# Determination of Gas Permeation Properties in Polymer Using Capacitive Electrode Sensors

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}, He, N

_{2}, and Ar, that are absorbed in polymers. Simultaneous three-channel real-time techniques for measuring the sorption content and diffusivity of gases emitted from polymers are developed after exposure to high pressure and the subsequent decompression of the corresponding gas. These techniques are based on the volumetric measurement of released gas combined with the capacitance measurement of the water content by both semi-cylindrical and coaxial-cylindrical electrodes. This minimizes the uncertainty due to the varying temperature and pressure of laboratory environments. The gas uptake and diffusivity are determined as a function of the exposed pressure and gas spices in nitrile butadiene rubber (NBR) and ethylene propylene diene monomer (EPDM) polymers. The pressure-dependent gas transport behaviors of four different gases are presented and compared with those obtained by different techniques. A linear correlation between the logarithmic diffusivity and kinetic diameter of molecules in the gas is found between the two polymers.

## 1. Introduction

^{−11}m

^{2}/s and with a thickness above 3 mm, it takes at least a few days to reach the adsorption/desorption equilibrium and then complete the permeation measurement. Furthermore, the variation in both temperature and pressure across the days affects measurements of aspects such as the gas volume and then increases the uncertainty in the determination of permeation parameters. Thus, the instability due to temperature and pressure should be minimized to achieve precise measurement and compensation.

## 2. Experimental Aspects

#### Sample Preparation and Gas Exposure Conditions

_{2}gas exposure. N

_{2}gas charging for 48 h is needed to attain the equilibrium state for N

_{2}sorption because of its slow diffusion rate. After exposure to gas, the valve was opened and the gas in the chamber was released. After decompression, the elapsed time was recorded from the moment (t = 0) at which the high-pressure gas in the chamber was reduced to atmospheric pressure when the time was set to zero. Since the specimen was loaded in the graduated cylinder after decompression, it took approximately 5–10 min to start the measurement. The gas content emitted for the inevitable time lag could be measured later by offset determination via the simulation.

## 3. Two Types of Capacitor Electrodes to Measure the Water Level

#### 3.1. Semi-Cylindrical Capacitor Electrode

_{a}) due to water gas is connected in series with the capacitance (C

_{tw}) of the acrylic dielectric tube wall. The total capacitance (C

_{t}) between the semi-cylindrical electrodes can be expressed as:

#### 3.2. Coaxial-Cylindrical Capacitor Electrode

_{1}is the radius of the solid cylindrical conductor (electrode 2) made of thin copper wire, and R

_{2}is the inner radius of the coaxial cylindrical shell (electrode 1) made of copper plate. ${\epsilon}_{0,\text{}}{\epsilon}_{w},\text{}$and ${\epsilon}_{g}$ are the permittivity of free space, water, and gas, respectively.

## 4. Volumetric Analysis Measurement System

#### 4.1. Volumetric Measurement of Emitted Gas

^{−5}m

^{3}·atm/(mol·K).

_{2}gas, ${m}_{H2\text{}gas}$ is 2.016 g/mol. ${m}_{sample}$ is the mass of the specimen. By measuring the change in the water level ($\mathsf{\Delta}V$), we obtained an increased number of moles and thus transformed the mass concentration of the emitted gas. Therefore, the time-dependent mass concentration by released gas can be obtained by measuring the water level change, $\mathsf{\Delta}V,\text{}$versus the time elapsed since decompression. The water level data were transformed from the capacitance by the precalibration data of the polynomial form between the capacitance and the position of the water level.

#### 4.2. Time-Dependent Emitted Gas Concentration versus Specimen Shape

#### 4.3. Diffusion Parameter Analysis through Programmed Capacitance Measurement

- (a)
- To obtain the precalibration data, the user measures the water level versus the capacitance at the corresponding channel with decreasing water levels. Then, the 2nd polynomial equation related to the position of the water level and capacitance is obtained by quadratic regression, as shown in Figure 3a. The 2nd polynomial equation originates from Equation (4). The position of the water level is measured by a digital camera.
- (b)
- According to the precalibration data, the capacitance is transformed to the water level, as shown in Figure 3b. The black and blue squares correspond to the capacitance and position of the water level, respectively, versus the time elapsed.
- (c)
- Last, the diffusion parameters D$\text{}\mathrm{and}$ ${C}_{\infty}$ are determined using a diffusion analysis program by applying Equation (10) based on least-squares regression, as shown in Figure 3c.

## 5. Results and Discussion

#### 5.1. Stability Test of the Volumetric Measurement System

#### 5.2. Pressure Dependence on the Permeation Parameter

^{2}> 0.990, as indicated by the black and blue lines in Figure 8a for NBR, and black, blue, and gray lines in Figure 9a for EPDM. This implies that gas does not dissociate and penetrates into the specimen as a gas molecule. The slopes in the two specimens indicate Henry’s law of solubility. As shown in Figure 8b, the diffusivity does not represent a distinct pressure dependency. Thus, we take the average diffusivity, as indicated by the black and blue horizontal lines. Meanwhile, Figure 9b shows that the diffusivity decreases as the pressure increases above 6 MPa, except for H

_{2}diffusivity. This may be ascribed to the bulk diffusion associated with the mean free path, which is normally observed for high-pressure gas diffusion. The error bars indicate the relative expanded uncertainty of 10%, as evaluated in previous research. At pressures below 6 MPa in Figure 9b, we also take the average diffusivity, as indicated by black and blue horizontal lines. As shown in Figure 8 and Figure 9, no dependence of the permeation parameters on the thickness in cylindrical-shaped NBR and EPDM was observed.

_{g}is the molar mass of gas used, and d is the density of the rubber. The permeabilities of the four gases in the NBR and EPDM polymers are obtained from the solubility and the average diffusivity by using the relation of P = D

_{ave}S. The permeation parameters for four gases in NBR and EPDM are summarized with those obtained by different methods in Table 1.

_{2}gas are consistent with those in the present experimental investigation within expanded uncertainty.

_{He}> D

_{H2}> D

_{Ar}> D

_{N2}and P

_{He}> P

_{H2}> P

_{Ar}> P

_{N2}in both NBR and EPDM. Although there are many factors affecting the permeation parameters of rubber, we focus on the molecule size in the gas. The size of the permeant molecule affects the diffusivity. As the effective size of the molecule increases, the diffusivity decreases. As expected for both NBR and EPDM (Figure 10a), we found a linear correlation with a squared correlation coefficient of R

^{2}> 0.90 between the logarithmic diffusivity and kinetic diameter of the molecules in the gas, which is the size of the sphere of influence that can lead to a scattering event and is also related to the mean free path of molecules in a gas [24,25].

_{c}). The relationship between gas solubility and the critical temperature is generally expressed as [26,27]:

_{c}

_{2}gas, which deviates from linearity. A similar relationship was reported for polyvinylpyridine film [27].

## 6. Conclusions

_{2}, He, N

_{2}, and Ar. This simple and effective method combines a volumetric measurement using a graduated cylinder with water level detection by capacitance measurement with two different types of electrodes in real time. This technique is able to simultaneously evaluate three sets of diffusion characteristics of gas by quantitatively analyzing the amount of gas released after high-pressure gas charging and subsequent decompression. With the autoreading and autocontrol of temperature and pressure sensors, fluctuations due to variations in the temperature and pressure of the laboratory environment were removed, resulting in good-quality permeation data. The results achieved for polymers demonstrate that the H

_{2}permeation properties determined by the developed method are in agreement with those determined by the differential pressure method and gas chromatography.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Configuration of the semi-cylindrical capacitor electrode, indicated in blue. (

**b**) Configuration of the coaxial-cylindrical capacitor electrode.

**Figure 2.**Schematic diagram of the three-channel volumetric measurement system in which three cylinders are standing. The blue part indicates the distilled water filling the water containers and cylinders. A frequency response analyzer GPIB interfaced with a PC at three channels is employed for automatic real-time capacitance measurement with both semi-cylindrical and coaxial-cylindrical electrodes.

**Figure 3.**A sequence acquiring diffusion parameters measured for a NBR cylindrical rubber by employing coaxial-cylindrical electrodes in a frequency response analyzer. (

**a**) Precalibration data expressed as a 2nd polynomial equation between the water level and capacitance by quadratic regression, (

**b**) water level transferred from the capacitance with black and blue squares corresponding to the capacitance and transformed water level, respectively, versus time and (

**c**) diffusion parameters D$\text{}\mathrm{and}$ ${C}_{\infty}$ determined using a diffusion analysis program by application of Equation (10). The blue line is the total compensated emission curve restoring the missing content due to the lag time.

**Figure 4.**A sequence acquiring the diffusion parameter in NBR cylindrical rubber by employing a digital camera without precalibration. (

**a**) Water level versus time after decompression and (

**b**) diffusion parameters D$\text{}\mathrm{and}$ ${C}_{\infty}$ determined using a diffusion analysis program. The blue line is the total compensated emission curve restoring the missing content due to the lag time.

**Figure 5.**A sequence acquiring diffusion parameters measured for EPDM cylindrical rubber by employing semi-cylindrical capacitor electrodes in a frequency response analyzer. (

**a**) Precalibration data expressed as a 2nd polynomial equation between the water level and capacitance by quadratic regression; (

**b**) water level transformed from the capacitance, where black and blue squares correspond to the capacitance and transformed water level, respectively, versus elapsed time; and (

**c**) diffusion parameters D$\text{}\mathrm{and}$ ${C}_{\infty}$ determined using a diffusion analysis program by the application of Equation (10). The blue line is the total compensated emission curve restoring the missing content due to the lag time.

**Figure 6.**Sequence of acquiring the diffusion parameter in EPDM cylindrical rubber by employing a digital camera without precalibration. (

**a**) Water level versus time after decompression and (

**b**) diffusion parameters D$\text{}\mathrm{and}$ ${C}_{\infty}$ determined using a diffusion analysis program. The blue line is the total compensated emission curve restoring the missing content due to the lag time.

**Figure 7.**Stability for volumetric measurement with variations in the temperature and pressure over three days.

**Figure 8.**(

**a**) Gas uptake (${C}_{\infty}$) and (

**b**) diffusivity (D) versus exposed pressure for four gases in cylindrical-shaped NBR with different thicknesses. R and T indicate the radius and thickness, respectively, of cylindrical-shaped NBR.

**Figure 9.**(

**a**) Gas uptake (${C}_{\infty}$) and (

**b**) diffusivity (D) versus exposed pressure for four gases in cylindrical-shaped EPDM with different thicknesses and spherical-shaped EPDM. R indicates the radius of cylindrical-shaped and spherical-shaped EPDM. T indicates the thickness of the cylindrical-shaped EPDM.

**Figure 10.**(

**a**) A linear correlation between the logarithmic diffusivity and kinetic diameter and (

**b**) a linear correlation between the logarithmic solubility and kinetic diameter of molecules in gas.

Specimen | Solubility (mol/m^{3}·MPa) | Diffusivity (×10^{−11} m^{2}/s) | Permeability (mol/m·s·MPa, ×10 ^{−10}) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

H_{2} | He | N_{2} | Ar | H_{2} | He | N_{2} | Ar | H_{2} | He | N_{2} | Ar | |

NBR | 34.2 (35.3) | 8.96 | 11.0 | 22.5 | 5.60 (6.50) | 21.5 | 1.14 | 2.01 | 19.2 (22.8) | 19.3 | 1.25 | 4.53 |

EPDM | 25.6 (26.2) [23] | 7.79 | 17.0 | 38.6 | 19.7 (24.1) [23] | 83.1 | 7.24 | 10.5 | 50.3 (63.1) [23] | 64.8 | 12.3 | 40.4 |

Parameter | Coaxial-Cylindrical | Semi-Cylindrical |
---|---|---|

Sensitivity | ~3 pF/mL | ~1 pF/mL |

Resolution | ~0.5 wt·ppm | ~2 wt·ppm |

Stability | <10 wt·ppm | <15 wt·ppm |

Detection range | ~max 1000 wt·ppm for H_{2} | ~max 1000 wt·ppm for H_{2} |

Response time | <1 s | <1 s |

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**MDPI and ACS Style**

Jung, J.; Kim, G.; Gim, G.; Park, C.; Lee, J.
Determination of Gas Permeation Properties in Polymer Using Capacitive Electrode Sensors. *Sensors* **2022**, *22*, 1141.
https://doi.org/10.3390/s22031141

**AMA Style**

Jung J, Kim G, Gim G, Park C, Lee J.
Determination of Gas Permeation Properties in Polymer Using Capacitive Electrode Sensors. *Sensors*. 2022; 22(3):1141.
https://doi.org/10.3390/s22031141

**Chicago/Turabian Style**

Jung, Jaekap, Gyunghyun Kim, Gahyoun Gim, Changyoung Park, and Jihun Lee.
2022. "Determination of Gas Permeation Properties in Polymer Using Capacitive Electrode Sensors" *Sensors* 22, no. 3: 1141.
https://doi.org/10.3390/s22031141