Chloé Souillard

Laurent Chazeau
email: laurent.chazeau@insa-lyon.fr

Jean-Yves Cavaillé

Sébastien Brun

Regis Schach

On the β relaxations in Poly(Butadiene) and Poly(Styrene-Butadiene) rubbers

Keywords: mechanical spectrometry, dielectric spectrometry, beta relaxation, styrene butadiene copolymer

The influence of the chemical microstructure on the secondary mechanical relaxations of PB and SBR has been studied by varying the content of vinyl, cis, trans butadiene and styrene groups. Two relaxational mechanisms are involved in their β mechanical relaxations with two distinct activation energies. The fitting by the summation of two Havriliak Negami functions of the experimental isochronal and isothermal curves prove that the vinyl groups are responsible for the contribution of the High Temperature part of the β-relaxation, whereas the butadiene 1,4 groups, cis and trans are at the origin of the low temperature part of this relaxation. Moreover, the intensity of the relaxation associated to each monomer appears to be proportional to their volume (and molar) fraction. Given the random characteristics of the studied copolymer, this suggest that the involved mechanisms are localized at the level of only one monomer unit.

Introduction

Styrene Butadiene rubber are mainly used at temperature well above their glass transition temperature; nevertheless, in some applications such as tires, the frequency domain at which they are dynamically deformed is so large that their mechanical response can involve relaxations usually occuring in the glass-rubber transition and also in the glassy state [START_REF] Moore | A review of hysteresis theories for elastomers[END_REF]. Moreover, these elastomers usually contain nanofillers. Their presence is known to decrease the polymer mobility in their surface neighborhood and as a consequence, should enhance the influence of these mechanical relaxations [START_REF] Berriot | Evidence for the shift of the glass transition near the particles in silica-filled elastomers[END_REF]. When these relaxations are activated, more viscoelastic dissipation occurs, which may be wished -for instance to promote traction or braking efficiency -or unwished on normal rolling, where energy saving is targeted.

For sake of material optimization, the understanding of the microstructural parameters governing these relaxations is therefore mandatory.

The α-relaxation is the dominating relaxation in glass-forming amorphous systems. It is highly cooperative and attributed to segmental relaxation of the main chain [START_REF] Perez | Physics and mechanics of amorphous polymers[END_REF]. In the glassy state, additional relaxations, so called secondary relaxations (lettered β, γ etc…when decreasing the temperature…), can be active on shorter time scales. Their characteristic time has an Arrhenius temperature dependence, and they have traditionally been related to local motion in the main chain consisting of twisting or crankshaft motions of the polymer backbone, or when they are present, to the local movements of side groups [START_REF] Mccrum | Molecular theory for the rheology of glasses and polymers[END_REF]. It has also been proposed that the β-relaxation, usually ascribed to crankshaft motions, is the precursor of the α one, since local movements are first needed to enable larger scale movements [5].

Styrene Butadiene rubbers contain four specific groups which can be involved in the βprocess, namely, (i) 1,2 butadiene (also called vinyl), (ii) cis-1,4 butadiene and (iii) trans-1,4 butadiene, and at last (iv) the styrene groups. Poly(butadiene) homopolymers, 1,2PB and 1,4 PB were studied by dielectric spectroscopy by Quan et al [6 1 . These authors ascribed the βrelaxation of the 1,4 PB to local rotations (crankshaft motions) of the main chain, whereas they proposed that the β-relaxation of the 1,2 PB is produced by the rotation of the vinyl pending group. Their study on different di-block copolymers was later completed by the work of Hoffman et al [START_REF] Hofmann | Secondary and segmental relaxation in polybutadienes of varying microstructure: dielectric relaxation results[END_REF], who systematically characterized the dielectric response of statistical PB copolymers with varying amount of 1,4 Cis and Trans Butadiene and of 1,2 Butadiene monomer units. They confirmed the existence of two different relaxation mechanisms, and in particular showed that the intensity of the dielectric relaxation is linearly related to the 1,4 butadiene content. They also established that very few monomer units are involved in the βmechanisms. In dielectric measurements, it is expected that the trans units do not significantly contribute to the dielectric response. To the authors' knowledge, there is no similar study in the literature using mechanical spectroscopy, for which both trans and cis units should contribute to the β-relaxation. Moreover, the mechanical coupling of the polymer units being different from the dielectric one, the intensity of their mechanical relaxations might evolve differently with their content. The same questions arise when studying the β-relaxation of styrene-butadiene rubber, in which a fourth monomer unit, styrene, is added. Cerveny et al. [START_REF] Cerveny | Dielectric α-and βrelaxations in uncured styrene butadiene rubber[END_REF] concluded that the mechanical relaxation of their SBR could be ascribed to the rotation of the phenyl group, whereas two years later, the same authors suggested from dielectric spectroscopy that the β-relaxation of SBR originates solely from the butadiene units [START_REF] Cerveny | Glass-transition and secondary relaxation in SBR-1502 from dynamic mechanical data[END_REF]. Unfortunately, they did not directly compared their dielectric and mechanical results as their mechanical study was performed on only one type of SBR. Thus, our work aims at completing the Hoffman's study on polybutadiene by comparing his dielectric results to mechanical results obtained by mechanical spectroscopy. This work is also extended to the study of the β-relaxation of different styrene-butadiene rubbers, in order to better understand the contribution of the different monomer units of this copolymernamely, styrene, butadiene 1,4 cis, and trans and butadiene 1,2, on this relaxation. Thanks to a phenomenological modelling approach, their contribution is then quantified and enable to understand the molecular origin of the β-relaxation mechanism.

Experiments

6 elastomers with different microstructures are studied: 3 poly(butadiene) and 3 poly (styrene-co butadiene) rubbers. Their different vinyl, cis, trans-and styrene unit contents (in molar fraction) are reported in Table 1. They were measured by RMN 1D 13 C with the following protocol:

The polymers were dissolved in CDCl3 to obtain 60 g/L solutions. All NMR experiments were recorded on a Bruker Avance III spectrometer operating at 11.7 T ( 13 C Larmor frequency of 125.83 MHz) at ambient temperature using a 5 mm broadband Helium cryoprobe. For all experiments 1 H decoupling was applied only during signal acquisition. The 13 C quantitative spectra were recorded using a flip angle of 30° (pulse length of 4us) and 4096 acquisitions were co-added using a recycle delay of 10 s to ensure complete recovering of the longitudinal magnetization. The 13 C NMR spectra were referenced using the NMR resonance of CDCl3 at 77 ppm. Polymers microstructures were calculated according to the norm ISO 21561-2:16. The 13 C NMR resonances between 43.5ppm and 45.2ppm were assigned to aliphatic CH of isolated vinyl units (Visol), i.e. vinyl units between two other units (butadiene 1,4 cis (C), butadiene 1,4 trans (T) and styrene (S)) as CVC, TVT, SVS, CVT, TVS, CVS, TVC, SVT and SVC.

The isolated vinyl fraction i.e. the fraction of the vinyl units (Visol) between two 1,4 butadiene units is calculated from the integration of the peaks of the aliphatic CH of the vinyl units between 43.5 ppm and 45.2 ppm by the integration of the carbon of all the vinyl units (Vtotal) [START_REF] Sato | Carbon-13 NMR signal assignment of styrene-butadiene copolymer[END_REF] following :

% = / (Eq.1)
This equation assumes that the resonances from SSS and SSV triad can be neglected. We have not detected theses resonances with the 1 H/ 13 C HSQC and HMBC NMR correlation experiments.

The average length of vinyl sequence and 1,4 butadiene sequence are conventionally calculated [START_REF] Caprio | Structural Characterization of Novel Styrene-Butadiene Block Copolymers Containing Syndiotacec Styrene Homosequences[END_REF] as the ratio of the number of total vinyl units by half the number of vinyl units bonded to another polymer unit (C, T and S) and, the ratio of total 1,4 butadiene units (C+T) by half the number of 1,4 butadiene bonded to another polymer unit (V and S) respectively. The materials were processed following the Rauline patent [START_REF] Cerveny | Glass-transition and secondary relaxation in SBR-1502 from dynamic mechanical data[END_REF]. First, the gum was introduced in an internal mixer and sheared for 2 min at 60°C. Then, the vulcanization recipe was added and the mix was sheared for 5 min, with the following composition: for 100 g of polymer, 1.5 g of DPG (diphenylguanidine), 3.8 g of CBS (n-cyclohexyl-2-benzothiazylsulfénamide), 1.5 g of Zinc oxide (ZnO), 1.5 g of ozone wax, 2 g of 6PPD (N-(1,3-dimethylbutyl-N'-phenyl-P-phenylenediamin), 2g of stearic acid, and 2.5 g of sulfur. The material was afterward sheared in an open mill for five minutes at 60°C. Sample sheets of 0.5 or 2 mm thickness were then obtained by hot pressing at 150°C during 90 min, which is the time needed to obtain 98% of the maximal torque during rheological measurement in plan/plan mount at 150°C.

Mechanical spectroscopy was performed in torsion mode with a Metravib apparatus enabling measurement in a frequency range [10 -4 Hz; 1Hz] over a temperature range [100 K;

250 K] [START_REF] Sato | Carbon-13 NMR signal assignment of styrene-butadiene copolymer[END_REF]. Samples were parallelepipeds with a 0.5x4x10 mm 3 or 2x6x12 mm 3 dimensions.

Dielectric measurements were performed with a Novocontrol Concept 40 apparatus using sample disc film with 2cm diameter and 1 mm thickness. The frequency domain of this apparatus was set as [0,1 Hz, 1MHz], slightly overlapping with the frequency domain of the mechanical spectrometer. This overlap will be used in the following, to compare the material mechanical and dielectric responses at the same frequency. However, the much lower frequency domain of the mechanical spectrometer is an advantage compared to the one of the dielectric as it enables a better separation of the secondary relaxations. .

Results

Isochronal measurements

As shown in Figure 1a, PBs have two mechanical relaxations in the studied temperature range, namely, a relaxation at low temperature so called β and the α-relaxation at higher temperature. The β-relaxation appears to be very wide, which might mean that it results from the overlapping of several contributions acting more or less independently the one from the other. Moreover, it is noteworthy that its width depends on the polymer chemical structure.

The temperature of the G'' β-peak is reported in Table 2. At increasing vinyl content, i.e.

decreasing Cis/Trans units content, the β relaxation amplitude decreases, its maximum shifts towards higher temperature and its width increases. As this corresponds to a decrease of the low temperature part of this peak (90-135 K) and an increase of its high temperature part (135-200K), thissuggests that two distinct mechanisms are involved in the secondary relaxation. Same experiments were performed with SBR samples and show α and β relaxations (Figure 1b). As reported in Table 2, the temperature at the maximum of the G'' β peak is the same for SBR 19/22,5/20 and SBR 20/29/14, but is 20K higher for SBR 42/15/25. As for the

Sample name

Isothermal measurements

Mechanical spectroscopy

Frequency sweep curves [2.10 -3 ; 4.10 -3 ; 8.10 -3 ; 1.10 -2 ; 2.10 -2 ; 4.10 -2 ; 8.10 -2 ; 1.10 -1 ; 2.10 -1 ;

4.10 -1 ; 8.10 -1 ; 1 Hz] have been performed with the different materials over the temperature range of their β relaxation (temperature increment of 4K). Assuming the time-temperature equivalence, master curves were plotted at a given reference temperature. As an example, the G' and G'' master curves of SBR 20/29/14 are presented in Figure 2 and validate the thermorheological simplicity assumption as a first approximation, taking as reference temperature, Tref= 152K. The curves of the other materials are given as supporting information. The shift factors used for the master curve construction can be plotted, on a logarithmic scale, as a function of 1/T (Figure 2a and2b). For all the materials, except PB5/59 for which the high temperature part of the β relaxation overlaps with the α relaxation, two slopes are visible. This confirms the presence of two Arrhenius mechanisms, the energy of which being higher for the high temperature mechanism. The activation energies (Eaβ), are deduced from the Arrhenius law given by:

( ) = exp (Eq.2)
where R is the perfect gas constant, τ is equal to 1/2πf. f and T are the frequency and the temperature corresponding to the peak maximum. Defining the shift factors between two curves obtained at different temperatures, by aT=τ(T1)/τ(T2), it is then easy to determine Eaβ (as displayed in

Dielectric spectroscopy

The isochronal curves of the loss factors obtained via the dielectric spectroscopy technique, at the same frequency 0,1Hz can be compared to the previous mechanical results (for instance Figure 4a and4b). The HT° part of the dielectric α-relaxation is masked by the increase in the ionic conductivity; nevertheless its peak maximum is observed at the same temperature as the one of the mechanical α peak. At 0,1Hz, the dielectricand mechanical βrelaxation both spread over a same temperature domain, suggesting that they originate from very similar mechanisms. However, it must be recalled that the trans isomer being initially nonpolar, it does not significantly participate to the dielectric relaxations (its contribution coming only from induced polarization), conversely to the cis and vinyl monomers. Note also that for this reason, and given the different nature of the dielectric and mechanical solicitations, the very similar intensity of the mechanical and dielectric relaxation seen on the curve is fortuitous. The dependence of the dielectric relaxation time on temperature can be directly deduced from the peak maximum position on the isochronal curves like the one presented in Figure 6a for SBR 19/22,5/20. All these data show an Arrhenius behavior with only one slope;

for the 3 SBRs, almost the same activation energies (48 < Eaβ < 50kJ.mol -1 ) were calculated.

They are close to the one found for the LT° part of the β-mechanical relaxation (Table 3). The pre-exponential times are very close to each other: τo is found equal to 5.10 -19 s for SBR 19/22,5/20 and SBR 20/29/14 and to 1.10 -20 s for SBR 42/15/25. Thus, these dielectric shift

Discussion

As expected, the isochronal curves from both techniques have shown that a modification of the copolymers microstructure leads to a modification of the secondary relaxations. To sum up our experimental results, styrene has only a « diluting » effect as the increase in its content simply decreases the content of the other monomers and therefore the intensity of the relaxations in which they are involved (one can note however that this phenomenon is much less visible with dielectric spectroscopy; the authors having no explanation for this). In both PBs and SBRs, increasing the vinyl content shifts the position of the β relaxation peak towards higher temperatures and increases its width.

The evolution of the shift factors with temperature, deduced from mechanical spectroscopy, the large frequency domain on which the β relaxation spread in the "master curve", as well as the large temperature domain overwhich it spreads in the isochronal curve, indicate that two mechanisms are involved in the β relaxation. Given the influence of the different monomers contents, the HT° mechanism can be ascribed to the vinyl isomers whereas the LT° one could be due to the movements of the cis and/or the trans units, whose respective contribution is impossible to distinguish from mechanical spectroscopy. The HT° and LT° contributions are difficult to characterize from the isothermal curves , as the frequency range over which the isothermal are performed are short, and as they seem to overlap over large temperature and frequency domains.

To solve this problem, we have chosen to deconvolute the G'' contributions of the mechanical β relaxation. This deconvolution was performed thanks to PeakFit software ©. The isochronal curves at 0.1Hz of the different materials have been analyzed following the same method [START_REF] Hofmann | Secondary and segmental relaxation in polybutadienes of varying microstructure: dielectric relaxation results[END_REF]: two peaks are defined with independent parameters, i.e. temperature at the peak maximum, the half widths for the left and the right side of the relaxation, and its amplitude A. The use of two peaks was motivated by the fact that the experimental peak is, for most of the materials, too large to be fitted by a single HN function (and, as said previously, by the fact that the previously seen influence of the comonomers contents on the shape of the β relaxation is incompatible with the assumption of a single process). The optimization of these parameters is based on the optimal fit of the experimental peak with the summation of the two simulated peaks. For instance, with PB 48/16, the two deconvoluted peaks have their maximum at 115K et 155K respectively (cf. Figure 7): other curves are presented as supporting information. R is the perfect gas constant , τ is equal to 1/2πf with f the frequency of the test (0,1Hz) and

T the temperature at the peak maximum. The activation energies are those previously deduced from the shift factors: we have assumed the same relaxation mechanisms in all the samples and therefore the same activation energy, i.e. 49 kJ/mol for the LT° mechanism and 69kJ/mol for the HT° one. As reported in For the three SBRs, the mechanical relaxation times of the HT° contributions are superimposed; the same result is found for the mechanical relaxation times of the LT° contributions (Figure 9). Now that we have obtained more information on the relaxation times of both mechanisms, and therefore less free parameters, the mechanical isochrones and isothermal curves can be fitted with the sum of two Havriliak-Negami functions (HN) with the two following assumptions:

-Two different contributions exist in the β-relaxation of PBs and SBRs : one at HT° due to the relaxations of the 1,2 budadiene units (vinyl) and one at LT° due to the relaxation of the 1,4 butadiene cis/trans.

-From a polymer to another, i.e. from a chemical microstructure to another, the width, the asymmetry and the peak positions (in other word the relaxation times) of each contribution does not change. The HN function for the complex modulus is:

* ( ) = + ∆ (1 + ($ %& ) ' () ) * () (eq. 4)
with α controlling the peak asymmetry, γ its width and ΔG its amplitude. The real and imaginary parts are given by: (eq. 7)

+ ( ) = + ∆ cos (0 %& 1) 21 + 2( ) ' () . sin 6(1 -7 %& ) 2 + ( )
At the loss peak, = ? sin 67 2(@ + 1) sin 67@ 2(@ + 1) A B '

(eq. 8)

The evolution of the complex modulus with temperature is therefore the consequence of the evolution of the relaxation times (τ). As suggested by the previous results, these times follow the Arrhenius equation in which the activation energies are fixed at 69kJ.mol -1 for the HT° contribution and at 49kJ.mol -1 for the LT° contribution.. The fixed pre-exponential times are also the ones deduced from equation 8, for these two materials (table 4). Our second assumption is that αHN and γHN are constants for each contribution, whatever the polymers.

Their value is fixed from the fitting of the isochronal curves obtained at f = 0.1Hz (helped by the initial curve fitting with peakfit). It is indeed impossible to estimate them from the isothermal curves since the frequency domain tested is too small. Note also that these two parameters are deduced with the assumption that the width of the times distribution of the relaxational processes do not depend on the temperature. Such dependence was discussed in literature, for instance, for the modelling of the β relaxations of PMMA [START_REF] Muzeau | Mechanical spectrometry of the. beta.relaxation in poly (methyl methacrylate)[END_REF] or PVC [START_REF] Flores | Mechanical Spectroscopy of the. beta. Relaxation in Poly (vinyl chloride)[END_REF]. It is related to the distribution of the activation entropy of the relaxations. Taking into account such dependence add more complexity and an additional parameter to the fitting procedure. Moreover, in references 15 and 16, the found dependence seems difficult to characterize (the data are scattered), and in any case relatively small (less than 10% variation of the width of the time Gaussian distribution over the whole temperature range of the relaxation). For these reasons, neglecting it seems very reasonable, and to our opinion, has no significant influence on the conclusion of our work.

Given the fact that there are two contributions within the β relaxation, it is not satisfactory to use the fitting of the built master curves, as these ones assume a time-temperature equivalence which is a rough approximation. However, the amplitude of each relaxation can be deduced from the simultaneous fitting of the isothermal and isochronal data. A satisfactory fit of both isothermal and isochronal curves is usually difficult to obtain and its success must always be seen as strong support of the employed procedure. For all the studied materials, the isochronal fitting is very satisfactory given the simplicity of the procedure, except for PB 5/59 (Figure 10). It is indeed difficult to fit its HT° contribution because it merges with the α-relaxation. The fitting of the isothermal curves is also satisfactory, as shown on figure 11 . Still with the same parameters, this procedure has been also applied to the isochronal curves obtained at 2.10 -3 Hz (cf. Supporting Information) and gives very good results, which also validates our approach. The amplitude found for each contribution can now be plotted on figure 12 as a function of the volume fraction of the 1,2 butadiene (vinyl) and 1,4 butadiene (cis and trans) content. The volume fraction is preferred to other parameter (weight or molar fraction) as the mechanical response of a material is usually related to the volume fraction of its different phases. To calculate this volume fraction, we have assumed that each unit has the molar volume of its homopolymer (60 cm 3 /mol for butadiene, and 99 cm 3 /mol for styrene). A linear relationship is found for both HT° and LT° contributions. (Note that the data for PB5/59 is not included in the trend curve calculation as its value is calculated with a more important error (+-0.1), due to the proximity of the α and β relaxation in this material). A plot as a function of the molar fraction of the butadiene units leads to the same conclusion (see Supporting Information Figure SI17). This is not surprising as there is very small difference between molar, volume and weight fractions in the considered materials, (the styrene content being low in the studied SBRs). As seen in Figure 12, the fitting line passing close to the origin, this nicely confirms that the HT° contribution is due to the movements of the 1,2 units and the LT° contribution to those of the 1,4 units. Moreover, it must be emphasized that our results also prove that both cis and trans units are involved in the LT° contribution of the mechanical relaxation, for two reasons. First, a plot of the LT° relaxation amplitude as a function of only the trans units volume fraction cannot be fitted by a straight line (see Figure SI16 Supporting Information).

Moreover, as also shown in the Supporting Information (Figure SI15), the amplitude of the β- In random copolymers, a low molar fraction of one monomer leads to a large number of isolated units of this monomer in the polymer chains. As reported in table 1 the average length of the vinyl, and of the cis+trans sequences in the studied copolymer measured by NMR, as well as the % of isolated vinyl units are in relatively good agreement with the theoretical values calculated for perfectly random copolymers. The LT° and HT° relaxation amplitudes have been plotted (Figure 13) as a function of the volume fraction of units in sequence of more than one units and in sequence of more than two units (using, when available, the experimental data from NMR, otherwise theoretical values for random copolymer, reported in Table 1). Clearly, for both LT° and HT° mechanical β-relaxation, not taking into account the fraction of isolated units immediately shifts the fitting linear curve far from the origin (again, a plot as a function of molar fractions would leads to the same conclusion, as seen in Supporting Information (cf.

Figure SI18). These results strongly suggest that both LT° and HT° mechanisms only needs one butadiene unit to occur. Some comments can finally be made concerning the dielectric data. Our analysis of the mechanical relaxation of the three PB materials is consistent with the one performed by Hoffman on the dielectric response of PB with different comonomers contents. Moreover, as said in the experimental part, both dielectric and mechanical relaxations are, at the same frequency of 0,1 HZ (figure 5) , similar for all the SBR materials. In both cases, the β relaxation is the narrowest and at lower temperature for the material having the highest Cis unit content (SBR 20/29/14), whereas it is spread over a larger temperature domain for the material having a high Vinyl unit content (SBR 42/15/25). The influence of the Cis and Vinyl units content on the LT° and HT° parts of the relaxation is therefore the same in dielectric measurements, the difference with the mechanical response being that the Trans units do not have a significant dielectric response, whereas they participate to the mechanical relaxation.

This conclusion is also supported by the characterization of the relaxation times. The dielectric ones found by Hoffman have been plotted on Figure 8 Hoffman which in addition, hardly follow an Arrhenius law. The activation energy of the PB 7/41 was found equal to 33 kJ.mol -1 , which is not so far from the 49 kJ/mol found for the PB 5/59. Note that conversely to our mechanical data, the dielectric ones of Hoffman do not enable to evidence a clear difference of activation energy of the LT° and HT° part of the relaxation (a slight difference can however be observed in figure 7 of Hoffman's article, between its PB07 and PB95 materials). This might be partly explained by the fact that in dielectric measurements, the data used to extract the relaxation times (from the frequency at which the β peak maximum is observed) are in a temperature/frequency domain where the the LT° and HT° relaxation times are closer (cf. Figure 8). Despite this remark, the comparison of the dielectric and mechanical relaxation times of PB suggests a same molecular origin for both relaxations. The dielectric and mechanical relaxation time of the SBR can be compared on figure 9. Having deduced the dielectric relaxation times from the isothermal curves, without any deconvolution, it it is expected for their value to be significant of the relaxation process with the largest amplitude (as the signatures of both processes overlap).

As said previously, the Trans unit does not participate to the dielectric response. Therefore, the dielectric response depends on the CIS and Vynil units. Two of the SBRs (SBR 20/29/14 and SBR 19/22,5,20) tested contains slightly more CIS units than vinyl ones, and present an activation energy very close to the one of the LT° process of the mechanical relaxation. This is consistent with Hoffman's finding that the dielectric response of the Cis unit is much more intense than the one related to the Vinyl ones [START_REF] Hofmann | Secondary and segmental relaxation in polybutadienes of varying microstructure: dielectric relaxation results[END_REF]; the main contribution in the dielectric peak, which therefore mainly influences the peak maximum position is indeed that of the Cis unit relaxation. The deduced activation energy for the dielectric relaxation of the SBR 42/15/25 is close to the one of the other SBR, in spite of the fact that the vynil unit content is 3 times the one of the Cis unit, also confirming (like the figure 5b) the main role of the Cis units in the dielectric β-relaxation.

Conclusion

The influence of the chemical microstructure on the secondary mechanical relaxations of PB and SBR has been studied by varying the content of vinyl, cis, trans butadiene and styrene groups. First, the addition of styrene decreases its amplitude without modifying the other characteristics. The plot of the master curves and of the evolution of the β-relaxation times of the different materials from dielectric and mechanical spectroscopies confirms the existence of two relaxational mechanisms with two distinct activation energies. Based on this result, the experimental isochronal and isothermal curves obtained by mechanical spectroscopy were fitted thanks to the summation of two Havriliak Negami functions. This enables to prove that the vinyl groups are responsible for the contribution of the HT° part of the β-relaxation, whereas the butadiene 1,4 groups, cis and trans are at the origin of the low temperature part of this relaxation. Contribution of the trans unit in the SBR dielectric β relaxation does not exist, whereas it is significant in the LT° part of the β mechanical relaxation. Like in the dielectric response, the intensity of β mechanical relaxation of the Cis units is more intense than the one of the vynil units. Moreover, the intensity of the β mechanical relaxation associated to each monomer appears to be proportional to their volume (and molar) fraction.

Given the random characteristics of the studied copolymer, this suggests that the involved mechanisms are localized at the level of only one monomer unit. Finally, this shows that it is relatively easy, by playing with the content of the butadiene 1,2 and butadiene 1,4 monomers, to pilot the width and intensity of the β mechanical relaxation of the styrene-butadiene copolymers and rubbers.

Figure 1 :

 1 Figure 1: Dynamic loss modulus as a function of temperature, at 0.1 Hz a) for PB 5/59 (□), PB 48/16 (△), PB 81/11 (○)b) for SBR 20/29/14 (◇), for SBR 19/22,5/20 (x), for SBR 42/15/25 (+).

  peak amplitude varies with the copolymer microstructure. The significant difference between the SBR 20/29/14 and the two SBR 19/22,5/20 and SBR 42/15/25 might come from the difference in their styrene content, the increase of which necessarily decreases the relative amount of the other monomers and therefore the intensity of the relaxations in which they are involved.Moreover, the β relaxation is weaker and more spread in temperature when the vinyl content increases while the Cis/Trans content decreases ; in other word, the evolution of the LT° part and of the HT°part of the relaxation are different. As previously for PBs, these results suggest that the increase of the vinyl content promotes the relaxational mechanism at high temperature, to the detriment of the low temperature mechanisms.

Figure 2 :

 2 Figure 2: G' and G'' master-curves for the SBR 20/29/14. Tref= 152K.

Figure 3 :

 3 Figure 3: Shift factors as a function of 1/T for a) for PB 5/59 (□), PB 48/16 (△), PB 81/11 (○), b) for SBR 20/29/14 (◇), for SBR 19/22,5/20 (x), for SBR 42/15/25 (+), in the β relaxation temperature domain.

Figure 4 :

 4 Figure 4: Dielectric and mechanical loss factors as a function of temperature at 0.1 Hz: a) for SBR 42/15/25 (dielectric (◇),DMA (△) ), b) for SBR 20/29/14 (dielectric (○), DMA (□)).

Figure 5 Figure 5

 55 Figure5presents the dielectric imaginary part of permittivity ε'' as a function of the temperature measured at 0.1 Hz for the 3 SBR. The height of the ε'' β peak is lower and occurs at higher temperature for SBR 42/15/25 than for SBR 20/29/14 and SBR 19/22,5/20, as previously found with mechanical spectroscopy.

  enable to evidence two relaxationnal mechanisms, conversely to the previous mechanical measurements and to what is suggested by dielectric experiments on different materials (cf. introduction). This will be further commented in the discussion part.

Figure 6 :

 6 Figure 6: a) loss permittivity ε'' as a function of 1/T, measured at different frequencies for SBR 19/22.5/20; b) dielectric β-relaxation times deduced from isochronal curves, for the 3 SBRs: for SBR 20/29/14 (◇), for SBR 19/22,5/20 (x), for SBR 42/15/25 (+)

Figure 7 :

 7 Figure 7: Deconvolution of the β-peak mechanical relaxation of PB 48/16.

Figure 8 :

 8 Figure 8: Arrhenius plot of the PBs β-relaxation times deduced from mechanical spectroscopy (PB 81/11 (△), PB48/16(○), PB 5/59 (□)) and dielectric spectroscopy (full symbols: PB 86/6 (▲), PB 52/19(•), PB 7/41(■ ) (Hoffman data, from Fig 7(b) in reference 7).

Figure 9 :

 9 Figure 9: Arrhenius plot of the SBRs β-relaxation times deduced from mechanical spectroscopy (SBR 20/29/14 (○), for SBR 19/22,5/20 (◇), for SBR 42/15/25 (□)) and dielectric spectroscopy (same full symbols).

14 Figure 10 :

 1410 Figure 10: fitting of the G'' isochronal curves at 0.1Hz with the HN model: data (circle symbol), HN fit of the HT° contribution (red line), HN fit of the LT° contribution (blue line), HN fit with both contributions (dark line)

Figure 11 :

 11 Figure11: fitting of the isothermal curves of the different materials with the HN model (some temperatures have been selected in order to ease an easier comparison between the fitting line and the HN model; it is important to recall that fitting has been performed simultaneously on the isothermal and isochronal curves).

Figure 12 :

 12 Figure 12: a) Amplitude of the LT° contribution in the β mechanical relaxation as a function of the cis/trans 1,4 butadiene volume fraction, full square symbol for PB 5/59 (the data for PB5/59 is not included in the trend curve calculation as its value is estimated with a more important error (+-0.1)) ; b) Amplitude of the HT° contribution in the β mechanical relaxation as a function of the 1,2 butadiene volume fraction .

Figure 13 :

 13 Figure 13: a) Amplitude of the LT° contribution in the β-mechanical relaxation as a function of vol. fraction of cis/trans 1,4 butadiene units in sequence of more than 0 unit(•), more than 1 unit (■), more than 2 units(▲) ; b) Amplitude of the HT° contribution in the β mechanical relaxation function of vol.% fraction 1,2 butadiene units in sequence of more than 0 unit•(), more than 1 unit (■), more than 2 units(▲) .

Table 1 : Microstructure and TgDSC (K) of the studied PB (monomer content expressed in mass fraction). For SBR, the molar fraction of the different units is also reported between parentheses.

 1

Table 2 : Height and temperature at the maximum of the β peak measured at 1Hz by mechanical spectroscopy .

 2

Table 3

 3 HT° and LT° refer to High Temperature and Low Temperature side of the relaxations

	). Eaβ of the low temperature (LT°) mechanism are between 43 and
	49 kJ.mol -1 ; the ones of the high temperature (HT°) mechanisms varie on a larger domain,
	between 62 and 90 kJ.mol -1 . Such result is explained by the proximity (in other word the partial

overlapping) of the α relaxation in the case of the materials with the lowest Tg (PB 5/59); this leads to an overestimate of the shift factors and consequently of the activation energy. *

Table 3 : Activation energy of the β-mechanical relaxation for the 6 different materials.

 3

Table 3

 3

	, 49 kJ/mol is indeed the activation energy of

This procedure enables to plot the relaxation times in absolute values for both mechanisms and for all the samples on Figure

8

. The average relaxation times of the HT° mechanisms of PB 48/16 and PB 81/11 are superimposed (those of PB5/59 cannot be deduced with enough certainty from the data as the α relaxation is too close from the β-one). The same superimposition is found for the relaxation times of the LT° mechanisms.

Table 4 : parameters used for the HN fitting of the isochronal curves

 4

  with our mechanical relaxation times. found for PB 81/11 by mechanical spectroscopy. 75 kJ/mol is found for the PB 52/19 ; this is much higher than what we found for PB 48/16 but is explained by the few data of

	68kJ/mol
		0.8			0.6
	LT relaxation amplitude	0.1 0.2 0.3 0.4 0.5 0.6 0.7	y = 0.01x -0.0234 R² = 0.962	HT relaxation amplitude	0.1 0.2 0.3 0.4 0.5	y = 0.0057x + 0.0496 R² = 0.9616
		0			0
		0	20 %vol. of1 ,4 unit 40 60	80	0	50 %vol of1 ,2 unit

Depending on the PB, they are either in between the LT° and HT° mechanical relaxation times (PB 7/41 and PB52/19) or close to the HT° mechanical relaxation times (PB 86/6). The activation energy is found equal to 56 kJ.mol -1 for PB 86/6, that is comparable with the


F Omnes

Destaing

Eric Lainé
email: eric.laine@ensma.fr

J C Grandidier

G Benoit

B Omnès

F Destaing

Effects of sorption and desorption of CO2 on the thermomechanical experimental behavior of HNBR and FKM O-rings -Influence of nanofiller-reinforced rubber

Keywords: Elastomer, CO2 pressure, mechanical tests, O-rings, identification, constitutive equation

INTRODUCTION

Carbon dioxide is a natural gas which is frequently encountered in hydrocarbon environments. Relatively low concentrations of CO2 in hydrocarbon mixtures can cause significant swelling of the seal. More significantly, the effect of absorbed CO2 upon rapid gas decompression (RGD) can be catastrophic if consideration is not given to the choice of polymer, cure, and particle reinforcement.

Hydrogenated nitrile butadiene rubber (HNBR) and fluorocarbon rubber (FKM) are well known for their resistance to chemical and thermal degradation [START_REF] Alcock | The effect of hydrocarbon ageing on the mechanical properties, apparent crosslink density and CO2 diffusion of a hydrogenated nitrile butadiene rubber (HNBR)[END_REF][START_REF] Grelle | Temperature-dependent leak tightness of elastomer seals after partial and rapid release of compression[END_REF][START_REF] Qamar | Mechanical and structural behavior of a swelling elastomer under compressive loading[END_REF]. Nonetheless, performance and functional life of polymer materials can be significantly affected when submitted to gas environment. Indeed, saturation conditions, especially in CO2, are known to alter the gas permeability due to plasticizing effects in almost all polymers and this effect is more pronounced for elastomer components [START_REF] Briscoe | Explosive decompression failure of rubbers -A review of the origins of pneumatic stress-induced rupture in elastomers[END_REF][START_REF] Briscoe | The effect of structure on gas solubility and gas induced dilation in a series of poly(urethane) elastomers[END_REF][START_REF] Major | Characterization of the fracture behavior of NBR and FKM grade elastomers for oilfield applications[END_REF][START_REF] Davies | The mechanical properties of elastomers in high-pressure CO2[END_REF]. In addition, they are specially designed for resistance to RGD.

Recently, Haroonabadi et al [START_REF] Haroonabadi | Investigation of the effect of thermal aging on rapid gas decompression (RGD) resistance of nitrile rubber[END_REF] have shown that the thermal ageing (7 days at 100°C) of NBR vulcanizates depends strongly on crosslink density and mechanical properties. Thermal ageing of nitrile rubber samples increased crosslink density and decreased tensile and tear strength, resulting in a decrease in RGD resistance. Chen et al. [START_REF] Chen | CO2 Solubility and diffusivity and rapid gas decompression resistance of elastomers containing CNT[END_REF] studied CO2 diffusivity and solubility, and RGD resistance of HNBR and fluoroelastomer (FKM) elastomers containing carbon nanotubes. While the addition of carbon nanotubes may lead to an increase in mechanical properties, they have shown that it reduces the CO2 diffusivity and solubility and therefore improves the RGD resistance of the reinforced elastomers.

However, a fundamental understanding of the behavior of elastomeric seals in a gas environment is necessary because it is still incomplete and more particularly on coupling effects (diffusomechanical). The lack of data in the literature comes from the difficulty of carrying out mechanical 2 tests to characterize the behavior under gaseous environment with a high gas pressure. Studies of the swelling behavior of elastomers under CO2 are the most common in literature [START_REF] Daou | Swelling of Elastomers in CO2 Environment: Testing Methodology and Experimental Data[END_REF]. However, it should be noted that Davies et al. [START_REF] Davies | The mechanical properties of elastomers in high-pressure CO2[END_REF] have developed a standard dumbbell tensiometer to measure the mechanical properties of elastomers saturated with CO2 and N2 (two gases with very different solubilities) at pressures up to 4 MPa. High-pressure vessels installed on traction machines can be used, but carrying out such tests is not easy due to very restricted metrology. If it is relatively easy to measure the applied load or the actuator displacement, understand the local deformation is not obvious and requires specific equipment and tools. In addition to these difficulties, questions about the representativeness of the microstructure of the samples are generally considered, elastomer blocks are generally envisaged but their curing conditions are not identical to those of the seals. As a result, extrapolate behavior can lead to hazardous approximations.

The aim of this article is to propose a methodology coupling mechanical tests under extreme conditions (temperature and CO2 pressure) with a local deformation measurement in order to identify the behavior of different elastomers. In addition, this method permits the characterization of the materials used in the structure (O-ring) obtained with the industrial process. In order to improve the measurements of the local strain, an in situ optical measuring system is used. This article focuses the study on HNBR and FKM respectively non-reinforced and reinforced with nanofillers in order to evaluate the matrices (HNBR, FKM) and the influence of these reinforcements on mechanical characteristics. Mechanical compression tests [START_REF] Lainé | Mechanical characterization under CO2 of HNBR and FKM grade elastomers for oilfield applications -effects of 10GE reinforcements, Constitutive Models for Rubber X, Lion & Johlitz Eds[END_REF] were carried out on O-rings under CO2 pressure (2, 4 and 6MPa) at two temperatures (60 and 130°C) and after CO2 desorption. The selected CO2 pressure and temperature values are in accordance with both NACE [START_REF]Evaluating Elastomeric Materials in Carbon Dioxide Decompression Environments[END_REF] and NORSOK M710 [START_REF]Qualification of non-metallic sealing materials and manufacturers[END_REF] standards. By comparing the different mechanical responses in the different configurations (temperature and CO2 pressure), this procedure will evaluate the behavior and durability of each material. Ultimately, the parameters of the behavior law are modified and are a function of the temperature and CO2 pressure.

EXPERIMENTAL

Materials and sample

Two elastomer types, a hydrogenated nitrile rubber (HNBR) and a fluorelastomer type (FKM) were selected for these investigations. The compounds were produced with a nominal hardness of 80 and 90 Shore A respectively for the HNBR and the FKM. HNBR and FKM were compounded as summarized in Table 1, respectively, using a base polymer which is 96% saturated with 36% acrylonitrile content and a 70% fluorine content. HNBR and FKM were vulcanized with peroxide curing systems, respectively dicumyl peroxide and DBPH.

The rubber matrices were reinforced with carbon black and nanofillers. The carbon black reinforcement is fixed at 100 phr. Both matrices were reinforced with 10 phr of nanofillers. The nanofiller chosen was expanded graphite with the reference TIMCAL (Timrex). The chosen denomination is 10GE for each rubber.

The compound of rubber was obtained with a "classical" compounding operating mode for an elastomer. An internal mixer was used to incorporate the nanofiller. Nanofillers were introduced before carbon black. To improve the homogenization of the compound and avoid delamination defect after curing, for FKM reinforced with nanofillers, two specific processing assistants were used. For HNBR, the incorporation of nanofillers reduces tensile strength and elongation at break. For FKM, the incorporation of nanofillers increases the loss factor for high strains.

Mechanical tests are not carried out on conventional specimens but directly on the industrial structure: O-ring. The nominal dimensional characteristics of the O-rings are 50.17mm x 5.33mm, respectively in terms of inner diameter and cross-section diameter.

Experimental device

An Instron 8802 servohydraulic fatigue machine (Figure 1a) was fitted with a pressure and temperature regulated chamber which allows mechanical testing in gaseous nitrogen, hydrogen or carbon dioxide up to 40MPa and 150°C. For safety reason related to hydrogen, the volume of the chamber is rather small (1.77liter with a diameter of 150mm and length of 100mm). More information on this device can be found in previous papers [START_REF] Sun | Fatigue crack propagation under gaseous hydrogen in a precipitation-hardened martensitic stainless steel[END_REF][START_REF] Castagnet | Mechanical testing of polymers into pressurized hydrogen: tension, creep and ductile fracture[END_REF]. To observe the specimen, the vessel has a front and a back optical access through a central cylindrical sapphire window of 40mm diameter.

The fatigue machine, with a maximum capacity of 20kN, can operate up to a frequency of 20Hz. Its maximum stroke is 25 mm (limitation to the dimensions of the lower water jacket). However, the height of the chamber limits the dimensions of the various assemblies and test pieces. The fatigue machine is provided with an external load cell and a pressurized column containing a pressure compensated internal load cell. The presence of the internal load cell allows direct measurement of the applied load without any sealing friction forces. The whole of this device is temperature controlled. This device, named HYCOMAT, combines a purely mechanical load to a load of gas, under nitrogen (N2), hydrogen (H2), or carbon dioxide (CO2).

Specific assembly

A specific assembly to test the seals was dimensioned and manufactured, for compressive tests (Figure 1b). A load reversal system is used in accordance of the ball joint alignment system of the test rig. This inverter assembly consists of two rigid U-shaped structures. Thus, the sample is placed on the upper U connected to the fixed jaw and the lower U is connected to the movable jaw to apply the compression (Figure 1b and Figure 1c). The trays are drilled in the center in order to avoid overpressure on the inside diameter of the O-ring during the compression test. The tensile mounting has been dimensioned so as to have at most one stroke a deformation in the seal of the order of 25%. The compression tests were limited to a 1.5mm crushing of the seal since this is equivalent to a local strain of the order of 25% in the section thereof. In practice, this type of seal in operation is compressed by a maximum of 15 to 25%. From the point of view of metrology, a system of non-contact extensometry is used. This method of markers, developed within the laboratory, has the advantage of being usable in extreme conditions (very high temperatures, high pressures ...). Markers (2 or 4) are placed on the O-rings's generatrix (Figure 2). This generatrix corresponds to the parting line of the O-ring, it is represented by a dotted line in the Figure 2. It is to follow the displacements of the barycentres of the tasks in the plane of a couple of markers (Figure 2). From this measurement of the relative displacement between two markers, a "local deformation" is deduced which is called deviation (dev).

(%) = ∆ = × 100 (1)
With regard to the O-rings, two or four markers are placed. This marking makes it possible to have a measurement of the dimensional changes by taking them two by two. The camera is centered between markers 2 and 3 (Figure 2). Markers 1 and 4 are the most misaligned. Deviations along the generatrix (Figure 2) at the parting line are measured respectively between markers 1 and 4 and markers 2 and 3. The measurement of deviations between the nearest (2 and 3) and furthest (1 and 4) markers respectively allows the values to be framed and the quality of measurements to be assessed with these markers. The average of the two is used to characterize the behavior of the material.

Figure 2 : Measurement deviations (dev 1-4 & 2-3) -complex markers Tracking Method 2.5 Protocol

The compression tests for each of the materials were carried out according to an identical protocol [START_REF] Lainé | Mechanical characterization under CO2 of HNBR and FKM grade elastomers for oilfield applications -effects of 10GE reinforcements, Constitutive Models for Rubber X, Lion & Johlitz Eds[END_REF]. This one consists in several following steps:

Step A: Positioning of the seal for compression test on the greased tray Step B:

Temperature stabilization at 60 or 130°C (at least six hours).

Step C:

Compression tests at isothermal temperature (60 or 130°C).

Step D:

Pressurization under CO2 (2,4 or 6MPa) at a speed between 2 and 4MPa/min, then stabilization for at least six hours (Figure 3a) in order to obtain the saturation.

Step E:

Compression tests at isothermal temperature (60 or 130°C) and constant CO2 pressure.

Step F:

Back to a zero CO2 pressure (Air) at a speed between 2 and 4MPa/min (Figure 3b), then stabilization for at least six hours in order to obtain the new level of saturation.

Step G:

Compression tests at isothermal temperature (60 or 130°C).

The pressurization under CO2 of the chamber consists in injecting CO2 into it initially filled with air at atmospheric pressure. Three pressures are imposed 2, 4 and 6MPa and at two temperatures. Thus, the actual pressure (partial pressure) in CO2 can be calculated by considering the amount of CO2 contained in the air with that added to reach the set pressure (2, 4 or 6MPa). In Table 2, the corresponding CO2 partial pressure is given for each desired pressure. In the rest of the document, to simplify reading, only the desired pressures are indicated.

The CO2 pressure and temperature values comply with both NACE [START_REF]Evaluating Elastomeric Materials in Carbon Dioxide Decompression Environments[END_REF] and NORSOK M710 [13] standards, and under NACE conditions the pressure is set at 5.2 MPa at room temperature. To study the impact of temperature and pressure on the diffusion effect (NORSOK M710), the values were gradually increased to 130°C and 6MPa. The temperature limit was imposed by the thermal resistance of the HNBR.

In addition, it should be noted that during these tests, the decompression rate (Figure 3b) is imposed by the machine. It is not possible to control this decompression rate. Before each mechanical test, load, displacement and deviation measurement are reset. The compression tests consist of loading up the specimen to reach the expected displacement value, and next the unloading step follow the same speed. Reproducibility tests were carried out to ensure the feasibility of the optical measurements (Figure 4a-b) and to evaluate the quality of the measurements. The set of results presented below is the average of two or three tests for each configuration.

Material Models

Seals with different materials (HNBR, FKM, HNBR-10GE, and FKM-10GE) are tested under uniaxial compression to establish load-displacement and deviation-displacement curves, so that an appropriate component model can be selected in the following finite element (FE) simulations. The tests were carried out around 25-30% compression, which corresponds to average deformations. To this end, a hyperelastic modeling model can be used to describe the behavior of elastomeric seals in our FE simulations. These simulations are performed using the commercial FEA (Finite Elements Analysis) software ABAQUS (User's Manual Version 6.13, Providence, RI, USA) [START_REF]Abaqus/CAE User's Guide. Ver. 6.13[END_REF].

To describe the behavior of the elastomers in this study, the neo-Hookean compressible form of the strain energy density function was chosen. Since only moderate strains are of concern in the current investigation. The strain energy density function W for a neo-Hookean compressible material is typically formed of the deviatoric and the volumetric terms [START_REF]Abaqus/CAE User's Guide. Ver. 6.13[END_REF][START_REF] Treloar | The physics of rubber elasticity[END_REF][START_REF] Yeoh | Developments in Finite Element Analysis[END_REF] and expressed as: W= C10 (I1;¯ -3) + D1 (J -1) 2 (2)

where C10 and D1 are temperature-dependent material parameters representing the resistance to shear and the compressibility of the material respectively; I1;¯ is the first deviatoric strain invariant defined as:

I1;¯ = λ1;¯2 + λ 2; ¯2 +λ 3; ¯2 (3)
where the deviatoric stretches λi;¯ = J -1/3 λi ; J is the total volume ratio and λi are the principal stretches. The initial shear modulus and bulk modulus are given by: µ0 = 2C10 and K0 =2/D1.

(4)

Finite elements compression models

Numerical simulations of a compression seal was used to evaluate the rigidity and compressibility of each material in different configurations (temperature, CO2 pressure). For this purpose, a parametric study was carried out to know the influence of each parameter according to the test conditions. In addition, in relation to the measurement of the deviation, the numerical tool allows to evaluate, for example, the effect of a marker positioning error on the measurement. First, two models can be considered depending on the test conditions: 3D and axisymmetric. The responses of these two models in load and deviation were compared to determine the most relevant in terms of calculation time. The 3D geometric models in compression is defined in Figure 5a. This represents the seal as used and positioned in the chamber. Thermal and diffusion (CO2) expansions are considered in the numerical model by adapting the initial geometry of the O-ring. Given the symmetry conditions, only a quarter of the O-ring is considered (Figure 5a), defined as a deformable solid. The compression plate and the lower support are represented by discrete rigid surfaces. The contact is managed between the different elements (seal and lower and upper plates) with a friction coefficient of 0.2 to ensure the stability of the numerical simulation. A parametric study of the friction coefficient showed that the compression response was independent of the friction coefficient in the observed deformation range. The finite elements used for the seal are C3D20H elements. The model is therefore represented by 8256 elements and 37645 nodes (Figure 5b). In the case of axisymmetric modeling (Figure 6), the rubber O-ring is meshed with eight node axisymmetric quadrilateral elements with hybrid formulation (CAX8H) accounting for the incompressibility of rubber materials. The model is composed of 2272 elements and 8485 nodes (Figure 6b). In 3D modeling, the deviation response is obtained by extracting the displacements of the nodes (Figure 5c) corresponding to the barycenter of the markers. Since only a quarter of the seal is represented thanks to the two symmetries, it is therefore assumed that the markers are perfectly symmetrical. Thus, it is enough to extract the coordinates of a single node. In the case of axisymmetric modeling, it is sufficient to also extract the coordinates of the node in the joint plane, external side of the seal (Figure 6c) and to project them in the perpendicular plane (XZ) in order to have the 3D coordinates of this node.

Figure 8 compares the different responses according to the two models and the laws of elastomer behavior. Figure 8a shows the load-displacement curves and Figure 8b shows the deviationdisplacement curves. Whatever the behavior law and for average deformations (<25%), the two models give almost the same load-displacement responses. In the incompressible case the relation deviation-displacement are exactly the same. On the other hand, there is a slight difference between the two models for a deviation of more than 1.5%. However, the difference observed numerically is less than the accuracy of the measurement. Thus, it is quite possible to use the axisymmetric model to identify the parameters of the behavior law of an elastomer up to 25% strain.

Influence of the parameters of the behavior law

First, a parametric study was conducted using the compression test simulation model. This study aims to evaluate the influence of the two parameters (C10 and D1) of the behavior law (equation 2). Figure 8a, shows that the variation of the C10 coefficient, when D1 is constant, has an important influence on the response in load. The loading is mainly compression, but the seal is free of shape, so only C10 participates in the stiffness since the volume change is not constrained. On the other hand, the evolution of the radius of the seal section is directly related to D1. To illustrate this point, Figure 8b shows that the variation in the C10 coefficient, when D1 is constant, is negligible on the deviation measurement. Conversely, if the coefficient D1 varies and C10 is constant (Figure 9a andb) then the measurement of the deviation also varies. This confirms that the measurement of the deviation is only dependent on the compressibility coefficient D1.

Moreover, Figure 9a and Figure 9b clearly show the dependence of the deviation on the coefficient D1, since the curves on these last two figures shift in much the same way. On the other hand, in small deformations (<5%), the influence of parameter D1 only starts at 0.1MPa -1 (which corresponds to a Poisson's ratio of 0.475) on the deviation measurement. Below this value, the measurements obtained during the tests can be considered to be within the measurement uncertainty.

Compression response for different stiffness values

Finally, from the compression tests on the seal, by simultaneously measuring the quantities: displacement of the compression plate and the load as well as the non-contact measurement of the swell (deflection), it is then possible to determine the set of parameters (C10, D1) of the behavior law (eq. 2) in small deformations.

RESULTS AND DISCUSSION

HNBR (Compression tests at 60°and 130°)

Compression tests on one HNBR seal at different CO2 pressures (2, 4 and 6MPa) and at two temperatures (60 and 130°C) were performed on four different seals. The load-displacement curves and deviation-displacement are shown in Figures 11a and11b at 60°C and 130°C respectively. The load-displacement curves at 60°C in Figure 11a show a slight loss of stiffness with increasing CO2 pressure. The C10 coefficient decreases by almost 20% between the unsaturated material and the material subjected to a pressure of 6MPa in CO2. The responses of HNBR without pressure (unsaturated) and at 2MPa are almost superimposed. However, the deviation-displacement curves at 60°C (Figure 11b) are all superimposed. This means that for HNBR, the effect of CO2 pressure is zero or negligible on the compressibility of the material (D1=0.075MPa -1 ) up to about 25% deformation. In Figure 11b, the load-displacement curves at 4 and 6 MPa pressure at 130°C are very close to each other, and very slightly distinct from the unsaturated material. The deviationdisplacement curves (figure 11b) are almost superimposed. The value of the compressibility coefficient is slightly higher for zero pressure than for the other two conditions (4 and 6MPa). Finally for HNBR, CO2 sorption reduces the compression stiffness of the material between 0 and 6MPa, about 20% and 15% respectively at 60°C and 130°C. However, at both temperatures, it appears that the compressibility coefficient is the same and is not affected by CO2.

FKM (Compression tests at 60°and 130°)

In the same manner compression tests on a FKM seal at different CO2 pressures (2, 4 and 6MPa) and at two temperatures (60 and 130°C) were carried out on four different seals. The loaddisplacement curves are shown in Figure 12a and Figure 12b respectively at 60°C and 130°C. As for the HNBR, the CO2 absorption at 60°C has an impact on the behavior of the FKM seal. Thus, the increase in the pressure of CO2 causes a loss of the compression rigidity of the seal. It is higher in comparison with the HNBR. On the other hand, the conclusion between the two materials is not the same at 130°C, since there is a significant influence on the stiffness in compression and in particular on the response to 6MPa for the FKM seal. Note that to more accurately model the behavior of FKM under air at 130°C, for moderate strains (for a displacement greater than 1mm, Figure 12), it would be necessary to increase the number of parameters of the behavior law (Mooney-Rivlin or Polynomial Type).

Compression tests after CO2 desorption (HNBR & FKM)

The final step of the test protocol (see 2.4) was to perform a compression test after total CO2 desorption of the seal. The objective is to evaluate the impact of the pressure level applied at step D of the protocol on the final compression stiffness of the material.

Thus, a comparison between load-displacement and deviation-displacement responses is presented in Figure 13a and b respectively at 60 and 130°C. It can be seen on these figures that for the material HNBR, all the curves almost overlap. This indicates that imposing up to 6MPa CO2 pressure on an HNBR seal has no effect on its mechanical characteristics (rigidity and compressibility). The seal suffers no damage and recovers its initial stiffness (C10=0.75MPa at 60°C and 0.68MPa at 130°C) and compressibility (0.075MPa -1 at 60 and 130°C) at both temperatures. For the FKM seal it is also possible to measure a loss of rigidity generated by the history combining the mechanical loading and the gas pressure, this loss is of the same order of magnitude as that observed on the responses under pressure. The material retained the memory of the pressure phase (Figure 14a). On the other hand, the loss of rigidity is also observed at 130°C after an exposure to 4 and 6 MPa of CO2. Thanks to the optical access, local swellings on the seal were observed during decompression. This swelling is the first demonstration of damage inside the materials (Figure 14b), the second is the loss of rigidity measured after exposure. Although this loss of stiffness is small, one can imagine that a succession of sorption/desorption at these pressures would lead to the rapid degradation of the FKM seal.

Effects of 10GE reinforcements on the HNBR matrix

Compression tests on a HNBR-10GE seal at different CO2 pressures (2, 4 and 6MPa) and at two temperatures (60°C and 130°C) were carried out on four different O-rings. The load-displacement curves are shown in Figure 15a and Figure 15b respectively at 60°C and 130°C. The results of compression tests with return to zero pressure are presented on Figure 16a and Figure 16b.

For HNBR-10GE, it is noted in Figure 15a and Figure 15b the rigidity decreases progressively with the increase in CO2 pressure. However, in a healthy state, this material is more rigid at 60°C than at 130°C. Note that to more accurately model the behavior of HNBR-10GE under air at 60°C, for moderate deformations (for a displacement greater than 1mm, Figure 15a), it would be necessary to increase the number of parameters of the behavior law (Mooney-Rivlin or Polynomial Type). However, when subjected to a pressure of 6MPa of CO2, it gives almost the same response at both temperatures. Thus, the loss of rigidity is 46% and 22.5% respectively at 60 and 130°C. The compressibility coefficient of the HNBR-10GE is slightly lower than for the HNBR. That seems obvious from the charges. If the load-displacement curves of figures 15a and b show that the compressibility of healthy material (0MPa) is different at 60 and 130°C, they also show that the presence of CO2 leads to a decrease in this coefficient and tends towards the incompressibility of the material. At 60°C, it can be considered that there is a transition, for a given pressure value between 2 and 4MPa, for which the compressibility of the HNBR-10GE changes.

The load-displacement curves of figures 16a (60°C) and b (130°C) show that after desorption of CO2, only seals subjected to a CO2 pressure of 2MPa regain the initial behavior. For the other two configurations (4 and 6MPa), the loss of stiffness is significant (30% for 6MPa). However, the displacement curves in Figures 16a (60°C) and b (130°C) show that sorption and CO2 desorption have no effect on the compressibility of HNBR-10GE. The curve after desorption at 4MPa is not retained because it seems that a measurement problem appeared after 0.2mm of displacement of the plate.

Finally, the compressibility values obtained at 60°C, are relatively close (0.05 and 0.075MPa -1 ) not to be distinguished. In addition, we found here the value identified for the HNBR seal at 60°C, which is not the case at 130°C. It is therefore obvious that, compared to the responses under the same conditions (temperature and pressure) with the HNBR matrix, this reinforced material degrades under the effect of CO2 (pressure and / or desorption). Thus, the 10GE reinforcements render the matrix having been subjected to a certain CO2 pressure (between 0 and 2 MPa) and a CO2 desorption following the imposed speed.

Effects of 10GE reinforcements on the FKM matrix

Compression tests on a FKM-10GE seal at different CO2 pressures (2, 4 and 6MPa) and at two temperatures (60°C and 130°C) were carried out on four different O-rings. The load -displacement curves and deviation -displacement are shown in Figure 17a and Figure 17b respectively at 60°C and 130°C. The results of compression tests with return to zero pressure are presented on Figure 18a and Figure 18b.

For FKM-10GE, it is noted in Figure 17a and Figure 17b the rigidity decreases progressively with the increase in CO2 pressure as for other materials. However, in a healthy state, this material is more rigid at 60°C than at 130°C. It can be seen in Figure 17a that its behavior at 60°C is more sensitive to CO2 pressure than at 130°C (Figure 17b), because its rigidity decreases significantly with increasing CO2 pressure. Under a pressure of 6MPa in CO2, the decrease in rigidity is nearly 40% at 60°C compared to 24% at 130°C. In addition, at both temperatures, the coefficient of compressibility tends to increase with increasing pressure.

The compression tests after desorption of CO2 clearly show that this reinforced material (FKM-10GE) is strongly damaged. Indeed, its residual rigidity is reduced from the 2 MPa exposition at 60°C (Figure 18a) and the 4 MPa exposition at 130°C (Figure 18b). This damage can be generated by the load applied under pressure but it can be also initiated during the CO2 desorption, but in any case it depends on the initial pressure. In order to characterize the damage in-situ during CO2 desorption, the acquisition of the images was carried out during the decompression after the compression tests (examples: Figure 19, Figure 20, Figure 21, Figure 22, Figure 23 and Figure 24). Table 3 presents the results for each material of the damage observed during CO2 desorption from the different conditions. By analyzing the different images, two types of damage were found which appeared in certain configurations (pressure, temperature) in the seals during CO2 desorption.

The first type of damage is the formation of humps observed at the sample surface by internal gas inflation -the blisters (Figure 20, Figure 21, Figure 22 and Figure 23). They are no longer visible after the chamber is opened because according to the protocol there are at least 6 hours between the time of decompression and the opening of the chamber. These blisters are more or less large, for example Figure 22b shows small blisters for HNBR-10GE (60°C and 6MPa), while large local swellings are present in Figure 19b for FKM (60°C, 4MPa).Thus, after total desorption of the seal, the blisters disappear and therefore reversible. However, it is possible that one or more cracks may be present in the seal section where the blister appeared.

The second type of damage observed is at the moulding junction of the manufacturing process (parting line of the O-ring) where a seal cracking appears to occur in this area. This damage is irreversible and can be seen after the seal has been removed from the enclosure.

First, there is no visible damage to the HNBR seal. This confirms the mechanical results presented above, since whatever the sorption pressure, neither the rigidity nor the compressibility of the seal had been modified after desorption into CO2. For the FKM seal, no damage appears at the time of desorption at 2MPa, either at 60 and 130°C. On the other hand, at 4 and 6MPa (and for both temperatures), blisters appeared during desorption (Figure 21). These may be the cause of the loss of stiffness that was observed in these configurations during compression tests. However, it seems that this does not affect the compressibility coefficient. The HNBR-10GE and FKM-10GE seals suffered extensive damage. If, as for HNBR and FKM, no damage occurred after desorption from 2MPa at 60 and 130°C, damage appeared under the other conditions. For the HNBR-10GE, blisters appeared in the following configurations: at 60°C and 130°C, 4 and 6MPa. On the other hand, at 60°C and 6MPa, only small blisters (Figure 22b) appeared during decompression. For other conditions, swelling was much more important. At 6 MPa and 130°C the HNBR-10GE seal appears to open in its parting line as shown in the Figure 23. Finally, for the FKM-10GE, blisters appeared at 60°C during the desorption of 4 and 6MPa. At 130°C for these last two pressures, blisters and a crack were present (Figure 23 and Figure 24).

It may be thought that the nature of the reinforcements and / or the process of implementation is at the origin of this weakness. It is important to note that the less intense damages correspond to more small local swelling (blister). Such damage seems to recover after a long time after desorption.

Extensions

Figure 25a and Figure 25b present the values identified for each material of the coefficient C10 of the behavior law (equation 2) at 60 and 130°C respectively, as well as the corresponding trendlines. Figure 25 a and Figure 25b show that the coefficient C10 can be considered linearly dependent (trendline) on both the CO2 pressure for HNBR, FKM and the two filled materials 10GE. If the FKM is more rigid than the HNBR in the initial state (Air), it becomes less rigid than the HNBR after the 2MPa pressure. It is therefore much more affected by CO2 than HNBR. On the other hand, the fillers completely change the CO2 behavior of the two initial matrices (HNBR and FKM). Figure 26 shows the effect of CO2 pressure on the compressibility of materials. The higher the pressure is, the more the material tends towards incompressibility. Only HNBR stands out, because its compressibility does not seem to be affected at 60°C and very slightly at 130°C. For HNBR, as already mentioned, there is a low linear dependence at 130°C but none at 60°C.

The behavior law (eq. 2) can therefore be written as follows:

W=

CONCLUSIONS

First of all, it should be noted that for the four materials in the study, their behavior is more or less affected by the presence of CO2. Overall, the higher the pressure is, the lower the rigidity is, making the material more and more incompressible (because the coefficient of compressibility increases) or remains unchanged.

HNBR seems not to be affected by CO2 under the conditions of the study. The behavior after decompression and total desorption of CO2 is not modified, whatever the mechanical loading seen by the O-ring. Whatever the temperature (60 and 130°C), the compression behavior of the FKM seals is affected by the CO2 pressure. Thus, as the pressure increases, the stiffness decreases. The effect of CO2 desorption and therefore decompression on compression stiffness seems to have an effect on the FKM matrix. It was only after having had less than 6MPa of CO2 at 60°C and 4MPa of CO2 at 130°C that the material saw its compression rigidity slightly decrease. The compression behavior of HNBR-10GE is affected by CO2 only at 60°C. At the second temperature (130°C), as for HNBR, there is no effect of pressure on the behavior. On the other hand, after desorption, there is a non-negligible loss of rigidity above 4MPa at 60°C and 2MPa at 130°C. The material appears to have been damaged either by the CO2 pressure or during decompression.

The behavior of the FKM-10GE is affected by CO2 in compression (loss of rigidity). Thus, the effect of the pressure under 2MPa of CO2 and the decompression lead to damage to the FKM-10GE which results in a loss of compression stiffness after return at zero pressure. This FKM-10GE material appears to associate the weaknesses of the FKM matrix with those induced by the 10GE reinforcements in a matrix. Finally, among the four materials studied in these temperature and CO2 pressure ranges, HBNR is the most suitable material for these critical environments (temperature, CO2 pressure). Although the materials are different, these results support those obtained by Davies et al [START_REF] Davies | The mechanical properties of elastomers in high-pressure CO2[END_REF] on other elastomers, on the critical condition of 4MPa.

It is easy to highlight the effect of the matrix on one hand and the effect of the reinforcements on the other hand. Thus, it can be concluded that these reinforcements have an adverse effect on behavior. In the end, from a certain pressure there is a modification of the behavior of the materials, which should be studied further in order to firstly better understand mechanisms then to be able to translate them from a point of view behavior law. But the pressure criteria does not applied because the breaks are delayed, there is no longer any external mechanical pressure and the diffusion has already acted, so that the prediction of the rupture in this framework of gaseous conditions under temperature is an open issue.

Figure 1 .

 1 Figure 1. a) global view and (b) magnification of the pressure CO2 chamber of the experimental testing machine. (c) Specific U-shaped mounting for seal compression

Figure 4 .

 4 Figure 3. (a) Time of stabilization -(b) Decompression rate, Pressure (PCO 2 ) vs Time (t) [11] Reproducibility of tests -compression test at 60°C for HNBR-10GE (a) Load -Displacement curves, (b) Load -Deviation curves 3 FINITE ELEMENTS SIMULATIONS

Figure 5 :Figure 6 :

 56 Figure 5 : 3D modeling of the quarter of the seal -Compression test (a) Geometry -(b) Mesh -(c) 3D Modeling -The black dots correspond to the nodes where the displacements are extracted to calculate the deviation in the cases

Figure 7 .

 7 Figure 7. Simulation answers for the compression test of an elastomeric seal (a) Load -Displacement curves (b) Deviation -Displacement curves

Figure 8 .

 8 Figure 10a and b show that by measuring the three quantities (load, displacement and deviation) simultaneously during a compression test, there is only one solution of the parameter set (C10, D1).

Figure 11 .

 11 HNBR -Compression tests at (a) 60°C and (b) 130°C

  Figure 12. FKM -Compression tests at (a) 60°C and (b) 130°C

  Figure 13 HNBR -Compression tests under air at (a) 60°C and (b) 130°C after CO2 desorption (a) (b) Figure 14. FKM -Compression tests under air at (a) 60°C and (b) 130°C after CO2 desorption 14

Figure 16 .

 16 Figure 16. HNBR-10GE -Compression tests under air at (a) 60°C and (b) 130°C after CO2 desorption

  Figure 17. FKM-10GE -Compression tests at (a) 60°C and (b) 130°C (a) (b) Figure 18. FKM-10GE -Compression tests under air at (a) 60°C and (b) 130°C after CO2 desorption 4.6 Observations

  Figure 19 : FKM O-ring (after compression test, 60° and 4MPa) (a) Photo before decompression t=0s (b) Photo during decompression t=9min.

Figure 20 .

 20 Figure 20. FKM-10GE O-ring (after compression test, 130° and 4MPa) -(a) Photo before decompression t=0s -(b) Photo during decompression t=4min.

Figure 22 .

 22 Figure 22. HNBR-10GE O-ring (after compression test, 60° and 6MPa) -(a) Photo before decompression t=0s -(b) Photo during decompression t=5min.

Figure 24 .

 24 Figure 24. FKM-10GE O-ring [11] (after compression test, 130° and 6MPa) -(a) Photo before decompression t=0s -(b) Photo during decompression t=3min.

2 ( 5 )

 25 C10 [PCO 2 , T] (I1;¯ -3) + D1[PCO 2 , T] (J -1) (a) (b) Figure 25. C10 coefficient variation as a function of CO2 pressure and temperature for each material-(a) 60°C, (b) 130°C (a) (b) Figure 26. D1 coefficient as a function of CO2 pressure and temperature for each material-(a) 60°C and (b) 130°C

Table 1 . Composition of the HNBR and FKM assessed in the paper.

 1

	Materials	HNBR	FKM
		phr*	phr*
	NBR / FKM	100	100
	N-330 HAF carbon black	70	20
	Antioxydant agent	1.5	1.5
	Vulcanisation agent		8
	Vulcanizing agent	8	2.5
	Vulcanizing accelerator	2	3
		+Nanofiller	+Nanofiller
	* Parts per hundred rubber parts in weight.

Table 2 . Equivalent imposed pressure -partial pressure of CO2.

 2

	Imposed pressure of CO2 (MPa)	2	4	6
	Partial pressure of CO2 (real) (MPa)	1.899	3.899	5.899

Table 3 . Summary for each material of the damage observed during CO2 desorption from the different conditions.

 3

	Temperature (°C)		60			130
	CO2 Pressure (MPa)	2	4	6	2	4	6
	HNBR			No Damage
	FKM		Blisters	Blisters		Blisters	Blisters
	HNBR-10GE	No Damage	No Damage	Small Blisters	No Damage	Blisters	Blisters + Cracking
	FKM-10GE		Blisters	Blisters		Blisters + Cracking	Blisters + Cracking

ACKNOWLEDGEMENTS

This work was financially supported by the French CPER and European FEDER.