Correlations between H2 Permeation and Physical/Mechanical Properties in Ethylene Propylene Diene Monomer Polymers Blended with Carbon Black and Silica Fillers

H2 permeation in peroxide-crosslinked EPDM blended with carbon black (CB) and silica fillers was studied at pressures ranging from 1.2 MPa to 90 MPa via the volumetric analysis technique. H2 uptake in the CB-filled EPDM revealed dual-sorption behaviors via Henry’s law and the Langmuir model, which were attributed to H2 absorption by the polymer chains and H2 adsorption at the filler interfaces, respectively. Additionally, single-sorption mechanisms were observed for neat EPDM and silica-blended EPDM according to Henry’s law, indicating H2 absorption by the polymer chain. The linear decreases in the diffusivity with filler content for the silica-blended EPDMs were attributed to increases in the diffusion paths caused by the filler. Exponential decreases in the diffusivity with increasing filler content and in the permeation with the physical/mechanical properties for CB-filled EPDMs were caused by decreases in the fractional free volume due to increased densities for the EPDM composites. Moreover, good filler-dependent correlations between permeability and density, hardness, and tensile strength were demonstrated for EPDMs used as sealing materials for O-rings. From the resulting equation, we predicted the permeation value without further measurements. Thus, we can select EPDM candidates satisfying the permeation guidelines used in hydrogen infrastructure for the future hydrogen economy.


Introduction
The infrastructure used for accelerating the hydrogen economy causes an increase in the number of materials or components coming into contact with high-pressure hydrogen. In particular, polymers are widely used in sealing components for hydrogen environments and are directly exposed to high-pressure H 2 in service environments [1][2][3][4]. O-ring seals, gaskets, control valves, connectors, and nonmetallic pipelines are the primary applications for the polymer materials [1,[5][6][7][8][9].
H 2 quickly penetrates into the polymer membrane up to its equilibrium level. When the high pressure is released into the atmosphere, the rapid depressurization causes supersaturation of the membrane [10,11]. When the gas is released faster than it diffuses, it is transported out of the polymer and exhibits bubble nucleation, which causes irreversible damage to the polymer, such as microcracking, swelling, fracture, and embrittlement. This ultimately causes sealing failure in the O-rings used in hydrogen refueling stations (HRSs) and hydrogen fuel cell vehicles (HFCVs) and results in gas leakage [10].
In addition, leakage due to damage of the seal and H 2 gas leakage through the O-ring under high pressure can be generated in two different situations [11]: one involves gap leakage between the seal and the groove due to insufficient contact, and the other involves gas

Transmission Electron Microscopy
The method and sample preparation used in obtaining transmission electron microscopy (TEM) images are described elsewhere [20]. Figure 1a-d show the TEM micrographs of EPDM HAF20 and SRF20. The homogenous distribution of CB as a form of black or gray spherical shape in the rubber matrix is shown in Figure 1a,b. As shown in Figure 1c,d, large agglomerates (indicated with yellow dotted circles) of SRF CB were observed in the EPDM SRF20 composite. The shapes and distributions of the CB filler were identified from the TEM image showing the CB filler particles in the rubber matrix. EPDM HAF20 and SRF20 had spherical shapes with the corresponding polarized particle sizes. In particular, the particles were distributed as partially dense aggregates, as shown in Figure 1c,d, indicated with blue dotted circles.
filler surface areas and strong interactions between the polymer and the filler, thus affecting the permeation properties. In the HAF CB-filled EPDM polymer crosslinked with peroxide, the degree of filler dispersion was measured according to the testing method (ASTM D7723 and ISO 11345). The measured dispersion degrees for the EPDM rubber composites blended with HAF CB and SRF CB fillers are shown in Table 1. The dispersions for EPDM HAF20 and SRF20 were found to have low dispersion degrees of 88∼90%. However, the dispersions for EPDM HAF40, HAF60, SRF40, and SRF60 were found to exhibit dispersion degrees of 97∼99%, which indicated well-dispersed fillers in the rubber network. To date, we have not found an appreciable correlation between permeation and dispersion degree for EPDM composites.  Well-dispersed fillers with small particle sizes, such as the HAF CB filler, cause large filler surface areas and strong interactions between the polymer and the filler, thus affecting the permeation properties. In the HAF CB-filled EPDM polymer crosslinked with peroxide, the degree of filler dispersion was measured according to the testing method (ASTM D7723 and ISO 11345). The measured dispersion degrees for the EPDM rubber composites blended with HAF CB and SRF CB fillers are shown in Table 1. The dispersions for EPDM HAF20 and SRF20 were found to have low dispersion degrees of 88∼90%. However, the dispersions for EPDM HAF40, HAF60, SRF40, and SRF60 were found to exhibit dispersion degrees of 97∼99%, which indicated well-dispersed fillers in the rubber network. To date, we have not found an appreciable correlation between permeation and dispersion degree for EPDM composites.

Measurement Method and Diffusion Analysis
For the volumetric measurements, we utilized graduated cylinders in which the H 2 emitted by the specimen was collected and measured. After exposure in the high-pressure chamber and subsequent decompression, the samples were loaded into their corresponding gas-cell spaces at the tops of the graduated cylinders. Details of the method are described elsewhere [19,20].
The number of moles (∆n) of H 2 released into the graduated cylinder was converted to a concentration [C(t)] per mass for the H 2 released from the rubber sample: where m H2 [g/mol] is the H 2 molar mass, equal to 2.016 g/mol, and m sample is the sample mass.
Assuming that H 2 desorption is a Fickian diffusion process, the concentration C E (t) of the emitted H 2 was computed as [34,35] where β n is the root of the zero-order Bessel function J 0 (β n ) with β 1 = 2.40483, β 2 = 5.52008, β 3 = 8.65373, . . . , β 50 = 156.295. Equation (2) is an infinite series expansion with two summations. It gives the solution to Fick's second diffusion equation for a cylindrical sample. Here, C E = 0 at t = 0 and C E = C ∞ at t = ∞. C ∞ is the saturated H 2 concentration at infinite time, i.e., the H 2 uptake. D is the diffusion coefficient. ρ and l are the radius and thickness of the cylindrical specimen, respectively. The D and C ∞ values for the EPDM composites were determined with a diffusion analysis program. The application example for the diffusion analysis program and the procedure are described in the literature [20].

Filler Effects on H 2 Uptake
The time-dependent H 2 emission after decompression from pressures ranging from 1.2 to 90 MPa at 23 • C was measured for ten EPDM composites, including neat EPDM and samples blended with CB or silica. Figure 2 shows plots of the H 2 uptake versus elapsed time for the 10 EPDM rubbers after hydrogen exposure at 8.6 MPa. The primary trend showed greater H 2 uptake by the CB-filled EPDM composites compared with neat EPDM. This was attributed to H 2 adsorption resulting from the presence of the CB filler. The H 2 content in the CB-filled EPDM composites increased with increasing CB content. The filler effects on the SRF CB-filled EPDM composites were similar to those of the HAF CB-filled EPDM samples. The minute increase seen in H 2 uptake for the HAF CB-filled EPDM might have been caused by the larger specific surface area of the HAF CB filler relative to that of the SRF CB filler. In the silica-filled EPDM composites, the H 2 uptakes seen with silica filler content were not detectably different from that seen for the neat EPDM polymer. This implied that H 2 was not adsorbed onto the silica surface, as it was with the CB filler. filler content were not detectably different from that seen for the neat EPDM polymer. This implied that H2 was not adsorbed onto the silica surface, as it was with the CB filler. We measured the H2 emission contents versus exposure pressures for the nine EPDM composites blended with fillers and the neat EPDM. Figure 3 shows representative H2 uptake data for the four EPDM composites as a function of pressure. Figure 3a-d show the pressure-dependent H2 uptake data for neat EPDM, EPDM composites with the silica filler, EPDM HAF20, and EPDM SRF20, respectively. We measured the H 2 emission contents versus exposure pressures for the nine EPDM composites blended with fillers and the neat EPDM. Figure 3 shows representative H 2 uptake data for the four EPDM composites as a function of pressure. Figure 3a-d show the pressure-dependent H 2 uptake data for neat EPDM, EPDM composites with the silica filler, EPDM HAF20, and EPDM SRF20, respectively.
The H 2 uptakes (C ∞ ) for neat EPDM ( Figure 3a) and EPDM S20 ( Figure 3b) were proportional to the applied pressure up to 90 MPa and thereby obeyed Henry's law [36,37]. This behavior was responsible for the absorption of H 2 into the polymer matrix. However, as shown in Figure 3c,d, the hydrogen uptake for EPDM HAF20 and SRF20 deviated from Henry's law at pressures above 15 MPa; this was caused by H 2 adsorbed onto the surface of the CB filler. Thus, dual sorption was observed for all CB-blended EPDM composites. The dual-mode sorption behavior for the pressure range up to 90 MPa is expressed as follows: where C ∞ is total H 2 uptake. The first term indicates Henry's law, with a Henry's law coefficient of k. The second term indicates the Langmuir model [38,39], where a is the  The H2 uptakes (C∞) for neat EPDM ( Figure 3a) and EPDM S20 ( Figure 3b) were proportional to the applied pressure up to 90 MPa and thereby obeyed Henry's law [36,37]. This behavior was responsible for the absorption of H2 into the polymer matrix. However, as shown in Figure 3c, d, the hydrogen uptake for EPDM HAF20 and SRF20 deviated from Henry's law at pressures above 15 MPa; this was caused by H2 adsorbed onto the surface of the CB filler. Thus, dual sorption was observed for all CB-blended EPDM composites. The dual-mode sorption behavior for the pressure range up to 90 MPa is expressed as follows: where is total H2 uptake. The first term indicates Henry's law, with a Henry's law coefficient of k. The second term indicates the Langmuir model [38,39], where is the maximum adsorption quantity (or capacity parameter) and is the adsorption equilibrium constant (or Langmuir hole affinity parameter). The fitting results for H2 uptake according to Equation (3) are summarized in Table 2.  The Langmuir contribution implied that the quantity of H 2 adsorbed increases with increasing filler content, as shown in Figure 4. The deviations at 60 phr CB in the filled EPDM composites indicated an abrupt increase in H 2 adsorption, which may be attributed to the formation of the H 2 channels that leads to percolation effects with many fillers.

EPDM SRF20
19. 24.5 0 0 0.99 0 * The Langmuir contribution was obtained from the total hydrogen uptake, which was the sum of the Henry and Langmuir uptake contributions.
The Langmuir contribution implied that the quantity of H2 adsorbed increases with increasing filler content, as shown in Figure 4. The deviations at 60 phr CB in the filled EPDM composites indicated an abrupt increase in H2 adsorption, which may be attributed to the formation of the H2 channels that leads to percolation effects with many fillers. Langmuir sorption is applied to porous solids in a gas-polymer system. The Langmuir sorption sites in a system are the holes or voids that arise from the nonequilibrium states of glassy polymers. A gas sorption isotherm for a glassy polymer occurs below the glass transition temperature (Tg) and is dependent on the pressure. This behavior is characteristic of dual-mode sorption composed of Henry's law absorption occurring in an equilibrium state and Langmuir adsorption occurring in a nonequilibrium state [40]. The nonequilibrium state is associated with the extra free volumes or unrelaxed free volumes of glassy polymers [41]. The validity of the dual-mode assumption was confirmed [42]. Therefore, the dual-sorption model is an effective tool for understanding sorption by glassy polymers.
It was previously demonstrated for HAF CB-blended NBR [43] that investigations of the rubbery polymer above Tg revealed dual-sorption behavior due to the presence of a porous HAF CB filler. H2 molecules could be absorbed by the rubbery NBR and simultaneously adsorbed by the porous filler, leading to dual-mode sorption similar to that seen for the glassy phase of the polymer. Thus, the porous HAF CB filler in the NBR composite Langmuir sorption is applied to porous solids in a gas-polymer system. The Langmuir sorption sites in a system are the holes or voids that arise from the nonequilibrium states of glassy polymers. A gas sorption isotherm for a glassy polymer occurs below the glass transition temperature (T g ) and is dependent on the pressure. This behavior is characteristic of dual-mode sorption composed of Henry's law absorption occurring in an equilibrium state and Langmuir adsorption occurring in a nonequilibrium state [40]. The nonequilibrium state is associated with the extra free volumes or unrelaxed free volumes of glassy polymers [41]. The validity of the dual-mode assumption was confirmed [42]. Therefore, the dual-sorption model is an effective tool for understanding sorption by glassy polymers.
It was previously demonstrated for HAF CB-blended NBR [43] that investigations of the rubbery polymer above T g revealed dual-sorption behavior due to the presence of a porous HAF CB filler. H 2 molecules could be absorbed by the rubbery NBR and simultaneously adsorbed by the porous filler, leading to dual-mode sorption similar to that seen for the glassy phase of the polymer. Thus, the porous HAF CB filler in the NBR composite indicated a substantial void structure in the glass phase polymer. The solubility of hydrogen in the HAF CB-filled EPDM also indicated dual-sorption behavior, as shown in Figure 3c,d.

Filler Effects on H 2 Diffusion
The hydrogen diffusivities of the neat EPDM and nine filled EPDM composites made with peroxide crosslinking were measured as a function of the applied pressure at 23 • C. The H 2 diffusivities in neat EPDM and the EPDM composites containing fillers were apparently dependent on the exposed pressure. The pressure dependence of the diffusivity may be associated with the mean free path for hydrogen, the tortuosity caused by the impermeable filler in the rubber network, the interactions between filler and rubber, and H 2 -attractive adsorption onto the CB filler surface.
The representative pressure-dependent diffusion shown for EPDM HAF20 and SRF20 in Figure 5a,b, respectively, can be divided into two contributions at the peaks marked by arrows. The contributions included Knudsen diffusion at low pressure and bulk diffusion at high pressure. The pressure-dependent diffusivity was explained as a result of Knudsen diffusion below 7~10 MPa and bulk diffusion above those pressures, which was analyzed with fractal theory in other studies [44,45]. Knudsen diffusion gradually increases with increasing pressure. Knudsen diffusion at low pressures normally occurs with large mean free paths for the diffusing gas molecules or low gas densities. The Knudsen diffusivity (D K, pm ) in a porous medium can be written as [46] where φ is the pressure-dependent porosity, τ is the tortuosity caused by adding the filler, d c is the pore diameter, and υ is the average velocity of the gas molecules.  MPa, the fillers extended the diffusion path due to the increased tortuosity provided by the impermeable filler, resulting in a decrease in the diffusivity. The diffusivity in the silica blended EPDM was negatively and linearly related to the filler content (i.e., filler content)), whereas the diffusivity in the CB-blended EPDM decreased in the form of a single exponential decay line (i.e., exp filler content . At pressures up to 8.6 MPa, the decrease in the diffusivity of the CB-blended EPDM was larger than that of the silica-blended EPDM, as expected; this was possibly related to additional filler-polymer interactions or attractive H2 adsorption. In other words, as shown in Figure 6a, b, the diffusivity for the silica-filled EPDM was responsible for the increased tortuosity of the diffusion path introduced by the filler. However, the diffusivity of the CB-filled EPDM was attributed to polymer-filler interactions, H2 adsorption, and increased tortuosity. From the linear and exponential relationships seen at pressures up to 8.6 MPa, we predicted the diffusivities for different filler contents in the EPDM composites without any further diffusion measure- The bulk diffusion coefficients for neat EPDM (Figure 5c), EPDM S20 (Figure 5d), and CB-filled EPDM composites above a critical pressure of 7 MPa~10 MPa were found to be inversely proportional to pressure, which was related to the mean free path (λ) for H 2 molecules. Bulk diffusion predominated for λ values less than the pore diameter and was found for large pores or with high-pressure gas diffusion. The bulk diffusion coefficient (D B ) can be written as [47] where µ is the viscosity of the diffusing molecule in units of kg·m/s, and P is the applied pressure. The experimental data for the diffusivity were fitted with Equations (4) and (5), as indicated by the blue and black lines, respectively, in Figure 5. In the region of Knudsen diffusion, the diffusivity was proportional to the pressure; this was caused by an increase in the porosity in Equation (4) due to the increased pressure. The decrease in the bulk diffusion coefficient in Equation (5) was caused by decreases in λ with increasing pressure. Figure 6a-c show the plots of diffusivity versus filler content for the three different pressures 1.2 MPa, 8.6 MPa, and 90 MPa, respectively. At pressures of 1.2 MPa and 8.6 MPa, the fillers extended the diffusion path due to the increased tortuosity provided by the impermeable filler, resulting in a decrease in the diffusivity. The diffusivity in the silica blended EPDM was negatively and linearly related to the filler content (i.e., (−filler content)), whereas the diffusivity in the CB-blended EPDM decreased in the form of a single exponential decay line (i.e., exp(−filler content)). At pressures up to 8.6 MPa, the decrease in the diffusivity of the CB-blended EPDM was larger than that of the silica-blended EPDM, as expected; this was possibly related to additional filler-polymer interactions or attractive H 2 adsorption. In other words, as shown in Figure 6a,b, the diffusivity for the silica-filled EPDM was responsible for the increased tortuosity of the diffusion path introduced by the filler. However, the diffusivity of the CB-filled EPDM was attributed to polymer-filler interactions, H 2 adsorption, and increased tortuosity. From the linear and exponential relationships seen at pressures up to 8.6 MPa, we predicted the diffusivities for different filler contents in the EPDM composites without any further diffusion measurements. However, with increasing pressures up to 90 MPa, the effect of filler on diffusion was reduced. Thus, the diffusivities for all specimens were almost constant and converged at approximately 1.5 × 10 −10 m 2 /s. In the pressure region of bulk diffusion, the decrease in mean free path of H2 molecules at 90 MPa could be a predominant factor in diffusivity behavior rather than filler content or filler species. However, with increasing pressures up to 90 MPa, the effect of filler on diffusion was reduced. Thus, the diffusivities for all specimens were almost constant and converged at approximately 1.5 × 10 −10 m 2 /s. In the pressure region of bulk diffusion, the decrease in mean free path of H 2 molecules at 90 MPa could be a predominant factor in diffusivity behavior rather than filler content or filler species. Figure 7a depicts the density variations versus filler content for twenty EPDM composites crosslinked with sulfur and peroxide. The density increased linearly with increasing filler content and exhibited a squared correlation coefficient R 2 = 0.94. Similarly, the linear correlation between hardness and density is represented in Figure 7b with R 2 = 0.90. Although divergence (R 2 = 0.76) with the data occurred, the linear correlation between tensile strength and density is also shown in Figure 7c. These three relationships indicated that their properties are linearly inter-correlated with each other. From the three linear relationships, the physical and mechanical properties of EPDM composites crosslinked with sulfur and peroxide can be easily predicted from the contents of either CB or silica fillers. The permeability P was obtained by multiplying the solubility S by the diffusion coefficient D, i.e., P = SD. The filler-dependent permeability characteristics observed in previous work were very similar to those for diffusivity at 1.2 MPa and 8.6 MPa (Figure 6a,  b), implying that permeability was mainly affected by the diffusivity rather than the solubility. Figure 8a-c show the permeability variations with density, hardness, and tensile The permeability P was obtained by multiplying the solubility S by the diffusion coefficient D, i.e., P = SD. The filler-dependent permeability characteristics observed in previous work were very similar to those for diffusivity at 1.2 MPa and 8.6 MPa (Figure 6a,b), implying that permeability was mainly affected by the diffusivity rather than the solubility. Figure 8a-c show the permeability variations with density, hardness, and tensile strength, respectively, for neat EPDM and the blended EPDM polymer composites crosslinked with sulfur and peroxide. As shown in Figure 8a, the negative linear relationship (P = −density) between permeability and density for silica-filled EPDM composites indicated a smooth decrease in permeation with increasing density and without any other interactions or the introduction of additional parameters. However, the effect of density on the permeability for CBblended EPDM composites decreased exponentially with filler content, i.e., P = ~exp(−density). The magnitudes of the effects for CB-blended EPDM composites were larger than those for the silica-blended EPDM composites. This indicated the operation of an additional effect, i.e., strong polymer-filler interactions or attractive adsorption of H2 at the CB interface for CB-blended EPDM composites was included as a cause of the permeability behavior, as already shown by the pressure-dependent diffusivity seen at 1.2 MP and 8.6 MPa.

Correlations of Permeation with Physical/Mechanical Properties
The plots of permeability versus hardness in Figure 8b and of permeability versus tensile strength in Figure 8c were very similar in form to the plots for permeability versus density in Figure 8a. Three trends may have originated from the same source. The relationships of permeation with physical and mechanical properties provide an opportunity to predict the H2 permeation characteristics of compounded EPDM candidates used in As shown in Figure 8a, the negative linear relationship (P = −density) between permeability and density for silica-filled EPDM composites indicated a smooth decrease in permeation with increasing density and without any other interactions or the introduction of additional parameters. However, the effect of density on the permeability for CB-blended EPDM composites decreased exponentially with filler content, i.e., P =~exp(−density). The magnitudes of the effects for CB-blended EPDM composites were larger than those for the silica-blended EPDM composites. This indicated the operation of an additional effect, i.e., strong polymer-filler interactions or attractive adsorption of H 2 at the CB interface for CB-blended EPDM composites was included as a cause of the permeability behavior, as already shown by the pressure-dependent diffusivity seen at 1.2 MP and 8.6 MPa.
The plots of permeability versus hardness in Figure 8b and of permeability versus tensile strength in Figure 8c were very similar in form to the plots for permeability versus density in Figure 8a. Three trends may have originated from the same source. The relationships of permeation with physical and mechanical properties provide an opportunity to predict the H 2 permeation characteristics of compounded EPDM candidates used in high-pressure seals at HRSs and HFCVs.
Moreover, to interpret the correlations between permeability and physical/mechanical properties for CB-filled EPDM composites, we must introduce the concept of free volume. This is defined as the volume of the total mass that is not occupied by the polymer chains themselves; hence, diffusing molecules could be located there. This could be due to the gaps or pores present between polymer chains. The physical/chemical parameters and density of the polymer could significantly influence the free volume of the polymer membrane.
According to free volume theory [22,26,48,49], the diffusivity and permeability are written as the fractional free volume (FFV = V f /V SP ): with specific free volume (V f ). V SP (cm 3 /g) is the specific volume of a polymer, equal to 1/ρ. ρ is the polymer density (g/cm 3 ), and a i , b i , c i , and d i are the parameters of the given penetrant/polymer couple. In Equations (6) and (7), the diffusivity and permeability decrease exponentially with the decreasing free volume of the polymer, which negatively affects the permeation parameters. The exponential decrease seen for the diffusivity with increasing CB filler content, as shown in Figure 6a,b, is identical to the decreases in permeability resulting from physical/mechanical properties, as shown in Figure 8a-c. According to Equations (6) and (7), the exponential behaviors imply that the CB filler content caused increases in the density, hardness, and tensile strength in the EPDM composite, leading to a decrease in the FFV, i.e., 1/FFV~density. Thus, the exponential decreases in diffusivity and permeation with density observed for the blended EPDM composites are associated with the decrease in free volume caused by adding the CB filler. Table 3 shows the formulations of the EPDM composites with CB and silica fillers, including one neat EPDM without filler, six specimens with CB fillers, and three specimens with silica fillers. The CB filler has two types: a high-abrasion furnace (HAF) CB and a semi-reinforcing furnace (SRF) CB, with particle sizes of 32 and 65 nm, respectively, and specific surface areas of 76 and 30 m 2 /g, respectively. The specific surface area of the silica used was 175 m 2 /g. The EPDM composites filled with fillers were designated EPDM HAFa, EPDM SRFb, and EPDM Sc, where a, b, and c denote the parts per hundred for the contents in the rubber (phr) of HAF, SRF, and silica, respectively. For example, EPDM HAF20 indicates EPDM filled with HAF CB at 20 phr. DCP (dicumyl peroxide) indicates that 1.5 phr was used as the crosslinking content. The EPDM polymers were compounded as described in the literature [50].

Exposure to H 2 Gas
The conditions for exposure and purging in the high-pressure chamber used in this work have been described elsewhere [20]. Cylindrical polymer specimens with diameters of 13 mm and thicknesses of~3 mm were exposed to H 2 gas for more than 24 h at pressures ranging from 1.2 to 90 MPa. After exposure to the high-pressure H 2 , the chamber valve was opened to emit the H 2 gas.

Conclusions
We investigated the H 2 permeation of peroxide-crosslinked EPDM composites using a volumetric analysis technique and a dedicated diffusion analysis program. The results are summarized below.
The pressure-dependent hydrogen uptake for pristine EPDM and silica-filled EPDM composites showed a single-sorption mechanism obeying Henry's law for absorption in a polymer network. The contribution from the silica filler was negligible. However, the hydrogen uptake for the CB-filled EPDM composites presented a dual-sorption mechanism obeying Henry's law and Langmuir's law. The hydrogen uptake for the CB-blended EPDM was contributed by absorption in the polymer network and by adsorption in the CB filler.
The diffusivity for CB-filled EPDM composites consisted of contributions from Knudsen diffusion and bulk diffusion. The increases in the Knudsen diffusion coefficient observed below ∼10 MPa were attributed to an increase in the porosity with pressure. The decrease in the bulk diffusivity above 10 MPa was related to a decrease in the mean free path with increasing pressure. However, the only bulk diffusivities observed for neat EPDM and EPDM S20 were inversely proportional to the applied pressure.
The diffusivities for all of the EPDMs investigated were dependent on the filler type. The decrease in diffusivity for the silica-filled EPDM compared with that for pristine EPDM below 8.6 MPa was responsible for the increase in the H 2 path tortuosity caused by introducing the filler. However, the decreases in diffusivity for the CB-filled EPDM below 8.6 MPa were caused by the polymer-filler interactions, H 2 adsorption, and tortuosity resulting from the filler.
The silica-filled EPDMs showed negative linear correlations between diffusion and filler content, whereas the CB-filled EPDMs revealed single exponential relationships between diffusion and filler content. These relationships were very similar to the correlations between permeability and the density, hardness, and tensile strength of the EPDM composites. From these relationships, we could predict the hydrogen permeabilities of EPDM composites proposed for use as seal materials under high pressure in hydrogen infrastructure.
The single exponential decreases in diffusivity with increasing filler content and in permeation with the physical/mechanical properties for CB-filled EPDMs are responsible for the decreases in fractional free volume; these were caused by increases in the densities of the EPDM composites investigated herein, regardless of the crosslinking agents (sulfur or peroxide).