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ATMOSPHERIC AEROSOLS
Multiphase buffer theory explains contrasts
in atmospheric aerosol acidity
Guangjie Zheng
1
, Hang Su
2
*, Siwen Wang
2
, Meinrat O. Andreae
2,3,4
, Ulrich Pöschl
2
, Yafang Cheng
1
*
Aerosol acidity largely regulates the chemistry of atmospheric particles, and resolving the drivers
of aerosol pH is key to understanding their environmental effects. We find that an individual buffering
agent can adopt different buffer pH values in aerosols and that aerosol pH levels in populated
continental regions are widely buffered by the conjugate acid-base pair NH
4+
/NH
3
(ammonium/
ammonia). We propose a multiphase buffer theory to explain these large shifts of buffer pH, and we
show that aerosol water content and mass concentration play a more important role in determining
aerosol pH in ammonia-buffered regions than variations in particle chemical composition. Our results
imply that aerosol pH and atmospheric multiphase chemistry are strongly affected by the pervasive
human influence on ammonia emissions and the nitrogen cycle in the Anthropocene.
Aerosol acidity has attracted increasing
interest in atmospheric research because
it influences the thermodynamics of gas-
particle partitioning and the chemical
kinetics of the formation and transfor-
mation of air particulate matter (1–8). Under-
standing the temporal and spatial variations
of aerosol pH in the atmosphere is crucial
for accurate predictions of the properties of
atmosphericaerosolsandtheireffectsonhealth,
ecosystems, and climate (9–12). In marine envi-
ronments, the uptake of acidic gases like SO
2
,
H
2
SO
4
,andHNO
3
may rapidly consume the
alkalinity and reduce the pH of sea salt aerosols
(13,14). For continental air masses in the south-
eastern United States, Weber et al. (15)have
suggested that aerosol pH is buffered in the
range of ~0 to 2 because of the interaction of
aqueous (NH
4
)
2
SO
4
-NH
4
HSO
4
with gaseous
NH
3
. However, their later studies have at-
tributed the elevated pH levels in northern
China (~3 to 6) (8,16–19) mainly to changes in
particle chemical compositions—i.e., a shift from
sulfate- to nitrate-dominated aerosols (12,19)—
whereas Cheng et al. (8) have highlighted the
role of ammonia and alkaline aerosol compo-
nents from natural and anthropogenic emissions
in understanding aerosol pH in this region.
Despite these advances, it is still unclear
how aerosol pH is buffered in other continen-
tal regions, such as northern China, compared
with the southeastern United States. To answer
this question, we first performed numerical
model calculations with the state-of-the-art
thermodynamic model ISORROPIA (20)to
examine the response of pH in aerosols upon
the addition of sulfuric acid under different
conditions that are characteristic of the south-
eastern United States (15,21), the North China
Plain (8,22), northern India (23), and western
Europe (24)[tableS1and(25)]. For reference,
we also calculated the response of an aqueous
solution of Na
2
SO
4
. As shown in fig. S1, the
Na
2
SO
4
solution exhibits the expected steep
decrease of pH upon acid addition. For aerosol
systems, however, the pH does not show a
substantial decrease until the added amount
of acid (H
+
equivalent) reaches ~20% of the
initial amount of anions in the aqueous par-
ticles (molar ratio), which indicates an ad-
ditional buffering effect. To further investigate
this phenomenon, we focus on the scenarios
for the southeastern United States (SE-US)
and for the North China Plain (NCP), which
have been intensively investigated and dis-
cussed in earlier studies. As indicated in
table S1, the SE-US scenario is characterized
by relatively low aerosol concentration, low
aerosol water content (AWC), and high tem-
perature, as observed under clean-air summer
conditions in the southeastern United States.
By contrast, the NCP scenario is characterized
by the high aerosol concentration, high AWC,
and low temperature observed during extreme
winter haze events in the Beijing region.
In aqueous solutions, the pH of different
buffer systems is usually determined by the pK
a
(where K
a
is the acid dissociation constant)
of the buffering agents (26). Accordingly, the
different pH buffer levels in fig. S1 would sug-
gest different buffering agents corresponding
to different particle chemical compositions.
To identify the most relevant buffering agents,
key controlling parameters, we introduce the
concept of a multiphase buffering capacity
that describes the resistance to pH changes
upon input of acids or bases in an aerosol
multiphase system in analogy to the traditional
buffering capacity of bulk aqueous solutions.
The buffering capacity bis defined as the ratio
between the amount of acid or base added
to the system (n
acid
or n
base
,inmolesper
kilogram) and the corresponding pH change
in the aqueous phase of the system, or b=
−dn
acid
/dpH = dn
base
/dpH. The larger the
buffering capacity b, the less the pH will change
upon the addition of acids or bases.
Figure 1A shows the buffering capacities for
the SE-US and NCP aerosol scenarios and for
bulk aqueous solutions of the individual buf-
fering agents (i.e., conjugate acid-base pairs
NH
4
+
/NH
3
, HSO
4
−
/SO
4
2−
, and HNO
3
/NO
3
−
)
as derived from numerical simulations of the
gas-liquid and acid-base equilibria [see mate-
rials and methods, section M1; results of the
northern India and western Europe scenarios
are in fig. S2; and results of organic buffers are
in the supplementary text, section S7 (25)]. In
both aerosol scenarios, the largest buffering
capacity is obtained for the acid-base pair
NH
4
+
/NH
3
followed by HSO
4
−
/SO
4
2−
and HNO
3
/
NO
3
−
. The peak buffer pH value (defined as the
pH corresponding to the highest local maxi-
mum of b) for the SE-US scenario is ~0.7, and
the peak buffer pH value for the NCP scenario
is ~4.5. Thus, the buffer pH ranges (i.e., peak
buffer pH ± 1) (26,27) closely match the aerosol
pH ranges previously reported for the southeast-
ern United States and for Beijing, respectively.
This indicates that the conjugate acid-base
pair NH
4
+
/NH
3
is the main buffering agent in
both the SE-US and NCP aerosol scenarios.
This finding raises the question of how the
same buffering agent can stabilize the aerosol
pH at verydifferent levels. As shown in Fig. 1A,
in bulk aqueous solution, the peak buffer pH
of NH
4
+
/NH
3
is ~9.2, but in the NCP and SE-US
aerosol scenarios, it shifts to much lower values
of ~4.5 and ~0.7, respectively. By contrast, the
peak buffer pH of the conjugate acid-base pair
HNO
3
/NO
3
−
shifts in the opposite direction
from ~−1.5 in the bulk aqueous solution to
higher values of ~0.2 and ~3.8 in the NCP and
SE-US scenarios, respectively. The conjugate
acid-base pair HSO
4
−
/SO
4
2−
, on the other hand,
exhibits similar peak buffer pH values of ~2
in all three scenarios (Fig. 1A). These differ-
ences and shifts of peak buffer pH reflect spe-
cial features of the aerosol multiphase buffer
system that go beyond the traditional buffer
theory for bulk aqueous solutions, and they
highlight the need for a mechanistic under-
standing of the multiphase buffering mech-
anism in atmospheric aerosols.
To elucidate the underlying mechanisms and
key parameters, we have developed a multi-
phase buffer theory and derived an analytical
expression for the buffering capacity of a buf-
fering agent X (conjugate acid-base pair) in an
aerosol multiphase buffer system as detailed
in section S1 (25)
b¼dnbase
dpH ¼2:303 Kw
½Hþþ½Hþþ
X
i
Ka;i½Hþ
ðKa;iþ½HþÞ2½Xitot
ð1Þ
RESEARCH
Zheng et al., Science 369, 1374–1377 (2020) 11 September 2020 1of4
1
Minerva Research Group, Max Planck Institute for
Chemistry, Mainz 55128, Germany.
2
Multiphase Chemistry
Department, Max Planck Institute for Chemistry, Mainz
55128, Germany.
3
Scripps Institution of Oceanography,
University of California, San Diego, La Jolla, CA 92093, USA.
4
Department of Geology and Geophysics, King Saud
University, 11451 Riyadh, Saudi Arabia.
*Corresponding author. Email: yafang.cheng@mpic.de (Y.C.);
h.su@mpic.de (H.S.)
on September 16, 2020 http://science.sciencemag.org/Downloaded from
Here, K
w
is the water dissociation constant,
[X
i
]
tot
* represents the total equivalent mol-
ality of the buffering agent X
i
, including the
gas phase and aqueous phase of both conju-
gate acid-base species—e.g., the sum of NH
3
(g),
NH
3
(aq), and NH
4
+
(aq) for the buffering agent
NH
4
+
/NH
3
.K
a,i
* is an effective acid dissociation
constant of the buffering agent X
i
and can be
expressed by
Ka;BOH ¼
½HþðaqÞ½BOHðaqÞ þ ½BOHðgÞ
½BþðaqÞ
¼Ka;BOH 1þrw
HiRT AWC
ð2AÞ
Ka;HA ¼½HþðaqÞ½AðaqÞ
½HAðaqÞþ½HA ðgÞ
¼Ka;HA =1þrw
HiRT AWC
ð2BÞ
for volatile base BOH and volatile acid HA that
dissociate in the form
BþðaqÞþH2O⇌HþðaqÞþBOHðaqÞð2CÞ
HAðaqÞ⇌HþðaqÞþAðaqÞð2DÞ
As shown in Eq. 2, the effective dissociation
constant K
a,i
* depends on the classical disso-
ciation constant K
a,i
as well as on the Henry’s
law coefficient H
i
(gas-particle partitioning
constant) (in moles per liter per atmosphere)
and on the AWC (in micrograms per cubic
meter)—i.e., the amount of liquid water in
the aerosol multiphase system. Here, r
w
is
the liquid water density (~10
12
mgm
−3
), Ris the
gas constant (8.205 ×10
−2
atm L mol
−1
K
−1
), and
Tis the absolute temperature (in kelvin). Note
that gas concentrations in square brackets are
expressed in units of equivalent molality (in
moles per kilogram of water) [see section M1
(25)]. The expression of Eqs. 1 and 2 in the
other unit system can be found in section S2.
By solving Eq. 1, we can find a local maxi-
mum of bat pH = pK
a,i
*; i.e., the peak buffer
pH of the agent X
i
is determined by K
a,i
*.
Therefore, a single buffering agent can have
its peak buffering capacity at very different
pH values in an aerosol multiphase buffer sys-
tem. According to Eq. 2A, for the buffering
agent NH
4
+
/NH
3
(volatile base), increasing
AWC results in a reduced K
a
*andincreased
pK
a
*. Thus, the traditional alkaline buffering
agent NH
4
+
/NH
3
effectively becomes an acidic
buffering agent (pK
a
* < 7) in multiphase sys-
tems (Fig. 1A). For volatile acid buffering agents
(HNO
3
/NO
3
−
), the AWC has the opposite effect
on pK
a
* (Fig. 1A). Moreover, the shift of pK
a
*
upon changes to the AWC is inversely pro-
portional to the partitioning coefficient H
i
.
Thus, the volatile buffering agents HNO
3
/NO
3
−
and NH
4
+
/NH
3
(low H
i
)exhibitlargeshifts,
whereas the peak buffer pH of HSO
4
−
/SO
4
2−
hardly changes (high H
i
) (table S2). As shown
in Fig. 1B, the effective dissociation constant
K
a
* converges with the standard acid-base
dissociation constant of the buffering agent
for high values of AWC (Eq. 2), and the multi-
phasebuffer theory converges with the con-
ventional buffer theory in solution chemistry
[see sections S1 to S4 (25)]. Note that ac-
tivity coefficients must be considered in the
calculation of nonideal systems [see section
S3 (25)].
Figure 2 further explains the thermodynam-
ics that causes the shift of buffer pH in a multi-
phase system. The conventional bulk buffer
solutions (e.g., NH
4
+
/NH
3
), assuming no ex-
change with a gas phase, achieve their largest
resistance to pH change when the molality of
NH
4
+
(aq) is equal to that of NH
3
(aq) (Eq. 3A) (26)
pH ¼pKa;NH3þlog10
½NH3ðaqÞ
½NH4þðaqÞ ð3AÞ
where
Ka;NH3¼Kw
Kb;NH3
¼½HþðaqÞ½NH3ðaq Þ
½NH4þðaqÞ ð3BÞ
and Kb;NH3is the base dissociation constant of
NH
3
(table S2).
For gas-liquid multiphase systems, this equi-
librium is extended to the gas phase, and pH
becomes a function of K
a
* and the ratio of total
NH
3
in both gas and aqueous phase to NH
4
+
in
the aqueous phase [Eq. 4A; section S1 (25)].
Accordingly, the largest resistance to pH change
under given [NH
3
]
tot
*([NH
3
]
tot
*=[NH
3
(aq)] +
[NH
3
(g)] + [NH
4
+
(aq)]) is achieved when the
molality of NH
4
+
(aq) is equal to the sum of
NH
3
(aq) and NH
3
(g). Note that Eq. 3 still holds
for the aqueous phase in the multiphase system
pH ¼pKa;NH3
þlog10
½NH3ðaqÞþ½NH3ðgÞ
½NH4þðaqÞ
ð4AÞ
where
Ka;NH3
¼
½HþðaqÞ½NH3ðaqÞþ½NH3ðgÞ
½NH4þðaqÞ
¼Ka;NH31þrw
HNH3RT AWC
ð4BÞ
Figure 2 shows the conditions where the
peak buffer pH values are achieved in different
systems—i.e., the same height of NH
4
+
and
NH
3
in each panel represents their same molar
numbers in each system. Compared with bulk
Zheng et al., Science 369, 1374–1377 (2020) 11 September 2020 2of4
Fig. 1. Buffering capacity
for aerosol multiphase
systems compared with
bulk aqueous solution.
(A) Buffer capacities (b) for
the SE-US and NCP aerosol
scenarios and for bulk
aqueous solution of indi-
vidual buffering agents
(solid lines). The overall
buffering capacity (black
dashed lines) is obtained
by adding the individual
buffer agent contributions
to the solvent background
of water [fig. S3 and sec-
tion S5 (25)]. The
composition of the bulk
solution is assumed to have
the same aqueous phase
molality as in the SE-US
scenario. (B) Dependence
of the peak buffer capacity
(pK
a
*) of NH
4+
/NH
3
on
aerosol water content
(AWC) and temperature.
RESEARCH |REPORT
on September 16, 2020 http://science.sciencemag.org/Downloaded from
solution, a fraction of NH
3
partitions to the gas
phase in the NCP scenario, which results in less
NH
3
(aq)andareduced[NH
3
(aq)]/[NH
4
+
(aq)]
ratio, which leads to a lower pH in the aqueous
phase according to Eq. 3. Further reduction of
AWC in the SE-US scenario will push more NH
3
to
the gas phase and further reduce the aerosol pH.
Figure 3 compares the contribution of in-
dividual factors in explaining the difference in
aerosol pH between the NCP (~5.4) and SE-US
(~0.7) scenarios in fig. S1 [sections M2, S3, S5,
and S6 (25)]. The AWC appears to be the most
important factor, contributing 2.2 units of pH
change (DpH), followed by T,whichcontributes
another 1.6 units of DpH. Although earlier
studies have hypothesized that the marked
observed pH difference is caused by a transi-
tion in particle chemical composition from a
sulfate- to a nitrate-dominated regime (12,19),
our results show that the change of chemical
composition only plays a minor role. Differ-
ent AWCs [mainly caused by different aerosol
concentrations at a given relative humidity
(RH)] and Tvalues can already explain a shift
of ~4 units of aerosol pH. The difference in
chemical composition contributes ~0.7 pH units
in total, with ~0.5 from the difference in total
NH
3
fraction and ~0.1 and ~0.1 from the dif-
ference in the fraction of NO
3
−
and nonvolatile
cations (NVCs), respectively. Overall, different
AWCs and Tvalues are the main drivers of the
pH difference between the NCP and SE-US
scenarios, whereas the higher fraction of total
NH
3
,NVCs,andNO
3
−
in the NCP further en-
larges the difference.
In Fig. 4, we performed global model sim-
ulations to identify the buffered regions and
used both simulation and observational data to
further compare the roles of AWC and chemical
compositions in determining the variabilities
of aerosol pH [sections M3, S3, and S6 and
table S3 (25)]. As shown in Fig. 4A, ~40% of
continental surface areas (not including Ant-
arctica) and 71% of urban populated areas
were buffered by the NH
4
+
/NH
3
agent with
aerosol pH values mostly within the buffer range
[pK
a,NH3
*±1(26,27)]. In these regions, without
knowing the temporal and spatial variability
of particle chemical composition, variations
in AWC alone explain almost 70% (R
2
= 0.66,
simulation; where R
2
is the coefficient of
determination) and 80% (R
2
=0.77,observa-
tion)ofthevariationofaerosolpH,assuming
an NH
4
+
/NH
3
–buffered system (Fig. 4B). On
the other hand, when a constant AWC is as-
sumed, distinct variations of aerosol acidity with
particle chemical composition were observed,
but they only played a secondary role (R
2
=
0.22 and 0.26 for simulation and observation,
respectively; Fig. 4C). We also found a reverse
role for AWC and composition in regions that
are not buffered by NH
4
+
/NH
3
,wherechem-
ical composition differences alone explain >90%
of the variations of aerosol pH (fig. S5). Overall,
the buffering effect of ammonia suppresses the
influence of compositional differences, making
aerosol water content the primary determinant
of aerosol pH.
The multiphase buffering of aerosols and
the key role of AWC in determining the peak
buffer pH (pK
a
*) have implications for atmo-
spheric research and air pollution control.
Drivers of historical trends in aerosol pH can
now be better understood and quantified [sec-
tion S8 (25)]. In populated continental regions
with high anthropogenic emissions and atmo-
spheric concentrations of ammonia (28), aero-
sol pH is likely controlled by the buffering pair
NH
4
+
/NH
3
and can thus be approximated on
the basis of aerosol mass concentration and
Zheng et al., Science 369, 1374–1377 (2020) 11 September 2020 3of4
Fig. 2. Schematic diagram of buffer pH transition from aerosol multiphase systems to bulk aqueous
solution for NH
4+
/NH
3
.AWC concentrations are not drawn to scale, for illustration purposes. Diagrams for
a generic volatile acid and base are shown in fig. S4.
Fig. 3. Fractional contribution of individual drivers to the aerosol pH difference between SE-US and
NCP scenarios. Red and blue lines mark the corresponding values in the SE-US and NCP scenarios,
respectively [see table S1 for detailed scenario information (25)].
RESEARCH |REPORT
on September 16, 2020 http://science.sciencemag.org/Downloaded from
water content (Eq. 4). This opens up possibili-
ties to reconstruct long-term trends and large-
scale spatial distributions of aerosol pH. Other
buffering agents, such as HSO
4
−
/SO
4
2−
,HCl/Cl
−
,
or HCO
3
−
/CO
3
2−
,arelikelytocontrolaerosol
pH over the oceans (13,14,29,30), but the buf-
fering effects of NH
4
+
/NH
3
may extend over
ammonia-rich coastal and downwind regions.
Thus, the notable human influence on ammo-
nia emissions and the global nitrogen cycle in
the Anthropocene substantially affects aerosol
pH and atmospheric multiphase chemistry on
a global scale.
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ACKNO WLED GME NTS
Funding: This study is support by the Max Planck Society (MPG).
Y.C. thanks the Minerva Program of MPG. Author contributions:
Y.C. and H.S. conceived the theory and led the study. G.Z., Y.C.,
and H.S. performed the research. S.W. performed the GEOS-Chem
simulation. M.O.A. commented on the manuscript. H.S., Y.C., G.Z.,
and U.P. wrote the manuscript with inputs from all coauthors.
Competing interests: The authors declare no competing interests.
Data and materials availability: All data used in the analysis are
provided in the supplementary materials.
SUPPLEMENTARY MATERIALS
science.sciencemag.org/content/369/6509/1374/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S15
Table S1 to S4
References (31–97)
Data S1
29 November 2019; accepted 21 July 2020
10.1126/science.aba3719
Zheng et al., Science 369, 1374–1377 (2020) 11 September 2020 4of4
Fig. 4. Drivers of aerosol pH diversity in ammonia-buffered regions. (A) Global distribution of continental
surface regions buffered by NH
4+
/NH
3
. The color coding shows the maximum buffer capacity by NH
4+
/NH
3
(inmolespercubicmeterofair).(B) Correlation of aerosol pH modeled by ISORROPIA with the predicted pH
derived using constant buffering agent and multiphase buffer theory. Sim., simulation; Obs., observation.
(C) Correlation of aerosol pH modeled by ISORROPIA with the predicted pH by ISORROPIA using constant
AWC but variable compositions. Black circles and gray dots represent analysis based on model simulations and
observations, respectively (see section M3 and table S3). Note that the observations are based on individual case
studies and thus show a wider range of aerosol pH than the annual average simulation results.
RESEARCH |REPORT
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Multiphase buffer theory explains contrasts in atmospheric aerosol acidity
Guangjie Zheng, Hang Su, Siwen Wang, Meinrat O. Andreae, Ulrich Pöschl and Yafang Cheng
DOI: 10.1126/science.aba3719
(6509), 1374-1377.369Science
, this issue p. 1374Science
important influence of ammonia emissions in the Anthropocene.
important role for water content in determining pH in ammonia-buffered regions. Their conclusions underscore the
considered how buffering capacity in a multiphase aerosol system differs from bulk solution and found anet al.Zheng
is their acidity, so understanding what determines aerosol pH is fundamental for determining their environmental effects.
Aerosols exert a primary influence on atmospheric chemistry. One of the main controls on their internal chemistry
A multiphasic effect
ARTICLE TOOLS http://science.sciencemag.org/content/369/6509/1374
MATERIALS
SUPPLEMENTARY http://science.sciencemag.org/content/suppl/2020/09/09/369.6509.1374.DC1
REFERENCES http://science.sciencemag.org/content/369/6509/1374#BIBL
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