ARTICLE pubs.acs.org/JPCA
Bond Energies and Structures of AmmoniaSulfuric Acid Positive Cluster Ions Karl D. Froyd*,† and Edward R. Lovejoy‡ NOAA Earth System Research Laboratory, Chemical Sciences Division, Boulder, Colorado, United States † Cooperative Institute for Research in Environmental Science, University of Colorado, Boulder, Colorado, United States
bS Supporting Information ABSTRACT: New particle formation in the atmosphere is initiated by nucleation of gas-phase species. The small molecular clusters that act as seeds for new particles are stabilized by the incorporation of an ion. Ion-induced nucleation of molecular cluster ions containing sulfuric acid generates new particles in the background troposphere. The addition of a proton-accepting species to sulfuric acid cluster ions can further stabilize them and may promote nucleation under a wider range of conditions. To understand and accurately predict atmospheric nucleation, the stabilities of each molecular cluster within a chemical family must be known. We present the first comprehensive measurements of the ammonia-sulfuric acid positive ion cluster system NH4+(NH3)n(H2SO4)s. Enthalpies and entropies of individual growth steps within this system were measured using either an ion flow reactor-mass spectrometer system under equilibrium conditions or by thermal decomposition of clusters in an ion trap mass spectrometer. Low level ab initio structural calculations provided inputs to a master equation model to determine bond energies from thermal decomposition measurements. Optimized ab initio structures for clusters up through n = 3, s = 3 are reported. Upon addition of ammonia and sulfuric acid pairs, internal proton transfer generates multiple NH4+ and HSO4 ions within the clusters. These multiple-ion structures are up to 50 kcal mol1 more stable than corresponding isomers that retain neutral NH3 and H2SO4 species. The lowest energy n = s clusters are composed entirely of ions. The addition of acidbase pairs to the core NH4+ ion generates nanocrystals that begin to resemble the ammonium bisulfate bulk crystal starting with the smallest n = s cluster, NH4+(NH3)1(H2SO4)1. In the absence of water, this cluster ion system nucleates spontaneously for conditions that encompass most of the free troposphere.
’ INTRODUCTION Binary ion-induced nucleation of sulfuric acid and water can produce large concentrations of new aerosol particles throughout the free troposphere.14 Laboratory measurements of sulfuric acidwater cluster ions indicate that nucleation of the negative ion system is significantly favored over the positive system58 due to the strong intracluster bonding between HSO4 and H2SO4.9,10 Weaker bonding of H2SO4 in positive clusters allows H2SO4 to be driven out by H2O under most tropospheric conditions. However, adding a stabilizing agent to strengthen H2SO4 bonding within the positive cluster ions can reduce the barrier to growth sufficiently to produce new particles. Theoretical treatments predict that ammonia, amines, and other high proton affinity compounds that accept an acidic proton from sulfuric acid will form strong bonds that stabilize both neutral and ionic clusters containing H2SO4.1113 In bulk sulfuric acid water solutions, addition of ammonia reduces the sulfuric acid vapor pressure by several orders of magnitude.14 Ammonia is the most abundant basic species in the atmosphere with concentrations that often greatly exceed gas phase sulfuric acid.15 Ammonia partitions to acidic aerosols and is the principal neutralizing agent of condensed phase sulfuric acid in the troposphere. Positive r 2011 American Chemical Society
cluster ions containing ammonia have been observed in the atmosphere as NH4+(H2O)w.16,17 These cluster ions, and those that incorporate additional ammonia molecules, may bind gas phase sulfuric acid more readily than H+(H2O)w, ultimately promoting particle growth. A number of research groups have performed thermodynamic laboratory measurements of NH3 binding to cluster ions, with the NH4+(NH3)n family receiving considerable attention.18,19 The most complete and updated studies are equilibrium constant measurements using high pressure mass spectrometry (HPMS) by Deakyne et al.,20 Meot-Ner and Sieck,21 Arshadi and Futrell,22 Tang et al.,23 and Payzant et al.,24 who also measured the ammoniawater mixed clusters, NH4+(NH3)n(H2O)w. Bzdek et al.25,26 have reported kinetics and reactivity of positive NH3H2SO4 cluster ions with methyl amines. Several recent ab initio studies have reported structures and thermodynamics for Special Issue: A. R. Ravishankara Festschrift Received: October 14, 2011 Revised: November 18, 2011 Published: November 21, 2011 5886
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selected neutral11,12 and negative ion13 NH3H2SO4 clusters. No experimental measurements of NH3H2SO4 cluster ion thermodynamics have been reported. We present experimental measurements of stepwise reaction thermodynamics for the binary ammoniasulfuric acid cluster ion system, NH4+(NH3)n(H2SO4)s, notated here as NH4+(n,s). These studies follow our previous thermodynamic measurements of the positive and negative H2SO4/H2O ionic systems.710 The most stable NH3H2SO4 clusters (bond enthalpies ΔHo > 24 kcal mol1) were thermally decomposed in an ion trap mass spectrometer to measure activation energies. Low level ab initio calculations of cluster structure provided vibrational frequencies and rotational constants necessary to determine bond enthalpies using a master equation kinetic analysis.10 For less strongly bound clusters that were inaccessible to thermal decomposition measurements, equilibration experiments in an ion flow reactor quadrupole mass spectrometer system yielded temperaturedependent equilibrium constants. Using the combination of both techniques, we present stepwise ammonia and sulfuric acid bond enthalpies, free energies, and entropies for all relevant clusters in the NH4+(NH3)n(H2SO4)s system, n e 10 and s e 5. Ab initio structures provide insight into acidbase proton transfer within the clusters, and a fully ionic structure is often found to be the lowest energy isomer. The transition from molecular clusters to bulk crystalline solids is discussed. The potential for nucleation of this cluster system is investigated, and atmospheric implications for hydration are discussed.
’ EXPERIMENTAL METHODS Equilibrium Measurements. Stepwise equilibrium reactions of positive cluster ions with NH3 were measured using a low pressure, laminar ion flow reactor coupled to a quadrupole mass spectrometer described previously.7 A small flow of ammonia gas was added to a helium carrier gas upstream of a filament electron source, where NH4+ ions were generated. Sulfuric acid gas was added to the reactor by passing He over a heated liquid source (∼85 wt % H2SO4) located downstream of the filament. The gas mixture entered a 95 cm reaction zone maintained at fixed temperature ((0.5 K) between 237 and 391 K, where NH4+(NH3)n(H2SO4)s cluster ions were generated by association and decomposition reactions. The main carrier gas flow through the reactor ranged from 80175 STP cm3 s1 (STP = 1 atm, 273 K), and residence times in the temperature-controlled region were 10360 ms. Ions were extracted into a high vacuum region through an attractively charged (20 atoms, many potential isomers (e.g., 10) had to be examined to determine the lowest energy structure, which precluded the use of more expensive theories. Starting geometries for large clusters were constructed based on bonding patterns of smaller clusters while maximizing the number of hydrogen bonds and minimizing bond angles. In total, 44 stable cluster ion structures were identified. The success of RHF theory in this application is not surprising. The presence of a core ion generates stronger intermolecular bonds of higher ionic character than corresponding neutral clusters. For the current study, relative isomer stability and ultimately the identification of the most populated isomer will have some uncertainty because of the limitations of RHF theory, particularly when comparing isomers with single or multiple ions. We report RHF cluster structures and thermodynamics and encourage a more detailed study using a higher level of theory, starting with the thermally populated isomers.
’ RESULTS The combination of flow reactor equilibrium measurements and ion trap thermal decomposition yielded ΔH° values for reactions in both NH3 and H2SO4 coordinates for all atmospherically relevant NH4+(NH3)n(H2SO4)s cluster ions, n e 5 and s e 3, as well as some larger species. Reaction enthalpies that were not directly measured were determined via thermodynamic reaction cycles using the experimental values. ΔS° values were measured for most reactions using the equilibration flow reactor, and values from ab initio calculations are reported for other reactions. Equilibrium Measurements. Figure 1 shows mass spectra of the NH4+(NH3)n(H2SO4)s cluster ion family recorded at 298 K for three concentrations of ammonia. Groups of cluster ion signals correspond to equilibrium distributions of NH3 over the s = 1, 2, ..., 6 cluster families. Peak ratios change sharply, indicating that NH3 stability falls rapidly with each successive NH3 molecule. Significant growth occurs in both the NH3 and H2SO4
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Figure 1. Ion flow reactor mass spectra of NH4+(NH3)n(H2SO4)s, s = 06, recorded at 298 K. NH3, H2O, and H2SO4 concentrations are given in molecules cm3. The most intense cluster ion peak in each NH3 distribution is labeled as (n,s).
coordinates as ammonia is increased. For similar H2SO4 levels, clusters in Figure 1b grow to s = 4, whereas a higher concentration of NH3 in Figure 1c yields detectable clusters out at s = 6. This example of one species enhancing stability of the other was observed throughout the ammonia-sulfuric acid cluster ion family. For the lowest ammonia concentration in Figure 1, the NH3 envelopes for s = 1 and 2 begin abruptly with the NH4+(1,1) and NH4+(2,2) clusters. Even using [NH3] , 1012 cm3, no n < s cluster ions were ever observed. At all ammonia concentrations, the equilibrium population was shifted strongly toward n g s, suggesting that NH3 ligands in n < s are significantly more stable than in n g s clusters. We measured equilibrium constants for the association reactions of NH3 with NH3H2SO4 positive clusters ions (reaction 1) for n e 10 and s e 5 at 237391 K. Reaction ΔH° and ΔS° values were obtained by fitting the data to a weighted (inverse variance), linear van’t Hoff equation, ln K ¼ ΔH ° =RT þ ΔS° =R
ð3Þ
As in previous studies,7,8 a less restrictive nonlinear fit was found to overfit the data (see Appendix A). A representative van’t Hoff plot for the s = 2 cluster ion family is shown in Figure 2. Experimental reaction enthalpies and entropies for the equilibrium measurements are summarized in Figure 3a,b and Table 1. Experimental free energies for individual equilibration reactions are given in Table S1 in Supporting Information. Temperature-Dependent Thermal Decomposition. Ion trap mass spectra of NH4+(NH3)n(H2SO4)s clusters taken at short 5888
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Figure 2. Van’t Hoff plot for association of NH 3 to form the NH4+(NH3)n(H2SO4)2 cluster ion series. Points are the average of 226 individual measurements of the equilibrium constant for each cluster ion, and error bars are one standard deviation of ln K. The lines are weighted, linear least-squares fits to the data.
storage times showed a wide range of ammonia content, similar to the quadrupole mass spectra in Figure 1. As trapping time was increased, the initial ion distribution rapidly relaxed by evaporation of NH3. The clusters that persisted at the longest reaction times were separated by units of NH3H2SO4, suggesting that clusters of the form n = s are the most stable. The kinetics of the following decomposition reactions were studied in the ion trap. NH4 þ ðH2 SO4 Þ f NH4 þ þ H2 SO4
ð3Þ
NH4 þ ðNH3 ÞðH2 SO4 Þ f NH4 þ ðNH3 Þ þ H2 SO4
ð4Þ
NH4 þ ðNH3 ÞðH2 SO4 Þ2 f NH4 þ ðNH3 ÞðH2 SO4 Þ þ H2 SO4
ð5Þ NH4 þ ðNH3 Þ2 ðH2 SO4 Þ2 f NH4 þ ðNH3 ÞðH2 SO4 Þ2 þ NH3
ð6Þ NH4 þ ðNH3 Þ2 ðH2 SO4 Þ3 f NH4 þ ðNH3 Þ2 ðH2 SO4 Þ2 þ H2 SO4
ð7Þ NH4 þ ðNH3 Þ3 ðH2 SO4 Þ3 f NH4 þ ðNH3 Þ2 ðH2 SO4 Þ3 þ NH3
ð8Þ Example signal decays and exponential fits to determine first order decomposition rate constants for reaction 6 are given in Figure 4a. The variation of the first order rate constants are shown as a function of He concentration and temperature in Figure 4b. The kinetics for the NH4+(2,2), (2,3), and (3,3) decomposition were in the fall off region between the low and high pressure limits for these conditions. The kinetics of the decomposition of NH4+(1,1) were in or near the low pressure limit. The variation of first-order rate coefficients over pressure and temperature was fit using a master equation analysis that uses
Figure 3. Experimental enthalpy (a) and entropy (b) for NH3 association to form NH4+(NH3)n(H2SO4)s, s = 05, derived from van’t Hoff analyses (open points). Error bars are one standard deviation. Reaction enthalpy values for n = s magic clusters are measured by thermal decomposition, and entropies are from ab initio calculations (filled points). Values for NH4+(NH3) are the averages of refs 2024. (c) Experimental reaction enthalpies for H2SO4 addition derived from thermal decomposition (filled points) and thermodynamic cycles (open points).
the first-order rate coefficients and ab initio vibrational frequencies and rotational constants as inputs.10 The solid lines in Figure 4b are the best fit master equation predictions that yield 5889
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Table 1. ΔH° (kcal mol1) and ΔS° (cal mol1 K1) Values for the NH3 and H2SO4 Association Reactions, NH4+(n1,s) + NH3 f NH4+(n,s) and NH4+(n,s1) + H2SO4 f NH4+(n,s)a NH3 in product, n H2SO4 in product, s
0
1
2
3
4
5
6
7
8
9
10
15.1
12.9
35.4
29.4
NH3 Reactions: ΔH°n1,n 0
24.8e
15.4
13.9
12.2
9.1
1 2
31.8e (33.6c)
16.0 28.0b
15.3 16.7
14.5 15.3
12.7 13.4
12.0 13.1
11.7
3
(35.4c)
(27.2c)
26.3b
19.1
16.5
13.0
13.8
12.6
23.3
14.8
14.8
15.1
24.0
20.4
16.7
4 5 NH3 Reactions: ΔS°n1,n 0
25.2e
18.8
24.2
27.8
1
32.4e
20.9
24.9
28.3
27.8 27.2
28.1
2
33.7c
29.0d
28.7
29.4
27.7
29.8
27.3
3 4
36.9c
30.1c
31.9d
36.1
34.9 45.4
25.9 30.0
32.4 32.8
30.3 35.1
47.2
45.8
38.4
5 H2SO4 Reactions: ΔH°s1,s 1 2
18.7b d
(22.3 )
25.7b
26.3c
27.7c
29.9c
33.6c
24.1
36.1
37.5
38.4
39.0c
40.1c
31.2
35.1
38.2
38.0c
40.2c
52.9c 50.1c
55.3c
b
c
c
c
3
(20.7 )
(22.5 )
21.7
1
23.4d
30.6d
32.7c
33.4c
33.9c
33.3c
2 3
36.6 32.5d
37.9 35.8d
45.9 36.9d
49.8 40.1c
50.8 46.8c
51.3c 54.0c
d
d
b
c
c
c
H2SO4 Reactions: ΔS°s1,s d
d
c
c
c
Unmarked values are flow reactor equilibration measurements. Ion trap measurements. Determined via thermodynamic reaction cycle. d Values from ab initio calculations. e Average value from refs 2024. The ΔH° values in parentheses are ab initio estimates for three clusters that were not accessible experimentally and are shown for context only. a
b
c
the bond energies, E0, and energy transfer parameters listed in Table 2. Bond enthalpies, ΔH°298.15K, are derived from bond energies and ab initio structural properties using standard formulas. Ammonia and sulfuric acid bond enthalpies from the ion trap measurements are included in Table 1 and Figure 3. The kinetics of the association reaction NH4 þ ðNH3 ÞðH2 SO4 Þ2 þ NH3 þ He f NH4 þ ðNH3 Þ2 ðH2 SO4 Þ2 þ He
ð-6Þ
were also measured in the ion trap. These data combined with the kinetics for the decomposition reaction 6 provide an independent measurement of the Gibbs free energy change that can be compared directly to the master equation determination of the enthalpy change in an effort to validate that method. Measurements of the forward and reverse rate constants for the clustering reaction
NO3 ðHNO3 Þ þ HNO3 f NO3 ðHNO3 Þ2
ð9Þ
yielded Gibbs free energy changes in good agreement with those derived from equilibrium measurements33 and temperature dependent thermal decomposition studies,29 suggesting that both forward and reverse reactions in the ion trap are close to being in thermal equilibrium with the trap bath gas. Second order rate coefficients of 0.75, 1.17, 1.68, and 1.56 1010 cm3
molec1 s1 for reaction 6 were measured at 346 K for helium concentrations of 0.70, 1.12, 2.30, and 3.50 1013 molecules cm3. These results combined with decomposition rate coefficients of 0.0137, 0.0167, 0.0221, and 0.0256 s1 for reaction 6 at the same conditions yields an average ΔGo(346 K) = 17.6 kcal mol1. Using the ab initio entropy change gives ΔHo(346 K) = 27.6 kcal mol1. This compares favorably with the master equation determination of ΔHo(346 K) = 28.0 kcal mol1 and provides a direct validation of the master equation approach. Bimolecular reactions of the NH4+(NH3)n(H2SO4)s cluster ions with H2O, CH3CN, (CH3)2CO, and pyridine (C5H5N) were also studied. The measured rate coefficients and products are listed in Table 3.
’ DISCUSSION Experimental Thermodynamics. Laboratory measurements of equilibrium constants for the protonated ammonia clusters, NH4+(NH3)n, have been performed by several research groups. Figure 5 shows results from three temperature dependent HPMS studies,2224 one temperature-dependent drift tube study,34 two sets of ion flow reactor measurements at room temperature,35,36 and single-temperature measurements of ΔG°(400 K) using HPMS.37 The study by Payzant et al.24 represents the revised measurements of the NH4+(NH3)n system by the Kebarle group. 5890
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Figure 4. Ion trap thermal decomposition kinetics for the NH 4+ (2,2) cluster ion. (a) Signal intensity decays at 478 K with error bars of one standard deviation, where slopes yield pressuredependent first order rate coefficients. Ion trap helium concentrations for each decay are labeled as 1013 cm3 . Lines are weighted, linear fits to the data. (b) Pressure dependence of first order rate coefficients for a range of temperatures. Lines are master equation fits to the data. 10
However, this study was published prior to their investigations of cluster ion fragmentation38 and unimolecular decomposition39 during sampling, and the susceptibility of the results of Payzant et al. (and all other HPMS studies) to these phenomena have not been fully addressed. Temperature-dependent equilibria in the present study were measured at lower temperatures than the HPMS experiments, and sampled clusters were less susceptible to unimolecular decomposition (see Appendix A). Most thermodynamic values from the present work agree with literature values to within 2 standard deviations, including the single temperature point for NH4+(NH3) compared to extrapolated HPMS van’t Hoff lines. The ΔG°(400 K) values from Wincel37 underestimate the stability of NH4+(NH3) and NH4+(NH3)2, cluster ions, possibly due to ion fragmentation during sampling or background NH4+ signals. The combined measurements of ΔH° and ΔS° for the NH4+(NH3)n(H2SO4)s cluster ions reactions from both experimental techniques are plotted in Figure 3. The first NH3 molecules are attracted to the proton on the central ion due to their high proton affinity, PA(NH3) = 204.0 kcal mol1.40 The first NH3 on the NH4+ core ion is bound by ΔH°0,1 = 24.8 kcal mol1, but bond enthalpies for successive NH3 ligands weaken as the ion becomes solvated. The n = 4 reaction enthalpy is 12.2 kcal mol1 and completes one solvation shell around NH4+.41 The n = 5 ligand, located in the second solvation shell, has a reaction enthalpy of only 9.1 kcal mol1. However, the enthalpy of condensation of ammonia is ΔH°cond(298 K) = 4.7 kcal mol1,42 indicating that the influence of the NH4+ core ion extends to ligands beyond the first solvation shell. Similar trends in NH3 bond enthalpy are also evident for the H2SO4-containing clusters. The NH4+(NH3)n(H2SO4)s, n = s, clusters were the smallest cluster ions observed in each s series in flow reactor mass spectra (Figure 1). Ion trap measurements indicate that NH3 molecules within these clusters exhibit much higher stability than clusters with additional NH3 (n > s). This stability of NH3 in NH4+(1,1), NH4+(2,2), and NH4+(3,3) cluster ions must be due to very favorable interaction with H2SO4 molecules within the cluster. Likewise, H2SO4 bond enthalpies listed in Table 1 and Figure 3c show that H2SO4 is highly stabilized when n g s. These results indicate that, for the NH4+(NH3)n(H2SO4)s, s e 3, cluster ions, equal numbers of NH3 and H2SO4 molecules produce so-called magic clusters that exhibit unusually high stability within this system. This high relative stability was also observed recently by Bzdek et al.,43 where NH3H2SO4 positive cluster ions generated using electrospray preferentially relaxed to n = s. Bond strength drops
Table 2. Thermodynamic Parameters Derived from Master Equation Analysis of the Thermal Decomposition Kinetics for NH4+(n,s) Cluster Ions reaction NH4 þ ð0, 1Þ f NH4 þ þ H2 SO4 NH4 NH4 NH4 NH4 NH4 a
þ þ þ þ þ
Tavg a (K)
E0b (kcal mol1)
βc (kcal mol1)
ΔH°298.15K (kcal mol1)
391
18.8
0.73
18.7
ð1, 1Þ f NH4
þ
ð1, 0Þ þ H2 SO4
434
26.0
1.10
25.7
ð1, 2Þ f NH4
þ
ð1, 1Þ þ H2 SO4
355
24.1
0.89
24.1
ð2, 2Þ f NH4
þ
ð1, 2Þ þ NH3
421
27.6
1.08
28.0
ð2, 3Þ f NH4
þ
ð2, 2Þ þ H2 SO4
309
22.0
0.80
21.7
ð3, 3Þ f NH4
þ
ð2, 3Þ þ NH3
351
25.9
1.18
26.3
b
c
Average temperature of the measurements. Best-fit master equation bond energy. Best-fit master equation average energy transferred in up collisions. 5891
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Table 3. Ion Trap Rate Coefficients for Bimolecular Reactions of NH4+(NH3)n(H2SO4)s ion trap pressure
temperature
rate coefficienta
(mTorr He)
(K)
(cm3 mol1 s1)
NH4 þ ðH2 SO4 Þ þ NH3 f NH4 þ ðNH3 Þ þ H2 SO4
0.6
307
1.8 109
NH4 þ ðH2 SO4 Þ þ H2 O f products
1.0
303
H2SO4 > H2O. This is consistent with the known bond enthalpies for the NH4+(NH3) and NH4+(H2O) cluster ions and the bond enthalpy derived for NH4+(H2SO4) in the present study. NH4 þ ðNH3 Þ f NH4 þ þ NH3 , ΔH ° ¼ 24:8 kcal mol1 , ΔS° ¼ 25:2 cal mol1 K 1
ð10Þ
NH4 þ ðH2 SO4 Þ f NH4 þ þ H2 SO4 , ΔH ° ¼ 18:7, ΔS° ¼ 23:4
ð3Þ
NH4 þ ðH2 OÞ f NH4 þ þ H2 O, ΔH ° ¼ 19:0, ΔS° ¼ 22:2
ð11Þ Reaction 10 enthalpies and entropies are averages from refs 2024, and reaction 11 are from refs 24 and 44. The ligand 5892
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displacement trends observed here suggest that the Meot-Ner and Speller44 values may be anomalously high. No bimolecular or termolecular reactions were observed between any of the magic clusters NH4+(NH3)n(H2SO4)s (n = s = 15) and H2O, CH3CN, or (CH3)2CO. This is probably related to the fact that ammonia has a higher proton affinity than all of these species. However, fast bimolecular ligand switching reactions were observed between the clusters NH4+(NH3)n(H2SO4)s (n = s = 14) and pyridine, leading to the elimination of NH3. NH4 þ ðNH3 Þn ðH2 SO4 Þs þ C5 H5 N f C5 H5 NHþ ðNH3 Þn ðH2 SO4 Þs þ NH3
ð12Þ
Viggiano et al.45 found that pyridine displaced ammonia in NH4+(NH3)n(H2O)w clusters with similar efficiency. This displacement is not surprising considering that the proton affinity of pyridine is about 10 kcal mol1 higher than that of ammonia.40 The pyridine product ions with a small number of NH3 ligands, that is, C5H5NH+(NH3)n(H2SO4)s (n = s = 1 and 2) also reacted with pyridine to displace a second ammonia molecule. C5 H5 NHþ ðNH3 Þn ðH2 SO4 Þs þ C5 H5 N f C5 H5 NHþ C5 H5 NðNH3 Þn1 ðH2 SO4 Þs þ NH3
ð13Þ
The larger clusters, C5H5NH+(NH3)n(H2SO4)s (n = s = 3 and 4), appeared to equilibrate with the pyridine, suggesting that for these clusters the second pyridine ligand may be bound more weakly than or comparable to the ammonia. These observations are consistent with recent measurements by Bzdek et al.25 who showed that di- and trimethyl amines displace NH3 from n = s = 13 clusters with ΔG°rxn(298 K) values from 1.7 to 6.0 kcal mol1. Cluster Ion Structure. In addition to providing vibrational frequencies and rotational constants for the master equation analysis of thermal decomposition kinetics, structural properties for the NH4+(NH3)n(H2SO4)s cluster ion system were examined to help explain experimental findings. In particular, the high stability of the n = s magic clusters was examined. Structures for all the convergent isomers identified are shown in Figure S2 in Supporting Information. Table S2 lists thermochemical values calculated using rigid rotor and harmonic oscillator approximations with vibrational frequencies scaled to 0.89.46 As observed in other studies of cluster structure for similar neutral and ionic systems,1113,4749 the NH3H2SO4 positive clusters are comprised of a network of hydrogen bonds. Stable geometries containing either a single or multiple ionic species were found for NH4+(NH3)n(H2SO4)s, as found previously in HSO4(H2SO4)s(H2O)w cluster ions.8 The most stable singleand multiple-ion isomers are shown in Figure 6. The single-ion structures are built on the stable NH4+(NH3)n backbone with H2SO4 molecules bonding exclusively to the cluster exterior. The positive ion stabilizes H2SO4 to the extent that two or three H2SO4 molecules can be linked via neutralneutral bonds. This general bonding arrangement leads to a strong charge separation within the cluster (dipole moments > 6.9 D). Another single-ion series was found where H2SO4 is also linked to the cluster exterior but forms eight-member ring conformations similar to those found in neutral H2SO4(H2O)w structures,4749 in neutral (NH3)n(H2SO4)s clusters, 12,50 and in the larger
Figure 6. Lowest energy single-ion and multiple-ion structures for all NH4+(NH3)n(H2SO4)s cluster ions measured in thermal decomposition studies. The multiple-ion isomers are the global minimum energy structures and were used as inputs for the master equation analysis. The relative stability of the multiple-ion structures are compared to single-ion structures in terms of their total internal energies (δEint, kcal mol1) and entropies (δS°, cal mol1 K1) at 298.15 K. Molecular symmetry and center-of-mass dipole moments (Debye) are given. Lowest energy structures for the (1,1), (2,2), and (3,3) “magic” clusters are composed entirely of ions. A complete list of all stable structures identified in this study is given as Supporting Information, Figure S2.
HSO4(H2SO4)s(H2O)w cluster ions.8 However, this series (see Figure S2) is higher in energy than the single-ion structures in 5893
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Figure 6. Isomers with multiple ions, formed by proton transfers within the cluster, are all many kcal mol1 lower in energy than corresponding single-ion geometries (δE in Figure 6). Proton transfer to form multiple NH4+ species occurs within clusters whenever possible, NH4 þ ðNH3 Þn ðH2 SO4 Þs f NH4 þ ðNH4 þ 3 HSO4 Þc ðNH3 Þnc ðH2 SO4 Þsc
ð14Þ
starting with as few as three molecules, n = s = 1. This and all other magic n = s clusters are composed entirely of ions, forming acidbase pairs, NH4+(NH4+ 3 HSO4)c, c = 13. Formation of (NH4+HSO4) ion pairs via internal proton transfer has also been predicted for neutral systems, NH3(H2SO4)s, s g 2, and NH3(H2SO4)(H2O)w, w g 2.11,12 The high stability of the magic clusters observed experimentally is explained by this acidbase pairing. In these structures, charge centers are more spatially mixed within the clusters, leading to lower overall dipole moments, and an alternating acidbaseacidbase bonding pattern begins to emerge. Excess unpaired H2SO4 molecules (n < s) cannot ionize because all NH3 molecules are fully protonated. Excess NH3 molecules can induce further proton transfers to yield structures containing an SO42 species starting at NH4+(2,1) (see Figure S2), but these isomers were several kcal mol1 higher in energy than the global minimum structures. Total entropy values for the multiple-ion species are considerably lower and indicate a more rigid bonding environment than for single-ion structures. Measured ΔH°n1,n and ΔS°n1,n values suggest that for the s = 1 and 2 series, excess NH3 molecules not paired to an H2SO4 are bound to the cluster by single hydrogen bonds. However, large negative ΔS°n1,n ( s) to larger clusters containing 4 or more H2SO4 (Figure 3b), and NH3 bond enthalpies in NH4+(5,4) and NH4+(6,5) approach values similar to that of n = s magic clusters (ΔH°n1,n ≈ 25 kcal mol1). These values suggest that for larger clusters, excess NH3 may be bound by more than one bond and may even undergo proton transfer to form (NH4+)2SO42 species. As n > s clusters grow in size, the presence of excess NH3 ligands will eventually result in a molecular environment similar to the ammonium sulfate crystal, (NH4+)2SO42. Experimental reaction enthalpies and entropies are compared to ab initio values in Figure 7. The single-ion structure set gives reaction enthalpies that are weaker than experimental values by up to 18.4 kcal mol1. In contrast, ΔH° calculations from the species with multiple ions are all within 1.7 kcal mol1 of the experimental results, providing evidence that the multiple-ion species in Figure 6 were present in the flow reactors. Bond enthalpies within 3 kcal mol1 of experimental values were calculated previously9 for the HSO4(H2SO4)s system, where ΔH° < 20 kcal mol1. The stronger electrostatic forces in the multiple-ion NH3H2SO4 species and the HSO4(H2SO4)s system9 are likely treated with greater accuracy by RHF theory than the weaker intermolecular forces, for example, of H2O binding in the HSO4(H2SO4)s(H2O)w clusters.8 Reaction enthalpies predicted for four structures calculated at the B3LYP DFT level were less accurate (within 3.9 kcal mol1) and less consistent. Approach to Bulk Properties. Crystalline ammonium bisulfate, NH4HSO4(cr), is composed entirely of NH4+ and HSO4 ions. The present work demonstrates that formation of the ammonium bisulfate nanocrystal is initiated in positive NH3H2SO4
Figure 7. Comparison of experimental (black line) and ab initio reaction enthalpies, shown in order of increasing cluster size. The green line plots ab initio enthalpies for successive reaction steps of isomers containing a single NH4+ ion, whereas the blue line is for isomers with multiple NH4+ and HSO4 ions. Reaction enthalpies for multiple-ion product clusters containing an SO42 species are shown separately (blue triangles). DFT reaction enthalpies are also shown for corresponding single- and multiple-ion structures calculated at the B3LYP/6-31+G(d) level (squares).
cluster ions with as few as three gas phase molecules (two NH3 and one H2SO4) and a proton. To investigate the transition from molecular clusters to bulk crystalline properties, we compare the removal of one ammoniasulfuric acid pair from the n = s fully ionic clusters, NH4 þ ðNH4 þ 3 HSO4 Þc f NH4 þ ðNH4 þ 3 HSO4 Þc1 þ NH3 þ H2 SO4 , c ¼ 1 3
ð15Þ
to the pairwise removal of ammonium and sulfuric acid from the ammonium bisulfate crystal. NH4 HSO4 ðcrÞ f NH3 ðgÞ þ H2 SO4 ðgÞ
ð16Þ
Experimental values for the cluster reaction 15 are 49.6, 52.1, and 48.0 kcal mol1 for c = 13 (Table 1). For bulk ammonium bisulfate, the enthalpy change for the analogous reaction 16 can be derived using various combinations of the crystal lattice enthalpy, enthalpies of formation, and ion energetics. Derivation using heats of formation for the neutral species and the crystal5154 gives ΔH°(16) = 58.2 kcal mol1. Using the NH3 and HSO4 proton affinities and heats of formation for neutral and ionic species40,51,5557 gives 58.8 kcal mol1. House and Kemper57 measured the thermal decomposition of ammonium bisulfate by calorimetry and reported ΔH°(16) = 40.4 kcal mol1. These authors also estimated the ammonium bisulfate lattice enthalpy, giving ΔH°(16) = 48.7 kcal mol1. A theoretical lattice energy calculation58 yields ΔH°(16) = 43.5 kcal mol1. A simple average of these derivations for reaction 16 is ΔH° = 49.9 ( 8.4 kcal mol1 compared to the reaction 15 average of ΔH° = 49.9 ( 2.1 kcal mol1. While the exact agreement is somewhat fortuitous and the uncertainties in the literature values limit this comparison, this exercise provides some quantitative evidence that even the smallest cluster ions of this family are thermodynamically similar to the bulk crystal. 5894
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Figure 8. Intracluster distances for nearest neighbor nitrogen and sulfur atoms within charged clusters containing multiple ions. As cluster size increases (downward), intracluster distances converge toward those of the ammonium bisulfate crystal measured by X-ray diffraction.59
Figure 9. Comparison of structural arrangements between (a) the fully ionic NH4+(3,3) cluster (isomer A) and (b) a portion of the ammonium bisulfate crystal cell.59 Distances are given in Å. Hydrogens (and oxygens in b) are removed for clarity.
As small NH3H2SO4 ionic clusters grow in size, the charge centers will eventually orient themselves into the lowest energy configuration of the ammonium bisulfate crystal. In Figure 8 we compare distances between charge centers for the calculated multiple-ion clusters with those of bulk crystalline ammonium bisulfate.59 Sulfursulfur distances are >1 Å shorter in small calculated structures than in the bulk crystal because sulfuric acid molecules are drawn closer together to solvate the positively charged NH4+. As clusters grow, the relatively limited bonding sites and strained bonds of the NH4+(1,1) cluster give way to a more relaxed structure, and sulfursulfur distances converge toward the crystal. This convergence is most striking for the NH4+(3,3) isomer B, where sulfursulfur distances are within 0.2 Å of crystal distances. Cluster ion and bulk crystal structures are directly compared in Figure 9. The largest cluster ion studied here, NH4+(3,3), has two isomers with similar energy. While overall isomer B has a slightly lower free energy, isomer A has a bonding structure that strongly resembles a portion of the bulk ammonium bisulfate crystal cell.59 Comparing only identical linkages, the average deviation between the cluster and crystal distances is 0.20 Å. The NN distance at the top of the figure is longer in the cluster ion because the cluster has one less H2SO4 molecule and has an overall positive charge. A comparison between infrared absorption spectra calculated for isomer A and experimental spectra60 for crystalline
Figure 10. Cluster thermodynamics and growth at atmospheric conditions of 290 K, [NH3] = 1.3 109 cm3 (50 pptv), and [H2SO4] = 1.0 106 cm3. (a) A discrete free energy surface representing cumulative free energy changes to form each NH4+(NH3)n(H2SO4)s cluster starting from NH4+. (b) The corresponding equilibrium cluster population normalized to a total ion concentration of 1000 cm3.
ammonium sulfate and ammonium bisulfate shows that most molecular vibrational modes in the crystal are represented in the cluster with only small shifts in frequency (see Figure S3). Atmospheric Implications. A free energy surface can be generated for the NH4+(NH3)n(H2SO4)s cluster ion system for particular ambient temperature and concentration conditions. The cumulative free energy change to generate the NH4+(NH3)n(H2SO4)s cluster ion starting from NH4+ is determined by adding stepwise reactions. ΔGn, s ¼
∑n ΔGn1, n þ ∑s ΔGs1, s
ð17Þ
Figure 10a shows a representative surface for clean lower tropospheric conditions. The minimum pathway with the lowest ΔGn,s values follows the n = s magic clusters. Under most atmospheric conditions the ionic binary ammonium-sulfate system grows 5895
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Figure 11. Nucleating potential for the positive ammoniasulfuric acid ionic system under atmospheric conditions. In each panel, the H2SO4 saturation vapor pressure over the clusters, [H2SO4]ssat, is plotted for four ambient gas-phase ammonia concentrations. The shaded region represents typical daytime maximum concentrations of gas-phase H2SO4. Sulfuric acid condensation is spontaneous for atmospheric conditions where points are below the shaded region. Clusters evaporate where points are above the shaded region. A thermodynamic nucleation barrier exists at 298 K for low NH3 concentrations, but the barrier disappears at 270 K and below.
from the bare NH4+ ion by following the path of ammonium bisulfate, NH4+/HSO4 = 1:1. The cluster concentrations corresponding to the free energy surface are also shown in Figure 10b. These concentrations are representative of equilibrium conditions in both ammonia and sulfuric acid. Under atmospheric conditions, the clusters will not be in equilibrium with sulfuric acid, and these populations are shown only to illustrate the thermodynamic driving forces for cluster formation. Figure 10b ultimately represents the maximum growth potential. In this case, and under many tropospheric conditions, the n = s magic clusters dominate the population. Clusters that are richer in ammonium (n > s), including those analogous to letovicite (n:s = 3:2) or ammonium sulfate (2:1), have low populations even for very high ambient ammonia concentrations. Conditions Favorable for Nucleation. Using the current measurements, we can determine the conditions under which the ammoniasulfuric acid binary system may nucleate. Here we present an analysis of the nucleating ability of a cluster system that involves determining the saturation vapor pressure for the limiting component (H2SO4) over each cluster and comparing that value to atmospheric partial pressures. This method is equivalent to calculating thermodynamic barrier heights along a free energy surface. For a cluster association reaction, A i1 þ A a A i
ð18Þ
the saturation vapor pressure, pisat, of component A over the cluster Ai can be defined using the standard free energy change, ΔG°i1,i, for the reaction. pi sat =p° ¼ expðΔG°i1, i =RTÞ
ð19Þ
where p° is the standard pressure of 1 atm. Saturation vapor pressures of H2SO4, pssat(n,s), were calculated for each NH4+(NH3)n(H2SO4)s cluster ion, n = 05 and s = 13, from stepwise reaction ΔG°s1,s values in Table 1. Ab initio estimates of ΔH° were used for three cluster reactions inaccessible experimentally (see Table 1), but these clusters have negligible populations for all tropospheric conditions, and the estimates do not affect the atmospheric results. We then apply the condition that
gas phase ammonia is in equilibrium with the clusters, which is reasonable for most regions of the troposphere (NH3 > 10 pptv). Individual pssat(n,s) values were weighted by the relative cluster ion populations in the NH3 dimension, fn, to yield average H2SO4 saturation vapor pressures for each s series. psat s ¼
∑n fnpsats ðn, sÞ
ð20Þ
Under ammonia equilibrium conditions this simplification is robust and introduces no approximation. Cluster growth and evaporation can then be represented as a quasi-unary system with stepwise changes in only the s dimension. Values of psat s fully describe the thermodynamic driving force for growth of NH4+(NH3)n(H2SO4)s cluster ions, properly accounting for equilibration with NH3, at each step in the H2SO4 coordinate. While this analysis accurately predicts the thermodynamic potential of a system to nucleate, it does not consider kinetic processes such as ionion recombination and aerosol scavenging, which will ultimately determine whether the system does indeed nucleate in an ambient environment. Average H2SO4 saturation vapor pressures for the NH4+(NH3)n(H2SO4)s cluster ion system are plotted as molecular concentrations, [H2SO4]ssat, for each step in the H2SO4 coordinate in Figure 11. Values are calculated for three temperatures and several ammonia levels ranging from the remote troposphere15 (0.05 ppbv) through intense agricultural plumes61 (50 ppbv). Clusters grow spontaneously when ambient concentrations [H2SO4] are greater than [H2SO4]ssat (i.e., ambient ΔGs1,s < 0). Similarly, when [H2SO4] < [H2SO4]ssat, cluster decomposition is more favorable than growth (ΔGs1,s > 0), and a free energy barrier to nucleation exists. However, at each step a fraction of the cluster ion population equal to [H2SO4]/ [H2SO4]ssat will grow on average, so that nucleation is not completely deactivated under these conditions. Points with very high saturation concentrations (e.g., [H2SO4] < 1000[H2SO4]ssat) or conditions where [H2SO4] < [H2SO4]ssat for several H2SO4 association steps effectively prevent nucleation. Figure 11 shows how the nucleating potential of the NH4+(NH3)n(H2SO4)s system is highly dependent on temperature and the ambient concentrations of NH3 and H2SO4. In the troposphere, maximum daytime sulfuric acid concentrations are typically 1 106 to 5 107 cm3.62,63 At 298 K, the first H2SO4 5896
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The Journal of Physical Chemistry A addition step is not thermodynamically favorable for ambient levels of 106 cm3. Increasing the sulfuric acid concentration to 2 107 cm3 gives s = 1 cluster concentrations approximately equal to s = 0. Adding the second H2SO4 molecule to the clusters is spontaneous at 298 K only for [H2SO4] > 106 cm3 or [NH3] > 0.05 ppbv. By increasing ammonia concentrations or decreasing temperature, the H2SO4 saturation pressure of the clusters decreases and growth in the s coordinate becomes more favorable. At 270 K and below, all clusters s = 13 form spontaneously for [H2SO4] g 106 cm3 and [NH3] > 0.05 ppbv. Overall, the ammoniasulfuric acid binary system has no thermodynamic barrier to nucleation for the first three growth steps for a substantial part of the troposphere. Related Nucleating Systems. The above analysis represents the zero relative humidity (RH) case. The cluster ions described in this work will be hydrated in the atmosphere, with the level of hydration effectively dependent on ambient RH. Hydration of these clusters may increase their overall stability, and it is likely that the high stability of the n = s magic clusters will drive growth in the ternary system as well. However, the overall effect of H2O on their ability to nucleate is difficult to predict. While the reported NH3 and H2SO4 bond energies may not change dramatically for low levels of hydration, if water molecules within the NH4+(NH3)n(H2SO4)s(H2O)w ternary clusters have a strong affinity for ammonium as observed in the NH4+(NH3)n(H2O)w system,24 sulfuric acid may become less well solvated, in which case the H2SO4 saturation vapor pressure would actually increase with RH and limit growth. Initially, water molecules will likely bind to the outside of the ammonia/ sulfuric acid cluster ion. As hydration increases, the water molecules will incorporate into the central crystal, eventually leading to complete separation of the acidbase ionic pairs. This process is analogous to deliquescence in bulk solutions. Once this phase transition takes place, the thermodynamics of the system change abruptly. Trends in bond strength associated with hydrated acidbase core clusters are likely to be quite different from that of a deliquesced cluster and consequently, difficult to predict. The complicated interplay among constituents of the ternary system should be explored in future experimental studies. Atmospheric molecular clusters are either neutral or have an overall ionic charge. The measurements described here are directly applicable to positive ionic systems, but trends in cluster growth may also apply to neutral species. The ion can enhance intracluster bond energies for clusters as large as 10 or 20 molecules in size, and ultimately the bonding properties and sign of the core ion determine the overall chemistry of the cluster. For example, NH3 and H2SO4 are bound to these positively charged clusters with similar strength, whereas for clusters built around a negative core ion, NH3 binding is probably much weaker than H2SO4. Recent observations of negative sulfuric acid clusters in the laboratory5,43,64,65 and field66,67 indicate that, at small sizes, ammonia and amines are bound less strongly than in the positive clusters studied here. The prevalence of fully ionic clusters predicted here under atmospheric conditions suggests that small (NH3)n(H2SO4)s neutral clusters may also prefer the n = s stoichiometry and are composed entirely of ions. High level ab initio studies predict that some neutral ammonium sulfuric acid clusters arrange to form ion pairs with as few as three molecules.11,12 As cluster size increases, binding energies for ionic clusters will approach those for the neutral system. Study of the corresponding negative ion system will help bracket bond
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energies of the important neutral cluster system, which is difficult to probe experimentally.
’ CONCLUSIONS Ammoniasulfuric acid positive cluster ions, NH4+(NH3)n(H2SO4)s, form crystal-like structures in the gas phase with as few as three molecules. Acidbase pairing stimulates internal proton transfers to produce clusters containing multiple ions, NH4+(NH4+HSO4)c, c = 13, that are considerably more stable than isomers with only the single NH4+ core ion. Cluster components in excess of a 1:1 NH3/H2SO4 ratio usually remain neutral. This acidbase pairing explains the synergistic stabilization of NH3 and H2SO4 and the formation of very stable n = s magic clusters observed experimentally. RHF/6-31+G(d) calculations predict experimental bond enthalpies within 1.7 kcal mol1 for these ionic species. Ionization occurs in smaller clusters than for the HSO4(H2SO4)s(H2O)w system8 due to the high proton affinity of NH3 and, ultimately, the very effective solvation of HSO4 by NH4+. As the size of these molecular clusters increases, their chemistry will converge toward bulk properties. The NH4+(n = 3, s = 3) cluster ion has a structural configuration that strongly resembles bulk ammonium bisulfate. Ammonia within the clusters is displaced by pyridine, which will sequester the proton and become the core ion. Pyridine can displace multiple ammonias within a cluster, and it is likely that internal proton transfer will generate multiple ions within pyridinesulfuric acid clusters. However, the substituted nitrogen, planar structure, and larger size of pyridine will hinder the formation of multiple hydrogen bonds with sulfuric acid that is characteristic of the ammoniasulfuric acid clusters. Consequently, sulfuric acid stability is difficult to predict; it may actually evaporate more readily from pyridine clusters due to strained bonding arrangements than from the ammoniasulfuric acid clusters. Other species with higher proton affinities than ammonia such as methyl amines12,25 also promote ammonia displacement and may be viable systems for positive ion-induced nucleation. The relative abundance of basic species in the atmosphere and the sulfuric acid bond strengths within their associated ionic clusters will ultimately dictate whether these acidbase positive ion systems can promote new particle formation. This study demonstrates that ammoniasulfuric acid positive cluster ions in their unhydrated form would spontaneously nucleate to form small aerosol particles throughout the free troposphere. However, the bonding properties of this cluster ion system will change upon addition of water. At atmospheric water levels, the enhanced stability of the acidbase paired magic clusters may be somewhat offset due to incorporation of water molecules into the NH3H2SO4 core and the possible displacement of NH3 by H2O. In order for ammonia to enhance sulfuric acid stability beyond that of sulfuric acidwater positive ion clusters,7 it is likely the addition of at least two ammonia molecules is required so that the first hydrated magic cluster is formed, NH4+(NH4+HSO4)(H2O)w. ’ APPENDIX A: MEASUREMENT UNCERTAINTIES The uncertainties inherent in the mass spectrometric methods employed here are described previously for the equilibrium thermodynamic measurements7,8 and decomposition kinetics measurements.9,10,29 For the equilibrium studies, potential systematic uncertainty sources include the ammonia concentration 5897
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The Journal of Physical Chemistry A measurement, SO3 contamination, and cluster decomposition during sampling (see Experimental Methods). For flow reactor studies, unimolecular decomposition of cluster ions can occur during the short time between sampling and mass analysis.8,39 The result is an anomalous shift in the van’t Hoff lines that is difficult to distinguish from a valid measurement. The clusters most susceptible to unimolecular decomposition are large, weakly bound species where the thermal vibrational energy is well above the cluster dissociation energy. Sunner and Kebarle39 suggest reducing reaction temperatures so that equilibrium measurements are made only where Kn1,n > 10 Torr1 to limit decomposition during sampling. For the current study, we performed a more rigorous estimation by simulating unimolecular decomposition during mass analysis8,10 for several NH4+(n,s) species. Simulations require structural information and therefore could not be performed for every cluster, and for this analysis some cluster properties had to be extrapolated from smaller clusters. Equilibrium measurements for several s = 2 and 3 clusters were then reanalyzed by adjusting raw signal values to account for cluster decomposition. For example, at a reactor temperature of 391 K, 58.6, 28.5, and 0.0% of the NH4+(4,2), NH4+(3,2), and NH4+(2,2) populations are predicted to decompose in the high vacuum region. Indeed, the highest temperature measurements for each cluster often indicated systematically low values of ln K, which, when corrected for decomposition, were more consistent with van’t Hoff lines determined at lower temperatures. While this reanalysis affected some thermodynamic results significantly, the corrections were not consistent within each cluster family, and some clusters that were predicted to completely decompose were still observed with our system. These unimolecular decomposition predictions appear to be too large by at least a factor of 23, and consequently, the reanalyzed data became overcorrected. A probable explanation is that, at high reactor temperatures, clusters were cooled by expansion when passing from the flow reactor to the vacuum chamber. While clusters did not undergo sufficient collisions with ammonia to re-equilibrate during the expansion, collisions with the helium carrier gas were much more frequent. During the ∼1 μs expansion, large clusters collide with ∼10 helium atoms, which imparts some thermal relaxation and reduces cluster decomposition. Therefore, we report uncorrected measurements for all reactions where Kn1,n > 4 Torr1, which typically corresponded to simulated cluster decomposition of
