S Tamboura

H Meftah

J Fitoussi

H Bendaly

A Tcharkhtchi

Thermal aging kinetic and effects on mechanical behavior of fully recycled composite based on polypropylene/polyethylene blend

The effect of thermal oxidation of a fully recycled carbon fibers reinforced stabilized polypropylene/polyethylene blend on the mechanical properties has been studied at 120, 130 and 140 8C. In a first step, several analyses by FTIR and UV spectrometry and differential scanning calorimetry were performed in order to detect and monitor the evolution of the antioxidants and oxidation products in the materials. This approach aims to well understand and identify the aging mechanisms that will be modeled in a second step in a kinetic model capable of predicting the evolution of carbonyl build-up while taking into account the presence of the different antioxidants. Modeling results showed a good correlation between the kinetic behavior and the obtained experimental data. Furthermore, the effect of thermal aging on the mechanical behaviors of the composite and the matrix were studied at the macroscopic scale at different strain rates. It has been shown that the thermal oxidation affects only the elongation at break. The numerical values of the oxidation products generated by the kinetic model allowed linking the evolution of the mechanical behavior under aging with the physicochemical state of the material.

INTRODUCTION

The worldwide use of composite materials in several applications has shown an exponential increase during the past decades thanks to their lightness and mechanical performance. [START_REF] Bos | EU Waste Legislation and the Composites Industry[END_REF] In consequence, wastes from manufacturing and end-of-life products increased as well. Therefore, environmental awareness has increased and led to new global agreements to use more and more recyclable material. [START_REF] Pickering | [END_REF] Because of their complex compositions (fibers, matrix, and fillers), it is difficult to completely recycle the composites. For this reason, in the majority of the cases only fibers can be reclaimed using several techniques. Among them is the pyrolysis which is the most widespread used technic to recover fibers. [START_REF] Pickering | [END_REF]3 In fact, after pyrolysis, the recycled carbon fibers keep more than 90% of their mechanical properties. 4,5 Furthermore, the recycling of polymers has developed during the last two decades. New chemical techniques allow to recycle polymers and reused them as raw materials for new polymer using suitable chemical solvents. 6 The current study focus on a recycled stabilized blend (polypropylene/polyethylene) reinforced up to 20% wt with recycled short carbon fibers obtained by pyrolysis and milled in order to get an average length of 180 mm. The proposed polymer contains two kinds of stabilizers: one is a phenolic and the second is an organic phosphites. The elaborated composite is intended for automotive applications to absorb higher crashworthiness in a harsh environment (near to the engine where the temperature is relatively high). Thus the composite is subjected to physical and chemical aging condition which may degrade the material during its life time and alter the mechanical performance of the part. Therefore, automakers must take into account the parallel effect of chemical ageing (e.g., oxidation) and mechanical ageing (for example fatigue) on applied performance (e.g., crashworthiness application). In fact, the mechanical behavior of an aged bumper for example during an accident is different from the virgin one. So, in order to increase time to embrittlement and so improve the mechanical properties, agents and stabilizer are added to polymers during extrusion or injection molding.

To characterize the phenomena involved in stabilizer disappearance, a good understanding of its physico-chemistry is required. In fact, this latter can be consumed not only by chemical reactions but also lost by extraction or evaporation and many researches have been realized studying its effect on polymers ageing in terms of its induction period and its consumption rate. [START_REF] Schwarzenbach | Plastics Additives Handbook[END_REF][START_REF] Calvert | [END_REF][START_REF] Billingham | Plastics Additives Handbook[END_REF] In order to be able to detect antioxidants, follow their disappearance and carbonyls build up, many analytical methods are proposed in literature such as IR and UV spectrophotometry and differential scanning calorimetry (DSC) under oxygen (OIT). [START_REF] Ritter | [END_REF][START_REF] Bataillard | Plastics Additives Handbook[END_REF][START_REF] Lundb€ Ack | [END_REF][13][14] Coupling the chemical consumption and physical loss of stabilizers and proposing valid kinetic models is a complex and interesting field that's why in recent years many researchers have been attracted to study it. 15,16 This work aims to study in one hand, the thermal aging of the two materials mentioned above, characterize the stabilizer influence on the induction period and propose a kinetic model capable of predicting the consumption of the antioxidants, the induction time and the carbonyl build-up evolution. The mechanistic scheme involving stabilizer used in the current work was used in previous work and some assumptions have been made to simplify the mechanism and the modeling. [17][18][19] In the other hand, the effect of oxidation on the mechanical behavior is studied in order to link the thermal aging influence on the embrittlement of the composite and the matrix in the quasistatic and dynamic loading.

EXPERIMENTAL

Materials

In this work, two materials are proposed. The first is a 100% recycled polypropylene/polyethylene blend matrix (RPP) designed for crashworthiness in automotive applications. A phenolic antioxidant and an organic phosphites, more precisely the tri (alkylaryl) phosphites, have been added to the matrix during elaboration process in order to better withstand environmental temperatures and delay oxidation. For confidential reasons, the exact structure and formula of the stabilizers will not be communicated. The second material used in this work is a composite made of the RPP matrix and a 20% of short recycled carbon fibers obtained by pyrolysis and then milled. The recycled fibers have a density of 1.8 g/cm 23 , a diameter of 7 lm and a nominal length of 180 lm. The composite plates were first elaborated by extrusion in order to obtain a homogeneous matrix-fibers compound and then by injection molding. As for the matrix plates, they were obtained only by injection molding. The elaboration process configurations are more detailed in Ref. 20.

Characterization

Film Purification. In the literature, some authors were able to identify IR peaks related to the phosphites that others could not. [22][23][24][25] So to better identify the peaks corresponding to the two antioxidants and to monitor their consumption during aging using FTIR and UV spectrophotometry, the phenol and phosphites were extracted for analyzing. The purification was performed on RPP and RPP-CF180 films having an average thickness of 25 lm and obtained by microtoming. The extraction procedure was carried out using a chloroform-ethanolhexane (1:1:4) mixture under reflux for 48 h and then dried under vacuum at 40 8C. 21 After extraction operation, the residual sample was dried to obtain the pure stabilizer.

Infra-Red Spectrophotometry. FTIR spectrophotometry was performed in transmission mode on free standing films using a Frontier spectrophotometer (PerkinElmer). For each test, 32 scans were averaged in the 400 to 4000 cm 21 wavenumber range to be able to obtain a 4 cm 21 resolution. The obtained spectra were analyzed using Spectrum software (PerkinElmer) in order to determine the absorbance value and therefor the concentrations of oxidant and antioxidant products by using Beer Lambert law:

A5E k Á 1 Á C k
where A is the absorbance value, E k (L mol 21 UV Spectrophotometry. Beside the IR spectrophotometry, UV analyzes were performed to follow the concentration evolution of the phenolic function. Since the concentration of phenolic stabilizer is very low (<1%), its value obtained by FTIR spectroscopy is not accurate. To do so, tests have been realized using a UV Perkin Elmer Lamba 35 Spectrophotometer.

Oxidation Induction Time Measurements. To characterize the presence of antioxidant in the matrix and composite, DSC tests under oxygen were performed in the aim of measuring the oxidation induction time (OIT). The experiments were realized on 4-7 mg mass samples heated from 50 to 200 8C at a heat rate of 10 8C min 21 under 1 bar of pure oxygen with a gas flow maintained at 50 mL/min. Mechanical Characterization. Mechanical behavior of RPP and RPP-CF180 throw thermal aging was characterized under dynamic (high speed strain rate) and quasi-static loading. Dynamic tests were realized at 10 s 21 strain rate using a servohydraulic test machine (Schenck) equipped with a high speed camera (FASTCAM-APX RS) with the capacity of 250,000 frames per second to be able to record the pictures during high speed tensile test. The geometry of the specimen was optimized using ABAQUS finite element code in order to obtain a homogeneous strain distribution and a continued strain rate in the specimen's effective zone. 20 The quasi-static tests were performed at 10 22 s 21 , using INSTRON tensile-compression electromechanical device on specimen respecting ISO 527-2:1996 type 5A.

Exposure Conditions. Thermal aging under atmospheric air was carried out in ventilated oven at 120, 130, and 140 8Co n matrix and composites films and specimens.

RESULTS AND DISCUSSION

FTIR Analysis

Figure 1 shows the infra-red spectrum of RPP matrix before and after purification. One can notice the presence of two peaks at 1743 and 3646 cm 21 related to the ester group and phenol function of the first antioxidant, respectively. Furthermore, four peaks related to the phosphites stabilizer are present: two medium at 768,876 cm 21 , a weak one at 1195 cm 2125 and a strong peak at 1234 cm 21 corresponding to the phosphonate (Typical Infrared Absorption Frequencies). The Ester absorption has a higher molar absorptivity than the phenol and does not interfere with the matrix absorption meantime OH signal does. 26 The same results were validated in the case of the composite.

OIT Measurements

Figure 2 shows measurement result of the OIT at 200 8C of the RPP matrix. It shows two endothermic peaks at 127 and 163 8C corresponding to the melting temperature of the polyethylene and polypropylene present in the blend respectively followed by a constant plateau due to the anti-oxidizing effect. After 343 min, an exothermic peak appears due to the oxidization of the material. It should be noted that a non-stabilized polypropylene that shows an average of OIT of 5 min. 27 A comparison between the OIT of the two materials is illustrated in Figure 3. This figure shows a lower OIT, about 331 min, for the composite compared to the pure matrix. This difference can be explained by a consumption of a part of the antioxidants during the extra extrusion process that the composite has undergone. This decrease of the antioxidant quantity will have a direct impact on the induction time.

Carbonyl Build-Up and Stabilizers Disappearance FTIR spectra evolution of the RPP matrix during exposure at 140 8C is shown in Figure 4. During exposure, the absorbance of ester peak (at 1742 cm 21 ) decreases as another start to appear and increases at 1718 cm 21 which corresponds to the carbonyl build-up. The distinction between these different groups is not easy from a theoretical and experimental point of view. In fact, carbonyl and ester group are superposed in the same absorption peak. So, to be able to measure the real contribution of each group, a Gaussian deconvolution, using Origin Lab software was necessary. Once the spectrum deconvoluted, and by applying Beer Lambert law, mentioned above, the evolutions of ester and carbonyl groups are determined. Figure 5(a) compares the evolution of carbonyl group in the matrix and in the composite at 140 8C. One can note that the oxidation products appear and stabilize in the form of a plateau faster in the case of the composite. Thermal aging follow-up was stopped after 175 and 359 h for the composite and the matrix respectively. Since the ester group is not involved in the stabilization reactions, it is considered chemically stable. Thus, the evolution of its optical density will directly inform us about its physical loss, because of the evaporation. 24 Ester band starts to disappear from the very first moments of exposure and decays almost linearly as shown in Figure 5(b). It is obvious that the ester group in the composite decreases faster than RPP which affects the induction time and consequently the carbonyl build up rate. The maximum rate of the ester group loss (initial slope of the curves) is an increasing function of temperature. This rate are grouped in Table II for each exposure temperatures. As it can be seen, the ester groups disappear rapidly with the increase of exposure temperature. As for the evolution of the phenol concentration [Figure 5(c)], it shows a drop during the induction period followed by a plateau. Its evolution and concentration are different compared to literature. In fact, several works have shown that the phenol group disappears by chemical reaction and physical loss before the induction time is reached and its concentration value is much lower than the one shown in Figure 5(c). 15 Thus, one can suppose that another additive product is present at the same spectral range as the phenol; and its concentration does not change during the induction period. However, the results of the purification show previously in Figure 1 show that it is not possible to detect the presence of any other product. Thus, the concentration evolution of this stabilizer will be realized through UV spectrometry and discussed in the following paragraph. Figure 5(d), represents the phosphites concentration decrease for the composite and the matrix. It shows that in one hand the initial concentration of this antioxidant is higher in the matrix than in the composite (0.0399 mol/L compared to 0.0375 mol/L) and in the other hand that this stabilizer is not totally consumed during the induction period but in the contrast, it disappears once the oxidation process stabilizes and it happens first in the case of the composite. It has been verified for each exposition temperature that the oxidation in the composite appears faster than in the matrix. Table I summarizes the induction time (t i ) for the two materials for each exposure temperature.

The UV spectrometry analysis of the two materials though aging at 140 8C is shown in Figure 6. The results show a wide UV absorption band consisting of two contributions between 250 and 300 nm related to the phenolic and phosphites antioxidants.

Since phosphites stabilizers have an aromatic group that contributes in the absorbance at 283 nm, it was not possible to determine exactly the contribution of phenol from the UV spectrum. To deal with this problem, the contribution of the phosphites aromatic group in the peak is subtracted. For that, the concentration of the latter is calculated thanks to IR spectrum and the UV contribution of phenol is given by the following equation:

½Phenol5 A 283 2½PhosÁE Ar2O2P Á l l Á E Ar2OH
where A 283 is the absorbance peak at 283 nm, [Phos] is the phosphites concentration measured by FTIR spectrometry, E Ar2O2P (731 L mol 21 cm 21 )a n dE Ar2OH (1439 L mol 21 cm 21 )a r et h e molar absorptivity of phosphites and phenol at 283 nm, respectively. [START_REF] Vogel | Th eorie « simpliste » de la couleur (spectroscopie UV-Visible)[END_REF] By applying the precedent formula the initial concentration of phenol is slightly lower than that obtained by subtracting the plateau from the phenol curve in Figure 5(c). The kinetic curves of Phenol concentration consumption of the matrix and composite at 140 8C are represented in Figure 7. Contrary to the results shown previously in Figure 5(c), these results show that the initial value of the concentration of phenols is in a concentration range similar to that found in the literature. 15 Moreover, the phenol concentration present in the matrix (0.0375 mol L 21 ) is greater than that of the composite (0.0307 mol L 21 ). In addition, these results show that the phenolic antioxidant is fully consumed before the induction time. Therefore, the shorter induction time in the case of the composite is explained by a lower initial concentration of the phenolic antioxidant.

Kinetic Model

A standard mechanism has been chosen considering both uniand bimolecular hydroperoxide decomposition [START_REF] Audouin | [END_REF] and taking into account the antioxidants effect. [30][31][32] This mechanism is given by the following scheme:

(Iu) POOH !2P8 1 Y CO PC 5 OK 1u (Ib) POOH 1 POOH !P8 1 POO8 1 Y CO PC 5 OK 1b (2) P8 1 O 2 !POO8 K 2 (3) POO8 1 PH !POOH 1 P8 K 3 (4) P8 1 P8 !inactive product K 4 (5) P8 1 POO8 !inactive products K 5 (6) POO8 1 POO8 !inactive products 1 O 2 K 6 (S1) AH 1 POO8 !A8 1 POOH K S1 (S2) A8 1 POO8 !POO -A K S2 (Phos) POOH1PHOS!inactive products K Phos
Basing on these reactions, the following set of differential equations is derived:

d½P 8 dt
where d AH , d Phosh , and d A8 are the evaporation coefficients of phenol and phosphites and their radicals, respectively.

The system was solved numerically using Matlab Ode23s solver with the following boundaries conditions: [A8] 5 0

The kinetic curves for the carbonyl build-up were generated using the following equation: III. The orders of magnitude of the termination rate constants verify the relationship K 4 ! K 5 ) K 6 found in the literature. 34 The rate constants K 2 , K 4 , and K 5 involving a primary radical P8 which is very reactive, are independent of the temperature. This indicates that their activation energy is relatively zero. The value of k 3, responsible for the carbonyl build-up rate, remains approximately the same for the matrix and the composite and increases with the increase of the temperature. The parameters k S1 , K S2 , and k Phos responsible for the disappearance of the different antioxidants are changed. In fact, they increase as well with the increase of the temperature and are lower in the case of the composite since the oxidation occurs faster.

The determination of the model parameters for the tree exposure temperatures (Table III) allowed the calculation of the activation energy corresponding to each parameter. The different values of the activation energies are shown in Table IV. The activation energies values of the initiation and propagation steps calculated are realistic and similar to those found by Richaud et al. 19 Influence of Thermal Oxidation on the Mechanical Behavior The mechanical behavior of the matrix and composite was characterized through tensile tests at quasi-static (10 22 s 21 ) and high strain rate loading (10 s 21 ). The obtained stress/strain curves of the composite and the matrix specimens, taken at different times of aging at 140 8C, are represented in Figure 9. It is clear that the Young's modulus and the ultimate stress remain the same and are not affected by thermal aging but the elongation at break (E r ) is. Indeed, the elongation at break evolution at the quasi-static rate, illustrated in Figure 10, shows a dramatic drop by 40% and 45% for the RPP and RPP-CF180, respectively, from the very first moments of exposure to the induction time followed by a slow decrease until the end of the oxidation which is different from the results found in the literature. In fact Fayolle et al. 35,36 showed in their work on polypropylene, that the elongation at break is the most affected mechanical parameter by thermal aging. However, its evolution is characterized by a very small decrease during the induction period followed by a dramatic drop once the induction time is reached. In high strain rate loading, the two materials show a less important drop during the induction period, 25% and 34% for the matrix and the composite, respectively, but a same behavior of a small decrease till the end of oxidation. This phenomenon is due to the embrittlement of the matrix during exposure and to the weakening of the fiber/matrix interface in the case of the composite.

From an experimental point a view, during the induction period the carbonyl value is taken equal to zero because it remains too small and it is difficult to detect any changes. But in reality, it is not the case. In fact during this period, the polymer chains break to initiate the formation of radicals and then POOH responsible for carbonyl growth. In the case of the studied materials, the embrittlement occurs from the first moments of exposure during the induction period, so one can wonder what really happened during this duration. By taking a close look at the induction period given by the model when the embrittlement at the quasi-static loading of the matrix and composite occurs, as represented in Figure 11, it is clear that the carbonyls start to appear but with a very small concentration that does not exceed 10 24 mol/L. Thus, it is possible not only to link the elongation at break with exposure time (Figure 10) but also with the quantity of [CO] present within the materials during the induction period as shown in Figure 12. As studied in the literature, the oxidation due to the penetration of oxygen in a thick exposed material occurs only at the surface, 100-200 mm, leading to an embrittlement and then final failure. In the case of the current study, the concentration of carbonyls formed at the beginning of exposure, even if it is too small considering their value after the induction time, participate in the embrittlement of the composite and the matrix causing a drop in the elongation at break. Hence, it is possible to couple the affected mechanical properties with a quantified parameter directly linked to the oxidation.

A direct relation between the oxidation products, [CO], and the elongation at break has been identified. Indeed, the oxidation is a surface phenomenon which affects on one hand the cracking of the matrix and on the other hand the fiber/matrix interface weakening. Thus, surface micro-cracking is favored and propagates into the material leading to failure. It has been shown that embrittlement of the surface by oxidation justifies the decrease of the elongation at break. Moreover, the results presented in this work make it possible to quantify this relationship. Further analyses dealing with the surface oxidative embrittlement phenomena will be the subject of a forthcoming publication.

CONCLUSIONS

In this article, the stabilization by phenol and phosphites of a new recycled blend and its reinforced carbon fibers composite has been studied during thermal oxidation at 140 8C. The induction time of the composite appeared to be shorter than that of the matrix due to a decrease in the concentration of the antioxidant during the extrusion and the injection molding processes. Several methods were used in the aim of determining the different evolutions of antioxidants concentration and carbonyl build-up through aging. A kinetic model which is based on a classic mechanistic scheme that takes into account in one hand uni-and bimolecular hydroperoxide decomposition and in the other hand the antioxidants effect was proposed and the elementary rate constants of the model were determined by inverse method. The obtained simulations of kinetic curves of carbonyl growth and the antioxidants' consumption showed a good correlation with those obtained experimentally with a reasonable physical loss. Thermal aging effect on the mechanical behavior of the studied materials was characterized under quasi-static and high strain loading. At both strain rates the overall mechanical behavior was not affected during thermal aging except for the strain at break which shows a decrease from the very first moment of exposure due to matrix embrittlement and fiber/ matrix weakening. At low strain range, the drop of the elongation at break is higher than at high strain load. In fact, it is about 40% compared to 25% for the matrix and 45% compared to 34% in the case of the composite.

In further study, the obtained results will be coupled with damage investigation at a micro scale in order not only to characterize but also to quantify the damage initiation and kinetics during thermal aging at different temperature of exposure.

Figure 1 .Figure 2 .

 12 Figure 1. IR specter of RPP before (1) and after (2) stabilizer extraction. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3 .

 3 Figure 3. Comparison between OIT measurement for the matrix and the composite. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 4 .Figure 5 .

 45 Figure 4. FTIR spectra of RPP matrix at 140 8C. [Color figure can be viewed at wileyonlinelibrary.com]

At t 5

 5 0: [P8] 5 [POO8] 5 0 [POOH] 0 5 10 24 mol L 21 [PH] 5 24 mol L 21 [O 2 ] 5 S O2 3P O2 ; S O2 being the oxygen solubility in the matrix and P O2 the external oxygen pressure of the atmosphere.

Figure 6 .

 6 Figure 6. UV spectra evolution of (a) RPP and (b) RPP-CF180. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 8 (

 8 Figure 8(a, b) show the different simulations of the carbonyl build-up and phenol extinction for the matrix and the composite at 140 8C. A good correlation between numerical kinetic curves and those obtained experimentally is clearly noticed. Figure 8(c) represents the numerical and experimental curves of phosphites concentration evolution for the two materials. The rate constants values that provided the best simulations of the experimental results corresponding to the different exposure temperatures are summarized in TableIII. The orders of magnitude of the termination rate constants verify the relationship K 4 ! K 5 ) K 6 found in the literature.34 The rate constants K 2 , K 4 , and K 5 involving a primary radical P8 which is very reactive, are independent of the temperature. This indicates that their activation energy is relatively zero. The value of k 3, responsible

Figure 7 .Figure 8 .

 78 Figure 7. Phenol disappearance through oxidation of RPP and RPP-CF180. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 9 .

 9 Figure 9. Stress-strain curves at quasi-static and dynamic loading: (a) RPP, (b) RPP-CF180 at 10 mm/min, (c) RPP, (d) RPP-CF180 at 10 s 21 for 140 8C. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 10 .Figure 11 .Figure 12 .

 101112 Figure 10. Elongation at break evolution at quasi-static and dynamic loading for 140 8C: (a) RPP and (b) RPP-CF180. [Color figure can be viewed at wileyonlinelibrary.com]

  cm 21 ) the molar absorptivity taken equal to E 3646 5 117 L mol 21 cm 21 , E 1743 5 590 L mol 21 cm 21 , E 1718 5 350 L mol 21 cm 21 , E 768 5 440 L mol 21 cm 21 , E 887 5 318 L mol 21 cm 21 , E 1195 5 350 L mol 21 cm 21 , E 1234 5 250 L mol 21 cm 21 , 22-26 (Typical Infrared Absorption Frequencies) L (cm) is the film thickness and C k (mol L 21 ) is he concentration of the considered species.

  52k 1u ½POOH1k 1b ½POOH 2 2k 2 ½P 8 ½O 2 1k 3 ½POO 8 ½PH 22k 4 ½P 8 2 2k 5 ½P 8 ½POO 8 ½POOH 2 1k 2 ½P 8 ½O 2 2k 3 ½POO 8 ½PH 2k 5 ½P 8 ½POO 8 22k 6 ½POO 8 2 2k S1 ½POO o ½AH2k s2 ½POO 8 ½A 8

				(1)
	d½POO 8 dt	5k 1b (2)
	d½POOH dt 1k 3 ½POO 8 ½PH1k S1 ½POO8½AH2k PHOS ½POOH½PHOS 52k 1u ½POOH2k 1b ½POOH 2	(3)
			d½PH dt	52k 1u ½POOH1k 3 ½POO 8 ½PH	(4)
			o½AH ot	52k s1 ½POO 8 ½AH2d AH ½AH	(5)
	d½A 8 dt	52k s1 ½POO 8 ½AH2k S2 ½POO 8 ½A 8 2d A o ½A 8	(6)
	o½PHOS ot	52k PHOS ½POOH½PHOS2d Phos ½PHOS

Table I .

 I Induction Time for the Matrix and the Composite for Each Exposure Temperature

	Temperature (8C)	120	130	140
	Induction time t i (h)
	RPP	175	60	42
	RPP-CF180	95	36	24

Table II .

 II Disappearance Rate of the Ester Group at 120, 130, and 140 8C COu k 1u ½POOH1Y CO b k 1b ½POOH 2

	d½PC50	5Y
	dt
	T (8C)			120		130	140
	Dispersion rate of the ester	RPP	Composite	RPP	Composite	RPP	Composite
	groups (mol L 21 s 21 )	22 3 10 29	28.3 3 10 29	22 3 10 28	24.7 3 10 28	22.7 3 10 28	25.5 3 10 28

Y COu and Y CO b are the carbonyl yields of the uni-and bimolecular POOH decomposition, respectively.

33

Table III .

 III Kinetic Parameters of the RPP and RPP-CF180

	Temperature (8C)	120		130		140
	Parameters	Matrix	Composite	Matrix	Composite	Matrix	Composite
	K 1u (s 21 )2 3 10 26	2.5 3 10 26	7 3 10 26	9 3 10 26	10 25	1.6 3 10 25
	K 1b (L mol 21 s 21 )2 3 10 23	2 3 10 23	8 3 10 23	7 3 10 23	10 22	10 22
	K 2 (L mol 21 s 21 )1 0 7	10 7	10 7	10 7	10 7	10 7
	K 3 (L mol 21 s 21 )	0.011	0.012	0.019	0.02	0.026	0.027
	K 4 (L mol 21 s 21 )2 3 10 9	2 3 10 9	2 3 10 9	2 3 10 9	2 3 10 9	2 3 10 9
	K 5 (L mol 21 s 21 )1 0 8	10 8	10 8	10 8	10 8	10 8
	K 6 (L mol 21 s 21 )	1.4 3 10 6	2 3 10 6	2.1 3 10 6	2.5 3 10 6	2.9 3 10 6	3.1 3 10 6
	K S1 (L mol 21 s 21 )	0.12 3 10 2	0.1 3 10 2	0.22 3 10 2	0.14 3 10 2	0.3 3 10 2	0.2 3 10 2
	K S2 (L mol 21 s 21 )	1.25 3 10 10	1.2 3 10 10	1.35 3 10 10	1.3 3 10 10	1.5 3 10 10	1.4 3 10 10
	K Phos (L mol 21 s 21 )6 3 10 26	5 3 10 26	1.5 3 10 25	1 3 10 25	2.5 3 10 25	2 3 10 25
	d AH	0.45 3 10 25	0.7 3 10 25	0.82 3 10 25	1 3 10 25	0.16 3 10 24	0.28 3 10 24
	d A8	10 23	10 23	10 23	10 23	10 23	10 23
	B Phos	0.4 3 10 26	0.45 3 10 26	0.8 3 10 26	1.8 3 10 26	1.6 3 10 26	2.5 3 10 26
	Y COu	1111	11
	Y COb	1111	11

Table IV .

 IV Activation Energies of the Two Materials

				K 1b	K 2	K 3	K 4	K 5	K 6	K S1	K S2	K PHOS
			K 1u	(L mol 21	(L mol 21	(L mol 21	(L mol 21	(L mol 21	(L mol 21	(L mol 21	(L mol 21	(L mol 21
	Parameters	(s 21 )	s 21 )	s 21 )	s 21 )	s 21 )	s 21 )	s 21 )	s 21 )	s 21 )	s 21 )
	Activation	RPP	109.101 108.71 0	54.836 0	0	51.554 61.99	12.28	96.27
	energy	RPP-CF180 125.64 109.1	0	54.83	0	0	27.381 46.75	10.4	93.53
	(KJ Mol 21 )


Alexis Roche

Maître

INFLUENCE OF THE SIZE ORGANIZATIONS ON RECOGNITION EXPECTATIONS IN SMALL ORGANIZATIONS

Keywords: Recognition, intervention-research, Socio-Economic Approach to Management (SEAM), small organizations INFLUENCE

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Recognition is a polysemous word and an object of interdisciplinary research: it feeds philosophical, psychological, sociological, anthropological and economic and even biological reflections. Management sciences can profit from eliciting the link between these approaches to recognition and management practices, as it is a key issue in Human Resource Management [START_REF] Malherbe | Reconnaissance et GRH : au-delà de l'affirmation d'un mot un enjeu de représentations[END_REF]. Indeed, there are many challenges connected to the different types of recognition : ethical issues related to the predominance of economic rationality on social rationality [START_REF] Meda | Le travail : une valeur en voie de disparition[END_REF][START_REF] Chanlat | Sciences sociales et management : plaidoyer pour une anthropologie générale[END_REF][START_REF] Heller | Reconnaissance et gouvernement des salariés. Au-delà du mépris[END_REF], social issues as recognition impacts individuals , including mental health [START_REF] Enriquez | Les jeux du pouvoir et du désir dans l'entreprise[END_REF]Brown & al., 2003 ;[START_REF] Morin | La santé mentale au travail, une question de gros bon sens[END_REF] and community life associated with well-being at work [START_REF] Brun | La reconnaissance au travail : analyse d'un concept riche de sens[END_REF][START_REF] Autissier | Manager par le sens. Les clés de l'implication au travail[END_REF]. Recognition also contributes to identity through a "constitutive temporality" (Ricoeur, 2004) and psychological stability. This requires that organization build a social relationship over time (Stone, 2002). And finally, the economic stakes because the relations set up during the recognition process and practices have impacts on diverse economic performance: absenteeism, turnover, productivity, quality, responsiveness, innovation and cooperation among others. In this perspective, Human is the only factor of sustainable performance and therefore there is a need to work on human potential (Savall, 1975;Savall & Zardet, 1987). This concept is right at the junction between the social dimension and the economic dimension in organizations.

These relationships were analyzed by [START_REF] Roche | Reconnaissance et performance : proposition du concept de reconnaissance activatrice et d'un modèle intégrateur[END_REF][START_REF] Roche | La recherche-intervention comme révélatrice des dimensions des pratiques de reconnaissance dans les organisations[END_REF][START_REF] Roche | Définition de deux systèmes dialectiques de reconnaissance présents au sein des organisations[END_REF] through the concept of "activating-recognition". We first discuss the problem, the theoretical foundations and research methodology. Then we present and discuss the results and the contribution of proxemics before concluding.

PROBLEMS

Recognition is thus a key concept that company actors increasingly require their vows [START_REF] Lazzeri | La reconnaissance aujourd'hui : enjeux théoriques, éthiques et politiques du concept[END_REF][START_REF] Caillé | La quête de reconnaissance : nouveau phénomène social total[END_REF] especially when they experiencing times of existential crisis. Work in particular is a key issue for self-recognition [START_REF] Dubar | La crise des identités : l'interprétation d'une mutation[END_REF] because it would have become the central place of social ties [START_REF] Carpentier-Roy | Être reconnu au travail : nécessité ou privilège ?, actes du colloque Travail, reconnaissance et dignité humaine[END_REF].

Awareness of interest in this research topic is becoming more significant to both the side of researchers [START_REF] Bourcier | La reconnaissance : un outil de motivation pour vos salariés[END_REF][START_REF] Malherbe | Reconnaissance et GRH : au-delà de l'affirmation d'un mot un enjeu de représentations[END_REF][START_REF] Brun | La reconnaissance au travail : analyse d'un concept riche de sens[END_REF][START_REF] Autissier | Manager par le sens. Les clés de l'implication au travail[END_REF][START_REF] St-Onge | Pour une meilleure reconnaissance des contributions au travail[END_REF][START_REF] Peretti | Tous reconnus[END_REF][START_REF] Gavrancic | Échelle de mesure de la reconnaissance au travail[END_REF]Terramorsi, 2010) as the professionals. Recognition definition that we hold is: "Confirmation by others of belief acquired by a person of his/her own value, after various identification processes" (Renault, 2004, p. 181).

A regional director in a security company reflects very well the issue of the concept of recognition in the interface between social performance and economic performance with these words: "There is a need for social change in the business and not only in the economy. If we only give figures, any employee cares. What is it in for him? Training, money, employability? You need to link economic and social performance. Economic performance, the employees do not care if it does not change anything in their lives. For more information about links and impacts of the recognition performance see the "activating recognition" concept [START_REF] Roche | La "reconnaissance activatrice[END_REF][START_REF] Roche | Reconnaissance et performance : proposition du concept de reconnaissance activatrice et d'un modèle intégrateur[END_REF].

In fact, managers and HR professionals better integrate the requirement to understand the processes and systems of recognition because they are faced with the stakeholders needs, wants and requirements that they no longer control. Also, the recognition approach gives the possibility to obtain levers for Human Resource Management. There is therefore company responsibility in terms of management recognition [START_REF] Brun | An analysis of employee recognition: Perspectives on human resources practices[END_REF]. Indeed, "institutions do not produce themselves recognition or denial of recognition, but constitute the conditions which can stabilize recognition relations between individuals or perpetuate barriers to their development" (Renault, 2004, p.193). Some authors denounce the managerial disability to provide adequate forms of recognition [START_REF] Dubar | La crise des identités : l'interprétation d'une mutation[END_REF]. It is therefore interesting for practitioners to have the tools and knowledge to improve their practices.

The organizations growth associated with globalization and internationalization, through the development of communication tools and multiculturalism, allows other individuals comparisons. These comparisons and the increase of people with whom employees are connected, developed application on some recognition forms especially with the increase of organizations size. Geographical dispersion and time constraints also lower the ability to communicate and to recognize [START_REF] Townsend | Virtual teams: Technology and the workplace of the future[END_REF][START_REF] Kayworth | The Global Virtual Manager: A Prescription for Success[END_REF].

These various elements are linked to a proximity factor impacting recognition [START_REF] Torres | Essai de conceptualisation proxémique de la petitesse des entreprises, 6ème Congrès International Francophone PME (CIFPME 2002)[END_REF][START_REF] Roche | Reconnaissance et performance : proposition du concept de reconnaissance activatrice et d'un modèle intégrateur[END_REF]. The research field we met in our intervention-research highlight the importance of the size of the organization and the proximity between actors to explain the metamorphosis of some actor's expectations. This paper aims to shed light on these relations through an analysis of professional recognition expectations in different small organizations sizes. Our core hypothesis is that: "The small organization size impacts the expectations of recognition especially as it affects the proximity factor."

THEORETICAL FOUNDATIONS

Recognition concept is increasingly mobilized by the management authors and is found in the background of many management science theories. The issue of recognition impacts the emergence of humans desires by recognition need and challenges social and economic issues. Thus, theories are interested in recognition concept by three main types of approaches that we have identified: an approach by recognition needs, an approach by recognition process and an approach based on recognition practices (Figure 1).

-

----------------------------------------- Insert Figure 1 about here. ----------------------------------------------
The approach by needs can be found in line with the needs theories, including the famous author [START_REF] Maslow | A theory of human motivation[END_REF]. The approach by recognition process is found in sociological perspectives and management and the school of human relations, and translated by many authors into the motivation theories. One of the key authors in connection with recognition is [START_REF] Herzberg | Work and the Nature of Man[END_REF] with the two factors theory. Finally, a number of previous theories and some others have a behavioral approach, focusing on practices stimulation, related to the recognition, for a type of performance. This is the case of so-called classical theories that are more focused on practices in connection with the performance but also many motivation theories. Some transversal studies, focusing on the recognition concept, emerged contemporaneously in several disciplines, starting with philosophy (Hegel, 1802;[START_REF] Honneth | The Struggle for Recognition: The Moral Grammar of Social Conflicts[END_REF]Ricoeur, 2004). Honneth defines three modes of recognition from the tripartite theoretical of [START_REF] Hegel | Système de la vie éthique[END_REF] on the ethical life division: loving recognition, legal recognition and cultural recognition. In organizations coexist these three type of recognition. In sociology, currents, such as the work psychodynamic [START_REF] Dejours | Travail : usure mentale[END_REF][START_REF] Dejours | Souffrance en France. La banalisation de l'injustice sociale[END_REF], are generally interested in the recognition under its impact on the health of individuals. The socio-economic management theory (Savall, 1975), which draws on other theories and currents such as job enrichment, provides a backdrop vision about recognition. Furthermore, the recognition concept itself is becoming more significant. It was driven by management authors such as [START_REF] Bourcier | La reconnaissance : un outil de motivation pour vos salariés[END_REF] and more recently [START_REF] Brun | La reconnaissance au travail : analyse d'un concept riche de sens[END_REF][START_REF] Autissier | Manager par le sens. Les clés de l'implication au travail[END_REF] for a more detailed review of literature see [START_REF] Roche | Reconnaissance et performance : proposition du concept de reconnaissance activatrice et d'un modèle intégrateur[END_REF]. We classify the recognition, according to our works (2013), in three modes based on those of [START_REF] Honneth | The Struggle for Recognition: The Moral Grammar of Social Conflicts[END_REF]:

-"Relationship-recognition" appears in through practical recognition confirming the value of individuals through the encounter of a "similar" giving value to individual characteristics in an exchange.

-"Reward-recognition" takes the form of an object, service or symbolic status valued by a part of the community and who is generally given after a result. It may thus be more formalized and thus disconnected from relationship but recoverable out of the relationship when it was acquired. This is the case, for example, of salary which was automatically reset at the month end.

-"Achievement-recognition" brings an awareness of the existence and individual usefulness that causes a sense of achievement, social usefulness and completion giving meaning to the individual existence. This mode seems powered by the two previous.

Representation of recognition varies according to the people and moments, takes many forms (see Table 2: Mapping of the recognition system) because "confirmation by others of belief acquired by a person of his own value, following different processes of identification" (Renault, 2004, p. 181) can be done in many ways in social relations. We present some examples to link abstract concept and managerial practices: the money giving, object giving, congratulations, the granting of time to the person, to thank, to shake hands, to improve the living environment at work, give a title valued, to bring the person in a socially valued group, to give the opportunity to create, assign an area of responsibility, etc.

Recognition being placed in social relationships that can only be done by interaction between individuals and proximity (Mahé de [START_REF] Mahé De Boislandelle | L'effet de grossissement chez le dirigeant de PME : ses incidences sur le plan du management des hommes et de la GRH[END_REF][START_REF] Torres | Essai de conceptualisation proxémique de la petitesse des entreprises, 6ème Congrès International Francophone PME (CIFPME 2002)[END_REF] both physical, mental and social, which plays a major role. It therefore deserves particular interest in relation to the organizations size which scattered actors in a geographical point of view and increases the number of individuals with whom to interact. However, these physical, mental and social interactions are limited in this particular geographical dispersion and the necessarily limited time given to each relationship. We will focus on these elements in the Results and Discussion section.

RESEARCH METHODOLOGY

The study of recognition management is recent, which justifies and motivates the exploratory focus of this research. Our goal is to throw light on all aspects connected with recognition in the system aspects related to it. In addition, further studies are often limited to psychological, sociological and philosophical level.

We will use some the qualimetric intervention research methodology (Savall & Zardet, 2004). The qualimetric intervention research is part of a constructivist orientation favorable to the questions connected with the field of human resource management [START_REF] Martinet | Epistémologies et sciences de gestion[END_REF][START_REF] Brabet | [END_REF] while allowing the production of generic knowledge with a certain degree of validity according to the generic contingency principle.

Constructivism assumes the relativity of "real" and the subjectivity of the concept of "truth." In this, it goes well with the intervention research and methods residing in the subjectivities actors confrontation to create a "intersubjective representation of reality."

This methodology alternates inductive and deductive periods. In inductive periods, researcher observes and extracts field material for creating hypotheses. In deductive periods, the researcher creates hypotheses from his thoughts and bibliography, and then he/she will test in organizations.

We will here state on the qualitative methodological section whose concerns diagnosis interviews and quantitative evaluation because the analysis is built on content. This quantitative section seeks to illustrate the qualitative case studies and not to make a quantitative demonstration. Other devices (training meetings, project meetings, observations, non-formal individual interviews) came to power this analysis, but will not be detailed in this paper. This paper thus focuses on a static analysis through study of 17 diagnoses from 12 research fields treated in an expert database, SEGESE. These 12 cases were selected based on a variety of criteria in terms of size, type of population and business sector. Characteristics of the sample are shown in Table 1 below. - -----------------------------------------Insert Table 1 about here. ----------------------------------------------We constitute three categories of small organizations size with the sample we have: "1 to 20 employees", "300 to 450 employees" and "700 employees". The number 1b, 1c and 1d belong to the same company 1a and have been included as all entity in "300 to 450 employees" size in the following tables. The number 2b belong to the same company 2a and have been included as all entity in "700 employees" size in the following tables. The number 12b belong to the same company 12a and have been included as all entity in "300 to 450 employees" size in the following tables.

We used semi-structured interviews as data collecting method. Semi-structured interviews are in line with clinical research which is based on listening people [START_REF] De Gaulejac | Pratiques de consultation, histoire, enjeux, perspectives[END_REF]Levy, 1997;[START_REF] Giust-Desprairies | De la recherche-action à l'intervention psychosociale clinique[END_REF]. We use comprehensive notes to capture data.

In the case of this communication, interviews are covered by a questioning of the "dysfunctions" perceived by the actors. These are presented as differences between daily practices and observations and implicit individuals norms. These implicit norms constructed through social representations are elements that the individual judges "abnormal" or "desirable" and that would be "a priori" for him a basis for progress. This can be seen as a recognition and satisfaction way if the gap was reduced by others. Thus, these perceived differences are interpreted by researcher as "expectations of recognition" standardized, if that they were filled, would potentially be perceived as recognition given to actor. Individual may then feel recognized because somebody took into account these concerns and / or aspirations. To illustrate, we take two examples from 5150 verbatim witnesses present in the appendices of our thesis [START_REF] Roche | Reconnaissance et performance : proposition du concept de reconnaissance activatrice et d'un modèle intégrateur[END_REF], the staff of a trading company of building materials evokes: "The computer program is too complicated for deliveries, and it is not clear. It is written too small and it greatly complicates things" and the frame of a security company said: "There is too little positive feedback on what we do. It is very rare and informal. By cons, negative returns are common". In both cases, if a member of the organization, including the manager, decides to solve the software problem, there is a good chance that the individual sees the inclusion of its suggestions and thus develops a feeling of gratitude for the individual confirmed that he existed. This approach by recognition dysfunction has also the advantage of avoiding biases of recognition word in interviews. In fact, this word, when pronounced, has a variety of definitions and representations that depend on their expectations at the moment and of their history but is not representative of its most general definition. Knowledge collected in different interviews are then aggregated to obtain an intersubjective representation of reality.

The data collected for this analysis of 403 interviews, which allowed each extraction 10-15 verbatim illustrating a control malfunction, were made directly to a hundred of them by the researcher. The other part being derived from interviews conducted by other researchers in the research center. All researchers in the research center use the same methodology for diagnosis of malfunctions, which makes possible the use of data collected by other researchers.

Categorization of the content of interviews is conducted through a expert system called Segese. It breaks down verbatim semantically into a list of ideas that we developed specifically for this research subject: recognition. It is therefore not ranked by importance but by category across the list. Each verbatim is thus distributed according to its semantics in a theme, sub-theme, sub-subtheme and a key idea to gather verbatim by forms and issues of recognition. This tree distribution allows to make an analysis at different level of detail. We have uploaded more than 5,000 verbatim in our diagnosis nomenclature with regard to their lexical register and their meaning. This categorization by themes, subthemes, sub-subthemes and key ideas which were charged verbatim allows, by consolidation, to observe changes in recognition expectations expressed by stakeholders as sets which constitute a analysis grid. The latter is certainly necessarily conventional and illustrative but meaningful. It was built by successive back and forth between a literature review of representative major thematic sets mentioned by the authors and a semantic consolidation of verbatim by using keywords and ideas can be successively gathered near key ideas, sub-themes, sub-subthemes and themes.

RESULTS AND DISCUSSION

Our first result is the creation of a recognition mapping that we present in Table 2 below. - -----------------------------------------Insert Table 2 about here. ----------------------------------------------We now present the results of this research. To improve reading and considering our sample, we resort to three categories of small organization according to their size: the first from 1 to 20 employees, the second from 300 to 450 employees and third from 700 employees. These sizes were developed under our sample and allows a gradual reunification. The tables contained in this chapter include rounding unit and are illustrative. The results presented in bold are the most significant. Percentages correspond to the total count of the number of verbatim for each theme, sub-themes and subsubthemes. They allow us to illustrate trends we observed on the ground in our case studies. We first present a table (Table 3) to observe the distribution patterns between the three major themes we have used (conditions of working life, status and achievement) in relation to the organization size. Trends show the evolution of the distribution as organizational size decreases. Percentages are made on the basis of a total of approximately 5150 verbatim. The average is calculated per item as the total of all the themes for all tables.

- -----------------------------------------Insert Table 3 about here. ----------------------------------------------We observe that expectations regarding the conditions of work at life were relatively stable across the themes, even if small businesses seem to be more affected by this item.

In contrast, we observe, on status, lower expectations on the part of small businesses while levels are nearly equivalent across companies and those of 700 employees 300 to 450 employees. One explanation is that the titles, functions and career opportunities offer less potential for small organizations. Directly on the achievements mentioned by the actors, we observe a progressive increase as the size decreases. We suggest that, on the one hand, small organizations can probably better appropriate some creations and achievements working in the field of achievement, and secondly, we must take into account the fact that the category of leaders companies, compared to the number of interviews, is proportionally represented in smaller organizations. However, they almost all evoke the notion of fulfillment through the development of their organization. We will analyze more thoroughly the sub-themes and sub-subthemes for each theme.

Conditions of work life and organizational size

Table 4 below summarizes the sub-themes of the working conditions with regard to the organization size, and Table 5 is focused on the sub-themes.

- -----------------------------------------Insert Table 4 about here. ----------------------------------------------------------------------------------------Insert Table 5 about here. ----------------------------------------------These tables suggest lower expectations on earnings, particularly in terms of regular salary in the small organizations as compared to other sizes of organization. The most limited means of small structures can explain this trend. As opposed to mundane belief, the compensation is far from being the first recognition issue. Indeed, it represents between 1% and 4% of the recognition expectations of staff according to the organizations sizes.

Applications for improving the physical working conditions increase relatively proportionally as we approach small organizations, from 12 % to 25 %. We suggest that these are the expectations that weigh most heavily on employees of small businesses and they consider most likely to evolve. Indeed, we observed that the actors evoke as recognition expectations during the interviews those that are more stringent but also those that seem, according to them, the more likely to evolve. Another explanation may contribute to this result: it is the most important investment opportunity for large organizations that can bridge some of the expectations in terms of equipment and work environment. In this respect, it is interesting to note that in-kind benefits are fringe more and more requested in smaller organizations, probably because without having possibility of salary increases, it is a cheapier and easier form of recognition to implement.

Intangible working conditions is the larger sub-theme in terms of expression of actors for all sizes of organization with 48 % to 58 % of the total expression. However, these expectations seem to decrease when organization size decreases. We suggest as an explanation, a stronger proximity between individuals who are most rarely geographically scattered. They better know and are forced to help each other because of this proximity. Thus, according to the data, bibliography [START_REF] Torres | Essai de conceptualisation proxémique de la petitesse des entreprises, 6ème Congrès International Francophone PME (CIFPME 2002)[END_REF] and our field observations, recognition expectations and acts provided are reduced due to a stronger interaction between the actors who favors in particular information transmission, involvement, support and proximity. An additional suggestion is that the low financial ressources of small organizations may limit some "reasonable expectations for actors" to obtain some recognition types as training and therefore they do not mention it in interviews. This item also decreases sharply and linearly with size. In addition, some expectations of this sub-subtheme may be absent in small organizations because of their apparent uselessness. For example, financial ressources will mostly be of interest to the leader than other actors in small businesses.

Another interesting feature of our sample is the lower expectations concerning employment stability which seems to correlate with the size decrease. We suggest that small organizations are less likely to downsize because of the higher relative importance of relationships within staff. Indeed, the observation shows that the staff is more polyvalent and more difficult to replace because the function is generally based on conventions and informal modes of operation built through the relationship between individuals. This explanation is consistent with the effect of proportion mentioned by Mahé de [START_REF] Mahé De Boislandelle | L'effet de grossissement chez le dirigeant de PME : ses incidences sur le plan du management des hommes et de la GRH[END_REF], "the individuals importance is (often) inversely proportional to the structure size." This informal operation of small organizations is impossible for large organizations which have to formalize and register in "depersonalization" contexts of work through many rules and procedures. However, it should be noted that expectations about the rules and procedures appear to be very similar, regardless of the organization size. This is probably explained by the diversity of key ideas, the last generalization link between verbatim and sub-themes, which do not appear in the table (see Appendix, [START_REF] Roche | Reconnaissance et performance : proposition du concept de reconnaissance activatrice et d'un modèle intégrateur[END_REF]. They often concern the lack of formalization for small organizations while for larger organizations, the key ideas deal with the rules and too cumbersome procedures, plentiful, unappropriate, unfulfilled, but also missing.

Level of human pressure seems relatively stable since the work, through the management and / or customers, always involve a form of pressure, which needs to be reduced or legitimized, and so calls for recognition. However, small differences are observed: 3 % in large organizations can be linked, according to our field observations, to more pressure on productivity, a lack of proximity, attitudes more lax, sources of inequity. A higher percentage observed in small organizations, with 4 %, could be explained by the increased opportunities of visible conflicts, because of the proximity which reinforces "mandatory" interaction between actors. In this case, the question of territory has undoubtedly also plays a role. Indeed, the need for a self territory co-exists with the need for proximity with others. A territory is defined as a physical, mental or social area which is perceived as belonging to the individual, to feel alive and have a sense of autonomy.

There is thus a threshold that limits the spatial proximity because of dissatisfaction generated from a certain degree of proximity. These elements are connected with work on the intimate sphere, the personal sphere, the social sphere, the public sphere, etc. [START_REF] Hall | A System for the Notation of Proxemic Behavior[END_REF] where proxemics varies across cultures, places, time and registrants in the interaction. Finally, time management issues and work organization result in significant claims around 10% for all organizations. Time is, we believe, a major constraint and it is crow-cutting the other elements in all organization sizes. Now we will analyze the "status" theme.

Status and organization sizes

We present below in Table 6 summarizes the sub-themes and on sub-subthemes related to the status in Table 7.

- -----------------------------------------Insert Table 6 about here. ----------------------------------------------------------------------------------------Insert Table 7 about here. ----------------------------------------------We observe both a decrease of role definitions problems but also in terms of status requests on some items in approaching small organizations. Titles and promotions are less required, probably because the number of bonuses and promotion prospects decrease.

Expectations regarding the responsibilities are relatively consistent, with an average of 9% which is the sub-subcategory most in demand regardless of the organization size. The key ideas in organizations ranging from 300 to 450 people, with 11 % of expectations concern especially challenged by other employees of the statutes, of autonomy or organizations decisions. Instead, these expectations in small organizations represent 7 % of the total. Field observations and bibliography [START_REF] Torres | Essai de conceptualisation proxémique de la petitesse des entreprises, 6ème Congrès International Francophone PME (CIFPME 2002)[END_REF] suggest lower demands on certain aspects of multi-skill responsibilities of smaller prospects of small organizations and sense responsibilities were less diluted by the number of persons.

Concerning the assessment of the value of work, we suggest that varied and low formalized roles involve sharing tasks considered as unattractive most important and / or most accepted in small organizations where they are very few mentioned.

There seems to be differences regarding the assessment of working practices and skills with a stable 3% for larger companies, but a difference of 4 points, with 7 % for small businesses. We suggest several explanations to account for it. First, critics and mutual expectations on skills appear in the field, enforced by proximity and frequency of interactions as well as, in small organizations, the slightest lack of skills is immediately noticed because it is more difficult embedded in collective responsibility. Another explanation is that in the absence of other form of recognition (pay, status), the need that skills be recognized becomes important to differentiate and is therefore a major challenge to claim in interviews. The assessment by others of the results of work will be a constant demand, at around 2% for individuals of all organizations. This item is constitute by the lack of feedback, especially positive but also negative, on the job. We also note that the smallness of organizations seems to bring more significant demands on the pro-activity of others where it should be more valued and expected, particularly by managers, by the requirement for this company size to be very reactive because is flexibility is one of its benefits [START_REF] Torres | Essai de conceptualisation proxémique de la petitesse des entreprises, 6ème Congrès International Francophone PME (CIFPME 2002)[END_REF]. The assessment by others of individuals' characteristics appears slightly stronger in large organizations. According to our field observations, different cultures, numerically more important, and distance make it easier to criticize other people, through ignorance and / or no risk return and therefore intensify the necessity to be considered in this register. Indeed, the physical, psychological and / or social distance, allows to increase denial of individuals, even contempt, of each other because they do not face each other daily. Indeed, it helps to keep misunderstandings and remote representations of the reality of others.

We also observe that expectations regarding relationships with recognized individuals for obtaining recognition and free pass by the mere fact of attending, are much criticized in large organizations, especially the feudal practices and favoritism. Expectations regarding membership appreciation of the group, like the membership of organization, also seem slightly more significant in larger organizations. We offer several explanations to account for it. First, the number of relationships and therefore sub-groups (functional, geographic, etc.) which can be created mechanically decreases as the organization size is reduced.

Second, the name and reputation of organizations is less symbolic value, because of a smaller internal and external marketing, in small organizations.

Achievement and organization sizes

Table 8 summarizes the sub-themes and Table 9 the sub-subthemes related to achievement.

- -----------------------------------------Insert Table 8 about here. ----------------------------------------------------------------------------------------Insert Table 9 about here. ----------------------------------------------We emphasize that direct requests concerning achievements are cross-cutting with the two other themes. This implies that we can indirectly see the concept of accomplishment in all other themes. For example, training can be seen as a request for completion at the skills development. These indirect requests for achievements drastically reduce percentage of direct expectations suggested in the theme of "achievement". On the subthemes and sub-subthemes of achievement, we see stronger "expectations" about the meaning of work and about the possibility to create something, particularly at the direction of smaller companies. Recognition makes it possible to give meaning to the work [START_REF] Autissier | Manager par le sens. Les clés de l'implication au travail[END_REF][START_REF] Fender | Redonner du sens au travail : essai de modélisation de la reconnaissance au travail[END_REF].

Thus, it appears that employees of small businesses are slightly more sensitive to the direct search for personal fulfillment in creation terms. This is the case in the personal assessment of the creation / evolution of the group and especially for leaders of organizations. These are, we recall, proportionally more represented in the sample when we do interviews with less than 20 people in organizations compared of larger organizations. We also see this trend in the impact to evolution in individual personal skills. However, the need of a clear strategy, of goals set by others and of work meaning remains particularly represented in all organization, around 2 %.

According to our results, it seems that the differences between organizations of 700 employees and organizations ranging from 300 to 450 employees are much slighter between the latter and those of 1-20 employees. One explanation is that the proximity -in geographical, physical and mental terms -to a certain population threshold becomes much more difficult. We establish this threshold at a few dozen employees. It refers to cognitive and temporal boundaries to set up the relationships we have already mentioned.

Proximity is a prominent criterion seems explanatory the changes in expectations of recognition compared to the organizations size [START_REF] Roche | Reconnaissance et performance : proposition du concept de reconnaissance activatrice et d'un modèle intégrateur[END_REF]. It also plays a role with the autonomy factor, who is another factor affecting perceptions of recognition. This factor is more difficult to manage as the organization sire increase and therefore it generates more requests. Equity, another factor affecting perceptions of recognition, also tends to evolve towards iniquity with the size because it generates a multiplication of relations between individuals and increases the complexity of maintaining a fair system. We return hereinafter in more detail on the proximity factor.

THE CONTRIBUTION OF PROXEMICS

First, we emphasize that the lack of recognition was an origin of research on proximity management (Thevenet, 1992). In fact, close relations are essential elements of psychological needs satisfaction and are considered zd symbolic recognition practices [START_REF] Stajkovic | A Meta-analysis of the Effects of Organizational Behavior Modification on Task Performance, 1975-1995[END_REF][START_REF] Brun | La reconnaissance au travail : analyse d'un concept riche de sens[END_REF][START_REF] Autissier | Manager par le sens. Les clés de l'implication au travail[END_REF][START_REF] St-Onge | Gestion de la rémunération : théorie et pratique[END_REF][START_REF] Akremi | Rôle de la reconnaissance dans la construction de l'identité au travail[END_REF]. Thus, proximity is seen as a sign of interest and appreciation for individual. Conversely, the distance is a recognition lack who can be seen as a sign of denial, that ignore other, even contempt, that underestimate other.

Human being is by nature self-centered. [START_REF] Moles | [END_REF] explained the importance of people, things and events falls with distance as their perception decreases, what they call proxemics law. We translate this by the fact that is distant thing can more easily be denied. Denial is the failure to consider a part of reality. It also seems important to state that there is a maximum physical and mental threshold who was limiting by the individual body and ego (Figure 2) which results in a threshold of "territory" [START_REF] Hall | A System for the Notation of Proxemic Behavior[END_REF]. Figure 2 below is purely illustrative.

- -----------------------------------------Insert Figure 2 about here. ----------------------------------------------There are also events wall (Moles & Rohmer, 1972), which are a separation between an interior and an exterior. They be seen as an element which decreases the phenomena importance beyond of a singular point [START_REF] Torres | Essai de conceptualisation proxémique de la petitesse des entreprises, 6ème Congrès International Francophone PME (CIFPME 2002)[END_REF]. For example, a wall phenomenon can be social across between organizational subgroups (service, peer group) or physical as a partition in an office, a building, site, etc. We suggest that the number of physical, mental and social walls grow as organizational size grows.

Proximity is thus not only physical but takes many forms in terms of temporality, physical and geographical space, economic space, symbolic and emotional space, mental space and social space through groups. Across the board, all these types of proximities is rather promoted by the small organizations size. Indeed, the size of the structure reduces the number of interaction territories, in terms of individuals' number, and the time allocated to the interaction between each individual constituting the group. Proximity allows to better understand language and common representations that facilitate dialogue, mutual listening and helping others. The organizations smallness facilitates the development of a harmonized regulatory framework by the intensity of trade [START_REF] Lepley | Le conflit est-il possible dans les PME ?[END_REF], cited by Torres, 2002) causing recognition expectations partly different as large organizations.

CONCLUSION

As a conclusion, the small organization size, mainly through the proximity factor, appears to be important. Recognition expectations and demands forms differs with the organizations size. Expectations filled more easily proved by small organizations, in relation to proximity, this is the case of : involvement of other individuals, mutual work, sensory stimulation through the frequency of interaction, security of employment or responsibilities that are shared because of the more consistent relative importance of each individual. Other expectations are met more easily by the passage of small to medium organizations, such as: investment in equipment or work in the physical work environment. These recognition expectations thus appear less in the expression of the actors as they no longer need to be met.

Another issue is the "reasonable expectations", that is to say those which are considered realistic, especially because other people in the organization or area organizations have achieved, but also in relation to the promises made by organization members to other members. Thus, a common example is the promising developments in wages and status when employees are recruited, with the recognition desires in these areas, are claimed later on. Organizational size generates a number of social representations based on actual or displayed trends by the media. Thus, the increase of organizations size correspond to an increase of investment capacity. These elements make more plausible desires in large organizations such as the positive development of remuneration, training expectations, title valued, promotion, membership of organizational subgroups valued, reputation of the organization, etc., then they are less observed and applied in small organizations.

Conversely, employees of small organizations consider plausible and tend to wait for fringe benefits, better equipment and working environment considered financially accessible by the organization, use of their abilities by others, good social relations work as well as more structured goals.

Other items of recognition expectations seem not to be much impacted by the organizations size in the analysis of sub-subtopics, although we note differences in key ideas. This is the case of expectations regarding human resources available, the transmission of information, time management and organization of work and the rules and procedures that are expectations rather stable regardless of the organization size.

However, if we take the example of rules and procedures, expectations rather relate to excess, heaviness and lack of respect for rules in large organizations and lack of rules formalization in small organizations. Dynamic maintenance of proximity through tools and management methods of proximity seems essential for large organizations where the stakes for some forms of recognition are strong. This means creating a dynamic reconciliation who's complicated by the organization size and sometimes by established habit. Reconciliation corresponds to a feeling of being actively listened, more regular meetings with different interfaces and sharing a common project. For small organizations, the issues appear to be from a investment lack in equipment and work skills development. There is also a lack of formalization and organization emphasized by the expectations, in terms of rules and procedures, time management and work organization.

This working paper could be expanded by the analysis of more cases in various activity sectors and to other sizes of organization, which is both a limit and a research perspective. Further quantitative methodology would also draw results beyond an illustrative support of qualitative methodology. We suggest that this study sheds new light on the relationship between the organization size, proximity and recognition expectations that can enrich other research and help find the most appropriate professional recognition practices.

  FIGURE 1

TABLE 2 : Mapping of the recognition system

 2

	THEMES	SUBTHEMES	SUB-SUBTHEMES
			Regular salary
		REMUNERATION	Bonuses
			Stock exchange actions
	CONDITIONS OF WORKING LIFE	PHYSICAL WORKING CONDITIONS	Work equipment Work physical environment Human ressources
	Report to the		Fringe benefits
	possession and		Rules and Procedures
	living conditions		Training
	compared to others		Financial resources
			Active listening and freedom to voice
	Conditions for the exercise of work	INTANGIBLE WORKING CONDITIONS	Transmission and use of information Sensory stimulation and proximity Involvement and support in the work
			Level of human pressure on individuals
			Time management and work organization
			Employment stability
	STATUS	STATUS IN CONNECTION WITH A TITLE	Appreciation of a title or a promotion
		STATUS IN CONNECTION	Appreciation of the responsibility of an activity
	Relative to each	WITH ANY LIABILITY	Appreciation of the work value
	other, facing each other and the judgment of other	STATUS IN CONNECTION WITH THE SKILLS	Appreciation by others of working practices and skills Appreciation by others of results of a work Appreciation by others of pro-activity
		STATUS IN CONNECTION	Relationships with persons recognized
	Or positioning in the	WITH THE RELATIONS WITH	Appreciation of the group membership
	working groups and	OTHER INDIVIDUALS	Appreciation by others characteristics of the individual
	positioning of these	STATUS IN CONNECTION
	groups	WITH THE REPUTATION OF	Appreciation of belonging to the organization
		THE ORGANIZATION
	ACHIEVEMENT		Personal appreciation of the creation / production of a
			product / service
	Relation to oneself		Personal appreciation of the creation / evolution of a group
	and its creative	ACHIEVEMENT THROUGH	Personal appreciation of the development of individual
	usefulness judgment	THE CREATION	skills
	on itself, its		Personal appreciation of the contribution to the development
	activities and		of others
	development		Innovation sense of the individual
	opportunities
		ACHIEVEMENT THROUGH	Achieving a goal set by others and work meaning
	Sense of movement	THE ESTABLISHMENT OF AN
	through the work	OBJECTIVE AND MEANING
	and meaning of	OF WORK	Achieving a goal set by the individual himself/herself
	work

TABLE 3 Relationship between small organization size and distribution of the issues of recognition

 3

		Tendance	700 Employees	300 to 450 Employees	1 to 20 Employees	Average
	CONDITIONS OF WORKING LIFE	↘↗	73%	72%	75%	73%
	STATUS	↗↘	23%	24%	19%	22%
	ACHIEVEMENT	↗	3%	4%	6%	4%
	Total on all topics (excluding		100%	100%	100%	100%

TABLE 4 Relationship between small organization size and the sub-themes of working conditions

 4

		Trend	700 Employees	300 to 450 Employees	1 to 20 Employees	Average
	REMUNERATION	↗↘	3%	4%	1%	3%
	PHYSICAL WORKING CONDITIONS	↗	12%	18%	25%	18%
	INTANGIBLE WORKING CONDITIONS	↘	58%	50%	48%	52%
	Total on all topics (excluding rounded)	73%	72%	75%	73%

TABLE 5 Relationship between small organization size and the sub-subthemes of working conditions

 5

		Trend	700 Employees	300 to 450 Employees	1 to 20 Employees	Average
	Regular salary	↗↘	2%	3%	0%	2%
	Bonuses	→	1%	1%	1%	1%
	Stock exchange actions	/	0%	0%	0%	0%
	Work equipment	↗	5%	7%	14%	9%
	Work physical environment	↗	4%	7%	8%	6%
	Human ressources	↗↘	3%	4%	3%	3%
	Fringe benefits	↗	0%	0%	1%	0%
	Rules and Procedures	↘↗	6%	5%	7%	5%
	Training	↘	7%	5%	3%	5%
	Financial resources	↗↘	0%	1%	0%	0%
	Active listening and freedom to voice	↗↘	2%	3%	2%	2%
	Transmission and use of information	↘	9%	9%	8%	9%
	Sensory stimulation and proximity	↘↗	8%	5%	6%	6%
	Involvement and support in the work	↗↘	9%	10%	7%	9%
	Level of human pressure on individuals	↘↗	3%	2%	4%	3%
	Time management and work organization	↘↗	11%	9%	12%	11%
	Employment stability	↘	2%	1%	0%	1%
	Total on all topics (excluding rounded)	73%	72%	75%	73%

TABLE 6 Relationship between small organization size and the subthemes of status

 6

	Trend	700 Employees	300 to 450 Employees	1 to 20 Employees	Average

TABLE 7 Relationship between small organization size and the sub-subthemes of status

 7

		Trend	700 Employees	300 to 450 Employees	1 to 20 Employees	Average
	Appreciation of a title or a promotion	↘	2%	2%	1%	2%
	Appreciation of the responsibility of an activity	↗↘	9%	11%	7%	9%
	Appreciation of the work value	→	1%	1%	0%	1%
	Appreciation by others of working practices and skills	↗	3%	3%	7%	4%
	Appreciation by others of results of a work	→	2%	2%	2%	2%
	Appreciation by others of pro-activity	↗	0%	1%	1%	1%
	Relationships with persons recognized	↘	1%	0%	0%	0%
	Appreciation of the group membership	↘	2%	1%	0%	1%
	Appreciation by others characteristics of the individual	↘	1%	1%	0%	1%
	Appreciation of belonging to the organization	↘	2%	2%	1%	2%
	Total on all topics (excluding rounded)		23%	24%	19%	22%

TABLE 8 Relationship between small organization size and the subthemes of achievement

 8

	Trend	700 Employees	300 to 450 Employees	1 to 20 Employees	Average

TABLE 9 Relationship between small organization size and the sub-subthemes of achievement

 9

	Trend	700 Employees	300 to 450 Employees	1 to 20 Employees	Average