Development of a portable laser-flash photolysis Faraday rotation spectrometer for measuring atmospheric total OH reactivity

Quantitative measurements of atmospheric total OH reactivity ($k_{\mathrm{OH}}^{\prime }$) provide crucial insights into atmospheric photochemistry. However, widespread application of total OH reactivity measurements is challenging due to insufficient equipment and the complexity of existing instrumentation. In this work, we report the development of a portable laser-flash photolysis Faraday rotation spectroscopy (LP-FRS) instrument for real-time and in situ measurement of $k_{\mathrm{OH}}^{\prime }$. To achieve efficient overlapping between the pump and probe laser and realize a long effective absorption path length, thus enabling high-sensitivity measurement, a specific Herriott-type pump–probe optical multi-pass cell was designed. The instrument's optical box dimensions were 130 cm × 40 cm × 35 cm. The obtained effective absorption path was ∼ 28.5 m in a base length of 77.2 cm. The $k_{\mathrm{OH}}^{\prime }$ detection precisions of the LP-FRS instrument were 2.3 and 1.0 s⁻¹ with averaging times of 60 and 300 s, respectively. The $k_{\mathrm{OH}}^{\prime }$ measurement uncertainty was evaluated to be within 2 s⁻¹. Field measurement was performed, and the difference between the measured $k_{\mathrm{OH}}^{\prime }$ and the model simulated from the measured reactive species was analysed. The developed portable LP-FRS instrument extends the measurement methods of atmospheric total OH reactivity and has certain advantages in terms of cost, operation, and transportation, which will play an increasingly important role in future atmospheric chemistry research.

1 Introduction

The hydroxyl (OH) radical is the most important oxidant in the atmosphere during daytime. It initiates the oxidation of most natural and anthropogenic trace gas species, thereby dominating their atmospheric lifetimes. Knowledge of tropospheric OH chemistry contributes to our understanding of air pollution and climate change (Lu et al., 2018; Nicely et al., 2018). However, due to the large number (10⁴–10⁵) of volatile organic compounds (VOCs) (Goldstein and Galbally, 2007), a comprehensive interpretation of the sink mechanisms of OH is extremely challenging.

Total OH reactivity ($k_{\mathrm{OH}}^{\prime }$), the inverse of the OH chemical lifetime (τ_OH), serves as a crucial parameter for estimating the total loss rate of OH due to all atmospheric OH reactants (Yang et al., 2016). It is defined as the sum of OH reactant concentrations ([X]) weighted by their reaction rate coefficient with OH (k_OH+X), which can be expressed as

$$\begin{array}{}\text{(1)}& k_{\mathrm{OH}}^{\prime }={\mathit{\tau }}_{\mathrm{OH}}^{-\mathrm{1}}=\sum k_{\mathrm{OH}+X_i}\left[X_i\right],\end{array}$$

where X_i is the ith reactant. Measurement of $k_{\mathrm{OH}}^{\prime }$ provides a powerful tool for both field campaigns and laboratory studies in atmospheric photochemistry (Stone et al., 2012; Fuchs et al., 2013). The balance between OH production and loss rate provides additional information on the OH sources (Martinez et al., 2003; Hens et al., 2014). The difference between measured and calculated $k_{\mathrm{OH}}^{\prime }$ can be used to estimate the contribution from individually measured species, the total missing reactivity, and the role of unknown VOCs (Di Carlo et al., 2004; Mao et al., 2010; Sinha et al., 2012). The measured total OH reactivity can also be used as the chemical closure of the reactive carbon budget (Hunter et al., 2017; Safieddine et al., 2017; Heald et al., 2020). In addition, $k_{\mathrm{OH}}^{\prime }$ measurements help to estimate instantaneous production potential and the production regime of ozone (Sinha et al., 2012; Li et al., 2021, 2022; Kohno et al., 2022). Recently, the long-term trend in $k_{\mathrm{OH}}^{\prime }$ has been proven to be a key atmospheric oxidation capacity parameter for the formulation of ozone (O₃) pollution mitigation strategies (Wang et al., 2023).

Several methods for OH reactivity measurement have been developed (Yang et al., 2016; Fuchs et al., 2017), which can be divided into three categories: the indirect method, known as the comparative reactivity method (CRM) (Sinha et al., 2008, Kumar and Sinha, 2014; Michoud et al., 2015; Kim et al., 2016; Praplan et al., 2017; Yang et al., 2017); the semi-direct technique, involving flow tube–chemical ionization mass spectrometry (FT-CIMS) (Muller et al., 2018); and the direct method, including flow tube–laser-induced fluorescence (FT-LIF) (Kovacs and Brune, 2001; Mao et al., 2009; Ingham et.al., 2009; Hansen et al., 2014) and laser-flash photolysis–laser-induced fluorescence (LP-LIF) (Sadanaga et al., 2004; Lou et al., 2010; Parker et al., 2011; Stone et al., 2016).

The CRM indirectly determines $k_{\mathrm{OH}}^{\prime }$ by the competitive kinetics for OH between a reference molecule not present in normal atmospheric conditions (e.g. pyrrole) and all reactive atmospheric species in ambient air. Commercial proton-transfer-reaction mass spectrometry (PTR-MS) or gas chromatography (GC) is employed to detect the concentration change in pyrrole (Nölscher et al., 2012). The direct method determined $k_{\mathrm{OH}}^{\prime }$ from the measured time-dependent OH decay. The FT-LIF directly measures OH decay by controlling the reaction time through the movement of an OH injector along a flow tube. An LIF instrument is positioned downstream of the flow tube to monitor the OH concentration signal intensity. The sample is then drawn into the low-pressure (∼ 1.5 Torr) cell of the LIF via gas expansion. A 308 nm dye laser is used to excite OH, and the resulting 308 nm fluorescence emitted by OH is collected for concentration evaluation. The LP-LIF is a pump–probe technique where OH decay can be observed with high time resolution after each flash, without needing to determine the reaction time from the point of OH production to the sampling position. In this technique, OH is produced by laser-flash photolysis of O₃ at 266 nm across the entire illuminated area in the presence of water vapour. This makes it less susceptible to the recycling process caused by nitric oxide (NO) compared to the above instruments using water vapour photolysis (Sadanaga et al., 2004; Lou et al., 2010) because water vapour photolysis with a 184.9 nm ultraviolet (UV) lamp not only generates OH but also produces HO₂ radicals. In the presence of high atmospheric NO concentrations, the reaction of HO₂ with NO can lead to the reformation of OH, which may affect the measurement of $k_{\mathrm{OH}}^{\prime }$. In the semi-direct technique of FT-CIMS, sulfuric acid (H₂SO₄) instead of OH is measured by a CIMS instrument to record the data point of OH decay at each reaction time. The reaction time can be varied by adding 10 ppmv SO₂ at different fixed positions within the flow tube. Due to the titration reaction, OH is nearly completely converted to H₂SO₄, so the measured change in the H₂SO₄ concentration serves as an indicator of the OH.

Several intercomparisons of the techniques and instruments mentioned above have been conducted. Zannoni et al. (2015) reported a field intercomparison of two CRM instruments in the Mediterranean Basin. Hansen et al. (2015) carried out an intercomparison between the CRM and LP-LIF techniques in an urban environment. The series of intercomparison experiments conducted in the SAPHIR simulation chamber at Forschungszentrum Jülich involved all types of existing methods and nine instruments from around the world (Fuchs et al., 2017). The results show that indirect or semi-direct methods exhibit more scatter in measurements and are most likely limited by the corrections for known effects, such as high NO concentrations for CRM and high-reactivity conditions for FT-CIMS. In comparison, the direct methods (LIF) that combine laser-flash photolysis offer advantages in detection precision and accuracy. Overall, the existing techniques can give reasonable measurement results for a wide range of atmospheric conditions. However, the high cost of development and operation (e.g. the expensive and complex dye laser system and mass spectrometer system), limited instruments, the complex operation and calibration procedures, and the relatively large size of these instruments hinder the widespread application of measuring OH reactivity.

Figure 1 (a) Schematic diagram of the developed laser-flash photolysis Faraday rotation spectrometer (LP-FRS), which consists of a mid-infrared Faraday rotation spectroscopy system and a laser photolysis system. The OH radicals are generated by laser-flash photolysis at 266 nm in a Herriott cell wound with copper wires and detected simultaneously by Faraday rotation spectroscopy via the overlapping mid-infrared optical paths. P, polarizer; FM, foldable mirror; SM, silver mirror; L, lens; PD, photodetector; YM, Nd:YAG mirror; BE, beam expander; DAQ, data acquisition card. (b) Assembly diagram of the Herriott-type pump–probe multi-pass cell (MPC). The coil is wound around the body of the MPC. A water-cooling interlayer is designed for temperature control of the solenoid coil and the cell.

In this work, we report the development of a portable laser-flash photolysis Faraday rotation spectroscopy (LP-FRS) instrument for total OH reactivity measurement. The time-resolved LP-FRS is a novel technique that employs a mid-infrared semiconductor diode laser as the probe laser (with a much cheaper commercial price than the dye laser system and good stability) for $k_{\mathrm{OH}}^{\prime }$ measurement, making the technique both cost-effective and simple to operate (Wei et al., 2020). Since FRS relies on the detection of the probe light polarization state rotation induced by paramagnetic molecules in a longitudinal magnetic field, the laser noise and molecule interferences are significantly reduced, which enables the FRS system to directly and completely monitor the concentration of OH in a highly sensitive manner without any chemical interferences (Litfin et al., 1980; Zhao et al., 2018). The dimensions of the developed instrument were 130 cm × 40 cm × 35 cm. The achievable detection precision of $k_{\mathrm{OH}}^{\prime }$ was 1.0 s⁻¹ with 300 s averaging time. A field test in a suburban area was performed to demonstrate the capability of the LP-FRS instrument.

2 Experimental setup

A schematic diagram of the developed LP-FRS instrument is given in Fig. 1a. The instrument comprises a mid-infrared FRS system for direct measurement of OH and an ultraviolet (UV) laser-flash photolysis system for generating OH. The probe light and the UV beam overlap in a Herriott-type optical multi-pass cell (MPC), enabling simultaneous monitoring of OH by the FRS system during the generation and reaction with reactants. Optical components from both systems are integrated into a single unitary box, with all communications and gas tubes connected to designated interfaces. The optical box has dimensions of 130 cm × 40 cm × 35 cm and a total weight of ∼ 90 kg. The instrument's total operation power consumption is ∼ 3 kW. These factors make the developed LP-FRS instrument both cost-effective and portable for field applications.

2.1 Mid-infrared Faraday rotation spectrometer

A mid-infrared continuous-wave distributed-feedback laser (cw-DFB laser, Nanoplus GmbH) emitting at 2.8 µm is used as the probe laser. The current and temperature of the laser chip are controlled by a laser controller (LDC501, Stanford Research Systems). By changing the injection current from 90 to 130 mA at an operating temperature of 33 °C, the wavelength of the DFB laser can be tuned from 3568.939 to 3568.362 cm⁻¹. The current tuning coefficient is about 0.0024 ${\mathrm{cm}}^{-\mathrm{1}}{\mathrm{mA}}^{-\mathrm{1}}$ near the target Q(1.5e) line of the ${}^{\mathrm{2}}{\mathrm{\Pi }}_{\mathrm{3}/\mathrm{2}}$ state of OH at 3568.523 cm⁻¹. The selected line has the strongest line strength of S = 9.032 × 10⁻²⁰ ${\mathrm{cm}}^{-\mathrm{1}}(\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{2}})$ at 296 K (Gordon, et al., 2022) with the largest effective g_J value of 0.936 in the infrared region, which make it preferable for the FRS detection (Zhao et al., 2011, 2012). The collimated beam output from the laser head passes through a Rochon prism (Foctek Photonics), with an extinction ratio of ξ < 5 × 10⁻⁶, to establish a linearly polarized state, and then is incident into a Herriott-type pump–probe MPC. A He−Ne laser serves as an indicator. The beam waists of both lasers are aligned at the centre of the MPC to minimize beam divergence after each reflection (Pilgrim et al., 1997). A flipper optical mount facilitates switching between the two lasers. A second Rochon prism is placed at the output path to analyse the polarization state. The exit beam from the MPC is focused on a thermoelectrically cooled mercury cadmium telluride (MCT) photodetector (PVI-4TE-3.4, VIGO system). To effectively modulate the magnetic circular birefringence in a static magnetic field (Zhao et al., 2018; Fang et al., 2020; Wei et al., 2020), a 33 kHz sinusoidal wave from a lock-in amplifier (SR830, Stanford Research Systems) is added to the laser injection current. The detector signal is processed by the lock-in amplifier to demodulate the second harmonic (2f) of the FRS signal. As the laser current is fixed at the absorption peak of the OH radical, a time-resolved Faraday rotation spectrum that directly reflects the concentration variation in OH radicals can be measured (Wei et al., 2020; Cheng et al., 2023).

The pump–probe MPC, as shown in Fig. 1b, consists of a cylindrical stainless steel tube with an inner diameter of 5 cm, a total length of approximately 89 cm, and a sample volume of 1.5 L. At both ends, a pair of 6.8 cm diameter calcium fluoride (CaF₂) windows are used for sealing and light transmission. Two gold-coated concave spherical mirrors, each 5 cm in diameter, are spaced 77.2 cm apart within the cell. Each mirror features a 5 mm diameter hole for probe light incidence and exit and a central 32 mm diameter hole (i.e. the maximum diameter permissible for the UV beam passage) for the expanded photolysis beam. Mirror tilt and spacing are adjustable via three screws distributed circularly on the mirror mount. At each end of the MPC, there are eight circular quartz observation windows near the mirrors to facilitate multi-pass light adjustments. A total of 25 reflection spots are arranged on the mirror surfaces in a circular pattern with 2 cm radius. The total path length of the MPC is 37.8 m.

A solenoid coil, wrapped with 1 mm diameter red-copper enamelled wires, is wound around the stainless steel tube and operates in DC mode to offer a static magnetic field for FRS. The length and the outer diameter of the coil are 59 cm and 10 cm, respectively. The magnetic intensity tuning coefficient at the centre of the coil is 73 G/A. A water-cooling interlayer is designed for temperature control of both the solenoid coil and the cell.

2.2 Ultraviolet laser-flash photolysis system

A flashlamp pumped Nd:YAG laser (Big Sky Laser Ultra 100, Quantel) is employed as the photolysis laser. The laser wavelength is frequency doubled to generate the fourth harmonic radiation at 266 nm with a pulse energy of 25 mJ, energy stability of ∼ 2 %, pulse length of ∼ 6 ns, and beam diameter of ∼ 4 mm. The water-cooled laser head has a size of ∼ 30.6 cm × 7.6 cm × 5.6 cm and is controlled by an integrated cooling and electronics unit. The 266 nm pulse emitted from the laser head is directed coaxially into the MPC using two dielectrically coated 1 in. diameter mirrors. Prior to entering the cell, the diameter of the 266 nm beam is expanded to 32 mm using a beam expander consisting of a quartz concave lens with a focal length of 12.5 mm and a quartz convex lens with a focal length of 100 mm.

A digital delay generator (DG645, Stanford Research Systems) was used to control the time sequence of laser-flash photolysis to record the time-resolved OH decay curve. The pump and Q switch of the Nd:YAG laser are synchronized with two 4 Hz transistor–transistor logic (TTL) pulses delayed by 30 ms relative to the data acquisition to achieve the baseline of the OH decay curve. The rising edges of the pulses are used for triggering. The spectrum is sampled with 1000 data points, each separated by a time interval of 0.2 ms.

Figure 2 (a) Schematic of the Herriott multi-pass cell and the beam pattern on mirror surface for the pump–probe; (b) multi-pass light waist (r_c), g value, and overlapping factor (η) as functions of θ. θ is half of the angle between two adjacent reflection spots. The θ of 158.4° is selected, achieving an r_c = 3.7 mm and an η of 75.4 %.

Table 1 Overlapping factor comparison of MPCs used for laser photolysis in pump–probe techniques.

3 Instrument performance

3.1 Characterization of the pump–probe MPC

The MPC in the instrument determines the effective absorption path length of the FRS system for OH measurement (Wei et al., 2020; Yan et al., 2020). As shown in Fig. 2a, the mid-infrared light undergoing multiple passes between two mirrors within the MPC is used for OH detection; the expanded 266 nm UV pulse is employed for producing OH. The overlapping factor ($\mathit{\eta }=l/d$) can be defined as the ratio of the overlapping length (l) to the base length (d) of the MPC. To develop portable instruments, increasing the overlapping factor is crucial for achieving a long effective path length while reducing the MPC base length. The Herriott MPC in the developed LP-FRS instrument is specially designed with a small multi-pass light distribution circle radius at the centre to achieve a high overlapping factor. The radius of the multi-pass light distribution circle at the centre of the Herriott MPC can be calculated with (Trutna and Byer, 1980)

$$\begin{array}{}\text{(2)}& r_{\mathrm{c}}=r{\left({\displaystyle \frac{g_{\mathrm{1}}+\mathrm{2}{g}_{\mathrm{1}}{g}_{\mathrm{2}}+g_{\mathrm{2}}}{\mathrm{4}{g}_{\mathrm{2}}}}\right)}^{\mathrm{1}/\mathrm{2}},\end{array}$$

where g ($g=g_{\mathrm{1}}=g_{\mathrm{2}}=\cos \mathit{\theta }=\mathrm{1}-d/R$) is the parameter that describes the optical resonance stability of the optical cavity or MPC. When the g value is less than zero, the base length of the multi-pass cell exceeds the curvature radius of the mirror, causing the resonance to become unstable. An incident parallel beam or a beam whose waist is not properly aligned with the cell's centre will quickly diverge and cannot be collected. However, a beam with its waist well matched to the centre can effectively prevent divergence. θ is half of the angle between two adjacent reflection light points on the mirror surface. d is the base length, and $R_{\mathrm{1}}=R_{\mathrm{2}}=R$ is the curvature radii of the mirrors. r is the radius of the spot distribution circle.

Figure 2b illustrates the variations in r_c, g, and η as functions of θ. When the θ value is below 79.2, r_c exceeds the 16 mm radius of the photolysis beam, resulting in no overlapping path. As θ approaches −1, the value of r_c decreases, and the η value increases. Considering the difficulties in processing and testing mirror curvature, θ was set to 158.4°, yielding an r_c value of 3.7 mm. The achieved η was up to ∼ 75.4 %, corresponding to an overlapping path length of ∼ 28.5 m.

In fact, from an optical structure perspective, the overlap factor characterizes both the utilization efficiency of the optical path length and the compactness of the pump–probe MPC, making it an ideal parameter for performance characterization. To demonstrate the efforts in reducing instrument size, a comparison of effective overlapping path lengths and overlapping factors with the literature-reported pump–probe MPCs is shown in Table 1. The effective overlapping path length of these MPCs ranged from several metres to tens of metres with base lengths around 100 cm (Pilgrim et al., 1997; Luo et al., 2019; Qian et al., 2000; Lewis et al., 2018; Luo and Horng, 2020; Luo, 2020; Wei et al., 2020; Yan et al., 2020; Teng et al., 2021; Cheng et al., 2023). The overlapping factor of our MPC was comparable to that developed by Luo et al. (2019) for a similar base length, while our effective overlapping path length was twice as long.

Figure 3 (a) Noise and (b) signal-to-noise ratio analysis of the FRS system. The optimum offset angle of the analyser is 8°.

3.2 Optimization of the FRS system

For weak absorption, the FRS signal (S_FRS) and total noise (N_tot) of the system can be expressed as functions of the analyser offset angle (ϕ) from the crossed polarization of the light (Zhao et al., 2011; Wei et al., 2020):

$$\begin{array}{}\text{(3)}& {\displaystyle }& {\displaystyle }{S}_{\text{FRS}}\left(\mathit{\nu }\right)=\mathit{\gamma }NS{\text{LP}}_{\mathrm{0}}\sin \left(\mathrm{2}\mathit{\varphi }\right)\mathit{\chi }\left(\mathit{\nu }\right),\text{(4)}& {\displaystyle }& {\displaystyle }{N}_{\text{tot}}\left(\mathit{\varphi }\right)=\sqrt{\begin{array}{c}{N}_{\mathrm{0}}^{\mathrm{2}}+{\left(N_{\mathrm{1}}\sqrt{\left({\sin }^{\mathrm{2}}\right(\mathit{\varphi })+\mathit{\xi })}\right)}^{\mathrm{2}}\\ +{\left(N_{\mathrm{2}}\left({\sin }^{\mathrm{2}}\right(\mathit{\varphi })+\mathit{\xi })\right)}^{\mathrm{2}},\end{array}}\end{array}$$

where ν is the laser frequency, γ is the instrumentation factor, N is the OH concentration, S is the absorption line strength of OH, and χ is the Faraday rotation line shape (Westberg and Axner, 2014). N₀, $N_{\mathrm{1}}\sqrt{\left({\sin }^{\mathrm{2}}\right(\mathit{\varphi })+\mathit{\xi })}$, and N₂(sin ²(ϕ)+ξ) are the detector noise, shot noise, and laser noise of the system, respectively. It is noted that the FRS signal reaches its maximum value when ϕ =  ± 45°, while the total noise is more sensitive to sin ²(ϕ). The maximum signal-to-noise ratio (SNR) usually occurs at a small offset angle, which depends on system noise (Lewicki et al., 2009).

The total noises at various offset angles and the detector noise were measured with the lock-in amplifier to determine the noise sources and the optimum angle (ϕ_opt) for maximizing the SNR of the FRS system (Zhao et al., 2011). Figure 3a shows a fit analysis of the data using Eq. (4). For offset angles below 5.5°, detector noise is the main noise of the system. The measured detector noise was 300 $\mathrm{nV}{\mathrm{Hz}}^{-\mathrm{1}/\mathrm{2}}$, which closely agreed with the manufacturer's specified value of 290 $\mathrm{nV}{\mathrm{Hz}}^{-\mathrm{1}/\mathrm{2}}$. Laser noise dominates and rapidly increases beyond an offset angle greater than 11.5°. Since the FRS signal is proportional to sin (2ϕ), the relative SNR for a given absorption at a fixed laser frequency can be evaluated from $\mathrm{SNR}\propto \sin \left(\mathrm{2}\mathit{\varphi }\right)/N_{\text{tot}}$. As shown in Fig. 3b, the SNR of our system peaks at the ϕ_opt of ∼ 8°. At this angle, the laser noise was suppressed to 310 $\mathrm{nV}{\mathrm{Hz}}^{-\mathrm{1}/\mathrm{2}}$, equivalent to the detector noise level. The total system noise was 610 $\mathrm{nV}{\mathrm{Hz}}^{-\mathrm{1}/\mathrm{2}}$, which was 1.4 times higher than the measured shot noise of 440 $\mathrm{nV}{\mathrm{Hz}}^{-\mathrm{1}/\mathrm{2}}$.

Figure 4 FRS signal intensity as functions of the (a) modulation amplitude and (b) current of the coil. The optimum modulation amplitude and magnetic field strength are 360 mV_rms and 307 G, respectively.

In this work, the magnetic circular birefringence of OH was effectively modulated with wavelength modulation in a static magnetic field generated by the DC coil. The modulation amplitude and magnetic field strength are critical parameters that affect the intensity of the demodulated FRS signal (Zhao et al., 2018; Fang et al., 2020). The theoretical optimum modulation amplitude is 2.2 times the half-width at half-maximum (HWHM) of the absorption line shape (Schilt et al., 2003). The optimum magnetic field strength (B_opt) is the value that can make the Zeeman splitting comparable with the HWHM (Brecha et al., 1997). A direct and effective approach for determining the two optimum parameters is recording the signal intensity values under series amplitudes of the sinusoidal wave output from the lock-in amplifier and different coil currents. As shown in Fig. 4, the FRS signal intensity value is calculated from the difference before and after the laser flash. The maximum intensity occurred at an amplitude of 360 mV and a coil current of 4.2 A, which corresponds to a wavelength modulation amplitude of ∼ 0.048 cm⁻¹ (∼ 2.45 times the calculated OH absorption linewidth of ∼ 0.020 cm⁻¹ in air) and a B_opt of 307 G, respectively.

3.3 OH concentration in the cell

To produce sufficient OH in the MPC, a small flow rate (∼ 0.25 L min⁻¹) of zero air, which passed through a UV lamp (UVP Pen-Ray, Analytik Jena) and a bubbling bottle to generate O₃ and water vapour, is added to the main sampling flow (∼ 6.0 L min⁻¹), resulting in a total flow rate of 6.25 L min⁻¹. The operation pressure in the MPC is set to 200 mbar and maintained by a butterfly valve (DN40, VAT). The flow velocity in the cell is 27 cm s⁻¹, corresponding to a Reynolds number of ∼ 170, which met the laminar flow condition. OH is produced by the 266 nm laser photolysis of O₃ and then followed by reaction of O(¹D) with water vapour (Sadanaga et al., 2004):

$$\begin{array}{}\text{(R1)}& {\displaystyle }& {\displaystyle }{\mathrm{O}}_{\mathrm{3}}+hv(\mathit{\lambda }=\mathrm{266}\mathrm{nm})\to {\mathrm{O}}_{\mathrm{2}}+\mathrm{O}{(}^{\mathrm{1}}\mathrm{D}),\text{(R2)}& {\displaystyle }& {\displaystyle }\mathrm{O}{(}^{\mathrm{1}}\mathrm{D})+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\to \mathrm{2}\mathrm{OH}.\end{array}$$

The concentrations of O₃ and the water vapour directly influence the OH produced. A dew point sensor was used to measure the water vapour mixing ratio of the total flow. Based on the Magnus–Tetens formula (Lawrence, 2005), the absolute water vapour mass concentration can be evaluated from $\mathit{\rho }\left({\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right)=e/(R_{\mathrm{w}}\cdot T)$, where R_w = 461.52 J (kg K)⁻¹, T is the sample temperature, $e=C\times {\mathrm{10}}^{(A\cdot T_{\mathrm{d}}/(B+T_{\mathrm{d}}\left)\right)}\cdot (P/P_{\mathrm{0}})$ is the actual water vapour pressure at a current pressure of P, A = 17.625, B = 243.04 °C, C = 610.94 Pa, P₀ is the standard atmospheric pressure, and T_d is the measured dew point temperature. The calculated water vapour volume concentration was ∼ 0.13 % when using zero air for the system test, while it increased to ∼ 1.5 % when measuring the real atmosphere. The O₃ concentration is estimated by measuring the energy of the photolysis laser pulse with the UV lamp on and off. Only about 0.3 % of the pulse energy was absorbed by O₃. Based on the Beer–Lambert law and the O₃ absorption cross section of σ = 9.65 × 10⁻¹⁸ cm² at 266 nm (Sadanaga et al., 2004), the O₃ concentration is determined to be ∼ 800 ppbv. The recommended quantum yield of the O(¹D) produced by laser-flash photolysis is ∼ 0.9 (Atkinson et al., 2004), resulting in ∼ 2.2 × 10¹¹ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ of O(¹D). The number density of OH produced by each O(¹D) can be estimated by (Wei et al., 2020)

$$\begin{array}{}\text{(5)}& \left[\mathrm{OH}\right]={\displaystyle \frac{\mathrm{2}{k}_{\mathrm{6}}\left[\mathrm{O}{(}^{\mathrm{1}}\mathrm{D}\right)]\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]}{\left(k_{\mathrm{5}}\right[M]+k_{\mathrm{6}}\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right])\left[\mathrm{O}{(}^{\mathrm{1}}\mathrm{D}\right)]}}\cong {\displaystyle \frac{\mathrm{2}{k}_{\mathrm{6}}}{k_{\mathrm{5}}}}{\mathit{\chi }}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}},\end{array}$$

where [OH], [O(¹D)], [H₂O], and [M] represent the number densities of the corresponding molecule. M is the “bath” gas during the chemical reaction of OH formation. ${\mathit{\chi }}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ is the volume concentration of water vapour. k₅ and k₆ are 2.9 × 10⁻¹¹ and 2.2 × 10⁻¹⁰ ${\mathrm{cm}}^{\mathrm{3}}\mathrm{molec}{.}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$ at 298 K, respectively. The concentration of OH produced in the cell was ∼ 4.3 × 10⁹ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ during the system test and ∼ 5 × 10¹⁰ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ during the field application due to different ${\mathit{\chi }}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ in the sample.

3.4 Kinetics test

The performance of the LP-FRS instrument in measuring different reaction rates was verified with three well-known reactions (Wei et al., 2020; Yan et al., 2020). Reactants from the cylinders (i.e. CH₄ (99.999 %, Nanjingteqi), CO (2.01 %, Nanjingteqi), and NO (100 ppmv, Linde)) were added to the main flow at different flow rates. When the concentrations of reactants are much higher than those of OH, the OH decay rate (k_decay) follows pseudo-first-order kinetics and can be determined by fitting the measured decay spectra to the following exponential equation:

$$\begin{array}{}\text{(6)}& S_t=S_{\text{background}}+S_{\mathrm{0}}\exp (-k_{\text{decay}}t),\end{array}$$

where S₀ and S_t are the FRS signal intensities proportional to the OH concentration at the time when the fitting started and at the time t, respectively. S_background is the background signal intensity. Since the fitted values for y and k_decay do not depend on the selected time period of the decay curve (Stone et al., 2016), the fit is started at the time of 36 ms rather than the peak to avoid any fluctuations affecting the fitting result. Figure 5 shows two typical decays with loss rates of k_decay = 8.4 s⁻¹ and k_decay = 50.2 s⁻¹, which are given with a 60 s averaging time during the measurements. The recorded time-resolved decay spectra clearly depict the entire event, including the baseline, the instant generation of OH by laser photolysis, and the decay process.

Figure 5 Two typical OH decay spectra with different loss rates. Time zero is defined as the moment when the data acquisition trigger occurs.

Figure 6 Plots of the measured pseudo-first-order rate coefficients vs. (a) CH₄ concentrations, (b) CO concentrations, and (c) NO at 298 K. The measured reaction rate constants obtained from the slopes are $k_{\mathrm{OH}+{\mathrm{CH}}_{\mathrm{4}}}={\mathrm{6.4}}_{+\mathrm{0.1}}^{-\mathrm{0.1}}\times$ 10⁻¹⁵, $k_{\mathrm{OH}+\mathrm{CO}}={\mathrm{1.6}}_{+\mathrm{0.1}}^{-\mathrm{0.1}}\times$ 10⁻¹³, and $k_{\mathrm{OH}+\mathrm{NO}}={\mathrm{3.0}}_{+\mathrm{0.1}}^{-\mathrm{0.1}}\times$ 10⁻¹² ${\mathrm{cm}}^{\mathrm{3}}\mathrm{molec}{.}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$, which agree with the recommended values of ${\mathrm{6.4}}_{+\mathrm{1.3}}^{-\mathrm{1.1}}\times$ 10⁻¹⁵, ${\mathrm{1.6}}_{+\mathrm{0.2}}^{-\mathrm{0.2}}\times$ 10⁻¹³, and ${\mathrm{3.0}}_{+\mathrm{0.8}}^{-\mathrm{0.6}}\times$ 10⁻¹² ${\mathrm{cm}}^{\mathrm{3}}\mathrm{molec}{.}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$, respectively.

The OH decay rates in the reactions with three different species were measured and can be expressed as $k_{\text{decay}}=k_{\mathrm{OH}+X}\left[X\right]+k_{\mathrm{0}}$, where k_OH+X is the measured rate constant for the reaction of OH with X, [X] is the concentration of reactant X, and k₀ is a background value. As shown in Fig. 6, the obtained reaction rate constants for OH + CH₄, OH + CO, and OH + NO at 298 K were found to be $k_{\mathrm{OH}+{\mathrm{CH}}_{\mathrm{4}}}={\mathrm{6.4}}_{+\mathrm{0.1}}^{-\mathrm{0.1}}\times$ 10⁻¹⁵, $k_{\mathrm{OH}+\mathrm{CO}}={\mathrm{1.6}}_{+\mathrm{0.1}}^{-\mathrm{0.1}}\times$ 10⁻¹³, and $k_{\mathrm{OH}+\mathrm{NO}}={\mathrm{3.0}}_{+\mathrm{0.1}}^{-\mathrm{0.1}}\times$ 10⁻¹² ${\mathrm{cm}}^{\mathrm{3}}\mathrm{molec}{.}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$, respectively. The measured values are in agreement with the International Union of Pure and Applied Chemistry (IUPAC) recommended values of ${\mathrm{6.4}}_{+\mathrm{1.3}}^{-\mathrm{1.1}}\times$ 10⁻¹⁵, ${\mathrm{1.6}}_{+\mathrm{0.2}}^{-\mathrm{0.2}}\times$ 10⁻¹³, and ${\mathrm{3.0}}_{+\mathrm{0.8}}^{-\mathrm{0.6}}\times$ 10⁻¹² ${\mathrm{cm}}^{\mathrm{3}}\mathrm{molec}{.}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$, respectively (Atkinson et al., 2004, 2006).

3.5 Precision and uncertainty of $k_{\mathrm{OH}}^{\prime }$ measurement

When the LP-FRS instrument is used for measuring atmospheric $k_{\mathrm{OH}}^{\prime }$, the fitted k_decay value requires corrections for dilution and instrument zero (k_zero). Incorporating these corrections, the atmospheric $k_{\mathrm{OH}}^{\prime }$ is expressed as

$$\begin{array}{}\text{(7)}& k_{\mathrm{OH}}^{\prime }=f\times (k_{\text{decay}}-k_{\text{zero}}),\end{array}$$

where f, given by $f=f_{\text{pressure}}\times f_{\text{flow}}$, is the total dilution factor, which arises from the low operating pressure of 200 mbar and the additional small flow of humidified air containing a constant mixing ratio of O₃. f_pressure represents the pressure dilution factor given by the ratio of the ambient pressure to the operation pressure, equal to ∼ 5. f_flow is the flow dilution factor calculated as the ratio of the total flow rate of 6.25 L min⁻¹ to the sample flow rate of 6.0 L min⁻¹, equal to 1.04. Therefore, the total correction factor (f) is 5.2.

The instrument zero is critical for calculating $k_{\mathrm{OH}}^{\prime }$ from the observed OH decay rate and is usually assumed constant over a certain observation period. To evaluate instrument zero, OH decay rates were measured in zero air produced by a portable zero gas generator, yielding a k_zero of 5.2 s⁻¹. Several factors affect the instrument zero, including the self-reaction of OH, reaction of OH with O₃, OH diffusion, and reaction of OH with residual reactive species in zero air. The self-reaction rate constant of OH is 1.48 × 10⁻¹² ${\mathrm{cm}}^{\mathrm{3}}\mathrm{molec}{.}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$ at 298 K (Atkinson et al., 2004), contributing to ∼ 1.5 % of the instrument zero at the current OH concentration. The reaction rate constant of OH with O₃ is 7.3 × 10⁻¹⁴ ${\mathrm{cm}}^{\mathrm{3}}\mathrm{molec}{.}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$ at 298 K (Atkinson et al., 2004), leading to an OH loss rate of 0.3 s⁻¹, which accounts for ∼ 6 % of the instrument zero. The OH loss rate due to diffusion (k_dif) under laminar flow conditions can be calculated from (Ivanov et al., 2007; Liu et al., 2009)

$$\begin{array}{}\text{(8)}& k_{\text{dif}}=K_{\text{dif}}\times {\displaystyle \frac{D_{\mathrm{OH}}}{r_{\text{tube}}^{\mathrm{2}}}},\end{array}$$

where K_dif=3.66 (for a cylinder cell) is the dimensionless geometric parameter, r_tube is the radius of the cell, and D_OH = 1.3 cm² s⁻¹ is the OH diffusion coefficient at 200 mbar and 298 K in air. The calculated OH diffusion loss rate was 0.8 s⁻¹, giving a contribution of ∼ 15 % of the instrument zero.

To assess the measurement precision of the LP-FRS instrument, an Allan deviation analysis was conducted on time series of zero-air measurements. The measured values were processed by subtracting the instrument zero. As shown in Fig. 7, the averaging time of the $k_{\mathrm{OH}}^{\prime }$ data point was 10 s, with a total measurement time of about 4000 s. The measurement precisions of $k_{\mathrm{OH}}^{\prime }$ were 2.3 and 1.7 s⁻¹ with an acquisition time of 60 s and 120 s, respectively. When the averaging time increased to 300 s, the atmospheric $k_{\mathrm{OH}}^{\prime }$ measurement precision could be further improved to 1.0 s⁻¹.

Figure 7 (a) Time series of zero air with 10 s time resolution and (b) the Allan deviation analysis of the time series. The measurement precision of $k_{\mathrm{OH}}^{\prime }$ can be improved to 2.3 and 1.0 s⁻¹ with averaging times of 60 s and 300 s, respectively.

A comprehensive approach to evaluating the instrument's total uncertainty is measuring zero air. Figure 8 illustrates the $k_{\mathrm{OH}}^{\prime }$ values obtained from zero air on different days. Each value was obtained from 1 h continuous measurements. The time intervals for these zero-value measurements are longer than 2 weeks. The error bars of the data points agreed well with the $k_{\mathrm{OH}}^{\prime }$ measurement precision obtained from Allan deviation analysis. No significant drift was found during measurements, with a mean value close to zero at 0.2 s⁻¹. The $k_{\mathrm{OH}}^{\prime }$ measurement uncertainty of the developed LP-FRS instrument, which can be determined from the deviations of these measurements, was within 2 s⁻¹. The uncertainty of the LP-FRS instrument arises from two main sources: the dilution factor and the instrument zero. The uncertainties associated with the mass flowmeters and the pressure controller used were ∼ 1 % and < 1 %, respectively, resulting in a total uncertainty of the dilution correction factor of less than 2 %. The uncertainty of the instrument zero primarily originates from various influencing factors, such as changes in O₃ concentrations and residual reactants in zero air and water.

Figure 8 Measured $k_{\mathrm{OH}}^{\prime }$ values of zero air on different days. The total instrument uncertainty, determined from the measurement deviations, is within 2 s⁻¹.

4 Field performance

The capability of the developed LP-FRS instrument was demonstrated through field measurements of atmospheric total OH reactivity. Measurements were conducted at the park of the Hefei Institutes of Physical Science, Chinese Academy of Sciences (31°91^′ N, 117°16^′ E) (Khayyam et al., 2024). This observation site is situated on a peninsula in a suburban area, surrounded by water on three sides. There were also an optical factory and several mechanical processing factories located on the peninsula. The observation period spanned 1 to 4 May 2023.

The LP-FRS instrument was housed in a container with the sampling port positioned ∼ 1.2 m above the container's roof. In addition to measuring OH reactivity, concentrations of 115 kinds of VOCs were analysed using a gas chromatograph coupled with a flame ionization detector and mass spectrometer (GC-FID/MS; TSQ 9000, Thermo Fisher) with a time resolution of 1 h. The VOCs included 29 alkanes (alka), 12 alkenes (alke), 16 aromatic hydrocarbons (arom), 35 halogenated hydrocarbons (halo), 21 oxygenated volatile organic compounds (OVOCs), 1 alkyne, and 1 carbon disulfide. Concentrations of NO, NO₂, and O₃ were measured employing an NO_x analyser (42i, Thermo Fisher) and an O₃ analyser (49i, Thermo Fisher). Data of ambient temperature (T) and relative humidity (RH) were obtained from an automatic monitoring station located ∼ 100 m from the container. The photolysis rate constant of J(NO₂) was measured with a photolysis spectrometer (PFS-100, Focused Photonics).

Figure 9 Time series of observed meteorological and chemical parameters, including ambient temperature; relative humidity; total OH reactivity; photolysis frequencies (J(NO₂)); and concentrations of O₃, NO, NO₂, and VOCs. The time period is from 1 to 4 May 2023.

Figure 10 (a) Stack of diurnal profiles of observed $k_{\mathrm{OH}}^{\prime }$ compared with calculated OH reactivity from individual groups of measured atmospheric species; (b) pie chart of contributions from each group to total reactivity.

An overview of observed meteorological and gas concentrations is given in Fig. 9. The average temperature and relative humidity during the observation period were 25.6 °C (range from 21.9 to 30.8 °C) and 53.8 % (range from 21 % to 90 %), respectively. The large changes in J(NO₂) were due to the rainy weather on 3 May and cloudy conditions on 4 May. Table 2 summarizes the mean and median concentrations of the measured species during the observation period. The mean concentrations of NO, NO₂, and O₃ were 1.5, 10.0, and 36.7 ppbv, respectively. Alkanes, OVOCs, and hydrocarbons were the three VOCs with the highest concentrations during the period. The corresponding mean concentrations were 9.1, 7.1, and 4.9 ppbv, respectively. The measured BVOCs only include isoprene, with a mean concentration of 0.2 ppbv. The minimum and maximum values of $k_{\mathrm{OH}}^{\prime }$ were 10.6 and 30.0 s⁻¹, respectively.

Table 2 The mean and median concentrations of measured species during the observation period in the form of classification.

The reactive species and $k_{\mathrm{OH}}^{\prime }$ exhibited distinct daily variations on 1 May (the first day of the International Labour Day holiday). The peak of VOC concentrations (60 ppbv) appeared at 03:00 LT. The concentrations of NO began increasing significantly from 03:00 LT onwards, reaching a peak of 23.7 ppbv around 05:00 LT. Concurrently, the abundant NO reacted with O₃, resulting in the lowest observed O₃ concentration (∼ 5 ppbv) and an increase in NO₂ level. $k_{\mathrm{OH}}^{\prime }$ and NO₂ reached their peak values of 30.0 s⁻¹ and 29.3 ppbv at about 08:00 LT in the morning, declining rapidly as sunlight intensified, with the lowest values observed between 12:00 and 13:00 LT. The highest O₃ concentration (59.3 ppbv) occurred around 17:00 LT in the afternoon. $k_{\mathrm{OH}}^{\prime }$ and reactive species exhibited relatively low values in the following days, and no significant peak in NO concentration was observed in the afternoon. These changes could be attributed to the “holiday effect” (Fatahi et al., 2021), which reflects extensive vehicle travel on the eve and the first day of the holiday and decreased human activities near the observation site during the holiday (Song et al., 2022).

A zero-dimensional box model (Framework for 0-Dimensional Atmospheric Modelling, F0AM) based on the Master Chemical Mechanism (MCM3.3.1, https://mcm.york.ac.uk/MCM/, last access: 30 July 2024) was applied for comparison with the observed total OH reactivity (Wolfe et al., 2016; Wei et al., 2023). The model was constrained by the measured species and parameters of meteorology and photolysis. Figure 10a shows the diurnal profiles of observed and simulated $k_{\mathrm{OH}}^{\prime }$. The observed $k_{\mathrm{OH}}^{\prime }$ ranged from 14.6 s⁻¹ (at 14:00 LT) to 21.9 s⁻¹ (at 08:00 LT), with an average value of 17.5 s⁻¹. According to the pie chart analysis in Fig. 10b, inorganic species, alkenes, OVOCs, and alkanes contributed 26.4 %, 10.8 %, 10.5 %, and 5.0 % to the $k_{\mathrm{OH}}^{\prime }$, respectively. Contributions from aromatic and halogenated hydrocarbons were relatively low, accounting for 3.0 % and 0.6 %. The contribution of photochemical secondary products (others) was as high as 20.9 %, while the missing reactivity (i.e. the difference between observed and simulated $k_{\mathrm{OH}}^{\prime })$ averaged ∼ 20.5 %, highlighting the significant role of photochemical and unidentified components in local atmospheric chemistry.

5 Conclusions

A portable LP-FRS instrument was developed. A specific Herriott-type pump–probe MPC with a small multi-pass beam distribution circle radius of 3.7 mm at the centre of the cell was designed to offer an effective overlapping path length of ∼ 28.5 m between the mid-infrared probe light and the photolysis light with a high overlapping factor of 75.4 %. Such an overlapping factor benefits from reducing instrument size, resulting in dimensions of just 130 cm × 40 cm × 35 cm. The precision and uncertainty of the LP-FRS instrument for measuring atmospheric $k_{\mathrm{OH}}^{\prime }$ were 1.0 s⁻¹ (1σ, 300 s) and within 2 s⁻¹, respectively. A field test was performed at a suburban site, where the averaged measured $k_{\mathrm{OH}}^{\prime }$ was 17.5 s⁻¹ with a missing reactivity of 20.5 % compared to the model-simulated result based on measured species. The developed portable LP-FRS instrument expands the measurement capabilities for atmospheric total OH reactivity and will be employed in more field observations.