1. INTRODUCTION
Gases such as hydrogen, nitrogen, and helium are widely utilized across industrial,
environmental, medical, and research sectors, where their leakage or variations in
concentration can significantly impact safety and process efficiency [1-15]. Hydrogen has gained attention as a next-generation clean energy source, but its
high diffusivity and explosion risk necessitate real-time detection. Nitrogen is essential
for combustion processes and life support systems and requires precise concentration
control in industrial applications. Helium plays a critical role in superconductivity
research, semiconductor manufacturing, aerospace, and vacuum system maintenance, necessitating
highly sensitive leakage detection. Given these characteristics, high-sensitivity
and highly reliable gas sensor technology should be developed to ensure safety and
efficiency.
Gas sensors are extensively employed across various industries, enabling real-time
detection to prevent accidents and optimize processes. Hydrogen sensors are crucial
technology to detect hydrogen leaks in fuel cell vehicles, hydrogen refueling stations,
and industrial storage facilities. Nitrogen sensors are utilized in medical gas monitoring,
semiconductor manufacturing, and food preservation for regulating nitrogen concentration.
Helium sensors are indispensable in semiconductor manufacturing, superconductivity
research, aerospace applications, and high-vacuum system maintenance. As outlined
above, gas sensors are not only vital for industrial safety but also for process control
and environmental monitoring [16-39].
With the activation of the hydrogen economy, hydrogen refueling stations and hydrogen
fuel cell vehicles have proliferated, leading to an increased technical focus on containing
hydrogen gas containment and preventing leakage. Hydrogen detection technologies capable
of precisely analyzing the gas permeability and leakage rates of polymer O-ring materials
thus have become increasingly critical. Alongside this, research on the mechanical
properties, physical stability, and long-term durability of these materials is essential
for ensuring reliable performance in hydrogen systems.
Gas sensors employ various detection methods tailored to the specific characteristics
of each gas, including semiconductor-based [40-42], electrochemical [43-48], catalytic combustion [49-51], non-dispersive infrared (NDIR), fiber optic-based [52,53], gas chromatography [54-59] and gravimetric-based [60-67] sensors. Semiconductor-based sensors are cost-effective and highly durable but suffer
from low selectivity and susceptibility to environmental factors. Electrochemical
sensors offer high sensitivity and accuracy but have a limited lifespan and require
frequent maintenance. Catalytic combustion sensors are advantageous for detecting
flammable gases but are affected by fluctuations of oxygen concentration. NDIR sensors
provide high accuracy and long-term stability but are bulky and costly. Fiber optic
sensors enable ultra-low concentration gas detection with high responsiveness but
require complex and expensive measurement systems. The selection of a sensor should
therefore consider factors such as the target gas characteristics, industrial applicability,
cost, and environmental conditions. Developing highly sensitive and reliable sensors
has become a key challenge in gas safety management.
Conventional gas sensing methods have inherent limitations, highlighting the need
for more effective and reliable measurement techniques. Reducing uncertainties in
gas permeation parameters caused by temperature and pressure variations in laboratory
environments and accurately assessing gas permeability when gases dissolve into materials
are crucial challenges. To address these issues, a volumetric analysis technique with
two capacitive sensors is developed in this study. The performance of the proposed
approach is validated through a comparison with the results of a camera and electrode
sensors. The results demonstrated a high level of consistency between these methods,
confirming the reliability of capacitive measurement in gas permeability measurements.
To overcome the limitations of conventional methods and enhance the accuracy of gas
permeability measurements, an integrated technique combining volumetric measurements
using a graduated cylinder with automated capacitance measurements using a frequency
response analyzer (FRA) interfaced with a PC [57] is proposed in this study. This approach reduces uncertainties in gas permeation
parameter estimation caused by environmental fluctuations in temperature and pressure.
The proposed technique is applied to polymers, specifically nitrile butadiene rubber
(NBR), low density polyethylene (LDPE), and high density polyethylene (HDPE), which
are commonly used as gas sealing materials under high-pressure gas environments. The
solubility, diffusivity, and permeability of the three different gases in these polymers
are analyzed as a function of exposure pressure and compared with results obtained
using different methods with estimation of uncertainty. Additionally, the applicability
of these polymer materials for gas sealing in high-pressure environments is assessed.
2. EXPRIMENTAL
2.1 Sample preparation and gas enriching method
In this study, polymer specimens commonly used as sealing materials in hydrogen refueling
stations and hydrogen fuel cell vehicles were selected for to evaluate the proposed
sensor. The tested polymer materials are NBR, LDPE, and HDPE, with the LDPE and HDPE
specimens supplied by King Plastic Corporation. Each sample was prepared in a sheet
form with a thickness of ~2.4 mm and plane dimensions of 15 mm × 15 mm. However, the
HDPE specimens were provided in a spherical form with a diameter of ~12 mm. NBR specimens
were manufactured by Kumho Petrochemical and prepared as flat cylindrical samples
with a diameter of 14.0 mm and a thickness of ~1.2 mm. The chemical composition of
NBR is displayed in Table 1. Note that the compositions of LDPE and HDPE are omitted in Table 1 because the chemical composition information of King Plastic Corporation is not open
to the public . Sulfur is added as a crosslinker in NBR.
To achieve gas enrichment in the specimens, samples were placed in a stainless steel
(SUS 316) high-pressure chamber with an internal diameter of 50 mm and a height of
90 mm at room temperature, as shown in Figure 1(a). Before gas exposure at the target pressure, a purging process was conducted three
times at 1 MPa to eliminate any residual gases within the chamber. The specimens then
were exposed to the testing gas (H2 or He or N2) in a pressure range from 1 to 10 MPa for 36 hours to ensure complete gas saturation
under high pressure.
After the sample was fully saturated with gas, the valve was opened to release the
pressurized gas from the chamber, allowing the sample to be extracted. As gas began
to release from the sample immediately upon depressurization, the start time was recorded
using a timer. Once the chamber pressure stabilized at atmospheric levels within a
few seconds, the gas release from the sample continued. To minimize gas loss due to
release, the sample was promptly transferred into the upper space of the graduated
cylinder (Figure 1 (b)) (i.e. within 5 to 10 minutes). Emitted gas lost during this loading process was
quantified and compensated for using a self-developed diffusion analysis program.
The methodology for gas loss compensation through this program has been previously
described in our earlier papers [68,69].
2.2 Volumetric measurement system employing semi-cylindrical and coaxial-cylindrical
capacitor electrodes
Figure 1 is a schematic diagram showing the gas enriching chamber with the gas bombe and graduated
cylinder with the changed water level by emitted gas in the polymer specimen. The
gas pressure (P) inside the graduated cylinder in volumetric measurement system is expressed as [57].
where P0 is the external atmospheric pressure outside the cylinder, ρ is the density of distilled water in the water bath, and g is gravitational acceleration. h is the height of the distilled water level inside the graduated cylinder measured
from the water level in the water bath. V is the volumes of gas inside the graduated cylinder filled with gas, as shown in
the upper part of Figure 1(b). The gas inside the cylinder is governed by the ideal gas equation PV = nRT, where R is a gas constant of 8.2×10-5 m3·atm/(mol·K). The total number of moles (n) of gas inside the cylinder is expressed as follows [57].
where n0 is the initial moles of air present already in the cylinder before the gas is released.
After decompression, the gas released from the specimen lowers the water level of
the cylinder. Thus, the increased gas moles (Δn) in the cylinder by the released gas are obtained by measuring the increase in volume
(ΔV) in the graduated cylinder. The relation between the increased gas moles and the
increased volume can be expressed as follows:
The increased number of moles are converted to the corresponding mass concentration
(C(t)) of the gas emitted from the polymer sample as follows:
where mgas is the molar mass of the testing gas. For example, for N2 gas, mN2 gas is 28.01 g/mol. msample is the mass of the sample. The increase in water level (ΔV) by released gas corresponds to the increased gas moles. It can be converted to the
mass concentration of released gas according to Eq. (4). Therefore, the mass concentration over time by released gas can be obtained by measuring
the change in water level, ΔV, versus the time elapsed after decompression.
Figure 2 presents the three-channel volumetric measurement system consisting of three graduated
cylinders and three electrode configurations designed for real-time monitoring of
gas release. The electrode setup comprises two semi-cylindrical electrodes positioned
on the left side and middle part of the cylinder and one coaxial-cylindrical electrode
on the right side of the cylinder.
Following exposure to a high-pressure chamber, the specimen is decompressed and transferred
into the gas space within the graduated cylinder. The three vertically aligned graduated
cylinders are partially submerged in a water bath so that gas emitted from the specimen
can be measured. The semi-cylindrical and coaxial-cylindrical electrodes are connected
in parallel to the capacitance measurement channel of a frequency response analyzer
(FRA, VSP 300). The semi-cylindrical electrodes are affixed externally to the acrylic
tubes on the left and middle channels. Meanwhile, the coaxial-cylindrical electrode
configuration on the right channel consists of one electrode attached to the outer
surface of the acrylic tube and another positioned along the central axis as a rod
electrode.
The high-precision FRA is interfaced with a general-purpose interface bus (GPIB) and
a programmed PC to provide automatic control and real-time detection of temperature
and pressure. The GPIB system, connected to the three measurement channels, automatically
measures the capacitance through the semi-cylindrical and coaxial-cylindrical electrodes,
as illustrated in Figure 2. Water level data are converted from capacitance by pre-correction data in the form
of a polynomial between the capacitance and the water level position. Additionally,
real-time temperature and pressure data collected near the sample are automatically
incorporated into the gas absorption calculations to ensure an accurate permeability
analysis.
The diffusion characteristics of the NBR, LDPE, and HDPE polymer specimens are investigated
using the semi-cylindrical and coaxial-cylindrical capacitors. The results obtained
from the three samples are then compared.
2.3 Structure of semi-cylindrical and coaxial-cylindrical capacitor electrodes
We used two types of capacitive sensors with semi-cylindrical and coaxial-cylindrical
electrodes. The structure of the capacitive electrode sensor made from a semi-cylindrical
electrode mounted on the outside of an acrylic tube is shown in Figure 3 (a). The inner volume of the acrylic tube surrounded by two semi-cylindrical electrodes
is filled with water and gas. The electrodes attached to the outer wall of the acrylic
tube are made from copper with a semi-cylindrical shape and thickness of 1 mm. The
capacitance of the sensor depends on the dielectric constant of the medium present
between the electrodes. The dielectric constant of water is 78.4 times greater than
that of the gas inside the graduated cylinder. Therefore, the positional shift of
the water level in the two electrodes leads to a detectable change in capacitance.
In the case of the semi-cylindrical electrodes, the actual capacitance (Ca) due to water and gas is connected in series with the capacitance (Ctw) of the acrylic dielectric tube wall. The total capacitance (Ct) between the semi-cylindrical electrodes can be expressed as follows:
The actual permittivity εa by water and gas inside the cylinder is given by Eq. (6), and it depends on the volume of the two media.
where Vw is the volume of water in the cylinder, εw is the dielectric constant of water, V0 is the volume of gas in the cylinder, ε0 is the permittivity of the gas, and Vt is the total volume.
The actual capacitance of the semi-cylindrical electrodes is calculated as follows
[9].
where A is the area of the electrode, ε*0 is the dielectric constant in free space, d is the distance between the two electrodes, R is the radius of the graduated cylinder, and Δd is the increment in distance between the curved two electrodes. In this experiment,
all of these variables are constant except for εa in Eq. (7). The capacitance value for the water content is obtained by combining Eqs. (5)-(7). We measured the actual change in capacitance (Ca) with the change in εa occurring at the changing water level position of the graduated cylinder. Thus, the
water level corresponding to the changed capacitance is determined by a pre-calibration
equation between the capacitance and the water level position.
Another capacitive sensor is designed with coaxialcylindrical electrodes in the center
and outside of the acrylic tube, as shown in Figure 3 (b). The acrylic tube is filled with water and gas between the two coaxial electrodes.
The change in capacitance ΔC with respect to the water level, h is given as follows [70].
where h is the water level, L is the length of the cylindrical capacitor, R1 is the radius of the solid cylindrical conductor (electrode 2) made of thin copper
wire, and R2 is the radius of the coaxial cylindrical shells (electrode 1) made of copper plates.
ε0, εw and εg are the dielectric constants of free space, water and gas, respectively.
For a fixed configuration of coaxial cylindrical electrodes, Eq. (8) shows that the second term on the right remains constant. The equation thus shows
that ΔC is linearly related to the change in water level, h. The water level of the coaxial
electrode was also obtained by measuring the change in capacitance using a pre-calibration
equation, similarly to the semi-cylinderical electrode.
The two types of electrodes were used to measure the change in capacitance by the
water level (increased gas volume, ΔV) in the graduated cylinder. The equipment used to measure the capacitance was the
VSP-300 model of Biologics Inc. The capacitance was measured with the VSP-300 and
a PC based on the GPIB system at a frequency of 1MHz.
2.4 Diffusion analysis program for obtaining gas diffusion parameters
Adsorbing gas at high pressure releases the gas dissolved in rubber after it is decompressed
to atmospheric pressure. Assuming that the adsorption and desorption of gas are diffusion
controlled processes, the concentration of gas
C
E
s
h
e
(
t
)
for spherical samples released during the desorption process is expressed as follows
[71,72]:
Eq. (9) is a solution to Fick's second law of diffusion for spherical samples with initially
uniform gas concentrations and constant spherical surface concentrations. C∞ is the gas mass concentration of saturated gas at infinite time or the total gas
uptake released during the adsorption process. D is the diffusion coefficient of desorption and a is the radius of the spherical rubber.
Similarly, the emitted gas content
C
E
c
y
l
(
t
)
for the cylindrical specimen is expressed under the boundary condition; i.e., a uniform
gas concentration is initially maintained and the cylindrical surfaces are kept at
a constant concentration [72,73].
In Eq. (10), l is the thickness of the cylindrical rubber sample, ρ is the radius, and βn is the root of the zero-order Bessel function.
The emitted gas content
C
E
s
h
e
(
t
)
for the sheet shaped sample is expressed as follows[71,72]:
Eq. (11) represents the solution to Fick’s second law of diffusion for a plane sheet specimen,
assuming an initially uniform gas concentration in the material and a constant concentration
maintained at the surface. T is the thickness of the sheet shaped sample.
To analyze the mass concentration data by the complicated formulas given in Eqs. (9), (10), and (11), we developed a diffusion analysis program using Visual Studio to calculate D and C∞, based on least-squares regression [57,73]. Figure 4 illustrates the diffusion analysis program to determine D and C∞ from the gas emission content. In the bottom left side, the information of the material
(sample) shape and its dimension is inserted. In the top right side, the plot of emission
content (wt·ppm) versus time (sec) is represented, where the black solid line is the
amount of measured gas emission. At the middle right side, the list of unknown parameters
1, 2, 3 indicate the D, C∞ and C-offset values with the fitting error, respectively. Unknown parameters of the
sheet shape for LDPE are calculated from Eq. (11) in Figure 4. C-offset is a compensation value corresponding to the loss of emitted gas caused
by the time lag between decompression and the start of measurement after the sample
is loaded. In the plot of emission versus time at the top right side in Figure 4, the yellow solid line is the gas emission curve
C
E
s
h
e
(
t
)
derived via Eq. (11), where the amount of lost emitted gas has been compensated. Finally, D and C∞ are obtained as 2.514×10-11 m2/s and 1612 wt·ppm, respectively.
3. RESULTS AND DISCUSSION
3.1 Sequence to acquire diffusion parameters through pre-calibration process
The gas released from the specimen causes a reduction in the water level with the
elapse of time. When the specimen has fully discharged the gas for a sufficient amount
of time, the decrease in the water level is saturated. By utilizing programmed capacitor
measurements with the capacitive electrodes, the diffusion parameters for the specimens
can be determined from the diffusion analysis program. Figures 5 and 6 illustrate the method for extracting the diffusion parameter in an LDPE sheet shape
using the coaxial and semi-cylindrical electrodes, respectively, through the following
steps:
1) The user records the water level versus the capacitance in the corresponding channel
as the water level decreases. A quadratic regression is then applied to derive a second-degree polynomial that relates
the water level position to the capacitance [as shown in Figures 5(a) and 6(a)]; this polynomial is based on Eqs. (7) and (8). The water level is measured as a pixel unit using a digital camera.
2) Using the pre-calibration data, the measured capacitance values are converted into
the corresponding water level, as depicted in Figures 5(b) and 6(b). In these graphs, the black and blue squares represent the capacitance and water
level positions, respectively, plotted over time. The decrement in water level indicates
the increased gas volume (by emitted gas.
3) The increased gas volume is converted to increased gas moles by Eq. (3). According to Eq. (4), the increased gas moles are converted to the corresponding mass concentrations (C(t)) of the gas emitted from the polymer sample. Finally, by applying Eq. (11) through the diffusion analysis program that employs least-squares regression, the
diffusion parameters D and C∞ are determined, as shown in Figures 5(c) and 6(c).
3.2 Measured diffusion properties of H2, He, and N2 gas for NBR, LDPE, and HDPE
We have investigated pressure dependent diffusion properties of H2, He, and N2 gas for NBR, LDPE, and HDPE. Figure 7 presents representative results of measured volume and gas emission content versus
time after decompression for HDPE, NBR, and LDPE with these three gases. Figure 7(a) presents the H2 results with the coaxial-cylindrical capacitor. Figures 7(b) and (c) give the He and N2 results, respectively, with the semi-cylindrical capacitor. The measured volume (blue
filled circles) on the left side axis of Figure 7 was obtained from the measured capacitance using pre-calibration data. According
to Eqs. (3) and (4), the measured volume is converted into the amount of gas emission (black open squares)
on the right side axis of Figure 7. The blue solid curve represents the fitted line obtained using Eqs. (10)-(11) through the diffusion analysis program. In Figure 7 (a), the determined H2 diffusivity (D) of HDPE is 28.75×10-11 m2/s at 6 MPa H2 gas pressure and the gas uptake (C∞) is 53.13 wt·ppm. In Figure 7 (b), the He diffusivity and uptake of NBR at 7.6 MPa He gas pressure were determined
as D=2.14×10-10 m2/s and C∞=197 wt·ppm, respectively. In Figure 7(c), the N2 diffusivity and uptake of LDPE at 6.4 MPa N2 gas pressure are D=2.50×10-11 m2/s and C∞=1589 wt·ppm, respectively. The results indicate that gas diffusion and desorption
follow a single-mode diffusion process.
Figure 8 shows the gas uptake (C∞) and diffusivity (D) as a function of pressure in the LDPE, HDPE, and NBR polymer specimens with three
gases (H2, He, N2). The results are obtained via two capacitive electrodes. The NBR results with He
and N2 were obtained in our previous investigation [69]. The data acquisition for NBR with H2 gas pressure was carried out using the coaxial-cylindrical electrode. The solid lines
in Figure 8(a) represent the linear fit of the gas uptakes for the exposed pressure with the slope
value. The linear trend shows that the gas uptake (C∞) for all tested polymers increases linearly with pressure, which is consistent with
Henry's Law [74]. This indicates that the amount of gas absorbed by each polymer is directly proportional
to the applied pressure. NBR exhibits the highest gas uptake among the three polymers
across all tested gases, suggesting it has higher solubility compared to HDPE and
LDPE.
Unlike the gas uptake trend, the diffusivity (D) in Figure 8(b) does not exhibit a strong dependence on pressure. Each polymer demonstrates a relatively
constant diffusivity across the tested pressure range. The horizontal solid lines
represent the average diffusivity (Davr) with the values for three samples. The stability of diffusivity across different
pressures suggests that the diffusion mechanism is predominantly controlled by the
intrinsic properties of each polymer rather than external pressure conditions.
Meanwhile, solubility can be determined from the linear slopes in Figure 8(a) as follows [69].
mg is the molar mass of the gas used and d is the density of the specimen. Permeability (P) is determined by the product of diffusivity (D) and solubility (S); i.e., P=DavrS. Davr, S, and P obtained for the NBR, HDPE, and LDPE specimens are represented in Table 2. The investigation results provide a comprehensive comparison of how each polymer
interacts with different gases, which is essential for selecting materials suitable
for specific applications such as gas barriers or gas transmission devices.
3.3 Expanded uncertainty analysis in volumetric measurement system
In our previous analysis of the volumetric measurement system, the main uncertainties
in diffusivity measurements were due to variability in repeated measurements [17,75], changes in sample volume after decompression, and the standard deviation between
experimental data and Eqs. (9)-(11). These uncertainty analysis methods are found in previous research results[76-78]. These uncertainties can be distinguished as type A or type B uncertainty. Type A is statistical uncertainty such as standard deviation among repeated measurement
data. In this paper, the type A uncertainty from repeated diffusivity measurements was determined using three separate
measurements. Type B estimates uncertainty from all information excluding type A.
Type B uncertainty applies a factor according to the shape of a probability density
function. Type B uncertainty excluding the graduated cylinder resolution uncertainty
was calculated by dividing the respective uncertainty by
3
of a rectangular distribution.
Assuming a rectangular distribution, the uncertainty in the mass measurement of sample
was derived from the accuracy of the electronic balance. After the sample was exposed
to high pressure, its dimensions varied by up to 2.5 %. This was used to calculate
the type B uncertainty stemming from inconsistencies in the sample volume. Thus, type
B uncertainty is obtained as 1.4 % by dividing
3
of a rectangular distribution. The standard deviation for gas enrichment data ranged
from 0.5 % to 1.7 %. Therefore, a maximum of 1.7 % corresponds to type B uncertainty
of 1.0 % by applying a rectangular distribution. The graduated cylinder has an accuracy
of 0.5 %, which results in a type B uncertainty of 0.3 %. Furthermore, when using
a graduated cylinder with a 10 mL scale, the smallest readable increment was 0.1 mL
(A 1% relative uncertainty). Given that the resolution was effectively half of this
minimum increment, the type B uncertainty due to resolution was calculated as 0.2
% by dividing
6
corresponding to a triangular distribution.
A manometer is used to measure the exposure pressure with accuracy of 1 % classified
as grade A, and type B uncertainty is determined as 0.6 % by applying a rectangular
distribution. In the laboratory, temperature and pressure fluctuated by ±0.5 °C and
±5 hPa, respectively; however, programmable compensation reduced the resulting type
B uncertainty to less than 0.2 %. Using type A and type B uncertainties, the combined standard uncertainty is obtained with the
root sum square method. Finally, the product of the coverage factor (k=2.1, confidence level of about 95 %) and combined standard uncertainty (uc) is obtained (U=k×uc) to yield the expanded uncertainty (U). Table 3 summarizes the sources of uncertainty along with the expanded uncertainty for the
volumetric measurement system.
3.4 Performance test for two types of capacitive sensors
Table 4 presents the performance test results for the two types of capacitive electrode sensors.
Sensitivity, resolution, stability, detection range, and response time were evaluated
in the performance test. The sensitivity is defined as the slope of the change of
capacitance according to the water level, which corresponds to 4.4 pF/mL for the coaxial-cylindrical
sensor and 1.3 pF/mL for the semi-cylindrical sensor. The resolution corresponding
to the minimum reading value is determined as 0.5 wt·ppm for the coaxial-cylindrical
sensor and 2 wt·ppm for the semi-cylindrical sensor. Stability is defined as the standard
deviation obtained 24 hours after the gas release measurement is completed, and it
was found to be 10 wt·ppm for the coaxial-cylindrical sensor and 15 wt·ppm for the
semi-cylindrical sensor. The maximum length of the electrode determines the maximum
volume of gas that can be measured. Therefore, since the two electrodes have the same
length, both have a detection range of up to 1000 wt·ppm for hydrogen uptake. Response
time was measured as less than 1 second by a GIPB interfaced real-time measurement
system with a frequency response analyzer with a repetition rate of 1 MHz. The above
performance test was already carried out in our previous study [69].
The coaxial-cylindrical sensor outperforms the semi-cylindrical sensor in terms of
sensitivity, resolution, and stability, and thus is a more accurate and reliable choice
for detecting changes in capacitance due to gas diffusion. Its higher sensitivity
and better resolution are particularly advantageous when precise measurement is critical.
However, both sensors offer a similar detection range and quick response time, indicating
that both are suitable for real-time monitoring applications.
3.5 Comparison of measured results determined by different methods
Figures 9 (a) and (b) shows the representative N2 gas uptake (C∞) and diffusivity (D), respectively, for LDPE at 6.4 MPa. These values were compared with the results
obtained by the semi-cylindrical and coaxial-cylindrical electrode with the VSP-300
and a manual digital camera. The error bar indicates the extended uncertainty for
each method. The average value of the gas uptake of LDPE calculated by four measurements
is 1616 wt·ppm and the relative standard deviation is 1.1 %. The average value of
the diffusion coefficient is 2.59×10-11 m2/s and the standard deviation is 3 %. The results obtained from the semi-cylindrical
and coaxial electrodes and the manual camera in each experiment agree well.
4. CONCLUSION
A volumetric measurement system incorporating two types of capacitive sensors (coaxial-cylindrical
and semi-cylindrical electrodes) to analyze gas transport properties in polymers was
successfully developed and its performance was evaluated in this study. The diffusion,
solubility, and permeability of hydrogen, helium, and nitrogen gases were measured
in three polymer materials—NBR, LDPE, and HDPE. Diffusion parameters were determined
using a self-developed analysis program based on Fick’s Law, enabling precise calculations
of diffusion coefficients (D) and gas uptake (C∞). The results confirmed that the gas transport properties adhered to a single-mode
diffusion process, with data consistency verified across both sensor types and conventional
camera-based measurement techniques.
In performance tests the coaxial-cylindrical sensor outperformed the semi-cylindrical
sensor in terms of sensitivity (4.4 pF/mL), resolution (0.5 wt·ppm), and stability
(<10 wt·ppm). Both sensor types exhibited rapid response times of under one second
and were capable of detecting gas concentrations up to approximately 1000 wt·ppm for
H₂. Additionally, the expanded uncertainty analysis demonstrated that the coaxial-cylindrical
sensor provided superior accuracy in measuring changes of capacitance, and is therefore
more suitable for precise detection of gas diffusion properties. This performance
advantage is attributed to the coaxial sensor's enhanced sensitivity to changes in
the water level due to gas emissions.
Overall, the capacitive sensor-based measurement technique proved to be robust and
reliable for evaluating gas transport properties, even under varying experimental
conditions. The findings suggest that the coaxial-cylindrical sensor is the preferable
option for applications requiring high sensitivity and precision in gas permeation
measurements. In conclusion, the proposed measurement system, utilizing both coaxial-cylindrical
and semi-cylindrical capacitive sensors, provides a viable, accurate, and rapid approach
for analyzing gas transport properties in polymeric materials, offering significant
potential for future applications in materials science and industrial research.