Impedance spectroscopy for in situ and real-time observations of the effects of hydrogen on nitrile butadiene rubber polymer under high pressure

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.

. Chemical composition of the NBR specimen. Impedance spectroscopy system. The IS system (Fig. 2) for the in situ measurement under high pressure comprises a hydrogen gas supply, input and vent valves, a pressure gauge, a hydrogen vessel, and an impedance analyser with a general purpose interface bus (GPIB) interface to a PC. The hydrogen vessel contains the specimen, electrodes and a high-pressure feed-through to withstand the seal at high pressure. The NBR used for this measurement was disc-shaped, 49 mm in diameter and 2 mm in thickness. The specimen was inserted between two electrodes and later fixed in place by mechanical pressure. The variation in the impedance of the specimen was monitored in real time using an Agilent 4294 A impedance analyser and an automated measurement program at the frequencies of the applied voltage of 40 Hz ≤ frequency ≤ 10000 Hz. The in situ capacitance C NBR and DF DF NBR were simultaneously measured as a function of pressure and exposure time for several days.
Thermal desorption analysis. Thermal desorption gas analysis (TDA) was performed using a 7890A analyser with a pulsed discharge detector from Agilent. To quantify the charged hydrogen content in the NBR, a specimen that had been exposed to H 2 gas at 10 MPa for 24 h was mounted in the tube furnace of the analyser. The specimen was 20 mm in diameter and 2 mm in thickness. The release of H 2 gas was measured by gas chromatography every 5 min for the first hour and then at intervals of 1 h for 16 h.

Results and Discussion
COMSOL simulation. To quantify the relationship between the measured C NBR and the relative dielectric constant ε r of the rubber, COMSOL software was used to model the hydrogen vessel and the electrodes (Fig. 3). The electric current conservation equations, J = σE + J e , E = −∇V, where J is the current density, σ is the conductivity, J e is the external current density, E is the electric field, and V is the electric potential, are solved with a boundary condition set by a ground domain at one electrode extending to the outer cylinder and a 1 V potential domain at the other electrode. A default mesh condition with a fine mesh size was used. The capacitance is equal to the total charge accumulated at the electrode, because we applied a unit potential of 1 V. The charge was calculated by surface integration of the surface charge over the front and side faces of the counter electrode, including the centre rod. In order to simulate the grounded vessel, the surface charge integration was carried over the counter electrode only excluding the vessel. The COMSOL simulations (Fig. 3, Csimul) show the capacitance C versus the electrode gap d. For d < 1 mm, the Csimul deviated from the capacitances (Canalytic) calculated using an ideal parallel-plate model, C NBR = ε 0 · R 2 /d (where R is the radius of the parallel electrode face), because of the limits of the geometric precision in the mesh modelling. The deviation between Csimul and Canalytic for d > 10 mm is attributed to a stray field that primarily forms between the side faces of the electrodes. It should be noted that the stray field between electrode faces and the inner faces of the vessel does not make any effect in capacitance because the vessel is electrically grounded. This is the main reason why the deviation for d > 10 mm is not very large. For high sensitivity and to avoid the stray field effect, we chose d = 2 mm. Another simulation with the rubber inserted between the electrodes was performed by varying the relative dielectric constant of the rubber material for d = 2 mm. The result was a simple linear relationship: C NBR = 0.31 + 8.22ε r [pF]. The linear relationship is expected to be maintained for other values of d.
H 2 effect on the impedance spectra. The effect of H 2 on the spectra of C NBR versus frequency for NBR in the sequential overall processes was quantified in three steps. (1) The C NBR spectra versus frequency were measured before H 2 pressurization (HP) (Fig. 4a). (2) The pressure was increased to 10 MPa over 30 min, and the C NBR spectra versus frequency were subsequently measured after HP at 10 MPa for 25 h ( Fig. 4b; several lines overlay). (3) H 2 decompression (HD) was conducted for 20 min, and then the C NBR spectra versus frequency were measured after HD for 30 h ( Fig. 4c; several lines overlay). The capacitance decreased by more than an order of www.nature.com/scientificreports www.nature.com/scientificreports/ magnitude after HP and then recovered to almost its original value after HD. The DF NBR spectra versus frequency showed behaviour similar to that of the C NBR spectra. The observed large change in both C NBR and DF NBR implies that IS responds very rapidly to pressurization and decompression and is therefore an appropriate tool for detecting the effects of H 2 .
The duration of exposure to H 2 affected C NBR (Fig. 5) at frequencies of 90, 1040, and 10,000 Hz during H 2 exposure at a pressure of 10 MPa. Figure 5 is an enlargement of Fig. 4b and shows C NBR as a function of exposure time at the three frequencies. C NBR decreased exponentially with increasing exposure time to H 2 ; this trend is caused by the diffusion of H 2 into the NBR. In many polymers, such diffusion of high-pressure H 2 induces plasticization [13][14][15] , which results in a reduction in the dielectric constant and capacitance. The decrease in the dielectric constant will be discussed later.
The change in the capacitance is expected only depend on the penetrated H 2 content by assuming a first-order approximation. Thus, the evolution of the capacitance was affected by the diffusion-controlled process of H 2 . The content c(t) of H 2 and the change in capacitance, which are the solutions of the diffusion equation, are expressed as follows 11 .
(1) where c(t) is the hydrogen content at time t and c(0) is the equilibrium hydrogen content. D is the diffusion coefficient (diffusivity) with a unit of [m 2 /s]. z and r are the thickness and radius of the disc-shaped specimen, respectively. β n is the root of the zero-order Bessel function. We obtain the diffusion coefficient of H 2 by fitting the data of the capacitance evolution to Eq. (1). The experimental data were well fitted to Eq. (1) by assuming a single-exponential decay of C = C 0 • exp(−AD 1 t) (Fig. 5, solid lines), where C 0 is the capacitance at t = 0, and A is  with z = 2 mm and r = 24.5 mm. The obtained value of D 1 is a diffusion coefficient that depends on frequency (Table 2) for the H 2 penetration into the rubber. Meanwhile, the recovery of the capacitance over time at atmospheric pressure after the decompression of the H 2 pressure of 10 MPa exhibited an exponential increase at all frequencies to maxima that decreased with increasing frequency (Fig. 6). Figure 6 is an enlargement of Fig. 4c and presents C NBR versus time after decompression. The exponential increase over time is a result of H 2 desorption from the rubber by deplasticization after the release of pressure. The evolution of the capacitance was also controlled by the diffusion process of H 2 . An exponential function C = C ∞ • [1 − exp(−AD 2 t)], where C ∞ is a saturated capacitance at infinite time, was also fitted to the data, and the diffusion coefficient D 2 for the H 2 desorption from the rubber was already obtained (Table 2). Single-exponential growth was also assumed for this fit.
The diffusion of H 2 into the rubber saturates at ~12 h during pressurization (Fig. 5), and the clearance from the rubber during decompression takes ~15 h (Fig. 6). D 2 is slightly larger than D 1 ; this difference implies that the H 2 desorption is slower than the absorption; therefore, a hysteretic phenomenon occurs, possibly because H 2 interacts with the polymer chains.
We have also measured the penetrated H 2 content into NBR as a function of time using TDA 11 and electronic balances. According to the results in two methods, it takes about 10 h for the H 2 contents to reach the maximum. This is consistent with the capacitance measurement as shown in Fig. 5. Thus, we could say the long-term change in capacitance is due to slow diffusion of H 2 . The results for decompression of Fig. 6 also shows similar behavior. The temperature and relative humidity were maintained within (23 ± 2) °C and (50 ± 5) %, respectively, in national calibration laboratory. The long-term drift effect on impedance analyser 4294A for several hours with a fresh specimen without H 2 penetration was found to be negligible, which was less than approximately 3% of measured value. Therefore, the additional effects except of H 2 was not included in the measurement.
C NBR (Fig. 6) was transformed to the imaginary part of the impedance, Z im = 1/(ωC) for a comparison with the TDA data. To find a correlation between IS and TDA, Z im normalized by C ∞ was compared with the normalized H 2 content obtained by TDA (Fig. 7). The two results were consistent overall, which implies again that the change in Z im is directly related to the desorbed H 2 content. Such consistency is compatible with previous results obtained with TDA and NMR 16 . However, the IS data show a slower desorption of H 2 than the TDA data (Fig. 7). Although there are unique measurement conditions with different dimensions in both of the specimens, this difference implies that the physics of the dependence of the impedance on the hydrogen content is different from that of the hydrogen diffusion process in the specimen. The TDA measurement only detects the hydrogen content released through the diffusion process. In addition to the effect of the released hydrogen content, IS is also affected by the chemical/physical interaction of hydrogen with the rubber polymer. Furthermore, the IS results may also due to the slow relaxation, i.e., the pressurization-induced state of the polymer matrix, or the fact that the filler distribution slowly relaxes towards another equilibrium and can continue to relax even after all the free H 2 molecules are released during decompression. The relaxation may be irreversible; therefore, the original status cannot be recovered.   Table 2. Diffusion coefficients D 1 and D 2 for pressurization (Fig. 5) and decompression (Fig. 6), respectively, at three frequencies. www.nature.com/scientificreports www.nature.com/scientificreports/ The TDA experimental data (Fig. 7) could not be fitted well with a single exponential function; therefore, a two-exponential fit on the basis of Eq. (1) was employed (Fig. 7, inset)    www.nature.com/scientificreports www.nature.com/scientificreports/ The normalized capacitance C nor was also obtained during cyclic pressurization and decompression under H 2 and Ar gases (Fig. 8). The pressure dependences of C nor were similar at all three frequencies. C nor decreased exponentially as the pressure increased during pressurization and later increased as the pressure decreased during decompression. The behaviours are very similar to those of C NBR versus time (Figs 5 and 6).
The large change in the dielectric constant of the rubber at the low frequency of 40 Hz under high-pressure H 2 (Fig. 8) can be explained by a change in the polarizability of the polymer chain matrix and the fillers, because the H 2 in the rubber region contributes little to the total polarization. The strong frequency dependence of the dielectric constant of the rubber at the low frequency is explained by the polarization arising from the displacement or rotation of the fillers that have a net charge or a net dipole moment in the interface region around the fillers due to the interfacial polarization known as the Maxwell-Wagner-Sillars effect 17,18 .
The decrease in the dielectric constant with the exposure to high-pressure ambient H 2 is expected, because the degrees of freedom of the polymer chain and the fillers decrease as the gas molecules occupy more space. A similar phenomenon was observed by pressurizing with Ar gas (Fig. 8).
According to the COMSOL simulation result C NBR = 0.31 + 8.22ε r , the relative dielectric constant ε r of the rubber sample at a pressure >5 MPa was found to be ~3, which has also been observed in silicon dioxide 19 and many rigid plastic materials, such as epoxy glass 20 and Bakelite 21 . A dielectric constant (~3) smaller than the value in a normal rubber polymer suggests that the decrease in the dielectric constant may occur because, due to the solvent, H 2 causes the formation of a rigid plastic phase or a glass phase. This finding suggests that the penetration of high-pressure H 2 with a low molecular mass in the process of pressurization, which generally induces Figure 10. SEM images of the fresh NBR (a,a') without exposure to hydrogen, NBR (b,b') exposed to H 2 at 10 MPa and NBR (c,c') exposed to Ar at 10 MPa. Left column: image sequences obtained from the same spot; scale bar = 50 μm. Right column: sequences obtained from the same spot at a higher magnification; scale bar = 100 μm. www.nature.com/scientificreports www.nature.com/scientificreports/ plasticization for many polymers [13][14][15] , resulted in a reduction in the dielectric constant and capacitance of the polymers, whereas the increase in C nor during decompression (Fig. 6) was caused by deplasticization after the release of pressure.
The normalized DF NBR was also affected by the pressure during both pressurization and decompression under both H 2 and Ar gases at all three frequencies (Fig. 9). The behaviour was similar to that of C nor under H 2 and Ar gases. The measurement time for Figs 8 and 9 is about 2 h in the process of the pressurization and decompression. In Fig. 9, normalized dissipation factor (DF) value at 40 Hz is −0.06, for the capacitance of 25 pF in Fig. 8. In the case with the value of lowest frequency of 40 Hz and small capacitance under the applied AC voltage of 0.5 V, the magnitude of the measured DF is regarded as very small, because the 40 Hz is the lowest limit of the impedance analyzer 4294 A used and the manufacturer's specification 22 say the uncertainty of DF at this frequency and capacitance level amounts to 10%. Thus, the measured DF is virtually regarded as zero and the negative sign is attributed to the measuring instrument having large uncertainty of DF at low frequency of 40 Hz. However, with increasing the frequency, the uncertainty decreases.
The normalized C NBR and normalized DF NBR were affected more in H 2 than in Ar during cyclic pressurization and decompression under the same pressure conditions (Figs 8 and 9). This difference implies that H 2 has a greater permeation capability than Ar, possibly because of the molecular mass of H 2 . The most remarkable difference between H 2 and Ar was that the recovery of the dielectric constant and the DF after decompression was considerably lower under H 2 than under Ar (Figs 8 and 9). After 124 h of decompression in H 2 , the capacitance and the DF recovered to 40~60% of the initial values, whereas after 150 h of release in Ar, the rubber polymer recovered to 90~100% of the initial capacitance and DF. This failure to recover completely implies that H 2 reacts chemically with the polymer and causes voids, defects, and a scission of the polymer chain, whereas inert Ar gas only causes a scission of the polymer. The SEM results partially support these findings, but further analysis is required.
SEM results. SEM images (Fig. 10) were obtained from the NBR without exposure to H 2 and the NBR specimens exposed to H 2 and Ar at 10 MPa. After exposure to H 2 , the morphology of the NBR (b, b') changed from a random distribution to a uniaxial directed distribution. One possibility is that percolated channelling between low-density regions occurs during the permeation of H 2 gas under 10 MPa of ambient pressure stress and causes a density modulation. In this instance, the distance between the valleys is ~10 μm. The NBR specimen exposed to Ar (c, c') was modified to a circular type of modulation, which is reminiscent of a swollen balloon under gas injection instead of uniaxial channelling. The morphology of the Ar-exposed NBR reveals an Amoeba-like circle without any directional preference. These results demonstrate that different types of gases can result in different morphological responses at the same pressure. Thus we think it causes percolated channelling to an uniaxial directed distribution due to greater permeation than that exposed to Ar. Consequently, H 2 effect on NBR are consistent with that already proposed by IS in views of greater permeation capability, stronger effects on physically and chemically in H 2 more than Ar.
conclusions This paper presents the development and evaluation of an IS system to measure the effects of high-pressure H 2 gas on rubber polymers. The in situ capacitance measurement enables the observation of the correlation between macroscopic and microscopic phenomena under high pressure. The developed IS system could be used as an in situ probe to gather information such as diffusivity in H 2 diffusion and desorption processes in rubber polymers.
Although there is a difference in the time evolutions between IS and TDA, the results of this study indicate that IS may be a useful probe to observe real-time and in situ changes in the H 2 content with time and pressure during pressurization and subsequent decomposition and could supplement the ex situ TDA method and other methods. The proposed IS system could also clarify in situ the effect of the permeation properties of a gas as a function of time and pressure in rubber during sequential pressurization and decompression processes.