Formation mechanism of methanesulfonic acid and ammonia clusters: A kinetics simulation study

Journal Pre-proof Formation mechanism of methanesulfonic acid and ammonia clusters: A kinetics simulation study Dongping Chen, Danfeng Li, Changwei Wang, Fengyi Liu, Wenliang Wang PII:

S1352-2310(19)30800-3

DOI:

https://doi.org/10.1016/j.atmosenv.2019.117161

Reference:

AEA 117161

To appear in:

Atmospheric Environment

Received Date: 26 July 2019 Revised Date:

14 November 2019

Accepted Date: 16 November 2019

Please cite this article as: Chen, D., Li, D., Wang, C., Liu, F., Wang, W., Formation mechanism of methanesulfonic acid and ammonia clusters: A kinetics simulation study, Atmospheric Environment (2019), doi: https://doi.org/10.1016/j.atmosenv.2019.117161. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

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Formation mechanism of methanesulfonic acid and ammonia clusters:

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a kinetics simulation study

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Dongping Chen, Danfeng Li, Changwei Wang, Fengyi Liu, Wenliang Wang ∗

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Key Laboratory for Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical

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engineering, Shaanxi Normal University, Xi’an 710119, Shaanxi, China.

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Abstract: The formation mechanism of methanesulfonic acid (MSA) and ammonia

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(NH3) clusters is investigated using density functional theory (DFT) and Atmospheric

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Cluster Dynamic Code (ACDC) in different conditions. The results suggest that

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hydrogen bonding and electrostatic interactions induced by proton transfer could

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provide the primary driving force that forms these clusters. NH3 can effectively

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promote the formation of MSA-based clusters at pptv levels, but high concentrations

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of precursors ([MSA] ≥ 2 × 107 molecules cm−3 and [NH3] ≥ 1 ppbv) is necessary for

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effective formation. The formation of the initial (MSA)2 dimer is a rate-determining

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step of cluster growth. The formation rate is proportional to the monomer

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concentration and inversely proportional to the temperature in the troposphere.

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Hydration has a great influence on the evaporation rate, formation rate, and nucleation

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mechanism of the MSA-NH3 system. The relative evaporation rate of all clusters is

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significantly affected by humidity, especially for the (MSA)(NH3) dimer. The

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evaporation rate of the (MSA)(NH3) dimer can be reduced by approximately a factor

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of 10−5 at a relative humidity (RH) ≥ 40%. The formation rate increases significantly

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with RH and reached up to a factor of 105 at RH = 100%. The formation of the initial

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(MSA)(NH3) dimer is the rate-determining step, which indicates that the nucleation

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mechanism is fundamentally different from anhydrous cases. In addition, the results

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showed that the formation of MSA-NH3 molecular clusters is relatively weak under

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typical atmospheric conditions. In addition to the high concentration of precursors and

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atmospheric humidity, the formation of MSA-based ternary clusters through the

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participation of other species such as SA that may be more important in promoting

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effective nucleation of MSA-NH3 system in the coastal atmosphere. ∗

Corresponding authors: Tel: +86-029-81530815; E-mail: [email protected] (W. L.Wang). 1

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Keywords: Methanesulfonic acid, Evaporation rate, Formation rate, Growth pathway,

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Hydration

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1. Introduction

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New particle formation (NPF) from low-volatile gas precursors, as an important

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source of atmospheric aerosol particles (Pope and Dockery, 2012; Seinfeld and Pandis,

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2006), remains one of the least understood micro-processes in the atmospheric

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troposphere. Atmospheric aerosol particles significantly contribute to cloud

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condensation nuclei (CCN) (Dameto de España et al., 2017), atmospheric

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transmittance, air quality, morbidity and premature mortality of human beings and

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remain one of the leading uncertainties in global climate modeling and prediction

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(Stocker et al., 2013). Despite recent advances in experimental and theoretical

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methods, the mechanism governing the formation of seeds for thermally stable aerosol

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particles involving multiple components is still unclear (Kumar et al., 2018),

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especially in Northern China. It is well-known that sulfuric acid (SA) is closely

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related to atmospheric NPF events (Weber et al., 2001) and is therefore of decisive

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importance for the formation of atmospheric aerosol particles. It has also become

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clear within the last decades that more stabilizing species, such as organic acids,

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nitrogenous compounds, and highly oxygenated molecules (HOMs) (Ahlberg et al.,

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2017) likely participate in the nucleation of atmospheric NPF (Wang et al., 2019;

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Zhang et al., 2012). However, the nucleation mechanism involving organic acids and

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nitrogenous bases remains unclear.

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Methanesulfonic (MSA), one of the simplest organic organosulfur acids in the

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atmosphere, is a prominent oxidation product from organosulfur compounds that

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originate from biological processes, biomass combustion, industrial emissions, and

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agriculture (Barnes et al., 2006), which appreciably contribute to atmospheric NPF

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events in certain conditions (Chen and Finlayson-Pitts, 2017; Chen et al., 2016;

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Dawson et al., 2012). MSA has been measured in atmospheric aerosol particles nearly

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all geographic regions, ranging from coastal areas (Sorooshian et al., 2009) to the

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hinterland (Gaston et al., 2010), and is present in concentrations of ~ 10-50% of 2

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gaseous SA concentration (Berresheim, 2002). In a recent study (Dall'Osto et al.,

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2012), the gaseous concentration of MSA was found to decrease during marine

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particle formation events, suggesting that MSA contributed to the formation of initial

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clusters. Station observations also reported a strong correlation between the

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concentration of MSA and NPF events (Willis et al., 2016). In addition, results from

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later studies by Dawson (Dawson et al., 2012) and Bzdek (Bzdek et al., 2011) found

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that ammonia/amines distinctly increased the formation rate of MSA-based aerosol

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particles using a flow tube experiment with simple ab initio calculations. Ammonia,

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an important component of increasing atmospheric NPF (Jiang and Xia, 2017), is

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ubiquitous in the atmosphere due to various emission sources ranging from livestock

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farming to marine organism biodegradation (Ge et al., 2011). The concentration of

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ammonia ranges from tens to tens of thousands of pptv in the troposphere (Ge et al.,

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2011), which easily participates in forming particles (Glasoe et al., 2015; Kurtén et al.,

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2008; Zollner et al., 2012). An increased MSA concentration was detected in small

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particles when NH3 participated in NPF in several field observations (Kerminen et al.,

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1997), which ultimately substantiated the role of NH3. Therefore, understanding the

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mechanism governing atmospheric NPF and its relationship to MSA and NH3 is

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important (Karl et al., 2007). The studies on the binary systems of MSA and ammonia

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(Chen et al., 2016; Dawson et al., 2012) provide meaningful results regarding cluster

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formation as well as useful information on the electronic structure. Numerous studies

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involving MSA-NH3-H2O (Chen and Finlayson-Pitts, 2017; Chen et al., 2016; Li et

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al., 2007; Wen et al., 2019) experimentally revealed that humidity has an important

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influence on the formation of MSA-NH3 system. The research results (Bork et al.,

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2014) showed that MSA-enhanced clustering involves clusters containing one MSA

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molecule that contributes significantly to the growth of the SA-DMA system at low

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temperatures. However, several fundamental questions involving the formation and

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growth of clusters at the initial stage including the detailed dynamic growth

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mechanism, the rate-determining step of clusters formation, and the effect of humidity

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on the formation mechanism at the molecular level, remain unresolved.

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To our knowledge, theoretical studies regarding the formation mechanism and 3

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the influence of humidity on the formation mechanism of MSA-NH3 clusters at the

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molecular level have not been previously reported. In addition, DFT and ACDC

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methods have been successfully used to study the mechanism governing the formation

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of SA-based systems in recent years (Kurtén et al., 2006; Li et al., 2017; Li et al.,

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2018; Loukonen et al., 2010; Ortega et al., 2012). Herein, adopting the same method

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based on DFT and ACDC, the thermodynamic properties, evaporation rate, formation

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rate, growth pathway, and hydration level were investigated in order to gain a deeper

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understanding into the mechanism governing the formation of (MSA)x(NH3)y (x, y ≤

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4) clusters under different monomer concentrations (MSA and NH3), temperature, and

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relative humidity (RH) conditions.

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2. Computational details

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2.1 Theoretical calculation and analysis methods

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The Gibbs free energy (G) of clusters is the most critical parameter for

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identifying the formation mechanism of clusters. The calculated reliability of G was

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determined by the structure of the global minimum (here it refers to energy minimum)

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of (MSA)x(NH3)y (x, y ≤ 4) clusters. The global minimum sampling technique is an

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efficient and convenient tool for searching for atmospheric clusters (Elm et al., 2013b;

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Elm et al., 2016a; Elm et al., 2015). In this study, this method was used to locate

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global minima for (MSA)x(NH3)y (x, y ≤ 4) clusters; a detailed flow chart is shown in

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Fig. S1. Theoretical calculations and kinetics simulations were performed using the

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ABCluster (Zhang and Dolg, 2015; Zhang and Dolg, 2016), MOPAC (Stewart, 1990)

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and GAUSSIAN 09 programs (Frisch et al., 2009). The molecular structure of the

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precursor was described using the CHARMM36 force field (Yin and MacKerell, 1998)

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in the ABCluster program. The M06-2X functional and 6-31++G(d,p) basis set was

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used to describe the noncovalent interaction and equilibrium structure of the

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atmospheric clusters (Elm et al., 2013a; Elm and Kristensen, 2017). Single point

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energy calculations at the DLPNO-CCSD(T) (domain-based local pair natural orbital

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coupled cluster)/aug-cc-pVTZ level (Riplinger and Neese, 2013; Riplinger et al., 2013)

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were performed in ORCA version 4.0.0 (Neese, 2012). The DLPNO-CCSD(T)/ 4

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aug-cc-pVTZ level of theory was utilized to yield a mean absolute error of 1.3

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kJ·mol−1 compared to CCSD(T) complete basis set limit (CBS) estimates, based on a

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test set of 10 small atmospheric cluster reactions (Myllys et al., 2016). Herein, the

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value of G for monomers and clusters was estimated by combining the single-point

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energy with the Gibbs free energy correction term at the DLPNO-CCSD(T)/

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aug-cc-pVTZ and M06-2X/6-31++G(d,p) level at 298.15K. The 6-31++G(d,p) basis

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set is widely used for the optimization of atmospheric clusters because of its fast

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convergence rate and reliable results compared with other larger basis sets (Elm et al.,

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2013a; Elm and Kristensen, 2017). Additionally, the Gibbs free energy of the

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formation (∆Gref) of the clusters was calculated at different temperatures under the

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approximation that the enthalpy of formation (∆Href) and entropy of formation (∆Sref)

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remain unchanged in the troposphere. Considering the concentration of precursors in

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the atmosphere, the actual Gibbs free energy of the formation (∆Gact) of the clusters

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was obtained by converting the ∆Gref from 1 atm to the actual vapor pressure of a

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particular species. ∆Gact is different from ∆Gref, which can be used as a

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thermodynamic criterion to evaluate the spontaneity of cluster formation (a detailed

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description of ∆Gref and ∆Gact are shown in the SI). Analyses of Atoms in Molecules

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(AIM) theory (Bader, 1990) and the noncovalent interaction (NCI) index (Johnson et

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al., 2010) for the dimers were performed using Multiwfn 4.3 software (Lu and Chen,

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2012) in this study. (MSA)x(NH3)yWz (x, y ≤ 2, where “W” stands for water, and z is

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the number of water molecules) clusters were investigated while considering the

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effect of hydration on the MSA-NH3 system. This was similar to procedures used for

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anhydrous clusters in order to search for the global minimum of the hydrated clusters.

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Moreover, for the purposes of comparing the formation rate of SA-NH3 and the

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MSA-NH3 system directly, the corresponding ∆G values of (SA)x(NH3)y (x, y ≤ 4)

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clusters were re-calculated at the same theoretical level (DLPNO-CCSD(T)/

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aug-cc-pVTZ//M06-2X/6-31++G(d,p)) based on those cluster structures reported

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(Olenius et al., 2017).

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2.2 Kinetics simulation

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The kinetics simulation of the atmospheric clusters is important for 5

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understanding their nucleation mechanism in a real atmospheric environment. One

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note is that the key input file for a kinetics simulation is the ∆G values of relevant

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clusters based on the DLPNO-CCSD(T)/aug-cc-pVTZ//M06-2X/6-31++G(d,p) level.

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ACDC is widely used to determine certain key parameters of cluster growth, such as

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the evaporation rate, formation rate, and growth pathway. Moreover, ACDC is useful

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for understanding the dynamic mechanism of cluster growth at the molecular level.

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We refer readers to the study from McGrath et al (McGrath et al., 2012) for a detailed

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theoretical description of the ACDC program. In brief, equations for the time

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derivative of the concentration of any cluster are generated in the code using the

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Matlab ode15s routine (Shampine and Reichelt, 1997), which are then used to solve

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differential equations and simulate the time-dependent concentration of various

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clusters. These differential equations, called birth-death equations, mainly comprise

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source terms for small molecules (clusters) that collide to form large clusters, as well

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as large clusters that evaporate into small molecules (clusters) and so on. In addition,

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the formation rate of clusters in the ACDC program is defined as the flux outside the

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system. The flux outside of the system for a cluster is determined by the boundary

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condition. In an ACDC simulation, hydration is considered by regarding H2O as a

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nucleation species that influence the evaporation rate, formation rate, and nucleation

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mechanism of the clusters (Henschel et al., 2016). A “4 × 4 box” system was

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simulated for the anhydrous system, where 4 is the maximum of MSA or NH3

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molecules in the studied system. This is required for (MSA)5(NH3)5 to grow outside

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the MSA-NH3 system and all other clusters crossing the box edge are brought back to

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the simulation box by monomer evaporations (detailed discussion of the boundary

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condition can be found in the SI). Low temperature is very helpful for the NPF

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because of the lower entropy penalty from the second term in the free energy (∆G =

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∆H − T∆S). In this work, in order to comprehensively evaluate the influence of

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temperature on the formation rate of MSA-NH3 clusters, a temperature range from

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220 to 290 K was chosen in our ACDC simulations. The primary ACDC simulation

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was conducted at 278.15 K, while additional simulations were performed to study the

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effect of temperature at 220, 240, 260, 280, and 290 K. Regarding the SA-containing 6

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system, 2.6 × 10−3 s−1, was used as the constant coagulation sink coefficient, which

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corresponds to a typical value observed in a boreal forest (Olenius et al., 2013). In

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addition, it was reported that the constant coagulation sink coefficient has a slight

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effect on the formation rate in the SA-containing system (Olenius et al., 2017).

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Therefore, a value of 2.6 × 10−3 s−1 was used as the constant coagulation sink

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coefficient in the MSA-containing system. In addition, the concentration of MSA was

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defined in the range from 104 to 108 molecules·cm−3, and the concentration of NH3

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ranged from 10 to 1000 pptv; these ranges are also relevant for atmospheric NPF

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(Almeida et al., 2013). It is worth mentioning that the acid concentration is considered

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to be the total concentration of any neutral cluster that includes one acid molecule

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(Almeida et al., 2013). Therefore, the simulated system becomes a “2 × 2 box” when

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hydration is considered. For (MSA)x(NH3)y (0 ≤ x, y ≤ 2) clusters, the average

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collision and evaporation coefficients based on the hydrate distribution are used in the

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birth-death equations for [MSA] = 106 molecules·cm−3, [NH3] = 100 pptv, and T =

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278.15 K. For each cluster, we calculated the equilibrium hydrate distribution with the

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equilibrium constant in terms of the value of ∆Gref for the hydrate (Henschel et al.,

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2016).

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3. Results and discussion

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3.1 Structure, topology, and average partial charge analysis

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(MSA)x(NH3)y indicates a cluster containing x (x ≤ 4) MSA and y (y ≤ 4) NH3

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molecules, and therefore the proton transfer status does not need to be clearly

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specified. The structures of pure (NH3)y (y = 2 to 4) clusters were also discussed in

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previous studies (Ling et al., 2017). Herein, (MSA)x(NH3)y (1 ≤ x ≤ 4 and y ≤ 4)

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clusters will be the primary focus. All structures are shown in Fig. S2. In general,

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proton transfer does not occur in (MSA)x (x = 2 to 4) and (NH3)y (y = 2 to 4)

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homomolecular clusters, and they are typically stabilized by hydrogen bonding.

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Regarding pure (MSA)x clusters, more complicated network structures were formed

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due to the presence of more O−H···O hydrogen bonds from x = 2 to 4 (see Fig. S2).

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Similar to pure MSA clusters, a typical parallelogram ring, six-membered ring, and 7

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eight-membered ring form by two, three, and four N−H hydrogen bonds in the (NH3)2,

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(NH3)3 and (NH3)4 clusters, respectively (detailed structural information is shown in

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Fig. S2). In pure clusters, the length of a hydrogen bond (N−H···N) in pure NH3

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clusters is longer than that in (O−H···O) of a pure MSA cluster. (MSA)x (2 ≤ x ≤ 4)

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and (NH3)y (2 ≤ y ≤ 4) clusters tend to form spherical and planar configurations due to

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the structural differences in MSA and NH3 molecules as x and y increase, respectively.

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This also indicates that hydrogen bonding in pure MSA clusters is stronger than that

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in pure NH3 clusters.

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For all heteromolecular clusters, proton transfer occurred from an MSA molecule

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to an NH3 molecule when the number of NH3 molecules is equal or larger than that of

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MSA molecules, except for (MSA)(NH3). All stabilized via hydrogen bonding and

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electrostatic interactions between positive and negative species. Several studies (Elm,

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2017; Elm et al., 2016b; Olenius et al. 2013; Olenius et al. 2017) show that clusters

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with an equal number of acid and base molecules are more stable and play an

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important role in subsequent cluster growth. Herein, the structures of the

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(MSA)x(NH3)y (x ≠ y ≠ 0) clusters are not described in detail; more information is

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presented in Fig. S2. In an (MSA)(NH3) dimer, no proton is transferred, but one

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six-membered ring is formed by one strong hydrogen bond (O−H···N) and one weak

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hydrogen bond (N−H···O) (see Fig. S2). This is consistent with the conclusion from

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Born-Oppenheimer molecular dynamics (BOMD) simulations, i.e., proton transfer

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between one MSA and one NH3 molecule in the absence of water at 298.15 K and

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1atm is impossible (Kumar and Francisco, 2017). In (MSA)2(NH3)2, four strong and

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four weak hydrogen bonds form alternately between MSA and NH3 molecules. It

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should be mentioned here is that (MSA)2(NH3)2 is the most stable cluster due to its

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high structural symmetry and saturated hydrogen bonds. In (MSA)3(NH3)3, six strong

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hydrogen bonds form by anchoring two NH3 molecules to form a discus shape

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composed of three MSA molecules on the upper and lower sides. One should note that

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the unique net structure forms through proton transfer in (MSA)4(NH3)4. Here, four

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NH+4 and four CH3 SO3 ions alternately occupy 8 vertices in this structure. For

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(MSA)x(NH3)y (x = y ≠ 1) clusters, proton transfer helps form a more stable 8

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three-dimensional spherical structure. In addition, the patterns of proton transfer in the

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MSA-NH3 system (see Fig. S2) are different from those in the SA-NH3 system

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(Olenius et al., 2017; Olenius et al., 2013) due to the difference in the number of −OH

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and −CH3 groups of acid molecules. The steric hindrance of the –CH3 in clusters is

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unfavorable for cluster formation. Moreover, the contribution of the stronger acidity

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of SA than MSA cannot be ignored in the different acid-base clusters (Elm et al.,

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2016b; Elm et al., 2015). These factors together cause the formation capability of

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MSA to be far lower than that of SA in the formation of atmospheric clusters.

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Results from previous studies (Olenius et al., 2017) showed that the formation of

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initial dimers is critical for the overall formation process. Herein, only three initial

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dimers, i.e. (NH3)2, (MSA)2, and (MSA)(NH3), were chosen for AIM and NCI

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analyses to obtain useful information about the formation of the initial clusters.

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Topological analysis of AIM indicates that the electron density (ρ) at bond critical

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points (BCPs) in the N−H…N, O−H…O, and O−H…N hydrogen bonds in (NH3)2,

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(MSA)2 and (MSA)(NH3) clusters are 0.013 (0.013), 0.040 (0.039), and 0.079 a.u.,

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respectively (see SI Text and Table S1). The value of ρ represents the hydrogen bond

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strength. As an extension of AIM theory, the NCI analysis also shows that there are

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low-reduced gradient spikes (blue or green color) at low density of the sign(λ2)ρ value

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of −0.013, −0.040 and −0.079 a.u., which suggests that two weak, two strong, and one

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strong hydrogen bonds are present in (NH3)2, (MSA)2, and (MSA)(NH3), respectively

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(see the lower panel in Fig. 1). In addition, the color-coding of these bonding

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isosurfaces in the dimers switches from green to blue in the upper panel in Fig. 1,

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indicating that the strength of a hydrogen bond ranges from weak to strong. From the

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three analyses presented above, hydrogen bonding in (MSA)2 and (MSA)(NH3) is far

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stronger than that in (NH3)2, especially (MSA)2 (see SI Text). Average partial charge

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(δA) analysis also shows that δA in NH3 ranges from 0.8280 to 0.8845, except for one

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(MSA)(NH3) cluster (δA = 0.1285) (see Table S2). Larger values (δA > 0.8) indicate

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that electrostatic force from ion pairs formed by proton transfer from MSA to NH3

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becomes stronger, which favors the growth of large clusters (see SI Text and Table

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S2). 9

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3.2 Thermodynamic properties and evaporation rate

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∆Gref for the (MSA)x(NH3)y (x, y ≤ 4) clusters from their component molecules

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at 298.15 K is shown in Fig. 2a, whereas the corresponding thermodynamic properties

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(∆Href and ∆Sref) are shown in Table S3. For the (MSA)x(NH3)y (x, y ≤ 4) clusters, the

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values of ∆Gref and ∆Href decreased as x and y increased, respectively. Although Href is

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related to the stability (Curtiss and Blander, 1988), the Gibbs free energy is essentially

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the determining factor for the stability of a cluster. The entropy contribution to the

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formation process of clusters is very important. This indicates that the stability of the

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cluster was gradually enhanced as the total number of cluster molecules increased.

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Herein, ∆Gref for the three initial dimers ((NH3)2, (MSA)2, and (MSA)(NH3)) is

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highlighted because its value is important for the initial formation and subsequent

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growth of clusters. ∆Gref = −8.92, −5.37, and 3.95 kcal·mol−1 for (MSA)2,

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(MSA)(NH3), and (NH3)2, respectively. From a thermodynamics perspective, the

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formation of (MSA)2 is the most favorable. In addition, for the MSA-NH3 and

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SA-NH3 systems, a ∆Gref for (MSA)x(NH3)y (x, y ≤ 4) clusters is generally higher than

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that for the corresponding (SA)x(NH3)y (x, y ≤ 4) clusters (see Fig. S3). For example,

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the noncovalent interaction in (MSA)x(NH3)y clusters is weaker than that of the

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(SA)x(NH3)y clusters. The main reason for this is the difference in the ability to form

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hydrogen bonds and steric hindrance between −OH and −CH3 functional groups. Two

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−OH groups in SA are more favorable for the formation of hydrogen bonds than one

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−OH and one −CH3 in MSA. It is tempting to conclude that the −CH3 functional

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group in an MSA molecule hinders the formation of (MSA)x(NH3)y clusters.

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Considering the growth of clusters at a specific concentration, the formation rate

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(details are present in section 3.3) can be exported by comparing the collision and

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evaporation rates of the clusters, which is important for better understanding their

291

formation mechanism. Although the collision and evaporation rates of clusters can be

292

easily determined using ACDC kinetics simulations, the difference in collision rates

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for all clusters is small; thus, the evaporation rate is used to evaluate the stability of

294

clusters in this section. Those with an evaporation rate in the range of 10−4 to 10−3 s−1

295

are considered stable when the concentration of the precursors (MSA and NH3) is 10

296

approximately equal to or above pptv levels (Kulmala, 2013; Kulmala et al., 2000).

297

(MSA)3(NH3)3 can be considered stable because its evaporation rate is lowest and is

298

far lower than that of all others in the system studied at 278.15 K (see Fig. 2b). All the

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evaporation pathways were also checked (see Table S4), and it was found that

300

evaporation of the NH3 monomer was the main decomposition channel for all relevant

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clusters when x = y. When x < y, evaporation of the NH3 monomer is always preferred

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in the studied clusters. For example, an (MSA)2(NH3)3 cluster is easily converted to

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(MSA)2(NH3)2 by NH3 monomer evaporation due to its high evaporation rate (4.92 ×

304

106 s−1). Evaporation of an (MSA)2 dimer or MSA monomer is the dominant

305

dissociation channels when x > y. In other words, when an (MSA)3(NH3)2 cluster

306

changes to (MSA)2(NH3)2 by evaporation of an MSA monomer, its evaporation rate

307

reaches 104 s−1. Moreover, when the total number of molecules in different clusters is

308

equal, the evaporation rate of abundant NH3 clusters is higher than the corresponding

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abundant MSA clusters, and the evaporation of an NH3 monomer is faster than that of

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MSA because MSA combines with clusters more easily than NH3. Overall, the

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evaporation rate of clusters on or near the diagonal is far lower than that of clusters

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away from the diagonal of the MSA-NH3 system. This also indicates that the channel

313

with a low evaporation rate is more favorable for cluster growth. It is also true that the

314

ability for an acid to bond is stronger than that of a base, and evaporation of a base

315

monomer is the primary decay route for larger clusters in the SA-NH3 (McGrath et al.,

316

2012), SA-MA (Olenius et al., 2017), SA-DMA (McGrath et al., 2012), and SA-MEA

317

systems (Xie et al., 2017). It is also interesting to compare the total evaporation rate of

318

the MSA-NH3 and SA-NH3 systems in identical simulation conditions. In general, the

319

evaporation rate of the MSA-NH3 system is higher than that of the SA-NH3 system,

320

showing that the SA-NH3 system is more stable (see Fig. S4). The essential

321

differences are that SA is much more acidic than MSA, and the ability to form the

322

non-covalent interaction for −OH is far stronger than that for −CH3. The former is to

323

form hydrogen bonding whereas the latter is Van der Waals interaction.

324

3.3 (MSA)2 dimer concentration and formation rate of the MSA-NH3 system

325

Similar to the discussion regarding SA-base systems (Olenius et al., 2017; Xie et 11

326

al., 2017), the concentration of the precursors also affects cluster formation, especially

327

the initial dimers. As described in section 3, for three initial dimers, the evaporation

328

rate of (MSA)2 (102 s−1) is lower than that of (MSA)(NH3) (5 × 105 s−1) and (NH3)2 (3

329

× 1012 s−1) by 3 and 10 orders of magnitude, respectively. This confirms that (MSA)2

330

forms more easily than (MSA)(NH3) and (NH3)2 during cluster growth. Herein, the

331

concentration of the (MSA)2 dimer (hereafter called [(MSA)2]) will be the primary

332

focus. As shown in Fig. 3a, [(MSA)2] increases in proportion to [MSA] and [NH3],

333

and the low [NH3] (≤ 100 pptv) has little effect on [(MSA)2]. In contrast, the high

334

[NH3] (> 100 pptv) has an apparent influence on [(MSA)2] in the aforementioned

335

condition, where T = 278.15 K and P = 1 atm. Overall, [(MSA)2] ranges from 10−3 to

336

107 molecules·cm−3, which is higher than that of [(MSA)(NH3)] and [(NH3)2]. Thus, it

337

is clear that [(MSA)2] is critical for determining the formation rate and the overall

338

formation process. Regarding the SA-NH3 system, [(SA)2] and [SA] or [NH3] exhibit

339

linear relationships at low and medium [SA], which is slightly different compared to

340

the MSA-NH3 system (see Fig. S5a).

341

The formation rate, an important quantification index for cluster formation, is

342

used to evaluate the capability of NH3 to promote MSA-based cluster formation in

343

this section; this is similar to the case with SA-based clusters (Olenius et al., 2017).

344

Fig. 3b shows that the formation rate is a function of the monomer concentration

345

([MSA]: 104, 105, 106, 107, and 108 molecules·cm−3, [NH3]: 10, 100, and 1000 pptv)

346

in the MSA-NH3 system at 278.15 K. Generally, the formation rate is proportional to

347

[MSA] and [NH3], and [NH3] is inversely proportional to [MSA] when the formation

348

rate is constant. This figure also shows that the MSA-NH3 system progressively

349

inclines toward saturation at high [MSA], thus cluster growth is dominated by MSA.

350

The simulation results also show that NH3 could reinforce MSA-based NPF when the

351

atmospheric concentration of MSA and NH3 reach or exceed ppbv levels, which is

352

consistent with the experimental results (Chen et al., 2016). Regarding the MSA-NH3

353

system, the formation rate between MSA and NH3 exhibits a linear relationship with

354

[MSA] when 104 ≤ [MSA] ≤ 107 molecules·cm−3. However, when [MSA] > 107

355

molecules·cm−3, the formation rate increased moderately due to the significant 12

356

deposition of pure MSA clusters. In addition, the effect of high [MA] on the formation

357

rate was less than that of high [MSA] for the MSA-NH3 system (see Fig. 3b). This

358

difference in the SA-NH3 system arises because the −OH functional group acts as a

359

strong donor in a SA molecule, which contains more −OH than an MSA molecule. In

360

addition, the formation rate is inversely proportional to the temperature within the 220

361

to 290 K range. The reduced formation rate at high temperatures is more obvious than

362

that at low temperatures (see Fig. S6). The reverse effect of temperature dependence

363

on the concentration of precursors is not clear. In this work, considering the

364

concentration of precursors and temperature in the lower troposphere, subsequent

365

kinetics simulations were performed with the NH3 concentration set to 100 pptv, MSA

366

concentration set to 106 molecules·cm−3 and temperature set to 278.15K. Furthermore,

367

the formation rates of the MSA-NH3 (4 × 4) system are far lower than those of the

368

SA-NH3 (4 × 4) system under typical atmospheric conditions (see Fig. S5b). This

369

further implies that, in addition to the high concentration of precursors, the

370

participation of other species is also very important to promote the effective

371

nucleation of the MSA-NH3 system by forming stable MSA-based ternary clusters in

372

the lower troposphere over coastal areas.

373

3.4 Actual Gibbs free energy and growth pathway

374

The actual Gibbs free energy (∆Gact) and growth pathway in the MSA-NH3

375

system are shown in Figs. 4 and 5a, where [MSA] = 106 molecules·cm−3, [NH3] = 100

376

pptv, and T = 278.15 K. Considering the concentration of precursors in the

377

atmosphere, ∆Gact is obtained by converting the free energy change from 1 atm to the

378

actual vapor pressure of a particular species. ∆Gact for the clusters along or near the

379

diagonal is much lower than that far from the diagonal. For the MSA-NH3 system, the

380

growth pathway along or near the diagonal is the most advantageous, but free energy

381

barriers in all directions in this system signified that these small clusters are difficult

382

to grow in a typical atmosphere. Herein, we note that ∆Gact is different from ∆Gref.

383

The ∆Gact is greater than zero for all clusters, which cannot be used as a

384

thermodynamic criterion to assess the spontaneity of the process (see SI Eqs. 7 and 8).

385

Combined with the discussion in the previous section, (MSA)2 is a greater 13

386

determinant in the first step of cluster formation than (MSA)(NH3) and (NH3)2 from

387

the perspective of topology analyses, thermodynamics, and evaporation rate. The

388

primary flux out of the simulated box is the (MSA)4(NH3)5 cluster, and some features

389

can be observed through the growth pathway and the Gibbs free energy of the

390

formation of clusters. First, the cluster growth pathways do not fully follow the lowest

391

free energy pathway; they deviate from the diagonal in the acid-base grid. The first

392

step of cluster formation is primarily controlled by collisions between MSA molecules

393

due to strong hydrogen bonding and the low evaporation rate of the (MSA)2 dimer

394

(see section 3.1 and 3.2). The second step is primarily controlled by the collision

395

between (MSA)2 and an NH3 monomer because the concentration of (MSA)2 is larger

396

than the other dimers. Thus, (MSA)2 plays a key role in subsequent cluster growth,

397

which is also an important reason why growth deviates from the diagonal in the grid

398

at the initial stage. Thirdly, the primary flux out, i.e., (MSA)4(NH3)5 cluster, has two

399

pathways. The initial stage before formation of (MSA)2(NH3)2 is the same, and

400

subsequent growth is divided along two pathways as follows: (1) (MSA)2(NH3)2→

401

(MSA)4(NH3)4 → (MSA)4(NH3)5 and (2) (MSA)2(NH3)2 → (MSA)4(NH3)2 →

402

(MSA)4(NH3)3→(MSA)4(NH3)4→(MSA)4(NH3)5. Regarding the flux out, pathway (1)

403

is more important because its proportional contribution is as high as 89%. From the

404

discussion in section 3.1, although (MSA)3(NH3)3 is the most stable cluster in the

405

whole system, however, the (MSA)3(NH3)3 cluster is difficult to form, as both the

406

(MSA)2(NH3)3 and (MSA)3(NH3)2 clusters have high evaporation rates. Therefore, no

407

(MSA)3(NH3)3 cluster is present in the favorable growth pathways on the acid-base

408

grid. Finally, one can conclude that the formation of an (MSA)2 dimer is the

409

rate-determining step for cluster growth when the growth pathway and evaporation

410

rate are considered. One should note that temperature has no effect on the growth

411

pathways in the initial stage; however, it has obvious effects in the subsequent stage

412

after the formation of an (MSA)2(NH3)2 cluster (see Fig. S7).

413

The growth pathways in the MSA-NH3 and SA-NH3 systems are presented in

414

Figs. 5a and S8 under the same simulation conditions, respectively. One common

415

characteristic is that homogeneous dimers initially form from two MSA or two SA 14

416

molecules in the initial stage at 278.15 K, which is critical for initiating cluster growth.

417

Nevertheless, there are some differences regarding all growth pathways for the

418

MSA-NH3 and SA-NH3 systems at different temperatures (see Figs. 5a, S7, and S8).

419

Regarding the SA-NH3 system, the formation of the initial (SA)(NH3) and (SA)2

420

dimers are more important for determining subsequent growth channels at low (220 K)

421

and high (278.15 K) temperatures, respectively (see Fig. S8). Based on the results of a

422

previous study (McGrath et al., 2012), one conclusion can be drawn that a collision

423

comprising (SA)(NH3) is dominant for the SA-NH3 cluster growth at low

424

temperatures, where growth proceeds along the diagonal in the acid-base grid.

425

Regarding the MSA-NH3 system, the effect of temperature on the growth pathway is

426

different from that in the SA-NH3 system. The temperature has no effect on the initial

427

formation stage for (MSA)x(NH3)y cluster and vice versa. For example, the cluster

428

growth pathway is complicated at low temperature, as shown in Figs, S7 and S8a.

429

3.5 Effect of hydration on the nucleation mechanism of MSA-NH3 system

430

Water is more abundant than acids and bases in the troposphere by several to 10

431

orders of magnitude. Therefore, the effects of hydration on the evaporation rate,

432

formation rate, and growth pathway of clusters were investigated in this work

433

(DePalma et al., 2014). As found in previous studies (DePalma et al., 2014; Henschel

434

et al., 2016), clusters containing SA, ammonia, or simple organic amines are primarily

435

hydrated by a few water molecules. Herein, small anhydrous clusters and a few water

436

molecules are considered together to study the effect of hydration on the formation

437

mechanism in the studied system. In addition, for the purposes of saving computing

438

resources, small (MSA)x(NH3)y (x, y ≤ 2) clusters were selected as the testing system

439

to study hydration. The equalizing hydrate distribution was converted from the ∆Gref

440

of clusters hydrated at different RH values, a temperature of 278.15 K and 1 atm. One

441

can conclude that pure MSA and heterogeneous clusters are hydrated from Fig. S9. A

442

detailed discussion regarding ∆Gref, structure, and average number of water molecules

443

in individual clusters was presented in SI Text, Figs. S10, and S11, respectively. In

444

this study, the effect of hydration on the kinetics simulation for cluster formation was

445

the primary focus. 15

446

In principle, the formation rate of clusters can be affected by hydration due to

447

changes in the collision rate and evaporation rate. However, hydration has little or no

448

effect on the collision rate because the collision diameter, which is a significant factor

449

for the collision rate in the kinetic collision theory adopted in ACDC, has less

450

dependence on hydration (Henschel et al., 2016). Herein, the effect of hydration on

451

the evaporation rate, formation rate, and growth pathway are discussed. Fig. 6 show

452

that the evaporation rate and formation rate serve as a function of RH at 278.15 K in

453

comparison to anhydrous conditions. Overall, the presence of water produces a

454

variety of effects on the evaporation rates for specific clusters.

455

Fig. 6a shows that the RH value can slightly affect the evaporation rate of

456

(MSA)2(NH3), whereas the RH value has almost no effect on that of (NH3)2 and

457

(MSA)(NH3)2, but it effectively increases the evaporation rate of (MSA)2 by

458

approximately a factor of 103. In addition, the evaporation rates of (MSA)(NH3) and

459

(MSA)2(NH3)2 are significantly reduced by factors of 10−5 and 10−3 compared to the

460

anhydrous case, respectively. From Table S5, the extra stabilization energy from water

461

dominated the change of the evaporation rate of clusters. The results of the

462

Finlayson-Pitts group (Chen et al., 2016) showed that the effect of hydration (RH =

463

42%) on the formation was up to a factor of 106, which is generally consistent with

464

our simulated results. Therefore, it is clear that hydration has the most obvious effect

465

on the evaporation rate of the initial (MSA)(NH3) cluster, which is critical for the

466

overall formation process. Similar to the discussion presented in section 3.3, the

467

primary flux out of the simulated box (2 × 2) consists of (MSA)3(NH3)2 and

468

(MSA)3(NH3)3. The growth pathways of the (MSA)3(NH3)3 (77%) and (MSA)3(NH3)2

469

(23%) clusters are as follows: MSA→(MSA)(NH3)→(MSA)2(NH3)2→(MSA)3(NH3)3

470

and MSA→(MSA)(NH3)→(MSA)2(NH3)2→(MSA)3(NH3)2, respectively (see Fig. 5b).

471

When Figs. 5a and 5b are compared, hydration clearly changes the initial cluster

472

formation compared with anhydrous cases. Apparently, (MSA)(NH3) plays a more

473

important role than (MSA)2 in cluster formation at the initial stage, which is

474

completely different from anhydrous conditions. As shown in Fig. 6b, the relative

475

formation rate can be increased by approximately 105 times when RH = 100%, which 16

476

further confirms that humidity has a major influence on the studied system. This also

477

explains why humidity can affect the formation rate and mechanism. Based on the

478

discussion presented above, SA is more important than MSA in the NPF process in

479

anhydrous cases, but the formation rate of the MSA-NH3 system increases

480

significantly in the presence of water (up to a factor of 106), which is even higher than

481

that in the water-free SA-NH3 system. This indicates that the effect of hydration on

482

the formation rate in the MSA-NH3 system cannot be ignored in a heavily polluted

483

atmosphere ([NH3] ≥ 1ppbv) with high humidity, especially in coastal areas where the

484

concentration of precursors are also relatively high ([MSA] ≥ 2 × 107 molecules cm−3).

485

In addition, one should note that the influence of humidity on the formation rate is

486

closely related to the structure of nucleation precursors. Due to the steric hindrance of

487

−CH3 in MSA, hydrogen bonds are less likely to form in the MSA-NH3 system, and

488

the formation rate of the MSA-NH3 system is lower than that of the SA-NH3 system

489

in anhydrous cases. Although a box (2 × 2) can introduce bias into the absolute

490

formation rate compared with the actual formation rate, attention should be paid to the

491

fact that the relative formation rate stated is favorable to reduce the bias generated

492

through the small box used in this work. Results from kinetics simulations involving

493

small hydrated clusters allow one to conclude that hydration has a significant effect

494

on the formation mechanism and greatly increases the formation rate of the MSA-NH3

495

system. Although the use of larger clusters and more water molecules in

496

contemporary studies should not lead to different qualitative conclusions, such a case

497

is still worth studying in the future, with the goal of reaching a conclusion regarding

498

the effect of humidity on the kinetics governing MSA-NH3 cluster formation.

499

4. Conclusions

500

In this work, the MSA-NH3 system was investigated using quantum mechanics

501

and kinetics simulations under different conditions. The findings suggest that

502

hydrogen bonding and electrostatic interactions provide the primary force that drives

503

cluster formation. The different concentrations of MSA and NH3 have a significant

504

influence on the formation rate of MSA-NH3 clusters under the water-free condition, 17

505

and the formation of (MSA)2 dimer is the rate-determining step. Compared to

506

anhydrous cases, hydration causes the formation of (MSA)(NH3) dimer to be the

507

rate-determining step. The formation rate increased significantly by 105 times. This

508

suggests that the effect of humidity on the formation of the MSA-NH3 clusters is

509

significant in the coastal atmosphere. Generally, the effective nucleation for the

510

MSA-NH3 system is difficult to occur due to its weak stability under typical

511

atmospheric conditions. The high concentration of precursor and atmospheric

512

humidity is necessary for the effective nucleation of the MSA-NH3 system in an

513

atmospheric environment. Other species such as SA are involved in forming the

514

MSA-SA-NH3 ternary clusters that may be more effective to promote the occurrence

515

of effective nucleation. The results presented in this study are essential for better

516

predicting NPF. Therefore, this study provides theoretical guidance for a better

517

understanding of atmospheric pollution.

518

Acknowledgments

519

This work was supported by the National Natural Science Foundation of China

520

(No: 21473108, 21873060, 21636006) and Fundamental Research Funds for the

521

Central Universities (Grant No. GK201901007).

522

We gratefully acknowledge the valuable help of Hanna Vehkamäki (University

523

of Helsinki), Tinja Olenius (Stockholm University), Zhang Xiuhui (Beijing Institute

524

of Technology), LUO Yi (Dalian University of Technology), Liu Yirong (University

525

of Science and Technology of China), ZHANG Jun (University of Illinois), ZHAO

526

Xianwei (Shandong University) and LIN Jinfei (Shenzhen Transsion Holdings

527

Limited).

528

We thank Dr. Anand Parkash and LetPub (www.letpub.com) for its linguistic

529

assistance during the preparation of this manuscript.

530

Reference:

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23

a

b

c

Fig. 1 NCI (lower) and RDG (upper) analyses among global minima for (a) (NH3)2, (b) (MSA)2 and (c) (MSA)(NH3) clusters. Red, yellow, blue, gray and light gray spheres represent oxygen, sulfur, nitrogen, carbon and hydrogen atoms, respectively.

a

b Fig. 2 ∆Gref (a) and total evaporation rate (b) for (MSA)x(NH3)y clusters (x, y ≤ 4) by the DLPNO-CCSD(T)/aug-cc-pVTZ//M06-2X/6-31++G(d,p) level on the MSA-NH3 grid at 298.15 K and 278.15 K, respectively. 7

10

[NH3] = 10 pptv

-3 [(MSA)2] (molecules⋅ cm )

[NH3] = 100 pptv [NH3] = 1000 pptv

4

10

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10 10 -3 [MSA] (molecules⋅ cm ) a

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10 .08x10 .12x10 .16x10 1.2x10 1.04x 1 1 1 8

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10

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10

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[NH3] = 10 pptv [NH3] = 100 pptv

-8

[NH3] = 1000 pptv

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J (cm ⋅ s )

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-13

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10

-23

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-28

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10 10 -3 [MSA] (molecules⋅ cm )

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b Fig. 3 Concentration of (MSA)2 dimer (molecules·cm−3) (a) and the formation rate J (cm−3·s−1) of the studied system (b) as a function of MSA monomer concentration at 278.15 K.

Fig. 4 ∆Gact for (MSA)x(NH3)y (x, y ≤ 4) clusters at 278.15 K. ([MSA] = 106 molecules·cm−3 and [NH3] = 100 pptv).

a

b Fig. 5 Main clustering pathways and flux out for (a) (MSA)x(NH3)y (x, y ≤ 4) at RH = 0% and (b) (MSA)x(NH3)y(W)z (x, y ≤ 2, z ≤ 4) at RH = 80% where [MSA] = 106 molecules·cm−3, [NH3] = 102 pptv, and T = 278.15 K. Pathways contributing less than 5% to the flux of the cluster are not shown for clarity.

2

Relative Evaporation Rate

10

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10

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10

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10

(MSA)2

(MSA)(NH3)2

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10

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Relative Formation Rate (Jrel)

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20

40 RH %

60

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b Fig. 6 Relative evaporation rate (a) and relative formation rate (b) of (MSA)x(NH3)y (x, y ≤ 2) clusters as a function of RH where [MSA] = 106 molecules·cm−3, [NH3] = 100 pptv and T = 278.15 K.

Highlight: 1.

Hydrogen bonding is the primary driving force that forms the MSA-NH3 clusters.

2.

NH3 effectively promotes the formation of MSA-based clusters at ppt levels.

3.

Formation of (MSA)2 is a rate-determining step under anhydrous condition.

4.

Formation of (MSA)(NH3) is a rate-determining step under hydrous condition.

5.

The formation rate increases with RH, reaching up to a factor of 105 at RH = 100%.

Dongping Chen, Fengyi Liu and Wenliang Wang analyzed the results and wrote the manuscript. Dongping Chen prepared Figs. 2-6 and Tables S1–S6. Changwei Wang prepared Figs. 1, S1, S2, S9, and S10. Danfeng Li prepared Figs. S3-S8 and S11. All authors contributed to the manuscript.

The authors declared that they have no conflicts of interest to this work.