Optimization of spectrophone performance for quartz

Sensors and Actuators B 174 (2012) 24–30

Contents lists available at SciVerse ScienceDirect

Sensors and Actuators B: Chemical journal homepage: www.elsevier.com/locate/snb

Optimization of spectrophone performance for quartz-enhanced photoacoustic spectroscopy Yingchun Cao ∗ , Wei Jin, Hoi Lut Ho Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

a r t i c l e

i n f o

Article history: Received 9 May 2012 Accepted 8 August 2012 Available online 17 August 2012 Keywords: Photoacoustic spectroscopy Quartz tuning fork Spectrophone Acoustic microresonator Gas detection

a b s t r a c t We numerically investigate the effects of spectrophone parameters, including the operating acoustic frequency, the relative position of the quartz tuning fork and the excitation laser beam, the gap between the resonant tubes and the tuning fork, and the diameter and length of the resonant tubes, on the performance of gas sensors based on quartz-enhanced photoacoustic spectroscopy. A pair of rigid tubes with inner diameter of 0.2 mm and length of 5.1 mm, placed 0.6 mm down from the opening and 20 ␮m away from the edge of the tuning fork, is suggested for optimal performance. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Quartz-enhanced photoacoustic spectroscopy (QEPAS), in which periodic light absorption is converted into a localized acoustic pressure wave through photoacoustic (PA) effect and the pressure wave is detected with a tiny quartz tuning fork (QTF), has been demonstrated for trace gas detection with outstanding performance [1,2]. To further enhance the PA signal, a pair of rigid tubes, one on each side of the QTF facet (Fig. 1), was introduced, which acts as an acoustic microresonator (mR) to amplify the acoustic signal [3–5]. An enhancement factor as high as 30 was achieved by properly selecting the dimensions of the tubes [6]. Early work used two resonant tubes with a total length around half of the acoustic wavelength S in gas, to form an antinode in the middle of the tubes [2]. Later experiments showed that a larger PA signal can be obtained by using a mR with each of the tubes having a length of around S /2, because the gaps between the tube facets and tuning fork surfaces make the acoustic mode in each of the tubes relatively independent from each other [5]. Further detailed studies revealed that tube length for achieving optimal performance is somewhere between S /4 and S /2 [6,7], and the size of the gaps significantly affects the acoustic coupling between the tubes. Dong et al. [6] carried out experimental investigations on spectrophone optimization, but the samples are limited that it prevents a comprehensive investigation being carried out. Multiple parameters, including length and inner diameter (ID) of the tube, gap between the tube and tuning fork,

∗ Corresponding author. Tel.: +852 3400 8437; fax: +852 2330 1544. E-mail address: [email protected] (Y. Cao). 0925-4005/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.snb.2012.08.014

gas pressure, dimension of the tuning fork, could play important roles on the acoustic coupling and consequently the PA signal, and the relationships among them are not straightforward. To better understand the acoustic coupling between the mR and tuning fork, and to optimize the performance of the spectrophone, we report a numerical model based on COMSOL Multiphysics software with finite element method [8]. With this model, the influence of acoustic frequency, tuning fork position, and tube dimensions on the acoustic coupling and pressure distribution, and hence the generated acoustic signal are studied, and a set of parameters for optimal spectrophone performance is identified.

2. Numerical model As the physical processes involved in QEPAS are complicated and no simple analytical model can be applied, we developed a numerical model based on the COMSOL software. Two modules, pressure acoustics and piezo solid, are used for investigating acoustic coupling and piezoelectric effect of QTF respectively. Considering the symmetry of the mR and QTF, only half of the tuning fork (marked in blue) and the resonant tubes (marked in red) are included in our numerical model, as shown in Fig. 2. The boundary of gas involved is assumed to be of a spherical shape and an outer spherical shell is introduced as the perfectly matched layer (PML) to absorb the reflected acoustic wave from the boundary. Considering that the diameter of the light beam through the resonant tubes is relatively small (∼0.05 mm at waist [9]) compared to the gap between the QTF prongs (0.2 mm) and the ID of the tubes (typically ≥0.2 mm), the acoustic pressure wave may be regarded to be originated from

Y. Cao et al. / Sensors and Actuators B 174 (2012) 24–30

25

a line source along the axis of the tube and propagate all around. The source term setting in COMSOL is given by [10]: iS = i

Fig. 1. Schematic of a QEPAS spectrophone comprising of a tuning fork and two rigid resonant tubes. Light is focused though the tubes and the gap between the two prongs of tuning fork.

( − 1)˛P0 0 cS2

,

(1)

where i is the sign of imaginary part, is the adiabatic coefficient of target gas, 0 and cS are the gas density and the sound velocity in the gas, respectively, ˛ is the light absorption coefficient of the gas, and P0 is the laser power. In our simulation, the gas involved in the model is assumed to be at atmospheric pressure. The dimension of the QTF (Raltron R38) used in this model is the same as in [11], i.e., 3.636 mm × 0.54 mm × 0.232 mm for each prong and 0.2 mm for the gap between the two prongs. To better match the actual structure, the base of the QTF that is exposed to the gas is subdivided into a fixed section with a length of 2 mm and a free section with a length of 0.1 mm with rounded corner. The QTF subdomains are only active in the piezo solid module, resonant tubes are assumed to be rigid and not active, while the other subdomains are active in the pressure acoustics module. The detailed subdomain and boundary setting can be found in Ref. [10]. The acoustic pressure applied to the tuning fork prong excites mechanical oscillation of the QTF, which results in the

Fig. 2. Numerical model for spectrophone optimization. The red domains are resonant tubes and the blue ones are QTF. The unit of scale is meter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

26


electric charge accumulation in the inner and outer surface of QTF through piezoelectric effect. With an external connection between the two surfaces, an electric current signal is generated and it can be obtained by integrating the surface charge density S throughout the outer surface of QTF as Iout = ω S dA, where ω is the radial frequency of the acoustic wave. The current signal can be further converted into voltage signal through a transimpedance amplifier, which is demodulated by a lock-in amplifier. Pay attention to the fact that both the flow source (i.e., the acoustic line source) and generated current signal in this model are only half of actual case. For comparison with previous experimental results, the output current signal is normalized to absorption coefficient and laser power throughout this article.

3. Results

Fig. 3. Frequency response of the model QTF structure without resonant tubes. (For interpretation of the references to color in the text, the reader is referred to the web version of this article.)

3.1. Frequency response of QTF The resonance of QTF is determined by its geometry, material and surrounding gas pressure. And the fundamental or primary resonant frequency may be, to the first approximation, estimated from the first longitudinal resonance of a cantilever model [12]: 1.015 h f0 = 2 L2

Y , Q

(2)

where h is the thickness of prong in the direction of motion, L is the length of prong, Y is Young’s modules and Q is the density of material (78.7 GPa and 2650 kg/m3 , respectively, for Quartz). For the dimensions of Raltron R38 QTF given in Section 2, the theoretical resonant frequency is calculated to be 35.96 kHz. This is reasonably close to the experimental value of ∼32.768 kHz, considering that the effect of the QTF base is not included in this simplified cantilever model. In calculating the frequency response, a structural loss parameter of 9 × 10−6 and a dielectric loss factor of 9 × 10−4 are used for Quartz material [10], these parameters were found to give a Q-factor approaching the experimental result of the QTF in vacuum [2]. In the following simulation, the loss factors are kept the same as above. The frequency response of the model without mR in vacuum, i.e., without viscous damping, is plotted in Fig. 3 as the green line. The resonant frequency is ∼32.542 kHz and the Q-factor is calculated to be ∼93,975, very close to the experimental result of 93,456 [2]. In reality, gas sensing is usually carried out at atmospheric pressure, so the acoustic radiation and viscous damping are two main factors that affect the energy loss of QTF. Therefore, the frequency response of the model at atmospheric pressure is also simulated and shown in Fig. 3 as the blue line. The resonant frequency and Q-factor are found to be ∼32.536 kHz and 22,035, respectively. The frequency shift from vacuum to atmosphere is ∼6 Hz, but the Q-factor suffers a significant decrease, which is consistent with experimental observation [2].

3.2. Light beam offset from QTF For better acoustic detection, the light beam usually passes through the middle of the prong gap, with a small offset from the QTF opening as shown in Fig. 4(a). To obtain the optimal beam position, the light beam is moved from the opening of QTF step by step, and the corresponding normalized PA signal is recorded and plotted in Fig. 5. The optimal offset is found to be ∼0.6 mm, agreeing with the reported theoretical [9] and experimental [1] results. In the following section, the light beam is fixed at 0.6 mm down from the opening. To further test our model, we compare our result with the experimental result in Ref. [13] under the same condition. The PA signal in [13] was 2.869 mV with a feedback resistor of 10 M, a laser power of 8 mW and an absorption coefficient of 0.01 cm−1 , corresponding to a normalized current signal ∼3.6 ␮A/(W cm−1 ). This is on the same order of magnitude as our simulation result of ∼8.5 ␮A/(W cm−1 ), indicating our numerical modeling is reasonably reliable. 3.3. Performance with resonant tubes In order to enhance the PA signal, a pair of rigid tubes is usually added along the absorption path as shown in Fig. 4(b). The dimensions and relative position of the tubes could significantly affect the PA signal. 3.3.1. Effect of gap between tubes and QTF The PA signals was calculated by varying gap size between the tubes and the QTF, and Fig. 6 shows the results when the ID of the tube is fixed to 1 mm and the length of each tube to 5 mm at a frequency of 32.528 kHz. It is apparent that the PA signal decrease with increasing gap size. This is expected because a larger gap causes more acoustic energy leakage from the gap and reduces the acoustic coupling between the resonant tubes. A smaller gap is then more effective for acoustic coupling and QTF oscillation. However,

Fig. 4. (a) Relative position of light beam to QTF prongs (side view) and (b) dimensions of resonant tube and its position. ID, inner diameter.


Fig. 5. Normalized piezoelectric current as a function of beam offset from the QTF opening without resonant tubes.

if the gap is too small (