H2 Uptake and Diffusion Characteristics in Sulfur-Crosslinked Ethylene Propylene Diene Monomer Polymer Composites with Carbon Black and Silica Fillers after High-Pressure Hydrogen Exposure Reaching 90 MPa

We investigated the influence of two fillers—CB (carbon black) and silica—on the H2 permeation of EPDM polymers crosslinked with sulfur in the pressure ranges 1.2–90 MPa. H2 uptake in the CB-blended EPDM revealed dual sorption (Henry’s law and Langmuir model) when exposed to pressure. This phenomenon indicates that H2 uptake is determined by the polymer chain and filler-surface absorption characteristics. Moreover, single sorption characteristics for neat and silica-blended EPDM specimens obey Henry’s law, indicating that H2 uptake is dominated by polymer chain absorption. The pressure-dependent diffusivity for the CB-filled EPDM is explained by Knudsen and bulk diffusion, divided at the critical pressure region. The neat and silica-blended EPDM specimens revealed that bulk diffusion behaviors decrease with decreasing pressure. The H2 diffusivities in CB-filled EPDM composites decrease because the impermeable filler increases the tortuosity in the polymer and causes filler–polymer interactions; the linear decrease in diffusivity in silica-blended EPDM was attributed to an increase in the tortuosity. Good correlations of permeability with density and tensile strength were observed. From the investigated relationships, it is possible to select EPDM candidates with the lowest H2-permeation properties as seal materials to prevent gas leakage under high pressure in H2-refueling stations.


Introduction
The fundamental properties of rubbery polymers can be improved by blending fillers. Fillers in polymer composites achieve multiple purposes, the most important including reinforcement, improvement in processing, diffusing molecule impermeability, an increase in oil resistance, and a reduction in material cost [1][2][3][4][5][6][7]. The rubber industry uses a wide range of fillers because of their merits in rubber compounding. In particular, carbon black (CB) filler compounding with rubber enhances the mechanical properties of rubber composites, such as hardness, tear strength, tensile strength, modulus, and abrasive strength [8][9][10]. The size and surface area of CB filler particles are important factors affecting reinforcements in rubbers [11]. Furthermore, the reinforcement originates from filler-filler and rubber-filler interactions.
Among nonblack fillers, silica filler provides unique strength characteristics that enhance the abrasion resistance, tear strength, aging resistance, and adhesion properties of rubber [12,13]. Precipitated silica provides the highest degree of reinforcement. Silane coupling agents enhance the chemical compatibilities of silica fillers with the rubber matrix for more efficient reinforcement [14][15][16].

Exposure to H 2 Gas
The high-pressure chamber and purge conditions used in this work are described elsewhere [29]. Cylindrical rubber samples with diameters of 13 mm and thicknesses of 3 mm were exposed to hydrogen gas for more than 20 h at pressures ranging from 1.2 to 90 MPa. After exposure to high-pressure H 2 , the chamber valve was opened to emit the H 2 gas. After decompression, a specimen was loaded into a graduated cylinder. The amount of H 2 gas released during the lag time was determined by measuring the offset value using a diffusion analysis program [29].

Transmission Electron Microscopy
The microstructures of the EPDM specimens were investigated with a combination of focused ion beam (FIB) and transmission electron microscopy (TEM). Thin foil samples for TEM image observation were prepared with an FIB. The morphology, distribution, and size characteristics of the CB filler particles in EPDM were observed with a transmission electron microscope (TECNAI F20, FEI company, Hillsboro, OR, USA) operating at an accelerating voltage of 200 kV.

Volumetric Measurement for Emitting H 2
The volumetric measurement utilized the graduated cylinders in which the emitted H 2 from the specimen was collected and measured. After exposure in the high-pressure chamber and subsequent decompression, the samples were obtained. The samples were loaded into their corresponding gas cell spaces at the top of the graduated cylinder. The details for the method are comprehensively described elsewhere [28,29].
To obtain the increased number of moles (∆n) due to the hydrogen gas released in the graduated cylinder, we measured the volume increase (∆V); that is, we measured the reduction in the water level in the cylinder as follows [29]: where ρ is the distilled water density, g is the gravitational acceleration, h is the height (vertical position) of the water level in the cylinder measured from the water level in the corresponding water container, and P 0 is the atmospheric pressure outside the cylinder. The ∆n in the cylinder is converted to the mass concentration [C(t)] of H 2 released from the rubber sample: where m H2 [g/mol] is the H 2 molar mass, which is equal to 2.016 g/mol and m sample is the sample mass.

Diffusion Analysis Program
Assuming that H 2 desorption is a Fickian diffusion process, the concentration C E (t) of the emitted H 2 is computed as follows [30,31]: where β n is the root of the zeroth 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 (3) is an infinite series expansion with two summations. This equation is a solution for Fick's second diffusion equation for a cylindricalshaped sample. In this study, C E = 0 at t = 0 and C E = C ∞ at t = ∞. C ∞ is the saturated H 2 concentration at infinity, i.e., the H 2 uptake. D is the diffusion coefficient, and l and ρ are the thickness and radius of the cylindrical specimen, respectively.
The derivative at t = 0, ( dC E (t=0) dt ), of two summations in Equation (3) is −∞. This finding implies that the initial H 2 emission rate is extremely fast; it originates from the distribution difference of H 2 caused by the discontinuous pressure difference between the high pressure inside the specimen and the atmosphere outside the specimen after decompression. This result means that, according to Equation (3), there is a possibility of showing different evolution characteristics with time just after decompression.
Because Equation (3) has two infinite terms, we estimate that the finite number of terms (n) in the actual calculation of the two summations should be contained to obtain D and C ∞ . Thus, we calculate the contributions in two summations of Equation (3), reaching n = 50 terms with three different times t. Figure 1 shows the normalized and calculated product of two summations versus n at three different times (t = 1 s, 100 s, and 10,000 s) at fixed parameters of l = 3.0 mm, ρ = 6.5 mm, and D = 2 × 10 −10 m 2 /s. With increasing n up to 50, the products of the two summations for all t = 1 s, 100 s, and 10,000 s converge to 1 (the value when n is infinite). The horizontal red line in Figure 1 corresponds to a 0.98 value of converged value 1. The corresponding n-term value on the x-axis exceeds 0.98 on the y-axis, for which n should be contained in two summations as nearly equal to the converged value of 1. Thus, a, b, and c, which are obtained from the intersection between the 98% line and the product of two summations (data on y-axis), indicate the minimum number of terms, n, to be included in the summations; these values correspond to 2 at t = 10,000 s, 8 at t = 100 s, and 17 at t = 1 s, respectively, in n. When t is sufficiently greater than 10,000 s, the two terms of the two summations in Equation (3) mainly contribute to the C E (t) value. However, if t is less than t = 100 s, Equation (3) cannot easily converge, and eight more n terms are needed, as shown by arrow b in Figure 1. For the calculation with an uncertainty less than 2% using Equation (3), we should include many terms that are greater than the n = 64 terms (8 × 8) in the product of the two summations at t = 100 s. Thus, a dedicated calculation program is needed. We developed a diffusion analysis program to calculate D and C ∞ , including up to n = 100 terms of the first summation and n = 50 terms of the second summation, reaching β 50 in Equation (3) for covering small time values, t = 1 s. 8 at t = 100 s, and 17 at t = 1 s, respectively, in n. When t is sufficiently greater than 10, s, the two terms of the two summations in Equation (3) mainly contribute to the value. However, if is less than = 100 , Equation (3) cannot easily converge, and ei more n terms are needed, as shown by arrow b in Figure 1. For the calculation with uncertainty less than 2% using Equation (3), we should include many terms that greater than the n = 64 terms (8 × 8) in the product of the two summations at t = 10 Thus, a dedicated calculation program is needed. We developed a diffusion analysis p gram to calculate D and , including up to n = 100 terms of the first summation and 50 terms of the second summation, reaching in Equation (3) for covering small ti values, t = 1 s.    Figure 2 shows the overall flowchart of the diffusion analysis program developed to analyze the C E (t) data using Equation (3) by a Nelder-Mead simplex nonlinear optimization algorithm [32]. As a result of the application of the developed program, the solubility, diffusivity, and permeability were finally obtained in a rubber composite system. The contents indicated by the blue color in Figure 2 are related to the selection of the solution to the diffusion equation of Equation (3); for this equation, we chose an appropriate diffusion model corresponding to the rubber shape and the number of superposition models.
The D and C ∞ for EPDM composites were determined by utilizing a diffusion analysis program based on Figures 1 and 2. An example application for the analysis program and the detailed procedure were already described in the previous literature [29]. The method of restoring H 2 content using the diffusion analysis program is regarded as a novel aspect of our research. The precise measurement of H 2 content, in particular, is possible as a result of including up to n = 100 terms in the summations with the help of the diffusion analysis program.  Figure 3d, a large agglomeration of SRF CB occurs in the EPDM composite with a concentration of 20 phr. The CB filler shapes and distributions are identifiable in the visible TEM image exhibiting the CB filler particles on the rubber matrix. EPDM HAF20 and SRF20 exhibit spherical island shapes with polarized particle sizes of approximately 32 and 65 nm, respectively. The CB particles are distributed as partially condensed aggregates. The aspect ratio is defined by the ratios of the horizontal lengths to the vertical lengths of the particles. For EPDM HAF20 and SRF20 specimens with spherical shapes, the aspect ratios are 1.
Moreover, well-dispersed filler particles with small particle sizes on average, such as HAF CB filler, lead to similar results as filler particles with a high filler surface area and strong interactions with the polymer, thus affecting the gas diffusion and permeation processes. In HAF CB-filled EPDM composites crosslinked with sulfur, we measured the degree of filler dispersion according to the testing method (ASTM D7723). The measured dispersion degrees for two EPDM HAF20 and HAF60 were determined to be 98%; thus, these specimens are regarded as well-dispersed fillers in the rubber network. We did not find any remarkable differences in the dispersion degrees for samples with different filler contents.  Moreover, well-dispersed filler particles with small particle sizes on average, such as HAF CB filler, lead to similar results as filler particles with a high filler surface area and strong interactions with the polymer, thus affecting the gas diffusion and permeation processes. In HAF CB-filled EPDM composites crosslinked with sulfur, we measured the degree of filler dispersion according to the testing method (ASTM D7723). The measured dispersion degrees for two EPDM HAF20 and HAF60 were determined to be 98%; thus, these specimens are regarded as well-dispersed fillers in the rubber network. We did not find any remarkable differences in the dispersion degrees for samples with different filler contents.

Filler Effects on H2 Uptake
The time evolution characteristics of H2 emission after decompression at pressures ranging from 1.2 to 90 MPa were measured in ten EPDM composites blended with CB and silica, and in neat EPDM. Figure 4 shows a plot of H2 uptake versus the elapsed time in ten EPDM rubbers after hydrogen exposure at 8.9 MPa for 20 h. The prominent characteristic is the increase in hydrogen uptake in CB-filled EPDM composites relative to that in neat EPDM. This phenomenon is attributed to H2 adsorption due to the presence of the CB filler. Increasing the HAF CB content in the HAF CB-filled EPDM composites increased the H2 emission content. The filler effect on the SRF CB-filled EPDM composites is similar to that of HAF CB-filled EPDM. The slight increase in H2 uptake for HAF CBfilled EPDM might be explained by the larger specific surface areas of the HAF CB filler compared with those of the SRF CB filler. In the silica-filled EPDM composites, the variation in H2 uptake with silica filler content is not obviously different from that of the neat EPDM polymer. This result implies that hydrogen is not adsorbed at the silica filler sur-

Filler Effects on H 2 Uptake
The time evolution characteristics of H 2 emission after decompression at pressures ranging from 1.2 to 90 MPa were measured in ten EPDM composites blended with CB and silica, and in neat EPDM. Figure 4 shows a plot of H 2 uptake versus the elapsed time in ten EPDM rubbers after hydrogen exposure at 8.9 MPa for 20 h. The prominent characteristic is the increase in hydrogen uptake in CB-filled EPDM composites relative to that in neat EPDM. This phenomenon is attributed to H 2 adsorption due to the presence of the CB filler. Increasing the HAF CB content in the HAF CB-filled EPDM composites increased the H 2 emission content. The filler effect on the SRF CB-filled EPDM composites is similar to that of HAF CB-filled EPDM. The slight increase in H 2 uptake for HAF CB-filled EPDM might be explained by the larger specific surface areas of the HAF CB filler compared with those of the SRF CB filler. In the silica-filled EPDM composites, the variation in H 2 uptake with silica filler content is not obviously different from that of the neat EPDM polymer. This result implies that hydrogen is not adsorbed at the silica filler surface.
We measured the hydrogen emission content as a function of exposed pressure for nine EPDM composites blended with fillers and one neat EPDM. Figure 5 shows a plot of the representative hydrogen uptake data versus the pressure for four EPDM composites. Panels (a), (b), (c), and (d) of this figure display the pressure behaviors of H 2 uptake with neat EPDM, EPDM composites compounded with silica filler, EPDM HAF40, and EPDM SRF40, respectively. All EPDM composites blended with HAF CB and SRF CB fillers reveal similar uptake behaviors versus pressure. To avoid redundancy, we only present the representative hydrogen uptake data for two CB-filled EPDM composites. The H 2 uptakes (C ∞ ) of neat EPDM and EPDM S20 (Figure 5a,b) are proportional to pressures reaching 90 MPa, which is in accordance with Henry's Law [33,34]. This behavior is responsible for the absorption of H 2 into the polymer matrix. However, as shown in Figure 5c,d, the hydrogen uptakes for EPDM HAF40 and SRF40 deviate from Henry's law at pressures above 15 MPa; this phenomenon is attributed to the adsorbed hydrogen at the surface of the CB filter. Thus, dual sorption is observed for all CB-blended EPDM composites. The dual mode sorption behaviors that cover the overall pressure range reaching 90 MPa are introduced as follows: where C ∞ is the total H 2 gas uptake. The first term indicates Henry's law with the Henry's law coefficient k. The second term presents the Langmuir model [35,36], where a is the maximum adsorption quantity (or capacity parameter) and b is the adsorption equilibrium constant (or the Langmuir hole affinity parameter). The fitting results of the H 2 uptake characteristics according to Equation (4) are summarized in Table 2. The H2 uptakes (C∞) of neat EPDM and EPDM S20 (Figure 5a,b) are proportional to pressures reaching 90 MPa, which is in accordance with Henry's Law [33,34]. This behavior is responsible for the absorption of H2 into the polymer matrix. However, as shown in Figure 5c,d, the hydrogen uptakes for EPDM HAF40 and SRF40 deviate from Henry's law at pressures above 15 MPa; this phenomenon is attributed to the adsorbed hydrogen at the surface of the CB filter. Thus, dual sorption is observed for all CB-blended EPDM composites. The dual mode sorption behaviors that cover the overall pressure range reaching 90 MPa are introduced as follows: where C∞ is the total H2 gas uptake. The first term indicates Henry's law with the Henry's law coefficient k. The second term presents the Langmuir model [35,36], where is the maximum adsorption quantity (or capacity parameter) and is the adsorption equilibrium constant (or the Langmuir hole affinity parameter). The fitting results of the H2 uptake characteristics according to Equation (4) are summarized in Table 2.  The Langmuir contribution is obtained with respect to total hydrogen uptake, which is the uptake sum of Henry and Langmuir contributions. The Langmuir contribution indicates that the adsorption quantity of hydrogen increases with increasing filler content, as shown in Figure 6. The deviations from linearity above 60 phr for CB-filled EPDM composites indicate an abrupt increase in hydrogen adsorption; this phenomenon may be caused by the formation of hydrogen path channels and thus lead to a percolation effect by many fillers.
The Langmuir contribution is obtained with respect to total hydrogen uptake, which is the uptake sum of Henry and Langmuir contributions. The Langmuir contribution indicates that the adsorption quantity of hydrogen increases with increasing filler content, as shown in Figure 6. The deviations from linearity above 60 phr for CB-filled EPDM composites indicate an abrupt increase in hydrogen adsorption; this phenomenon may be caused by the formation of hydrogen path channels and thus lead to a percolation effect by many fillers. Langmuir sorption is related to the porous solids in the gas-polymer system. The Langmuir sorption site in a glassy polymer corresponds to holes or microvoids that arise due to the nonequilibrium nature of glassy polymers. A gas sorption isotherm in a glassy polymer below the glass transition temperature (Tg) generally depends on the pressure exposure. This behavior is characteristic of dual-mode sorption with Henry's law absorption in an equilibrium state and Langmuir adsorption in a nonequilibrium state [37]. The nonequilibrium state is directly related to the excess free volume or unrelaxed free volume in a glassy polymer [38]. Bondar et al. [39] confirmed the validity of dual mode behaviors. Therefore, the dual mode sorption model for gas sorption in glassy polymers is an effective method for investigation.
However, Jung et al. [25] demonstrated that, for HAF CB-filled NBR, the experimental data at the rubbery phase polymer show dual mode sorption due to the presence of porous HAF CB filler. H2 molecules are absorbed by rubbery NBR and are simultaneously adsorbed by porous filler, leading to dual mode sorption similar to that at the glass Langmuir sorption is related to the porous solids in the gas-polymer system. The Langmuir sorption site in a glassy polymer corresponds to holes or microvoids that arise due to the nonequilibrium nature of glassy polymers. A gas sorption isotherm in a glassy polymer below the glass transition temperature (T g ) generally depends on the pressure exposure. This behavior is characteristic of dual-mode sorption with Henry's law absorption in an equilibrium state and Langmuir adsorption in a nonequilibrium state [37]. The nonequilibrium state is directly related to the excess free volume or unrelaxed free volume in a glassy polymer [38]. Bondar et al. [39] confirmed the validity of dual mode behaviors. Therefore, the dual mode sorption model for gas sorption in glassy polymers is an effective method for investigation.
However, Jung et al. [25] demonstrated that, for HAF CB-filled NBR, the experimental data at the rubbery phase polymer show dual mode sorption due to the presence of porous HAF CB filler. H 2 molecules are absorbed by rubbery NBR and are simultaneously adsorbed by porous filler, leading to dual mode sorption similar to that at the glass phase. Thus, the porous HAF CB filler in the NBR composite corresponds to the robust void structure in the glass phase polymer. The solubility result in HAF CB-filled NBR supports the dual sorption behavior.

Filler Effects on H 2 Diffusion
Similar to the pressure-dependent H 2 uptake, the H 2 diffusivities of the neat EPDM and nine filled EPDM composites were measured as functions of exposed pressure. The H 2 diffusivities of neat EPDM and the EPDM composites blended with fillers apparently depend on the exposed pressure. The pressure dependence of the diffusion coefficient is related to the decrease in the mean free path of H 2 , the increased tortuosity caused by the impermeable filler in the rubber networks and the increased interactions between the filler and the rubber.
All EPDM composites blended with HAF CB and SRF CB fillers revealed similar diffusion behaviors versus pressure. To avoid redundancy, the representative pressuredependent diffusion for EPDM HAF20 and SRF20, as shown in Figure 7a,b, respectively, can be divided into two contributions at the peak, as indicated by arrows. The contributions correspond to Knudsen diffusion for low pressure and bulk diffusion for high pressure. The pressure-dependent behavior for diffusivity is interpreted by the results of Knudsen diffusion below 7-10 MPa, and bulk diffusion above this pressure range; this combined diffusion was observed and analyzed by fractal theory in other studies [40,41]. Knudsen diffusion gradually increases with increasing pressure. Knudsen diffusion below the pressure range normally occurs when there is a large mean free path of diffusing gas molecules or a low gas density. The Knudsen diffusion coefficient (D K, pm ) in porous media is expressed as follows [42]: where φ is the pressure-dependent porosity, τ is the tortuosity caused by introducing the filler, d c is the pore diameter, and υ is the average molecular velocity derived from the kinetic theory of gases.
pendent diffusion for EPDM HAF20 and SRF20, as shown in Figure 7a,b, respectively, can be divided into two contributions at the peak, as indicated by arrows. The contributions correspond to Knudsen diffusion for low pressure and bulk diffusion for high pressure. The pressure-dependent behavior for diffusivity is interpreted by the results of Knudsen diffusion below 7-10 MPa, and bulk diffusion above this pressure range; this combined diffusion was observed and analyzed by fractal theory in other studies [40,41]. Knudsen diffusion gradually increases with increasing pressure. Knudsen diffusion below the pressure range normally occurs when there is a large mean free path of diffusing gas molecules or a low gas density. The Knudsen diffusion coefficient ( , ) in porous media is expressed as follows [42]: where is the pressure-dependent porosity, is the tortuosity caused by introducing the filler, is the pore diameter, and is the average molecular velocity derived from the kinetic theory of gases. Moreover, the bulk diffusion for neat EPDM (Figure 7c) and EPDM S20 (Figure 7d), and the bulk diffusion above a critical pressure of 7 MPa-10 MPa for CB-filled EPDM composites, are inversely proportional to pressure; this phenomenon is associated with the mean free path between the H2 molecules. Bulk diffusion is predominant when the mean free path (λ) in large pores is smaller than the pore diameters, or when high-pressure gas diffusion occurs. The bulk diffusion coefficient ( ) is expressed as follows [43]: where μ is the viscosity of the diffusion molecule in units of /s and is the pressure. The factor 5/8 considers the Maxwell-Boltzmann distribution of molecular velocity. The experimental results of the diffusivity shown in Figure 7 are fitted by both Equations (5) and (6), as indicated by the blue and black lines, respectively. In the region of Knudsen diffusion, the diffusion coefficient is proportional to the pressure; this phenomenon may Moreover, the bulk diffusion for neat EPDM (Figure 7c) and EPDM S20 (Figure 7d), and the bulk diffusion above a critical pressure of 7-10 MPa for CB-filled EPDM composites, are inversely proportional to pressure; this phenomenon is associated with the mean free path between the H 2 molecules. Bulk diffusion is predominant when the mean free path (λ) in large pores is smaller than the pore diameters, or when high-pressure gas diffusion occurs. The bulk diffusion coefficient (D B ) is expressed as follows [43]: where µ is the viscosity of the diffusion molecule in units of kg m/s and P is the pressure. The factor 5/8 considers the Maxwell-Boltzmann distribution of molecular velocity. The experimental results of the diffusivity shown in Figure 7 are fitted by both Equations (5) and (6), as indicated by the blue and black lines, respectively. In the region of Knudsen diffusion, the diffusion coefficient is proportional to the pressure; this phenomenon may be caused by an increase in the porosity in Equation (5) due to an increase in the pressure. The decrease in the bulk diffusion coefficient is attributed to a decrease in the mean free path with increasing pressure.
Regarding the H 2 sorption and diffusion mechanism, we again justify the hydrogen sorption (diffusion) mechanism considering the role of CB. According to the hydrogen uptake data shown in Figure 5, the hydrogen sorption mechanisms in the EPDM composites blended with CBs (HAF and SRF) revealed two types of sorption (or diffusion): fast diffusion due to the hydrogen absorbed in the polymer network and slow diffusion due to the hydrogen physically adsorbed at the CB filler interface. In other words, the sorption (or diffusion) mechanism in CB-filled EPDM represents dual sorption (or diffusion) behaviors. In this study, the sorption and desorption processes of most H 2 are reversible; this finding may be attributed to physisorption rather than chemisorption by penetrated H 2 .
However, a single hydrogen sorption (or diffusion) behavior in silica-filled EPDM is observed only with a fast-diffusing polymer network. The single-mode behavior is also shown in neat EPDM due to fast H 2 sorption for the polymer network. Hydrogen in the silica-filled EPDM was not adsorbed at the interface between the silica and rubber. This finding indicates that hydrogen sorption in silica or at the interface between silica and the rubber matrix did not occur. Thus, as shown in the H 2 uptake characteristics ( Figure 5) for silica-filled EPDM specimens, the value (uptake) for silica-filled EPDM composites is nearly identical to that for neat EPDM. The result for CB-filled EPDM composites indicates that the fast component shows the permeation characteristics of H 2 absorbed onto the parent component of the rubber (Henry's law); the slow component shows the permeation characteristics of H 2 adsorbed by the filler (Langmuir law). Figure 8a-c shows the variations in the diffusivity characteristics with the filler content at the three different pressures of 1.2 MPa, 8.9 MPa, and 90 MPa, respectively. At a low pressure of 1.2 MPa, all fillers extend the diffusion path due to increased tortuosity by the impermeable filler, resulting in a decrease in the diffusion rate. The diffusivity in the silica-blended EPDM is negative and it decreases linearly with increasing filler content; the diffusivity in the CB-blended EPDM decreases in the form of an asymptotic line (~1/filler content). At the low pressure of 1.2 MPa, the decrease in diffusivity of the CBblended EPDM is larger than that of the silica-blended EPDM; this phenomenon is expected and possibly related to the additional filler-polymer interactions. However, with the increasing pressure reaching 90 MPa, the filler effect on diffusion decreases; the diffusivity characteristics for all specimens converge at values of approximately 2 × 10 −10 m 2 /s. Two general models [18] are employed to explain the change in diffusivity by the presence of filler particles. These models differ in their descriptions of the interactions between filler particles and the polymer matrix. One model is based on the concept of free volume. Free volume ascribes the change in diffusivity to an increase or decrease in the microscopic friction coefficient of the diffusing species. This change is responsible for the influence of the filler surface on the mobilities of diffusing molecules in the vicinity of the filler particles through filler-polymer interactions. The second model is an obstacle model. Obstacles apparently decrease the diffusivity by increasing the tortuosity of the diffusion path or by creating bottlenecks without affecting the friction experienced by the diffusing species. A change in free volume can increase or decrease the polymer diffusivity; the presence of obstacles always decreases the polymer diffusivity. As shown in Figure 8a, the diffusivity for silica-filled EPDM is responsible for the tortuosity of the diffusion path by introducing filler (second model). Moreover, the diffusivity for CB-filled EPDM is attributed to both polymer-filler interactions and tortuosity (first and second model). tent; the diffusivity in the CB-blended EPDM decreases in the form of an asymptotic line (~1/filler content). At the low pressure of 1.2 MPa, the decrease in diffusivity of the CB blended EPDM is larger than that of the silica-blended EPDM; this phenomenon is ex pected and possibly related to the additional filler-polymer interactions. However, with the increasing pressure reaching 90 MPa, the filler effect on diffusion decreases; the diffu sivity characteristics for all specimens converge at values of approximately 2 × 10 −10 m 2 /s.

Correlations of Permeation with Density and Tensile Strength
The permeation P was determined by multiplying the solubility S by the diffusion coefficient D, i.e., P = SD. Figure 9a,b shows the permeability variations with density and tensile strength, respectively, for neat EPDM and blended EPDM polymer composites. The trends are similar to those of diffusivity at 1.2 MPa (Figure 8a), implying that permeation is predominantly affected by diffusivity rather than by solubility.

Correlations of Permeation with Density and Tensile Strength
The permeation P was determined by multiplying the solubility S by the diffusion coefficient D, i.e., P = SD. Figure 9a,b show the permeability variations with density and tensile strength, respectively, for neat EPDM and blended EPDM polymer composites. The trends are similar to those of diffusivity at 1.2 MPa (Figure 8a), implying that permeation is predominantly affected by diffusivity rather than by solubility. Figure 9. Correlations between permeability and (a) density and (b) tensile strength for neat EPDM and EPDM composites blended with CB/silica. The data for neat EPDM are included as pink and black curves for consistency with the fittings of the filler-blended EPDM composites. The value in parentheses indicates the phr of CB and silica. R 2 is squared correlation coefficients of fitting.
As shown in Figure 9a, the negative linear relationship (density) between permeability and density for silica-blended EPDM composites indicates a smooth decrease in permeation with increasing density, without introducing other interactions or additional parameters. However, the density effect on the permeability for CB-blended EPDM composites is inversely proportional to the filler content, i.e., ~1/density. The magnitude of the effects for the CB-blended EPDM composites is larger than that for the silica-blended As shown in Figure 9a, the negative linear relationship (density) between permeability and density for silica-blended EPDM composites indicates a smooth decrease in permeation with increasing density, without introducing other interactions or additional parameters. However, the density effect on the permeability for CB-blended EPDM composites is inversely proportional to the filler content, i.e.,~1/density. The magnitude of the effects for the CB-blended EPDM composites is larger than that for the silica-blended EPDM composites. This result again implies an additional effect; that is, the polymer-filler interaction for CB-blended EPDM composites may originate the permeability behavior, as already shown in the pressure-dependent effect on diffusivity at 1.2 MPa. A similar behavior for the density influence on permeability was found in polyethylene gas permeability investigations with different permeants [44,45]. The decrease in permeability in polyethylene with increasing density is attributed to the volume dilution of the amorphous fraction by the relatively impermeable crystalline phase.
Moreover, the permeability changes with tensile strength shown in Figure 9b exhibit identical behaviors to the permeability changes with density, as shown in Figure 9a. The two trends may be closely related to the same origin. From the investigated relation function for physical and mechanical properties, we provide a possibility for predicting the H 2 -permeation properties of compounded EPDM candidates used as seal materials under high pressure in H 2 -refueling stations.

Conclusions
By using a volumetric analysis technique and an ungraded diffusion analysis program calculating up to a hundred summation terms in an expansion series of the concentration C E (t) of emitted H 2 , we investigated the H 2 -permeation characteristics of EPDM composites. The investigated results are summarized below.
The pressure-dependent H 2 uptakes for neat EPDM and silica-filled EPDM composites show single sorption models that satisfy Henry's law; this phenomenon was dominated by absorption by the polymer. The contribution from the filler was negligibly small. Moreover, H 2 uptakes for CB-filled EPDM composites followed dual sorption models that obey Henry's law and Langmuir law. The H 2 uptake in the CB-filled EPDM received contributions from absorption by the polymer networks and adsorption by the CB filler. The difference between the two CBs is attributed to the distinct specific surface areas.
The diffusivity values in all EPDMs investigated depended on pressure. The decrease in the diffusivity for silica-filled EPDM relative to that for neat EPDM was responsible