contributions and the panel of the international reviewers for their time and efforts in evaluating these papers and hard work towards the successful publication of this special issue.

Innovation in particulate processes is a challenging task in many industrial applications, such as for drug formulations, paints, coatings, ceramics and green products. This special issue, whose idea came from a French workshop, does not have the ambition to raise an exhaustive state of innovation in powder technology. Focusing on some examples of works performed in this domain, it aims to show that innovation can take several facets. It can be oriented either on the material, creating new products having creative properties or on the process itself, based on new routes for product synthesis or on conventional processes but used in non-conventional conditions. This special issue gathers 20 of the nearly 120 papers presented at the French Symposium on Particulate Processes which was held in Toulouse from the 4th to 6th of July, 2012. This congress was the 7th of a conference series aiming to bring together researches from industry and academia to debate the latest developments in particulate processing.

The first group of papers mainly involves particulate processes where the focus is on examining the synthesis conditions or process routes on achieving innovative materials such as composite materials having desired properties in relation with their application. A major sub-group is focused on biomaterials either to produce innovative materials for biological applications or to use bio-waste materials to produce new materials. In paper [START_REF] Vandecandelaere | Peroxide-doped apatites: preparation and effect of synthesis parameters[END_REF], the preparation of peroxidedoped calcium phosphate apatites used as bioactive bio-ceramics was investigated. The production of new materials on the base of bio-waste materials and biodegradable matrix is described by Koutsomitopoulou et al. [START_REF] Koutsomitopoulou | reparation and characterization of olive pit powder as a filler to PLA-matrix bio-composites[END_REF]. The next two papers [START_REF] Tourbin | Study on the stability of suspensions based on biomimetic apatites aimed at biomedical applications[END_REF] and [START_REF] Demnati | Synthesis of fluor-hydroxyapatite powder for plasma sprayed biomedical coatings: Characterization and improvement of the powder properties[END_REF] also concern bio-materials based on apatites for therapeutics or diagnosis purposes [START_REF] Tourbin | Study on the stability of suspensions based on biomimetic apatites aimed at biomedical applications[END_REF] or for the production of coatings [START_REF] Demnati | Synthesis of fluor-hydroxyapatite powder for plasma sprayed biomedical coatings: Characterization and improvement of the powder properties[END_REF]. The following papers [START_REF] Champion | Development of characterisation methods on U(Mo) powders for material testing reactors (MTRs)[END_REF][START_REF] Bolay | Production of PVAc-starch composite materials by co-grinding -Influence of the amylopectin to amylose ratio on the properties[END_REF][START_REF] Fatnassi | Optimization of spray-dried hyaluronic acid microspheres to formulate drug-loaded bone substitute materials[END_REF][START_REF] Bazer-Bachi | Towards industrial use of metal-organic framework: Impact of shaping on the MOF properties[END_REF][START_REF] Kenouche | NMR investigation of functionalized magnetic nanoparticles Fe3O4 as T 1 -T 2 contrast agents[END_REF][START_REF] Murrieta-Pazos | Evolution of particle structure during water sorption observed on different size fractions of durumwheat semolina[END_REF][START_REF] Cassiano-Gaspar | Novel extrudates based on the multiscale packing of alumina particles and boehmite or aluminophosphate binders[END_REF] concern composite or functionalized materials for a wide spectrum of applications. Thus, the work of Champion et al. [START_REF] Champion | Development of characterisation methods on U(Mo) powders for material testing reactors (MTRs)[END_REF] is focused on the development of adense fissile material, made of γ-U[Mo] particles embedded in an Al based matrix. The two next papers concern composite materials, made of a polymer-organic compound (mixtures of polyvinyl acetate and starch) in Ref. [START_REF] Bolay | Production of PVAc-starch composite materials by co-grinding -Influence of the amylopectin to amylose ratio on the properties[END_REF] and an organic-mineral cement (formulation of a drug-based bone substitute) in Ref. [START_REF] Fatnassi | Optimization of spray-dried hyaluronic acid microspheres to formulate drug-loaded bone substitute materials[END_REF]. An example of the shaping process is then given in paper [START_REF] Bazer-Bachi | Towards industrial use of metal-organic framework: Impact of shaping on the MOF properties[END_REF] reporting the effect of compression on the structural and catalytic properties of metal-organic frameworks. In the following paper, Kenouche et al. [START_REF] Kenouche | NMR investigation of functionalized magnetic nanoparticles Fe3O4 as T 1 -T 2 contrast agents[END_REF] analyze functionalized magnetic nanoparticles for a potential application as contrast agents in nuclear magnetic resonance imaging. An application of composite synthesis in food is then reported in Ref. [START_REF] Murrieta-Pazos | Evolution of particle structure during water sorption observed on different size fractions of durumwheat semolina[END_REF].And finally, another kind of composite material is described in Ref. [START_REF] Cassiano-Gaspar | Novel extrudates based on the multiscale packing of alumina particles and boehmite or aluminophosphate binders[END_REF] where porous extrudates were obtained based on the packing of multi-sized alumina particles and boehmite or aluminophosphate binders.

A second group of papers [START_REF] Subra-Paternault | Preparation of naproxen-excipient formulations by CO 2 precipitation on a slurry[END_REF][START_REF] Ouattara | Grinding of calcite suspensions in a stirred media mill: Effect of operational parameters on the product quality and the specific energy[END_REF][START_REF] Page Mostefa | A purification route of bio-acrylic acid by melt crystallization respectful of environmental constraints[END_REF][START_REF] Turchiuli | Use of different supports for oil encapsulation in powder by spray drying[END_REF][START_REF] Da Costaneto | Preparation and evaluation of chitosan-hydrophobic silica composite microspheres: Role of hydrophobic silica in modifying their properties[END_REF][START_REF] Aubin | Modeling and simulation of drying operations in PVC powder production line: Experimental and theoretical study of drying kinetics on particle scale[END_REF][START_REF] Gerard | Effect of calcium based additives on the sodium bicarbonate crystallization in a MSMPR reactor[END_REF] focuses on the analysis of innova-tive processes used to produce powders with the desired properties. In the first paper, the work is focused on the CO 2 -induced precipitation of a

  This is an author's version published in: http://oatao.univ-toulouse.fr/20265 To cite this version: Frances, Christine and Le Bolay, Nadine Special issue on innovative processes and materials. (2014) Powder Technology, 255. 1-2. ISSN 0032-5910 Official URL: https://doi.org/10.1016/j.powtec.2014.01.066


Ariston Reis

François Sarrazin

Elodie Richalot

Philippe Pouliguen
email: philippe.pouliguen@intradef.gouv.fr

Mode-Stirring Impact in Radar Cross Section Evaluation in Reverberation Chamber

Keywords:

This paper presents the evaluation of the Radar Cross Section (RCS) pattern of a rectangular metallic plate from Reverberation Chamber measurement. It is seen that the measured RCS strongly depends on the environment and especially on the stirrer position. An approach based on averaging the measurement over a stirrer rotation is presented and allows increasing the measurement accuracy when compared to simulated data.

I. INTRODUCTION

Radar Cross Section (RCS) is the commonly used parameter to describe the scattering behavior of an object. It is of interest in a wide range of topics including stealth optimization, radar detection, RFID interrogation [START_REF] Nikitin | Theory and measurement of backscattering from RFID tags[END_REF] and antenna characterization [START_REF] Sarrazin | Antenna Physical Poles Extracted From Measured Backscattered Fields[END_REF]. Its determination is usually obtained thanks to S11-parameters measurement performed in a large anechoic chamber. It requires an accurate calibration of the measurement setup using a well-known canonical target such as a sphere, as well as a fine time-windowing implying Fourier transformations and also a hardware time-gating. Recently, Reverberation Chambers (RCs) have been investigated to measure the RCS of metallic objects. Indeed, the statistically uniform and isotropic incident field within the usable volume is very suitable to obtain the Absorption Cross Section, as well as the total RCS [START_REF] Lerosey | Scattering cross section measurement in reverberation chamber[END_REF]. However, the monostatic or bistatic RCS retrieval within an RC is not as obvious. Based on earlier works on antenna directivity pattern measurement [START_REF] Lemoine | Antenna directivity measurement in reverberation chamber from Rician K-factor estimation[END_REF], authors in [START_REF] Besnier | Estimating Radar Cross-Section of Canonical Targets in Reverberation Chamber[END_REF] proposed a novel approach to retrieve the ballistic wave between an antenna and a scattering object within a diffuse environment such as an RC, which enables RCS pattern measurement. This method presents the advantages to avoid any Fourier transformations as well as to use a cheaper measurement setup compared to classical anechoic chamber measurement.

The considered method is a two steps process that requires S11-parameters measurement with and without the target. The difference between the two then leads to the object RCS though a regression process. Thus, the RCS accuracy depends on the overall Signal-to-Noise Ratio (SNR). In [START_REF] Besnier | Estimating Radar Cross-Section of Canonical Targets in Reverberation Chamber[END_REF], the mode stirrer is kept in a fixed position while in this paper, we suggest taking advantages of the stirring process to average the measurement over a stirrer rotation and thus lower the overall measurement noise. This paper is constructed as follows: Section II presents the measurement process details. Then, the RCS extraction procedure is exposed in Section III. Measurement results compared to simulation ones in Section IV clearly show the contribution of mechanical stirring to RCS measurement accuracy.

II. MEASUREMENT PROCESS

A. Measurement setup

For this measurement, a horn-antenna is placed within the working volume of the RC and connected to a port of a vector network analyzer (VNA) Rohde&Schwarz ZNB8. The rectangular metallic plate (of dimensions 20 cm horizontally and 25 cm vertically), which represents the target, is positioned on a cardboard box at a distance 𝑅=2.29 m from the antenna and is centered at the same height (Fig. 1). As the chosen frequency band for this measurement is 6 GHz -6.4 GHz, this distance R is large enough so that the ballistic wave can be considered as spherical on the target. It has to be noticed that the horn antenna, the rectangular plate and the mode stirrer are aligned. To evaluate the RCS pattern in the azimuth plane, the target is rotated around the vertical axis from -30 to 30 degrees with a 1 degree step. The horn-antenna is vertically polarized with an electric field along the height of the RC. The considered frequency range is very high compared to the RC Lowest Useable Frequency (around 400 MHz), so that the field within the cavity can be considered as isotropic and uniform.

B. Measurement in the empty Reverberation Chamber

During this measurement without the target (but with its support), the RC is excited by the horn-antenna at a frequency 𝑓 # in the 6-6.4 GHz frequency range. The purpose of this first measurement is to determine the response of the cavity itself. Hence, the scattering parameter 𝑆(𝑓 # ) is measured by the VNA (once calibrated at the antenna's connector level) over a stirrer rotation (with a rotation step of 30°). It can be expressed as follows [START_REF] Besnier | Estimating Radar Cross-Section of Canonical Targets in Reverberation Chamber[END_REF]:

𝑆 (𝑓 # ) = 𝑆 )* (𝑓 # ) + (1 -|𝑆 )* (𝑓 # )| / )𝐻(𝑓 # )𝜂 234 (1)
In this equation, the term 𝑆 )* (𝑓 # ) represents the reflection coefficient of the antenna in free space (it can be found by calculating the mean of the reflection coefficient over a stirrer rotation in the empty RC. The second term is composed by the expression (1 -|𝑆 )* (𝑓 # )| / ) that represents the losses due to antenna mismatch, the antenna radiation efficiency 𝜂 234 corresponding to the losses related to antenna performance, and 𝐻(𝑓 # ) that represents the chamber transfer function at the antenna location and is supposed to follow a normal Gaussian distribution versus frequency as well as stirrer position in a well-operating RC.

C. Measurement of the target backscattering

Measurements are then performed after inserting the target. For each position of the target, the reflection coefficient is measured over a stirrer rotation (with a 30° rotation step). When the RC is loaded by a target, the previous equation for the reflection coefficient is changed with the appearance of the term 𝐶(𝑓 # )6𝜎 8 (𝑓 # ) :

𝑆 8 (𝑓 # ) = 𝑆 )* (𝑓 # ) + 𝐶(𝑓 # )6𝜎 8 (𝑓 # ) + (1 -|𝑆 )* (𝑓 # )| / )𝐻 8 (𝑓 # )𝜂 234 (2)
This additional term represents the backscattering by the target of the ballistic wave towards the antenna. In particular, the complex quantity 𝐶(𝑓 # ) describes the wave propagation forwards from the antenna to the target and backwards from the target to the antenna at the frequency 𝑓 # . The term 𝜎 8 stands for the Radar Cross Section of the target at the same frequency𝑓 # . As the distance between the antenna and the target is sufficient for the ballistic wave to be considered as almost plane at the target level, the amplitude of 𝐶(𝑓 # ) can be simplified as:

|𝐶(𝑓 # )| = : ;<= (> ? ) @ ? (AB) C D E F D (1 -|𝑆 )* (𝑓 # )| / ) (3)
We can notice that this term is proportional to antenna gain 𝐺 234 , and inversely proportional to the square distance 𝑅 between antenna and target.

As the dimension of the target is much smaller than the distance R, the phase is considered as constant along the target and this leads to the following simplified expression:

𝐶(𝑓 # ) = |𝐶(𝑓 # )| • 𝑒𝑥𝑝 LM/B> ? /F N • 𝑒𝑥𝑝 (𝑗𝜙 # ) (4)
with 𝜙 # an arbitrary constant phase. The phase variation corresponds to a wave propagation at the speed of light 𝑐 along the path 2𝑅 forwards and backwards between the measuring antenna and the target.

D. Radar Cross Section retrieval

To obtain the expression that permits to extract the RCS, we compute the difference between the two previous measurements:

𝑆 8 (𝑓 # ) -𝑆 (𝑓 # ) = (1 -|𝑆 )* (𝑓 # )| / )S𝐻 8 (𝑓 # ) -𝐻(𝑓 # )T𝜂 234 +6𝜎 8 (𝑓 # ) : ;<= (> ? ) @ ? (AB) C D E F D (1 -|𝑆 )* (𝑓 # )| / ) × 𝑒𝑥𝑝 LM/B> ? /F N • 𝑒𝑥𝑝 (𝑗𝜙 # ) (5)
This equation ( 5) consists in two terms. The first one is proportional to 𝐻 8 (𝑓 # ) -𝐻(𝑓 # ) that is assumed to be a random variable following a centered Gaussian distribution (when the frequency or the stirrer position varies) as each term of this difference does. This assumption will permit to consider this term as an additive random noise 𝑁(𝑓) and to extract the RCS from the second one. The latter contains the magnitude of the backscattered signal from the target. If we consider either its real or imaginary part, this term varies as a sine wave versus frequency. Thus, we can write:

Simplifying this equation, it becomes:

𝑅𝑒S𝑆 8 (𝑓 # ) -𝑆 (𝑓 # )T = 𝐴 × 𝑐𝑜𝑠 Y /B> ? /F N -𝜙 # Z + 𝑁(𝑓) (7)
where 𝐴 stands for the amplitude of the signal and is calculated while minimizing the following expression:

𝐴 𝑐𝑜𝑠 Y /B> ? /F N -𝜙 # Z -𝑅𝑒S𝑆 8 (𝑓 # ) -𝑆 (𝑓 # )T (8)
Once 𝐴 is found, the RCS can be deduced as the other coefficients are known.

III. RESULTS

A. Extraction of the backscattered ballistic wave according to the angle of the target

The Fig. 2 shows the waveform when the target is orthogonal to the direct path between the antenna and the target (this target position is mentioned as the 0° one), and the stirrer position is at its initial position (labelled as 0° stirrer position). We notice the sine wave pattern related to the second term of ( 5) is partly hidden by the random signal expressed by the first term of [START_REF] Besnier | Estimating Radar Cross-Section of Canonical Targets in Reverberation Chamber[END_REF]. Despite this additional term, the amplitude A can be extracted (red curve in Fig. 2). The amplitude of the signal related to the target backscattering appears to be constant over the considered frequency band.

The Fig. 3 corresponds to a target position of 5°, for which the target backscattering is of smaller amplitude than in the previous target position (Fig. 2). As a consequence, the amplitude of the signal of interest is smaller and its extraction becomes more difficult. The lack of precision in this amplitude extraction when the RCS decreases will be obvious in the following of this paper. Fig. 4. Waveform versus frequency of the real part of the difference between the measured reflection coefficients of the loaded and empty cavities, at target position 0°. The blue curve corresponds to the stirrer position 0°, the green curve to the average difference over a stirrer rotation, and the red is the sinusoidal fitting curve. Fig. 5. Waveform versus frequency of the real part of the difference between the measured reflection coefficients for loaded and empty cavities, at target position 5°. The blue curve corresponds to the stirrer position 0°, the green curve to the average difference over a stirrer rotation, and the red curve is the sinusoidal fitting curve.

B. Advantages of the mean over a stirrer rotation

The Fig. 4 shows the average over a stirrer rotation (green curve) of the difference between both measured reflection coefficients, with and without the target. We can see that it permits to reduce the noise associated to the first term of (5) and makes easier the extraction of the sine-wave signal amplitude.

This advantage of the mode-stirring process increases for target positions related to low RCS as the low amplitude of the backscattered field makes it difficult to extract from noise. As an example for the target position of 5° (Fig. 5), the sinusoidal shape of the signal of interest appears after averaging over a stirrer rotation, easing the extraction of its amplitude.

C. Extracted Radar Cross Section pattern

The RCS of the rectangular metallic plate has been firstly extracted for fixed stirrer positions and compared to the one obtained through simulations using ANSYS HFSS software. As no calibration measurement has been performed (using a standard target), the obtained results have been normalized so that the maximal RCS value (corresponding to the target Fig. 6. RCS patterns for all stirrer positions, at a frequency of 6.2 GHz. (with 𝑆 the target section and 𝑐 the light velocity). As shown in the Fig. 6, the RCS patterns vary according to the stirrer rotation. The maximal RCS values are obtained when the target is orthogonal to the direct path between the antenna and the target (position 𝜃 = 0°) and close to this position. In this angular range, the amplitude of the backscattering term is sufficient to permit its extraction with a good accuracy; this explains why the curves related to the different cavity configurations are superimposed for 𝜃 ≤ 7°. At larger angles, the RCS decreases and becomes more difficult to extract; as a consequence, a dispersion of the results obtained with different stirrer positions is observed. The Fig. 7 presents the extreme RCS values obtained for each target position when considering all stirrer positions, and compares them to the simulation results. The theoretical RCS globally stays between these extreme values, except for very low RCS that are hard to evaluate. As shown in the previous section, averaging the difference between the measured reflection coefficients is of help to extract the RCS, in particular when the amplitude of the backscattered signal is low. This averaging technique has thus been used at each target position and results are presented in Fig. 8. It shows a good agreement between measurement and simulation except for very low RCS. Thus, this averaging approach improves the RCS estimation accuracy.

IV. CONCLUSION

The RCS of a 20×25 cm 2 metallic plate is estimated at 6.2 GHz thanks to measurement performed inside an RC. This RCS can be evaluated by retrieving the ballistic wave between the reference antenna and the target by comparing Sparameters with and without the target. This method is based on a regression process and thus is sensitive to the measurement noise. The general pattern of the RCS is well retrieved, except for target positions related to low RCS values, while compared to simulated data. However, we show that this RCS pattern strongly depends on the stirrer position during the measurement. Thus, we suggest to take benefit from the mode stirrer to average the measured S-parameters over a stirrer rotation in order to increase the overall SNR. Such process allows obtaining a much better agreement to the simulated RCS, especially for target positions related to low RCS values.

Fig. 1 .

 1 Fig. 1. Radar Cross Section measurement setup in Reverberation Chamber.

Fig. 2 .

 2 Fig. 2. Waveform versus frequency of the real part of the difference between the measured reflection coefficients of the loaded and empty cavities, at target position 0° and stirrer position 0°.

Fig. 3 .

 3 Fig. 3. Waveform versus frequency of the real part of the difference between the measured reflection coefficients for loaded and empty cavities, at target position 5° and stirrer position 0°.

Fig. 7 .

 7 Fig. 7. Comparison between extreme RCS values among all stirrer positions and simulated RCS, at a frequency of 6.2 GHz.

Fig. 8 .

 8 Fig. 8. Comparison between RCS pattern extracted after averaging the scattering difference over a stirrer position and simulated RCS, at a frequency of 6.2 GHz.

ACKNOWLEDGMENT

This work was financially supported by the French Ministry of Defence (DGA/MRIS).


Nadine Le Bolay
email: nadine.lebolay@ensiacet.fr

Sonia Molina-Boisseau

Production of PVAc-starch composite materials by co-grinding-Influence of the amylopectin to amylose ratio on the properties

Keywords:

Mixtures of polyvinyl acetate (PV Ac) filled with two starch types containing different amylopectin to amylose ra tios were co-ground in a laboratory tumbling ball mill. The influence of the starch nature and of the co-grinding treatment on the production mechanism and on the composite properties was studied. The thermal and mechan ical properties were characterized, as well as the behavior in water.

Introduction

Millions of tons of petrochemical polymer materials are produced each year for life usage. Most of them are used during a short period and become rapidly wastes. These materials are always more expensive. That is why starch filled composite materials were subjects of great interest during these Iast decades due to the biodegradability and the Iow price of starch.

A lot of studies are reported in literatures on composites combining starch and various polymers such as polystyrene [START_REF] Tap | Preparation and characterization of blends of recycled polystyrene with cassava starch[END_REF][START_REF] Ha Pushpadass | Expansion, morphological and mechan ical properties of starch-polystyrene foams containing various additives[END_REF], polyethylene [START_REF] Danjaji | Sago starch-filled linear low-density polyethylene (LIDPE) films: their mechanical properties and water ab sorption[END_REF][START_REF] Abdul Khalil | The effect of anhydride modification of sago starch on the tensile and water absorp tion properties of sago-filled linear low-density polyethylene (LIDPE)[END_REF], polyvinyl acetate [START_REF] Vargha | Biodegradable polymers by reactive transesterification ofther moplastic starch with poly (vinyl acetate) and poly (vinyl acetate-co-butyl acry late)[END_REF][START_REF] Waly | Chemical modification of starch-poly ( vinyl acetate) materials[END_REF][START_REF] Lu | Controlled grafting of poly(vinyl acetate) onto starch via RAFT poiymerization[END_REF][START_REF] Zhang | Study on film ofpolyvinyl acetate emulsion modified by starch[END_REF][START_REF] Nie | Research on starch-g-polyvinyl acetate and epoxy resin-modified corn starch adhesive[END_REF], polyvinyl alcohol [START_REF] Tang | Recent advances in starch, polyvinyl alcohol based polymer blends, nanocomposites and their biodegradability[END_REF][START_REF] Sin | Computer aided injection moulding process analysis of polyvinyl alcohol-starch green biode gradable polymer compound[END_REF][START_REF] Sreekumar | Studies on compatibility ofbiodegradable starch/polyvinyl alcohol blends[END_REF][START_REF] Parvin | Preparation and char acterization of starch/PVA blend for biodegradable packaging material[END_REF], and polylactic acid [START_REF] Zhang | Sun, Mechanical properties of poly(lactic aeid)/starch composites compatibilized by maleic anhydride[END_REF][START_REF] Aeioli-Moura | Thermal degradation and physical aging of poly(lactic add) and its blends with starch[END_REF][START_REF] Wang | Mechanical properties of poly(lactic aeid) and wheat starch biends with methyienediphenyI diisocyanate[END_REF][START_REF] Wang | Influence of formamide and water on the proper ties ofthermoplastic starch/poly (lactic add) blends[END_REF]. Different processes are used to produce these materials: blending, chemical synthesis, and extrusion. In most cases, there are no interactions between starch and matrix, Ieading to Iow mechanical properties of materials. Indeed starch is hydrophilic while most poly mers are hydrophobie or Jess hydrophilic than starch. To avoid this problem, authors proposed to use compatibilizers, starch modification, grafting, crosslinking, and plasma treatment. Kovacs and Tabi [START_REF] Kovacs | Examination of starch preprocess drying and water absorption of injection-molded starch-filled poly(lactic aeid) products[END_REF], when producing polylactic acid-starch blends by injection molding, found that by using adequate drying conditions, it is possible to develop strong adhesion between starch granules and polylactic acid matrix, without any coupling agent.

Co-grinding is a simple process favoring dispersion of small tiller particles in a matrix and interactions between both constituents. This process allows improving the use properties of the materials with regard to a simple mixture, without using any treatment by a chemical agent [START_REF] Zapata | Production of smalt composite particles by co-grinding in a media mill -characterization of the granulometric and the mechanical properties[END_REF]. It was applied to fill non-degradable or biodegradable matri ces with minerais [START_REF] Zapata-Massot | Effect of the minerai filler on the surface properties of co-ground polymeric composites[END_REF], non-degradable polymers [START_REF] Pan | Effect of processing parameters on material properties of me chanically processed polyamide[END_REF] or starch [START_REF] Seyni | Matrix-filler interactions in a co-ground ecocomposite -surface properties and behaviour in water[END_REF][START_REF] Bolay | How to combine a hydrophobie matrix and a hydrophilic filler without adding a compatibilizer -co-grinding en hances use properties of renewable PIA-starch composites[END_REF].

Starches con tain a mixture of amylose, which has a linear structure, and amylopectin, which has a branched structure, in various propor tions depending on the sources [START_REF] Ramesh | Amylose content of rice starch[END_REF]. In most studies reported in litera tures, authors used only one starch, and few studies were performed on the influence of the amylose to amylopectin ratio on properties. Zhang and Thomas [START_REF] Zhang | Preparation and properties ofpolyhydroxybutyrate biended with different types of starch[END_REF] produced blends of polyhydroxybutyrate filled with two starches containing 30 and 72% amylopectin. They concluded that the presence of starch improves thermal, rheological and mechanical properties due to intermolecular hydrogen bonding, and the improve ment is more significant with the starch containing the higher amylose rate. Taghvaei-Ganjali et al. [START_REF] Taghvaei-Ganjali | Effect of amylose/amylopectin ratio on physico-mechanical properties of rubber compounds filled by starch[END_REF] studied the effect of amylose to amylo pectin ratio on physico-chemical properties of rubber compounds filled by three types of starches with different amylopectin contents. They showed that the tiller rubberization is enhanced with high amylopectin contents because of a higher branched structure, what influences the me chanical properties of the mixtures. Zou et al. [START_REF] Zou | Effects of amylose/amylopectin ratio on starch-based superabsorbent polymers[END_REF] prepared starch-based superabsorbent polymers using four starches. They studied the effect of the amylose to amylopectin ratio on the grafting reactions and the perfor mance of the mixtures. They noted that the high molecular weight and branched structure of amylopectin reduces the polymer chain mobility and increases the viscosity, resulting in a lower grafting efficiency.

In a previous paper [START_REF] Seyni | On the interest of using degradable fillers in co-ground composite materials[END_REF], composites of polyvinyl acetate filled with a waxy starch, almost essentially made of amylopectin, were produced by co-grinding. The work was mainly concentrated on the identification of grinding and co-grinding mechanisms, based on the one hand on granulometric and morphological analyses and on the other hand on the characterization of surface properties.

In the present study, two starches with different amylose to amylo pectin ratios were used as fillers of a polyvinyl acetate matrix and the mixtures were co-ground in a tumbling ball mill during different times. Thermal and mechanical properties, as well as the behavior in water were analyzed.

Products, apparatus and experimental procedure

Iwo types of starch were used in this study. The first one is from waxy maize (Waxilys -Roquette Frères). It is a starch of crystalline type A, containing more than 99% of amylopectin. Grains are of polyhe dral shape (Fig. la) and the average particle size is 13 µm. The second starch is a Eurylon also issued from corn (Roquettes Frères), but of crys talline type B, containing 70% of amylose and 30% of amylopectin. Grains are rounder than those of Waxilys starch, and they are individualized or form agglomerates, some of them being rather big (Fig. 1 b ). The average size of the particles is 8.7 µm.

Polyvinyl acetate (PVAc) was gracefully supplied by the society Elotex -Switzerland. It is constituted by particles with a spheroidal shape, which are the result of the agglomeration of small grains produced by emulsion polymerization followed by drying. These spher oid particles can be single or agglomerated between them (Fig. 2, big particles). The average size of the PVAc particles is 120 µm.

In order to understand their own behavior, the three materials were dry milled alone in a 5 L ceramic laboratory tumbling ball mill (Prolabo) containing 20 vol.% ceramic balls with sizes between 5 and 12.5 mm. This range permits to always have an adapted ball to particle size ratio during grinding. The powder proportion in the mill was fixed at 20 vol.% of the interstitial void space between the balls. The rotation speed of the mill chamber was fixed at 100 rpm, corresponding to 75% of its critical rotation speed. Different experiments were performed dur ing various times, and the whole powder was recovered after each experiment to be submitted to different analyses.

Then the same runs were realized with PVAc-Waxilys and PVAc Eurylon mixtures containing 25 wt.% of starch. This rate was fixed in agreement with previous results [START_REF] Zapata | Production of smalt composite particles by co-grinding in a media mill -characterization of the granulometric and the mechanical properties[END_REF][START_REF] Seyni | Matrix-filler interactions in a co-ground ecocomposite -surface properties and behaviour in water[END_REF] which indicated that it permits to have better use properties.

Characterizations

Powder analyses

Sorne analyses were done on powders directly picked up in the mill chamber. Indeed, the particle size distribution, expressed in volume, and the median size, d50, were obtained on dry particles, using a laser diffraction granulometer Mastersizer 2000. The data were treated with the Mie theory. Three measurements were done on each sample and a maximum difference of 0.5 µm was observed between the values of the median size of a sample. Particles were also observed with a scanning electron microscope LEO 435 VP after metallization.

Other particles of the samples were analyzed by differential scanning calorimetry (DSC) using TA instruments Q2000 in nitrogen atmosphere. The temperature was increased between O and 200 °C at a rate of 10 °C•min-1. Iwo cycles were carried out and the thermo grams shown refer to the second heating, while the first cycle was used to eliminate any thermal history and moisture content in the sam ples [START_REF] Othman | Thermal properties of poiyvinyl alcohol (PVOH)/corn starch biend film[END_REF]. The glass transition temperature, Tg, of the matrix was deter mined from the thermograms. Sorne analyses were repeated 3 times and the difference between the Tg values was lower than 0.5 °C.

Analyses on films

For other analyses, films of a thickness around 0.5 mm were molded in a brass mold using a Carver Laboratory Press. Powder was introduced in the mold and heated during 10 min at 150 °C, i.e. above the melting temperature of the matrix. Then a pressure of 69 bars was applied during 30 s. Finally the films were cooled in cold water in order to avoid any crystallization of the matrix.

Test specimens of 25 mm x 5 mm were eut in the films in order to characterize their mechanical properties in traction by means of an ap paratus Instron 4301, at ambient temperature and with a cross-head speed of 5 mm-min-1. The initial gap between jaws was adjusted at 10 mm. The force (F) versus elongation was obtained for each sample. The nominal stress ( a) and the nominal strain ( e) were respectively calculated by equations:

( 1 ) [START_REF] Ha Pushpadass | Expansion, morphological and mechan ical properties of starch-polystyrene foams containing various additives[END_REF] where Sois the initial crosssection of the film, Lis the sample length and Lo its initial length. The Young modulus, E, was determined from the tangent slope of the low strain region. The strength (ab) and the maxi mum strain ( E b ) were reported for each sample. Mechanical tensile data were averaged over at least five specimens. The maximum error observed on each parameter was lower than 5%. Films were also cooled in liquid nitrogen and then broken. Their sections were observed with a scanning electron microscope JMS 6100 JEOL after metallization.

Finally, circular pellets with a diameter of 15 mm were eut in films and placed during several months in closed flasks containing distilled water at 22 °C, in order ta study their behavior in the liquid. The water was regularly changed and the pellets weighted after removal of water from their surface with an absorbent paper sheet. The water uptake was calculated by equation:

WU= m t - m i * 100 m i (3)
where m i is the initial pellet mass before immersion in water, and m t the pellet mass after an immersion time timm• The reproducibility on water uptake was determined on three pellets of some samples for various immersion times and experiments were started at different periods of the year. A difference in WU of less than 2% was observed between the results.

Since error values are indicated in this section for each analysis and are very low, we decided not ta report error bars on figures in order ta present clearly the results.

Experimental results and discussion

Results of powder analyses 4.1.1. Particle size and morphology

Since these results were developed in details in a previous paper [START_REF] Seyni | On the interest of using degradable fillers in co-ground composite materials[END_REF] for the PVAc-waxy maize starch mixture, we only synthesize here those necessary for understanding the study presented in this article, and we add data on PVAc-Eurylon mixture.

During their individual grinding, Waxilys particles are not fragmented because their initial size (given in Section 2) is lower than the limit size being able ta be reached during macromolecule grinding (few tens ofµm) [START_REF] Schèinert | Size reduction (fundamentals) -chap. 1, Ulmann's Encyclopedia ofin dustrial[END_REF]. On the contrary, they even agglomer ate and the median size tends ta increase slightly ta reach 30 µm. As for Eurylon, big agglomerates break during the first minutes. Then one observes the same agglomeration behavior as with the Waxilys starch.

Fig. 3 shows the variation of the median size of PVAc particles ground atone and of the co-ground mixtures.

Concerning the matrix, big agglomerates observed in Fig. 2 are first fragmented at the level of the particle joints ta individualize the particles constituting them. Then, the individual particles are fragmented progressively, leading ta a decrease of their median size down ta 40 µm. When this minimum size is reached, fragment agglomeration occurs and the median size increases. Finally, this one oscillates due ta a competition between agglomerate fragmenta tion and re-agglomeration.

Bath PVAc-starch mixtures have the same behavior during co grinding, but their median size evolves differently from the matrix atone. Indeed, in the mixtures, matrix particle are first broken and those of starch stick on PVAc fragments. This is confirmed by the SEM micrograph of Fig. 4a taken after one hour co-grinding: one can observe big PVAc fragments on which small starch grains are stuck The median size decreases. Starch coats gradually the PVAc fragments, the fragmen tation of which continues. The whole is then compacted under the effect of balls (Fig. 4b andc). However, contrary ta what was noted during the grinding of the matrix atone, we observe few re-agglomeration phe nomena with mixtures. The median size stabilizes then towards 25 µm. One can say that, in a mixture, agglomeration of starch grains on matrix fragments is favored compared ta matrix-matrix fragment agglomeration.

Thermal properties

DSC analyses were done on powders of the two starches, the matrix and the mixtures unground and co-ground at different times, and we focused on the second heating scan. As Sreekumar et al. [START_REF] Sreekumar | Studies on compatibility ofbiodegradable starch/polyvinyl alcohol blends[END_REF] and Othman et al. [START_REF] Othman | Thermal properties of poiyvinyl alcohol (PVOH)/corn starch biend film[END_REF] have already observed previously, the thermograms of bath starches are fiat. One can note on these figures an inflection of the curves at a temper ature lower than 50 °C. This corresponds to the PVAc glass transition temperature which was determined from ail the thermograms. The values are gathered in Fig. 6.

As for polyvinyl acetate, it was noticed that the glass transition temperature, initially at 40 °C, decreases when grinding is operated. This treatment can lead to a scission of the molecular chains of the poly mer [START_REF] Molina-Boisseau | Characterisation of the physico-chemical prop erties ofpolymers ground in a vibrated bead mill[END_REF], leading to a reduction ofits molecular weight, and as a conse quence, of its glass transition temperature. The grinding time does not have a significant effect on Tg. When mixing starch to PVAc (t = 0), the matrix glass transition temperature is decreased because ofhydrogen bonding between matrix and tiller. Othman et al. [START_REF] Othman | Thermal properties of poiyvinyl alcohol (PVOH)/corn starch biend film[END_REF] determined the melting and the crystalliza tion temperatures of polyvinyl alcohol and corn starch blends. They ob served the same decrease in these temperatures. Moreover the value of Tg, at t = 0 in Fig. 6, is very slightly lower in the presence of the starch with the higher amylose rate. Indeed, the linear structure of amylose favors hydrogen bonding compared to the crosslinked structure of amylopectin. Zhang and Thomas [START_REF] Zhang | Preparation and properties ofpolyhydroxybutyrate biended with different types of starch[END_REF] produced blends of poly hydroxybutyrate and starches with various amylose to amylopectin ra tios and they also noticed a lower value ofîg with blends containing higher amylose rate. Nevertheless, co-grinding increases the glass transition tempera ture. This can be due to a better dispersion of the tiller in the matrix ( that will be contirmed in the next section), leading to a more stable sys tem in which the mobility of the molecular chains is reduced. With co grinding, the difference between the values of Tg for the two mixtures is more important in favor of the mixture containing the starch with the higher amylopectin rate.

Properties detennined on films 4.2.1. SEM observation of film section

Fig. 7 presents micrographs of the sections of composite films tilled with Waxilys, respectively by simple mixture, and after 10 and 20 h of co-grinding. The same type of micrographs was obtained with the mixture PVAc-Eurylon.

On micrographs a and b, the starch grains are clearly recognizable. Moreover, adhesion between starch grains and the matrix is weak, what is highlighted by the absence of any physical contact between both components. The starch grains seem extracted from the matrix c)

during the cutting of the composite film. Finally, we note zones of tiller concentration, while other zones are exempt from it.

When matrix and tiller are co-ground before molding, the film sections are very different. Indeed, some starch grains are still observable after 10 h, but they seem stuck in the matrix (micrograph c). After 20 h, no grain is observable (micrograph d).

These observations allow validating the interest of co-grinding to improve the dispersion of the tiller in the polyvinyl acetate matrix.

Mechanical properties

The evolutions of the tensile modulus, strength and maximum strain versus co-grinding time are shown in Fig. 8 for the three materials (PVAc films, mixture PVAc-Eurylon, mixture PVAc-Waxilys).

The untilled matrix displays a viscoelastic behavior with a high tensile modulus (around 250 MPa), a high strength (around 15 MPa) and a low strain (around 6). The grinding time does not have a signiti cant effect on the mechanical properties of PVAc films what is consistent with the results obtained on the evolution of the glass transition temperature of the powder samples.

For low grinding times, adding starch particles results in an increase of the tensile modulus and in a decrease of both the strength and maximum strain. The PVAc materials tilled by starch particles became brittle. This result is therefore an indication of the Jack of intimate adhe sion between both components of the composite structure. This is con firmed by the observation of the SEM micrographs of the film sections (Fig. 7a andb).

Vargha and Tru ter [START_REF] Vargha | Biodegradable polymers by reactive transesterification ofther moplastic starch with poly (vinyl acetate) and poly (vinyl acetate-co-butyl acry late)[END_REF] studied the mechanical behavior of mixtures produced by partial trans-esteritication of polyvinyl acetate and starch. They could not measure the mechanical properties of samples of such composites which were very brittle contrary to polymer alone.

d)

0 t = 0 ■PVAc □ PVAc+W ■PVAc+E -.. - - - l = Sh - - - - - - l-!Oh l -20h �-- - - -- - - - - t-25h
•PVAc □PVAc+W •PVAc+E After 10 h of co-grinding, the filled films display a higher relative reinforcing effect. For instance, the Young modulus of a film reinforced with 25 wt.% of starch increased by a factor of 1.5 and the strength was of the same order as that for the unfilled materials. These results confirm that the co-grinding process allows a better cohesion between the tiller and the matrix. Nevertheless, the composite materials remain brittle with a low strain. Concerning the influence of the starch type on the mechanical prop erties, we cannot conclude because the tendency varied with the oper ating conditions.

I"' - - ., l-Sn � - ;:::: - - -� l-!Oh t = 20h - --- - - - - �-- l = 25h •PVAc □PVAc+W •PVAc+E ---
•t = O +--------------1 ô. t = 5h +-----------< • t = l Oh o t = 15h

Behavior in water and characterization of diffusional phenomena

Fig. 9 presents the variation of the water uptake of the matrix pellets immersed during different times, parameterized by the grinding time. The time scale is logarithmic to better analyze the phenomena taking place within the first immersion hours.

WU increases first with the immersion time, as water diffuses in pellets, to level off after 1000 min at a maximum value between 50 and 55%, corresponding to equilibrium in water uptake. This progressive increase may be attributed ta a hydrophilic behavior of PVAc which is moderate given the maximum values of WU. We observe a small influ ence of the grinding time on the maximum value reached, due to a mod ification of the molecular chains as expressed previously. Finally, the water uptake decreases progressively during the few months of the experiment As for mixtures (Fig. 10), similar evolutions are observed when the matrix is filled with starch having a high amylose rate. Eurylon seems ta have the same hydrophilic behavior in water than PVAc.

On the contrary, Waxilys is a highly hydrophilic starch due ta the fact that amylopectin structure is more open and consequently can absorb more water than amylose. Kibar et al. [START_REF] Kibar | Gelatinization ofwaxy, normal and high amylose corn starches[END_REF] also noted that water uptake of mixtures filled with starch increases as the amylose rate decreases. Mani and Bhattacharya [START_REF] Mani | Properties of injection moulded starch/synthetic polymer biends -Ill. Effect of amylopectin to amylose ratio in starch[END_REF] evoked an increase of the gelatinization and a degradation of the ramified structure of amylopectin that make the mixture more sensitive ta water. Without co-grinding (t = 0), the maximum water uptake is a little bit lower than for the two other systems, but this difference must be taken with care because of the dis persion irregularity of starch in matrix when unground. Indeed, in order the filler plays its real role, it needs to be well dispersed within the matrix to create a network. Bridges generated by the contact between starch grains will favor the water absorption in the whole pellet. How ever, as can be seen on the micrographs of Fig. 7b, pellets contain aggre gates of starch grains surrounded with unfilled matrix. A simple mixture of the constituents does not thus generate this network. However, once water has saturated matrix, it can reach concentrated starch zones and water absorption by the very hydrophilic starch can proceed. This is translated by the peak in the WU curve after 100 000 min of immersion. Water uptake kinetics and maximum value are greatly influenced by the co-grinding time, WU at equilibrium being close to 100% in some cases. Co-grinding favors the progressive dispersion of starch grains and the formation of a network through the pellets. Once this network established (after 10 h co-grinding) a longer co-grinding treatment has no significant effect on the first part of the curves and on water up take equilibrium. As for the WU decrease (last part of the curves ), it is more pronounced than for the two other systems. This may be attribut ed to starch release, as already suggested by Vargha and Truter [START_REF] Vargha | Biodegradable polymers by reactive transesterification ofther moplastic starch with poly (vinyl acetate) and poly (vinyl acetate-co-butyl acry late)[END_REF] and by Angellier et al. [START_REF] Angellier | Processing and structural properties of waxy maize starch nanocrystals reinforced natural rubber[END_REF].

Above the polymer glass transition temperature, chain relaxation is rapid and water diffusion within the polymer network may happen according to Fick laws. Below the glass transition temperature, chain relaxation is slower. According to Alfrey et al. [START_REF] Alfrey | Diffusion in glassy polymers[END_REF], transport phenome na into glassy polymers may be described by three models:

-The water diffusion rate is lower than the relaxation rate of polymer ic chains. The mechanism is controlled by diffusion which is Fickian; -The relaxation rate is lower than the water diffusion rate. The mech anism is thus controlled by chain relaxation; -Both rates are comparable.

Frisch [START_REF] Frisch | Sorption and transport in glassy polymers -a review[END_REF] expressed the mechanism of water diffusion by the following equation, valid for values of the left member of the equation lower than 0.6:

m1-mi _ k. tn . m«'-m i - mn ( 4 )
where m� is the pellet mass at equilibrium, timm the immersion time, k the system constant and n the diffusional exponent depending on the diffusion mechanism. The exponent n is equal to 0.5 if the diffusion is Fickian. This equation was applied to the results presented in Figs. 9 and 10, by expressing the logarithm of the left member of the equation versus the logarithm of the immersion time. Exponents n, equal to the slope, were determined for the various operating conditions and are gathered in Fig. 11. They are close to 0.5, indicating that the mechanism of water penetration into the pellets is controlled by Fickian diffusion. The inter cept points of the straight lines were also determined. ln that case, Crank [START_REF] Crank | Mathematics ofDiffusion[END_REF] precised that the constant k is equal to (4 / e) • (D / rr) 0 •5, where e is the pellet thickness and D the diffusion coefficient. D was thus calculated from the intercept points of the lines and the values are shown in Fig. 12, as well as the water uptake at equilibrium.

0 0 n (-) u r, ■ r, � � -• - •PVAc □PVAc+W ■ PVAc+E t (h) 5 l() 15
For the reason previously evoked of a bad dispersion of the filler in the matrix, data obtained for unground materials will not be discussed. When grinding is performed, one can notice that the diffusion coeffi cient is lower for mixtures than for the matrix alone. Moreover, the higher the amylopectin rate, the lower the diffusion coefficient. Finally the diffusion coefficient increases slightly with an increase of the co grinding time up to 20 h. This may be attributed to higher inter-and intra-molecular interactions in the presence of starch, which reduce chain mobility. These interactions slow down water diffusion. This is particularly the case for waxy starch with its ramified structure. These results are in accordance with the evolution of the glass transition temperature previously discussed, which is the highest in the presence of waxy starch and the lowest for the matrix alone. When the grinding time increases, the chain length decreases leading to a small enhance ment of the diffusion coefficient.

Concerning the values of WU�, they are similar and constant for the matrix and the mixture filled with starch containing the high amylose rate, whatever the grinding time, while those of mixtures containing starch with a high amylopectin rate are higher, in accordance with explanations given for Figs. 9 and 10 on the variation of the water uptake.

Conclusions

A study on co-grinding polyvinyl acetate filled with starch was per formed in order to show the opportunity of partially replacing the syn thetic matrix by a vegetable, degradable and available filler. Iwo starches having different amylopectin to amylose ratios were used.

Granulometric and morphological analyses have permitted to define the mechanism by which the composite material is formed. Co-grinding permits a better dispersion of the tiller in the matrix than a simple mixing, thus favoring PVAc-starch interactions. Mechanical properties of materials in traction are thus improved.

The glass transition temperature of polyvinyl acetate was deter mined by DSC analysis. The tiller presence leads to an increase of Tg due to a limitation of the polymeric chains mobility. Consequently, the higher the ramitied amylopectin rate, the higher the glass transition temperature.

Moreover, the presence of starch with a high amylopectin rate favors the composite water uptake if starch is well dispersed in the matrix under the effect of an optimized co-grinding treatment. Starch nature, linked to its botanical origin, influences the properties of composites produced by co-grinding.

Nomenclature

Fig. 1 .

 1 Fig. 1. SEM micrographs of starch partides. a. Waxilys. b. Eurylon.

Fig. 2 .

 2 Fig. 2. SEM micrographs of PVAc-starch mixtures before grinding. a. PVAc-Waxilys mixture. b. PVAc-Eurylon mixture.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Variation of the median size of the samples with and without starch during grinding.

  Fig. Sa gathers PVAc thermograms for three grinding times, white Fig. Sb and c present those of the mixtures for the same times. The samples taken at other times were also analyzed but their thermograms are not presented in these figures to have them clear enough.

-D-Fig. 5 .

 5 Fig. 5. Thermograms of the matrix and the mixtures for some grinding times. a. PVAc thermograms. b. Thermograms of PVAc + Waxilys. c. Thermograms of PVAc + Eurylon.

■ 30 Fig. 6 .

 306 Fig. 6. Glass transition temperature (Tg) of the samples as a function of the grinding time.

Fig. 7 .

 7 Fig. 7. SEM micrographs of PVAc-Waxilys film sections. a. Without co-grinding. b. Without co-grinding -detailed view. c. 10 hour co-grinding. d. 20 hour co-grinding.

Fig. 8 .

 8 Fig. 8. Mechanical properties of the matrix and the mixtures. a. Tensile modulus. b. Strength. c. Maximum strain.

F ig . 9 .

 9 Influence of immersion and grinding rimes on PVAc water uptake.

Fig. 10 .

 10 Fig. 10. Influence of immersion and co-grinding times on mixture water uptake. a. PV Ac-Waxilys mixtures. b. PVAc-Eurylon mixtures.

1

 1

() 25 30 Fig. 11 . 30 Fig. 12 .

 30113012 Fig. 11. Diffusional exponent versus co-grinding time.


Nicolas Glade
email: nicolas.glade@imag.fr

Computing with the Cytoskeleton : A Problem of Scale

Microtubules and actin filaments are dynamic fibres constituting the skeleton of living cells. They show seemingly computational behaviours. Indeed, depending on conditions of reaction, they self-organise into temporal and/or spatial morphologies in vitro and act as micro-machine processors and actuators in living cells. Other systems -such as the bacterium-actin system -exist that 'know'how to re-use the cytoskeleton for their own use (e.g. propulsion inside the cell).

We discuss here about the possible reuse of the cytoskeleton for constructing fibrillar-based computational systems. I analyze particularly the possible existence of computational events based on 'chemical collisions' between microtubules. A molecular model of microtubule disassembly has been developed to verify that heterogeneities of composition and/or concentration of the chemical medium can form from shrinking microtubules and persist. They could serve as an efficient communication channel between fibrillar agents. Numerical simulations show that only very weak heterogeneities of composition form around the microtubule ends. However, the model predicts that they are notable when produced by arrays of numerous fibres such as microtubule arrays or comets of actin.

Introduction

Computing by using the dynamic fibres of the cytoskeleton (microtubules, actin filaments and microfilaments) is a dream shared by many physicists since a long time. The befefits would be indeed the possibility to develop massive parallel computing devices or micromachines at the micrometer scale.

Those fibres are supramolecular assemblies always reacting, aggregating their subunits or restituting them to the medium, and consuming the chemical energy provided by triphosphated nucleotides. The cytoskeleton has its own reactive properties and behaviour but, in the cells, it is also combined with numerous associated proteins that give a cohesion to the cytoskeletal structure, organise it and add new properties to individual fibres. The cytoskeleton is controlled and used by the living cells to maintain or change their shape and to perform numerous functions -and form the associated organites -such as cell division, internal transport of vesicles, and the structuration and actuation of cytoplasmic extensions such as cilia, flagella and pseudopods. Examples where the cytoskeleton is particularly implied in a cellular process are numerous. Striking examples are the mitosis -during which a cell divides into two identical cells -, the exploration ability of lymphocytes or macrophages of the immune system driven by the cytoskeleton, and morphogenetic processes, for instance the symmetry breaking of the cell shape in early tissues -e.g. the formation of 'bottle' cells from cubic cells that constitute the mesoderm of the ventral furrow (future digestive tube) [START_REF] Leptin | Cell Shape Changes during Gastrulation in Drosophila[END_REF][START_REF] Forest | A General Formalism for Tissue Morphogenesis Based on Cellular Dynamics and Control System Interactions[END_REF] -due to local metabolic or energetic changes in the cells. Further, parasitic bacteria such as Listeria or Shigella re-use the actin network to propel within cells [START_REF] Alberts | In Silico Reconstitution of Listeria Propulsion Exhibits Nano-Saltation[END_REF][START_REF] Boukella | Soft Listeria: Actin-Based Propulsion of Liquid Drops[END_REF].

Finally, the fibrillar proteins of the cytoskeleton, in particular microtubules, are well known for their ability to show self-organising behaviours. Solutions in vitro, starting from homogeneous 'soups of molecules', develop oscillatory temporal series [START_REF] Pirollet | An oscillatory Mode for Microtubule Assembly[END_REF][START_REF] Carlier | Synchronous Oscillations in Microtubule Polymerisation[END_REF], spatio-temporal behaviours (wave propagation as in excitable media) [START_REF] Mandelkow | Spatial Patterns from Oscillating Microtubules[END_REF][START_REF] Sept | Model for Spatial Microtubule Oscillations[END_REF] or well structured morphologies made of ordered populations of fibres [START_REF] Tabony | Microtubular Dissipative Structures in Biological Auto-Organization and Pattern Formation[END_REF][START_REF] Papaseit | Reaction-Diffusion Microtubule Concentration Patterns Occur During Biological Morphogenesis[END_REF][START_REF] Tabony | Biological Self-Organisation and Pattern Formation by Way of Microtubule Reaction-Diffusion Processes[END_REF]. Temporal oscillations of the concentration of microtubules in the solution are now well described by models of microtubular population dynamics. Spatio-temporal behaviours are also well described at the macroscopic scale by reaction-diffusion kinetics [START_REF] Sept | Model for Spatial Microtubule Oscillations[END_REF] but little is known about their spatial self-organisation. Theoretical models based on collective systems and reaction-diffusion dynamics at the level of individual microtubules were advanced in order to explain this phenomenon [START_REF] Tabony | Biological Self-Organisation and Pattern Formation by Way of Microtubule Reaction-Diffusion Processes[END_REF][START_REF] Glade | Numerical Simulations of Microtubule Self-Organisation by Reaction-Diffusion[END_REF][START_REF] Tabony | Microtubules Viewed as Molecular Ant Colonies[END_REF]. In this scheme, the microtubules, due to their dynamics, modify locally the chemical medium -that way generating a trail of chemicals when disassembling and a depleted area when assembling -and information is then shared between neighbouring individuals. Unfortunately, at least three counter arguments contradict strongly the idea that the microtubular cytoskeleton self-organises spatially from microscopic to macroscopic levels due to a chemical communication between individuals. (i) in vitro spatially self-organising solutions have a composition that favorises microtubule stability [START_REF] Panda | Suppression of Microtubule Dynamic Instability and Treadmilling by Deuterium Oxide[END_REF][START_REF] Itoh | The Effects of Deuterium Oxide (2H2O) on the Polymerization of Tubulin in Vitro[END_REF][START_REF] Glade | Tubulin Trails are Very Weak and May Have no Effect During Microtubular Macroscopic Spatial Self-Organising Phenomena[END_REF] ; (ii) in such concentrated solutions, mechanical effects or electrostatic interactions should have intense effects compared to the relative effect of the action of chemical communications [START_REF] Baulin | Self-Assembled Aggregates in the Gravitational Field: Growth and Nematic Order[END_REF][START_REF] Tuszynski | Physical Interpretation of Microtubule Self-Organization in Gravitational Fields[END_REF][START_REF] Liu | DNA Nanotubes Self-Assembled from Triple-Crossover Tiles as Templates for Conductive Nanowires[END_REF] ; (iii) the existence of the hypothetic chemical trails, possible vectors of a short range communication between microtubules, is being called into question because the diffusion of the released subunits that form the trail is such that the trail becomes inconsequential [START_REF] Glade | Existence and Persistence of Microtubule Chemical Trails -A Step Towards Microtubule Collision-Based Computing[END_REF][START_REF] Glade | Tubulin Trails are Very Weak and May Have no Effect During Microtubular Macroscopic Spatial Self-Organising Phenomena[END_REF].

Viewed by a computational scientist, these living systems look like micromachines that integrate external signals and transform them into deterministic behaviours. This keeps out of sight the fact that those macroscopic observable deterministic-like behaviours emerge from a multitude of stochastic processes occuring at the lower scales between individual molecules. But the cells 'know' how to control this stochasticity: their structures self-organise from the lower scales to the higher scales, constituting imbricated meta-structures, until the level of the cell, the units of life. Stimulated by externals signals or by signals intrinsic to the cell (genomic signals induced by internal metabolic cycles for instance), the cytoskeletal structures reorganise, producing an adapted response of the cell. Within this theoretical context, the cytoskeleton appears to be a central system in those biological 'micromachines'.

The article reviews different manners to concieve a computation based on the cytoskeleton (see [START_REF] Glade | Existence and Persistence of Microtubule Chemical Trails -A Step Towards Microtubule Collision-Based Computing[END_REF] for further details) ; they depend on the scale considered for the computation. Then, we will focus on a possible computation based on chemical collisions between agents assimilated to dynamic fibres. The potential of such an approach would be biochemical -or bio-inspired artificial -massive parallel computers based on real collective agents interacting at the micrometer scale.

Different scales, different manners to compute

Different -imbricated -levels of cytoskeletal-based computation can be considered :

G The fibrillar scale. A computation effectuated directly inside the fibre or at its surface has been proposed initially by R. Penrose, S. Hameroff and J. Tuszinsky [START_REF] Hameroff | Information Processing in microtubules[END_REF][START_REF] Tuszynski | The Enigma of Microtubules and their Self-Organizing Behavior in the Cytoskeleton[END_REF][START_REF] Tuszynski | Dieletric Polarization, Electrical Conduction, Information Processing and Quantum Computation in Microtubules. Are they Plausible ?[END_REF][START_REF] Hameroff | Conduction Pathways in Microtubules, Biological Quantum Computation, and Consciousness[END_REF][START_REF] Hameroff | Search for Quantum and Classical Modes of Information Processing in Microtubules: Implications for the Living State[END_REF][START_REF] Tuszynski | Ionic Wave Propagation along Actin Filaments[END_REF][START_REF] Faber | Information Processing in Brain Microtubules[END_REF] for microtubules or actin filaments. Charges or conformational states inside or captured by the monomers of these supramolecular assemblies could be used as biochemical bits of information. Such biochemical states were predicted by models to be able to propagate within a fibre or at its surface. Computational events could then occur such as collisions of propagating waves of biochemical states. Moreover, they predict that communication between fibres could be relayed by the associated proteins that connect individual fibres in the cytoskeletal network. This process is thought to play an important role in integration and 'pre-computation' of the bioelectrical signals in neurons. It's difficult to ignore such possible effects considering that microtubules represent 10% of the proteins in a brain. This suggests a new manner (subcellular) to understand the functioning of the brain, in addition to the concepts used habitually for describing neural networks.

G The scale of a small number of fibrillar agents (small population). At this scale can be described the chemical relationships between individual reacting agents and the chemical environment, connecting correspondingly and indirectly each agent to other neighbouring fibres (see Fig. 2A andB). This system is similar to ant colonies where a population self-organizes by way of the chemical trails -constituted by messenger molecules called pheromones -that the ants release behind them. The neighbourhood is delimited by the ratio between the diffusion rate of the molecules that constitute the released trails and the reaction rate of the agents (here, the reacting ends of the fibres). When this ratio increases, the neighbourhood extends far away from the reacting tip from which the signal (the trail) originates, but in the same time the signal decreases in intensity. The intensity of the signal is related to the number of messenger molecules per unit of space. In those systems, an important parameter is also the amounts of matter implied in the chemical trails. Moreover long fibres diffuse less rapidly than their monomers. They stay more or less in the same element of volume during their existence and are constituted by subunits taken from this element of volume. When they disasssemble, they restitute the monomers to this small volume. The total amount of fibres in the considered element of volume depends on the conditions that have permitted their formation : in favourable conditions, numerous fibres can form (and reciprocal). In consequence, in this scheme, the supramolecular assemblies -or groups of fibres -can be viewed as 'memories' than store locally the information (the reactive conditions that prevaled before their assembly) into a condensed form.

G A population at the millimeter scale (huge number of individuals). Now, a description of macroscopic ordering is possible. This level can be viewed as the manifestation of a computation based on chemical communications between agents. When considering nanofibres (e.g. actin, microtubules), other mechanisms, however, such as mechanical effects (buckling of individual fibres, bundling into parallel arrays . . . ) that can not be controlled easily, can cause local self-ordering of fibres but also global self-ordering when influenced by global effects such as weak external fields (gravity, magnetic fields . . . ) [START_REF] Baulin | Self-Assembled Aggregates in the Gravitational Field: Growth and Nematic Order[END_REF][START_REF] Liu | DNA Nanotubes Self-Assembled from Triple-Crossover Tiles as Templates for Conductive Nanowires[END_REF]. Nevertheless, reactive conditions exist where mechanical effects are inconsequentials and where the reaction-diffusion effects -as described before -are dominating. This explains how individual microtubules are synchronized within the propagating waves of microtubular concentration observed by Mandelkow et al [START_REF] Mandelkow | Spatial Patterns from Oscillating Microtubules[END_REF][START_REF] Sept | Model for Spatial Microtubule Oscillations[END_REF], or how they synchronize within the entire solution for generating periodic temporal oscillations [START_REF] Pirollet | An oscillatory Mode for Microtubule Assembly[END_REF][START_REF] Carlier | Synchronous Oscillations in Microtubule Polymerisation[END_REF].

G The same scale enhanced by the control of regulatory systems and organizing centers. Finally, one can consider the same level of description, but in a different context, by adding cellular features such as organising centres (centrioles, linking or branching associated proteins (e.g. kinesin, dynein, Arp2/3), . . . ), associated enzymes (e.g. ADF cofiline for the Actin network), energetic molecules (ATP, GTP) or ionic species (Mg 2+ , Ca 2+ , . . . ) that regulate the reactivity of the fibres, and genetic regulatory systems that control the amounts of components in the system. Using this 'arsenal', living cells control accurately the cytoskeleton for realising various actions (moving, dividing, . . . ). This is close to the description of a micromachine.

3 Multi-agents collision-based computation

Considering individual fibres as units of a collective system

In order to showcase the existence of a possible communication between individual fibres, a molecular model of microtubule has been concieved where all monomers (tubulin-GTP and tubulin-GDP) are represented and where an unique fibre or an array of fibres disassembles. During the simulation, we observe the distribution of the released particles (tubulin-GDP) all around the reacting tips of the microtubules [START_REF] Glade | Existence and Persistence of Microtubule Chemical Trails -A Step Towards Microtubule Collision-Based Computing[END_REF][START_REF] Glade | Tubulin Trails are Very Weak and May Have no Effect During Microtubular Macroscopic Spatial Self-Organising Phenomena[END_REF]. In this model, all molecules (monomers and polymers) are assimilated to ellipsoids, and their diffusion rates along their 3 axes are calculated in function of their 3 respective radiuses. This allows observing the effect of anisotropic diffusion, particularly for the polymers that have a very long axis compared to their diameter and a limited diffusion perpendiculary to this principal axis. It results from this very simple model that the homogeneization by diffusion of the 'hypothetic trail' formed by the released subunits is largely faster than its formation. Small heterogeneities of composition of the medium (weakly concentrated isles of tubulin-GDP in very high concentrated regions of tubulin-GTP) can be measured when allowing several grouped microtubules to disassemble (see Fig. 1).

Figure 1: (Up, Left) Scheme of a microtubule while treadmilling: the microtubule grows at the right end and disassembles at its left end. (Up, Right) Concentrated area of tubulin-GDP (black) forming at the shrinking end of a microtubule. Tubulin-GTP heterodimers are displayed in grey. In this simulation, the microtubule disassembles about 1000 times faster (2000 µm.min -1 ) than a normal microtubule. (Down, Right) Density profile of tubulin-GDP around the tips of disassembling microtubules, measured during a similar simulation from the origin of an array of 5 diffusing microtubules (inset: transverse cross section of the x axis and of the 5 MTs at their initial position), each of them respectively separated by 30 nm (one microtubular diameter). All microtubules disassemble simultaneously at 20 µm.min -1 (1.85 ms.heterodimer -1 ) which is a quite quick disassembling rate. The macroscopic diffusion rate of individual tubulin dimers corresponds to that measured in the cytoplasm (5.9 10 -12 m 2 .s -1 ) [START_REF] Salmon | Diffusion Coefficient of Fluorescein-Labeled Tubulin in the Cytoplasm of Embryonic Cells of a Sea Urchin: Video Image Analysis of Fluorescence Redistribution After Photobleaching[END_REF]. The quantity of released tubulin-GDP molecules is very low and needs to be integrated in time for obtaining average profiles. The graphic has been reconstructed by integration of the density maps of 6 independent simulations, during 1.8 ms, between the simulation times 9.2 ms and 11 ms, along the 3 axis. (Down, Left) The same in water at 37˚C. The average value of the global diffusion constant obtained (4.9 10 -11 m 2 .s -1 ) is about 8x larger than in the cytoplasm, as measured in water by [START_REF] Salmon | Diffusion Coefficient of Fluorescein-Labeled Tubulin in the Cytoplasm of Embryonic Cells of a Sea Urchin: Video Image Analysis of Fluorescence Redistribution After Photobleaching[END_REF]. The resulting density profile of tubulin is weaker but detectable with 5 disassembling microtubules.

The result given in figure 1 means that the probability that the reactivity of a growing microtubule in the neighbourhood (able to 'see' the present chemical medium) is modified is very low. In a solution at 10 µM (5400 monomers.µm -3 ) the maximum ratio of tubulin-GDP, produced by 5 disassembling microtubules, versus tubulin-GDP would be about 1/1500 in the cytoplasm and 1/6000 in water. This is also the probability that the growing mmicrotubule encounter one molecule of tubulin-GDP ; this probability multiplied by the probability the microtubule reacts with this molecule gives an idea of the very low frequency of microtubular catastrophe (disassembly) induced by tubulin-GDP in these conditions.

Chemical communication is consequently not very efficient when one consider only a few number of fibres. Nevertheless, the chemical species released by numerous fibres have a real effect, visible on the behaviour of some in vitro solutions of fibres. In the conditions found by Mandelkow et al [START_REF] Mandelkow | Spatial Patterns from Oscillating Microtubules[END_REF][START_REF] Sept | Model for Spatial Microtubule Oscillations[END_REF], the microtubules are synchronized over long distances (millimeters). Propagating waves of microtubular concentration can appear due to this synchronization. Moreover, in the other conditions found by Pirollet et al [START_REF] Pirollet | An oscillatory Mode for Microtubule Assembly[END_REF] and Carlier et al [START_REF] Carlier | Synchronous Oscillations in Microtubule Polymerisation[END_REF], the synchronization also appears over the whole sample (several millimeters to centimeters). Finally, during the spatial self-organising process as observed by Tabony [START_REF] Tabony | Microtubular Dissipative Structures in Biological Auto-Organization and Pattern Formation[END_REF][START_REF] Papaseit | Reaction-Diffusion Microtubule Concentration Patterns Occur During Biological Morphogenesis[END_REF][START_REF] Tabony | Biological Self-Organisation and Pattern Formation by Way of Microtubule Reaction-Diffusion Processes[END_REF][START_REF] Tabony | Microtubules Viewed as Molecular Ant Colonies[END_REF], an unique overshoot is observed at the beginning of the reaction (5 minutes after the beginning). The presence of an overshoot signifies that at the early stage of the reaction, microtubules react in a synchronized manner during a few minutes over the whole sample. The reactivity of microtubules increases with the concentration of magnesium. The more reactive microtubules are found in Mandelkow's solutions (20 mM Mg 2+ ), then in Pirollet's or Carlier's solutions (10 mM Mg 2+ ) and finally in Tabony's (1 mM Mg 2+ ). For a synchronization at the scale of only one micrometer, one would necessitate reactivities 100 to 1000 times faster than those of Mandelkow's solutions (waves of 1 mm large) [START_REF] Mandelkow | Spatial Patterns from Oscillating Microtubules[END_REF]. Microtubules in vitro have typical disassembling rates of about 1 to several tens of µm.min -1 . Increasing the reactivity 1000 times would mean microtubules disassembling at about 1000 to 10000 µm.min -1 . This is in agreement with the simulation that predicts the formation of consistent tubulin-GDP trails (Fig. 1 Left).

Zoom-out: the agents are synchronized arrangements of fibres

We just have seen that the greater is the reactivity and the weaker is the diffusion, the shorter is the range of synchronization of the fibrillar agents. Unfortunately, until then, there's no evidence that conditions exist -with very high reactivity -allowing to synchronize the activity of cytoskeletal fibres by chemical communications at a microscopic scale. Of course, Mandelkow's microtubular waves are consistent objects emerging from a chemical communication between individuals, but this doesn't correspond to our idea of developing a computing system based on molecular ants.

A system exists that looks similar to what we expect : the system composed by intracellular parasitic bacteria and the actin cytoskeleton [START_REF] Alberts | In Silico Reconstitution of Listeria Propulsion Exhibits Nano-Saltation[END_REF][START_REF] Boukella | Soft Listeria: Actin-Based Propulsion of Liquid Drops[END_REF]. Some bacteria such as the Listeria family or the Shigella family infect cells and hijack their actin cytoskeleton to propel in the cytoplasm. As they express at their surface actin nucleators, a 'comet' develops, composed of actin filaments and associated proteins (e.g. Arp2/3). The propulsion process is not completely understood, but it seems that the addition of new actin monomers between the surface of the bacterium and the comet causes the movement. Such systems are very interesting for the design of a computing system because they solve numerous problems:

G Communication between agents can exist. The comets form by addition of free diffusing actin monomers to the existing filaments connected to the bacterium. The growing rate is about several micrometers per minute and the diffusion rate of actin monomers is about 10 -11 m 2 .s -1 . The typical size of the bacterium-actin comets is about 5 to 10 µm long and hundreds nanometers large. That means that the size of the elongated objects (bacterium + comet) is comparable to the extend of the molecular diffusion. Moreover, the comets are constituted by thousands of actin filaments. That means that the intensities of the chemical signals emitted by the reacting ends of the system (a depletion of actin monomers at the growing end (bacterium) and a concentrated trail of actin monomers at the shrinking end) are notable. As we already said, a communication and a synchronisation of the activity of neighbouring individual agents is possible if the heterogeneities caused by the reactivity of the 'fibres' do not extend too much and have a sufficient intensity. That's the case in this system. The comets are sharing their components in the chemical medium. A comet travelling in the neighbourhood of another one will capture components of the other, and reciprocal. This will induce a change of direction of both objects ; in other terms, a chemical collision occur.

G Flexibility. Contrary to individual filaments of actin or microtubules, due to their big size, the comets of actin are pliable. This allows the system exploring the chemical medium by following the most concentrated regions of reactants (gradient searching). This is very similar to the behaviour of individual ants that follow the concentrated trails of pheromones instead of walking randomly. This is also similar to the original idea proposed several years ago that microtubules could self-organise as molecular ants [START_REF] Tabony | Biological Self-Organisation and Pattern Formation by Way of Microtubule Reaction-Diffusion Processes[END_REF][START_REF] Glade | Numerical Simulations of Microtubule Self-Organisation by Reaction-Diffusion[END_REF][START_REF] Tabony | Microtubules Viewed as Molecular Ant Colonies[END_REF], a hypothesis not verified and now contradicted by recent studies [START_REF] Glade | Existence and Persistence of Microtubule Chemical Trails -A Step Towards Microtubule Collision-Based Computing[END_REF][START_REF] Glade | Tubulin Trails are Very Weak and May Have no Effect During Microtubular Macroscopic Spatial Self-Organising Phenomena[END_REF].

G Spatial stationary states and symmetry breaking. When nucleators of actin are distributed over all the surface of the object (it's the case in some bacterium mutants or on artificial systems composed of latex bead with nucleators), the actin network grows in every direction. As long as it is the case, the object stays in a stationary position until a accident occurs or another comet chemically collides, that way breaking the symmetry (its stationarity) [START_REF] Van Der Gucht | Stress Release Drives Symmetry Breaking for Actin-Based Movement[END_REF][START_REF] Paluch | Cracking Up : Symmetry Breaking in Cellular Systems[END_REF].

Conclusion

We proposed to imagine a system where fibrillar shaped objects reacting at their ends could be used for a new kind of computation based on chemical collisions. For the reason it is composed by such fibres, the dynamic skeleton of living cells appeared to be a good candidate. We have shown however that, due to an unadapted reactivity compared to molecular diffusion and to the dimensions of the fibrillar agents, the use of such systems at the level of individual fibres is call into question. Fortunately, another system appears to be a better candidate for the role of 'molecular ant' : the bacteriumactin comet system. Due to its size, it is less sensitive to thermal agitation and is theoretically able to realise chemical communications based on concentrated trails or depletions of free diffusing components.

People know now how to realise artificial systems of actin comets. They use latex beads covered by actin associated proteins. These systems behave exactly as bacteria systems. Moreover, other physicists are currently trying to develop artificial dynamic nanotubes. Some succeed with self-assembling tiles of DNA [START_REF] Rothemund | Design and Characterization of Programmable DNA Nanotubes[END_REF][START_REF] Liu | DNA Nanotubes Self-Assembled from Triple-Crossover Tiles as Templates for Conductive Nanowires[END_REF] although their reactivity is not yet well controlled. Nevertheless, one can expect two realise one day an artificial system that behaves as actin-bacteria systems for realising unconventional chemical computers based on the principle of elastic chemical collision between molecular ant-like molecules.

In this context, a new algorithmic framework has to be developed as proposed by Adamatzky [START_REF] Adamatzky | Collision-Based Computing in Biopolymers and Their Cellular Automata Models[END_REF]. The problem is similar to collision-based computing systems in cellular automata [START_REF] Rennard | Implementation of Logical Functions in the Game of Life[END_REF][START_REF] Rendell | Turing Universality of the Game of Life[END_REF] but now new features have to be taken into account such as variable angles, speeds and distances between colliding objects, and most of all randomness.

Seeing natural processes as computing processes gives to biologists and physicists a different point of view and sometimes helps to break accepted paradigms. Microtubules, actin and intermediate filaments serve as simple mechanical elements in the cell structure (tensegrity models of the cytoskeleton). In addition, the cytoskeleton is acting as an autonomous system sensible to external stimuli, conferring very complex behaviours to the cell. Comparing behavioural phenomena at the cellular scale and those that exist at the level of whole organisms is revealing. The motion of a migratory cell looks similar to that of an octopus, an organism more complicated. Flagella organelles are primitive caudal fins of swimming cells (e.g. spermatozoids). The bacteria Listeria and Shigella reuse the actin cytoskeleton as a propelling motor in infected cells. Those simple organisms developed many techniques to reuse the cytoskeleton, creating that way micro-machines.

In addition to the aspects of micro-machinery, it's tempting to imagine the role of primitive brain the cytoskeleton could have had in simple organisms (e.g. ciliate organisms) during millions years of evolution. About the 'seemingly intelligent' behaviours of single cell protozoa, C. S. Sherrington said "of nerve there is no trace, but the cytoskeleton might serve" (yet mentioned by Hameroff and Tuszynski in [START_REF] Hameroff | Search for Quantum and Classical Modes of Information Processing in Microtubules: Implications for the Living State[END_REF]).

Figure 2 :

 2 Figure 2: (A) Scheme of the idealized chemical collision between three individual microtubules. The two microtubules behind can sense the tubulin trail let by the microtubule moving upstream. (B to C) Scheme of the possible chemical collision between two 'actin -bacterium' systems. (D) Simulation with a 2D toy-model showing what could be a lateral chemical collision, (E) or a frontal one, in a similar system.

Acknowledgements

I'm very indebted to J. Demongeot (TIMC-IMAG, CNRS) for offering me the access to his Lab, allowing me to continue this unconventional work. I also thank J. Berro (TIMC-IMAG, CNRS) for all stimulating discussions about the actin system and its helpful suggestions and A. Adamatzky for his interest in that work.