Quartz-Enhanced Photoacoustic Spectroscopy (QEPAS) Detection of the ν 7 Band of Ethylene at Low Pressure with CO 2 Interference Analysis

Abstract

Ethylene (C₂H₄) was detected using quartz-enhanced photoacoustic spectroscopy (QEPAS) at 10.5 µm with a continuous wave, distributed-feedback quantum cascade laser as the light source. The QEPAS sensor was operated at low pressures (≤200 torr) to eliminate the cross-talk spectral interference between C₂H₄ and CO₂, a major interfering species in practical applications. The sensor was calibrated to show a good linear response to C₂H₄ concentration and the Allan deviation analysis demonstrated a minimum detection limit of 8 ppb at an integration time of 90 s. Although no spectral overlap between C₂H₄ and CO₂ was confirmed at the pressure ≤200 torr by the direct absorption measurement using a 28-m multipass cell, we observed the apparent influence of the CO₂ addition to the C₂H₄/N₂ mixture on the photoacoustic signal of C₂H₄. An energy transfer model involving the vibration–vibration (VV) and vibration–translation (VT) transitions in the C₂H₄–CO₂–N₂ system was constructed to interpret the experimental data. Additionally, the vibrational relaxation times of C₂H₄ were obtained based on the QEPAS technique and the energy transfer model, which were in good agreement with the previous studies.

Keywords

Photoacoustic spectroscopy multipass absorption spectroscopy vibrational relaxation ethylene detection quantum cascade laser

Introduction

Ethylene (C₂H₄) is treated as a major pollutant produced from automobile exhaust and industrial emissions,¹ a biomarker in people’s exhaled breath to identify relevant disease,² and a plant hormone affecting the growth, ripening, and decay of plants.³ In past years, various spectroscopic methods including cavity ring-down spectroscopy (CRDS),^4,5 multipass absorption,^6–8 photoacoustic spectroscopy (PAS),^9–12 and quartz-enhanced photoacoustic spectroscopy (QEPAS)^13–15 were utilized for the C₂H₄ detection with different sensitivities.

Among these trace gas sensing techniques, PAS is often carried out by means of a broadband microphone for the acoustic wave detection. In this process, the target molecules at the ground state are excited by absorbing the optical radiation, followed by the vibration–translation (VT) relaxation to convert the excitation energy to the translational molecular motion. The VT relaxation process causes local heating and thermal expansion that are the key steps in determining the generation of acoustic waves. Quartz-enhanced photoacoustic spectroscopy, a novel PAS technique, has advantages of high Q-factor, compact acoustic cell (a few mm³), immunity to ambient noise, and low fabrication cost.^16–21 Different from the traditional PAS using a photoacoustic resonant cell with a Q-factor around 40–200, the QEPAS sensor detects the acoustic wave using a quartz tuning fork (QTF) with a Q-factor around 10 000. The QTF acts as a resonant acoustic transducer that converts the photoacoustic wave into the electrical signal via the piezoelectric effect. The ambient acoustic waves with much longer wavelengths tend to apply a force in the same direction upon the two prongs of the QTF without exciting its piezo-electrically active mode.

We recently reported a QEPAS-based C₂H₄ sensor to achieve a minimum detection limit (MDL) of 50 ppb at the detecting pressure of 500 torr.¹⁵ In that work, a distributed feedback (DFB) quantum cascade laser (QCL) was used to exploit the strongest absorption line of C₂H₄ at 10.53 µm in the v₇ fundamental band. However, CO₂ serves to be a possible interference for the C₂H₄ detection at the atmospheric pressure because these two species have a spectral overlap near the diagnostic wavelength. Normally a low gas pressure can be selected to eliminate the cross-talk spectral interference between the interfering species. However, in QEPAS detection, the standard QTF available commercially has a resonant frequency f₀ = 32.768 kHz, which may exceed the VT relaxation rate of certain gas molecules at relatively low pressures.^22,23 The lag between VT relaxation rate and high f₀ of the QTF leads to a significant attenuation of the observed photoacoustic signal.^24–26 Note that the custom-designed QTF with a lower resonant frequency provides a possibility to reduce the attenuation effect.²⁷ Hence, the variation of ambient species may affect the photoacoustic response by changing the original energy transfer processes even though this species has no spectral overlap with the target analyte.

In this work, we reported the development of a QEPAS-based C₂H₄ sensor working at low pressure to eliminate the spectral interference from other species by exploiting the C₂H₄ spectra near 10.5 µm. The sensor sensitivity and long-term stability were evaluated and presented in this paper. We also investigated the influence of the CO₂ molecular relaxation dynamics on the photoacoustic detection of C₂H₄ using the QEPAS sensor system. The observed distinct photoacoustic spectra of C₂H₄ with varied CO₂ concentrations were well interpreted by a simplified molecular energy transfer model.

Experimental Setup

A 10.5 µm continuous wave (CW), DFB-QCL (Alpes Lasers) with integrated thermoelectric cooling (TEC) was utilized as the light source. The schematic of the C₂H₄ QEPAS setup is depicted in Figure 1. The QCL was controlled at 37℃ by a commercial laser driver (ILX Lightwave, LDC 3736) and tuned across the absorption feature of C₂H₄ centered at ∼949.3 cm⁻¹ to obtain an output power of ∼16 mW. The laser beam was directed into an acoustic detection module (ADM) enclosing a QTF and two micro-resonator (mR) tubes (L: 4.3 mm, ID: 0.9 mm) by two plano–convex lenses, L₁ (f = 20 mm) and L₂ (f = 40 mm). A slightly wedged pinhole with a diameter of 400 µm was placed at the focal point of L₁ to improve the beam quality. Two wedged ZnSe windows were mounted on the custom-designed ADM to allow for optical transmission.

Figure 1.

Schematic of the QEPAS setup integrated with a multipass gas cell. FM₁ and FM₂, flip mirrors; L₁, L₂ and L₃, plano–convex lens; M₁, focusing mirror; ADM, acoustic detection module; QTF, quartz tuning fork; mR, micro-resonator; DAQ, data acquisition; MGC, multipass gas cell; NV, needle valve.

The injection current of the QCL was sinusoidally modulated at half of the QTF resonant frequency (f₀) for performing wavelength modulation spectroscopy. The absorption line of C₂H₄ was crossed twice during each modulation period giving rise to acoustic waves at f₀ that excited the piezo-electrically active mode of the QTF. The piezo-electrical signal generated by the QTF was amplified by a transimpedance preamplifier with a 10 MΩ feedback resistor and a 30× voltage amplifier, and then demodulated by a lock-in amplifier (Signal Recovery) to obtain the second harmonic (2f ) signal.

Besides the QEPAS sensor system, a Herriot multipass gas cell (MGC) (Aerodyne Research) was added to perform the simultaneous direct absorption measurement of the C₂H₄/CO₂ spectra. A visible He–Ne laser (635 nm) was aligned collinearly with the QCL beam using two flip mirrors (FM₁ and FM₂) to assist the MGC alignment. We employed a mode matching lens L₃ (f = 200 mm) to effectively couple the laser radiation into the MGC and achieved an optical path length of 28 m in total. The laser radiation exited from the MGC was collected by a focusing mirror M₁ onto a photovoltaic detector (PVM-10.6, VIGO System S.A.).

The MGC and ADM were connected in series to ensure the same gas mixture to flow through both sensor systems. The gas mixtures with different concentrations were generated by diluting 100 ppm C₂H₄/N₂ and 10% CO₂/N₂ with the pure N₂ (99.999%) using a commercial gas dilution system ( Jinwei Electronics). The generated mixtures were estimated to have 1% uncertainty of the concentration. The gas pressure inside the ADM and MGC was monitored by a pressure transducer (MKS Instruments, 722B) and controlled by adjusting two needle valves (Swagelok) and a rotary-vane vacuum pump.

Experimental Results

C₂H₄ and CO₂ Spectra Near 10.53 μm

According to the HITRAN database,²⁸ there is a possible interfering line of CO₂ at 949.48 cm⁻¹ (ν₃–ν₁ band) next to the target C₂H₄ line centered at 949.34 cm⁻¹. The possible spectral interference between C₂H₄ and CO₂ was first investigated by performing the direct absorption measurement of C₂H₄–CO₂–N₂ mixtures using the MGC at three pressures of 50, 100, and 200 torr.

The QCL was wavelength-scanned to cover both C₂H₄ and CO₂ absorption lines at a scanning frequency of 1 Hz. Figure 2 presents the measured absorption spectra of C₂H₄–CO₂–N₂ mixtures at varied concentrations and pressures along with the corresponding absorption lines listed in the HITRAN database.²⁸ In Figure 2a, the measured absorption spectra correspond to 14 ppm C₂H₄ with the CO₂ concentrations varying between 0 and 8% at the pressure of 50 torr. Similarly, the absorption spectra of 9 ppm C₂H₄ with the varied CO₂ concentrations at the pressure of 100 torr and 200 torr were plotted in Figure 2b and c, respectively. At each pressure, the CO₂ absorption at 949.48 cm⁻¹ changes accordingly with the varied concentrations of CO₂ in the mixtures, while the strongest absorption peak of C₂H₄ at 949.34 cm⁻¹ remains unchanged. Hence, the variation of CO₂ concentration in the range of 0–8% causes no spectral interference with the target C₂H₄ line centered at 949.34 cm⁻¹ within the current pressure range.

Figure 2.

Measured C₂H₄–CO₂ spectra at different pressures: (a) 14 ppm C₂H₄, 50 torr, (b) 9 ppm C₂H₄, 100 torr, and (c) 9 ppm C₂H₄, 200 torr. The corresponding C₂H₄/CO₂ lines from HITRAN database were illustrated at the bottom panels.

The QEPAS spectra of 20 ppm C₂H₄/N₂ and 5% CO₂/N₂ mixtures were measured separately at 200 torr (see Figure 1 in the Supplemental Material). The QEPAS method and measurement procedures in detail can be found in our previous work.¹⁵ Over the spectral range under investigation, there exist five strong C₂H₄ peaks located at 949.08 cm⁻¹, 949.18 cm⁻¹, 949.34 cm⁻¹, 949.42 cm⁻¹, and 949.53 cm⁻¹, while the only CO₂ absorption peak was observed at 949.48 cm⁻¹. The separate measurements of QEPAS 2f spectra of CO₂ and C₂H₄ confirm no spectral overlap between the target C₂H₄ peak at 949.34 cm⁻¹ and CO₂ when the gas pressure is lower than 200 torr.

Quartz-Enhanced Photoacoustic Spectroscopy Sensor Performance

The QEPAS C₂H₄ sensor was calibrated using a series of C₂H₄ mixtures of known concentration at 100 torr. The measured 2f signals at different C₂H₄ concentrations are illustrated in Figure 3a and the corresponding 2f peak amplitudes are plotted in Figure 3b as a function of C₂H₄ concentration (5–55 ppm). A linear fit to the experimental data yields an R-square value of 0.998, indicating a good linear response of the sensor. In order to evaluate the precision and stability of the sensor system, an Allan deviation analysis was conducted by measuring pure N₂ for 1 h with the result illustrated in Figure 4. The sensor achieves a MDL of 69 ppb of C₂H₄ at the integration time of 0.05 s. The turning point of the Allan deviation curve is approximately 8 ppb at an integration time of 90 s, corresponding to a normalized noise equivalent absorption (NNEA) coefficient of 1.79 × 10⁻⁸cm⁻¹W/Hz^1/2.

Figure 3.

(a) Representative QEPAS 2f signals measured for varied C₂H₄ concentrations at 100 torr. (b) Measured 2f peak amplitude as a function of C₂H₄ concentration with the best linear fit.

Figure 4.

Allan deviation plot of the QEPAS C₂H₄ sensor.

In order to investigate the influence of CO₂ vibrational relaxation dynamics on the C₂H₄ detection, we performed QEPAS measurements of C₂H₄–CO₂–N₂ mixtures at different pressures. The CO₂ concentration was varied between 0 and 8% at each pressure. Note that the addition of CO₂ into C₂H₄/N₂ mixtures may change the in-phase and quadrature components of the measured QEPAS 2f signal by changing the relaxation time of excited C₂H₄ molecules. Hence, the detection phase of the lock-in amplifier must be adjusted each time when a new CO₂ concentration was analyzed. In this work, we recorded the amplitude of the 2f signal which was insensitive to the variation of the detection phase. The experimental results shown in Figure 5 reveal the evident influence of the CO₂ addition on the measured C₂H₄ QEPAS signal at three pressures of 50, 100, and 200 torr. At each pressure, the QEPAS 2f signal of C₂H₄ changes with the varied CO₂ concentrations while the C₂H₄ concentration was fixed.

Figure 5.

Measured QEPAS 2f spectra of C₂H₄–CO₂–N₂ at different pressures: (a) 14 ppm C₂H₄, 50 torr, (b) 9 ppm C₂H₄, 100 torr, and (c) 9 ppm C₂H₄, 200 torr. The CO₂ concentration was varied between 0 and 8% at all three pressures.

The measured 2f peak amplitudes of CO₂ at 949.48 cm⁻¹ and C₂H₄ at 949.34 cm⁻¹ are plotted in Figure 6. The 2f peak amplitude of CO₂ changes linearly with the CO₂ concentration at all three pressures as depicted in Figure 6a. In comparison, the C₂H₄ QEPAS signal increases monotonously with the CO₂ concentration at 50 torr as illustrated in Figure 6b. At a higher pressure of 100 torr, the QEPAS signal of C₂H₄ increases with the CO₂ concentration but reaches a plateau level when the CO₂ concentration is >4%. However, at 200 torr, the QEPAS C₂H₄ signal reaches a peak value at the concentration of 1% and then drops with the increased CO₂ concentration.

Figure 6.

(a) Linear response of CO₂ QEPAS 2f amplitude at 949.48 cm⁻¹ to CO₂ concentration; (b) variation of C₂H₄ QEPAS 2f peak amplitude at 949.34 cm⁻¹ at different CO₂ concentrations.

Discussion

The experimental results indicate that the addition of CO₂ into the C₂H₄/N₂ mixture significantly affects the QEPAS spectra of C₂H₄ and such influence is also pressure dependent. Note that the added CO₂ molecules with a relatively slow VT relaxation rate participate in the vibrational relaxation of the excited C₂H₄. Near the target C₂H₄ line at 949.34 cm⁻¹, the associated vibrational states of the C₂H₄–CO₂–N₂ system include the v₂ state of CO₂ centered at 667.4 cm⁻¹ and four vibrational states of C₂H₄ at 1026.5 cm⁻¹ (ν₄), 949.3 cm⁻¹ (ν₇), 940.6 cm⁻¹ (ν₈), and 826.0 cm⁻¹ (ν₁₀), respectively.²⁸ The energy transfer processes involved in the current C₂H₄–CO₂–N₂ system can be simplified and are summarized in Figure 7.^29,30

Figure 7.

The multi-level energy transfer model for the C₂H₄–CO₂–N₂ gas system. Dashed line, VV transition; dash-dotted line, VT transition.

Considering the VV transition is much faster than the VT transition, the VV transitions of (C₂H₄)ν₇–(CO₂)ν₂ and (C₂H₄)ν₇–(C₂H₄)ν₀–(CO₂)ν₂ can be assumed to have the same relaxation rate. The overall VV transition is described by the following process:

C_{2} H_{4} (ν_{7}, ν_{10}) + {CO}_{2} \to k_{2} C_{2} H_{4} + CO (ν_{2}), Δ E_{2} = 281.9 {cm}^{- 1}

(1)

where k₂ is the rate of the process which is a function of CO₂ concentration, x; ΔE₂ is the energy to be deactivated during the process. The ν₁₀ deactivation process by the VT transition can be expressed as:

C_{2} H_{4} (ν_{10}) + N_{2} \to k_{1} C_{2} H_{4} + N_{2}, Δ E_{1} = 826.0 {cm}^{- 1}

(2)

where k₁ is the relaxation rate of the process which equals to the reciprocal of the VT relaxation time τ₁ of C₂H₄ at the ν₁₀ state. Note that the VT deactivation caused by C₂H₄–C₂H₄ collisions is ignored because of the ppm-level low concentration of C₂H₄ in the mixture. Similarly, the excited CO₂ of the ν₂ state relaxes slowly to the ground state by colliding with CO₂ and N₂ as described by:

{CO}_{2} (ν_{2}) + N_{2} ({CO}_{2}) \to k_{3} {CO}_{2} + N_{2} ({CO}_{2}), Δ E_{3} = 667.4 {cm}^{- 1}

(3)

where k₃ is the relaxation rate of the process which can be expressed by the following equation:³¹

k_{3} = P_{tot} (K_{{CO}_{2} - {CO}_{2}} x + K_{{CO}_{2} - N_{2}} (1 - x))

(4)

where P_tot,

K_{{CO}_{2} - {CO}_{2}}

, and

K_{{CO}_{2} - N_{2}}

are the total gas pressure, rate constants of CO₂–CO₂ and CO₂–N₂ collisions, respectively. Note that the rate constants

K_{{CO}_{2} - {CO}_{2}}

and

K_{{CO}_{2} - N_{2}}

were measured previously^32,33 and adopted in this work for the modeling analysis. The contribution of C₂H₄ in this process is also ignored due to its very low concentration.

The QEPAS signal is proportional to the rate of heat produced per unit volume, dH/dt, during the relaxation of the molecular vibrational energy,³⁴

\frac{dp}{dt} = \frac{{AC}_{ν}}{NR} \frac{dH}{dt}

(5)

where A is the sensor constant relevant to the characteristics of QTF and mR, C_V is the total heat capacity of the gas at constant volume, N is the number of moles of gas molecules, and R is the gas constant, respectively. The rate of the produced heat is given by:

\frac{dH}{dt} = Δ E_{1} k_{1} N^{*} + Δ E_{2} k_{2} N^{*} + Δ E_{3} k_{3} N^{*}

(6)

where N* and N₁* are the number of moles of the excited C₂H₄ and CO₂ molecules, respectively. Note that N* and N₁* can be calculated by the following dynamic balance equations:

\frac{{dN}^{*}}{dt} = W - k_{1} N^{*} - k_{2} N^{*}

(7)

\frac{{dN}_{1}^{*}}{dt} = k_{2} N^{*} - k_{3} N_{1}^{*}

(8)

where W is the excitation rate of the C₂H₄ molecules by the laser radiation and can be expressed as:³⁴

W = W_{0} (a + {be}^{i ω t})

(9)

where ω = 2πf, f is the thermal input modulation frequency (∼32.7 kHz). By solving Eqs. 5–9, we obtain a general expression of the QEPAS amplitude:

| p | (x) = \frac{p_{0}}{\sqrt{1 + (C_{1} + C_{2} x) 2}} \times \sqrt{{(Δ E_{1} C_{1} + Δ E_{2} C_{2} x) 2 + \frac{2 Δ E_{1} Δ E_{3} C_{1} C_{2} x + (2 Δ E_{2} Δ E_{3} + Δ E_{3}^{2}) (C_{2} x) 2}{1 + (\frac{ω}{k_{3}})^{2}}}}

(10)

where

p_{0} = \frac{{AC}_{V} W_{0} b}{N ω R}

C_{1} = \frac{1}{τ_{1} ω}

C_{2} x = \frac{k_{2}}{ω}

. In Eq. 10, the only unknown parameters are p₀, τ₁, and C₂, which can be fitted to the experimental data of

| p | (x)

Figure 8 plots the best fit using Eq. 10 to the measured QEPAS signal of C₂H₄ for varied CO₂ concentrations and pressures. The obtained parameters from the best fit lead to realistic values of the VT relaxation time τ₁. The fitting results are summarized in Table 1, which are in relatively good agreement with the previously measured values in the literature.³¹ As illustrated in Figure 8, the current model accurately predicts the observed dependence of the photoacoustic signal of C₂H₄ on the CO₂ concentration and gas pressure. At 50 torr, C₂H₄ has a VT relaxation time of ∼20 µs that is comparable with the modulation period (30 µs) of the laser radiation. The added CO₂ provides extra energy deactivation processes, the VV transitions of (C₂H₄)ν₇–(CO₂)ν₂ and (C₂H₄)ν₁₀–(CO₂)ν₂, to enhance the QEPAS signal of C₂H₄. However, such an enhancement caused by the additional VV transitions is mitigated at higher pressures (200 torr) because the energy deactivation starts to be dominated by the VT relaxation of C₂H₄ at the ν₁₀ state. The excited CO₂ at the ν₂ state cannot be effectively relaxed due to its much longer VT relaxation time, thus attenuating the photoacoustic signal with the increased CO₂ concentration. Hence, the added CO₂ changes the energy relaxation process of the C₂H₄ at the excited state, leading to the varied response of the QEPAS sensor to the CO₂ concentration and gas pressure.

Figure 8.

Best model fit to the measured QEPAS 2f amplitude of C₂H₄ for the varied CO₂ concentrations. Symbol, experimental data; solid line, best fit using Eq. 10.

Table 1.

Summary of the best-fitted τ₁ with a comparison to the previous study.

Pressure (torr)	τ₁* (µs)	τ₁^† (µs)
50	20.1	24.4
100	15.2	12.2
200	8.4	6.1

VT relaxation time of C₂H₄ at the ν₁₀ state obtained in this work.

†

VT relaxation time of C₂H₄ at the ν₁₀ state measured by Yuan and Flynn.³¹

Conclusion

We reported the QEPAS-based C₂H₄ sensor at low pressures by exploiting the strongest absorption line of C₂H₄ near 10.5 µm using a DFB-QCL. A good linear response to the C₂H₄ concentration was observed and the long-term stability and precision of the sensor were evaluated to show a MDL of 8 ppb at 90 s integration time. Then we performed the QEPAS and direct absorption measurements of C₂H₄ in the C₂H₄–CO₂–N₂ mixtures at varied CO₂ concentrations and pressures. The added CO₂ influences the photoacoustic detection of C₂H₄ at different pressures. An energy transfer model for the C₂H₄–CO₂–N₂ system was constructed to successfully interpret the experimental data. It was also found that the QEPAS technique can be used to measure the vibrational relaxation time of gas molecules. This work emphasizes the importance of species interference in photoacoustic detection affected by the additional energy deactivation processes even though the target analyte and interfering species have no spectral overlap.

Footnotes

Conflict of Interest

The authors report there are no conflicts of interest.

Funding

This research is supported by the Early Career Scheme (ECS) grant from the Research Grants Council of the Hong Kong SAR, China (24208515).

Supplemental Material

All supplemental material mentioned in the text, consisting of quartz-enhanced photoacoustic spectroscopy 2f spectra, is available in the online version of the journal.

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Supplementary Material

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Quartz-Enhanced Photoacoustic Spectroscopy (QEPAS) Detection of the ν 7 Band of Ethylene at Low Pressure with CO 2 Interference Analysis

Abstract

Keywords

Introduction

Experimental Setup

Experimental Results

C2H4 and CO2 Spectra Near 10.53 μm

Quartz-Enhanced Photoacoustic Spectroscopy Sensor Performance

Discussion

Conclusion

Footnotes

Conflict of Interest

Funding

Supplemental Material

References

Supplementary Material

C₂H₄ and CO₂ Spectra Near 10.53 μm