Parameterization and Application of Hydroperoxyl Radicals(HO2) Heterogeneous Uptake Coefficient

Huan Song; Qi Zou; Keding Lu

doi:10.7536/PC200749

Progress in Chemistry ›› 2021, Vol. 33 ›› Issue (7) : 1175-1187 DOI: 10.7536/PC200749

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Parameterization and Application of Hydroperoxyl Radicals(HO₂) Heterogeneous Uptake Coefficient

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Abstract

The heterogeneous uptake reactions of hydroperoxyl radicals(HO₂) on ambient atmospheric aerosols have been proposed to be a significant sink of HO₂ radicals, thus could influence the atmospheric oxidation capacity and properties of atmospheric particles. The quantitative description of the heterogeneous reaction process of HO₂ is of great significance to the exploration of atmospheric oxidation and ozone generation capacity in different regions. The HO₂ uptake coefficients measured by different research groups can differ by 3 to 5 orders of magnitude. Exploration of the heterogeneous uptake mechanism of HO₂ radical on different types of aerosols under different conditions, accurately parameterized expression of the uptake coefficient is the key to quantifying its environmental impacts. This article introduces the mechanism and parameterized expressions of HO₂ heterogeneous uptake, reviews the existing research results and progress, summarizes and analyzes the different influencing factors, and makes suggestions and prospects for the future development.

Contents

1 Introduction

2 Research progress of HO₂radical heterogeneous reaction

3 Measurements of$\gamma_{HO_{2}}$with aerosol particles

4 Factors influencing HO₂heterogeneous uptake

4.1 Effects of relative humidity and temperature on HO₂heterogeneous uptake

4.2 Promoting effect of transition metal ions on$\gamma_{HO_{2}}$

4.3 Effects of reaction time and initial HO₂concentration on$\gamma_{HO_{2}}$

4.4 Effect of aerosol pH on$\gamma_{HO_{2}}$

5 Parameterized expressions of HO₂heterogeneous uptake

5.1 Expression and characteristic time of each sub-step of heterogeneous reaction

5.2 Resistance model

5.3 Application of empirical equations of$\gamma_{HO_{2}}$in the model

6 Conclusion

Graphical abstract

Keywords

hydroperoxyl radicals(HO₂) / heterogeneous / aerosol / atmospheric oxidation capacity

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Huan Song, Qi Zou, Keding Lu. Parameterization and Application of Hydroperoxyl Radicals(HO₂) Heterogeneous Uptake Coefficient. Progress in Chemistry, 2021, 33(7): 1175-1187 DOI:10.7536/PC200749

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1 Introduction

Free radical chemistry is the core driving force of atmospheric oxidation, which plays a leading role in the formation and regional distribution of gaseous pollutants in the atmosphere^[1]. The HOx cycle is the main cycle of free radical chemistry, in which hydroxyl peroxy radical (HO₂) is an important intermediate oxidizing substance, and its source, sink and chemical lifetime have a significant impact on the atmospheric environment. As early as the 1980s, Chameides et al. Found that the gas-liquid heterogeneous reaction between HO₂ radicals and cloud water is an important way to remove HO₂ radicals, and also an important source of hydrogen peroxide in the atmosphere^[2]. Near the ground, the heterogeneous reaction of HO₂ with atmospheric particles reduces its chemical lifetime, and some studies have shown that the heterogeneous uptake of HO₂ delays the increase of tropospheric ozone concentration to a certain extent^[3]. The research on the heterogeneous reaction of HO₂ radicals is of great significance to the regional coordinated control strategy of air quality in China. However, due to many interference factors, it is difficult to measure the HO₂ uptake coefficient by direct measurement in the field. In laboratory studies, the heterogeneous reaction coefficients of different aerosols and HO₂ have great differences and uncertainties. The accurate measurement and parameterization of the heterogeneous uptake coefficient of HO₂ is the key to quantify the atmospheric lifetime of HO₂ radicals.

2 Research Progress of Heterogeneous Reaction of HO₂ Radical

The gas-liquid heterogeneous reaction between HO₂ and cloud water has been studied since 1972^[2]. Until the 1980s, researchers found that gas-phase HO₂ molecules were transported into the liquid phase through heterogeneous media, which promoted the relevant liquid-phase reactions in cloud water^[4⇓⇓~7]. Schwartz proposed a basic model in 1984, which combines the significant characteristics of gas-liquid two-phase chemical coupling of HO₂ in liquid cloud water, and simplifies the calculation and simulation of heterogeneous reactions on the basis of Fuchs et al^[8]^[9]. Subsequently, in 1985, Bielski et al. sorted out the reaction mechanism and reaction rate of in liquid phase, studied the influence of pH value of cloud water on the equilibrium of $HO_{2}/{O_{2}}^{-}$, and proposed that transition metal ions (TMI), such as copper ions, would catalyze the transformation of HO₂ into H₂O₂^[10]. At the same time, due to the control of pH value, the reaction rate constant of $HO_{2}/{O_{2}}^{-}$ with divalent copper ion in cloud water and aerosol condensation phase should be 1.5×10⁷M^-1·s^-1 (still overestimated), rather than 1×10⁹M^-1·s^-1 as generally believed. Schwartz et al. (1986) further proposed that the following sub-processes exist in the gas-liquid heterogeneous reaction process of cloud water medium: (1) mass transfer of gaseous reactants to the gas-liquid interface^[11]; (2) mass transfer across the interface and dissolution equilibrium at the interface; (3) liquid-phase equilibrium reactions of dissolved gas-phase reactants, such as hydration or acid-base equilibrium; (4) liquid phase mass transport of the relevant reactants in the droplets; (5) liquid phase chemical reaction; (6) mass transfer of the reaction product in the liquid phase; (7) re-volatilizing the volatizable product to the gas phase.

The above heterogeneous reactions are mainly concentrated between cloud water and HO₂. After that, Mozurkewich et al. First measured the HO₂ heterogeneous uptake aggregation coefficient α of copper-containing aerosols in 1987^[12]. Unlike cloud droplets, aerosol particles are smaller in size, and the gas phase diffusion limitation of gas phase reactants is not significant, but the tendency of volatile substances to return to the gas phase system is stronger than that of cloud droplets. The experimental results show that the HO₂ aggregation coefficient of copper-bearing NH₄HSO₄ particles is 0.4 ~ 0.21, and the HO₂ aggregation coefficient of copper-bearing LiNO₃ particles is 0.95 ~ 0.5. The catalytic effect of copper ions in the condensed phase of aerosol particles on the

O 2 -

of HO₂/ was confirmed for the first time, and the variation curve of HO₂ with copper ion concentration was obtained. It was proposed that the reaction products of HO₂ and copper ions were the possible source of H₂O₂ in the atmosphere. Subsequently, in 1991, Ross et al. Further studied the heterogeneous reaction of Cu-catalyzed HO₂, simulated the effects of relative humidity, pH value, particle size and other factors on the reaction rate, used the characteristic time to show the contribution of each sub-step of the uptake reaction to the overall reaction, and corrected the ionic strength of the reactants^[13]. The simulation results show that the reaction rate of copper-containing aerosol particles with HO₂ in the atmosphere is of the same order of magnitude as the rate of gas-phase reaction to produce H₂O₂. This indicates the possibility that the uptake of HO₂ by aerosols has an impact on their atmospheric chemical lifetimes, which is related to the effective copper ion concentration in the aerosol condensed phase. When the relative humidity is less than 90%, the heterogeneous uptake coefficient of the HO₂ is mainly affected by the mass transfer. With the change of physical and chemical properties and composition of aerosol, its particle size, mass concentration and water content will change, which will affect the effective copper ion concentration in the condensed phase of aerosol, which is also a difficult point in the study of HO₂ and heterogeneous uptake of aerosol.

In 1994, Hanson et al. Referred to Danckwerts et al.'S parameterization formula for the uptake coefficient of thin sheet liquid surface in 1951 and 1970, and made further derivation and modification for the equivalent diameter of aerosol particles, and proposed a parameterization formula for the heterogeneous uptake of free radicals reacting with particles^[14]^[15,16]. The parameterization formula is based on the assumption of steady-state equilibrium, constant liquid diffusion rate and pseudo-first-order reaction in the liquid phase. In 1996, Cooper et al. Measured the gas-solid heterogeneous uptake coefficients of OH and HO₂ on ice crystal, NH₄HSO₄, and (NH₄)₂SO₄ surfaces from 220 K to 295 K. At low temperatures and on dry aerosol surfaces, the uptake coefficients of HO₂ are low (< 0.05)^[17]. In 1999, Sander proposed an experimental simplification of the heterogeneous uptake coefficient from the point of view of mass transfer flux, omitting the complex subprocess calculation^[18]. The formula is proved to be of practical value in the following experiments. Based on the pseudo-first-order reaction between HO₂ and aerosol, the heterogeneous reaction coefficient of HO₂ can be calculated by measuring the reduction rate of HO₂ at different reaction times and different effective concentrations of aerosol in the laboratory. Sander gave a formula for calculating the water content of aerosols under ideal conditions and proposed a relationship between the water content and the heterogeneous uptake rate. After that, Jacob reviewed in detail the heterogeneous reaction of free radicals in the troposphere and its impact on atmospheric ozone in 2000. He believed that the uptake coefficient of HO₂ in clouds could be directly taken as 0.2, while the

γ H O 2

of 0.2 in aerosols would lead to underestimation of the concentration of HO₂^[19]. At the same time, many research groups have experimentally measured the heterogeneous uptake coefficients of HO₂ on different aerosol surfaces.

The above study shows that although the reaction mechanism of HO₂ with aerosol liquid phase is not completely clear, it is generally believed that the uptake product is H₂O₂, and the ratio of 1 molecule of HO₂ to 0.5 molecule of H₂O₂. However, some subsequent observations have shown that H₂O₂, as a reservoir of HO₂, can photodegrade and regenerate OH to produce HO₂, and setting the product as H₂O₂ in the simulation calculation will overestimate the concentration of HO₂ by 2 to 5 times^[20]. It has been observed that the heterogeneous uptake of HO₂ does not produce HO₂ in some cases, but produces H₂O as a product, avoiding the re-production of HO₂^[21,22].

Therefore, Mao et al. Proposed a new copper-iron coupling mechanism in 2013. After the HO₂ enters the aerosol condensed phase, it is catalyzed by copper and iron and the valence state of copper and iron changes, and the final product is the HO₂. The relevant box model and global model calculations are carried out^[20]. This reaction mechanism will reduce the concentration of hydroxyl and HO₂ radicals in the troposphere, thus affecting the concentration of tropospheric ozone and atmospheric oxidation.

At the same time, several research groups have measured the heterogeneous uptake coefficients of HO₂ and aerosols with different components.

3 Measurement of surface $\gamma_{HO_{2}}$ of particulate matter

Since the first measurement of

γ H O 2

was realized in 1987, the laboratory research on the free radical uptake coefficient of HO₂ has been developed continuously for more than 30 years. At present, there are many measurement results for inorganic dry and wet aerosols, including NaCl dry film, dry aerosol, wet aerosol, ammonium sulfate dry wet aerosol, KCl dry wet aerosol and various wet inorganic aerosols containing free copper ions^[12]. Heterogeneous uptake coefficients on the surface of mineral aerosols have also been studied, although the

γ H O 2

on the surface of mineral aerosols tends to be lower than that of inorganic wet aerosols, due to the higher overall concentration of mineral aerosol.Especially in desert or desert dust-affected areas, the HOx cycle is significantly affected by the heterogeneous uptake of HO₂ radicals and mineral aerosols. In terms of organic aerosols, Bedjanian et al. First used the CRFT-MS measurement method to measure the uptake coefficient of HO₂ on organic aerosols such as kerosene and toluene soot in 2005^[23]. In the following decade, Lakey et al. Used the AFT-LIF method to measure the heterogeneous uptake coefficients of HO₂ on more than ten organic aerosols including glyoxal, malonic acid, squalene, oleic acid, humic acid and copper-containing organic aerosols at different humidities^[24].

In the field observation, Zhou et al. First measured the

γ H O 2

in the ambient atmosphere on line^[25]. This study used laser flash photolysis and laser-induced fluorescence (LFP-LIF) in combination with the Aerosol Concentration Enrichment System (VACES) to measure the total HO₂ reactivity caused by the ambient gas phase (kg ') and aerosol phase (ka') for the first time online in the summer of 2018. The mean uptake coefficient was 0.24 ± 0.2 (1σ). This is similar to the results of the previous research team's

γ H O 2

measurement of the re-occurrence of actual atmospheric particle film samples^[26].

Figure 1 summarizes the results of laboratory measurements of

γ H O 2

that are currently available. It can be seen from the figure that the uptake coefficients determined by different groups are quite different, and the difference can be 3 to 5 orders of magnitude. The experimental conditions of different groups are different, and the experimental conditions are summarized below by reaction medium. The surface medium of SS is mainly dilute sulfuric acid solution and pure water surface, the initial concentration of HO₂ radical is in the order of 1×10¹⁰molecular·cm^-3, and the reaction temperature is 249 ~ 275 K. The medium of TF film is mainly sodium chloride solid film, and its relative humidity varies greatly in the experiment of 0%~28%,HO₂ initial concentration, which is 4×10⁹~3×10¹¹molecular·cm^-3. The reaction pressure is atmospheric pressure, and the reaction temperature is 240 ~ 340 K. The relative humidity ratio of mineral aerosol DA medium is low in most studies, about 10%, and some studies have summarized the correlation between it and relative humidity, HO₂ the initial concentration is 3×10⁸~3.3×10¹²molecular·cm^-3, and the reaction pressure is atmospheric pressure^[27]. The relative humidity of the dry inorganic aerosol DIA reaction medium is low to maintain the dry aerosol state, the initial concentration of the HO₂ is in the order of ~10⁸molecular·cm^-3, the pressure is 760 Torr, and the temperature is around 296 K. WIA of wet inorganic aerosols is usually carried out at high relative humidity, generally above 40%, and the initial concentration of HO₂ is in the order of ~10⁹molecular·cm^-3, at normal temperature and pressure. The relative humidity of organic aerosols varies greatly from 20% to 80%.

A correlation between that uptake coefficient and the relative humidity was also found, as will be discus below. The peak size of aerosols is generally around 100 nm. The reaction conditions of Cu-SA, Cu-CA and organic aerosols containing copper are consistent with those of liquid phase aerosols and organic aerosols, respectively. The uptake coefficient of HO₂ is affected by the reaction medium, humidity, temperature, pH value of aerosol, initial concentration of HO₂ radical and reaction time.

4 Factors affecting the heterogeneous reaction of HO₂;

The heterogeneous uptake of HO₂ is affected by many factors, which can be summarized as the following three aspects:

(1) the properties of the aerosol or reaction film, such as water content, composition, effective surface area, etc.;

The mass transfer rate in the heterogeneous reaction process of (2)HO₂ radicals is mainly affected by the particle size, liquid ionic strength, aggregation coefficient and other factors.

The reaction rate between the surface and the liquid phase in the heterogeneous reaction process of (3)HO₂ radicals is mainly affected by the liquid phase composition of particles, temperature, pH value, initial concentration of HO₂ radicals and other factors.

These factors interact with each other, for example, the water content of the aerosol effectively affects the concentration and ionic strength of the particle liquid component, and the temperature affects the aggregation coefficient. The heterogeneous reaction process of free radicals is complex and unclear at present, and it is affected by both gas phase and liquid phase in many ways, so further research is needed to obtain the uptake rate of free radicals under different reaction conditions, and to comprehensively consider the role of atmospheric HOx cycle and atmospheric oxidation.

4.1 Effect of humidity and temperature on $\gamma_{HO_{2}}$.

At present, several research groups have proposed that the relative humidity of the reaction environment will affect the $\gamma_{HO_{2}}$^{[36~38,40,41]}. For hygroscopic inorganic aerosols, relative humidity usually has little effect on the particle size, but it can significantly affect the water content of aerosols and change the ionic strength and component balance of aerosol condensed phase. At the same time, higher humidity increases the effective surface area of particles and provides more reaction sites for HO₂ radicals. At the same time, some research groups pointed out that in some inorganic aerosols, such as NaCl, NaBr and MgCl₂·6H₂O, the heterogeneous uptake coefficient of HO₂ was little affected by RH, which indicated that the influence of RH on the uptake coefficient of HO₂ was related to aerosol components and needed further exploration^[35].

In the study of organic aerosols, a positive correlation between relative humidity and uptake coefficient was also found, which was presumed to be due to the fact that with the increase of relative humidity, water molecules diffuse to the surface of aerosol particles, alleviating the surfactant effect of organic matter, thus alleviating the diffusion barrier of water-soluble gases and increasing the accumulation coefficient^[24]. However, the response of HO₂ heterogeneous uptake coefficients of different components of organic aerosols to relative humidity is different, and there is no study on HO₂ heterogeneous uptake coefficients of mixed organic aerosols, so the interaction between them is still unknown.

For the study of mineral aerosols, Bedjanian et al. In 2013 pointed out that the

γ H O 2

on the ATD surface decreases with the increase of relative humidity^[27]. At lower humidities (

RH < 2 %

), the uptake coefficient remains constant, while above that it decreases exponentially;

(1)

γ 0 = 1.2 (18.7 + R H 1.1)

After that, the study of Arizona Test Dust (ATD) by Matthews et al. In 2014 showed that the HO₂ uptake coefficient increased slightly with the increase of relative humidity^[42]. But this tendency may be due to the influence of the wall effect. Moon et al. Pointed out that HO₂-H₂O complexes would be formed on the surface of TiO₂ aerosols to promote the uptake reaction, and measured and simulated the water monolayer^[43].

The effect of temperature on the heterogeneous uptake of HO₂ radicals is consistent, and it is found that both sea salt and sulfuric acid aerosols show a downward trend with the increase of temperature. However, the reaction mechanism is still unknown. Remorov et al explored the HO₂ uptake mechanism of halogen-containing aerosols, and believed that the change with temperature was due to the decrease of the surface reaction rate of halogen participation with the increase of temperature^[31].

4.2 The Promotion of Transition Metal Elements on $\gamma_{HO_{2}}$;

Mozurkewich et al. (1987) first measured the heterogeneous uptake reaction rate of copper-containing aerosols with HO₂ as a function of copper content^[12]. When the dissolved mass fraction of copper is less than the mol·L^-1 of the

(1 ~ 2) × 10 - 4

, the heterogeneous uptake of HO₂ is not significant. After the concentration threshold, the uptake reaction rate rises rapidly to the aggregation coefficient limit as the copper concentration increases.

In 2008, Thornton et al. Simulated the impact of copper concentration changes on

γ H O 2

through a model^[41]. The model results show that for aerosol particles with a diameter of 130 nm, the

γ H O 2

begins to rise when the copper concentration is of the order of 10^-9mol·L^-1, and the

γ H O 2

is only limited by the mass accumulation coefficient when the copper concentration is greater than 10^-6mol·L^-1. This result is contrary to the conclusion given by Mozurkewich et al. That the concentration of copper ions is greater than the mol·L^-1 of the

(1 ~ 2) × 10 - 4

. Zou et al. Recently showed that the HO₂ uptake coefficient of copper-containing ammonium sulfate aerosols increases when the copper ion concentration is greater than the 10^-3mol·L^-1, which is consistent with the measurement results of Mozurkewich et al^[44]. Similarly, the results of Matthews et al. At RH = 65% show that the

γ H O 2

increases after the concentration of copper ions reaches the 10^-4mol·L^-1, and is controlled by the aggregation coefficient when it reaches the 10^-2mol·L^-1 concentration, which is contrary to the model^[42].

The possible reason for the discrepancy between the measured and the model is that the model calculation results are based on the second-order reaction rate of divalent copper ions with

O 2 -

ions in the liquid HO₂/, but in fact it is limited by the ionic strength and pH value of the solution in the aerosol condensed phase.A reaction rate of

1 × 109 M · s - 1

cannot be achieved, and according to the measurements of Bielski et al., at the pH of the condensed phase of the liquid ammonium sulfate aerosol (about 4.1), the second order reaction rate of free copper ions with

O 2 -

ions in the liquid HO₂/ is

1.5 × 107 M · s - 1

^[10]. When the reaction rate is used to parameterize the uptake coefficient, it can be consistent with the experimental results in the case of high relative humidity. This indicates that due to pH control, at lower pH values, more than half of the HO₂ radicals accumulated in the condensed phase cannot be dissolved to form

O 2 -

ions, thus reducing the overall second-order reaction rate.

Copper ion not only affects the uptake coefficient of HO₂ radicals in inorganic aerosols, but also has a similar promotion effect on organic aerosols, but the promotion of heterogeneous uptake of HO₂ radicals by this transition metal will be slowed down due to the effect of some organic compounds. The effect of transition metals on uptake in organic aerosols is also affected by the type and nature of the organic matter.

Transition metal ions such as copper, iron, manganese, etc. Have similar catalytic promotion reactions. Matthews et al. measured the

γ H O 2

of ferrous sulfate and ammonium ferrous sulfate at a concentration threshold near the 0.05 mol·L^-1, above which ferrous iron promotes a rapid increase in

γ H O 2

, but not as much as copper^[42]. This is due to the slower reaction rate in the liquid phase and is limited by the ionic strength of the solution. The HO₂ uptake coefficients of iron-containing aerosols are poorly studied and need to be further explored. It is worth noting that the reaction of organic matter with iron may be more complex than that of copper.

4.3 Effect of Reaction Time and Initial Concentration of HO₂ on $\gamma_{HO_{2}}$;

Several studies have shown that the

γ H O 2

is negatively correlated with the uptake reaction time, especially for ammonium sulfate, two wet sols, and the increase of reaction time significantly reduces the uptake of HO₂ on their surfaces. This is due to the fact that the wall effect and self-reaction of the HO₂ radicals increase significantly as the reaction time in the reaction vessel increases. At the same time, if the initial concentration of HO₂ is too high, the self-reaction of HO₂ radicals will be more intense, so it is generally recommended to measure the concentration of HO₂ radicals in the ambient atmosphere to avoid the influence of secondary self-reaction on the hypothesis of quasi-primary uptake reaction. In the study of inorganic hygroscopic aerosols and copper-containing aerosols, there was a negative correlation between the initial concentration of HO₂ and the uptake coefficient. The dependence of the uptake coefficient on the initial concentration of HO₂ radicals may be due to a saturation mechanism, since at higher concentrations of HO₂ radicals, the reaction sites on the aerosol surface will be saturated at a faster rate. Therefore, in a given time, due to the lower saturation of the aerosol, the free radical uptake by the aerosol will be greater at a lower concentration of HO₂ free radicals than at a higher concentration of HO₂ free radicals. The free radical concentration dependence of that HO₂ is also consistent with the assumption that trace reactant in the aerosol have been depleted or inactivate. If this is the case, then at higher concentrations of HO₂ radicals, the active reactant will be consumed more quickly, resulting in a smaller

γ H O 2

measurement.

4.4 Effect of Aerosol pH on $\gamma_{HO_{2}}$;

The liquid-phase reaction of the HO₂ is influenced by the pH value of the aerosol condensed phase, which has been demonstrated in the case of transition metal-free aerosols^[42]. Without considering the influence of transition metals, nitrogen oxides, organic substances and other substances, the relevant chemical reaction mechanism is as follows when only hydroxide compounds play a role in the reaction in the liquid phase:

(2)

H O 2 (g) ↔ H O 2 (a)

(3)

H O 2 (g) ↔ H + + O 2 -

(4)

2 H O 2 (a) → H 2 O 2 (a) + O 2 (a)

(5)

H O 2 (a) + O 2 - + H 2 O → H 2 O 2 (a) + O 2 (a) + O H -

The above equation shows that the HO₂ and the

O 2 -

undergo a second-order reaction and are affected by the pH in the liquid phase. Since the HO₂ and the

O 2 -

in the liquid phase are in a chemical equilibrium state, when the reaction rate constants of the above equations (4) and (5) are k₄,k₅ and the equilibrium rate constant of the reaction (3) is k_eq, the liquid phase self-reaction second-order rate expression of the HO₂ can be obtained as follows:

(6) $k_{\text {self }}=\frac{k_{4}+k_{5}\left(k_{\mathrm{eq}} /\left[\mathrm{H}^{+}\right]\right)}{\left(1+k_{\mathrm{eq}} /\left[\mathrm{H}^{+}\right]\right)^{2}}$

The second-order rate constant of the self-reaction in the liquid phase of the HO₂ is closely related to the pH value of the liquid phase, and the calculation and experimental results are shown in Figure 2.

Thornton et al. Presented the effects of different aerosol pH values and particle sizes on HO₂ uptake in their model simulations^[41]. At a given pH value of the aerosol, the larger the particle size, the higher the HO₂ uptake coefficient. At the same time, the increase of aerosol pH value will promote the uptake of HO₂ radicals on the surface of particles with specific size. However, in later laboratory measurements, it was found that when hydrochloric acid or sodium hydroxide was added to the ammonium sulfate aerosol generator to adjust the pH of the aerosol condensed phase, the lower pH resulted in a higher HO₂ uptake coefficient^[42]. The reason may be that the lower pH value leads to the precipitation of metal ions in the aerosol generator system, which affects the aerosol composition. They then used potassium hydrogen phthalate or potassium dihydrogen phosphate to adjust the pH of the solution, but still did not find a significant upward trend in the uptake coefficient with increasing pH. This may be due to the change of aerosol composition, which affects the liquid phase or surface reaction rate of HO₂ radicals, or the change of aerosol viscosity, which affects the aggregation coefficient of HO₂ radicals.

The above studies on the factors affecting the uptake coefficient of HO₂ show that the theoretical results do not represent the actual situation of atmospheric aerosols, and it is impossible to have a comprehensive and in-depth understanding of the uptake reaction by controlling a single variable. In the study of heterogeneous uptake reaction of HO₂, various factors will interact with each other and ultimately affect the rate of uptake reaction. In laboratory studies, various factors in the reaction environment need to be quantified in detail and cross-studied, rather than controlling only one variable.

5 Parametric representation of heterogeneous uptake of HO₂.

The reaction mechanism of each sub-process in heterogeneous reaction and the expression of its related rate are the core of calculation and simulation. The calculation and comparison of the characteristic time of different processes is helpful to obtain the decisive step. At the same time, by using the approximate solution of the resistance model to the differential equation, the parametric expression of the uptake coefficient can be obtained, which is convenient for the preliminary calculation of the reaction rate. Through the calculation and simulation of the uptake coefficient, it is helpful for people to understand the importance of the HO₂ uptake reaction, which has a greater impact on the whole atmospheric oxidation, aerosol secondary production and climate change. This article will elaborate on each of the above parts.

5.1 Expression and characteristic time of each substep of heterogeneous reaction

Heterogeneous reaction is a comprehensive reaction of mass transfer and chemical reaction process, and these two factors need to be taken into account when calculating the reaction rate. Under the assumption of steady state, the characteristic time τ of heterogeneous reaction is composed of the reaction characteristic times of several subprocesses. The characteristic time is an order of magnitude estimation of the time scale of the system reaction, which can be roughly defined as the reciprocal of the reaction rate, and can intuitively reflect the impact of different reaction processes on the overall reaction. The characteristic time τ_total of the heterogeneous uptake process can be expressed as:

(7)

τ total = τ r + τ da + τ sat - g + τ sat - i

Where the τ_r is the characteristic time of the liquid phase chemical reaction, the τ_da is the diffusion time of the reactants in the particulate condensed phase, the τ_sat_-_g is the time required for the condensed phase to reach saturation due to gas diffusion, and the τ_sat_-_i is the time required for the condensed phase to reach saturation due to mass transport across the interface. By calculating and comparing the characteristic time of each self-reaction process under different conditions, it can be determined whether the heterogeneous reaction is limited by the mass transport process or the liquid phase chemical reaction kinetics process.

5.1.1 Characteristic time of chemical reaction in liquid phase

Defining the characteristic time of liquid phase chemical reactions and comparing it with the characteristic time of mass transfer processes is helpful to understand the mass transfer limitations in heterogeneous reactions. The characteristic time τ_r of liquid phase chemistry can be defined as the ratio of the concentration of reactant X in the liquid phase to its reaction flux under steady-state assumptions:

(8)

τ r = - [X (aq)] (d R [X] dt) ss

In the liquid phase reaction, the model calculation generally assumes that the pseudo-first-order liquid phase reaction occurs in the HO₂:

(9)

H O 2 + M - > Products

In the case of a transition metal (TMI), such as copper:

(10)

H O 2 + C u 2 + / C u + → Products

Applying the hypothesis of quasi-first-order reaction,

(11)

d R [X] dt = - k (1) [X]

Where k⁽¹⁾=k⁽²⁾[M], the second-order rate k⁽²⁾ is multiplied by the reactant M (e.g., copper ion) concentration to yield a pseudo-first-order rate k⁽¹⁾. That is, the characteristic time of the liquid phase reaction is equal to the reciprocal of the liquid phase pseudo-first-order reaction rate. For more complex reactions, it is necessary to calculate the equivalent pseudo-first-order reaction rate.

5.1.2 Characteristic time of mass transfer process

The mass transport process in heterogeneous reactions is divided into three modules: (1) gas diffusion to the surface of the droplet (or vice versa), (2) mass transport across the interface, and (3) gas diffusion to the surface of the droplet. (3) Liquid phase diffusion in a droplet. The above processes occur simultaneously, and the mass transfer process is difficult to reach steady-state equilibrium for the species with faster liquid phase reaction (such as the oxidation of S (Ⅳ) in the liquid phase by ozone). Fig. 3 is a process diagram of mass transfer. The relevant rate symbols in the process are as follows:

c g, ∞

= background gas phase reactant X concentration

Concentration of gaseous reactant X near the interface of the c_g_,_surf= (outside the liquid phase)

Liquid phase reactant X concentration near the interface of the c_a_,_surf= (inside the liquid phase)

c - a

= average concentration of reactant X in the liquid phase

(1) Characteristic time of gas phase mass transfer process

The J_c of gas diffusion flux can be described by Fick's first law of diffusion:^[45]

(13)

J c = 1 A dn dt = - D g dc dx

Where A is the diffusion cross section (m²),n is the number of moles of substance X (mol), t is the time (s),D_g is the diffusion coefficient of molecules X in the gas phase (

m 2 / s

), which is defined as the mass flow per unit area perpendicular to the direction of diffusion X per unit time when the concentration is one unit, and X is the direction of diffusion (m). On the assumption that the particle is spherical, the diffusion direction X is the radius of the particle, and A is equal to the 4πx². The flux J_c increases as the distance between the gaseous reactant X and the particles decreases. At this time, the flow

J^c

can be expressed by the following formula, and the flow

J^c

is 0 at steady state equilibrium:

(14)

J^c = J c A = dn dt = - D g (4 π x 2) dc dx

(15)

d J^c dx = - 4 π D g d (x 2 dc dx) dx = 2 x dc dx + x 2 d 2 c d x 2 = 0

The differential equation has the following analytical solution, taking into account both the background concentration and the near-interface gas phase concentration:

(16)

c (x) = c g, ∞ + (c g, surf - c g, ∞) r x

In the atmospheric environment, the distance between two aerosol particles is much larger than their radius. Therefore, the diffusion distance X between the gas phase substance X and the nearest particle is much larger than the radius of the particle, and the

c (x) ≃ c g, ∞

is obtained. Only near the surface of the particle does the concentration of X in the gas phase need to be different from the background concentration. The concentration gradient of substance X can be expressed by the following formula:

(17)

(dc dx) x = r = c g, ∞ - c g, surf r

(18)

J c = 1 A dn dt = - D g c g, ∞ - c g, surf r

The concentration gradient of the reactant X in the liquid phase, taking into account the equivalent volumetric V=4/3πr³ of the particles and the A=4πr² of the surface area, can be expressed by the following equation:

(19)

d c a dt = - J^c v = - A V J c = 4 π r 2 4 / 3 π r 3 D g c g, co - c g, surf r = 3 D g r 2 (c g, ∞ - c g, surf)

Thus, the pseudo-first-order reaction rate constant of gas phase diffusion can be defined as

(20)

k sat - g = 3 D g r 2 = λ v - r 2

In the formula, the diffusion constant D_g can be expressed by the mean free path λ (m) and the mean molecular motion rate

v -

(m/s). The characteristic time τ_sat_-_g is the reciprocal of the k_sat_-_g.

(2) Characteristic time of mass transfer across the interface

Not all of the reactants that reach the surface of the particles can cross the interface into the condensed phase. The aggregation coefficient α represents the probability of reaching the liquid phase from the gas phase across the interface. The

J k in

represents the flux entering the droplet through the gas-liquid two-phase interface, which can be expressed by multiplying the surface flux J_x by the aggregation coefficient α:

(21)

J k in = 1 A dn dt = α J x = c g, surf v - x

According to the Maxwell-Boltzmann velocity distribution law, the

v - x

can be expressed as:^[46]

(22)

v - x = 14 v - = - 14 8 RT Mπ

Where M is the molar mass (kg/mol), R is the gas constant and the (m³atm/(Kmol)),T is the ambient temperature (K). After the above formula is arranged, the

J k in

of the flux across the interface can be obtained:

(23)

J k in = - v - α 4 c g, surf

The flux in the opposite direction also needs to be taken into account, i.e. The flux of substance X from the liquid phase back to the gas phase is

J k out

(24)

J k out = v - a α a 4 c a, surf

Where the

v - a

is the liquid phase average molecular velocity and the α_a is the liquid phase concentration coefficient, describing the probability that a liquid phase reactant molecule reaching the surface will cross the interface and leave the droplet. The J_k of net flux across the interface can be expressed as:

(25)

J k = J k in + J k out = v - a α a 4 c a, surf - v - α 4 c g, surf

At equilibrium, that J_k=0, and the ratio of the concentration of reactant X in the liquid and gas phases is the effective dimensionless Henry's coefficient H^cc=H_effRT. The above formula can be modified as follows:

(26)

J k = v - α 4 (c a, surf H cc - c g, surf)

The concentration gradient of reactant X in the liquid phase can be expressed as:

(27)

d c a dt = - A V J k = - 4 π r 2 4 / 3 π r 3 v - α 4 (c a, surf H cc - c g, surf) = 3 v - α 4 r (c g, surf - c a, surf H cc)

In summary, the quasi-first-order reaction rate k_sat_-_i and the characteristic time τ_sat_-_i: of the mass transport across the interface can be obtained

(28)

k sat - i = 3 v - α 4 r

(29)

τ sat - i = 1 k sat - i

(3) k_mt of mass transfer coefficient

Under the assumption of steady state, the concentration of reactant X on the surface of particles does not change, so the mass transfer flux in the gas phase is equal to the mass transfer flux across the interface, and then we obtain the mass transfer coefficient k_mt:.

(30)

d c a dt = k mt (c g, ∞ - c a, surf H cc)

(31)

k mt = (1 k sat - g + 1 k sat - i) - 1

When the particle size is large, the k_mt is mainly determined by the gas diffusion constant D_g, and when the particle size is large, such as in cloud droplets, it is mainly determined by the aggregation coefficient. This expression is an approximate expression of the gas-liquid multiphase mass transfer rate. It unifies the two-phase mass transfer process into one expression, which is convenient for model calculation. This expression has been applied in many studies, and has played a very good role in promoting the simulation and calculation of heterogeneous reactions of trace gases^{[14,18,47,48]}.

(4) Characteristic time of liquid phase mass transfer process

After the reactant molecules cross the gas-liquid interface, they will diffuse in the liquid phase and distribute in the whole liquid phase. In the absence of chemical reaction, the liquid phase concentration c_a will eventually be the same as the surface concentration c_a_,_surf everywhere. However, if a rapid liquid phase reaction follows, the concentration profile will be affected by the liquid phase reaction. The c_a of the liquid phase concentration will decrease towards the center of the droplet, and the average concentration

c - a

will be less than the c_a_,_surf. Assuming that the chemical loss rate is uniform everywhere in the liquid phase and the k_r of the pseudo-first-order chemical reaction rate is maintained, the molecular concentration gradient in the liquid phase can be expressed as:

(32)

d c a dt = k a c - a

Wherein, the ratio of the

c - a

to the c_a_,_surf can be expressed by the following formula:^[49]

(33)

Q = c - a c a, surf = 3 (cothq q - 1 q 2)

Based on the steady state assumption, Q is a dimensionless constant, which is a combination of liquid diffusion and liquid reaction, and is defined as the

q = r k r D a

, where the D_a is the liquid diffusion constant (m²/s). The effective liquid phase pseudo-first-order reaction rate is defined as the =k_rQ of the

k r eff

, i.e., its characteristic time

τ da = 1 k r eff

It can be seen from the expression that the liquid phase diffusion process does not limit the entire heterogeneous reaction process under all conditions. The

c - a / c a, surf

is significantly less than 1 only when Q is greater than 1, i.e., the

k r > D a r 2

. In other words, when Q is less than 1, it can be approximated that the liquid phase concentration is close to the surface concentration. For the particulate condensed phase without transition metal TMI, the concentration of HO₂ at the surface is close to that in the liquid phase, which is due to the lower pseudo-first-order chemical reaction rate. In this case, the liquid phase diffusion rate is a rate-limiting step in the overall heterogeneous reaction rate. However, the heterogeneous reaction of HO₂ with particles containing transition metal ions (TMI) does not need to consider the limitation of liquid phase diffusion on the overall reaction rate, because the liquid phase chemical reaction rate is very fast. At this time, in the calculation and simulation of chemical reaction, due to the large difference between the HO₂ concentration and the surface concentration of the condensed phase, it is necessary to correct it:^[20,50]

(34)

[H O 2] surf = P H O 2 K 1 + ([H O 2] bulk) Q - 1

Where the

P H O 2

is the liquid phase production rate of the HO₂. If the k_a is greater than the k_mt, essentially all molecules that reach the surface of the droplet will react immediately, and the total rate depends only on their flux into the droplet. Therefore, the cases where liquid phase diffusion is important in the overall reaction are limited by the following ranges.

(35)

D a r 2 < k r < k mt

5.1.3 Characteristic Time and Uptake Coefficient of Heterogeneous Reaction Process of HO₂ Radical

The characteristic time τ_total of HO₂ radical heterogeneous reaction can be expressed by the following formula according to the above calculation of the characteristic time of different processes:

(36)

τ total = [H O 2] d [H O 2] dt + r 2 π 2 D a + r 2 H cc 3 D g + 4 H cc r α v -

Where [HO₂] is the concentration of the HO₂ radical in the liquid phase.

The rate-determining step of the heterogeneous uptake process of trace gases can be better understood by comparing the above characteristic times. For aerosol particles, because of their small particle size (

r ≃ 0.1 μm

), the uptake is mainly affected by the mass transfer rate across the interface, which is greatly affected by the aggregation coefficient.

Many research groups have studied the aggregation coefficient of HO₂ and found that the aggregation coefficient α is uniformly close to 0.5 in the uptake with TMI-containing aerosols^{[12,18,34,37,51]}. The concentration coefficient of gas molecules with high solubility on the wet surface is in the range of 0.1 to 2, and generally decreases with decreasing solubility and increases with decreasing ambient temperature^[19,52].

On the basis of steady state assumption, if the concentration of reactant X on the surface of aerosol particles is kept constant, that is, the gas diffusion flux is equal to the net transport flux across the interface, the uptake coefficient γ can be obtained from the aggregation coefficient α. This is because the concentration coefficient α considers the relationship between the concentration and flux of both gas and liquid reactants, while the uptake coefficient only considers the relationship between the concentration and flux of gas reactants.The aggregation coefficient represents the probability that molecules can reach the interface from the gas phase and enter the condensed phase, while the uptake coefficient represents the probability that molecules are actually consumed in this process. From the above, the following formula can be obtained:

(37)

J k = 1 A dn dt = v - α 4 (c a, surf H cc - c g, surf)

At the same time, the relationship between the aggregation coefficient and the uptake coefficient is as follows:^[14]

(38)

γ = α (1 - c a, surf H cc c g, surf)

You can get:

(39)

J k = 1 A dn dt = - v - γ 4 c g, surf

Applying the pseudo-first-order reaction assumption to the system, i.e., the

c g, surf dn dt = k

, the expression of the heterogeneous reaction uptake coefficient can be obtained as follows:

(40)

γ = 4 k A v -

The above formula is applied to many studies and has great significance, especially for laboratory experiments to calculate the heterogeneous uptake coefficient of the reaction gas. The uptake coefficient of the reaction gas can be obtained by measuring the concentration change of gas X and the effective surface area of aerosol or droplet after a period of reaction.

5.2 Resistance Model

From the above characteristic time, we can better compare which process controls the reaction rate of the whole heterogeneous uptake, and obtain the calculation formula of the uptake coefficient from the steady-state assumption and the pseudo-first-order reaction assumption. If the effective surface area of aerosol particles is difficult to determine, it will cause large errors. Researchers often use the drag model to approximately describe the heterogeneous uptake process and give the parametric expression of the uptake coefficient. The drag model means that in the uptake process, each self-process is treated according to the conductivity (

Γ

) and normalized according to the collision rate of the gas interface^{[51,53⇓⇓⇓ ~57]}.

5.2.1 Heterogeneous uptake of non-reactive game

The heterogeneous uptake of non-reactive gases is mainly controlled by mass transport processes and less by liquid phase reactions. That is, the rate of the uptake reaction is controlled only by the diffusion of gas molecules in the gas phase, mass transport across the interface, diffusion in the liquid phase, and the associated rate of their volatilization and dissolution back into the gas phase.

It follows from the above equation that the gas phase flux to the surface is determined by the local gas phase concentration directly above the particle surface and the aerodynamic collision rate. In the case of high surface uptake, the gas phase concentration near the surface may be reduced if the reactant molecules in the gas phase diffuse too slowly to replenish the molecules near the particle surface. This in turn limits the absorption of gas molecules by the particulate liquid phase. Therefore, the heterogeneous uptake of non-reactive gases requires consideration of gas phase mass transport limitations. The gas phase mass transfer limitation is described by the gas transfer coefficient

Γ diff

. The symbol

Γ

here represents the rate of some process (normalized to the collision rate) and may be greater than 1.

The empirical formula for gas phase transport has been verified by experimental results and can be expressed in terms of

1 Γ diff

as follows:^[58⇓~60]^[61]

(41)

1 Γ diff = 0.75 + 0.238 Kn Kn (1 + Kn)

Where Kn is the Knudsen number, defined as λ/R, λ is the gas phase mean free path (cm), and R is the particle radius (cm). The mean free path is expressed as follows:

(42)

λ = 3 D g v -

The inverse of the net uptake coefficient γ can now be expressed as the sum of the gas phase diffusion resistance and the inverse of the uptake coefficient γ₀(γ₀ representing the coefficient of uptake of gas phase reactive molecules by particles near the interface), due to gas-liquid interaction in the "zero pressure" limit, i.e., under conditions where gas phase diffusion does not limit the mass transport flux across the interface. From this, the following expression can be obtained:

(43)

1 γ = 1 Γ diff + 1 γ 0

In the atmosphere, for typical submicron-sized aerosol particles, gas phase diffusion generally does not limit the uptake coefficient of gas molecules unless the near-surface uptake coefficient is large. For example, for a droplet with a diameter of 0.1

μ

m at a pressure of 1 atm, Kn = 1.5 (assuming that the gas phase diffusion coefficient is 0.1atm·cm²·s^-1 and

v - = 4 × 104 cm · s - 1

), the liquid phase diffusion-limited

1 Γ diff = 0.3

is obtained. If the γ₀ is less than 0.1, the gas diffusion contribution is negligible, while if the γ₀ is close to 1, the calculated value of γ is 25% lower than before^[44]. For larger atmospheric particles, such as cloud droplets, gas diffusion limits gas uptake regardless of the γ₀. Therefore, in many laboratory experiments, it is necessary to consider the correction of gas diffusion limitation to the experimental results when analyzing the experimental data, especially for the uptake experiments of cloud droplets or more active reactive gas molecules, whose gas diffusion often leads to the reduction of the uptake coefficient calculated by the experiment.

Mass accumulation occurs when gas molecules strike the surface of a liquid and enter the liquid phase through the gas-liquid interface. The mass concentration coefficient α refers to the probability that a gas molecule diffuses to the surface of the liquid phase and collides with it to enter the liquid phase through the gas-liquid interface. In the absence of chemical reaction, α determines the maximum possible flux J of gas molecules entering the liquid phase. This maximum possible flux occurs only in the absence of gas phase diffusion and dissolution limitations.

After the gas molecules enter the liquid phase, they diffuse from the surface to the interior of the droplet. The ability of the liquid to absorb gas molecules at this time is limited by the ability of the liquid to dissolve trace gas molecules (solubility). Subsequently, the trace molecules in the liquid phase equilibrate with the gas phase. At equilibrium, the sum of the rate of molecular diffusion transfer to the surface and the rate of desorption is equal to the rate of molecular adsorption on the surface, so that the net amount of adsorption is zero. The resistance due to solubility limitation (liquid phase saturation) can be expressed by the following equation:

(44)

1 Γ sat = v - 4 H cc tπ D a

Where t is the gas-liquid interaction time and the

1 Γ sat

is expressed in terms of the mass transfer across the interface caused by the concentration gradient of the liquid molecules^[15,62]. It increases with increasing exposure time of the gas to the liquid, reflecting that the rate at which dissolved molecules evaporate back into the gas phase increases with increasing concentration of trace species in the liquid. This increased resistance causes the total net uptake of gas molecules by the particles to decrease over time.

After arranging the three processes described above, a parametric expression of the heterogeneous uptake coefficient of the non-reactive gas can be obtained by applying the drag model:

(45)

1 γ = 1 Γ diff + 1 α + 1 Γ sat

5.2.2 Heterogeneous uptake of reactive game

In addition to the mass accumulation limitation and the mass diffusional transport limitation of the gas-liquid phase, some gas molecules have high chemical reactivity and will undergo chemical reaction reduction in the liquid condensed phase (simultaneously with the diffusion process). When considering the heterogeneous reaction of gas molecules, it is necessary to consider the influence and limitation of the chemical reaction loss rate k_rxn(s^-1) in the condensed phase on the whole heterogeneous reaction^[63,64].

From the above, it can be seen that the ratio between the liquid phase concentration and the surface concentration of each droplet is represented by Equation (33) in the case of chemical loss, based on the pseudo-first-order reaction assumption and the steady-state assumption. The diffusion flux inside the liquid phase can be expressed by Fick's law as follows:

(46)

J a = D a d c a dr | a = r

The concentration gradient of the liquid-phase reactant molecules in the liquid phase can be obtained by differentiating Equation (33):

(47)

d c a dr | a = r = c a, surf r [qcoth (q) - 1]

Where,

q = r k 1 D a

, taking into account the defined relationship between the accumulation coefficient and the uptake coefficient, in Equation (38):

γ = α (1 - c a, surf H cc c g, surf)

, under the assumption of steady state, the net flux across the interface in Equation (39) is J_k limited by both chemical reaction and diffusion in the liquid phase, so that the saturation ratio of reactants on the particle surface is as follows:

(48)

c a, surf H cc c g, surf = 1 1 + 4 H cc D a rα v - [qcothq - 1]

The formula (48) is brought back to the definition formula (38) of the uptake coefficient to obtain the parameterization of the particulate matter uptake coefficient which is controlled by both the liquid phase chemical reaction limitation and the diffusion limitation. The γ in this formula does not consider the gas phase diffusion, so the gas phase diffusion limitation needs to be added to its expression, and then the parameterization formula of the uptake coefficient of reactive gas is obtained:

(49)

1 γ = Γ diff + 1 α + v - 4 H cc k 1 D a f (q)

(50)

f (q) = coth (q) - 1 q

This parameterization formula is based on the assumption of steady state and quasi-first-order reaction, that is, the calculation and simulation assume that the concentration of reactants on the surface of particles is constant and the inlet and outlet fluxes are equal, which will not cause the accumulation of the concentration of reactants on the surface to reach saturation directly. At the same time, in the calculation of the reaction rate of each process, it is assumed to be a first-order reaction. It has been proved that this parameterization formula is a more reliable parameterization method for raindrops, wetted walls and other surfaces^[65,66]^[67,68].

For most gaseous reactants, the parameterized expression of heterogeneous uptake on the surface of liquid aerosol particles can be expressed by Eq. (49), where the difficulty lies in the determination of the effective Henry coefficient H^cc and the determination of the quasi-first-order chemical reaction rate k¹. This is because the physical and chemical properties of aerosols, such as their composition, particle size, mass concentration, water content, as well as the changes of external relative humidity, pressure and temperature, will affect the Henry coefficient. At the same time, for HO₂ radicals, the quasi-first-order chemical reaction rate and the chemical reaction mechanism in the liquid phase of particulate matter will vary with the composition of particulate matter and the concentration of relevant reactants in the liquid phase.The k¹ will have a great impact on the uptake coefficient γ in the whole parameterization formula, especially when the size of aerosol particles is small, the gas phase diffusion limitation is not obvious, and the aggregation coefficient is large, so the liquid phase reaction mechanism is particularly important in the simulation of heterogeneous uptake of HO₂ radicals. In addition, the relevant empirical formulas are of great significance to the application of the model, which can assess the impact of global and regional heterogeneous uptake of cesium on the atmospheric environment through a more macroscopic and simple method.

5.3 Application of the empirical formula of heterogeneous uptake of HO₂ in the model

At present, studies have been conducted to simulate the

γ H O 2

of five kinds of aerosols: sulfate, sea salt (NaCl), black carbon, organic carbon and mineral aerosols with fixed-value global models. The main factors affecting the

γ H O 2

are attributed to the properties of particulate matter, temperature and humidity. The empirical formula is shown in Table 1^[69].

The development of relevant research on empirical formulas of

γ H O 2

is conducive to their wide application in the model. At present, the existing research mainly focuses on the aerosol particles without TMI. Because the presence of TMI in the liquid phase of particulate matter can significantly promote the increase of

γ H O 2

, the measurement of soluble transition metal concentrations in aerosols and the study of related parameterized or empirical formulas are the focus of future research in this area.

6 Conclusion

Heterogeneous uptake of HO₂ into aerosols has attracted much attention in recent years. Heterogeneous uptake of HO₂ radicals has a significant impact on the atmospheric HOx cycle, the concentration and trend of atmospheric oxidizing gases, and the formation of secondary organic aerosols.

The field measurement of the uptake coefficient of the (1)HO₂ faces many challenges, and the

γ H O 2

is found to be related to many factors in the laboratory measurement. The heterogeneous uptake of HO₂ is affected by mass transport and chemical reaction rates. The mass transfer process includes gas phase mass transfer, mass transfer across the interface and liquid phase diffusion. Chemical reactions include gas phase reactions, surface reactions, and liquid phase reactions. These reactions are affected by the concentration of free radicals and other trace gases in the atmosphere; Radius, composition, size distribution, water content and surface area of aerosol particles; Atmospheric temperature, relative humidity and other factors affect it at the same time, which is a very complex physicochemical reaction process. The higher the humidity is, the higher the

γ H O 2

is, and the wet aerosol is more conducive to the heterogeneous reaction of HO₂ than the dry aerosol. The presence of transition metal ions in aerosols can promote the liquid-phase reaction of HO₂ in the condensed phase of particles, and the threshold of copper ions is generally considered to be the 10^-4mol·L^-1.

(2) The accurate parameterization of the

γ H O 2

is beneficial to the study of its impact on the atmospheric environment in the model application. The difficulties in the application of the existing parameterization formulas lie in the determination of the H^cc of the effective Henry coefficient and the k¹ of the pseudo-first-order chemical reaction rate.

The liquid-phase reaction of (3)HO₂ radicals is the difficulty and emphasis of the current research. It is affected by the pH value, ionic strength and composition of the aerosol condensed phase, and the relevant rate constants need to be further updated in different cases. The products of heterogeneous uptake need to be further explored in order to gain a deeper understanding of the uptake process. At the same time, the research should focus on the global distribution of transition metals, because transition metals can greatly promote the liquid-phase reaction of HO₂ radicals, and a small amount of free metal ions can effectively improve their uptake coefficient. At the same time, the coupling effect of organic compounds on transition metal ions can not be ignored, so far, the heterogeneous uptake mechanism of HO₂ involving organic compounds still needs further exploration.

In this paper, the results of laboratory studies on the heterogeneous reaction of HO₂ radicals with aerosols are systematically reviewed, the influencing factors are analyzed, and the existing parametric expressions are calculated and summarized. Further studies need to do more specific parametric analysis for different conditions to obtain the uptake coefficient under different conditions, so as to deeply understand the atmospheric oxidation in China and provide reference and guidance for relevant air pollution control policies.

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Funding

National Natural Science Foundation of China(21976006)

National Natural Science Foundation of China(91844301)

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1 Introduction

2 Research Progress of Heterogeneous Reaction of HO2 Radical

3 Measurement of surface $\gamma_{HO_{2}}$ of particulate matter

4 Factors affecting the heterogeneous reaction of HO2;

4.1 Effect of humidity and temperature on $\gamma_{HO_{2}}$.

4.2 The Promotion of Transition Metal Elements on $\gamma_{HO_{2}}$;

4.3 Effect of Reaction Time and Initial Concentration of HO2 on $\gamma_{HO_{2}}$;

4.4 Effect of Aerosol pH on $\gamma_{HO_{2}}$;

5 Parametric representation of heterogeneous uptake of HO2.

5.1 Expression and characteristic time of each substep of heterogeneous reaction

5.1.1 Characteristic time of chemical reaction in liquid phase

5.1.2 Characteristic time of mass transfer process

5.1.3 Characteristic Time and Uptake Coefficient of Heterogeneous Reaction Process of HO2 Radical

5.2 Resistance Model

5.2.1 Heterogeneous uptake of non-reactive game

5.2.2 Heterogeneous uptake of reactive game

5.3 Application of the empirical formula of heterogeneous uptake of HO2 in the model

6 Conclusion

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RIGHTS & PERMISSIONS

2 Research Progress of Heterogeneous Reaction of HO₂ Radical

4 Factors affecting the heterogeneous reaction of HO₂;

4.3 Effect of Reaction Time and Initial Concentration of HO₂ on $\gamma_{HO_{2}}$;

5 Parametric representation of heterogeneous uptake of HO₂.

5.1.3 Characteristic Time and Uptake Coefficient of Heterogeneous Reaction Process of HO₂ Radical

5.3 Application of the empirical formula of heterogeneous uptake of HO₂ in the model