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The growth mechanism of sulfuric acid clusters: Implication for the formation of cloud condensation nuclei
Author’s Accepted Manuscript The Growth Mechanism of Sulfuric Acid Clusters: Implication for the Formation of Cloud Condensation Nuclei Boli Nie, Juan Wang, Baohan Qu, Lixiang Sun, Shihai Yan www.elsevier.com/locate/jaerosci
PII: DOI: Reference:
S0021-8502(17)30080-0 http://dx.doi.org/10.1016/j.jaerosci.2017.09.011 AS5186
To appear in: Journal of Aerosol Science Received date: 1 March 2017 Revised date: 13 May 2017 Accepted date: 8 September 2017 Cite this article as: Boli Nie, Juan Wang, Baohan Qu, Lixiang Sun and Shihai Yan, The Growth Mechanism of Sulfuric Acid Clusters: Implication for the Formation of Cloud Condensation Nuclei, Journal of Aerosol Science, http://dx.doi.org/10.1016/j.jaerosci.2017.09.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. 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.
The Growth Mechanism of Sulfuric Acid Clusters: Implication for the Formation of Cloud Condensation Nuclei Boli Nie,a Juan Wang,a Baohan Qu,a Lixiang Sun,b Shihai Yan a, * a
College of Chemistry and Pharmaceutical Sciences, Qingdao Agricultural University, Qingdao, 266109, China
b
School of Chemistry and Materials Science, Ludong University, Yantai 264025, China
Corresponding author: Shihai Yan, email: [email protected] QAU, Qingdao, 266109, China Phone: 86 532 86080954 FAX: 86 532 86080213
Abstract: The investigation on the growth mechanism of sulfuric acid clusters is helpful for the understanding about the formation of cloud condensation nuclei. The sulfuric acid may aggregate in linear, bent, or orbicular modes with two types of hydrogen bonds, viz. OH...OH and OH...O=S. The length of the linear mode polymers increases linearly along with the degree of polymerization (DP). The bent conformation distorts into the linear configuration when the DP is over 6. The diameter of the central ring generated by OH...OH hydrogen bonds in orbicular conformation increases distinctly from 3.441 Å in tetramer to 7.543 Å in nonamer. The IR spectra exhibit distinct variations along with both the DP and the coupling modes. As can be employed to infer the detailed geometrical structures of sulfuric acid polymers. The linear structure is more stable as compared to the bent and the orbicular conformations. The variation of the Gibbs free energy indicates that the sulfuric 1
acid can aggregate with a larger DP in linear mode. The temperature effect on the stability of the sulfuric acid polymer is more significant as compared with that of the pressure. The complex with high DP tends to be more stable at higher temperature, while the complex with low DP prefers low temperature. The findings are helpful for further study on atmospheric aerosol growth and the formation of cloud nucleation.
Keywords: Sulfuric Acid; Hydrogen Bond; Degree of Polymerization; IR Spectra; Gibbs Free Energy.
2
1.
Introduction The gas-to-particle conversion process of new particle formation generates the
atmospheric aerosols (AA) and influences the concentration of ambient particulate matter. Atmospheric nucleation is the dominant source of aerosol particles in the global atmosphere and an important player in aerosol climatic effects. The AA degrade visibility, negatively affect human health, directly or indirectly influence climate by absorbing and reflecting solar radiation and modifying cloud formation, as well as impact the air quality. Furthermore, the AA scatters and absorbs solar and terrestrial radiation, as well as influences the formation and properties of clouds. The impacts of aerosol particles on clouds are the largest individual source of uncertainty in estimates of the Earth's energy balance.1 The structures and reactivities of the molecular clusters have attracted extensive attentions experimentally and theoretically. AA is the basis for the formation of cloud condensation nuclei (CCN). Some useful information for particle formation has been afforded, although the underlying chemical mechanisms of AA and CCN have not been elucidated. The lack of complete understanding of the role of AA and CCN on the climate system forms a bottleneck for reliable and accurate projections of climate change. It has been observed that the atmospheric aerosol formation is essentially a two-step process, as proposed based on theoretical arguments2,
3
and laboratory experiments.4,
5
The
disagreement between the ambient data and the experiments, which is related to experimental design and sulfuric acid nucleation in ultraclean laboratory conditions, can explain the atmospheric nucleation rates.6To reveal the role of sulfuric acid in the AA formation and the following formation of CCN, extensive efforts have been devoted. Johnston discovered that the sulfuric acid uptake onto the investigated clusters had a small activation free-energy barrier.7,
8
The formation and growth of molecular cluster containing
sulfuric acid, water, ammonia, and dimethylamine were explored using a combination of Monte Carlo configuration sampling, semiempirical calculations, and density functional theory calculations.9 Compared the interactions of sulfuric acid with trimethylamine and water, it is observed that the binding energies decrease with the increasing of water molecules.10 Stimulated by a series of studies concerned with the formation of sulfuric acid, the gaseous formic sulfuric anhydride was observed and characterized by microwave 3
spectroscopy.
11
The characteristics involving the growth mechanism, the hydrate
distributions, the influences of humidity and temperature, as well as the Rayleigh scattering properties were determined using a basin-hopping algorithm with the density functional theory (DFT).12 The molecular interaction of pinic acid with sulfuric acid was studied by exploring the thermodynamic landscape of cluster growth, the favorable interactions between pinic acid and sulfuric acid imply that pinic acid could contribute to the subsequent growth of an existing nucleus by condensation.13 A computational study was executed on structures,
hydration,
and
electrical
mobilities
of
bisulfate
ion-sulfuric
acid-ammonia/dimethylamine clusters.14The protonation dynamics and hydrogen bonding in aqueous sulfuric acid were implemented combining simulations and experiments.15 It has been demonstrated that the sulfuric acid is the key atmospheric nucleation precursor owing mainly to its low vapor pressure and the propensity to form strong hydrogen bonds.16,
17, 18, 19, 20, 21
The atmospheric nucleation rates depends on the sulfuric
acid concentration, corresponding to a critical nucleus of four to nine sulfuric acid molecules, as agrees with predictions under classical nucleation theory. 22,
23, 24, 25
Strongly bound
dimer of sulfuric acid has been measured by means of chemical ionization mass spectrometry.26 It is imperative to precisely quantify the chemical makeup of the critical nucleus to improve models used to assess the environmental and climate impacts of aerosols.27 In this paper, the changes of structural characteristics, infrared spectra, as well as binding energies along with the growth of sulfuric acid molecules are explored employing the Becke's three-parameter Lee-Yang-Parr (B3LYP) exchange correlation functional within the DFT framework. The number of sulfuric acid in the cluster ranges from 2 to 9. The diameters of the orbicular clusters composed by more than 8 sulfuric acid molecules are larger than 1.0 nm. These sulfuric acid molecules interact through the hydrogen bonds, which play an important role in the formation of small atmospheric clusters. As can grow to form a critical nucleus and eventually an aerosol particle, that impacts climate. 28 The emphasis is put on the variation of chemistry and physical properties along the degree of polymerization (DP) of sulfuric acid cluster to present some useful information on nucleation and aerosol growth. 4
2.
Computational Methods The classical molecular dynamics (MD) simulations were conducted using the Forcite
program of Materials Studio 6.0, 29 with the COMPASS force field adopted. 30 The amorphous orthorhombic box containing 100 H2SO4 molecules (with a density of 1.84 g/cm3) was first geometrically optimized through the energy minimization. The lattice parameters of the box are 20.683 Å in lengths and 90.0° in angles. MD simulations were then performed in the NPT ensemble for 200 ps, in which the Nose thermostat31 and the Berendsen barostat32 were
used to maintain the temperature at 298 K and the pressure at 0.1 MPa, respectively. The particle motion was integrated by the velocity Verlet algorithm with a time step of 1 fs, and the
trajectory frame was outputted every 20 fs. The long-range electronic interactions were calculated by the Ewald summation method. All atoms of H2SO4 molecules were allowed to move freely during the MD simulations.
The hybrid DFT methods have been proven generally effective and inexpensive in describing large free radicals and intermolecular complexes. The B3LYP functional donates results whose accuracy matches that of the best ab initio results. Especially, the reliability of the B3LYP/6-311++G (d, p) level has been established. 33,
34 , 35
The optimizations of
sulfuric acid monomer and dimer are carried out employing several DFT functionals and MP2 method at 6-311++G (d, p) basis set. The results (Table S1) indicate the reliability of B3LYP functional. Therefore, the geometries of sulfuric acid clusters, (H2SO4)n, where 2 ≤ n ≤ 9, were optimized with the B3LYP 36 ,
37 , 38
DFT method in Gaussian09 39 at the
6-311++G(d, p) basis set. Accurate information about gas-phase molecular, electronic structure, and the stretching mode can be obtained from IR spectral analysis. In turn, it provides an important touchstone for computational studies. In addition, the absence of imaginary frequency in the IR vibrational spectra ensured that the optimized structures were local minina on the potential energy surfaces. The binding energy (Eb) is derived by subtracting the energies of monomers from that of the polymer. The zero-point vibrational energy (ZPE) is included in the calculation of Eb.
3.
Results and Discussion 5
The molecular dynamics (MD) simulations were performed at first to generate initial guess structures for the quantum chemistry geometry optimizations. Snapshot of the NPT simulation at the time of 50 ps was shown in Figure 1. During the 200-ps simulation, all the H2SO4 molecules moved freely to interact with each other. Hydrogen bonds acted as the major interactions between atoms of oxygen and hydrogen. Generally, two hydrogen bonds can be observed for each sulfuric acid unit. 3.1. Geometrical Structures. Two isomers of sulfuric acid (SA-Anti and SA-Syn) were optimized at B3LYP/6-311++G (d, p) level (Figure 2). The energy of SA-Anti, which is in C2 symmetry, is lower than that of SA-Syn by 1.3 kcal/mol (1.0 kcal/mol after ZPE correction). The OH bonds lengths in both isomers are all equal to the data reported by Meuwly.40 The distances of both single and double SO bonds in SA-Anti structure are in the middle of those optimized with MP2 and SCC-DFTB methods.41 To keep the hydrogen bonds between the approaching sulfuric acids as many as possible, the SA-Anti and SA-Syn configures are employed for middle and terminal molecules, respectively. The optimized dimer (SA2) and linear polymers (SAxL: x = 3 ~ 9) are collected in Figure 3. Two hydroxyl groups and one double bond oxygen of terminal SA generate three hydrogen bonds with the neighboring molecule. Two hydrogen bonds are observed between two adjacent middle SA molecules. They donate one hydroxyl group and one double bond oxygen to form the hydrogen bonds. Similar to that of DNA/RNA chain, the periodic arrangement of every three middle SA molecules can be observed for these linear polymers. The groove (~ 4.22 Å) in nonamer is marking with dotted line in Figure 3. The length of the system increases along with the degree of polymerization (DP: varies from 2 to 9) for linear polymers. As is clearly shown in Figure 4 with the distance between two terminal oxygen atoms, RTO (varies from 6.8 Å in dimer to 31.7 Å in nonamer), and the distance between two terminal sulfur atoms, RTS (increases from 3.9 Å in dimer to 29.5 Å in nonamer). Four bent structures (SAyB: y = 3 ~ 6) are optimized and shown in Figure 5. The angle composed by two terminals SA molecules and the middle point of the polymer decreases distinctly from obtuse angle to acute angle along with the DP. Two terminals approaching to each other with the alteration of this angle. The distance of two terminal oxygen atoms varies from 8.80 Å in SA3B to 10.69 Å in SA6B. For the larger polymer, heptamer and 6
octamer, they tend to the linear structures during the optimization (Supporting Information). Therefore, the stability of bent structure should be weaker as compared to those of linear structures. Figure 6 presents the optimized orbicular structures (SAzO: z = 4 ~ 9). The hydroxyl groups in tetramer (SA4O) interact with the head-to-tail mode. Totally, two layer, 8 hydrogen bonds are generated with the O...O distance of 2.827 Å. The hydrogen bonds of each layer form a ring structure with the diameter of 3.441 Å. The coupling mode of pentamer (SA5O) is similar to that of SA4O. The hydrogen bond length and the diameter of every hydrogen bond ring in SA5O are 2.916 and 4.654 Å, respectively. In both of these two polymers, the double bond oxygen atoms locate in the same plane determined by the sulfur atoms. The distance of two neighboring double bond oxygen atoms reduces distinctly from 3.446 Å in SA4O to 2.896 Å in SA5O. One hydrogen bond ring with the diameter of 4.868 Å is generated by one hydroxyl group of every SA in the orbicular hexamer (SA6O). The other hydroxyl group of each SA acts as the proton donor with one of double bond oxygen atoms of the proximate SA. This hydrogen bond forms another ring with a larger diameter of 9.104 Å. The distances of OH...OH and OH...O=S hydrogen bonds are 2.739 and 2.688 Å, respectively. Generally, the cribriform structure is observed in SA6O. Similar coupling mode can be observed in heptamer (SA7O) and octamer (SA8O). The diameters of the central hole composed by OH..O hydrogen bonds in SA7O and SA8O are 5.709 and 7.177 Å, respectively. The diameters of the peripheral ring consists of OH...O=S hydrogen bonds are 10.901 and 12.271 Å, respectively. The sulfur atoms in both SA7O and SA8O polymers are coplanar. Similarly, the OH...OH and OH...O=S type hydrogen bonds in SA9O surround two rings with the diameters of 7.543 and 12.673 Å, respectively. The distances of OH...OH and OH...O=S hydrogen bonds in these three polymers ranges at 2.90 ± 0.10 and 2.64 ± 0.02 Å, respectively. Different with the previous orbicular polymers, the sulfur atoms are not in the same plane any more in SA9O. 3.2. IR Spectra. IR spectra is an invaluable tool in organic, inorganic, material, and biological structural determination. The characteristics of IR in various structures are tightly related to their geometrical feature. The variation of the frequency value reflects the alteration of its chemical and physical environment. Here, the emphasis is put on the 7
frequency changes upon polymerization. The IR spectra of linear adducts (from trimer to nonamer) are collected in Figure 7. As comparison, the spectra of SA monomer and dimer are collected together with those of bent structures in Figure 8. Distinct signals can be observed for monomer around 3760 cm-1, which correspond to the OH stretching vibrations. While in the SA2, three OH groups participate in the hydrogen bonds with the double bond oxygen and the other OH group. The corresponding spectra of these three OH stretching red-shifted distinctly in varying degrees as compared to those in monomer. The vibrational frequency of the fourth OH, which participates into the hydrogen bond as the acceptor, red shifts slightly by ~ 10 cm-1. Both OH groups of middle SA in SA3L participate in two hydrogen bonds with one of double bond oxygen atoms of one terminal SA and one of OH groups of the other terminal SA. The chemical environments of these two OH groups of middle SA are same. As leads to the approximation of symmetrical and anti-symmetrical OH stretching vibration, locating at ~3115 cm-1. The OH groups of two terminal SA molecules generate two types of hydrogen bonds, viz. OH...O=S and OH...OH, which correspond to the characteristic peaks at ~3540 and 3600 cm-1, respectively. One OH group of medial SA in SA4L forms the hydrogen bond with one of the terminal double bond oxygen atom (locating at ~3195 cm-1), and the other OH group generates two hydrogen bonds with OH group and double bond O atom of neighboring SA molecules (3300 cm-1), respectively. The variation of terminal OH...O=S and OH...OH stretching vibrational frequencies from SA3L to SA4L is only few cm-1. The chemical environments of two OH groups on each intervening SA are different with the increase of DP from 4 to 9. As leads to the splitting of intervening OH...O=S stretching mode. While, the effect on terminal OH...O=S and OH...OH modes is slight. The bent structures are asymmetric, as is reflected by the IR spectra shown in Figure 8. The signals of two OH...O=S hydrogen bonds (OH belongs to central SA) in SA3B appear at 3010 and 3230 cm-1, respectively. The stretching of OH...OH hydrogen bond generated by terminal OH group and medial OH group populates at 3610 cm-1, almost equal to that observed in SA3L. The other OH groups of terminal SA molecules hydrogen bonded with medial double bond oxygen atoms, with the vibrational signals locating at 3500 and 3560 cm-1, respectively. The OH...OH stretching mode in SA4B is equal to that in SA3B. The 8
same phenomenon can be observed for SA5B and SA6B. The single signal at 3522 cm-1 denotes the vibrational stretching of OH...O=S hydrogen bonds in SA4O (Figure 9). As reflects the symmetrical characteristic of the geometry. This stretching shifts slightly to 3538 cm-1 in SA5O. Similarly, only one peak is observed in SA6O over 3000 cm-1. While two type hydrogen bonds, OH...OH and OH...O=S, do exist. It indicates that the strength of these two type hydrogen bonds just equal to each other. With the increase of DP from 7 to 9, the difference of these two type hydrogen bonds augments from 100 to 250 cm-1. In other words, the inner OH...OH interaction is stronger than the outer OH...O=S hydrogen bond. 3.3. Binding Energy. The binding energy (Eb: which is corrected with the zero-point vibrational energy) of linear SA polymer are plotted in Figure 10, together with the corresponding variation of internal energy (ΔU), enthalpy (ΔH), Gibbs free energy (ΔG), as well as entropy (ΔS) during the polymerization. The corresponding data of bent and orbicular conformations are presented in Figures 11 and 12, respectively. It is clear that the Eb of linear SA polymer decreases linearly from -0.7 to -5.3 kcal/mol along with the DP from 2 to 9 (Figure 10). Similarly, the ΔU and ΔH reduce linearly along with the DP. As indicates that the SA tends to aggregate and the polymer with larger DP can be generated. Although the ΔG also reduces with DP, the difference between ΔG and ΔH, viz. the product of temperature and entropy, of the same polymer increases along with DP. This demonstrates that the importance of the entropy increases along with the DP. The inset indicates that the entropy increases linearly from -1.8 cal/mol·K in SA2 to -13.4 cal/mol·K in SA9L. Similar phenomenon is observed for the bent polymers (Figure 11). Only the ΔG of hexamer does not decrease any more as compared with that of pentamer during the aggregation. The linear relationship disappears for the variation of relative energy for orbicular SA clusters owing to their geometrical features, i.e. only one type hydrogen bond exists in SA4O and SA5O, while the OH...O=S hydrogen bond coexists with the OH...OH interaction. The ΔG of orbicular structure is positive (Figure 12), which is unfavorable for the polymerization. Especially, the ΔG increases along with DP when it is over 6. Furthermore, for the same DP, the linear structure is more stable than the bent and the orbicular configurations. 9
Figures 13 & 14 present the temperature dependence of the ΔG and ΔS, where, the value at 298.15 K of each structure is taken as respective zero point. First of all, it can be observed from Figure 13 that the value of ΔG for every polymer decreases along with the enhancement of the temperature. As indicates that the stability of each structure increases at higher temperature while decreases at lower temperature. Comparing the variation of ΔG for all complexes with different DP, it is found that the temperature effect is more significant for those with high DP. As indicates that the complex with low DP prefers low temperature while the complex with high DP tends to be more stable at higher temperature. For the polymers with same DP (such as DP = 5 or 6), the energy of the orbicular conformation is lower at low temperature, while the linear structure is more stable at high temperature. Figure 14 shows that the ΔS increases following the enhancement of the temperature. Furthermore, the variation of the polymer with high DP is more distinguished as compared to that with low DP. The pressure dependence of the ΔG and ΔS in the ranges from 1 atm to 20 atm collected in Figure S1 and S2 shown that the values of ΔG and ΔS changes slightly along with the pressure. 4.
Conclusions The theoretical calculations, implemented at B3LYP/6-311++G (d, p) level, donate some
helpful information for the polymerization of sulfuric acid, and for the formation of cloud condensation nuclei. The sulfuric acid aggregation may take place in linear, bent, and orbicular modes. The length of the system increases linearly along with the degree of polymerization (DP) for the linear structures. The bent conformation distorts into the linear configuration when the DP is over 6. The diameter of the central ring generated by OH...OH hydrogen bonds in the orbicular conformation increases distinctly from 3.441 Å in tetramer to 7.543 Å in nonamer. There are two type hydrogen bonds in these polymers, viz. OH...OH and OH...O=S. The later generates the marginal bars of the cribriform structure. The IR spectra present distinct variations along with both the DP and the coupling modes. As can be employed to infer the detailed geometrical structures. The linear structure is more stable as compared to the bent and orbicular conformations. The variation of ΔG indicates that the sulfuric acid can aggregate with a larger DP in linear mode. The temperature effect on the stability of the sulfuric acid polymer is more significant as compared with that of the 10
pressure. The complex with high DP tends to be more stable at higher temperature, while the complex with low DP prefers low temperature. This investigation is helpful for further study on atmospheric aerosol growth and the formation of cloud nucleation.
ACKNOWLEDGMENT: This work is supported by National Nature Science Foundation of China (Grant No. 21203227, 21103080), Natural Science Foundation of Shandong Province (Grant No. ZR2016BM33), and the Research Foundation for Talented Scholars of the Qingdao Agricultural University (No. 6631113335). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.
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Figure 1. Snapshot of the box at the end of the 50 ps simulation. 100 H2SO4 molecules are included in the box. The color is yellow for sulfur, red for oxygen, and white for hydrogen. The lattice parameters of the box are 19.214 Å in lengths and 90.0° in angles.
1.439
SA-Syn
SA-Anti
Figure 2. Optimized sulfuric acid structures together with atom symboling and labeling (Syn and Anti)
15
SA2
SA9L
SA3L
SA8L
SA4L
SA7L
SA5L
SA6L
Figure 3. Optimized linear structures of sulfuric acid polymers.
RTO
30
RTS RIR
Distance (Å)
24 18 12 6
2
4
6 8 Degree of Polymerization
Figure 4. The length of linear polymers. RTO and RTS refer to the distance between two terminal oxygen and two terminal sulfur atoms, respectively. R IR denotes the diameter of the inner ring generated by OH...OH hydrogen bonds. 16
RTO: 8.800 RTS: 6.433
RTO: 10.142 RTS: 8.579
SA3B
SA4B
RTO: 9.641 RTS: 8.636
RTO: 4.719 RTS: 4.749
SA5B
SA6B
Figure 5. Optimized bent structures of sulfuric acid polymers. RTO and RTS refer to the distance between two terminal oxygen and two terminal sulfur atoms, respectively.
3.441
SA4O
SA5O
SA6O 4.654
SA7O
SA8O
7.543 12.673
SA9O Side View
Top View
Figure 6. Optimized orbicular structures of sulfuric acid polymer. 17
SA9L SA8L SA7L SA6L SA5L SA4L SA3L
0
1000
2000 3000 -1 Wavenumbers (cm )
4000
Figure 7. The infra red spectra of sulfuric acid linear polymers.
SA6B SA5B SA4B SA3B SA2 SA-Anti SA-Syn
0
1000
2000 3000 -1 Wavenumbers (cm )
4000
Figure 8. The infra red spectra of sulfuric acid monomer, dimer, and bent polymers. 18
SA9O SA8O SA7O SA6O SA5O SA4O
0
1000
2000 3000 -1 Wavenumbers (cm )
4000
Figure 9. The infra red spectra of sulfuric acid orbicular polymers.
Relative Entropy (cal/mol•K)
Relative Energy (kcal/mol)
0
-2
-4
Eb
-3
U H G
-6 -9 -12 2
4 6 8 Number of Sulfuric Acid
-6 2
4
6 8 Number of Sulfuric Acid
Figure 10. The binding energy (Eb) of linear sulfuric acid clusters. The variations of internal energy (ΔU), the enthalpy (ΔH) and the Gibbs free energy (ΔG) are presented together. Inset: the entropy (ΔS) of the linear polymers. 19
Eb
-2
-4
Relative Entropy (cal/mol•K)
Relative Energy (kcal/mol)
0
U H G
-4
-6
-8
3
4 5 6 Number of Sulfuric Acid
-6 3
4 5 Number of Sulfuric Acid
6
Figure 11. The binding energy (Eb) of bent sulfuric acid clusters. The relative thermal energy (ΔE), the relative enthalpy (ΔH), the relative Gibbs free energy (ΔG), as well as the relative entropy (ΔS) of the linear adducts are presented together.
Eb
-2
-4
-6
Relative Entropy (cal/mol•K)
Relative Energy (kcal/mol)
0 U H G
-6
-8
-10
-12
-14 4
5
6
7
8
Number of Sulfuric Acid
4
5 6 7 Number of Sulfuric Acid
8
Figure 12. The binding energy (Eb) of orbicular sulfuric acid clusters. The relative thermal energy (ΔE), the relative enthalpy (ΔH), the relative Gibbs free energy (ΔG), as well as the 20
relative entropy (ΔS) of the linear adducts are presented together.
Relative Energy (kcal/mol)
20 (a)
10 0
SA2 SA3L SA4L SA5L SA6L SA7L SA8L SA9L
-10 -20 240
270 300 330 Temperature (K)
360
Relative Energy (kcal/mol)
20 (b)
10 0 -10 SA3B SA4B SA5B SA6B
-20 240
270 300 330 Temperature (K)
21
360
Relative Energy (kcal/mol)
20 (c)
10 0 SA4O SA5O SA6O SA7O SA8O SA9O
-10 -20 240
270 300 330 Temperature (K)
360
Figure 13. The temperature dependence of the relative Gibbs free energy (ΔG). The value of ΔG at 298.15K is taken as respective zero point.
Entropy (cal/mol)
40
(a)
20 SA2 SA3L SA4L SA5L SA6L SA7L SA8L SA9L
0 -20 -40 240
270
300 330 Temperature (K)
22
360
Entropy (cal/mol)
40
(b)
20 0 -20
SA3B SA4B SA5B SA6B
-40 240
Entropy (cal/mol)
40
270 300 330 Temperature (K)
360
(c)
20 0 SA4O SA5O SA6O SA7O SA8O SA9O
-20 -40 240
270 300 330 Temperature (K)
360
Figure 14. The temperature dependence of the relative entropy (ΔS). The value of ΔS at 298.15K is taken as respective zero point.
23
Highlights:
The sulfuric acid may aggregate in linear, bent, or orbicular modes with two types of hydrogen bonds, viz. OH...OH and OH...O=S. The linear structure is more stable as compared to the bent and the orbicular conformations.
The length of the linear mode polymers increases linearly along with the degree of polymerization (DP). The bent conformation distorts into the linear configuration when the DP is over 6.
The diameter of the central ring generated by OH...OH hydrogen bonds in orbicular conformation increases distinctly from 3.441 Å in tetramer to 7.543 Å in nonamer.
The IR spectra exhibit distinct variations along with both the DP and the coupling modes. As can be employed to infer the detailed geometrical structures of sulfuric acid polymers.
The variation of the Gibbs free energy indicates that the sulfuric acid can aggregate with a larger DP in linear mode. Our findings are helpful for further study on atmospheric aerosol growth and the formation of cloud nucleation.
24
PII: DOI: Reference:
S0021-8502(17)30080-0 http://dx.doi.org/10.1016/j.jaerosci.2017.09.011 AS5186
To appear in: Journal of Aerosol Science Received date: 1 March 2017 Revised date: 13 May 2017 Accepted date: 8 September 2017 Cite this article as: Boli Nie, Juan Wang, Baohan Qu, Lixiang Sun and Shihai Yan, The Growth Mechanism of Sulfuric Acid Clusters: Implication for the Formation of Cloud Condensation Nuclei, Journal of Aerosol Science, http://dx.doi.org/10.1016/j.jaerosci.2017.09.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. 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.
The Growth Mechanism of Sulfuric Acid Clusters: Implication for the Formation of Cloud Condensation Nuclei Boli Nie,a Juan Wang,a Baohan Qu,a Lixiang Sun,b Shihai Yan a, * a
College of Chemistry and Pharmaceutical Sciences, Qingdao Agricultural University, Qingdao, 266109, China
b
School of Chemistry and Materials Science, Ludong University, Yantai 264025, China
Corresponding author: Shihai Yan, email: [email protected] QAU, Qingdao, 266109, China Phone: 86 532 86080954 FAX: 86 532 86080213
Abstract: The investigation on the growth mechanism of sulfuric acid clusters is helpful for the understanding about the formation of cloud condensation nuclei. The sulfuric acid may aggregate in linear, bent, or orbicular modes with two types of hydrogen bonds, viz. OH...OH and OH...O=S. The length of the linear mode polymers increases linearly along with the degree of polymerization (DP). The bent conformation distorts into the linear configuration when the DP is over 6. The diameter of the central ring generated by OH...OH hydrogen bonds in orbicular conformation increases distinctly from 3.441 Å in tetramer to 7.543 Å in nonamer. The IR spectra exhibit distinct variations along with both the DP and the coupling modes. As can be employed to infer the detailed geometrical structures of sulfuric acid polymers. The linear structure is more stable as compared to the bent and the orbicular conformations. The variation of the Gibbs free energy indicates that the sulfuric 1
acid can aggregate with a larger DP in linear mode. The temperature effect on the stability of the sulfuric acid polymer is more significant as compared with that of the pressure. The complex with high DP tends to be more stable at higher temperature, while the complex with low DP prefers low temperature. The findings are helpful for further study on atmospheric aerosol growth and the formation of cloud nucleation.
Keywords: Sulfuric Acid; Hydrogen Bond; Degree of Polymerization; IR Spectra; Gibbs Free Energy.
2
1.
Introduction The gas-to-particle conversion process of new particle formation generates the
atmospheric aerosols (AA) and influences the concentration of ambient particulate matter. Atmospheric nucleation is the dominant source of aerosol particles in the global atmosphere and an important player in aerosol climatic effects. The AA degrade visibility, negatively affect human health, directly or indirectly influence climate by absorbing and reflecting solar radiation and modifying cloud formation, as well as impact the air quality. Furthermore, the AA scatters and absorbs solar and terrestrial radiation, as well as influences the formation and properties of clouds. The impacts of aerosol particles on clouds are the largest individual source of uncertainty in estimates of the Earth's energy balance.1 The structures and reactivities of the molecular clusters have attracted extensive attentions experimentally and theoretically. AA is the basis for the formation of cloud condensation nuclei (CCN). Some useful information for particle formation has been afforded, although the underlying chemical mechanisms of AA and CCN have not been elucidated. The lack of complete understanding of the role of AA and CCN on the climate system forms a bottleneck for reliable and accurate projections of climate change. It has been observed that the atmospheric aerosol formation is essentially a two-step process, as proposed based on theoretical arguments2,
3
and laboratory experiments.4,
5
The
disagreement between the ambient data and the experiments, which is related to experimental design and sulfuric acid nucleation in ultraclean laboratory conditions, can explain the atmospheric nucleation rates.6To reveal the role of sulfuric acid in the AA formation and the following formation of CCN, extensive efforts have been devoted. Johnston discovered that the sulfuric acid uptake onto the investigated clusters had a small activation free-energy barrier.7,
8
The formation and growth of molecular cluster containing
sulfuric acid, water, ammonia, and dimethylamine were explored using a combination of Monte Carlo configuration sampling, semiempirical calculations, and density functional theory calculations.9 Compared the interactions of sulfuric acid with trimethylamine and water, it is observed that the binding energies decrease with the increasing of water molecules.10 Stimulated by a series of studies concerned with the formation of sulfuric acid, the gaseous formic sulfuric anhydride was observed and characterized by microwave 3
spectroscopy.
11
The characteristics involving the growth mechanism, the hydrate
distributions, the influences of humidity and temperature, as well as the Rayleigh scattering properties were determined using a basin-hopping algorithm with the density functional theory (DFT).12 The molecular interaction of pinic acid with sulfuric acid was studied by exploring the thermodynamic landscape of cluster growth, the favorable interactions between pinic acid and sulfuric acid imply that pinic acid could contribute to the subsequent growth of an existing nucleus by condensation.13 A computational study was executed on structures,
hydration,
and
electrical
mobilities
of
bisulfate
ion-sulfuric
acid-ammonia/dimethylamine clusters.14The protonation dynamics and hydrogen bonding in aqueous sulfuric acid were implemented combining simulations and experiments.15 It has been demonstrated that the sulfuric acid is the key atmospheric nucleation precursor owing mainly to its low vapor pressure and the propensity to form strong hydrogen bonds.16,
17, 18, 19, 20, 21
The atmospheric nucleation rates depends on the sulfuric
acid concentration, corresponding to a critical nucleus of four to nine sulfuric acid molecules, as agrees with predictions under classical nucleation theory. 22,
23, 24, 25
Strongly bound
dimer of sulfuric acid has been measured by means of chemical ionization mass spectrometry.26 It is imperative to precisely quantify the chemical makeup of the critical nucleus to improve models used to assess the environmental and climate impacts of aerosols.27 In this paper, the changes of structural characteristics, infrared spectra, as well as binding energies along with the growth of sulfuric acid molecules are explored employing the Becke's three-parameter Lee-Yang-Parr (B3LYP) exchange correlation functional within the DFT framework. The number of sulfuric acid in the cluster ranges from 2 to 9. The diameters of the orbicular clusters composed by more than 8 sulfuric acid molecules are larger than 1.0 nm. These sulfuric acid molecules interact through the hydrogen bonds, which play an important role in the formation of small atmospheric clusters. As can grow to form a critical nucleus and eventually an aerosol particle, that impacts climate. 28 The emphasis is put on the variation of chemistry and physical properties along the degree of polymerization (DP) of sulfuric acid cluster to present some useful information on nucleation and aerosol growth. 4
2.
Computational Methods The classical molecular dynamics (MD) simulations were conducted using the Forcite
program of Materials Studio 6.0, 29 with the COMPASS force field adopted. 30 The amorphous orthorhombic box containing 100 H2SO4 molecules (with a density of 1.84 g/cm3) was first geometrically optimized through the energy minimization. The lattice parameters of the box are 20.683 Å in lengths and 90.0° in angles. MD simulations were then performed in the NPT ensemble for 200 ps, in which the Nose thermostat31 and the Berendsen barostat32 were
used to maintain the temperature at 298 K and the pressure at 0.1 MPa, respectively. The particle motion was integrated by the velocity Verlet algorithm with a time step of 1 fs, and the
trajectory frame was outputted every 20 fs. The long-range electronic interactions were calculated by the Ewald summation method. All atoms of H2SO4 molecules were allowed to move freely during the MD simulations.
The hybrid DFT methods have been proven generally effective and inexpensive in describing large free radicals and intermolecular complexes. The B3LYP functional donates results whose accuracy matches that of the best ab initio results. Especially, the reliability of the B3LYP/6-311++G (d, p) level has been established. 33,
34 , 35
The optimizations of
sulfuric acid monomer and dimer are carried out employing several DFT functionals and MP2 method at 6-311++G (d, p) basis set. The results (Table S1) indicate the reliability of B3LYP functional. Therefore, the geometries of sulfuric acid clusters, (H2SO4)n, where 2 ≤ n ≤ 9, were optimized with the B3LYP 36 ,
37 , 38
DFT method in Gaussian09 39 at the
6-311++G(d, p) basis set. Accurate information about gas-phase molecular, electronic structure, and the stretching mode can be obtained from IR spectral analysis. In turn, it provides an important touchstone for computational studies. In addition, the absence of imaginary frequency in the IR vibrational spectra ensured that the optimized structures were local minina on the potential energy surfaces. The binding energy (Eb) is derived by subtracting the energies of monomers from that of the polymer. The zero-point vibrational energy (ZPE) is included in the calculation of Eb.
3.
Results and Discussion 5
The molecular dynamics (MD) simulations were performed at first to generate initial guess structures for the quantum chemistry geometry optimizations. Snapshot of the NPT simulation at the time of 50 ps was shown in Figure 1. During the 200-ps simulation, all the H2SO4 molecules moved freely to interact with each other. Hydrogen bonds acted as the major interactions between atoms of oxygen and hydrogen. Generally, two hydrogen bonds can be observed for each sulfuric acid unit. 3.1. Geometrical Structures. Two isomers of sulfuric acid (SA-Anti and SA-Syn) were optimized at B3LYP/6-311++G (d, p) level (Figure 2). The energy of SA-Anti, which is in C2 symmetry, is lower than that of SA-Syn by 1.3 kcal/mol (1.0 kcal/mol after ZPE correction). The OH bonds lengths in both isomers are all equal to the data reported by Meuwly.40 The distances of both single and double SO bonds in SA-Anti structure are in the middle of those optimized with MP2 and SCC-DFTB methods.41 To keep the hydrogen bonds between the approaching sulfuric acids as many as possible, the SA-Anti and SA-Syn configures are employed for middle and terminal molecules, respectively. The optimized dimer (SA2) and linear polymers (SAxL: x = 3 ~ 9) are collected in Figure 3. Two hydroxyl groups and one double bond oxygen of terminal SA generate three hydrogen bonds with the neighboring molecule. Two hydrogen bonds are observed between two adjacent middle SA molecules. They donate one hydroxyl group and one double bond oxygen to form the hydrogen bonds. Similar to that of DNA/RNA chain, the periodic arrangement of every three middle SA molecules can be observed for these linear polymers. The groove (~ 4.22 Å) in nonamer is marking with dotted line in Figure 3. The length of the system increases along with the degree of polymerization (DP: varies from 2 to 9) for linear polymers. As is clearly shown in Figure 4 with the distance between two terminal oxygen atoms, RTO (varies from 6.8 Å in dimer to 31.7 Å in nonamer), and the distance between two terminal sulfur atoms, RTS (increases from 3.9 Å in dimer to 29.5 Å in nonamer). Four bent structures (SAyB: y = 3 ~ 6) are optimized and shown in Figure 5. The angle composed by two terminals SA molecules and the middle point of the polymer decreases distinctly from obtuse angle to acute angle along with the DP. Two terminals approaching to each other with the alteration of this angle. The distance of two terminal oxygen atoms varies from 8.80 Å in SA3B to 10.69 Å in SA6B. For the larger polymer, heptamer and 6
octamer, they tend to the linear structures during the optimization (Supporting Information). Therefore, the stability of bent structure should be weaker as compared to those of linear structures. Figure 6 presents the optimized orbicular structures (SAzO: z = 4 ~ 9). The hydroxyl groups in tetramer (SA4O) interact with the head-to-tail mode. Totally, two layer, 8 hydrogen bonds are generated with the O...O distance of 2.827 Å. The hydrogen bonds of each layer form a ring structure with the diameter of 3.441 Å. The coupling mode of pentamer (SA5O) is similar to that of SA4O. The hydrogen bond length and the diameter of every hydrogen bond ring in SA5O are 2.916 and 4.654 Å, respectively. In both of these two polymers, the double bond oxygen atoms locate in the same plane determined by the sulfur atoms. The distance of two neighboring double bond oxygen atoms reduces distinctly from 3.446 Å in SA4O to 2.896 Å in SA5O. One hydrogen bond ring with the diameter of 4.868 Å is generated by one hydroxyl group of every SA in the orbicular hexamer (SA6O). The other hydroxyl group of each SA acts as the proton donor with one of double bond oxygen atoms of the proximate SA. This hydrogen bond forms another ring with a larger diameter of 9.104 Å. The distances of OH...OH and OH...O=S hydrogen bonds are 2.739 and 2.688 Å, respectively. Generally, the cribriform structure is observed in SA6O. Similar coupling mode can be observed in heptamer (SA7O) and octamer (SA8O). The diameters of the central hole composed by OH..O hydrogen bonds in SA7O and SA8O are 5.709 and 7.177 Å, respectively. The diameters of the peripheral ring consists of OH...O=S hydrogen bonds are 10.901 and 12.271 Å, respectively. The sulfur atoms in both SA7O and SA8O polymers are coplanar. Similarly, the OH...OH and OH...O=S type hydrogen bonds in SA9O surround two rings with the diameters of 7.543 and 12.673 Å, respectively. The distances of OH...OH and OH...O=S hydrogen bonds in these three polymers ranges at 2.90 ± 0.10 and 2.64 ± 0.02 Å, respectively. Different with the previous orbicular polymers, the sulfur atoms are not in the same plane any more in SA9O. 3.2. IR Spectra. IR spectra is an invaluable tool in organic, inorganic, material, and biological structural determination. The characteristics of IR in various structures are tightly related to their geometrical feature. The variation of the frequency value reflects the alteration of its chemical and physical environment. Here, the emphasis is put on the 7
frequency changes upon polymerization. The IR spectra of linear adducts (from trimer to nonamer) are collected in Figure 7. As comparison, the spectra of SA monomer and dimer are collected together with those of bent structures in Figure 8. Distinct signals can be observed for monomer around 3760 cm-1, which correspond to the OH stretching vibrations. While in the SA2, three OH groups participate in the hydrogen bonds with the double bond oxygen and the other OH group. The corresponding spectra of these three OH stretching red-shifted distinctly in varying degrees as compared to those in monomer. The vibrational frequency of the fourth OH, which participates into the hydrogen bond as the acceptor, red shifts slightly by ~ 10 cm-1. Both OH groups of middle SA in SA3L participate in two hydrogen bonds with one of double bond oxygen atoms of one terminal SA and one of OH groups of the other terminal SA. The chemical environments of these two OH groups of middle SA are same. As leads to the approximation of symmetrical and anti-symmetrical OH stretching vibration, locating at ~3115 cm-1. The OH groups of two terminal SA molecules generate two types of hydrogen bonds, viz. OH...O=S and OH...OH, which correspond to the characteristic peaks at ~3540 and 3600 cm-1, respectively. One OH group of medial SA in SA4L forms the hydrogen bond with one of the terminal double bond oxygen atom (locating at ~3195 cm-1), and the other OH group generates two hydrogen bonds with OH group and double bond O atom of neighboring SA molecules (3300 cm-1), respectively. The variation of terminal OH...O=S and OH...OH stretching vibrational frequencies from SA3L to SA4L is only few cm-1. The chemical environments of two OH groups on each intervening SA are different with the increase of DP from 4 to 9. As leads to the splitting of intervening OH...O=S stretching mode. While, the effect on terminal OH...O=S and OH...OH modes is slight. The bent structures are asymmetric, as is reflected by the IR spectra shown in Figure 8. The signals of two OH...O=S hydrogen bonds (OH belongs to central SA) in SA3B appear at 3010 and 3230 cm-1, respectively. The stretching of OH...OH hydrogen bond generated by terminal OH group and medial OH group populates at 3610 cm-1, almost equal to that observed in SA3L. The other OH groups of terminal SA molecules hydrogen bonded with medial double bond oxygen atoms, with the vibrational signals locating at 3500 and 3560 cm-1, respectively. The OH...OH stretching mode in SA4B is equal to that in SA3B. The 8
same phenomenon can be observed for SA5B and SA6B. The single signal at 3522 cm-1 denotes the vibrational stretching of OH...O=S hydrogen bonds in SA4O (Figure 9). As reflects the symmetrical characteristic of the geometry. This stretching shifts slightly to 3538 cm-1 in SA5O. Similarly, only one peak is observed in SA6O over 3000 cm-1. While two type hydrogen bonds, OH...OH and OH...O=S, do exist. It indicates that the strength of these two type hydrogen bonds just equal to each other. With the increase of DP from 7 to 9, the difference of these two type hydrogen bonds augments from 100 to 250 cm-1. In other words, the inner OH...OH interaction is stronger than the outer OH...O=S hydrogen bond. 3.3. Binding Energy. The binding energy (Eb: which is corrected with the zero-point vibrational energy) of linear SA polymer are plotted in Figure 10, together with the corresponding variation of internal energy (ΔU), enthalpy (ΔH), Gibbs free energy (ΔG), as well as entropy (ΔS) during the polymerization. The corresponding data of bent and orbicular conformations are presented in Figures 11 and 12, respectively. It is clear that the Eb of linear SA polymer decreases linearly from -0.7 to -5.3 kcal/mol along with the DP from 2 to 9 (Figure 10). Similarly, the ΔU and ΔH reduce linearly along with the DP. As indicates that the SA tends to aggregate and the polymer with larger DP can be generated. Although the ΔG also reduces with DP, the difference between ΔG and ΔH, viz. the product of temperature and entropy, of the same polymer increases along with DP. This demonstrates that the importance of the entropy increases along with the DP. The inset indicates that the entropy increases linearly from -1.8 cal/mol·K in SA2 to -13.4 cal/mol·K in SA9L. Similar phenomenon is observed for the bent polymers (Figure 11). Only the ΔG of hexamer does not decrease any more as compared with that of pentamer during the aggregation. The linear relationship disappears for the variation of relative energy for orbicular SA clusters owing to their geometrical features, i.e. only one type hydrogen bond exists in SA4O and SA5O, while the OH...O=S hydrogen bond coexists with the OH...OH interaction. The ΔG of orbicular structure is positive (Figure 12), which is unfavorable for the polymerization. Especially, the ΔG increases along with DP when it is over 6. Furthermore, for the same DP, the linear structure is more stable than the bent and the orbicular configurations. 9
Figures 13 & 14 present the temperature dependence of the ΔG and ΔS, where, the value at 298.15 K of each structure is taken as respective zero point. First of all, it can be observed from Figure 13 that the value of ΔG for every polymer decreases along with the enhancement of the temperature. As indicates that the stability of each structure increases at higher temperature while decreases at lower temperature. Comparing the variation of ΔG for all complexes with different DP, it is found that the temperature effect is more significant for those with high DP. As indicates that the complex with low DP prefers low temperature while the complex with high DP tends to be more stable at higher temperature. For the polymers with same DP (such as DP = 5 or 6), the energy of the orbicular conformation is lower at low temperature, while the linear structure is more stable at high temperature. Figure 14 shows that the ΔS increases following the enhancement of the temperature. Furthermore, the variation of the polymer with high DP is more distinguished as compared to that with low DP. The pressure dependence of the ΔG and ΔS in the ranges from 1 atm to 20 atm collected in Figure S1 and S2 shown that the values of ΔG and ΔS changes slightly along with the pressure. 4.
Conclusions The theoretical calculations, implemented at B3LYP/6-311++G (d, p) level, donate some
helpful information for the polymerization of sulfuric acid, and for the formation of cloud condensation nuclei. The sulfuric acid aggregation may take place in linear, bent, and orbicular modes. The length of the system increases linearly along with the degree of polymerization (DP) for the linear structures. The bent conformation distorts into the linear configuration when the DP is over 6. The diameter of the central ring generated by OH...OH hydrogen bonds in the orbicular conformation increases distinctly from 3.441 Å in tetramer to 7.543 Å in nonamer. There are two type hydrogen bonds in these polymers, viz. OH...OH and OH...O=S. The later generates the marginal bars of the cribriform structure. The IR spectra present distinct variations along with both the DP and the coupling modes. As can be employed to infer the detailed geometrical structures. The linear structure is more stable as compared to the bent and orbicular conformations. The variation of ΔG indicates that the sulfuric acid can aggregate with a larger DP in linear mode. The temperature effect on the stability of the sulfuric acid polymer is more significant as compared with that of the 10
pressure. The complex with high DP tends to be more stable at higher temperature, while the complex with low DP prefers low temperature. This investigation is helpful for further study on atmospheric aerosol growth and the formation of cloud nucleation.
ACKNOWLEDGMENT: This work is supported by National Nature Science Foundation of China (Grant No. 21203227, 21103080), Natural Science Foundation of Shandong Province (Grant No. ZR2016BM33), and the Research Foundation for Talented Scholars of the Qingdao Agricultural University (No. 6631113335). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.
11
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Figure 1. Snapshot of the box at the end of the 50 ps simulation. 100 H2SO4 molecules are included in the box. The color is yellow for sulfur, red for oxygen, and white for hydrogen. The lattice parameters of the box are 19.214 Å in lengths and 90.0° in angles.
1.439
SA-Syn
SA-Anti
Figure 2. Optimized sulfuric acid structures together with atom symboling and labeling (Syn and Anti)
15
SA2
SA9L
SA3L
SA8L
SA4L
SA7L
SA5L
SA6L
Figure 3. Optimized linear structures of sulfuric acid polymers.
RTO
30
RTS RIR
Distance (Å)
24 18 12 6
2
4
6 8 Degree of Polymerization
Figure 4. The length of linear polymers. RTO and RTS refer to the distance between two terminal oxygen and two terminal sulfur atoms, respectively. R IR denotes the diameter of the inner ring generated by OH...OH hydrogen bonds. 16
RTO: 8.800 RTS: 6.433
RTO: 10.142 RTS: 8.579
SA3B
SA4B
RTO: 9.641 RTS: 8.636
RTO: 4.719 RTS: 4.749
SA5B
SA6B
Figure 5. Optimized bent structures of sulfuric acid polymers. RTO and RTS refer to the distance between two terminal oxygen and two terminal sulfur atoms, respectively.
3.441
SA4O
SA5O
SA6O 4.654
SA7O
SA8O
7.543 12.673
SA9O Side View
Top View
Figure 6. Optimized orbicular structures of sulfuric acid polymer. 17
SA9L SA8L SA7L SA6L SA5L SA4L SA3L
0
1000
2000 3000 -1 Wavenumbers (cm )
4000
Figure 7. The infra red spectra of sulfuric acid linear polymers.
SA6B SA5B SA4B SA3B SA2 SA-Anti SA-Syn
0
1000
2000 3000 -1 Wavenumbers (cm )
4000
Figure 8. The infra red spectra of sulfuric acid monomer, dimer, and bent polymers. 18
SA9O SA8O SA7O SA6O SA5O SA4O
0
1000
2000 3000 -1 Wavenumbers (cm )
4000
Figure 9. The infra red spectra of sulfuric acid orbicular polymers.
Relative Entropy (cal/mol•K)
Relative Energy (kcal/mol)
0
-2
-4
Eb
-3
U H G
-6 -9 -12 2
4 6 8 Number of Sulfuric Acid
-6 2
4
6 8 Number of Sulfuric Acid
Figure 10. The binding energy (Eb) of linear sulfuric acid clusters. The variations of internal energy (ΔU), the enthalpy (ΔH) and the Gibbs free energy (ΔG) are presented together. Inset: the entropy (ΔS) of the linear polymers. 19
Eb
-2
-4
Relative Entropy (cal/mol•K)
Relative Energy (kcal/mol)
0
U H G
-4
-6
-8
3
4 5 6 Number of Sulfuric Acid
-6 3
4 5 Number of Sulfuric Acid
6
Figure 11. The binding energy (Eb) of bent sulfuric acid clusters. The relative thermal energy (ΔE), the relative enthalpy (ΔH), the relative Gibbs free energy (ΔG), as well as the relative entropy (ΔS) of the linear adducts are presented together.
Eb
-2
-4
-6
Relative Entropy (cal/mol•K)
Relative Energy (kcal/mol)
0 U H G
-6
-8
-10
-12
-14 4
5
6
7
8
Number of Sulfuric Acid
4
5 6 7 Number of Sulfuric Acid
8
Figure 12. The binding energy (Eb) of orbicular sulfuric acid clusters. The relative thermal energy (ΔE), the relative enthalpy (ΔH), the relative Gibbs free energy (ΔG), as well as the 20
relative entropy (ΔS) of the linear adducts are presented together.
Relative Energy (kcal/mol)
20 (a)
10 0
SA2 SA3L SA4L SA5L SA6L SA7L SA8L SA9L
-10 -20 240
270 300 330 Temperature (K)
360
Relative Energy (kcal/mol)
20 (b)
10 0 -10 SA3B SA4B SA5B SA6B
-20 240
270 300 330 Temperature (K)
21
360
Relative Energy (kcal/mol)
20 (c)
10 0 SA4O SA5O SA6O SA7O SA8O SA9O
-10 -20 240
270 300 330 Temperature (K)
360
Figure 13. The temperature dependence of the relative Gibbs free energy (ΔG). The value of ΔG at 298.15K is taken as respective zero point.
Entropy (cal/mol)
40
(a)
20 SA2 SA3L SA4L SA5L SA6L SA7L SA8L SA9L
0 -20 -40 240
270
300 330 Temperature (K)
22
360
Entropy (cal/mol)
40
(b)
20 0 -20
SA3B SA4B SA5B SA6B
-40 240
Entropy (cal/mol)
40
270 300 330 Temperature (K)
360
(c)
20 0 SA4O SA5O SA6O SA7O SA8O SA9O
-20 -40 240
270 300 330 Temperature (K)
360
Figure 14. The temperature dependence of the relative entropy (ΔS). The value of ΔS at 298.15K is taken as respective zero point.
23
Highlights:
The sulfuric acid may aggregate in linear, bent, or orbicular modes with two types of hydrogen bonds, viz. OH...OH and OH...O=S. The linear structure is more stable as compared to the bent and the orbicular conformations.
The length of the linear mode polymers increases linearly along with the degree of polymerization (DP). The bent conformation distorts into the linear configuration when the DP is over 6.
The diameter of the central ring generated by OH...OH hydrogen bonds in orbicular conformation increases distinctly from 3.441 Å in tetramer to 7.543 Å in nonamer.
The IR spectra exhibit distinct variations along with both the DP and the coupling modes. As can be employed to infer the detailed geometrical structures of sulfuric acid polymers.
The variation of the Gibbs free energy indicates that the sulfuric acid can aggregate with a larger DP in linear mode. Our findings are helpful for further study on atmospheric aerosol growth and the formation of cloud nucleation.
24