Supporting Information
Mishra et al. 10.1073/pnas.1200949109
SI Text
Experimental Methods.
The experimental setup is shown in Figs. S1
and S2. Nitrogen gas saturated with HNO
3
ð
g
Þ
by sparging a
2.25-M aqueous solution of HNO
3
(or DNO
3
) maintained at
278 K was introduced into the chamber of the electrospray mass
spectrometer (ESMS), where it collided with liquid microjets
of variable compositions. The concentration of HNO
3
ð
g
Þ
in the
saturated nitrogen gas was calculated by using reported partial
vapor pressures above H
2
O
∕
HNO
3
solutions (1, 2). We assumed
a similar liquid-vapor diagram for DNO
3
solutions. Typical ex-
perimental conditions were: drying gas flow rate,
10
L min
−
1
;
drying gas temperature, 340 °C; inlet voltage, -3.5 kV relative to
ground; fragmentor voltage, 26 V. HNO
3
(69%; Sigma-Aldrich)
and DNO
3
(D, 99%, 65
–
70% in D
2
O; Cambridge Isotope La-
boratories) were used as received. All solutions were prepared in
purified water (resistivity, 18.2 M
Ω
cm) from a Millipore Milli-Q
gradient water-purification system. Solution pH
BLK
was adjusted
by adding concentrated HCl or NaOH solutions and measured
with a calibrated pH meter (VWR). Selective adsorption of OH
−
on the stainless steel walls was observed by Duffin and Saykally
(3) in a similar setup, which led to the ejection of an acidic liquid
jet. We have independent evidence that our jets, in contrast, are
not acidic (4). It should be emphasized, however, that the velocity
at which the liquid jet emerges from the nozzle is approximately
500 times slower than that required for observing electrokinetic
effects in our experiments (3).
Computational Methods.
Energy-optimized water decamers, W
10
,
consisting of overlapping five-membered rings have been shown
to be most stable isomers (5, 6). In this configuration each water
molecule is hydrogen-bonded to three neighbors (7, 8). Nitric
acid binds to W
10
into optimized (W
10
·HNO
3
) adducts via two
hydrogen bonds with the release of
Δ
H
0
¼
−
13
.
0
kcal
∕
mol and
Δ
G
0
¼
−
1
.
2
kcal
∕
mol (Fig. 3
A
). The insertion of a chloride into
W
10
leads to a relaxed
ð
Cl·W
10
Þ
−
structure in which Cl
−
emerges
to the surface of the cluster and is hydrogen-bonded to the water
molecules of one of the rings (Fig. 3
B
) (9). The decreased
Mulliken electron population (
−
0
.
65
vs.
−
1
e
−
) on chloride in
ð
Cl·W
10
Þ
−
reveals that the surrounding waters have become bet-
ter proton acceptors via electron density delocalization.
Calculations of nitric acid interactions with W
10
and
ð
Cl·W
10
Þ
−
clusters were initialized by positioning a nitric acid molecule
close to one of the waters of the W
10
rings, and to the five waters
nearest to chloride in
ð
Cl·W
10
Þ
−
(Fig. 3
B
). Product structures
created out of the three lowest-energy adducts by separating the
proton from nitrate with none, one, or two waters were then en-
ergy-minimized. We found stable zwitterion products separated
by one and two waters in the presence of chloride, and by two
waters in its absence. The lowest-energy products in each case
correspond to ion pairs separated by two waters. Transition states
(TS) for transforming adducts into stable products were then
searched by optimizing structures in which the six O
─
H bonds
connecting nitrate with hydronium were constrained until the
chosen set of constraints led to an imaginary frequency vibration.
The path of steepest ascent was then followed by tracking the
eigenvector of the motion associated with the imaginary fre-
quency until an energy maximum was found. Full Hessian harmo-
nic calculations were then performed for the TS structures. We
also investigated whether nitric acid would transfer a proton
through, rather than assisted by, chloride. Structures in which
nitric acid was hydrogen-bonded or fully transferred its proton
to chloride were found to lie G
¼
1
.
6
kcal
∕
mol (H
¼
4
.
1
kcal
∕
mol) and G
¼
9
.
0
kcal
∕
mol (H
¼
8
.
38
kcal
∕
mol) above the
aforementioned lowest-energy adduct. Thus, chloride rather than
relaying proton transfer assists in this system.
Results.
From the frequency of HNO
3
collisions on water
’
s surface
given by the kinetic theory of gases [
f
ð
cm
−
2
s
−
1
Þ¼
1
∕
4
γ
cn
(
γ
≈
1
is the reactive uptake coefficient;
c
¼
3
.
2
×
10
4
cm s
−
1
is the mean speed of HNO
3
molecules at 300 K, and
n
their
number density in molecules cm
−
3
)] (10, 11), we deduce that
f
×
ð
τ
∕
Δ
Þ¼
1
.
9
×
10
18
protons cm
−
3
¼
10
−
2
.
5
M must be deliv-
ered to interfacial layers of thickness
Δ
½
cm
upon exposure to
n
¼
3
.
3
×
10
12
HNO
3
ð
g
Þ
molecules cm
−
3
during
τ
½
s
contact
times
—
i.e.,
ð
Δ
∕
τ
Þ¼
0
.
014
cm s
−
1
. Previous experiments have
shown that
τ
is approximately 10
μ
s (11). Thus, we estimate that
the thickness of the interfacial layers sampled in our experiments
is
Δ
∼
1
.
4
×
10
−
7
cm.
In Fig. 2
A
and
B
, the ratios
α
¼
I
117
∕
I
118
¼
PCOOH
2
þ
∕
PCOOHD
þ
,
β
¼
I
118
∕
I
119
¼
PCOOHD
þ
∕
PCOOD
2
þ
report
the H/D composition of the interfacial layers of 1-mM PCOOH
in
1
∶
1
∕
D
2
O
∶
H
2
O microjets exposed to either HNO
3
ð
g
Þ
or
DNO
3
ð
g
Þ
. The statistical protonation/deuteration (hydronation)
of PCOO
−
in interfacial layers of proton molar fraction
x
H
leads to:
α
¼
x
H
2
ð
1
−
x
H
Þ
;
β
¼
2
x
H
1
−
x
H
. From the asymptotic ratios
(
α
¼
1
.
92
,
β
¼
6
.
0
) measured under
ð
HNO
3
ð
g
Þ
Þ
>
7
×
10
12
molecules cm
−
3
, we derive:
x
H
¼
0
.
77
0
.
02
. Similarly, from
α
¼
0
.
93
,
β
¼
3
.
4
, under
ð
DNO
3
ð
g
Þ
Þ
>
6
×
10
12
molecules cm
−
3
,
we obtain:
x
H
¼
0
.
64
0
.
01
. As a reference, the
α
¼
1
.
31
ratio
measured in 1-mM PCOOH in
1
∶
1
∕
H
2
O
∶
D
2
O pH 3.0 microjets
not exposed to gaseous nitric corresponds to
x
0
H
¼
0
.
72
(rather
than
x
0
H
¼
0
.
50
). Therefore, the fraction of protons in interfacial
layers increases from
x
0
H
¼
0
.
72
to
x
H
¼
0
.
77
under HNO
3
ð
g
Þ
and
decreases to
x
H
¼
0
.
64
under DNO
3
ð
g
Þ
. Because
x
0
H
is perturbed
to similar but opposite extents (by
9%
on average) upon expo-
sure to HNO
3
ð
g
Þ
or DNO
3
ð
g
Þ
, we infer (
i
) a small kinetic isotope
effect for the interfacial dissociation of H
ð
D
Þ
NO
3
ð
g
Þ
, and (
ii
)an
approximately 90% contribution by the
1
∶
1
∕
D
2
O
∶
H
2
O solvent
to the isotopic composition of interfacial layers under present ex-
perimental conditions. Because approximately 0.6-mM hydrons
are delivered under
n
¼
7
×
10
12
H
ð
D
Þ
NO
3
ð
g
Þ
molecules cm
−
3
,
we infer that the effective water concentration in the interfacial
layers is approximately 0.03 M.
Discussion.
Consider a disk of interfacial water of radius R
S
, depth
Δ
¼
1
.
4
×
10
−
7
cm (see
SI Results
), and volume V
S
¼
π
R
S
2
Δ
,
centered at a chloride ion. At 30
μ
M (by assuming uniform
concentration throughout) there is 1 Cl
−
per N
W
¼
2
×
10
6
H
2
O molecules of volume V
W
¼
3
×
10
−
23
cm
3
. Therefore,
R
S
¼ð
V
W
×
N
W
×
Δ
−
1
×
π
−
1
Þ
1
∕
2
¼
117
nm. Thus, a HNO
3
molecule hitting the surface of a
>
30
-
μ
M solution will have
to diffuse on average R
S
<
1
.
2
×
10
−
5
cm to reach a Cl
−
and
undergo barrierless dissociation. By assuming that the frequency
of diffusional jumps between surface wells of depth E
D
can be
estimated from transition state theory as
ν
D
(s
−
1
) approximately
10
13
exp
ð
−
E
D
∕
k
B
T
Þ
, we obtain:
ν
D
approximately
7
×
10
10
s
−
1
,
with E
D
∼
3
kcal mol
−
1
at 300 K. The time to make 376 jumps of
length
3
×
10
−
8
cm to cover the distance R
S
¼
1
.
2
×
10
−
5
cm is
therefore
376
∕
ν
D
approximately 5 nanoseconds, which is compar-
able to the residence time of adsorbed gases on the surface of
water (11).
Mishra et al.
www.pnas.org/cgi/doi/10.1073/pnas.1200949109
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3
solubility.
Atmos Environ A
24:1945
–
1955.
2. Tang IN, Munkelwitz HR, Lee JH (1988) Vapor liquid equilibrium measurements for
dilute nitric-acid solutions.
Atmos Environ
22:2579
–
2585.
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microjets.
J Phys Chem C
111:12031
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12037.
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interface, in press.
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ð
H
2
O
Þ
n
¼
2
–
10
.
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114:11725
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Fig. S1.
Schematic diagram of the experimental setup. A microjet is created in the spraying chamber of an ESM spectrometer by injecting water through an
electrically grounded stainless steel nebulizer (100-
μ
m internal diameter) and briefly exposed to nitric acid vapors before it is broken up (after approximately
10 microseconds) into charged droplets by the nebulizer gas. After subsequent solvent evaporation and successive Coulomb explosions, excess ion ar
e ulti-
mately ejected to the gas-phase via field desorption and detected by mass spectrometry in <
1
millisecond. The spray chamber is at 1 atm of N
2
, 293 K through-
out.
Mishra et al.
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Fig. S2.
Functional diagram of our ESMS experimental setup.
Mishra et al.
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Fig. S3.
(
A
) Electrospray mass spectral nitrate signal intensities (I
62
) detected on aqueous MgSO
4
, KClO
4
, or NaCl microjets exposed to
3
×
10
12
moleculescm
−
3
of gaseous nitric acid for approximately 10
μ
s as functions of electrolyte concentration. Solid curves fit experimental data with Langmuir adsorption functions:
I
62
¼
I
62
max
½
electrolyte
×
ð
K
1
∕
2
þ½
electrolyte
Þ
−
1
;K
1
∕
2
¼
77
μ
M (MgSO
4
), 117
μ
M (KClO
4
), and 128
μ
M (NaCl).
Inset
shows ES mass spectra (signal intensities in
arbitrary units) on deionized water (red) and 1-mM NaCl (blue). All experiments under 1 atm of N
2
at 293 K. (
B
) Electrospray mass spectral nitrate signals
(
m
∕
z
¼
62
) detected on pure water, and on 1-mM HCl, NaCl, or NaOH microjets exposed to gaseous nitric acid for approximately 10
μ
s as a function of HNO
3
ð
g
Þ
concentration. All experiments in 1 atm of N
2
at 293 K.
Mishra et al.
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Fig. S4.
Electrospray mass spectral nitrate (
m
∕
z
¼
−
62
) signal intensities detected on microjets of deionized H
2
O, 1-mM NaCl
∕
H
2
O, D
2
O, and 1-mM NaCl
∕
D
2
O
exposed to 4-ppbv gaseous nitric acid for approximately 10
μ
s at pH of approximately 8. It is apparent that the extent of dissociation of gaseous nitric acid is
nearly independent of reactant or solvent deuteration KIEs. All experiments in 1 atm of N
2
ð
g
Þ
at 293 K.
Fig. S5.
(
A
,
B
) Schematics of TS for PTon water cluster in absence and presence of interfacial chloride. The internal reaction coordinate with the TS of Fig. 3
A
is
a combination of six O
─
H internal modes, whereas in the presence of chloride (Fig. 3
B
) the TS only involves motions of the H atoms being transferred along the
proton wire. While the preorganization of the surface of water in presence of chloride en route to TS leads to minimal requirement on the motion of heavy
oxygen atoms, in its absence the TS imaginary mode requires movements of the heavy oxygen atoms to accommodate PT (see animations at
http://www.wag
.caltech.edu/catalysis/projects/PT.html
).
Mishra et al.
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