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A compact hydrogen sensor based on the fiber-optic Fabry-Perot interferometer
Optics and Laser Technology 124 (2020) 105995
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A compact hydrogen sensor based on the fiber-optic Fabry-Perot interferometer
T
⁎
Xinlei Zhoua, , Fengxiang Mab, Haitao Linga, Binjun Yua, Wei Pengc, Qingxu Yua a
School of Optoelectronic Engineering and Instrumentation Science, Dalian University of Technology, Dalian 116024, China Electric Power Research Institute of State Grid Anhui Electric Power Co., Ltd., Hefei, Anhui 230601, China c School of Physics, Dalian University of Technology, Dalian 116024, China b
H I GH L IG H T S
fiber-optic hydrogen sensor based on the F-P interferometer is present. • AA compact time of 185 s and a sensitivity of 1.4 nm/% are obtained. • A response of 500 ppm and a good repeatability have been demonstrated. • Theresolution • sensor is compact, easy in fabrication, low cost.
A R T I C LE I N FO
A B S T R A C T
Keywords: Hydrogen sensors Fiber-optic Fabry-perot interferometer Pd film
We report an optical fiber hydrogen sensor based on the Fabry-Perot interferometer formed by inserting two ceramic ferrules, one with a flat fiber end facet and the other with a commercial Pd film on their tip, into a matched ceramic sleeve. The response time and sensitivity of the proposed hydrogen sensor are investigated both theoretically and experimentally. A response time of 185 s and a sensitivity of 1.44 nm/% have been obtained. In addition, the resolution and repeatability are investigated experimentally. A resolution of 500 ppm and a good repeatability have been demonstrated. The proposed sensor is compact, easy in fabrication, low cost and has a high potential for hydrogen detection.
1. Introduction Hydrogen gas (H2) has widespread applications in petroleum, chemical, and aerospace industries, and has been extensively investigated as an environmentally responsible, renewable fuel that has the potential to alleviate the global warming problem associated with fossil fuel consumption [1–5]. However, H2 has inherent difficulties in its use due to its high diffusion coefficient (0.16 cm2/s in the air), low spark ignition energy (0.02 mJ), high combustion heat (285.8 kJ/mol), tendency to leakage, and a wide flammable range (4–75%). Since H2 is odorless, colorless, and tasteless, it is undetectable by human senses. Thus, sensitive, accurate, and cheap reliable hydrogen sensors are urgently needed to ensure the safety in H2 usage, transportation and storage. In the past decades, a variety of technologies have been introduced to detect H2 by using mechanisms based on mechanical, thermal, acoustical, electrical, or optical reactions [6,7]. Compared to other methods, fiber-optic based sensors promise to be sensitive, reliable, and ⁎
immune to electromagnetic interference, which makes them an excellent candidate for operating in explosive environments [8–11]. There is no risk of gas ignition since the optical sensor has no electrical contacts and does not generate sparks nor relies on heat exchanges. Numerous optical fiber hydrogen sensors have been successfully demonstrated. According to the measurement method, optical fiber hydrogen sensors can be divided into four main types: intensity-based hydrogen sensors [12,13], fiber grating-based hydrogen sensors [14,15], surface plasmon resonance-based hydrogen sensors [16,17] and interferometer-based hydrogen sensors [18,19]. Each type of sensor has its advantages and disadvantages. Compared with other types of hydrogen sensors, the interferometer-based hydrogen sensor possesses a more flexible and simple structure and high sensitivity. However, the fabricating process of the interferometer-based hydrogen sensors are usually complicated and/or expensive instruments are needed. For instance, Wang et al. proposed an EFPI hydrogen sensor, in which the FPI cavity is fabricated by femtosecond laser micromachining near the fiber end [18]. However, the needed femtosecond laser is expensive. Ma
Corresponding author. E-mail address: [email protected] (X. Zhou).
https://doi.org/10.1016/j.optlastec.2019.105995 Received 11 October 2019; Received in revised form 8 November 2019; Accepted 1 December 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 124 (2020) 105995
X. Zhou, et al.
et al. present a miniature fiber-optic hydrogen sensor with a low detection limit of ~20 ppm and a short response time of 18 s by using a suspended Pd-decorated graphene [19], but the sensor fabrication process is complicated. In most optical-based sensing devices, palladium (Pd) is frequently utilized as the sensing material due to its high sensitivity and selectivity towards H2 and good reversibility [20,21]. So far, a variety of preparation methods for Pd films have appeared, including magnetron sputtering, sol-gel method, chemical vapor deposition, electroplating, and electroless plating, etc. Nevertheless, all these methods are complicated, time-consuming, and/or need expensive commercial instruments. In this paper, we propose a hydrogen sensor based on commercial Pd films and fiber-optic ceramic ferrules. The fabrication process of the proposed sensor is relatively simple and does not need complicated and expensive instruments. The structure, principle and fabrication process are introduced in Section 2. Then, we present the theoretic analysis and simulation results in Section 3. At last, in Section 4, the sensor’s performance is studied experimentally.
Fig. 2. The hydrogen single-side diffusion model.
3. Modeling and simulations 3.1. Response time To analyze the response time, we establish a hydrogen single-side diffusion model, in which the substrate that supports the Pd film cannot be penetrated by hydrogen. This model, as shown in Fig. 2, consists of hydrogen dissociating on the Pd film surface, diffusing in the inner Pd film, and restraining on the Pd-substrate interface [25]. As this is a diffusion-limited reaction in one dimension, we established a coordinate system with its origin at the center of the H2-Pd interface. The x-axis is perpendicular to the film surface. Based on the Fick’s second law, the H concentration satisfies [25]:
2. Principle The schematic of the proposed Fabry-Perot interferometer (FPI) based hydrogen sensor is shown in Fig. 1. Similar to the configuration of the fiber-optic connector, we insert two ceramic ferrules, one with a flat fiber end facet and the other with a commercial Pd film on their tips, into a matched ceramic sleeve to form the FPI. The ceramic sleeve act as a collimator to ensure the two ceramic ferrules parallel and coaxial. The flat fiber end facet and the Pd film surface act as two reflective mirrors and form the low-finesse F-P cavity. The low-finesse FPI can be approximately equivalent to the twobeam interferometer. The FPI works as a reflective device and its reflective optical intensity can be expressed as [22,23]:
I = I1 + I2 + 2I1 I2 cos(ϕ)
∂C (x , t ) ∂2C (x , t ) =D ∂t ∂x 2
(2)
where C(x,t) is the H concentration, which is a function of the time t and the position x in the Pd film. D is the diffusion coefficient of the H in the Pd film. As the H concentration in the Pd film is 0 before the Pd-H2 reaction, we get the initial condition: C(x,0) = 0. On the other hand, the H concentration on the Pd-H interface, Cs, determined by the H2 concentration in the surrounding environments, can be regarded as a constant concentration as the H2 are dissociated continuously into H when they contact with the Pd film. Thus, we get the first boundary condition: C(0,t) = Cs. The H diffuses to the opposite direction when they reach the Pd–substrate interface, which is similar to the reflection of a flat mirror. The concentration gradient of the incident H is equal to that of the reflected one. Thus, we have the second boundary condition: ∂C (x , t ) = 0 , where L is the thickness of the Pd film. ∂x
(1)
where I1 and I2 are intensities of the two reflected beams, respectively. ϕ = 4πd /λ is the phase difference of the two reflective beams, λ is the light wavelength, d is the cavity length of the FPI defined by the separation between the fiber end facet and the Pd film surface. The hydrogen concentration can be detected by monitoring the change in cavity length (Δd ) of the FPI, which is caused by the interaction between sensitive film (Pd film) and H2. When H2 appears near the Pd film, it will be dissociated into atomic hydrogen (H). The dissociated hydrogen atoms diffuse into the Pd film and form PdHx until reaching equilibrium, where x represents the atomic ratio of H to Pd. The Pd-to-PdHx transition causes the expansion of the Pd lattice, which reduces the cavity length d. The reduction in the cavity length results in the wavelength shift of the reflection spectrum and can be demodulated using a vernier-like demodulation algorithm with a subnanometer resolution [23,24]. Consequently, the H2 concentration encoded in the Pd film expansion can be extracted by measuring the change in cavity length (Δd ) of the FPI.
x=L
Solving Eq. (2) by using the Fourier method, we can get:
4 ⎛ C (x , t ) = Cs ⎜1 − π ⎝
∞
∑ m=1
(2m − 1) π , 2η0
1 ⎞ sin(μ 2m − 1 η) exp(−μ22m − 1)⎟ 2m − 1 ⎠ x Dt
L Dt
(3)
η= , η0 = . Eq. (3) shows the conwhere μ 2m − 1 = centration distribution of H as a function of the position x at any time, whose right-hand side can be expanded as follows:
Fig.1. (a) structure diagram and (b) 3D view of the FPI based hydrogen sensor. 2
Optics and Laser Technology 124 (2020) 105995
X. Zhou, et al.
C (x , t ) = Cs ⎜⎛1 − ⎝
(
= Cs 1 −
4 π
4 π
∞
∑ m=1
1 2m − 1
πx
sin( 2L ) exp( −D
sin
π 2t ) 4L2
(
−
(2m − 1) πm 2L 41 π3
) exp (−D
3πx
) ⎞⎠ ) − ··· )
(2m − 1)2π 2t 4L2
sin( 2L ) exp( −D
9π 2t 4L2
⎟
(4)
We choose the first two terms of the infinite series as the approximation of H concentration distribution, that is:
4 πx π 2t 41 3πx 9π 2t C (x , t ) ≈ Cs ⎛1 − sin( ) exp(−D 2 ) − sin( ) exp(−D 2 )⎞ π 2L 4L π3 2L 4L ⎠ ⎝ (5) ⎜
⎟
with a truncation error of:
4Cs π
δ=
∞
∑ m=3
1 (2m − 1) πx ⎞ (2m − 1)2π 2t ⎞ sin ⎛ exp ⎛−D 2m − 1 2 L 4L2 ⎠ ⎝ ⎠ ⎝ ⎜
⎟
(6)
In the actual measurement, the hydrogen sensor response to the average change of the Pd film. The average concentration of H in the Pd film along the x-axis direction can be expressed as:
C ¯(t ) =
L ∫0 C (x , t ) dx
π 2t 8 8 1 9π 2t ≈ Cs ⎛1 − 2 exp(−D 2 ) − 2 exp(−D 2 )⎞ π L π 4 9 4L ⎠ ⎝ (7) ⎜
L
Fig. 3. Percentage of response versus time with different film thicknesses.
⎟
We can see that the average hydrogen concentration in the Pd film only depends on the time t and film thickness L and not on the position x. Then, we denote η as the percentage of response to represent the completion level of the Pd-H reaction, which can be expressed as:
C ¯(t ) π 2t 8 8 1 9π 2t = 1 − 2 exp(−D 2 ) − 2 exp(−D 2 ) Cs π π 9 4L 4L
η=
(8)
We can see that η is an exponent function of the time t. Only when t approaches infinity can the η reach 100% and the reaction between Pd film and H reaches equilibrium. In the actual measurement, we define the response time tR as the time range from the start of the reaction to 90% of the completed reaction level. Therefore, the tR satisfies:
η≈1−
8 π 2t 8 9π 2tR ⎞ exp ⎛−D 2R ⎞ − exp ⎛−D = 90% 2 2 π 4L ⎠ 9π 4L2 ⎠ ⎝ ⎝ ⎜
⎟
⎜
⎟
(9)
Fig. 4. Percentage of response versus time with different diffusion coefficients.
The typical value of the tR changes within several seconds to tens of minutes. Thus, the second-order term in Eq. (9) is much smaller than the first-order term and can be neglected. So Eq. (9) can be approximated to:
8 π 2t exp ⎛−D 2R ⎞ = 90% 2 4L ⎠ π ⎝
1−
⎜
According to the simulation results in Fig. 4, it can be concluded that the response time is 507 s, 383 s, 306 s, 253 s for diffusion coefficients of 6 μm2/s, 8 μm2/s, 10 μm2/s, 12 μm2/s, respectively. The results in Figs. 3 and 4 show that, with the decrease of the film thickness and the increase of the diffusion coefficient, the response time reduces greatly, which is consistent well with the indication of the Eq. (11). In addition, we notice that the start value of the percentage of response is not 0 at the time of 0 s in Figs. 3 and 4. This is because of the truncation error, as shown in Eq. (6).
⎟
(10)
Solving Eq. (10), we can have:
tR =
4L2 π2 L2 ln ≈ 0.85 Dπ 2 80 D
(11)
We can see that, from Eq. (11), the response time tR depends on the film thickness L and diffusion coefficient D. Decreasing film thickness and increasing diffusion coefficient can reduce the response time. First, varying the thickness of Pd film, L = 400, 600, 800, 1000 nm, is proposed to study the influence of thickness on the response time. We suppose the diffusion coefficient D as 10 μm2/s. The percentage of response based on Eq. (8) is displayed in Fig. 3. The figure illustrates that the percentage of response rises as the reaction time increases and that the thinner the Pd film is, the earlier the reaction complete. From Fig. 3, we can see that, when the percentage of response reaches 90%, the corresponding response time is 136 s, 306 s, 542 s and 846 s for the thickness of 400 nm, 600 nm, 800 nm and 1000 nm, respectively. Then, the influence of diffusion coefficient D on the response time is investigated. Varying diffusion coefficient D = 6 μm2/s, 8 μm2/s, 10 μm2/s, 12 μm2/s, with a thickness of 60 μm, we get the percentage of response based on Eq. (8), as shown in Fig. 4.
3.2. Sensitivity For the proposed FPI-based hydrogen sensor, we define the sensitivity S as:
S=
Δd (nm /%) ΔC
(12)
where Δd is the change in cavity length, C is the hydrogen concentration and ΔC is the change in hydrogen concentration. The change in cavity length is induced by the strain in Pd film due to its expansion after absorbing H. Thus, we have:
Δd = −ΔL = −L·εPd
(13)
where εPd is the strain in the Pd film, L is the thickness of the Pd film. On the other hand, the strain in Pd film due to absorbing hydrogen can be expressed as [26]: 3
Optics and Laser Technology 124 (2020) 105995
X. Zhou, et al.
At first, only N2 is filled into the test chamber, followed by filling H2 with a fixed concentration until the cavity length response tends to steady. Then, H2 is shut off and, again, only N2 is filled into the gas chamber to allow the sensor to restore. We continuously record the cavity length of the hydrogen sensor (Pd film’s thickness: 70 μm) with a time interval of 1 s. The temporal response of the change in cavity length is shown in Fig. 7(a) as the H2 concentration increases from 0 to 10%. It can be seen from Fig. 7(a) that the original value of the cavity length has a tendency to increase, which is caused by the temperature influence. To eliminate the temperature influence, we connect an FBG in series with the F-P hydrogen sensor. The FBG detects the ambient temperature and can be used to eliminate the temperature cross-sensitivity as we have done in our previous work [23,27]. Fig. 7(b) shows the temporal response of the change in cavity length after eliminating the temperature influence. We can see that the original value of the cavity length keeps steady showing that the proposed hydrogen sensor has good recoverability. Additional, at 8% H2 concentration, the sensor’s response time is estimated to be 185 s as shown in the inset of Fig. 7(b). As we mentioned previously, thicker Pd films can improve the sensor’s sensitivity, but at the expense of the response speed. To verify this, the temporal responses of the sensors with Pd thickness of 100 μm, 85 μm, 75 μm, and 70 μm are investigated experimentally and the results are shown in Fig. 8. By linear fitting, we can get the sensitivity (slope) is 1.44 nm/%, 1.23 nm/%, 1.06 nm/% and 0.99 nm/% for the Pd film thickness of 100 μm, 85 μm, 75 μm and 70 μm, respectively. However, the response time is calculated as 401 s, 240 s, 200 s and 185 s for the Pd film thickness of 100 μm, 85 μm, 75 μm and 70 μm, respectively. Compared with the simulated results shown in Fig. 5, the sensitivity we get here is smaller. The main reason is that we assume the percentage of response reaches 100% in the simulation while in the experiments the percentage of response does not. Additional, some errors in experiments, such as the value of the hydrogen concentration and Pd film thickness, will also lead to differences between simulated results and experimental results. During the measurements, the whole temperature change is 1 °C, from 21 °C to 22 °C. The overall cavity length change is about 1.3 nm as shown in Fig. 7(a). Considering the sensitivity of the sensor, the influence of the temperature change on the concentration is 0.9%/°C, 1%/ °C, 1.2%/°C and 1.3%/°C for the Pd film thickness of 100 μm, 85 μm, 75 μm and 70 μm, respectively. Then we investigate the resolution of the hydrogen sensor. The result is shown in Fig. 9. Taking the standard deviation (SD) as the sensor resolution, a resolution of 0.08 nm for the cavity length has been obtained. Considering the sensitivity of the sensor (1.44 nm/%), a resolution of 5.5 × 10−4 (500 ppm) for the hydrogen concentration measurement is achieved. At last, the repeatability of the sensor is tested. The hydrogen sensor with a Pd film thickness of 85 μm is exposed to the hydrogen environment with a concentration of 6% for 5 times. The change in the cavity length for the 5 measurements are recorded as 7.74 nm, 7.54 nm, 7.63 nm, 7.77 nm, and 7.56 nm, which proves that the proposed hydrogen sensor has a good repeatability.
(14)
εPd = 0.026x
where x is the hydrogen content in the Pd film (i.e. the atomic ratio of H to Pd). The relationship between the hydrogen content and the partial pressure of the hydrogen follows the Sievert’s law: (15)
P = Kx
where P is the hydrogen partial pressure and K is the Sievert’s coefficient (K = 350 Torr1/2 = 4.36 Pa1/2). Combining Eqs. (13)–(15), we have:
Δd = −ΔL = −L·εPd = −0.026L
P K
(16)
When the reaction between H2 and Pd goes under atmospheric pressure (0.1 MPa), we can get the relationship between the hydrogen partial pressure and the hydrogen concentration:
P = 0.1 × 106·C (Pa)
(17)
Then we have:
Δd = ΔL = 0.026L·
0.1·106·C = 0.002·L· C K
(18)
Fig. 5 shows the change in cavity length Δd varies with hydrogen concentration C with different thicknesses of Pd film. The negative value means the cavity length decrease as the hydrogen concentration increase. The slope of the curve in Fig. 5 represents the sensitivity of the hydrogen sensor. As we can see, the sensitivity decreases as the hydrogen concentration increases. On the other hand, for a fixed hydrogen concentration, the change in cavity length increased with the thickness of Pd film increases, which means the thicker the Pd film, the higher the sensitivity. 4. Experiments and results 4.1. Experimental setup The schematic illustration of the experimental setup is shown in Fig. 6. An optical sensing interrogator (Micron Optics sm125, wavelength range: 1510–1590 nm, resolution: 5 pm) is used as the demodulation device. The light emitted from the sm125 is guided into the sensor through a circulator. The spectrum modulated by the sensor reflects back to the sm125 via the circulator again. Then the sm125 transfers the detected spectrum to a personal computer (PC) for data analysis. The sensor head is placed inside a custom-built gas chamber through a fiber-optic connector. The hydrogen concentration in the chamber is controlled by regulating the flow rate of H2 and N2 through two mass flow meters.
5. Conclusion In conclusion, a hydrogen sensor based on the fiber-optic FabryPerot interferometer is proposed, which has the advantages of simple structure, low cost and easy in fabrication. Response time, sensitivity, resolution and repeatability of the proposed hydrogen sensor are investigated detailed. A response time of 185 s, a sensitivity of 1.44 nm/ %, a resolution of 500 ppm and a good repeatability have been demonstrated. In addition, the temperature cross-sensitivity is studied and has been eliminated by integrating with an FBG sensor. The proposed
Fig. 5. Change in the cavity length as a function of the hydrogen concentration. 4
Optics and Laser Technology 124 (2020) 105995
X. Zhou, et al.
Fig. 6. The experimental setup of the hydrogen sensing system.
Fig. 7. Temporal response of the hydrogen sensor (a) before and (b) after the temperature calibration. Inset in (b): enlarged temporal response at 8% hydrogen concentration.
Fig.8. Change in cavity length as a function of hydrogen concentration with different thicknesses.
Fig. 9. Resolution measurement.
sensor has a high potential for hydrogen detection in H2 usage, transportation and storage applications.
Acknowledgments
Declaration of Competing Interest
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61727816 and 61520106013) and the authors would like to acknowledge the State Grid Corporation Science and Technology Project (521205190014).
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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A compact hydrogen sensor based on the fiber-optic Fabry-Perot interferometer
T
⁎
Xinlei Zhoua, , Fengxiang Mab, Haitao Linga, Binjun Yua, Wei Pengc, Qingxu Yua a
School of Optoelectronic Engineering and Instrumentation Science, Dalian University of Technology, Dalian 116024, China Electric Power Research Institute of State Grid Anhui Electric Power Co., Ltd., Hefei, Anhui 230601, China c School of Physics, Dalian University of Technology, Dalian 116024, China b
H I GH L IG H T S
fiber-optic hydrogen sensor based on the F-P interferometer is present. • AA compact time of 185 s and a sensitivity of 1.4 nm/% are obtained. • A response of 500 ppm and a good repeatability have been demonstrated. • Theresolution • sensor is compact, easy in fabrication, low cost.
A R T I C LE I N FO
A B S T R A C T
Keywords: Hydrogen sensors Fiber-optic Fabry-perot interferometer Pd film
We report an optical fiber hydrogen sensor based on the Fabry-Perot interferometer formed by inserting two ceramic ferrules, one with a flat fiber end facet and the other with a commercial Pd film on their tip, into a matched ceramic sleeve. The response time and sensitivity of the proposed hydrogen sensor are investigated both theoretically and experimentally. A response time of 185 s and a sensitivity of 1.44 nm/% have been obtained. In addition, the resolution and repeatability are investigated experimentally. A resolution of 500 ppm and a good repeatability have been demonstrated. The proposed sensor is compact, easy in fabrication, low cost and has a high potential for hydrogen detection.
1. Introduction Hydrogen gas (H2) has widespread applications in petroleum, chemical, and aerospace industries, and has been extensively investigated as an environmentally responsible, renewable fuel that has the potential to alleviate the global warming problem associated with fossil fuel consumption [1–5]. However, H2 has inherent difficulties in its use due to its high diffusion coefficient (0.16 cm2/s in the air), low spark ignition energy (0.02 mJ), high combustion heat (285.8 kJ/mol), tendency to leakage, and a wide flammable range (4–75%). Since H2 is odorless, colorless, and tasteless, it is undetectable by human senses. Thus, sensitive, accurate, and cheap reliable hydrogen sensors are urgently needed to ensure the safety in H2 usage, transportation and storage. In the past decades, a variety of technologies have been introduced to detect H2 by using mechanisms based on mechanical, thermal, acoustical, electrical, or optical reactions [6,7]. Compared to other methods, fiber-optic based sensors promise to be sensitive, reliable, and ⁎
immune to electromagnetic interference, which makes them an excellent candidate for operating in explosive environments [8–11]. There is no risk of gas ignition since the optical sensor has no electrical contacts and does not generate sparks nor relies on heat exchanges. Numerous optical fiber hydrogen sensors have been successfully demonstrated. According to the measurement method, optical fiber hydrogen sensors can be divided into four main types: intensity-based hydrogen sensors [12,13], fiber grating-based hydrogen sensors [14,15], surface plasmon resonance-based hydrogen sensors [16,17] and interferometer-based hydrogen sensors [18,19]. Each type of sensor has its advantages and disadvantages. Compared with other types of hydrogen sensors, the interferometer-based hydrogen sensor possesses a more flexible and simple structure and high sensitivity. However, the fabricating process of the interferometer-based hydrogen sensors are usually complicated and/or expensive instruments are needed. For instance, Wang et al. proposed an EFPI hydrogen sensor, in which the FPI cavity is fabricated by femtosecond laser micromachining near the fiber end [18]. However, the needed femtosecond laser is expensive. Ma
Corresponding author. E-mail address: [email protected] (X. Zhou).
https://doi.org/10.1016/j.optlastec.2019.105995 Received 11 October 2019; Received in revised form 8 November 2019; Accepted 1 December 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
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et al. present a miniature fiber-optic hydrogen sensor with a low detection limit of ~20 ppm and a short response time of 18 s by using a suspended Pd-decorated graphene [19], but the sensor fabrication process is complicated. In most optical-based sensing devices, palladium (Pd) is frequently utilized as the sensing material due to its high sensitivity and selectivity towards H2 and good reversibility [20,21]. So far, a variety of preparation methods for Pd films have appeared, including magnetron sputtering, sol-gel method, chemical vapor deposition, electroplating, and electroless plating, etc. Nevertheless, all these methods are complicated, time-consuming, and/or need expensive commercial instruments. In this paper, we propose a hydrogen sensor based on commercial Pd films and fiber-optic ceramic ferrules. The fabrication process of the proposed sensor is relatively simple and does not need complicated and expensive instruments. The structure, principle and fabrication process are introduced in Section 2. Then, we present the theoretic analysis and simulation results in Section 3. At last, in Section 4, the sensor’s performance is studied experimentally.
Fig. 2. The hydrogen single-side diffusion model.
3. Modeling and simulations 3.1. Response time To analyze the response time, we establish a hydrogen single-side diffusion model, in which the substrate that supports the Pd film cannot be penetrated by hydrogen. This model, as shown in Fig. 2, consists of hydrogen dissociating on the Pd film surface, diffusing in the inner Pd film, and restraining on the Pd-substrate interface [25]. As this is a diffusion-limited reaction in one dimension, we established a coordinate system with its origin at the center of the H2-Pd interface. The x-axis is perpendicular to the film surface. Based on the Fick’s second law, the H concentration satisfies [25]:
2. Principle The schematic of the proposed Fabry-Perot interferometer (FPI) based hydrogen sensor is shown in Fig. 1. Similar to the configuration of the fiber-optic connector, we insert two ceramic ferrules, one with a flat fiber end facet and the other with a commercial Pd film on their tips, into a matched ceramic sleeve to form the FPI. The ceramic sleeve act as a collimator to ensure the two ceramic ferrules parallel and coaxial. The flat fiber end facet and the Pd film surface act as two reflective mirrors and form the low-finesse F-P cavity. The low-finesse FPI can be approximately equivalent to the twobeam interferometer. The FPI works as a reflective device and its reflective optical intensity can be expressed as [22,23]:
I = I1 + I2 + 2I1 I2 cos(ϕ)
∂C (x , t ) ∂2C (x , t ) =D ∂t ∂x 2
(2)
where C(x,t) is the H concentration, which is a function of the time t and the position x in the Pd film. D is the diffusion coefficient of the H in the Pd film. As the H concentration in the Pd film is 0 before the Pd-H2 reaction, we get the initial condition: C(x,0) = 0. On the other hand, the H concentration on the Pd-H interface, Cs, determined by the H2 concentration in the surrounding environments, can be regarded as a constant concentration as the H2 are dissociated continuously into H when they contact with the Pd film. Thus, we get the first boundary condition: C(0,t) = Cs. The H diffuses to the opposite direction when they reach the Pd–substrate interface, which is similar to the reflection of a flat mirror. The concentration gradient of the incident H is equal to that of the reflected one. Thus, we have the second boundary condition: ∂C (x , t ) = 0 , where L is the thickness of the Pd film. ∂x
(1)
where I1 and I2 are intensities of the two reflected beams, respectively. ϕ = 4πd /λ is the phase difference of the two reflective beams, λ is the light wavelength, d is the cavity length of the FPI defined by the separation between the fiber end facet and the Pd film surface. The hydrogen concentration can be detected by monitoring the change in cavity length (Δd ) of the FPI, which is caused by the interaction between sensitive film (Pd film) and H2. When H2 appears near the Pd film, it will be dissociated into atomic hydrogen (H). The dissociated hydrogen atoms diffuse into the Pd film and form PdHx until reaching equilibrium, where x represents the atomic ratio of H to Pd. The Pd-to-PdHx transition causes the expansion of the Pd lattice, which reduces the cavity length d. The reduction in the cavity length results in the wavelength shift of the reflection spectrum and can be demodulated using a vernier-like demodulation algorithm with a subnanometer resolution [23,24]. Consequently, the H2 concentration encoded in the Pd film expansion can be extracted by measuring the change in cavity length (Δd ) of the FPI.
x=L
Solving Eq. (2) by using the Fourier method, we can get:
4 ⎛ C (x , t ) = Cs ⎜1 − π ⎝
∞
∑ m=1
(2m − 1) π , 2η0
1 ⎞ sin(μ 2m − 1 η) exp(−μ22m − 1)⎟ 2m − 1 ⎠ x Dt
L Dt
(3)
η= , η0 = . Eq. (3) shows the conwhere μ 2m − 1 = centration distribution of H as a function of the position x at any time, whose right-hand side can be expanded as follows:
Fig.1. (a) structure diagram and (b) 3D view of the FPI based hydrogen sensor. 2
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X. Zhou, et al.
C (x , t ) = Cs ⎜⎛1 − ⎝
(
= Cs 1 −
4 π
4 π
∞
∑ m=1
1 2m − 1
πx
sin( 2L ) exp( −D
sin
π 2t ) 4L2
(
−
(2m − 1) πm 2L 41 π3
) exp (−D
3πx
) ⎞⎠ ) − ··· )
(2m − 1)2π 2t 4L2
sin( 2L ) exp( −D
9π 2t 4L2
⎟
(4)
We choose the first two terms of the infinite series as the approximation of H concentration distribution, that is:
4 πx π 2t 41 3πx 9π 2t C (x , t ) ≈ Cs ⎛1 − sin( ) exp(−D 2 ) − sin( ) exp(−D 2 )⎞ π 2L 4L π3 2L 4L ⎠ ⎝ (5) ⎜
⎟
with a truncation error of:
4Cs π
δ=
∞
∑ m=3
1 (2m − 1) πx ⎞ (2m − 1)2π 2t ⎞ sin ⎛ exp ⎛−D 2m − 1 2 L 4L2 ⎠ ⎝ ⎠ ⎝ ⎜
⎟
(6)
In the actual measurement, the hydrogen sensor response to the average change of the Pd film. The average concentration of H in the Pd film along the x-axis direction can be expressed as:
C ¯(t ) =
L ∫0 C (x , t ) dx
π 2t 8 8 1 9π 2t ≈ Cs ⎛1 − 2 exp(−D 2 ) − 2 exp(−D 2 )⎞ π L π 4 9 4L ⎠ ⎝ (7) ⎜
L
Fig. 3. Percentage of response versus time with different film thicknesses.
⎟
We can see that the average hydrogen concentration in the Pd film only depends on the time t and film thickness L and not on the position x. Then, we denote η as the percentage of response to represent the completion level of the Pd-H reaction, which can be expressed as:
C ¯(t ) π 2t 8 8 1 9π 2t = 1 − 2 exp(−D 2 ) − 2 exp(−D 2 ) Cs π π 9 4L 4L
η=
(8)
We can see that η is an exponent function of the time t. Only when t approaches infinity can the η reach 100% and the reaction between Pd film and H reaches equilibrium. In the actual measurement, we define the response time tR as the time range from the start of the reaction to 90% of the completed reaction level. Therefore, the tR satisfies:
η≈1−
8 π 2t 8 9π 2tR ⎞ exp ⎛−D 2R ⎞ − exp ⎛−D = 90% 2 2 π 4L ⎠ 9π 4L2 ⎠ ⎝ ⎝ ⎜
⎟
⎜
⎟
(9)
Fig. 4. Percentage of response versus time with different diffusion coefficients.
The typical value of the tR changes within several seconds to tens of minutes. Thus, the second-order term in Eq. (9) is much smaller than the first-order term and can be neglected. So Eq. (9) can be approximated to:
8 π 2t exp ⎛−D 2R ⎞ = 90% 2 4L ⎠ π ⎝
1−
⎜
According to the simulation results in Fig. 4, it can be concluded that the response time is 507 s, 383 s, 306 s, 253 s for diffusion coefficients of 6 μm2/s, 8 μm2/s, 10 μm2/s, 12 μm2/s, respectively. The results in Figs. 3 and 4 show that, with the decrease of the film thickness and the increase of the diffusion coefficient, the response time reduces greatly, which is consistent well with the indication of the Eq. (11). In addition, we notice that the start value of the percentage of response is not 0 at the time of 0 s in Figs. 3 and 4. This is because of the truncation error, as shown in Eq. (6).
⎟
(10)
Solving Eq. (10), we can have:
tR =
4L2 π2 L2 ln ≈ 0.85 Dπ 2 80 D
(11)
We can see that, from Eq. (11), the response time tR depends on the film thickness L and diffusion coefficient D. Decreasing film thickness and increasing diffusion coefficient can reduce the response time. First, varying the thickness of Pd film, L = 400, 600, 800, 1000 nm, is proposed to study the influence of thickness on the response time. We suppose the diffusion coefficient D as 10 μm2/s. The percentage of response based on Eq. (8) is displayed in Fig. 3. The figure illustrates that the percentage of response rises as the reaction time increases and that the thinner the Pd film is, the earlier the reaction complete. From Fig. 3, we can see that, when the percentage of response reaches 90%, the corresponding response time is 136 s, 306 s, 542 s and 846 s for the thickness of 400 nm, 600 nm, 800 nm and 1000 nm, respectively. Then, the influence of diffusion coefficient D on the response time is investigated. Varying diffusion coefficient D = 6 μm2/s, 8 μm2/s, 10 μm2/s, 12 μm2/s, with a thickness of 60 μm, we get the percentage of response based on Eq. (8), as shown in Fig. 4.
3.2. Sensitivity For the proposed FPI-based hydrogen sensor, we define the sensitivity S as:
S=
Δd (nm /%) ΔC
(12)
where Δd is the change in cavity length, C is the hydrogen concentration and ΔC is the change in hydrogen concentration. The change in cavity length is induced by the strain in Pd film due to its expansion after absorbing H. Thus, we have:
Δd = −ΔL = −L·εPd
(13)
where εPd is the strain in the Pd film, L is the thickness of the Pd film. On the other hand, the strain in Pd film due to absorbing hydrogen can be expressed as [26]: 3
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At first, only N2 is filled into the test chamber, followed by filling H2 with a fixed concentration until the cavity length response tends to steady. Then, H2 is shut off and, again, only N2 is filled into the gas chamber to allow the sensor to restore. We continuously record the cavity length of the hydrogen sensor (Pd film’s thickness: 70 μm) with a time interval of 1 s. The temporal response of the change in cavity length is shown in Fig. 7(a) as the H2 concentration increases from 0 to 10%. It can be seen from Fig. 7(a) that the original value of the cavity length has a tendency to increase, which is caused by the temperature influence. To eliminate the temperature influence, we connect an FBG in series with the F-P hydrogen sensor. The FBG detects the ambient temperature and can be used to eliminate the temperature cross-sensitivity as we have done in our previous work [23,27]. Fig. 7(b) shows the temporal response of the change in cavity length after eliminating the temperature influence. We can see that the original value of the cavity length keeps steady showing that the proposed hydrogen sensor has good recoverability. Additional, at 8% H2 concentration, the sensor’s response time is estimated to be 185 s as shown in the inset of Fig. 7(b). As we mentioned previously, thicker Pd films can improve the sensor’s sensitivity, but at the expense of the response speed. To verify this, the temporal responses of the sensors with Pd thickness of 100 μm, 85 μm, 75 μm, and 70 μm are investigated experimentally and the results are shown in Fig. 8. By linear fitting, we can get the sensitivity (slope) is 1.44 nm/%, 1.23 nm/%, 1.06 nm/% and 0.99 nm/% for the Pd film thickness of 100 μm, 85 μm, 75 μm and 70 μm, respectively. However, the response time is calculated as 401 s, 240 s, 200 s and 185 s for the Pd film thickness of 100 μm, 85 μm, 75 μm and 70 μm, respectively. Compared with the simulated results shown in Fig. 5, the sensitivity we get here is smaller. The main reason is that we assume the percentage of response reaches 100% in the simulation while in the experiments the percentage of response does not. Additional, some errors in experiments, such as the value of the hydrogen concentration and Pd film thickness, will also lead to differences between simulated results and experimental results. During the measurements, the whole temperature change is 1 °C, from 21 °C to 22 °C. The overall cavity length change is about 1.3 nm as shown in Fig. 7(a). Considering the sensitivity of the sensor, the influence of the temperature change on the concentration is 0.9%/°C, 1%/ °C, 1.2%/°C and 1.3%/°C for the Pd film thickness of 100 μm, 85 μm, 75 μm and 70 μm, respectively. Then we investigate the resolution of the hydrogen sensor. The result is shown in Fig. 9. Taking the standard deviation (SD) as the sensor resolution, a resolution of 0.08 nm for the cavity length has been obtained. Considering the sensitivity of the sensor (1.44 nm/%), a resolution of 5.5 × 10−4 (500 ppm) for the hydrogen concentration measurement is achieved. At last, the repeatability of the sensor is tested. The hydrogen sensor with a Pd film thickness of 85 μm is exposed to the hydrogen environment with a concentration of 6% for 5 times. The change in the cavity length for the 5 measurements are recorded as 7.74 nm, 7.54 nm, 7.63 nm, 7.77 nm, and 7.56 nm, which proves that the proposed hydrogen sensor has a good repeatability.
(14)
εPd = 0.026x
where x is the hydrogen content in the Pd film (i.e. the atomic ratio of H to Pd). The relationship between the hydrogen content and the partial pressure of the hydrogen follows the Sievert’s law: (15)
P = Kx
where P is the hydrogen partial pressure and K is the Sievert’s coefficient (K = 350 Torr1/2 = 4.36 Pa1/2). Combining Eqs. (13)–(15), we have:
Δd = −ΔL = −L·εPd = −0.026L
P K
(16)
When the reaction between H2 and Pd goes under atmospheric pressure (0.1 MPa), we can get the relationship between the hydrogen partial pressure and the hydrogen concentration:
P = 0.1 × 106·C (Pa)
(17)
Then we have:
Δd = ΔL = 0.026L·
0.1·106·C = 0.002·L· C K
(18)
Fig. 5 shows the change in cavity length Δd varies with hydrogen concentration C with different thicknesses of Pd film. The negative value means the cavity length decrease as the hydrogen concentration increase. The slope of the curve in Fig. 5 represents the sensitivity of the hydrogen sensor. As we can see, the sensitivity decreases as the hydrogen concentration increases. On the other hand, for a fixed hydrogen concentration, the change in cavity length increased with the thickness of Pd film increases, which means the thicker the Pd film, the higher the sensitivity. 4. Experiments and results 4.1. Experimental setup The schematic illustration of the experimental setup is shown in Fig. 6. An optical sensing interrogator (Micron Optics sm125, wavelength range: 1510–1590 nm, resolution: 5 pm) is used as the demodulation device. The light emitted from the sm125 is guided into the sensor through a circulator. The spectrum modulated by the sensor reflects back to the sm125 via the circulator again. Then the sm125 transfers the detected spectrum to a personal computer (PC) for data analysis. The sensor head is placed inside a custom-built gas chamber through a fiber-optic connector. The hydrogen concentration in the chamber is controlled by regulating the flow rate of H2 and N2 through two mass flow meters.
5. Conclusion In conclusion, a hydrogen sensor based on the fiber-optic FabryPerot interferometer is proposed, which has the advantages of simple structure, low cost and easy in fabrication. Response time, sensitivity, resolution and repeatability of the proposed hydrogen sensor are investigated detailed. A response time of 185 s, a sensitivity of 1.44 nm/ %, a resolution of 500 ppm and a good repeatability have been demonstrated. In addition, the temperature cross-sensitivity is studied and has been eliminated by integrating with an FBG sensor. The proposed
Fig. 5. Change in the cavity length as a function of the hydrogen concentration. 4
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Fig. 6. The experimental setup of the hydrogen sensing system.
Fig. 7. Temporal response of the hydrogen sensor (a) before and (b) after the temperature calibration. Inset in (b): enlarged temporal response at 8% hydrogen concentration.
Fig.8. Change in cavity length as a function of hydrogen concentration with different thicknesses.
Fig. 9. Resolution measurement.
sensor has a high potential for hydrogen detection in H2 usage, transportation and storage applications.
Acknowledgments
Declaration of Competing Interest
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61727816 and 61520106013) and the authors would like to acknowledge the State Grid Corporation Science and Technology Project (521205190014).
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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