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In neat nitrile butadiene rubber (NBR), three relaxation processes were identified by impedance spectroscopy: α and α′ processes and the conduction contribution. We investigated the effects of different carbon black (CB) and silica fillers with varying filler content on the dielectric relaxations in NBR by employing a modified dispersion analysis program that deconvolutes the corresponding processes. The central frequency for the α′ process with increasing high abrasion furnace (HAF) CB filler was gradually upshifted at room temperature, while the addition of silica led to a gradual downshift of the center frequency. The activation energy behavior for the α′ process was different from that for the central frequency. The use of HAF CB led to a rapid increase in DC conductivity, resulting from percolation. The activation energy for the DC conductivity of NBRs with HAF CB decreased with increasing filler, which is consistent with that reported in different groups.

We investigated the influence of two fillers-CB (carbon black) and silica-on the H

We introduce a volumetric analysis technique to characterize the solubility of hydrogen dissolved in polymers and its diffusion coefficient by electrical capacitance measurement electrodes to determine the water level in graduated cylinders. This new and simple technique measures the volume of hydrogen released from rubber inside a graduated cylinder after a sample is exposed to high-pressure hydrogen and subsequent decompression. A diffusion analysis program is utilized to determine the total uptake (C0) and diffusivity (D) of hydrogen, which are used to calculate the solubility (S) and permeability (P). This method is applied to spherical rubber samples of nitrile butadiene rubber (NBR), ethylene propylene diene monomer (EPDM), and fluoroelastomer (FKM), which are potential sealing materials for H2 energy infrastructures. C0 follows Henry's law for all samples. No sample size and pressure dependence is observed for S, whereas an appreciable size dependence for the three rubbers is detected for D. The uncertainty is evaluated by considering uncertainty factors that affect the measurement. The correlation between D and density of rubber is found. The developed method can be utilized as a standard test for the transport properties versus pressure of various polymer membranes regardless of the sample shapes and size.

To find suitable sealing material with low permeability against hydrogen, the elaborated evaluation techniques for hydrogen transport properties are necessary. We developed two techniques determining the permeability of hydrogen including software for diffusion behavior analysis. The techniques contain gas chromatography and volumetric collection of hydrogen gas. By measuring the hydrogen released from polymer samples with respect to the elapsed time after being decompressed from the high pressure, total amount of adsorption and diffusivity (D) of hydrogen are evaluated with self-developed program of Fick's diffusion equation specified to a sample shape. The solubility (S) and permeability (P) of the polymers are determined through Henry's law and a relation of P = S D , respectively. Developed techniques were applied to three kinds of spherical-shaped sealing rubbers, NBR, EPDM, and FKM. The D, S and P have been measured as function of pressure. The permeability obtained by both methods are discussed with Comsol simulation.

We developed a method for characterizing permeation parameters in hydrogen sorption and desorption processes in polymers using the volumetric measurement technique. The technique was utilized for three polymers: nitrile butadiene rubber (NBR), ethylene propylene diene monomer (EPDM), and fluoroelastomer (FKM). The total uptake (C∞), total desorbed content (C0), diffusivity in sorption (Ds), and diffusivity in desorption (Dd) of hydrogen in the polymers were determined versus the sample diameter used in both processes. For all the polymers, the diameter dependence was not detected for C∞ and C0. The average C∞ and C0 at 5.75 MPa were 316 wt∙ppm and 291 wt∙ppm for NBR, 270 wt∙ppm and 279 wt∙ppm for EPDM, and 102 wt∙ppm and 93 wt∙ppm for FKM. The coincidence of C∞ and C0 in the sorption and desorption process indicated physisorption upon introducing hydrogen molecules into the polymers. The larger Dd in the desorption process than Ds could be attributed to an increased amorphous phase and volume swelling after decompression. The equilibrium time to reach the saturation of the hydrogen content in both processes was experimentally confirmed as proportional to the squared radius and consistent with the COMSOL simulation. This method could be used to predict the equilibrium time of the sorption time, depending on the radius of the polymers without any measurement.

We invented a dispersion analysis program that analyzes the relaxation processes from dielectric permittivity based on a combination of the Havriliak–Negami and conductivity contribution functions. By applying the created program to polymers such as nitrile butadiene rubber (NBR) and ethylene propylene diene monomer (EPDM), several relaxation processes were characterized: an α process due to segmental motions of the C-C bond, an α′ process attributed to fluctuations in the end-to-end dipole vector of the polymer chain, the conduction contribution by the filler observed above room temperature, and secondary relaxation processes β and γ of motion for the side group in NBR. In the EPDM specimen, the β process associated with the rotational motion of the side groups, the α process associated with the relaxation of local segmental motion, and the αβ process associated with the origin of the β process at high temperatures above 305 K were observed. The Maxwell–Wagner–Sillars effect and conduction contribution were also presented. The molecular chains responsible for the relaxation processes were assigned by building molecular models of the two polymers. The temperature dependence of the relaxation strength and the shape parameters that characterize the process were investigated. From the temperature-dependent relaxation analysis, the merged αβ process, activation energy, and glass transition temperature were determined and compared.

The dielectric permittivity in polymers, fluoroelastomers and ethylene propylene diene monomers was measured as a function of both frequency and temperature. Several relaxation processes were revealed and analyzed through a developed algorithm to analyze the relaxation. The β and the α relaxations were observed and occurred in that order as the temperature was increased. Maxwell-Wagner-Sillars contributions, including conduction, were present at high temperatures and low frequencies. The molecular chains responsible for the relaxation processes were assigned by using molecular modeling with the dipole moment included. The activation energy, Vogel-Fulcher temperature and glass transition temperature were also obtained.

To characterize the dielectric relaxation embedded in polymers, we developed a program algorithm that analyzes the relaxation processes from dielectric permittivity versus frequency data based on governing functions such as the Havriliak-Negami function including the conductivity contribution. With the help of the developed simulation program, we have identified three processes: an α process due to rotational and segmental motions of the C-C bond, an α’ process attributed to the fluctuation of the end-to-end dipole vector of the polymer chain, and the conduction contribution observed at high temperatures and low frequencies. The activation energy and glass transition temperature for the two main relaxations were independently determined from both the imaginary permittivity versus frequency and temperature by assuming Arrhenius dependence and the Vogel-Fulcher-Tamman law. The results obtained by the two methods for α and α’ relaxations were compared with each other and with that obtained by differential scanning calorimetry.

In the actual application of gas transport properties under high pressure, the important factors are sample size dependence and permeation efficiency, related to gas sorption. With a modified volumetric analysis technique, we firstly measured the overall diffusion properties and equilibrium times for reaching the saturation of hydrogen content in both hydrogen sorption and desorption processes. The measured parameters of total uptake (C∞), total desorbed content (C0), diffusion coefficient in sorption (Ds), diffusion coefficient in desorption (Dd), sorption equilibrium time (ts) and desorption equilibrium time (td) of hydrogen in two polymers were determined relative to the diameter and thickness of the cylindrical-shaped polymers in the two processes. C∞ and C0 did not demonstrate an appreciable volume dependence for all polymers. The identical values of C∞ and C0 indicate the reversibility between sorption and desorption, which is interpreted by the occurrence of physisorption by sorbed hydrogen molecules. However, the measured diffusivity of the polymers was found to be increased with increasing thickness above 5 mm. Moreover, the larger Dd values measured in the desorption process compared to Ds may be attributed to an increased amorphous phase and volume swelling caused by increased hydrogen voids and polymer chain scission after decompression. The ts and td were found to be linearly proportional to the square of the thickness above an aspect ratio of 3.7, which was consistent with the numerical simulations based on the solution of Fick’s law. This finding could be used to predict the ts in a polymer without any measurement, depending on the sample size.

Filler effects on H2 diffusion in nitrile butadiene rubbers (NBRs) blended with carbon black and silica fillers of different concentrations are first investigated by employing a volumetric analysis. Total uptake, solubility, and diffusivity of hydrogen for ten filled-NBR, including neat NBR, are determined in an exposed pressure range of 1.3 MPa~92.6 MPa. Filler dependence on hydrogen uptake and diffusion is distinctly observed in the NBRs blended with high abrasion furnace (HAF) carbon black (CB) fillers compared to NBRs blended with medium thermal furnace (MT) CB and silica filler, which is related to the specific surface area of carbon black and interface structure. The HAF CB filled-NBR follows dual sorption behavior combined with Henry’s law and the Langmuir model, responsible for two contributions of solubility from polymer and filler. However, a single gas sorption behavior coming from the polymer is observed satisfying Henry’s law up to 92.6 MPa for NBR blended with MT CB filled-NBR and silica filled-NBR. Diffusion demonstrates Knudsen and bulk diffusion behavior below and above, respectively, at certain pressures. With increasing pressure, the filler effect on diffusion is reduced, and diffusivity converges to a value. The correlation observed between diffusivity and filler content (or crosslink density) is discussed.

Filler effects on H2 permeation properties in sulfur-crosslinked ethylene propylene diene monomer (EPDM) polymers blended with two kinds of carbon black (CB) and silica fillers at different contents of 20 phr–60 phr are investigated by employing volumetric analysis in the pressure exposure range of 1.2 MPa~9.0 MPa. A linear relationship is observed between the sorbed amount and pressure for H2 gas, which is indicative of Henry’s law behavior. The hydrogen solubility of EPDM composites increases linearly with increasing filler content. The magnitude of hydrogen solubility for the filled EPDM composites is dependent on the filler type. The hydrogen solubility is divided into two contributions: hydrogen absorption in the EPDM polymer and hydrogen adsorption at the filler surface. Neat EPDM reveals pressure-dependent bulk diffusion behavior. However, with increasing filler content, the diffusivity for the filled EPDM composites is found to be independent of pressure. The magnitude of filler effects on the hydrogen permeation parameter is measured in the order of high abrasion furnace CB~semireinforcing furnace CB ˃ silica, whose effect is related to the specific surface area of CB particles and interfacial structure. The correlation between the permeation parameters and filler content (or crosslink density) is discussed.

With the increasing interest in hydrogen energy, the stability of hydrogen storage facilities and components is emphasized. In this study, we analyzed the effect of high-pressure hydrogen gas treatment in silica-filled EPDM composites with different silica contents. In detail, cure characteristics, crosslink density, mechanical properties, and hydrogen permeation properties were investigated. Results showed that material volume, remaining hydrogen content, and mechanical properties were changed after 96.3 MPa hydrogen gas exposure. With an increase in the silica content, the crosslink density and mechanical properties increased, but hydrogen permeability was decreased. After treatment, high-silica-content composites showed lower volume change than low-silica-content composites. The crack damage due to the decompression caused a decrease in mechanical properties, but high silica content can inhibit the reduction in mechanical properties. In particular, EPDM/silica composites with a silica content of above 60 phr exhibited excellent resistance to hydrogen gas, as no change in their physical and mechanical properties was observed.

We have investigated the volume effects on hydrogen diffusion properties in both sorption and desorption processes by employing a volumetric analysis technique. The total uptake (𝐶∞), total desorbed content (𝐶0), sorption diffusion coefficient (Ds), desorption diffusion coefficient (Dd), sorption and desorption equilibrium time of hydrogen in two rubbery polymers are determined relative to the diameter and thickness of the cylindrical sample in the two processes. 𝐶∞ and 𝐶0 do not demonstrate the appreciable volume dependence for all rubbers. The identical values in 𝐶∞ and 𝐶0 indicate the reversibility between sorption and desorption, which is interpreted by the occurrence of physisorption rather than chemisorption by introducing hydrogen molecules. The larger Dd values in the desorption process than Ds may be attributed to increased amorphous phase and volume swelling caused by increased hydrogen voids and polymer chain scission after decompression. The time to reach equilibrium in both sorption and desorption processes was found to be linearly proportional to the square of thickness above an aspect ratio of 3.7, which is consistent with the numerical simulations based on the solution of Fick’s law. This finding could be used to predict the equilibrium adsorption time depending on the sample size in the polymer.

We report volumetric analysis techniques to analyze the transport properties of hydrogen dissolved in cylindrical-shaped polymers. The techniques utilize the volume measurement of the released hydrogen from rubber by gas collection in a graduated cylinder after charging sample with high-pressure hydrogen and subsequent decompression. We further improve the graduated cylinder with some modifications, such as reading the electrical capacitance of the water level using electrodes and changing the sample loading position. From the measurement results, the uptake (C∞), diffusion coefficient (D), and solubility (S) of hydrogen are quantified with an upgraded diffusion analysis program. These methods are applied to three cylindrical rubbers. Dual adsorption behaviors with increasing pressure are observed for all the samples. C∞ follows Henry's law up to ~15 MPa, whereas Langmuir model applies up to 90 MPa. D shows Knudsen and bulk diffusion behavior below and above pressure, respectively. A COMSOL simulation is compared with experimental observations.

Nondestructive impedance spectroscopy (IS) was developed and demonstrated to detect the effects of hydrogen on nitrile butadiene rubber exposed to hydrogen gas (H2) at high pressures up to 10 MPa. IS was applied to obtain an in situ and real-time quantification of H2 penetration into and its desorption out of rubber under high pressure. The diffusion coefficients of H2 were also obtained from the time evolution of the capacitance, which were compared with those obtained by thermal desorption gas analysis. The in situ measurements of the capacitance and the dissipation factor under various pressures during cyclic stepwise pressurization and decompression demonstrated the diffusion behaviour of H2, the phase of the rubber under high pressure, the transport properties of H2 gas, and the physicochemical interaction between H2 and the rubber. These phenomena were supported by a COMSOL simulation based on the electric current conservation equation and scanning electron microscopy (SEM) observations.

This paper describes a method to determine absolutely the dissipation factor (DF) of a capacitor connected with resistor in series that doesn’t depend on any reference capacitor with a known DF. The method was applied to calibrate the DFs for two capacitor-resistor boxes that had DF ranges of 1 × 10−5 to 1 × 10−2 (C-R connecting box A) and 5 × 10−6 to 5 × 10−3 (C-R connecting box B), together with uncertainty estimation. The principle of the absolute determination is based on “elimination” of the DF of a reference capacitor by subtracting DF readings from two successive measurements. This method was applied to the calibration of DF in the range 5 × 10−6 to 1 × 10−2 at voltages up to 1 kV. Results obtained using this method were confirmed by comparing them with DF obtained using different methods The developed DF standard could be used to calibrate DF for commercial capacitors and DF methods.

Rubber materials play a key role in preventing hydrogen gas leakage in high-pressure hydrogen facilities. Therefore, it is necessary to investigate rubber materials exposed to high-pressure hydrogen to ensure operational safety. In this study, permeation, volume swelling, hydrogen content, and mechanical characteristics of acrylonitrile butadiene rubber (NBR), ethylene propylene diene monomer (EPDM), and fluorocarbon (FKM) samples exposed to pressures of 35 and 70 MPa were investigated. The results showed that the volume recovery and hydrogen desorption behavior of EPDM with the highest permeation were fast whereas those of FKM with the lowest permeation were slow. The volume of NBR with the highest hydrogen content expanded after decompression. In contrast, FKM swelled the most despite having the lowest hydrogen content. After exposure to high-pressure hydrogen, the compression set (CS) slightly increased due to internal cracks, but the tensile strength decreased significantly with increasing pressure despite the absence of cracks in the fracture area of all tensile specimens. It was concluded that the decrease in tensile strength is closely related to the volume increase because of the relationship between the relative true strength and the volume ratio.

We established an ex-situ technique for evaluating hydrogen gas permeability by thermal desorption analysis (TDA) gas chromatography (GC) and by self-developed diffusion analysis software. Absorbed hydrogen mass in rubber, related to the GC-peak area, is recorded as a function of elapsed time after decompressing the hydrogen under high-pressure. From the charging amount (CH0) and diffusivity (D) obtained by the developed diffusion analysis program, the solubility(S) and permeability(P) is evaluated via Henry’s law and P = SD, respectively. The techniques were applied to ethylene propylene diene monomer (EPDM) rubber, sealing material candidates in hydrogen infrastructures. EPDM sample mixed with carbon black fillers showed dual hydrogen diffusion behaviors, whereas EPDM sample without carbon black showed a single hydrogen diffusion behavior. There was no appreciable pressure or size dependence on D, S and P. P are consistent with that measured by different researcher within the expanded uncertainty.

The dielectric permittivity of synthetic rubber polymers, nitrile butadiene rubber (NBR) and ethylene propylene diene monomer (EPDM), with both frequency and temperature variations, was thoroughly investigated by dielectric relaxation spectroscopy (DRS). The spectrum versus frequency of DRS was analyzed with the semiempirical Havriliak–Negami formula and conductivity contribution by employing the newly developed “dispersion analyzer” analysis program. The main dielectric relaxations called the α- and β-processes, associated with the cooperative motion of chains in polymers, were discovered in the low-temperature region. In the high-temperature region, we found Maxwell–Wagner–Sillars (MWS) relaxation associated with polymer interfacing and normal-mode (α’) relaxation responsible for end-to-end dipole vector motion. The activation energies of schematic molecular chains responsible for the relaxation processes were obtained with the information about its motional mode. The glass transition temperature and dipole moment for the side group were also determined and compared with those from previous studies. In the EPDM specimen, the peaks of α- and β-relaxation merged at high temperature and were separated with decreasing temperature. The first observations of both merging and splitting were consistent with the results on the temperature dependency of the relaxation strength. Both contour mapping and three-dimensional plots for the two rubbers provide visual information for the distribution and mapping of relaxation.

We report two different volumetric analysis techniques to determine the transport properties of hydrogen dissolved in rubbery polymers. This measures the volume filled by the released hydrogen from rubber by gas collection in a graduated cylinder and by gas chromatography after exposure a sample with high-pressure hydrogen and decompression. From the measurement results, the uptake (C∞), diffusion coefficient (D), and solubility (S) of hydrogen are quantified by employing an upgraded diffusion analysis program. These methods are applied to three cylindrical rubber samples. Dual adsorption behaviors with increasing pressure are observed for all rubber samples. C∞ follows Henry's law up to ∼15 MPa, whereas the Langmuir model applies up to 90 MPa. No size dependence are observed for C∞ and S, whereas pressure-dependent D shows Knudsen and bulk diffusion behavior below and above a critical pressure, respectively. The S and D measured in two techniques are consistent with each other within the expanded uncertainty evaluated. A COMSOL simulation is compared with experimental investigations.

Permeation of hydrogen gas (H2) into nitrile butadiene rubber (NBR), which is one of the strong candidates for sealing material in H2 energy infrastructures, was quantified using a gas chromatography (GC) and a self-developed diffusion-analysis program. NBR samples were charged with H2 in a high-pressure chamber for 24 h then decompressed into atmosphere, and the mass of H2 released from the sample was measured as a function of elapsed time after decompression. The developed program calculated the total charging amount C0 and diffusivity D, which were then used to calculate the H2 solubility S and permeability P for variation of pressure. The samples were polymerized with and without carbon black (CB) filler in cylindrical shapes with different diameters. It appeared that the filler contributes to increase S and decrease D. The uncertainty analysis against the evaluated data was carried out, too, in order that the method could be applicable as a standard test for the permeation properties of various polymer membranes.

The dc high voltage is usually measured with high-voltage divider which plays the role of the ratio standard linking the unknown high voltage to the well-known low-voltage standards. A step-up method had been proposed to calibrate the dividing ratios of the high-voltage dividers at nominal test voltage. The step-up technique has been newly modified for improving the transfer accuracy of reference values determined in voltage stack stage, with employing an additional source voltage monitoring device, and successfully applied to precisely determine the dividing ratios up to 100 kV. Typical standard uncertainty for the dividing ratios is estimated to be approximately $5 \times 10^{{ {-6}}}$ .

This paper reports simulation and evaluation of the magnetic flux density (MFD) of a rotating Halbach magnet (RHM) composed of a rotating inner Halbach cylinder (HC) and a fixed outer HC. We first chose the dimension of a single HC, then determined the dimensions of an inner and outer HC to get MFD = 2 T. Simulation results were used to guide fabrication of an RHM; its magnetic field in the central axis direction agreed well with simulated values.

The complex dielectric permittivity of fluoroelastomers in response to both frequency and temperature variations was thoroughly investigated by dielectric relaxation spectroscopy. To characterize the various types of relaxation processes, the dispersion spectra of permittivity in the frequency domain were successively deconvoluted using a newly developed simulation program that uses the empirical Havriliak-Negami model based on the Debye dielectric model and conductivity contribution. At 233 K ≤ T ≤ 290 K, the α and β relaxation processes were independently observed; they merged at T ≥ 290 K. At T > 303 K, and both Maxwell-Wagner-Sillars (MWS) relaxation, known as interfacial polarization, and conductivity relaxation processes were observed. From the α relaxation process, which is related to the glass transition phenomenon, the glass transition temperature Tg was determined using the Vogel-Fulther-Tamman-Hesse (VFTH) temperature dependence law; the result was similar to the estimate of Tg obtained using differential scanning calorimetry. The temperature dependence of conductivity complies well with VFTH behaviors, whereas the β and MWS processes can be described using the Arrhenius temperature dependence law. The corresponding activation energies of the rotational side groups and DC conductivity were obtained.

Three techniques for determining the hydrogen permeation properties of rubber samples were developed based on the volumetric and gravimetric measurements of released H2 gas after sample decompression. These methods include gas chromatography (GC) by thermal desorption analysis (TDA), volumetric collection (VC) measurement of hydrogen by graduated cylinder and gravimetric (GM) measurement by electronic balance. By measuring the released hydrogen against elapsed time after the decompression of pressure, the charging amount (C0) and diffusivity (D) were obtained with the developed diffusion analysis program. From these values, the solubility (S) and permeability (P) of polymers were evaluated through the relations of Henry's law and P = S D , respectively. The developed techniques were applied to three kinds of spherically shaped sealing rubber materials. D, S and P were analyzed as a function of pressure. The transport behaviors obtained in the three methods are discussed and compared with the characteristics of each measuring technique. The correlations between transport parameters and carbon black filler or density are discussed.

Ratio correction factor and phase displacement of instrument transformers vary with the values of the external burden connected to the secondary of the transformers. Using the values measured at two burdens of the instrument transformers, the ratio correction factor and phase displacement at arbitrary burdens are theoretically obtained without any additional measurement. This is based on a theoretical analysis of the equivalent circuits of the instrument transformers. The validity of the methods was verified by comparing the theoretical value with measured value for several instrument transformers with different accuracy.