Alexandra Siot

Claire Longuet
email: claire.longuet@mines-ales.fr

Romain Léger

Belkacem Otazaghine

Patrick Ienny

Anne-Sophie Caro-Bretelle

Nathalie Azéma

Correlation between process and silica dispersion/distribution into composite: Impact on mechanical properties and Weibull statistical analysis

Keywords: Process dispersion, mechanical properties, Weibull theory, composite

Introduction

Polymer composites are widely used in applications such as transportation, high technology, and electronics products thanks to very promising mechanical, thermal, and electrical properties [START_REF] Dorigato | Fracture behaviour of linear low density polyethylenefumed silica nanocomposites[END_REF][START_REF] Mutiso | Electrical Conductivity of Polymer Nanocomposites[END_REF][START_REF] Kumar | Nanocomposites: Structure, Phase Behavior, and Properties[END_REF][START_REF] Nicolais | Nanocomposites with tailored optical properties[END_REF]. Reinforcements used for composites can take many forms (particles, platelets, nanotubes…). Silica is one of the most representative particulate reinforcements, and is used to reinforce mechanical properties [START_REF] Dorigato | Effect of Silica Nanoparticles on the Mechanical Performances of Poly(Lactic Acid)[END_REF] or to improve flame retardancy of polymers [START_REF] Fanglong | Influence of nanosilica on flame resistance behavior of intumescent flame retardant cellulosic textiles: Remarkable synergistic effect?[END_REF][START_REF] Takashi | Flame Retardant Mechanism of Silica Gel / Silica[END_REF]. One of the obstacles for the use of particles in polymer matrix is the poor control of its dispersion [START_REF] Crosby | Polymer Nanocomposites: The "Nano" Effect on Mechanical Properties[END_REF]. Even if for electrical properties, percolation is wanted [START_REF] Matzui | Electrical conductivity of epoxy resin filled with graphite nanoplatelets and boron nitride[END_REF], for mechanical properties, a good dispersion of particles is highly recommended. It is necessary to distinguish distribution and dispersion, in studies concerning particles repartition into a composite. The first one is limited to a homogeneous repartition of particles in a defined space. While, dispersion, try to access to single particles: isolated particles of each other's without the necessity of a homogeneous spatial repartition [START_REF] Tadmor | Principles of Polymer Processing[END_REF]. It is necessary to control the dispersion at each step of the process to ensure a good dispersion in the final composite, whether working in the molten or the solvent phase. The impact of the particles dispersion is highly studied in the literature for metallic and ceramic composites [START_REF] Barmouz | Effect of SiC Particles Dispersion on the Grain Size and Mechanical Properties of Cu/SiC Metal Matrix Nanocomposites Produced via MFSP[END_REF][START_REF] Chandran | Effect of carbon nanotube dispersion on mechanical properties of aluminum-silicon alloy matrix composites[END_REF][START_REF] Fujiwara | Effect of Microstructure on the Mechanical Properties of Magnesium Composites Containing Dispersed Alumina Particles Prepared Using an MM / SPS Process[END_REF]. While, for organic composites, only few characterizations of the dispersion were found in the literature [START_REF] Ramanathan | Graphitic Nanofillers in PMMA Nanocomposites-An Investigation of Particle Size and Dispersion and Their Influence on Nanocomposite Properties[END_REF][START_REF] Zare | Influences of nanoparticles aggregation/agglomeration on the interfacial/interphase and tensile properties of nanocomposites[END_REF][START_REF] Dorigato | Cycloolefin Copolymer/Fumed Silica Nanocomposites[END_REF][START_REF] Golbang | A method for quantitative characterization of agglomeration degree in nanocomposites[END_REF]. In these works, no comparison of same formulation with distinct dispersion state (well and poorly dispersed materials) were performed. To insure a well-dispersed composite, it is necessary to verify after every stage of the process that particles are not re-agglomerated. This is not always performed in the literature and constitutes, according to the authors, a lack. Nowadays, to our knowledge, there is no direct link between various dispersion states and final mechanical properties of composites while the interest of this dispersion was highlighted in various studies. Indeed, it is proven that the fillers agglomeration in the matrix causes premature failure of the composite [START_REF] Tessema | Effect of filler loading, geometry, dispersion and temperature on thermal conductivity of polymer nanocomposites[END_REF][START_REF] Ferreira | Correlation of surface treatment, dispersion and mechanical properties of HDPE/CNT nanocomposites[END_REF][START_REF] Ahmed | Effect of nano silica on the mechanical properties of Styrene-butadiene rubber ( SBR ) composite[END_REF] and lead, in some cases to decrease the composites Young's modulus [START_REF] Shin | Homogenization analysis of polymeric nanocomposites containing nanoparticulate clusters[END_REF]. Usually, most of the composites are a mix of isolated and agglomerated particles. To optimize the microstructure, it is necessary to characterize and control particles dispersion throughout the process of composite elaboration. One of the proposed methods to overcome the problem of dispersion in a given medium is to make them compatible. In this context, a lot of studies deal with the functionalization (e.g. silica in polymethylmethacrylate (PMMA) [START_REF] Junior | Friction spot welding of PMMA with PMMA/silica and PMMA/silicag-PMMA nanocomposites functionalized via ATRP[END_REF][START_REF] Chau | Preparation of transparent silica-PMMA nanocomposite hard coatings[END_REF]; rubbers [START_REF] Vijay | Studies on blends of natural rubber and butadiene rubber containing silica-Organomodified kaolin hybrid filler systems[END_REF][START_REF] Pourhossaini | Effect of silica particle size on chain dynamics and frictional properties of styrene butadiene rubber nano and micro composites[END_REF][START_REF] Varol | Multiscale effects of interfacial polymer confinement in silica nanocomposites[END_REF] ; Polyamide-imides (PAI) [START_REF] Kang | Dispersion of surface-modified silica nanoparticles in polyamide-imide (PAI) films for enhanced mechanical and thermal properties[END_REF]; Poly L lactic acid (PLLA) [START_REF] Wu | Inorganic silica functionalized with PLLA chains via grafting methods to enhance the melt strength of PLLA/silica nanocomposites[END_REF]), and in addition, to improve mechanical properties of composites. One of the drawbacks of this method is that it is not universal and has to be designed as a function of one particle for one medium.

Therefore, it is necessary to develop a dispersion method able to adapt to any medium and/with any particles. In the literature, methods such as hot melt extrusion [START_REF] Feng | Effects of the extrusion temperature on the microstructure and mechanical properties of TiBw/Ti6Al4V composites fabricated by pre-sintering and canned extrusion[END_REF] (with optimized screw profile, melting time or crew speed), ultrasound (US) process [START_REF] Cai | The effects of nanoSiO2 on the properties of fresh and hardened cement-based materials through its dispersion with silica fume[END_REF][START_REF] Kawashima | Dispersion of CaCO3 nanoparticles by sonication and surfactant treatment for application in fly ashcement systems[END_REF][START_REF] Hasani Baferani | The role of sonication time upon acoustic wave absorption efficiency, microstructure, and viscoelastic behavior of flexible polyurethane/CNT nanocomposite foam[END_REF] (generally in solution) are reported as promising solutions. According to these results this study has been focused on the using of US process.

To simplify the mechanical study it is important to choose a matrix without any nucleation or crystallization effects as described by Manias and al. [START_REF] Manias | Fundamentals of Polymer Nanocomposite Technology[END_REF]. An amorphous matrix is the best solution to avoid these structural modification problems. One of the most current polymers in the literature and thus used in this study, is the PMMA. This polymer is widely used as a substitute for inorganic glass thanks to its lightweight, transparency and ease of processing. The disadvantage of this material is its poor mechanical properties and many research groups have worked on the incorporation of inorganic fillers to this matrix in order to improve its physical properties [START_REF] Banks-Sills | Experimental determination of mechanical properties of PMMA reinforced with functionalized CNTs[END_REF][START_REF] Jindal | Mechanical Characterization of PMMA/MWCNT Composites Under Static and Dynamic Loading Conditions[END_REF][START_REF] Alzarrug | The use of different alumina fillers for improvement of the mechanical properties of hybrid PMMA composites[END_REF]. In this study, in order to keep the PMMA transparency, filler content was fixed to 1wt%. This load percent is currently used to reach good mechanical properties [START_REF] Fallah | Improving the mechanical properties of waterborne nitrocellulose coating using nano-silica particles[END_REF][START_REF] Mccarthy | Synthesis, structure, and properties of hybrid organic-inorganic composites based on polysiloxanes. I. Poly(dimethylsiloxane) elastomers containing silica[END_REF][START_REF] Bikiaris | Preparation by melt mixing and characterization of isotactic polypropylene/SiO2 nanocomposites containing untreated and surface-treated nanoparticles[END_REF][START_REF] Zou | Polymer / Silica Nanocomposites : Preparation , Characterization , Properties , and[END_REF]. In addition of load percent, a lot of studies deal with the effect of particles size. It is well known that the particle size influences the mechanical properties [START_REF] Yuan | Effect of the particle size of nanosilica on the performance of epoxy/silica composite coatings[END_REF][START_REF] Blivi | Experimental evidence of size effect in nano-reinforced polymers: Case of silica reinforced PMMA[END_REF][START_REF] Adachi | Mixture law including particle-size effect on fracture toughness of nano-and micro-spherical particle-filled composites[END_REF] especially the smallest ones with regards to Young's modulus [START_REF] Cho | Effect of inclusion size on mechanical properties of polymeric composites with micro and nano particles[END_REF]. Two submicronic particles sizes were thus synthesized in this work, in order to study a composite between a micro and a nanocomposite.

The aim of this paper was to study the impact of the process on the fillers dispersion and how this dispersion impacts the mechanical properties of PMMA-SiO 2 composites.

Several models were elaborated, each of them showing a good (uniform particle) or a poor (high agglomeration) SiO 2 dispersion. This study wants to show by experiments and statistical study, that the particle dispersion quality has much more influence than the particle size on mechanical properties.

Experimental details 1. Reagents

PMMA was supplied by Arkema (Altuglass V825T) and used as received. Deionized water was used throughout this work. Acetone, tetraethoxysilane (TEOS, 98%) and ammonia (35%) were purchased from Merck Schuchardt OHG.

Ethanol was purchased from Sigma-Aldrich. All reagents were used as received without any further purification.

Particles synthesis

Two silica particles powder were synthesized by a modified Stöber method already used in previous works [START_REF] Parpaite | Incorporation of modified Stöber silica nanoparticles in polystyrene/polyamide-6 blends: Coalescence inhibition and modification of the thermal degradation via controlled dispersion at the interface[END_REF][START_REF] Parpaite | Janus hybrid silica/polymer nanoparticles as effective compatibilizing agents for polystyrene/polyamide-6 melted blends[END_REF]. Both synthesis reactions were performed in a 100 mL glass reactor. First synthesis used 26 g NH 3 (25%) and 36 g pure water, injected into 212 g of pure ethanol (EtOH). Then, 20 g TEOS (silica precursor) was quickly added to the vial, while stirring at 50 °C for 10 h in view of the growth of silica.

For the second method, 24 g NH 3 (25%); 18 g H 2 O and 515 g EtOH are injected into the 100 mL glass reactor. Then, 20 g TEOS is added, while stirring at regulated room temperature (25 °C) for 2 days. Numerous studies have shown that all the process conditions, like the temperature, TEOS ratio or process time for example, have an important impact on the particles size [START_REF] Rao | A novel method for synthesis of silica nanoparticles[END_REF][START_REF] Chen | Facile synthesis and magnetic properties of monodisperse Fe3O4/silica nanocomposite microspheres with embedded structures via a direct solution-based route[END_REF][START_REF] Nozawa | Smart Control of Monodisperse Stöber Silica Particles: Effect of Reactant Addition Rate on Growth Process[END_REF]. Also, higher concentration of water resulted in larger size of the particle.

At the end of these two syntheses, ethanol was removed before use and replaced by water using evaporation under vacuum. Then, the dried silica was purified, in order to remove remaining reactants, by washing and centrifugation methods. First protocol has allowed to obtain 5.33 g (yield~92%) of silica with a size of 470nm (silica L), and second protocol 4.11 g (yield~71%) of silica with a size of 140nm (silica M).

Instrumentation and methods

Laser diffraction particle size analyzer

The instrument used is a laser granulometer LS 13 320 from Beckman-Coulter Company. A scattering of monochromatic light (λ=780nm) diffracted and transmitted through the suspension permits to obtain particle size distribution performed in acetone containing a few milligrams of silica powder. The optical model used for silica has been computed for a refractive index with a real part of 1.33 and an imaginary part of 1.5.

Zeta potential measurements

Zeta Potentials (ζ) of particles were all measured at 25 °C using a Zetasizer Nano ZS (Malvern instruments Ltd., England) with a red laser (633 nm). DTS1060-folded capillary cell was used as the sample container. Three repeats for each sample were conducted to estimate the error in measurements. A titration machine (MPT-2 Malvern instruments Ltd.; England) was used in order to determinate the zeta potential function of pH. The titration procedure was carried out by increasing (from the solution pH to 13) with a 1M NaOH solution and decreasing (from the solution pH to 1) with a 1M HCl solution.

Scanning Electron Microscopy (SEM)

SEM measurements were performed with an Environmental Scanning Electron Microscope with Energy Dispersive X-ray spectroscopy (ESEM-EDX) (Quanta 200 FEG) from the FEI Company.

Dispersion quality was investigated with this machine for the master-batch and the strand. To this end, the composites have been cut under nitrogen (freeze-fracture). Then, they were deposited on a sample holder with a carbon scotchand were metallized in high vacuum sputtering metallizer Bal-Tec CED 030 Balzers in order to ensure their stability during the analysis.

Mechanical properties

Uniaxial tensile tests of composites PMMA/silica were performed on a tensile machine (Zwick/Roell) equipped with a 2.5kN load cell and a clip-on extensometer with a reference length of 30 mm at room temperature (25°C). A crosshead speed of 1 mm/min was applied. The Young's modulus was determined by tangent method between 0.05 and 0.25% of elongation. Each test was carried out at least 4 times.

Processes

The composites were elaborated in three steps: the first one is the production of a PMMA/Silica master-batch, the second one is the dilution of this master-batch and the last one is the injection of the blend to obtain mechanical test specimens.

Master-batch formulations

Firstly, the synthetized silica particles were ultra-sonicated into suspension to reach several levels of dispersions. The most commonly used in the laboratories and investigated in this study are: a bath and a probe sonicator.

Fig1.Two different approaches of the particles dispersion

For the first procedure PMMA/silica/acetone suspension was introduced in a beaker (20mL) and sonicated using an ultrasonic bath.

For the second procedure silica/acetone suspension was introduced in a beaker (20mL) and sonicated using a probe. After dissolution of PMMA in acetone, the polymer was added to the dispersion and the solution was also sonicated.

Sonication times for both processes were chosen arbitrarily; 10 minutes for the first silica size and 65 minutes for the second one in order to reach an optimized dispersion.

The estimated power of bath and probe was respectively 240W and 59W.

After those dispersion processes, a film was obtained by a solvent casting procedure and dried at room temperature under a fume hood for 2 days.

Dilution method

The films obtained previously which exhibit several levels of silica dispersion (thanks to the processes described in the previous sections) were blended at molten state. 6.6g of PMMA was added with a twin screw compounder DSM ® . To obtain a homogeneous strand charged 1wt % silica, composites were blended at 250 °C for 4 minutes with a screw speed of 80 rpm.

Injection

The obtained strand was injected at 250 °C with an injection molding machine, Zamak Mercator with a molding pressure of 5 bar maintained for 10 seconds. We obtained ISO 527-2 type-1BA specimens for mechanical tests.

Statistical analysis: Weibull approach

The failure strength of several samples can be significantly different due to their microstructural heterogeneity. To analyze the statistical variation of the failure strength in such materials, Waloddi Weibull adopted in 1951 the statistics of extreme [START_REF] Weibull | A Statistical Distribution Function of Wide Applicability[END_REF]. This approach uses a probability distribution function that characterizes the local failure strength. This law (equation 1) depends on the experimental ultimate stress σ r , the shape parameter m (Weibull modulus) and the scale parameter or characteristic strength .

(

The experimental fracture probability is defined by the relation:

(2)
where k is the rank in strength from least to greatest, n denotes the total number of samples.

Equation (1) can be rewritten as:

(3)

The Weibull modulus, m, characterizes the degree of homogeneity in the structure and so the degree of scattering of failure strength. A high m value corresponds to a homogeneous structure with a uniform strength, whereas a low value of the Weibull modulus indicates a high scattering of the measured parameters. Besides, the characteristic strength is a location parameter. Hence a straight line is expected between and with slope m. From the value of m and intercept , the value of can be determined.

Around 20 specimens were tested to obtain good estimates of the Weibull parameters.

The samples that were not broken in the zone of interest were set aside.

Results and discussions

Particles analysis and dispersion study

The obtained silica particles were observed by SEM (Fig2). Micrographs show monodisperse spherical particles with two different sizes: (a) 470 nm (silica L) and (b) 140 nm (silica M). For the silica L particles the TEOS/water ratio was approximately 1/2, for the silica M particles the ratio was 1/1. This result confirms the impact of water concentration. A TEOS/water ratio which is multiplied by two implies a three-fold increase of the final size of silica particles. When NPs are in suspension they generally tend to agglomerate due to their high free surface energy [START_REF] Metin | Stability of aqueous silica nanoparticle dispersions[END_REF][START_REF] Poddar | Investigations in two-step ultrasonic synthesis of PMMA/ZnO nanocomposites by in-situ emulsion polymerization[END_REF]. Zeta-potential study was conducted to evaluate the particle dispersion. In order to optimize the silica dispersion, this study allowed the estimation of the suitable solution pH value knowing that a high zeta-potential predicts a good dispersion stability of particles [START_REF] Metin | Stability of aqueous silica nanoparticle dispersions[END_REF][START_REF] Rahul | Surface Modification of Silica Nanoparticles to Reduce Aggregation and Nonspecific Binding[END_REF]. Zeta potential values are given in Fig3. The best possible condition of dispersion was identified at pH=9 and the silica IEP (IsoElectric Point) was determined at pH=2. Values situated on a zeta stable tray between pH=7 and pH=11, and makes the control of its state of dispersion easier. The dispersal of both sizes of silica was performed. The silica dispersions have been confirmed by ESEM micrographs. A technique of drop pulling on a glass support with an optical paper, according to a previous work in the laboratory [START_REF] Autier | Mesostructure evolution of cement pastes with addition of superplasticizers highlighted by dispersion indices[END_REF], was used. Micrographs (Fig3) confirm and pH=3, silica particles showed an obvious tendency to form agglomerates.

At pH=9, particles dispersion is clearly improved. Nevertheless, some agglomerates remain due to the Van Der Walls interactions between particles. It will be a challenge to overcome these interactions and to find the best way during the process to improve dispersion of these agglomerates.

Fig3.Zeta potential vs pH of synthetized silica.

Elaboration process: influence on the dispersion

Suspension dispersion

A study on the sonication time required for the improvement of NPs dispersion in suspension was performed with laser granulometry and illustrated in Fig4. The statistical measure values are reported Table1. d max is the biggest size in suspension and principal mode the most represented size in suspension. The two processes of dispersions (bath and probe process describe part I.4.1) have been investigated and compared. A monodisperse size distribution with the probe process after 10 and 65 minutes respectively for the silica L and silica M was observed. As expected, silica L needs less time of sonication to be dispersed. Indeed, the smaller the particle, the more difficult it is to disperse. With the bath process the same conditions have been applied

but the monodisperse peak corresponding to an absence of agglomerates was not obtained. Agglomerates around 10-50 µm were still present in the solution at the end of this sonication time.

Fig4.Size distribution of NPs by laser granulometry in acetone of a) silica L/bath process b)

silica M/bath process c) silica L/probe process and d) silica M/probe process.

Master-batch dispersion

In Fig5, the microstructures of master-batch PMMA/silica L (top) and PMMA/silica M (bottom) obtained with bath (left) and probe (right) processes with the require sonication time (determine previously, 10min for silica L and 65min for silica M) are illustrated. The fracture surface observation of the composite confirms the results obtained by laser granulometry. A real improvement of NPs distribution into the PMMA matrix can be observed in the case of probe process. It can be concluded that unlike the bath process, the probe process allows obtaining a homogenous composite.

PMMA/silica obtained by bath process exhibits a large number of agglomerates between 10 µm to 50 µm diameter in the composite (approximately the same order size than agglomerates found Fig4). In this last case, it would be appropriate to consider that the composite produced is closer to a micro-structure than to a nano-structure. This kind of morphology should impact the mechanical testing results. These results will also help to clarify importance of the preliminary dispersion process in suspension for the production of a well-dispersed composite.

SEM micrographs (Fig5) were binarized and NPs domains (around 1000 objects, to be statistically representative of the overall microstructure) were identified (red objects in Fig6), labeled and filtered by surface area value with respect to the scale of observation.

The normalized volume frequency distribution is represented in Fig7 for both silica and each preliminary process of dispersion, it is clear that independently of particles size, probe process leads to a better dispersion of fillers. This quantification confirms SEM observations. The granulometry deduced from SEM micrographs (Fig7), confirms the distribution measured by laser granulometry (Fig4) on the different suspensions (Table2). These results show that the second part of the process (concerning the dilution with twin-screw compounder) has little effect on the dispersion of the final composite. Indeed, the dilution step by twin-screw compounding had only an effect on the biggest agglomerates present into the master-batch. The distribution difference between laser granulometry in suspension and images treatment of composite is the shift of d max with bath process. In fact, the applied energy during the compounding step is not sufficient to disperse the smallest agglomerates. These results demonstrated that pre-dispersion of NPs into the solvent process is the key for a good final dispersion of NPs into the system. It is important to note that silica has no tendency to re-agglomerate after the master-batch step. shows that the composite obtained by probe process has higher mean Young's modulus, even though large scatter is observed for all the formulations. This improvement is probably due to the natural affinity between silica and PMMA. For bath process, silica L does not exhibit any reinforcing effect while PMMA with silica M particles has an improvement of 4% in the Young's modulus. With probe process it was observed an improvement of 9% for both sizes. It is also interesting to note that, irrespective of the dispersion quality, the size effect on Young's modulus is negligible.

Fig9.Process impact and size effect on Young's modulus

This observation is not in contradiction with the well-known assumption that the smaller are the nanoparticles, the higher are the nanocomposites elastic properties. In the present study the particles are not really nanoparticles (their median diameter is larger than 100 nm) and their level of incorporation is much lower than traditional nanocomposites with low aspect ratio particles. A numerical study [START_REF] Peng | Modeling of nanoreinforced polymer composites: Microstructure effect on Young's modulus[END_REF] confirms the absence of sensitivity of elastic parameters for spherical particles, incorporated at 1vol%, with mean diameter value more than 10nm.

Concerning the ultimate properties, the associate standard deviation is lower for the probe process (Fig10), indicating that this process results in composites with less morphological defects. Indeed, in the bath process case, stresses have tendency to unchanged neat PMMA properties, for both particles sizes. In the contrary, ultimate stress has an increasing tendency for probe process case (∼ 21% for silica L and ∼ 26% for silica M). These results confirm that a good dispersion leads to better mechanical properties.

A study on the relationship between dispersion metric and mechanical properties of PMMA/SWNT nanocomposites points out that the measured dispersion is crucial for reproducibility of mechanical properties [START_REF] Kashiwagi | Relationship between dispersion metric and properties of PMMA/SWNT nanocomposites[END_REF].

Fig10.Process impact and size effect on stress at break

Statistical analysis

A linear curve fit method was used to obtain the two Weibul parameters, was plotted versus and the best linear fit was computed (Fig. 11). the R 2 parameters (coefficients of determination) of neat PMMA and filled PMMA (M, L bath procees and M, L probe process) are equal to 0.86, 0.90, 0.95, 0.77, 0.90 respectively.

For the lastest composite (PMMA/ silica L well dispersed) the plot is non-linear which explains the low R 2 coefficient (Fig. 11). A bi-modal Weibull distribution could be more efficient in that case [START_REF] Zhou | Fabrication and evaluation of carbon nano fiber filled carbon/epoxy composite[END_REF]. The Weibul parameters are given Table 3. These parameters are remarkably affected by the preparation process and composite microstructures. In Table 3, it was observed that the Weibull parameter m increases with the probe process and only for the smallest particules. Higher value of this parameter indicates a more uniform strength distribution, as it is expected with an improvement of particle dispersion. This is consistent with the improvement of the average stresses at failure where the highest characteristic strength was obtained for the composite with the better particle dispersion. Besides, poor particle dispersion leads to the degradation of the characteristic strength in comparison with the native PMMA. This trend is clearly observed in Fig. 11 with a cumulative probability density curve shifted towards right for probe process composites, and towards left for bath process composites. Besides, a size effect can be observed for well-dispersed silica composites where the predicted ultimate stress for M probe process composites is higher than the stress for L probe process composites. This size effect does not exist for bath process composites.

Conclusion

This study allowed highlighting the importance to disperse particles before incorporation into the polymer matrix. It also highlights the link between particles size and difficulty to disperse. Finally, it shows that the phenomena of re-agglomeration are insignificant in our conditions of processing.

The second objective of this study was to bring out the influence of dispersion and size effect on the mechanical behavior of composites. Finally, a good dispersion of particles conduct to an improved Young's modulus and ultimate stress while a poor dispersion lead to an unmodified Young's modulus and a lower ultimate stress in comparison with native polymer matrix. Weibull analysis allowed to highlighting that a good dispersion shows a size effect contrary to poorly-dispersed composites.

The dispersion process developed for this study allowed obtaining the desired composites. However it was found thanks to the SEM micrographs that the interface between matrix and particles presented a lack of cohesion. It would be interesting to work on a functionalization allowing the optimization of this interface between additive and matrix.

Fig2.

  Fig2.SEM micrographs of the synthetized (a) silica L and (b) silica M

Fig5. 2 . 3

 23 Fig5.SEM topography micrographs: influence of the process on NPs distribution into the composite

Fig6.Object selection via Aphelion software 14 Fig7.

 14 Fig6.Object selection via Aphelion software

Table2: quantitative granulometry by images treatment with Aphelion software 3

 3 Uniaxial tensile tests were conducted to determine the mechanical properties (ultimate stress and Young's modulus) and to quantify the influence of the dispersion of NPs in the composites (Fig8).

Fig8.

  Fig8. Stress-strain curves of a) well-dispersed and b) poorly dispersed compositesAs expected, the addition of well-dispersed particles in a PMMA matrix induces an increase in Young's modulus (Fig9) in comparison with the unfilled polymer. Fig9

Fig. 11 .

 11 Fig.11. Accumulated Weibull probability plots for the failure stress, in MPa

Fig. 12 .

 12 Fig.12.Weibull prediction

Table 3 :

 3 Weibull parameters

Boris Derjaguin, Lev Landau, Evert Verwey and Theodoor Overbeek

Acknowledgements

This work was supported by the GDR Polynano and IMT mines Alès. The authors would like to thank Carine Joly Chivas, member of the GDR Polynano for the talks around the nanoparticles dispersion problematics.

Thanks are due to Jean-Claude Roux for the electronic microscopy.

According to the DLVO 1 theory [START_REF] Elimelech | Particle Deposition and Aggregation: Measurement, Modeling, and Simulation[END_REF], thermal agitation induces a stable state of the particles and cause the agglomeration of the system. For the same sonication time, probe process induces a better dispersion than bath process. It could be expected that probe process leads to a better dispersion into the composite in comparison with the bath process. With probe process the principal mode is shift towards the individual particle size without second mode. On the other hand, with bath process, the main mode always remains the same despite the appearance of a secondary mode representing approximately the size of a single particle.

Table1. Laser granulometry: statistical measure values after sonication during 10 minutes for silica L and 65 minutes for silica M.


Sandrine Null Dury
email: sandrine.dury@cirad.fr

Véronique Meuriot

Geneviève Fliedel

Sandy Blancher

Fanta Bore Guindo

Djibril Drame

Nicolas Bricas

Lamissa Diakite

Jean-François Cruz

The retail market prices of fonio reveal the demand

come   L'archive ouverte pluridisciplinaire

Context and field of the study:

Food post-harvest activities have increased tremendously in the last 30 years in sub-Saharan Africa to accompany the demographic transition toward urbanization. This is a very difficult task to assess the macro-economic impact on income generation since most of these activities are in the "informal" sector, and concern many single working women [START_REF] Bricas | Agroalimentaire et lutte contre la pauvreté en Afrique subsaharienne[END_REF]. However, these authors showed at the same time the enormous changes currently on-going in the food supply in African cities, the innovativeness of the stakeholders, as well as the scattered nature of the evidences and study about these changes. Our study is part of a larger program dealing with the upgrading of food quality and competitiveness of fonio processing and gives an insight on the valuation of quality on both traditional and new segment of this cereal market.

Post harvests research or development programs lead either by public or private operators are based on changes concerning food products. Food innovation is a risky, difficult and long process, especially in very poor countries where purchasing power is weak. One should guess in advance if new product will be interesting and accepted by eaters, processors and purchasers. Most eaters express preferences when testing or tasting a "new product", and explain rational process to choose the type of product they prefer. However, it is difficult to say in advance if they will pay, and how much for this new food or new attribute, and hence if the proposed innovation may become a commercial success. In Mali, the country were our study was carried out, studies about demand for infant food characteristics (see [START_REF] Sanogo | A market-based approach to child nutrition: mothers' demand for quality certification of infant foods in Bamako, Mali[END_REF] for example) showed that mothers were ready to pay for quality and for quality certification.

Different methods are used in marketing studies or economics, based on consumers' surveys about their willingness to pay for new attributes or products. All these methods, even if quite sophisticated like conjoint analysis or market experiments, use declarations or artificial context of purchase. In our work, we design a protocol in order to capture the real purchases in retail markets of real differentiated existing products. We have made comparison of what people say they like, what product they buy and what price really pay for existing characteristics, using the classical hedonic approach (Rosen, 1972).

We are focusing on fonio, (Digitaria exilis) a cereal grown in West Africa, mainly in Guinea, Mali, Burkina Faso. This cereal is a "minor" product in terms of production (in Mali for instance, it represents less than 1% of all cereals consumed, and whole production in Africa is about 250 000 metric tons), but is well appreciated by most consumers who know it, and consumed occasionally for family or religious events [START_REF] Konkobo-Yameogo C | La consommation urbaine d'une céréale traditionnelle en Afrique de l'Ouest : le fonio[END_REF]. These authors shows also that the consumption is constrained both because of high prices and long and difficult processing.

Fonio processing is indeed a very long and complex task. Its tiny grain (less than 1 mm) makes dehusking and milling, traditionally done by women using a pestle and mortar, highly laborious. After threshing, fonio paddy grain is still surrounded by husks. Like rice, processing paddy fonio into milled fonio needs two steps. The first step, known as dehusking, removes husks from paddy grain to get the whole grain. The second step, the milling, removes bran (pericarp and germ) from the whole grain. Dehusking and milling fonio grain require four to five successive poundings alternated with as many winnowings. The productivity of this work is very low. It takes nearly one hour to mill just one or two kilos of fonio paddy. Moreover, before cooking or precooking milled fonio, all bran, dust and sand must be eliminated by washing it several times which increases processing time and effort. Thus, mechanizing all the processing steps seems to be essential both to reduce the laboriousness of women work and improve the quality and availability of marketed fonio product [START_REF] Cruz | Fonio: a small grain with potential. LEISA, magazine on low external input and sustainable agriculture[END_REF]. Several research and development projects aimed to foster the revival of fonio commodity chain by improving processing techniques and providing new designed equipments for a mechanization of the main post harvest operations. Once fonio is milled and cleaned, the cooking process is also a long and technical task. It requires three successive steam cooking. Since the mid nineties, several small scale enterprises have developed a new product: the pre-cooked fonio. After achieving all the milling and cleaning, they realize the first cooking, they dry the product, and then seal it in plastic bags of one kg. [START_REF] Konkobo-Yameogo C | La consommation urbaine d'une céréale traditionnelle en Afrique de l'Ouest : le fonio[END_REF] have shown an expending interest from urban consumers for fonio and the rapid emergence of small scale enterprises providing pre-cooked fonio.

In Bamako, consumers do not buy paddy for food consumption, but they can chose in-between different "traditional products" and several brands of pre-cooked "new products". "Traditional products" are usually divided, by all the buyers and sellers, into three main categories: decorticated or pre-milled1 fonio which is actually a mixture of paddy, dehusked and milled grains in various proportions, plus more or less sand, dust and bran. A few stakeholders of the market chain like restaurant keepers or traders are able to subdivide this broad category into subgroups according to region or country of origin, or to quality of the milling (they give quality grades to different lots). However, these subdivisions are not unanimous among traders and all final buyers. milled and not washed2 which contains milled grain plus dust and sand, milled and washed3 which is milled clean grain.

Traditional and new products differ mainly according to their place in a technological process (from less to more processed) but they are also sold in different places and to different people: « traditional products » are sold in open markets, while pre-cooked products are sold in small supermarkets or in small scale enterprise.

Data collection

The field part of the study was organised into two main activities. The first one intended to determine, using individual interviews, focus groups techniques, sensory tests, the habits and preferences of several types of consumers and stakeholders at different stage: purchase, processing including cooking, and eating. The second step aimed to collect market data concerning fonio purchases in different places of Bamako, chosen to be representative of the selling places in the city. This survey was implemented during September and October 2006. 174 purchases of traditional products and 65 of new products were observed in markets and supermarkets. Data collected concerned the price really paid, and the characteristics of (i) the supply (type of market, supermarkets) of (ii) the product itself (type, size, colour… estimated by the buyer it/herself) of (iii) the buyer (age, education level, sex…) and of (iv) the destination of the product (given, or eaten at home, or processed prepared in a meal or another).

Six focus groups were organized to check the list of quality traits collected through individual interviews and synthesize general data on local population behaviours. In order to avoid the emergence of leaders during the discussion, each focus group was composed of 6 persons recruited during individual interviews from a same group of stakeholders. Thus, there was successively a focus group of "big" processors, "small" processors, restaurant (cheap and expensive) cookers, traditional fonio consumers, precooked fonio consumers. After a general discussion on "what is for you a good fonio when you buy it, when you process it and when you consume it" following a list of questions, the 6 persons were asked to talk about 10 different types of fonio bought from retailers during individual interviews and justify their preference : a fonio from Guinea 1st quality, a fonio from Guinea 2nd quality, a fonio from Guinea 3rd quality, a fonio from Koutiala, Mali, a fonio from San, Mali, a roasted fonio from Guinea, a milled and washed fonio from Mali, a milled and washed fonio from Guinea, a "new" fonio from Mali (harvested this year), an "old" fonio from Mali.

Sensorial tests were conducted in order to have a better perception of the quality and consumer sensory preferences. Rank tests and triangular tests were performed. Rank tests were performed with 3 groups of 20 persons, 60 persons in total, who were asked to range five types of cooked fonio from the most preferred to the least preferred and precise for what reasons. Four different fonios (from Guinea, San, Bougouni, Dogon plateau) were first bought in the market, one of them (fonio from Guinea) was also parboiled in IER (soaked, steamed and dried). These five types of fonio were then milled with GMBF4 fonio dehuller, washed and cooked in optimal conditions for each one (various cooking time and quantity of water added) before being served in a same plate, in same quantity and at the same time to each person of the group.

Triangular tests were performed with the 6 persons of 5 of the 6 focus groups, 30 persons in total, in order to determine if they could differentiate two types of cooked fonio judged very close in the previous test. Three samples were presented to each person: two came from the same cooked fonio and the third one from the other. The question was: what sample is different from the two others? There are 6 possibilities to present samples in a plate: AAB, ABA, BAA, BBA, BAB, ABB. Samples were coded. To know if there is a significant difference between the two fonios, the number of correct answers must be counted and compared to the value in the table of binomial law for a probability of 1/3.

Model and method of analysis

Following [START_REF] Rosen | Hedonic Prices and Implicit Markets: Product differentiation in Pure Competition[END_REF] and [START_REF] Lancaster | A New Approach to Consumer Theory[END_REF] a product (a good) can be considered as a « package of characteristics » or a « bundle of attributes ». According to Rosen, in a competitive market, market prices reveal the preferences of the consumers for a specific combination of the characteristics.

In addition to the quality characteristics of the product itself, we supposed that prices also depend of the partners of the transaction, since information might be distributed in a heterogeneous way. This is the reason why we included characteristics of the seller and the buyer in the hedonic model. The model can be written as following:

p(z) = p(z1, z2,…, zn)
where p is the unit prix of the good and z i is the quantity of characteristics i incorporated in good z.

Regressing a quantitative variable over a large number of qualitative variables generates problems of colinearity because qualitative exogenous variables are less discriminant (modalities of each characteristic are in small numbers: for instance there is only four different colours) and the exogenous variables are often closely related (cleanliness with colour for instance). The OLS estimate drops the variables which are the most collinear in the dataset. The complete estimation cannot be achieved. The PLS method, due to [START_REF] Wold | The collinearity problem in linear regression. The partial least squares (PLS) approach to generalized inverses[END_REF], allows to exceed the colinearity problem at the time of estimate the coefficients of variables. It combines several techniques:

1. Projection of the variables on an axe (component), itself linear combination of the exogenous variables (Principal Component Analysis principle). One repeats the process on the residuals of the regression. 2. Linear estimate between the two first principal components which are orthogonal.

Because the estimate is realised between orthogonal components, we cannot obtain the t-Student coefficient to control the level of significance of the variables: we use the Jackknife criteria and the VIP table. [START_REF] Tenenhaus | La régression PLS -Théorie et pratique[END_REF].

Results of interviews: declared preferences by consumers when eating, processing or buying fonio

By interviewing all the eaters (including all different stakeholders of the fonio market chain) on "what's for you a good fonio when eating it", gustative but also visual and olfactive criteria have been standing out, with a particular emphasize on gustative criteria. The question concerned the foyo recipe which is a steamed fonio (foyo recipe, which is the most common recipe). Interviewed persons prefer first a well cooked, with a soft consistency (30/30), swollen, not sticky and with no sand (30/30). Grains must be individual (27/30), smooth (28/30), not rough (25/30). Visually, colour must be light (20/30), with a minimum of paddy, herbs and other impurities (26/30). A sugary (23/30) and wild (10/30) smell are well appreciated while dusty and old smell must be avoid (9/30).

The unanimous quoted quality attributes for home processing were the level of milling and the level of cleanliness. These attributes determine the duration of the processing, they were quoted both by professionals (street restaurant keepers, processors) and simple consumers. Professionals were able to talk longer about the characteristics of the grain itself: they said that some grains were breakable while others did not break when milled. When soaked into water for cleaning, some grains become smooth and lose starch, while others remained whole. They said the good grains were "mature", which is an image since all grain are mature when harvested. However, it reflected a real difference in technological properties of grain.

When buying fonio, all buyers said they prefer white, well decorticated and clean fonio. They usually think that fonio imported from Guinea was cleaner, better decorticated, whiter, and more "mature" than fonio coming from Mali, especially the dryer areas of Mali.

Results of the sensory tests

Among the 60 persons who participated to the rank test, 2 were put aside because of their incoherent answers. Considering the 58 persons left, cooked fonios were ranked in a decreasing order of preference as followed: Bougouni, Guinea, Dogon, San and in the last position fonio from Guinea parboiled in IER. The most preferred cooked fonio were fonio from Bougouni and fonio from Guinea.

According to Friedman test and using a rank sum analysis, we found that the panel has appreciated differently the five samples and there was not a significant difference of preference between fonio from Bougouni and fonio from Guinea. These two fonios appeared very close in the ranking. By looking at the percentage table, we noticed that when fonio from Bougouni came first, fonio from Guinea came in second position at 79.3 %, and on the other way, when fonio from Guinea came first, that is fonio from Bougouni which arrived just after at 71.4 %.

At the question "For what reasons do you prefer this fonio", the most frequently criteria named were first colour and taste then consistency; grain size, smell and cleanness arriving quite after. Colour was named as the first criteria at 50 %, taste at 25.9 % and consistency at 15.5%.

Discussion

Altogether, for everybody, and at each stage (purchase, processing, eating), cleanliness, and milling degree are essential quality requirements. A light colour is also quoted by everybody. These are vertical quality attributes and we ought to find difference in prices for the different level of these attributes. On the opposite, results are not clear for the other attributes. Texture of the grain ("maturity") is quoted mainly by professionals. Concerning size, big grains were sometimes considered as good quality, when for other persons, small grains are appreciated, and others were indifferent to grain size. Origin is an indicator of cleanliness and good milling, but is not always associated with good taste. We do not have any quantitative data about another common recipe in Bamako, djouka, a brown colour salted meal, based on fonio and roasted groundnut. It was very often said by interviewees that brownish or "immature" grains were used to do djouka.

Results of the retail prices' analysis

The market prices are essentially determined by technical status of the products. The average price of the 239 observed fonio purchases reached 538 CFAF/Kg5 and 85% of the variation of retailed price was explained by the type of fonio. An analysis of variance (ANOVA) showed that average price of each of the four main types of fonio was significantly different from each other (level of significance 1%). From the less to the most processed fonio, the price was multiplied by a factor of two to four (from 250 to 1000 CFAF/kg). The difference between average prices gives the average market value of milling (50 CFAF/kg), of washing (160 CFAF/kg) and pre-cooking + packaging (290 CFAF/kg).

At this stage, it is not clear to identify what is due to the processing costs, what is due to market segmentation or a monopole, and what is due to preferences of consumers in these prices' differences. For a series of reasons, one can suppose that traditional products are in competition (everyone knows the product, each seller has at least 2 or 3 different types of fonio) while for pre-cooked, very few suppliers have the product, it is mostly sold in supermarkets, where no traditional products can be found. Thus, in the case of traditional fonios, we can suppose that prices are really reflecting both supply and demand sides, and thus preferences of consumers, and willingness to pay for the different attributes. In the case of pre-cooked product, it is not so clear. When we analyse each type separately, we can show what really counts apart from the level of processing.

Prices of decorticated fonio depend mainly on recipe, grain origin, milling degree, and grain colour.

During the period of the survey, the prices of decorticated fonio ranged from 250 until 475 CFAF/kg. We supposed that variations in prices were linked with (i) the different characteristics of the products themselves (in the group of what is called "decorticated") including the purchase location and with (ii) the expertise of the consumers, or ability to recognise the different characteristics. The R2 of the PLS regression was 0.4 which was good for such a regression and indicated a relative good fit of the model. The model parameters are presented on Table 2. The significant modalities are in bold in the table. When the VIP value is above 0.8, the parameter of the variable is considered as being statistically different from zero. The result of the regression can be written as follows:

P fonio = 360,696 + 2,463(Medina market) -2,059(Lafiabougou market) -1,572(Magnambougou market) place of purchase -5,021(badly milled) + 5,021(quite or very well milled) milled degree -0,285(very dirty) -0,736(dirty) + 0,898(clean) cleanliness + 4,505(white) + 12,462(cream white) -1,157(grey) -4,812(red, brown, not white) colour + 1,679(big) + 1,002(small) -5,077(do not know) g r a i n size + 4,572(Guinea) -5,685(Mali) + 0,996(do not know) origin -5,858(Djouka) + 4,889(other salted meal) + 7,262(do not know) recipe -2,691(for sale or gift) -0,558(week-end meal) + 3,038(special event meal) + 0.996(regular meal) + 7,135(illness) occasion + 0,102(household consumption) -2,576(processing for sale in a small restaurant) + 4,377(processing for a gift) -0,183(gift : no home process) + 7,135(processing for sale in a pre-cooked type) destination + 2,675(mother or other woman in the family) -3,254(employee) + 2,1(father or other man in the family) -2,732(child, young of the family) status of the buyer -3,054(moins de 20 ans) + 3,751(entre 21 et 35 ans) -3,316(entre 36 et 50 ans)

age of the buyer -0,183(man) + 0,945(woman) s ex of the buyer + 0,928(employee) -2,391(independent worker) -2,446(others) + 4,71(housewife) activity of the buyer+ 0,866(region of production of fonio) -1,146(region with no production of fonio) region of origin of the buyer -1,042(primary school) -1,513(secondary school) + 2,264(lycee or more) + 0,872(other) education level of the buyer Note that each exogenous variable is binary, and takes the value 0 or 1. P fonio , the endogenous variable is quantitative; it is the unit price of fonio in CFAF/kg.

The most significant (first rank of VIP) characteristic of the model was fonio recipe: all modalities were different from zero and the parameters take the expected sign: when a consumer wants to prepare djouka, she/he buys a cheaper fonio than when she/he wants to prepare foyo. Grain origin, grain colour and milling degree were also very significant and with the expected parameters: positive for Guinea and negative for Mali, positive for white colour and negative for brown colour, positive for well milled and negative for badly milled. A comparison of means, done with an ANOVA using the Fisher test, for each characteristic confirms these results. The four characteristics that have a significant effect on average price are recipe, grain origin, colour and milling degree.

Other significant modalities were more difficult to analyse. Destination such as "processing for a sale in a small restaurant" was significant and negative while "processing for a gift" was positive. These results can be explained by the fact that women who cook for these street restaurants are used to buy fonio in large quantities and are specialised in very low cost food. On the opposite, someone who buy fonio in order to cook it and to give it, will not buy such large quantities, and may be, not in a regular rhythm. Characteristics of the buyer are less significant and difficult to analyse at this stage.

It was quite surprising that cleanliness level was not significant. During interviews it was always quoted as important, but the model showed the level of cleanliness as perceived by the buyer had no impact on the price of the decorticated. On one side, it could be argued it was a bias of the survey based on interviewees' perceptions, and not on physical measures. People may not have understood the question or they may be over-optimistic regarding the product they just have bought. On another side, other technological characteristics, collected with the same methodology, appeared to be significant, and coherent with empirical knowledge. At this stage, our interpretation consisted in saying that while buyers were able to assess milling degree, grain colour, size and origin, by themselves or with indications of the sellers, they are not able to assess the level of cleanliness during the purchase. This will be discovered when they go home and process the product. Each specific type was usually associated with a certain idea of a level of cleanliness for most buyers. Cleanliness was actually not a real issue inside this type of decorticated fonio for the majority of individual buyers, who bought fonio very rarely (from once a week to once a month), in very small quantities (in our survey, 80% of the purchases of decorticated or milled fonio weighted less than four kilograms). Since some retail and wholesale markets are very close to each others, one should be cautious not to make any confusion with wholesale markets where professionals such as restaurant keepers, and small scale entrepreneurs bought their decorticated fonio. These stakeholders were different and had greater expectations concerning quality. They bought larger quantities (from may be 10 kg every day to 500 kg every month), on a regular basis, and they really paid different prices for different level of cleanliness of decorticated fonio (our interviews). The same regression done at the wholesale market about larger quantities would have shown different results concerning level cleanliness.

Prices of milled fonio depend mainly on environment characteristics linked to supply and buyers, and less to characteristics of the grain (except for colour)

Analysis of variance was conducted within each characteristic and showed that average prices for the different purchase locations, colours, sizes, destinations, status of the buyer, sex of the buyer, activities of the buyer were different from each other (at 1% significance level), occasion, education level (at 5% level). The PLS regression and the VIP criteria gave more detailed results (see Table 2).

Compared to decorticated fonio, the milling degree had no effect on price any longer which is understandable since the type is more homogeneous. The recipe had the correct sign (minus for djouka and plus for other salted meal) but was not significant any longer since very few people buy this kind of fonio to process it and sale it in large quantities in street restaurants. Origin was not significant any longer. Level of cleanliness gave incoherent results. Colour remained the only common significant characteristic.

Characteristics of buyers were here more significant: men, civil servants, higher educated persons have paid a higher price compared to women or housewives or less educated persons. In addition, the location was significant: Prices in Magnambougou market and at the Niger riversides were higher than in Medina Koura and Korofina markets. This seemed logical and linked to the customers since Magnambougou is located in a wealthier area, and Niger riversides' purchasers are usually richer than people going to other markets.

Prices of pre-cooked fonio depend mainly on supply characteristics (brand and purchase location).

For precooked fonio, only purchase location and brand had a significant effect on the unit price average (ANOVA test). All other variables (quality, buyer characteristics, etc…) had a minor effect on price. The product was quite standardized and variations in technological quality are low. Besides, neither supply systems nor brands are really in competition. Each purchase location has a price policy and each processor as well. Because the product is new, one can supposed that consumers are not accustomed yet to the product and, as the do not have the prices in mind, they do not compare. In the case of these precooked fonios, prices result from a supply policy but not from the meeting between suppliers and purchasers.

Discussion and conclusion

We showed that fonio price was mainly determined by the grain milling degree. The four existing types of fonio, known by individual buyers at the retail markets, explained almost 90% of the price variation. In that sense, the market was well segmented for that product. In addition, for each type of fonio, the hedonic price estimation using PLS method showed that different attributes had a significant value.

For the decorticated fonio, the main determinants of the price variation around the average were the final recipe, grain colour, grain origin, and grain milling degree. Specific characteristics of buyers (related to their idiosyncratic competence or socio-cultural specificities) and supply (market places) play a second and minor role. Geographic origin of the grain was a proxy of level of cleanliness. Buyers, in spite of the fact that they claimed to look for clean fonio (no dust, no sand) did not have many ways to check this attribute when they buy the good, and used the origin as a mean to estimate ex ante the level of cleanliness. Decorticated fonio is a heterogeneous category in terms of technological characteristics compared to milled fonio and price variations are mainly linked with technological characteristics. For the milled fonio, the main determinants of price variation were the purchase location, the grain colour, the size of the grain, the occasion, the destination, the sex of the buyer, the activity of the buyer, and its level of education. Final recipe, milling degree and grain origin had no influence on price. For the precooked product, the main determinants of price variation were place of purchase and brands. Intrinsic characteristics of the product have little influence on the variation of price. Results of the hedonic models on the market prices were consistent with results from interviews and the sensory tests, and revealed the preference of consumers. It was an argument for saying that the fonio market is efficient for the traditional products (decorticated and milled).

This study contributes to the programming of technological and agronomic research since it gives quantified results concerning preferences of the buyers. It clearly showed that cleanliness, milling degree and colour are vertical attributes for almost all buyers. For decorticated fonio, which is the less processed and cheapest product, geographical origin was a valuable attribute since it gave indication on the other characteristics (cleanliness in particular). For more processed and more standardized products, origin had no influence on price. Size of the grain did not really contribute to the price for most products except for pre-cooked fonio.

This study did not tackle the question of access to the products which remain expensive compared to other cereals (2 to 3 times more expensive in terms of unit price). However, other analysis, based on the same surveys, not presented here, showed that consumers' profiles, as well as final uses differed from one type to another. Decorticated and milled fonio are bought mainly by women (90% of the buyers), who did all the final processing (pounding, cleaning) by themselves, and who often cooked this fonio for income generating activities (25% of the buyers of decorticated fonio processed it for sale in small restaurants). Milled and washed fonio as well as pre-cooked fonio were more often bought by men (30% of pre-cooked buyers), who belonged to higher income class (civil servants), and who gave fonio to their spouse. This fonio is usually eaten at home or given. It is never used in income generating activity. Other research is on going to assess the impact of the development of these new products on income generation and distribution. The hypothesis is that it creates new activities for small scale processors and their employees; it generates new incomes since it reaches new consumers, who were reluctant to clean and pound the milled or decorticated products. One risk is that the supply will not meet this growing demand and the price may increase.

If that happens, the actual decorticated and milled products may reach higher prices that would deprive poor women of their income generating activity.

Figure 1 :

 1 Figure 1: Retail prices of several types of fonio products in Bamako-Mali, October 2006

Table 1 : Sensory test: number of citations per criteria and as 1st criteria$

 1

	Criteria	Number of criteria citations	1 st criteria Frequency	%
	Colour	52	29	50.0
	Taste	52	15	25.9
	Consistency	43	9	15.5
	Size	15	3	5.2
	Smell	25	1	1.7
	Cleanness	8	1	1.7
	*all samples were clean and well milled

Table 2 : Parameters of the PLS regression for decorticated fonio.

 2

	parameters	VIP*>0.8	VIP rank

Table 3 : Descriptive statistics of prices for decorticated fonio

 3

	Frequency	Unit Price CFAF/kg

Table 4 : Milled fonio: descriptive statistics and parameters of the model

 4

	Characteristics	Modalities = variables of the model	Descriptive statistics (price in CFAF/kg) Results of the model
			N Average	Standard Deviation	Parameter VIP rank
	Total		99	416,21	52,98 constant = 431,614
		Medina Koura market	18	392	35	-7,08	15
		Korofina market	44	394	16	-9,30	6
	Purchase location	Lafiabougou market	11	400	0	-4,31
		Magnambougou market	21	450	32	10,19	8
		Niger Riversides	5	590	55	43,21	1
		Bad milled	2	400	0	-3,91
	Milling degree	Quite well milled	22	417	28	0,11
		Very well milled	75	417	59	0,31
		White	79	403	30	-15,54	3
	Grain colour	Cream white Grey	11 5	505 445	77 97	23,46 7,16	2
		Red/brown/not white	4	400	0	-3,99
		Big	23	425	37	2,77
	Grain size	Small	38	431	76	5,64	14
		Do not know	38	396	14	-7,72	9
		Guinea	67	422	54	4,02
	Grain origin	Mali	4	419	38	0,62
		Do not know	28	403	51	-4,45
	Recipe	Djouka Other salted meal	30 69	403 422	24 61	-4,47 4,47
		For sale or gift	21	401	24	-4,64
		Week-end meal	18	414	32	-0,67
	Occasion	Familial or religious event	13	390	50	-7,02	18
		Ordinary meal	45	433	66	7,07	11
		Other	2	400	0	-3,91
		Familial consumption	40	443	69	10,56	5
	Destination	Processing for a sale in a small restaurant 26 Processing for a gift 11	404 389	15 54	-3,77 -7,32
		Gift (no home process)	22	395	15	-6,30	17
		Mother or other woman	74	413	49	-3,09
	Buyer status in the family	Employee Father	7 3	411 550	28 132	-1,40 32,57	4
		Other household member	15	408	22	-2,19
		Less than 20 years	16	405	19	-3,24
	Age	Between 21 and 35 years	73	418	57	1,19
		Between 36 and 50 years	8	431	70	3,86
	Buyer sex	Man Woman	8 88	466 412	103 45	12,69 -9,58	12 13
		Employee	10	408	24	-2,29
		Self employed worker	24	424	46	2,48
		Student	10	400	0	-4,26
	Buyer job	Civil servant	9	478	93	15,99	7
		Unemployed	3	400	0	-3,95
		Retired	4	450	100	8,31
		Housewife	37	401	44	-5,60	16
	Buyer origin	region of fonio production region with no fonio production	57 40	414 421	46 63	-1,46 1,80
		primary or religious school	43	411	30	-2,35
	Buyer education level	secondary school high school or more	10 12	463 423	94 60	12,15 1,80	10
		Other	32	408	55	-2,93

Table 5 : Pre-cooked fonio: descriptive statistics and parameters of the model

 5 Note that VIP= Variable Importance in the Projection = 3.11 for rank = 1 ; VIP = 0.86 for rank = 20

	Characteristics	modalities = variables of the model	descriptive statistics (price in CFAF/kg)		Results of the model
		N	Average	SD		Parameter	VIP rank
	Total		65	867	88 constant = 874,483
	Purchase location	At the processing unit	12	858	76	4,553
		Speciality store	26	792	27	-55,107	1
		Supermarket 1	2	1 000	0	85,484	6
		supermarket 2 (Badalabougou)	11	879	29	1,784
		Supermarket 3 (Hippodrome)	11	995	15	51,369	2
		supermarket 4 (Hippodrome)	2	1 000	0	92,527	7
		supermarket 5 (Hippodrome)	1	830 .		-15,932
	Brand	brand-1	6	800	0	-34,238	9
		brand-2	1	1 000 .		83,788	18
		brand-3	2	900	71	-8,960
		brand-4	1	850 .		7,923
		brand-5	16	850	89	-4,370
		brand-6	15	790	39	-40,739	4
		brand-7	1	825 .		-24,197
		brand-8	18	953	54	43,287	3
		brand-9	2	830	0	-19,947
		brand-10	3	933	58	47,318
	Grain colour	Blanc	18	865	87	1,145
		Cream white	27	875	91	3,189
		Brown, red, grey, not white	20	858	87	-4,711
	Grain size	Big	7	936	94	15,704	5
		Small	24	856	86	-8,291
		Do not know	30	858	84	2,614
		several different sizes	4	874	95	-3,943
	Grain origin	Guinea	2	975	35	8,972	13
		Mali	1	850 .		-8,294
		Do not know	62	864	88	-3,224
	Recipe	Djouka	7	914	107	12,117	19
		other salted meal	53	866	87	-5,881
		Other	5	810	22	-3,930	20
	Occasion	for sale or gift	8	838	69	3,052
		week end	25	876	72	6,013
		familial or religious meal	9	827	83	-22,951
		ordinary meal	23	883	107	4,309
	Destination	household consumption	55	875	88	8,208	12
		Processing for sale	1	800 .		-10,608
		Gift (no home process)	8	819	84	-9,524	14
		Other	1	850 .		7,923
	Status of the buyer	Mother	39	849	80	-12,885	11
		Employee	4	911	86	-0,452
		Father	13	875	91	7,074
		other member of the family	9	911	105	16,653	15
	Buyer age	less than 20	2	900	141	10,385
		Between 21 and 35	15	889	100	-1,504
		Between 36 and 50	31	862	81	-1,770
		more than 51	17	853	87	2,065
	Buyer sex	Man	19	862	88	1,309
		Woman	46	869	89	-1,309
	Buyer job	Employee	13	858	74	-2,057
		independant worker	6	892	102	-3,335
		Student	4	950	100	11,938	10
		Civil servant	31	862	87	7,145
		Retired	5	859	89	-0,324
		Housewife	6	838	101	-21,964
	Buyer origin	region of production of fonio	29	879	90	4,725
		region with no production	35	861	83	1,147
	Buyer education level	primary school	13	902	91	8,652	16
		secondary school	23	843	78	-6,917	17
		more than secondary school	29	870	91	0,798
	1

"Décortiqué"

"Blanchi non lavé"

"Blanchi lavé"

GMBF = Guinée Mali Burkina France

656 CFAF = 1 Euro

This work was financed through the European Inco project FONIO "Upgrading quality and competitiveness of fonio for improved livelihoods in West Africa". The Moisa-Sustainable


Brigitte Deguin

Pierre Vogel

    Stabilizing Effect by Geminal Dioxy Substitution and Anomeric Effect in 3,6-Dihydro-6-methoxy-1,2-oxathiin 2-Oxides