1
2
Stabilization of Sulfuric Acid Dimers by Ammonia, Methylamine, Dimethylamine, and
Trimethylamine
3
Coty N. Jen1, Peter H. McMurry1, David R. Hanson2
4
5
[1] Department of Mechanical Engineering, University of Minnesota – Twin Cities, Minneapolis, MN,
USA
6
[2] Department of Chemistry, Augsburg College, Minneapolis, MN, USA
7
Supporting Information:
8
1. MCC Measurement of NLD:
9
The MCC operated in positive ion mode using charged water clusters to measure [B] (see Hanson
et al. [2011] for comparison). Figure S1 shows the measured [B] as a function of measured [A1] (in
11
negative ion mode of the MCC) for MA and TMA. Overall, the NLD is within 20% of the measured [B]
12
except for [MA]=7 pptv where NLD is a factor of 2 lower than measured. This could be due to MA
13
sticking to the walls of the base injection system and raising the amount of [MA] added to the flow
14
reactor. This would only affect the concentrations for the lowest [B]. Also from the graph, it can be seen
15
that [B] remains constant for increasing [A1].
Measured [B] (pptv)
10
10
2
10
1
10
NLD (pptv)
[MA]
7
110
[TMA]
100
30
8
10
9
-3
16
17
18
19
[A1]=[H2SO4] (cm )
Figure S1 Measured [B] as a function of [A1]. The different symbol types signify the base type and
the colors (as defined in the legend to the right) indicate the predicted NLD. The dashed lines are
NLD concentrations.
S1
20
2. Ion Induced Clustering (IIC) of the MCC:
21
The MCC dimer signal (195 m/z) is composed of both pre-existing neutral dimers that are
22
charged with nitric ion and charged monomers that go on to charge neutral A1 to form dimers. The latter
23
process is IIC, and its contribution to dimer signal is a source of uncertainty. Chen et al. [2012] (SI) lists a
24
series of possible IIC reactions, with the pertinent reactions given below.
k1
A1  HNO3 NO3  A1
k21
A1  A1  A2
k2
25
A2  HNO3 NO3  A2
k31
A2  A1  A3
k32
A1  A2  A3
k3
A3  HNO3 NO3  A3
26
where
27
A1 = neutral monomer
28
A1- = charged monomer
29
A2 = neutral dimer
30
A2- = charged dimer
31
ki = nitrate ionization rate constant
32
kij = IIC rate constant
33
Chen et al. [2012] provides two sets of rate constants: one set contains the collision rate constants
34
[Hanson et al., 2011; Su and Bowers, 1973] and the second are rate constants fitted from ambient data
35
[Zhao et al., 2010]. To determine which set of IIC rate constants to use for this study, the chemical
36
ionization (CI) reaction time of the MCC was varied by manipulating the electric field in the sampling
S2
37
region (see Figure 1) with constant [A1]. Changing the CI reaction time does not change the amount of
38
pre-existing neutral dimer but does affect the amount produced by IIC.
39
Consider first the ionization of A1. Integrating the ionization rate equation and assuming the
40
nitrate source ion (125 m/z) remains constant at short CI time scales, the ratio between signal 160 m/z and
41
125 m/z (S160/S125) can be used to calculate [A1]:
S160
 k1  A1  t
S125
Equation S1
42
where k1 has been experimentally measured [Viggiano et al., 1997] and is the collision rate constant.
43
Equation S1 matches that given in Berresheim et al. [2000] with the implicit assumption that the MCC is
44
able to transport and detect ions at 160 m/z and 125 m/z equally efficiently. However as is shown in Zhao
45
et al. [2010], lighter ions are transported and detected less efficiently than heavier ions. The difference in
46
efficiencies between these masses can be taken into account by dividing by the ratio of sensitivities for
47
the different masses (see equation S11 in Chen et al. [2012] as an example). For the MCC between the
48
masses of 125-195, the ratio of sensitivities is ~1.1-1.3, depending on the specific masses in the ratio;
49
therefore, we have left out this sensitivity ratio to simplify the equation but have taken it into account in
50
the MCC signal to concentration conversion. Figure S2 (left) shows S160/S125 vs. time at varying [MA].
51
The linear fits of S160/S125 vs. time gives a slope of k1[A1] with non-zero y-intercepts for all [MA]. Two
52
possible sources of uncertainty could cause this non-zero y-intercept. Other uncharacterized, ionizing
53
species (x-ray or electrons) may escape from the source holder and ionize clusters in the flow reactor.
54
Furthermore, the Po-210 lies inside an uncovered cavity within the source holder. Since the source holder
55
sits in the flow reactor (see Figure 1), small amounts of sulfuric acid flow can enter into the cavity and
56
mix with the nitrate ions. This would lead to longer than predicted CI reaction for some fraction of the
57
sulfuric acid clusters.
S3
Now consider both the nitrate ionization of A2 and the IIC formation of A2-. Integrating these
58
59
reaction equations at short time scales shows that the ratio of S195/S160 is composed of neutral A2 and A2-
60
formed by IIC.
S195 k2  A2  1

 k21  A1  t
S160 k1  A1  2
Equation S2
61
A comparison between the slopes from Equation S1and Equation S2 provides evidence if k21 is the
62
collision rate constant or not. A factor of 2 between the two slopes implies that k21=k1=collision rate
63
constant. From comparing the two graphs in Figure S2 at [MA]=0 and 10 pptv, k21=collision rate
64
constant; however at [MA]=150 pptv, the ratio of the slopes is 2.5 (see Table S1). Although we suspect
65
high uncertainty with these ratios, the trend still indicates that base effects IIC. Based upon conclusions
66
from the main paper, we hypothesize that the concentration and identity of B will affect IIC. For the
67
purpose of this paper, we assumed IIC proceeded at the faster collision rate. Thus, [A2] shown in Figure 2
68
is the lower limit. The actual [A2] will be higher (up to a factor of 4) than reported here but the fitted
69
evaporation rates will still fall in the range reported in Table 1 and 2.
The y-intercepts from the linear fits of Figure S2 (right) show that for [A1]=4x109 cm-3 and
70
71
[MA]=0 pptv, the pre-existing [A2]=6x107 cm-3. The baseline measurements detailed in the main paper
72
produced a fitted relationship for non-IIC corrected [A2] vs. [A1] of
 A2   1.32 1010  A1 
Equation S3
1.91
73
Therefore, at [A1]=4x109 cm-3, about 20% of the total 195 m/z signal is neutral dimer not produced via
74
IIC.
75
Table S1 Comparison between slopes of S160/S125 and S195/S160 vs. time
[MA] (pptv)
0
10
150
Slope
S160/S125
7.0
4.5
1.6
Slope
S195/S160
3.4
2.2
0.64
Ratio of slopes
S160/S125 to S195/S160
2.0
2.0
2.5
S4
[MA]=0 pptv
S160/S125
150
0.8
y=4.5x+0.05
2
R =0.97
0.4
0.0
0.00
76
0.6
y=7.0x+0.1
2
R =0.99
10
y=1.6x+0.01
2
R =0.99
0.05
0.10
0.15
CI Reaction Time, t (s)
S195/S160
1.2
y=3.4x+0.03
2
R =0.98
0.4
y=2.2x+0.04
2
R =0.96
0.2
0.0
0.00
y=0.64x+0.009
2
R =0.96
0.05
0.10
0.15
CI Reaction Time, t (s)
77
78
79
Figure S2 Left: Ratio of signals of 160 m/z and 125 m/z as a function of CI reaction time. Right:
Ratio of signals of 195 m/z and 160 m/z as a function of CI reaction time. Each color represents a
different [MA], and the lines are linear fits.
80
3. Repeatability of Flow Reactor Experiments and Uncertainty in Measurement:
81
Several experiments were done at constant [B] on different times and days to study daily
82
repeatability of measurements carried out in the flow reactor system. Figure S3 shows measurements of
83
[A1] and [A2] made [MA]=80 pptv on three different days. Between these three days, 12 experiments of
84
MA were conducted at [MA] from 10-260 pptv. The good daily repeatability (~10%) suggests that the
85
flow reactor is able to quickly adapt to new [B] without significant “memory" of contamination from
86
experiments carried out in the intervening period. Figure S3 also suggests that the base dilution/injection
87
system developed in Zollner et al. [2012] and MCC have minimal daily variation. In addition to day-to-
88
day variability, the total uncertainty also includes the systematic error of the MCC. The box on the bottom
89
right of Figure S3 illustrates the systematic error of the MCC measurement. The systematic error in [A2]
90
could lower the predicted E2mv and E1 values, but they will fall in the range given in Tables 1 and 2. [A2]
91
error of 70% was determined from varying chemical ionization times and comparing the measured [A2].
92
[A1] error of 50% was calculated from error propagation [Chen et al., 2012].
S5
[MA]=80 pptv
-3
[A2] (cm )
10
8
10
7
10
6
10
93
8/27/13
8/29/13
9/3/13
7
10
8
10
9
-3
10
10
[A1]=[H2SO4] (cm )
94
95
96
Figure S3 Measured [A2] vs. [A1] values for [MA]=80 pptv on three different days (black for
8/27/13, blue for 8/29/13, and red for 9/3/13 ). The box on the bottom right shows the systematic
error of the MCC.
97
4. Collision-Controlled Limit at Steady State:
98
99
The collision-controlled limit (CCL) is where every collision of A1 with another A1 or cluster
forms a larger cluster that does not evaporate (no backward reaction). However, clusters are still lost via
100
collisions with other particles (including monomer, clusters, or larger particles) and the wall of the
101
Augsburg flow reactor. The CCL is important because it corresponds to the highest concentration of
102
clusters that could be formed for a given [A1] [McMurry, 1983]. Observed cluster concentrations must be
103
equal or less than the cluster-controlled limit. If less, then the difference must be related to the extent to
104
which cluster concentrations are depleted by sulfuric acid evaporation. Figure S4 plots the measured [A2]
105
vs. [A1] with the solid black line showing the CCL calculated from measured [A1]. For all the bases
106
except TMA, the measured [A2] falls on or below the CCL curve. This implies that either the monomer or
107
dimer must be evaporating to depress the [A2] from the CCL concentration. Measured [A2] for TMA
108
appears to exceed the CCL, possibly due to fault in the steady state assumption where long lifetime
109
clusters would artificially raise the measured [A2]. If this were true, then DMA would also suffer from
110
inflated measured [A2]. This does not change the conclusion that the series of conditions examined here
111
predominately take place below CCL.
S6
112
Figure S4 also shows that the measured [A2] approaches CCL curve for the highest [A1] and [B].
113
In this region, the production of A2 (A2mv and A2LV from scheme 1 and A2 from 2) will dominate the
114
cluster balance equations due to high concentrations of reactants (e.g. [A1] and [B]). The rate of cluster
115
evaporation is overwhelmed by the production rates because the evaporation rates depend on cluster
116
composition and temperature but not on [A1] and [B].
9
10
-3
[A2] (cm )
MA= 10 pptv (2e8 cm-3)
20 (5e8)
70 (2e9)
80 (2e9)
180 (4e9)
220 (5e9)
260 (6e9)
NH3= 100 pptv (2e9 cm-3)
8
10
300 (7e9)
1100 (3e10)
1800 (4e10)
2300 (6e10)
3500 (8e10)
6000 (1e11)
7
10
6
10
5
10
(b) MA
(a) NH
4
3
10
-3
DMA= 2 pptv (5e7 cm )
3 (8e7)
6 (1e8)
20 (5e8)
60 (1e9)
100 (3e9)
200 (5e9)
8
10
-3
[A2] (cm )
-3
7
10
TMA= 4 pptv (1e8 cm )
12 (3e8)
30 (7e8)
54 (1e9)
95 (2e9)
140 (3e9)
300 (7e9)
6
10
5
10
7
8
10
9
10
10
-3
117
(d) TMA
(c) DMA
4
10 6
10
[A ]=[H SO ] (cm )
1
2
4
6
10
7
8
10
9
10
10
10
10
-3
[A ]=[H SO ] (cm )
1
2
4
118
119
120
121
Figure S4 Measured [A2] vs. [A1] with the calculated collision controlled limit drawn as a black line.
The collision-controlled [A2] was determined from measured [A1] and includes particle coagulation
and wall losses. No cluster evaporation or base reaction is present at this limit. Most [B] and [A1]
conditions produced measured [A2] below this limit. (a) NH3, (b) MA, (c) DMA, and (d) TMA
122
5. Scheme 1 Acid-Base Reaction Model for Nucleation:
123
124
Scheme 1 acid-base reaction model for nucleation is pictorially described on the left in Figure 4.
The resulting rate equations for each species are given below.
S7
d  A1 
dt
d  B
dt
 k11  A1   2 E2 mv  A2 mv   k21  A2 LV  A1   k31  A3  A1   E3  A3     A1     A1 
2
'
 k21
 A2mv  B   E2 Blv  A2lv     B 
d  A2 mv 
dt
1
2
'
 k11  A1   E2 mv  A2 mv   k21
 A2mv  B   E2 BLV  A2 LV   k22  A2 LV  A2 mv 
2
Equation S4
Equation S5
Equation S6
''
 k21
 A2mv     A2mv    A2mv 
2
d  A2 LV 
dt
k
'
21
 A2mv  B   E2 BLV  A2 LV   k21  A2 LV  A1   E3  A3 
Equation S7
'
 k22  A2 LV  A2 mv   k22
 A2 LV     A2 LV    A2 LV 
2
d  A3 
dt
125
 k21  A2 LV  A1   E3  A3   k31  A3  A1    3  A3     A3 
Equation S8
where
126
[A1] = monomer concentration
127
[A2mv] = more volatile dimer concentration
128
[A2LV] = less volatile dimer concentration
129
[A3] = trimer concentration
130
[B] = base concentration
131
E2mv = evaporation rate constant for sulfuric acid from A2mv
132
E2BLV = evaporation rate constant for base from A2LV
133
E3 = evaporation rate constant of sulfuric acid from A3
134
κi =first order coagulation rate to particles
135
η = wall loss rate
136
μ = base dilution coefficient
137
As an approximation, the forward rate constants, kii, are taken to be hard sphere collision rate for a
138
sulfuric monomer using its bulk liquid density (4x10-10 cm3 s-1) [McMurry, 1983; Ortega et al., 2012]. For
139
the transient solution, differential equations were solved numerically using Matlab’s ode45 with an input
S8
140
of an initial [A1] and [B]. Initial [A1] was based upon the baseline concentration for a given sulfuric acid
141
flow rate, and [B] was taken to be 10 times the NLD. The other cluster concentrations were assumed to be
142
zero at t=0 s.
143
6. Scheme 2 Acid-Base Reaction Model for Nucleation:
144
145
Scheme 2 acid-base reaction model is pictorially described on the right in Figure 4. The resulting
rate equations for each species are given below.
d  A1 
dt
d  B
dt
 k11 '  A1  B   E1  A1 B   k11  A1  A1B   k21  A1  A2   E3  A3     A1   1  A1 
 k11 '  A1  B   E1  A1B   k2 '  A2  B   k3 '  A3  B     B 
d  A1 B 
2
 k11 '  A1  B   E1  A1 B   k11  A1  A1 B   k22  A1B   k21  A1B  A2   E3  A3     A1   1  A1B 
dt
d  A2 
dt
d  A3 
dt
146
Equation S9
Equation S10
Equation S11
1
2
 k11  A1  A1 B   k11  A1B   k21  A1  A2   k21  A1B  A2   E3  A3     A2    2  A2 
2
Equation S12
 k21  A1  A2   k21  A1B  A2   E3  A3     A3    3  A3 
Equation S13
where
147
[A1] = monomer concentration
148
[A1B] = more neutralized monomer concentration
149
[A2] = dimer concentration
150
[A3] = trimer concentration
151
[B] = base concentration
152
E1 = evaporation rate constant of A1B
153
E3 = evaporation rate constant of sulfuric acid from A3
S9
154
κi =first order coagulation rate to particles
155
η = wall loss rate
156
μ = base dilution coefficient
157
7. Scheme 2 at Steady State and Applied to the Atmosphere:
158
We assume all collision rate constants, k, are equal and clusters are only lost to larger clusters and not to
159
the wall. The total signal at 160 m/z =[A1tot] where
 A1tot    A1    A1B
160
Equation S14
The monomer concentrations are assumed to be at equilibrium with [B] such that
 A1B 
k

E1  A1  B 
161
Combining Equations S14 with S15 gives an expression for [A1B].
 A1B  
162
Equation S15
k  B
E1  k  B 
Equation S16
 A1tot 
The steady state balance from Equation S13 gives
 A3  
k  A1tot  A2 
Equation S17
E3   3  
163
Combining the steady state balance from Equation S12 with Equations S14, S15, and S17 gives the
164
steady state concentration of [A2].
 A2   



E3
1 
 k  A1tot  1 
   2   
2k 
 E3   3   

Equation S18
2
1

2k
165




E3
k
2  E1
 
 k  A1tot  1 
   2     4k  A1B  
 E3   3   


  B 2 
From Chen et al. [2012], the nucleation rate is the formation of A4 (i.e., J=J4) and equals
S10
J 4  k  A1tot  A3 
166
Substituting Equation S18 into S17 then S19 produces
J4  P '
167
Equation S19
Equation S20
1
2
k  A1tot 
2
where P’ is a prefactor. P’ is always less than 1 and is defined as




E3
P
 k  A1tot  1 
   2   
E3   3   
 E3   3   

Equation S21
1
2




E3
k
2  E1

 
 k  A1tot  1 
   2     4k  AB  
E3   3   
 E3   3   

  B 2 
1
168
[A1B] is defined in Equation S19, leaving Equation S20 in terms of measurable concentrations.
169
8. [A2] / [A1] vs. [B] for Constant [A1]:
170
The dependence of [A2] on [B] is better illustrated by taking a vertical slice of Figure 2. This
171
creates the graphs in Figure S5 through Figure S8 where the measured [A2] / [A1] ratio is a function of
172
[B]. The lines on Figure S5 represent the steady state model of scheme 1 for the given fitted evaporation
173
rates. This model and solution method does well in capturing the trend of increasing then plateauing trend
174
of [A2] / [A1] with increasing [B]. The leveling off is the saturation point. The model also captures
175
decently well the dependence of the ratio on [A1]. The model does not capture the peaking behavior of
176
TMA curves. The steady state solution for scheme 2 is shown in Figure S6 and more accurately describes
177
the observations seen in the DMA graph. However, this model underpredicts the ratio at low [A1].
178
Using the transient solution for scheme 1, given in Figure S7, to predict the ratios produces worse
179
agreement with NH3 and MA but better for DMA and TMA. This is consistent with our hypothesis that
180
long-life time clusters are unsuited to be modeled via steady state. The transient solution for scheme 2 is
181
given in Figure S8. This model most accurately reproduces the shape of DMA out of the four solution
S11
182
methods/schemes. Overall, both schemes capture the correct trends of the ratio vs. [B] and the spread of
183
the curves.
184
185
186
187
Figure S5 The ratio [A2] /[A1] vs. [B] better illustrates the dimer dependence on [B]. Each color is at
a constant [A1] and the lines are the predicted steady state ratios from scheme 1. (a) NH3, (b) MA,
(c) DMA, and (d) TMA
188
189
190
Figure S6 Ratio of [A2] /[A1] vs. [B] solved at steady state for scheme 2 (lines). (a) NH3, (b) MA, (c)
DMA, and (d) TMA
S12
191
192
193
Figure S7 [A2] / [A1] vs. [B] at constant [A1]. The lines were calculated from the transient solution of
scheme 1. (a) NH3, (b) MA, (c) DMA, and (d) TMA
194
195
196
Figure S8 [A2] / [A1] vs. [B] at constant [A1]. The lines were calculated from the transient solution of
scheme 2. (a) NH3, (b) MA, (c) DMA, and (d) TMA
197
9. Time Dependent Behavior of Particle Coagulation Loss:
198
For this study, particle coagulation loss rate is calculated from the particle size distributions
199
measured by the DEG SMPS [Iida et al., 2009; Jiang et al., 2011] for particles >1.3 nm (geometric
200
diameter). The instrument sampled from a 1/8 inch stainless steel tube inserted into the center of the flow
201
reactor. The sampling point was ~2 cm above the MCC sampling region. The size distribution and thus
S13
202
loss rate to larger particles, κ, are functions of [A1], [B], and time. Figure S9 depicts κ as a function of
203
[A1] for varying [DMA]. From this figure, κ was described as a power law extrapolation as a function of
204
measured [A1]. For conditions investigated in this study, κ is smaller than the wall loss rate of η=0.05 s-1
205
for almost all [A1]. At high [A1], however, κ is large and plays a much larger role in the cluster balance
206
equations. This helps to explain the downturn of [A2] at high [A1].
κ plays a much more complicated role in the transient solution method due to the evolving
208
particle distribution with respect to time. The total number of particles at the point of injection is less than
209
at the 3 sec sampling point. This is due to base reacting with the clusters and forming stable clusters.
210
Therefore, κ will increase as time progresses. The maximum κ for the transient model can be
211
approximated from the 3 sec particle distribution and held constant from t=0 to 3 sec. This high κ changes
212
the model lines to those shown in Figure S10 and Figure S11 (cf. Figure 6 where total loss rate equals η).
213
The increase of loss prevents the calculated [A1] and [A2] from reaching the full range seen in the
214
measured data. However, increasing the loss rate does not alter the fitted evaporation rates.
-1
Sink Loss,  (s )
207
10
-1
10
-2
10
-3
10
-4
10
215
216
217
[DMA]= 9 pptv
[DMA]= 28
[DMA]= 55
8
10
9
-3
[A1] = [H2SO4] (cm )
Figure S9 Particle sink loss rate vs. MCC measured [A1]. Sink loss rate was determined from the
Afuchs of the DEG SMPS measured size distribution for particles >1.3 nm in this study.
218
S14
9
10
8
-3
[A2] (cm )
10
7
10
6
10
NH3= 100 pptv (2e9 cm-3)
MA= 10 pptv (2e8 cm-3)
20 (5e8)
70 (2e9)
80 (2e9)
180 (4e9)
220 (5e9)
260 (6e9)
300 (7e9)
1100 (3e10)
1800 (4e10)
2300 (6e10)
3500 (8e10)
6000 (1e11)
5
10
8
-3
[A2] (cm )
10
7
10
(b) E2mv= 15, E2BLV= 0 s-1
(a) E2mv= 300, E2BLV= 0.2 s-1
4
10
DMA= 2 pptv (5e7 cm-3)
3 (8e7)
6 (1e8)
20 (5e8)
60 (1e9)
100 (3e9)
200 (5e9)
TMA= 4 pptv (1e8 cm-3)
12 (3e8)
30 (7e8)
54 (1e9)
95 (2e9)
140 (3e9)
300 (7e9)
6
10
5
10
(c) E2mv= 2, E2Blv= 0 s
4
10 6
10
7
10
8
-1
9
10
(d) E2mv= 10, E2Blv= 0 s
6
10
10
7
10
-3
220
221
222
9
10
10
10
-3
[A1]=[H2SO4] (cm )
219
8
10
-1
[A1]=[H2SO4] (cm )
Figure S10 Transient solution to scheme 1 with maximum amount of particle coagulation loss. The
lines are the model predictions and points are measured concentrations. The fitted evaporation
rates remain unchanged. (a) NH3, (b) MA, (c) DMA, and (d) TMA
9
10
8
-3
[A2] (cm )
10
7
10
6
10
NH3= 100 pptv (2e9 cm-3)
MA= 10 pptv (2e8 cm-3)
20 (5e8)
70 (2e9)
80 (2e9)
180 (4e9)
220 (5e9)
260 (6e9)
300 (7e9)
1100 (3e10)
1800 (4e10)
2300 (6e10)
3500 (8e10)
6000 (1e11)
5
10
8
-3
[A2] (cm )
10
7
10
(b) E1= 25, E3= 0.4 s-1
(a) E1= 700, E3= 0.4 s-1
4
10
DMA= 2 pptv (5e7 cm-3)
3 (8e7)
6 (1e8)
20 (5e8)
60 (1e9)
100 (3e9)
200 (5e9)
TMA= 4 pptv (1e8 cm-3)
12 (3e8)
30 (7e8)
54 (1e9)
95 (2e9)
140 (3e9)
300 (7e9)
6
10
5
10
(c) E1= 0.1, E3= 0.4 s
4
10 6
10
223
224
225
7
10
8
10
9
10
[A1]=[H2SO4] (cm-3)
-1
(d) E1= 10, E3= 0.4 s
6
10
7
10
8
10
9
10
-1
10
10
[A1]=[H2SO4] (cm-3)
Figure S11 Transient solution of scheme 2 (lines) with maximum amount of particle coagulation
loss. (a) NH3, (b) MA, (c) DMA, and (d) TMA
S15
226
227
228
229
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