Identi ﬁ cation of swelling/shrinking coef ﬁ cients under CO 2 on an FKM O-ring – Comparison with HNBR and in ﬂ uence of reinforcements on the matrices

. A better understanding of elastomers ’ behavior during Rapid Gas Decompression (RGD) requires advanced knowledge of what is happening during gas sorption and desorption. This will offer to improve numerical simulation phenomena to consider a real environmental use of an O-ring, as for thermal applications. A previous experimental study developed testing protocols to investigate the performance of elastomeric O-rings. The non-contact measurement technique has been validated to identify the swelling and shrinking coef ﬁ cients during sorption and desorption of carbon dioxide (CO 2 ) from a Hydrogenated Nitrile Butadiene Rubber (HNBR) O-ring. The present work describes the effect of CO 2 pressures on Fluorocarbon rubber (FKM) seals behavior coupled with temperature. To evaluate the effect of reinforcing the HNBR and FKM matrices with nano ﬁ llers, experimental tests were carried out and compared with those of the two elastomers without ﬁ llers. The four materials ’ CO 2 sorption and desorption coef ﬁ cients are identi ﬁ ed, and their swelling upon decompression is measured. It appears that HNBR is the best candidate under the applied service conditions. On the other hand, the nano ﬁ llers introduced in the elastomers may cause some early damages under RGD conditions.


Introduction
Carbon dioxide is a natural gas that is frequently encountered in hydrocarbon environments.Relatively low carbon dioxide (CO 2 ) concentrations in hydrocarbon mixtures can cause significant swelling of the seal.In this context, seals or O-rings must resist and ensure tightness performance throughout their use, although they are prone to the so-called plasticization effect [1].More significantly, the effect of absorbed CO 2 during a Rapid Gas Decompression (RGD) [2][3][4] can be catastrophic, and damages depend on parameters, i.e., the decompression speed, the kind of polymer, the squeeze (Parker definition: The squeeze is a ratio of the amount of deformation applied to the seal expressed as a percentage of the free-state crosssectional thickness), their cure, and the particle reinforcement... Hydrogenated Nitrile Butadiene Rubber (HNBR) and Fluorocarbon rubber (FKM by ASTM standard) are well known for their resistance to RGD and, more generally, to chemical aggression and thermal degradation [5][6][7].Saturation conditions, especially in CO 2 , are known to alter the gas permeability due to plasticizing effects in almost all polymers, which is more pronounced for elastomer components [8][9][10][11][12][13].Besides, they are specially designed for resistance to RGD.Nonetheless, the lifetime sealing performance of polymer materials can be significantly affected when submitted to the gas environment for a long time coupled with high and fluctuating temperatures.
Recently, Haroonabadi et al. [14] stated that the thermal aging (7 days at 100 °C) of NBR vulcanizates depends strongly on crosslink density and mechanical properties.Thermal aging of nitrile rubber samples increased crosslink density and decreased tensile and tear strength, resulting in a decrease in RGD resistance.Thermal aging was studied by Alcock et al. [4] by looking at the effect of exposure to hot air at 150 °C during 12 weeks on the properties of the HNBR compounds with different degrees of carbon black content.The main results are that the permeability decreases following exposure to the hot air of the HNBR samples and that the HNBR samples with the highest carbon black content provide the best barriers to CO 2 .Chen et al. [15] investigated the CO 2 diffusivity, solubility, and RGD resistance of HNBR and FKM containing carbon nanotubes.These reinforcements lead to an increase in mechanical properties, reduce CO 2 diffusivity and solubility, and thus improve the RGD resistance of the reinforced elastomers.
Nevertheless, identifying useful diffuso-mechanical properties from O-rings is difficult.One of the first difficulties is related to the geometry of the sample, which is not well suited for classical mechanical tests.If many works exist in the literature, they generally concern materials made in bulk or plates [32,33].There is always a question about the properties of the O-rings, which are developed with an industrial process that can be slightly different from those of the laboratories.Finally, for identical processes, the polymerization parameters can change in function of the shape and impact the state of the material.Consequently, the present work is motivated by the lack of systematic investigations of CO 2 sorption and desorption through dedicated sealing materials and applications.The challenge is to characterize the behavior directly on the seal and avoid issues about the samples' microstructure compared to those generated by the industrial process.
The second challenge is to realize non-contact measurements in situ in a complex environment.The system couples mechanical tests under temperature and CO 2 pressure control with an in situ optical local deformation measurement that permits to follow the behavior of different elastomers (in the limit hypothesis of small strains).The experimental methodology was revisited to be adapted to seals geometries to be applied as widely as possible [32][33][34][35].
This article focuses the study on carbon black filler HNBR and FKM, with and without additional respectively reinforcement with nanofillers, to evaluate the matrices (HNBR, FKM) and the influence of these reinforcements on thermo-diffuso-mechanical characteristics.This work completes the study on the effect of gas on the mechanical behavior of the article [32].The coupling parameter diffusion swelling and diffusion are extracted from in-situ measurements during solubility-decompression tests.In Section 2, the material and the test bench are described.Then, the in-situ measurement technique is recalled; its complete description has already been described in [33].Finally, the test protocol [32] is also re-introduced.In Section 3, all the results of the CO 2 sorption and desorption tests at three pressures (2, 4, and 6 MPa) under isothermal conditions (60 and 130 °C) are presented.Comparisons of the results and comments are stated in Section 4. Finally, this work's conclusions and significant results are given in Section 5.

Materials and sample
Two elastomer types, a hydrogenated nitrile rubber (HNBR, Zetpol 2010, Zeon) and a fluoroelastomer type (FKM, FPO3730, Dyneon), were selected for these investigations.The compounds were produced with a nominal hardness of 80 and 90 Shore A, respectively, for HNBR and FKM.They were compounded as summarized in Table 1, using for both a base polymer that is 96% saturated with 36% acrylonitrile content for HBNR and 70% fluorine content for FKM.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 nanofiller.The chosen nanofiller was expanded graphite with the reference TIMCAL (Timrex).The chosen denomination is 10GE for each rubber.The rubber compound was obtained with a "classical" compounding operating mode for an elastomer.An internal mixer was used to incorporate the nanofiller.The nanofiller was introduced before carbon black.To improve the homogenization of the compound and avoid delamination defect after curing, for FKM reinforced with nanofiller, two specific processing assistants were used.A specific study was carried out to improve the incorporation of the nanofiller in the rubber matrix.Some difficulties were observed in the first samples, but a correction of the formulation allowed to enhance the quality of the finished part.Furthermore, using GE nanofillers, their better dispersion was observed with the liquid dispersion methodology.The curing process was optimized for each batch to obtain the optimal scorch time and the optimal cure time.Regarding the level of cross-linking density, a slight increase was observed when GE nanofillers were added to the formulation.Table 2 gives the main characteristics for each material, such as density, hardness, maximum stress, and elongation.The average thermal expansion coefficients given in Table 2 for each material were identified using the method described in [33].This is a DMA (Dynamic Mechanical Analyzer) test in compression.For HNBR, the incorporation of nanofiller reduces tensile strength and elongation at break.For FKM, the incorporation of nanofiller increases the loss factor for high strains.Note that FKM10GE has a lower density than FKM despite the incorporation of reinforcements.
On the other hand, its maximum elongation and thermal expansion coefficient are higher than FKM.This is contrary to what could be expected from the effect of the reinforcements and is not found for HNBR/HNBR10GE.The nominal dimensional characteristics of the O-rings are 50.17Â 5.33 mm, respectively, in terms of inner diameter and cross-section diameter.

Experimental device
An Instron 8802 servohydraulic fatigue machine was instrumented with a pressure and temperature regulated chamber, which allows mechanical testing in gaseous nitrogen (N 2 ), hydrogen (H 2 ), or carbon dioxide (CO 2 ) up to 40 MPa and 150 °C.The chamber volume is very limited (1.77L with a diameter of 150 mm and a length of 100 mm) to ensure the safety related to hydrogen.The device is  amply detailed in previous articles [32,33,[36][37][38].The particularity of this chamber is to have optical access with a central cylindrical sapphire window of 40 mm diameter at the front and at the back, which allows a complete view.
The O-ring is installed on a rigid U-shaped structure positioned horizontally [32,33] to perform the expansion measurement (thermal and gas).This support is linked to the fixed jaw of the traction machine.Placed on one of the plates, they are free to expand in all three directions, and to facilitate these kinematics; the lower plate is lubricated before the test.

The technique of dilatation measurement on a seal
The authors have already presented and validated the insitu strain measurement technique in previous papers [32,33].It is based on the follow-up of small marks placed on the seal to follow in situ the displacement in a thermoregulated gas chamber.For metrology, a system of noncontact extensometer is used [32,33].This method of markers has the advantage of being usable in extreme conditions (high temperatures, high pressures).Four Markers are placed on the O-rings' generatrix, corresponding to the O-ring's parting line projection.The technique consists of following the displacements of each barycenter of the four markers in the plane.To facilitate the analysis, the markers are distributed equidistantly with the following coding: M1 M2 M3 M4.This configuration is chosen to obtain a horizontal measurement of the elongations and gradient by taking them two by two [see [33] for more details].It is important to note that the camera must be centered between markers M2 and M3 to ensure good quality in the measurements.As markers M1 and M4 are the farthest away, the measurement between these two points incorporates the variabilities and is analyzed with a measurement between markers M2 and M3 closer together.The comparison gives us a first idea of the homogeneity of the deformation field.Two horizontal deviations (noted DevH) are calculated and noted DevH14 and DevH23 respectively in the following part of the paper, and they are defined as follow: See Equation (1) below where X Mi k ; X Mi k ; Y Mi 0 ; Y Mi 0 are the current coordinates and initial coordinates of the markers Mi.
A secant thermal expansion coefficient is used in the following, then the thermal strain is written as equation (2) following: where a th is the secant isotropic thermal expansion coefficient and T 0 is reference temperature.With this secant parameter, the transient phase cannot be represented correctly, as the temperature diffusion cannot be taken into account because of the gradients in the seal during the time.The thermal expansion calculated by equation ( 2) can be directly compared to the experimental responses.
Similarly, the secant CO 2 swelling (or shrinking) coefficient (a CO 2 ) is chosen.Finally, a similar expression of the equation ( 2) is proposed as follows: where e pressure À CO 2 is the strain due to CO 2 pressure.In the remainder of this paper, it is noted "pressure strain".The secant CO 2 swelling (or shrinking) coefficient (a CO 2 ) defined in equation ( 3), can be identified with the relation (4): However, temperature couplings can be more complex, and the CO 2 swelling or shrinkage coefficient can be influenced by temperature.Only two temperatures are considered in the test series, so at least the dependence will be regarded as linear.It is important to note that the CO 2 swelling and shrinkage coefficients (or CO 2 sorption and desorption coefficients) are identified similarly to the thermal expansion coefficient.Classically, the volume of an O-ring is calculated using the following simple formula: where r is the radius of the cross-section, and the median radius (average of inner and outer radii) is noted R. In this study, an O-ring with the dimensions 50.17Â 5.33 mm has been investigated.Consequently, parameters r and R have as values respectively 2.665 mm and 27.75 mm.When a volume change of the O-ring appears, radii increase or decrease, according to a thermal condition.More precisely, if it is noted Dr and DR the variation of the cross-section radius and the variation of the median radius respectively, due to a thermal increment, then under the assumption of isotropic volume expansion, these variations can be linked with experimental measure: In the end, the volume change (swelling-Sw) due to thermal or CO 2 pressure is determined with this equation: It is important to note that the mechanical deformation generated by the mechanical pressure is induced in this measurement.Using an additive law and calculating the mechanical part of the total strain, it turns out that under maximum pressure, the value corresponding to the compression of the joint is 0.02, 0.04, and 0.06% under 2, 4, and 6 MPa of pressure, respectively.These values are lower than the optical measurement accuracy, which depends on the quality of the markers and the optical settings.Taking this effect into account does not change the values of the coupling coefficients in this pressure range.

Protocol
An identical protocol [32] has been defined to characterize each material.The steps A to G, briefly described here, are applying: In the experiment, CO 2 is injected into the chamber with a pump.Initially, it is filled with air at atmospheric pressure.Then, three pressure values are imposed: 2, 4, and 6 MPa in the temperature-controlled chamber, two temperature levels are set.With this protocol, the real pressure (partial pressure Pp) in CO 2 is estimated by taking into account the CO 2 contained in the air with the one added to reach the imposed pressure of 2, 4, or 6 MPa.After all calculations, the corresponding partial pressure in CO 2 is 1.899, 3.899, and 5.899 MPa, respectively [32,33].To simplify the reading of the paper, only the mechanical pressures are shown.
The choice of CO 2 pressure and temperature values corresponds with NACE TM0192-98 [39] and NORSOK M710 [40], and under NACE TM0192-98 conditions, where the pressure is level is proposed to be 5.2 MPa under an ambient temperature.In the NORSOK M710 standard, the impact of temperature and pressure on the diffusion effect is apprehended by increasing the values to 130 °C and 6 MPa.It is important to note that the thermal resistance of the HNBR dictates the temperature limit.Besides, it should be pointed out that the machine imposes the decompression rate during these tests.The decompression rate cannot be controlled.However, the average depressurization rate is around 2 MPa.min À1 .

CO 2 sorption tests under isothermal conditions
Six different seals with material FKM, HNBR10GE, and FKM10GE under the conditions of temperature (60 and 130 °C) and CO 2 pressure (2, 4, and 6 MPa) are tested.In addition, HNBR seal, CO 2 pressurization tests have been performed before [33] and added in Figure 1 to analyze the results.All horizontal deviations are plotted in Figure 1 as a function of the time root during CO 2 pressurization, respectively, at 60 and 130 °C.The transient curves, i.e., before stabilization, have characteristic times identical to the diffusion and give the same response.Comparison of characteristic times shows that the more the pressure is important, the less the transient phase is prolonged.
After several tests, it turns out that the measurement errors on the deviations are in the order of 2 to 5% depending on the level of pressure applied.Despite the experimental complexity, the analysis of the images allows us to obtain measurements that are pretty precise since they will enable us to quantify the fluctuations in the expansion of the joint induced by the slight temperature oscillations imposed by the enclosure during the test.These fluctuations are caused by the regulation of the thermal system.They lead to a modulation in solubility coupled to thermal gradients.By comparing the responses of the two temperatures tested, the increase in the deviation during the pressurization phase under CO 2 reflects perfectly the effect of the temperature on the absorption phase and solubility.Looking at Figure 1, it is clear that the four materials do not behave in the same way when pressurized with CO 2 .The stability time and sorption coefficients in this phase are different and will be discussed more precisely in the following paragraph.

CO 2 desorption tests under isothermal conditions
Systematically on each solubility test at different pressures, measurements during the CO 2 desorption phase are carried out to evaluate the irreversible effects generated by the gas diffusion inside the rubber.The purpose is to know to what extent the behavior of the four seals (HNBR, FKM, HNBR10GE, and FKM10GE) has been modified or not by the CO 2 absorption phase at a given pressure.The deviations are also measured for each temperature during   the whole CO 2 depressurization phase until the return to ambient air and stabilization.Figure 2 shows the deflection responses at 60 and 130 °C, respectively, for each system.In the respective Tables 1A-4A (see Appendix), the values of the deviations measured after stabilization are given.The CO 2 shrinking coefficients were calculated from equation (4) for each test condition (initial temperature and pressure) for HNBR, FKM, HNBR10GE, and FKM10GE, respectively.In general, the curves in Figure 2 show a transient diffusion-type response within some cases substantial variations during the decompression phase.The responses are strongly dependent on material type, saturation pressure, and temperature, revealing a complex behavior during the RGD phase.The deviation does not return to zero, and the higher the saturation pressure, the greater the residual deviation.

Saturation time
Histograms of saturation time as a function of DP CO 2 at 60 °C (Fig. 3a) and 130 °C (Fig. 3b) show that these specific times are different, depending on the materials and the temperature.Thus, globally between 60 and 130 °C, the saturation time is strongly reduced (for 2 and 6 MPa respectively from 87.5% and from 5 to 75% depending on the material).At 60 °C, the effect of the imposed pressure is very marked; the saturation time decreases with the increase in pressure.On the other hand, this effect is weak at 130 °C.If at 60 °C and 2 MPa, the four materials have almost the same saturation time, for the other two pressures, it appears that HNBR saturates less quickly than FKM.This is also true at 130 °C and for all three pressures.Finally, while the reinforcements seem to delay saturation at 60 °C, this is not the case at 130 °C.

Swelling during CO 2 depressurization
A few seconds or minutes after depressurization, some seals inflated depending on the initial pressure and temperature conditions before returning almost to their initial situation.Table 3 shows the percentage of swelling, calculated according to equation (7), for each material at the initial (nominal) conditions.
HNBR seal swells during decompression at two temperatures only for the initial pressure of 6 MPa.At 60 °C, the HNBR seal shows a maximum deviation of about 7.69% after 16 minutes following the depressurization phase, which corresponds to 24.90% swelling.After 2 h 45, the O-ring returns to its initial position.After more than 22 h, the deviation stabilizes.At 130 °C, during the 6 MPa depressurization, the maximum deviation is 0.75% which corresponds to 2.27%, recorded 12 minutes after depressurization.
For the FKM seal, when depressurizing from 4 and 6 MPa at 60 and 130 °C, it starts to swell very quickly, even before the depressurization is completed.At 60 °C, after 123 s, the maximum deviation measurement is 12%, which corresponds to 40.50% of swelling.At 130 °C, the maximum average deviation is 2.27% or 6.96% swelling at 280 s.FKM seal returns to its initial geometry, before depressurization, at 60 and 130 °C at 409 and 326 s, respectively.As with HNBR, the swelling decreases with increasing temperature.On the other hand, the swelling at the time of depressurization to 6 MPa is much faster than for HNBR.Moreover, the time to recover its initial geometry is completely different between the two materials.For the desorption test in the HNBR10GE seal at 6 MPa and 130 °C, the data acquisition was lost quickly due to the swelling elastomer seal and, consequently, its damage (see Sect. 4.4).
For FKM10GE, during the test (4 MPa, 60 °C), it was impossible to measure the deviations due to a problem of data acquisition.In these conditions, the FKM10GE seal shows a maximum deviation of about 9.08% after less than 2 minutes of depressurization at 6 MPa, corresponding to 29.78% of swelling.Within 4 h following, the seal returned to its initial position; the deviation was stabilized.The stabilization time for a 2 MPa depressurization is about 16 h.At 130 °C, during the 6 MPa depressurization, the maximum deviation is 6.96%, which corresponds to 22.35% of swelling.

HNBR and FKM rubber matrices
The CO 2 compression tests carried out on HNBR, and FKM seals had been shown in articles [32,33].FKM appears more rigid than HNBR in the initial state (in the air), but it becomes less rigid than HNBR after a stage under 2 MPa CO 2 pressure.FKM is therefore much more affected by CO 2 than HNBR.
In Figure 4 are plotted the measurement of the "local deformation" or deviation (DevH) (Eq.( 1)) as a function of the variation of the pressure DP CO 2 (see Sect. 2.4) corresponding to each pressure (2, 4, and 6 MPa).For CO 2 sorption and desorption at 60 and 130 °C for (a) HNBR and (b) FKM, linear relationships are representative of the material RGD behavior in this range of pressure.For HNBR at 60 °C, the sorption deviations for 2, 4, and 6 MPa are respectively 1.0, 1.9, and 2.9% (Fig. 4a, Table 1A [see Appendix]).On the other hand, at 130 °C, they are about 40% lower than at 60 °C; the percent difference seems to increase with pressure or DP CO 2 of 2, 4, or 6 MPa.For FKM at 60 °C, the sorption deviations for 2, 4, and 6 MPa are respectively 1.9, 3.2, and 4.8% (Fig. 4b, Table 2A [see  Appendix]).On the other hand, at 130 °C, they are about 40-41% lower than at 60 °C, with a slight difference in percent increase with pressure.Desorption deviations for both HNBR and FKM show similar tendencies.We can notice that the linear regression calculation passes through zero (sorption: at 0 MPa, no swelling occurs, desorption: it is estimated that the CO 2 is completely released from the materials).For both temperatures (Fig. 4), the CO 2 swelling (or sorption) coefficients are independent of the pressure.For HNBR, the average values at 60 and 130 °C are 4.83 Â 10 À3 MPa À1 and 3.12 Â 10 À3 MPa À1 , respectively.For FKM, the average values at 60 and 130 °C are 8.13 Â 10 À3 MPa À1 and 5.05 Â 10 À3 MPa À1 , respectively.In Figure 5b, the average values between of the sorption and desorption coefficients are compared for the two temperatures for HNBR and HNBR10GE.The effect of the fillers is not negligible at 60 °C because the sorptiondesorption coefficient drops by about 22.82%.The nanofiller, therefore, prevents the HNBR matrix from swelling.Nanofiller improves barrier property by creating obstacles in the path of penetration of the gas.At 130 °C, the difference between the coefficients is only 4.08%.Thus, the nanofiller had a minimal influence at this temperature.Stiffening the HNBR matrix with nanofillers prevents gas from penetrating the polymer.This is especially true at 130 °C, as it is known that HNBR is more incompressible.
For HNBR10GE, blisters appeared in the following configurations: at 60 °C and 130 °C, 4 and 6 MPa [32].On the other hand, at 60 °C and 6 MPa, only small blisters (Fig. 6a) appeared during the decompression stage.For other conditions, the swelling was much more critical.At   6 MPa and 130 °C, the HNBR10GE seal seems to open in its parting line, as shown in Figure 6b.Thus, the damage is more significant at 130 °C.

Effects of 10GE reinforcements on FKM matrix
Figure 7a (Table 4A [see Appendix]) shows the deviations, during sorption and desorption phases, as a function of the pressure variation of CO 2 for the different pressures and both of the temperatures.As in the case of HNBR, a linear regression of the deviation as a function of the pressure is obtained for each configuration and allows to identify the coefficients of sorption and desorption.For FKM10GE at 60 °C, the sorption and desorption coefficients are 5.42 Â 10 À3 MPa À1 and 4.44 Â 10 À3 MPa À1 , respectively.
At 130 °C, these coefficients are, respectively, 3.44 Â 10 À3 MPa À1 and 3.51 Â 10 À3 MPa À1 identified for the pressure applied at 2 and 4 MPa since there is no measurement for desorption at 6 MPa.Between 60 and 130 °C, the sorption and desorption coefficients decrease by approximately 36 and 21%, respectively.As noted previously, the determination of the desorption coefficients at 60 and 130 °C, only from the two data at 2 and 4 MPa, is reasonable because these values are very close to those determined for the sorption on the range 2 at 6 MPa.The average value between sorption and desorption coefficients at both temperatures for both FKM and FKM10GE are compared in Figure 7b.The effect of nanofiller becomes substantial at 60 °C because the sorption-desorption coefficient drops by about 39.31%.At 130 °C, the difference narrows to 31.14%, which is much more important than the one observed on HNBR/ HNBR10GE.For this family of elastomers, the nanofiller significantly influences this temperature.Figures 8a-8d show, for different temperature and CO 2 pressure conditions, photos of the initial state and a state at a given time during decompression of the FKM10GE seal.If for both temperatures at 2 MPa, no damage was found during decompression and after observation of the seal at the end of the test, the same cannot be said for the other conditions.Thus at 60 °C, for the 4 and 6 MPa pressures (Figs.8a and 8c), bubbles (localized swellings) appeared around 3 and 4 min, after the start of decompression.For these same pressures at 130 °C (Figs.8b and 8d), in addition to the bubbles, ruptures were observed at the markers (on the Parting Line Projection of O-ring).

Sorption and desorption coefficients under CO 2
Interestingly, the CO 2 desorption shrinking coefficient is plotted as a function of the CO 2 sorption swelling coefficient in HNBR, FKM, HNBR10GE, and FKM10GE, as illustrated in Figure 9a, to evaluate the linear correlation.The error bars for each value are not shown on this graph because they are small, less than 5%.Thus, the size of each marker defines this error interval.The experimental points are very close to the    diagonal (dotted line; linear correlation coefficient is equal to 1.0), which shows that the expansion coefficients during the two phases of sorption and desorption are very comparable.At 130 °C, they are almost identical; a slight deviation is noted at 60 °C for FKM10GE.It seems reasonable to conclude that, for elastic behavior under small strains, the swelling coefficients can be considered undistinguishable to CO 2 sorption and desorption stages, and suggest that during these tests, the effect of the observed postdecompression damage does not affect these couplings.Without considering the accuracy of the measurements, the small deviations observed on FKM10GE and HNBR could be due to a residual deformation at the end of the protocol.
The correlations between the coefficients of thermal expansion and swelling under CO 2 for each material studied at 60 and 130 °C are illustrated in Figure 9b.It seems that a linear relationship exists between these coefficients for these two families of materials.However, this result must be confirmed for other materials to test its generality.

Conclusion
After presenting a new technique to measure the swelling of an elastomer during CO 2 sorption and desorption [33], the objective of this work was to validate this approach on other materials.Still, on O-rings to be as close as possible to reality (process), tests were carried out on another elastomer matrix (FKM) and the two reinforced matrices with nanofiller (10GE).The tests were carried out under two temperatures (60 and 130 °C) for different CO 2 sorption pressures (2, 4, and 6 MPa) and vacuum.All these tests first highlighted that this pressure range has almost no impact on the swelling ratio of rubber.The swelling ratio is almost constant with the pressure for each material.On the other hand, the values of swelling are highly dependent on temperature.
Under 6 MPa, the rapid decompression phase leads to a relatively high transient swelling that is the stage before the blistering.The maximum level of swelling during this decompressive phase is higher without a nanofiller in the elastomer.

Appendix:
Note: The letters S and D, in the second column of each table below, distinguish between the sorption (pressure) and desorption (decompression) phases, respectively.

8 E.
Figure 5a (Table3A[see Appendix]) illustrates the deviations as a function of the pressure variation of CO 2 for the different pressures and at the two temperatures for HNBR10GE.The deviations values obtained during sorption and desorption are presented.A linear regression of the deviation as a function of the pressure is made for each configuration and allows to identify the coefficients of sorption and desorption.The desorption coefficients at 60 and 130 °C are identified only from the measurements at 2 and 4 MPa.In the 6 MPa tests, the swelling of the seal at the start of decompression caused damage to the markers and thus the loss of optical measurement monitoring.For HNBR10GE at 60 °C, the sorption and desorption coefficients are 3.75 Â 10 À3 MPa À1 and 3.66 Â 10 À3 MPa À1 , respectively, in the stabilization phase.At 130 °C, these coefficients are respectively 2.93 Â 10 À3 MPa À1 and 3.01 Â 10 À3 MPa À1 .Between 60 and 130 °C, the sorption and desorption coefficients decrease by approximately 22 and 18%, respectively.Therefore, the determination of the

Fig. 4 .
Fig. 4. Deviation as a function of DP CO2 .Determination of CO 2 sorption and desorption coefficients at 60 and 130 °C for (a) HNBR and (b) FKM.

Fig. 5 .
Fig. 5. (a) Deviation as a function of DP CO2 .Determination of CO 2 sorption and desorption coefficients at 60 and 130 °C for HNBR10GE; (b) Comparison of the average desorption and desorption coefficients of HNBR and HNBR10GE at 60 and 130 °C.

Fig. 7 .
Fig. 7. (a) Deviation as a function of DP CO2 .Determination of CO 2 sorption and desorption coefficients at 60 and 130 °C for FKM10GE; (b) Comparison of the average desorption and desorption coefficients of FKM and FKM10GE at 60 and 130 °C.

Table 2 .
Properties in the initial state obtained on each mixing reference.
[33]rage coefficient measured between 20 and 100 °C according to the method described in[33].E. Lainé et al.: Matériaux & Techniques 110, 303 (2022) Table3A[see Appendix]) illustrates the deviations as a function of the pressure variation of CO 2 for the different pressures and at the two temperatures for HNBR10GE.The deviations values obtained during sorption and desorption are presented.A linear regression of the deviation as a function of the pressure is made for each configuration and allows to identify the coefficients of sorption and desorption.The desorption coefficients at 60 and 130 °C are identified only from the measurements at 2 and 4 MPa.In the 6 MPa tests, the swelling of the seal at the start of decompression caused damage to the markers and thus the loss of optical measurement monitoring.For HNBR10GE at 60 °C, the sorption and desorption coefficients are 3.75 Â 10 À3 MPa À1 and 3.66 Â 10 À3 MPa À1 , respectively, in the stabilization phase.At 130 °C, these coefficients are respectively 2.93 Â 10 À3 MPa À1 and 3.01 Â 10 À3 MPa À1 .Between 60 and 130 °C, the sorption and desorption coefficients decrease by approximately 22 and 18%, respectively.Therefore, the determination of the desorption coefficients at 60 and 130 °C only from 2 and 4 MPa is reasonable because these values are very close to those determined for the sorption on the range 2 at 6 MPa.

Table 2A :
FKM Deviations, CO 2 swelling, and CO 2 shrinking coefficients for the different CO 2 sorption and CO 2 desorption tests (2 temperatures and 3 CO 2 pressures).