Inﬂuence of atmospheric conditions on the role of triﬂuoroacetic acid in atmospheric sulfuric acid-dimethylamine nucleation

. Ambient measurements combined with theoretical simulations have shown evidence that the tropospheric degradation end-products of Freon alternatives, triﬂuoroacetic acid (TFA), one of the most important and abundant atmospheric organic substances, can enhance the process of sulfuric acid (SA) - dimethylamine (DMA) - based nucleation process in urban environments. However, TFA is widespread all over the world with different atmospheric conditions, such as temperature and nucleation precursor concentration, which are the most important factors potentially inﬂuencing the atmospheric nucleation 5 process and thus inducing different nucleation mechanisms. Herein, using the Density Functional Theory combined with the Atmospheric Cluster Dynamics Code, the inﬂuence of temperature and nucleation precursor concentrations on the role of TFA in the SA-DMA nucleation has been investigated. The results indicate that the growth trends of clusters involving TFA can increase with the decrease of temperature. The enhancement of particle formation rate by TFA and the contributions of SA-DMA-TFA cluster to the cluster formation pathways can be up to as much as 227 times and 95%, respectively, at relatively 10 low temperature, low SA concentration, high TFA concentration, and high DMA concentration, such as in winter or at relatively high atmospheric boundary layer and in megacities far away from industrial sources of sulfur-containing pollutants. These results provide the perspective of the realistic role of TFA in different atmospheric environments, revealing the potential inﬂuence of the tropospheric degradation of Freon alternatives under a wide range of atmospheric conditions. and the simulation by Atmospheric Cluster Dynamic Code. FQY conducted the simulation by global chemistry-transport model of GEOS-Chem. LL analyzed data with the contributions from XHZ, FQY and ZY. LL and XHZ wrote the paper with contributions from all of the other co-authors.

understood and species contributing to NPF under different environments remain to be studied. Thus, other possible species that may potentially enhance the NPF rates and the corresponding nucleation mechanism should be further explored. 25 Perfluorocarboxylic acids (PFCAs), widely distributed in the environment, can be formed from the oxidation of anthropogenically produced hydrofluorocarbons (HFCs), hydrochlorofluorocarbons (HCFCs) and hydrofluoro-olefins (HFOs) (Burkholder et al., 2015;Kazil et al., 2014;Pickard et al., 2018). Due to the worldwide distribution, chemical stability, and potential biological toxicity, PFCAs are generally believed to be an important class of environmental contaminants present in various environments. As the simplest and most abundant perfluorocarboxylic acid in the atmosphere (Tian et al., 2018), trifluoroacetic 30 acid (TFA) is the pivotal product of the oxidative degradation processes of the Freon alternatives emitted from human activities (Madronich et al., 2015;Tromp et al., 1995). The concentration of TFA is relatively high in regions with scant rainfall because precipitation is the only predominant environmental sink of TFA (Ellis et al., 2001). Thus, the continuous production of TFA from the degradation of Freon alternatives combined with the lack of rainfall in some areas is more likely to induce the accumulation of TFA. Recent ambient measurements and theoretical simulations have shown evidence for the participation of TFA 35 in the formation of SA-DMA-based clusters under certain atmospheric conditions in urban Shanghai, China (Lu et al., 2020).
The participation of TFA in NPF events can increase the number concentration of atmospheric aerosol particles and further potentially have effects on climate and human health.
The previous study on the role of TFA in SA-DMA-based NPF process is under the local atmospheric temperature and nucleation precursor concentrations of Shanghai (Lu et al., 2020). Whereas TFA is widely distributed all over the world with 40 different atmospheric conditions, among which temperature and concentrations of nucleation precursors are key influential factors in the nucleation process. Temperature can change with the variations of seasons, altitudes and climates, and nucleation precursor concentrations can vary with distances to the corresponding sources and altitudes. For example, DMA concentration is relatively high in polluted regions near its industrial, residential, or agricultural sources, but it is relatively low in the clean and upper troposphere due to its short lifetime in the atmosphere. SA concentration is relatively high in areas near coal-45 fired power plant or industry, but it is relatively low in the areas far away from the emission sources of sulfur-containing pollutants. Besides, although TFA is widely distributed around the world, its concentration is relatively high in regions with scant rainfall. Therefore, it is important to elucidate the role of TFA in the NPF events under broad atmospheric conditions to understand the effect of TFA on the atmospheric environment systematically. In the present study, the influence of the varying temperatures and precursor concentrations on the role of TFA in the SA-DMA-based clustering process was studied using 50 Density Functional Theory combined with the Atmospheric Cluster Dynamic Code (ACDC) (McGrath et al., 2012;Olenius et al., 2013). The studied clusters are ( Acid ) m · ( Base ) n , where 0 ≤ n ≤ m ≤ 3, in which acid molecules are TFA or/and SA and base molecule is DMA.

Methods
The M06-2X functional has been successfully used to describe noncovalent interaction (Elm et al., 2012;Zhao and Truh-55 lar, 2008) and estimate thermochemistry, equilibrium structures of atmospheric clusters (Bork et al., 2014;Elm et al., 2012Elm et al., , 2 https://doi.org/10.5194/acp-2020Elm et al., -1186 Preprint. Discussion started: 18 December 2020 c Author(s) 2020. CC BY 4.0 License. 2013). Furthermore, the 6-311++G(3df,3pd) basis set was chosen based on its excellent performance to estimate the properties of atmospheric relevant clusters when used in conjunction with the M06-2X functional (Herb et al., , 2013Nadykto et al., 2011Nadykto et al., , 2009). The single-point electronic energies were corrected using RI-CC2 method and aug-cc-pV(T+d)Z basis set performed with the TURBOMOLE program, because of the good agreement between the simulated results based on the single-60 point electronic energies at RI-CC2/aug-cc-pV(T+d)Z level of theory and the experimental or field measurements (Kürten et al., 2018;Lu et al., 2020). Structures and the thermodynamic data of the presently studied clusters at 280 K are taken from previous studies (Lu et al., 2020).
The Atmospheric Cluster Dynamics Code (ACDC) (McGrath et al., 2012;Olenius et al., 2013) was used to simulate the cluster formation process with the thermodynamic data generated by quantum chemistry calculations as input. Time develop-65 ment of the concentration of each cluster was solved by integrating numerically the birth-death equation (Kulmala et al., 2001) using the ode15s solver in MATLAB-R2013a program (Shampine and Reichelt, 1997).
The birth-death equation can be written as following Eq. (1): where c i is the concentration of cluster i, β i,j is the collision coefficient between clusters i and j, γ i→j is the γ evaporation 70 coefficient of a molecule or a smaller cluster j from cluster i, Q i is an outside source term of cluster i, and S i is other possible sink term of cluster i.
The collision rate coefficients β i,j between clusters i and j were calculated as hard-sphere collision (Chapman et al., 1990) in Eq. (2): where r i is the radius of cluster i given by Multiwfn 3.3.8 program (Lu and Chen, 2012), k B is the Boltzmann constant, T is the temperature and µ = m i m j /(m i + m j ) is the reduced mass. The cluster radius is half of the sum of the distance between the center of most distant atoms in cluster given by the Multiwfn 3.3.8 program (Lu and Chen, 2012) and the Van der Walls radii of these atoms.
Evaporation coefficients, γ i→j , were obtained from the corresponding collision coefficients and ∆G of clusters as shown in 80 Eq. (3): where P ref is the reference pressure (in this case 1 atm) where the formation free energies were calculated and ∆G i is the Gibbs free energy of formation of cluster i from monomers.

Influence of temperature and nucleation precursor concentrations on cluster stability and growth trend of clusters
The cluster stability is of great significance for the process of NPF. Atmospheric temperatures can vary with different seasons, altitudes, and climates. The temperature variation may have a significant influence on the aerosol cluster stability. Thermodynamically, Gibbs free energies of formation (∆G) for clusters at different temperatures (280 K and 260 K) within the temper-90 ature range of the atmospheric boundary layer are shown in Table S1 in the Supplement. It shows that the ∆G decreases with the decrease of temperature, which reflects that clusters are more thermodynamically stable at relatively lower temperatures.
Kinetically, if the collision frequency (β · C, β is shown in Table S2 in the Supplement) of a cluster with monomer molecule at the concentration of C is higher than its total evaporation frequency (Σγ, Table S3 in the Supplement), this cluster can be considered to have the potential to continue growing. Thus, in order to analyze the growth trends of clusters involving 95 TFA, ratios (β · C/Σγ) for collision frequencies with nucleation monomers versus total evaporation frequencies have been investigated (Table S4 in the Supplement). Here we take the ratio of β · C/Σγ for clusters involving one TFA molecule at different temperatures as an example shown in Fig. 1 to study the growth trend of clusters. The β · C/Σγ increases with the decrease of temperature ( Fig. 1 and Table S4 in the Supplement), which indicates that it is easier for these clusters to grow at lower temperatures. The reason for this is that the influence of temperature variation on the evaporation coefficients (γ,

100
where the temperature dependence is exponential (McGrath et al., 2012) is much greater than that on collision coefficients (β, where the dependence is in the square root of the temperature (McGrath et al., 2012)). At relatively low concentration of SA monomer, the ratios of β · C/Σγ for (SA) 1 · (DMA) 2 · (TFA) 1 and (SA) 2 · (DMA) 3 · (TFA) 1 clusters are all larger than 1.0 at different temperatures ( Fig. 1), which means that these two kinds of clusters tend to grow to larger clusters at 280 K and 260 K. Besides, β · C/Σγ will increase when the nucleation monomer concentration increases. Thus, the growth trend of clusters 105 can also be relatively high at higher concentrations of nucleation monomers. (0 ≤ x ≤ 2, 1 ≤ y ≤ 3, y ≤ x + 1) clusters at different temperatures (280 K and 260 K). Acid molecules are SA and TFA. C = 1.0 × 10 6 molecules cm −3 .
3.2 Influence of temperature and nucleation precursor concentrations on particle formation rates It can be seen that the stability and growth trend of clusters involving TFA vary with temperatures and concentrations of nucleation precursors from the above discussion. The stability and growth trend are closely related to particle formation rates. A study on the complicated influence of temperature and nucleation precursor concentration on particle formation rates becomes 110 increasingly important to understand the realistic role of TFA in different atmospheric environments. Therefore, the potential influences of temperatures and concentrations of nucleation precursors on the particle formation rates of SA-DMA-TFA system have been investigated, as described below.
The temperature was obtained from the NASA Langley Research Center (LaRC) POWER Project funded through the NASA Earth Science/Applied Science Program (NASA, 2020). The studied temperature is the monthly average of temperature at 2 115 meters above the surface of the earth for a given month, averaged for that month over the 30 years (Jan. 1984-Dec. 2013).
The lifetime of TFA and SA are relatively long enough to ensure their atmospheric concentration to be in the present studied concentration range. However, because of the relatively short atmospheric lifetime of DMA concerning chemical reaction loss (Carl and Crowley, 1998;Qiu and Zhang, 2013), Los Angeles, and New Delhi, as an example (Fig. 2). The corresponding temperature and data of [DMA] are shown in Table   125 S5 in the Supplement. The [SA] and [TFA] were chosen to be relatively low and high, 5.0 × 10 6 molecules cm −3 and 1.0 × 10 8 molecules cm −3 (Wu et al., 2014) respectively. The condensation sink (CS) is set to be 0.02 s −1 , which is the median of common CSs in the NPF events in the polluted areas .
As shown in Fig. 2, the enhancements on particle formation rate by TFA in the studied four cities are all higher than 1.0 in most of the months throughout the year, which indicates that TFA can enhance the SA-DMA particle formation rate in 130 most of the year. The particle formation rate and enhancement on particle formation rate by TFA of Beijing are all higher than those of the other three studied cities in the corresponding month. This can be attributed to that the [DMA] and temperature in Beijing is relatively higher and lower than those of the other three studied cities, respectively. Besides, the particle formation rate and enhancement on particle formation rate by TFA are relatively high in spring and winter approximatively. This can be attributed to that temperature in spring and winter is relatively lower than other time all the year-round, respectively. Moreover, 135 the enhancement on the particle formation rate by TFA is highest in Beijing among the studied four cities, which can be up to more than 13 times in January. Therefore, there is enough DMA in the realistic atmospheric boundary layer for TFA to enhance the SA-DMA nucleation process. atmospheric boundary layer (Fig. 3). The condensation sink (CS) in Fig. 3 is set to be 0.02 s −1 , which is the median of common CSs in the NPF events in the polluted areas . The results at other common CSs (0.01 s −1 and 0.03 s −1 ) in the polluted atmosphere will be discussed below. DMA is one of the most common basic nucleation precursors in the atmosphere and can be released from industrial, residential, or agricultural sources (Mao et al., 2018). The common atmospheric concen- ). In general, the particle formation rate of SA-DMA-TFA system ( Fig. 3 (a)) and the enhancement of particle formation rate by TFA (Fig. 3 (b)) increase with the decrease of temperature and increase with the increase of [DMA], which is in accordance with the negative dependence of the growth trend of clusters involving TFA on temperature and positive dependence on nucleation monomer concentration.
In addition to the basic molecules, SA is the key acidic nucleation precursor in the atmosphere and its main source is coalfired power plant and industry. The common atmospheric [SA] is in the range of 1.0 × 10 6 to 1.0 × 10 8 molecules cm −3 from clean areas to highly polluted areas (Kürten et al., 2012;Yao et al., 2018;Zheng et al., 2015). Given that the enhancement of TFA on particle formation rate is high at relatively high [DMA], the influence of [SA] on the role of TFA in NPF at [DMA] = 1.0 × 10 9 molecules cm −3 and different temperatures (280 K and 260 K) has been further studied. At different [SA], there are 160 negative dependencies of particle formation rate and the enhancement of formation rate by TFA on temperature. At different temperatures, the particle formation rates all increase with the increase of [SA] (Fig. 3 (c)). However, the enhancement of particle formation rate by TFA increases with the decrease of [SA] and can be more than 14 times at relatively low [SA] (1.0 × 10 6 molecules cm −3 ) at 260 K (Fig. 3 (d)). Thus, in addition to relatively high [DMA], the enhancement of particle formation rate by TFA is obvious in the regions with relatively low temperature and low [SA], such as in winter or at relatively of 1.0×10 6 molecules cm −3 , the influence of [TFA] on particle formation rate has been further studied at different temperatures (280 K and 260 K). Similar to the influence of temperature at different [DMA] or [SA], there are negative dependencies of the particle formation rate and the enhancement of particle formation rate by TFA on the temperature at different [TFA]. The particle formation rate (Fig. 3 (e)) and the enhancement of TFA on particle formation rate increase (Fig. 3 (f)) with the increase 175 of [TFA] at different temperatures, which is in accordance with the positive dependence of the growth trend for clusters on nucleation monomer concentration. At relatively high [TFA] (1.0 × 10 8 molecules cm −3 ) and at a relatively low temperature of 260 K, the particle formation rate is more than 17 cm −3 s −1 and the corresponding enhancement of particle formation rate by TFA can be as high as more than 227 times. Therefore, the role of TFA is obvious in the regions with relatively low temperatures and high [TFA], such as in winter or at relatively high atmospheric boundary layer and megacities or rural regions 180 with scant rainfall far away from industrial sources of sulfur-containing pollutants.
Relatively high aerosol concentration can cause a large condensation sink (CS), thus scavenging newly formed molecular clusters . The CS can be different in different atmospheric environments. The particle formation rates and the corresponding enhancements by TFA at other common CSs (0.01 s −1 and 0.03 s −1 ) in the polluted atmosphere are shown in Figs. S1 and S2 in the Supplement, respectively. Although the particle formation rate and enhancement by TFA increase with 185 the decrease of CS, the influence trend of temperature and nucleation precursor concentrations on them are the same.

Influence of temperature and precursor concentrations on the formation pathway of SA-DMA-TFA clusters
Variations of atmospheric conditions (temperature and concentration) can influence the particle formation rate of SA-DMA-TFA system as well as the corresponding enhancement by TFA. These trends of influence can be potentially explained by the detailed SA-DMA-TFA cluster formation mechanism at the molecular level. Thus, the detailed cluster formation mechanisms of SA-DMA-TFA system under different temperatures and different concentrations of nucleation precursors have been further explored.
The cluster formation pathway at different concentrations of nucleation precursors (DMA, SA, and TFA) are first studied at the common temperature (280 K) of the atmospheric boundary layer (Fig. 4 (a)). The SA-DMA-TFA cluster formation pathways at different [DMA] have  (Fig. 4 (b)). Compared to the cluster formation pathway at 280 K, additional pathways shown in blue arrows are present at 260 K. In addition to the two independent pathways of pure SA-DMA pathway and SA-DMA-TFA pathway starting from (SA) 1 · (DMA) 1 cluster, (SA) 2 · (DMA) 2 · (TFA) 1 cluster can contribute to the formation of (SA) 2 · (DMA) 2 cluster by the evaporation of one TFA molecule. The contributions of the cluster formation pathway involving TFA can be up to 95% (18% 220 + 77%). Therefore, the participation of TFA in the cluster formation process is extensive at the relatively low temperatures, such as in winter or at relatively high atmospheric boundary layer, which is in accordance with the negative dependence of SA-DMA-TFA cluster formation rates on temperature.