acp-20-7359-2020.pdf

Atmos. Chem. Phys., 20, 7359–7372, 2020

https://doi.org/10.5194/acp-20-7359-2020

the Creative Commons Attribution 4.0 License.

Enhanced growth rate of atmospheric particles from sulfuric acid

Dominik Stolzenburg

1,2

, Mario Simon

, Ananth Ranjithkumar

, Andreas Kürten

, Katrianne Lehtipalo

2,5

Hamish Gordon

, Sebastian Ehrhart

, Henning Finkenzeller

, Lukas Pichelstorfer

, Tuomo Nieminen

Xu-Cheng He

, Sophia Brilke

, Mao Xiao

, António Amorim

, Rima Baalbaki

, Andrea Baccarini

, Lisa Beck

Steffen Bräkling

, Lucía Caudillo Murillo

, Dexian Chen

, Biwu Chu

, Lubna Dada

, António Dias

Josef Dommen

, Jonathan Duplissy

, Imad El Haddad

, Lukas Fischer

, Loic Gonzalez Carracedo

Martin Heinritzi

, Changhyuk Kim

13,14

, Theodore K. Koenig

, Weimeng Kong

, Houssni Lamkaddam

Chuan Ping Lee

, Markus Leiminger

12,15

, Zijun Li

, Vladimir Makhmutov

, Hanna E. Manninen

Guillaume Marie

, Ruby Marten

, Tatjana Müller

, Wei Nie

, Eva Partoll

, Tuukka Petäjä

, Joschka Pfeifer

Maxim Philippov

, Matti P. Rissanen

2,20

, Birte Rörup

, Siegfried Schobesberger

, Simone Schuchmann

Jiali Shen

, Mikko Sipilä

, Gerhard Steiner

, Yuri Stozhkov

, Christian Tauber

, Yee Jun Tham

, António Tomé

Miguel Vazquez-Pufleau

, Andrea C. Wagner

3,7

, Mingyi Wang

, Yonghong Wang

, Stefan K. Weber

Daniela Wimmer

1,2

, Peter J. Wlasits

, Yusheng Wu

, Qing Ye

, Marcel Zauner-Wieczorek

, Urs Baltensperger

Kenneth S. Carslaw

, Joachim Curtius

, Neil M. Donahue

, Richard C. Flagan

, Armin Hansel

12,15

Markku Kulmala

, Jos Lelieveld

, Rainer Volkamer

, Jasper Kirkby

3,18

, and Paul M. Winkler

Faculty of Physics, University of Vienna, 1090 Vienna, Austria

Institute for Atmospheric and Earth System Research/Physics, University of Helsinki, 00014 Helsinki, Finland

Institute for Atmospheric and Environmental Sciences, Goethe University Frankfurt, 60438 Frankfurt am Main, Germany

School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK

Finnish Meteorological Institute, 00560 Helsinki, Finland

Atmospheric Chemistry Department, Max Planck Institute for Chemistry, 55128 Mainz, Germany

Department of Chemistry and Cooperative Institute for Research in Environmental Sciences,

University of Colorado Boulder, Boulder, CO 80309, USA

Laboratory of Atmospheric Chemistry, Paul Scherrer Institute, 5232 Villigen, Switzerland

Center for Astrophysics and Gravitation, Faculty of Sciences of the University of Lisbon, 1749-016 Lisbon, Portugal

Tofwerk AG, 3600 Thun, Switzerland

Center for Atmospheric Particle Studies, Carnegie Mellon University, Pittsburgh, PA 15217, USA

Institute for Ion Physics and Applied Physics, University of Innsbruck, 6020 Innsbruck, Austria

Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA

School of Civil and Environmental Engineering, Pusan National University, Busan 46241, Republic of Korea

Ionicon Analytik GmbH, 6020 Innsbruck, Austria

Department of Applied Physics, University of Eastern Finland, 70211 Kuopio, Finland

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 119991 Moscow, Russia

CERN, the European Organization for Nuclear Research, 1211 Geneva, Switzerland

Joint International Research Laboratory of Atmospheric and Earth System Sciences, School of Atmospheric Sciences,

Nanjing University, 210023 Nanjing, China

Aerosol Physics Laboratory, Tampere University, 33101 Tampere, Finland

Institute Infante Dom Luíz, University of Beira Interior, 6200-001 Covilhã, Portugal

Correspondence:

Paul M. Winkler (paul.winkler@univie.ac.at)

Received: 22 August 2019 – Discussion started: 15 November 2019

Revised: 12 May 2020 – Accepted: 31 May 2020 – Published: 25 June 2020

Published by Copernicus Publications on behalf of the European Geosciences Union.

7360

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

Abstract.

In the present-day atmosphere, sulfuric acid is the

most important vapour for aerosol particle formation and ini-

tial growth. However, the growth rates of nanoparticles (

10 nm) from sulfuric acid remain poorly measured. There-

fore, the effect of stabilizing bases, the contribution of ions

and the impact of attractive forces on molecular collisions are

under debate. Here, we present precise growth rate measure-

ments of uncharged sulfuric acid particles from 1.8 to 10 nm,

performed under atmospheric conditions in the CERN (Euro-

pean Organization for Nuclear Research) CLOUD chamber.

Our results show that the evaporation of sulfuric acid parti-

cles above 2 nm is negligible, and growth proceeds kineti-

cally even at low ammonia concentrations. The experimental

growth rates exceed the hard-sphere kinetic limit for the con-

densation of sulfuric acid. We demonstrate that this results

from van der Waals forces between the vapour molecules and

particles and disentangle it from charge–dipole interactions.

The magnitude of the enhancement depends on the assumed

particle hydration and collision kinetics but is increasingly

important at smaller sizes, resulting in a steep rise in the ob-

served growth rates with decreasing size. Including the ex-

perimental results in a global model, we find that the en-

hanced growth rate of sulfuric acid particles increases the

predicted particle number concentrations in the upper free

troposphere by more than 50 %.

1 Introduction

Sulfuric acid (H

) is the major atmospheric trace com-

pound responsible for the nucleation of aerosol particles in

the present-day atmosphere (Dunne et al., 2016). Sulfuric

acid participates in new particle formation (NPF) in the upper

troposphere (Brock et al., 1995; Weber et al., 1999; Weigel et

al., 2011), stratosphere (Deshler, 2008), polar regions (Joki-

nen et al., 2018), urban or anthropogenically influenced en-

vironments (Yao et al., 2018), and when a complex mixture

of different condensable vapours is present (Lehtipalo et al.,

2018). Especially in the initial growth of small atmospheric

molecular clusters, sulfuric acid is likely of crucial impor-

tance (Kulmala et al., 2013). The newly formed particles

need to grow rapidly in order to avoid scavenging by larger,

pre-existing aerosols and, thereby, contribute to the global

cloud condensation nuclei (CCN) budget (Pierce and Adams,

2007). Therefore, the dynamics in this cluster size range of

a few nanometres determines the climatic significance of at-

mospheric NPF, which is the major source of CCN (Gordon

et al., 2017) and can also affect urban air quality (Guo et al.,

2014).

The main pathway of cluster and particle growth is con-

densation of low volatility vapours, like sulfuric acid or

oxidized organics (Stolzenburg et al., 2018). Nanoparticle

growth rates depend on both the evaporation rates of the

condensing vapours and the molecular collision frequencies.

Uncertainty about the expected behaviour at the collision

(“kinetic”) limit influences the interpretation of experimental

data. One focus has been on the evaporation rates from small

particles and the potential growth rate enhancement from co-

agulation. In earlier laboratory measurements, it has been

shown that bases like ammonia can have a stabilizing effect

for growth below 2 nm (Lehtipalo et al., 2016). If amines,

which are stronger bases than ammonia, are added, nucle-

ation itself can proceed at the kinetic limit, i.e. evaporation

rates from the monomer onwards are zero (Jen et al., 2014;

Kürten et al., 2014; Olenius et al., 2013). In this case, cluster

coagulation also plays an important role in the growth pro-

cess due to the strong clustering behaviour of sulfuric acid

and amines (Kontkanen et al., 2016; Lehtipalo et al., 2016;

Li and McMurry, 2018). However, in the presence of ammo-

nia, the evaporation rates and the magnitude of cluster co-

agulation remain unmeasured, although ammonia is much

more important than amines globally due to its longer at-

mospheric lifetime. A second focus is on the collisional rate

coefficients themselves, which may be enhanced by either

charge–dipole interactions (Nadykto and Yu, 2003) or van

der Waals forces (Chan and Mozurkewich, 2001). In spite of

the importance of these coefficients, there are only few di-

rect measurements of the charge effect on growth (Lehtipalo

et al., 2016; Svensmark et al., 2017). Even if the charge–

dipole interactions are stronger, an enhancement due to van

der Waals forces might be more important at typical atmo-

spheric ionization levels. Several atmospheric studies have

demonstrated that sulfuric acid uptake proceeds at close to a

collision-limited rate (Bzdek et al., 2013; Kuang et al., 2010),

but they could neither provide a measurement of a collision

enhancement nor did they consider hydration effects in detail

(Verheggen and Mozurkewich, 2002). Both of these factors

might be significant in the free molecular regime below 5 nm,

where growth measurements are also affected by larger un-

certainties (Kangasluoma and Kontkanen, 2017). Here, we

address the questions of evaporation and collision enhance-

ment in sulfuric-acid-driven growth with precision measure-

ments (Stolzenburg et al., 2017) at the CERN (European Or-

ganization for Nuclear Research) CLOUD experiment (Du-

plissy et al., 2016).

2 Methods

2.1 Experimental approach

The CERN CLOUD chamber is a 26.1 m

stainless steel

aerosol chamber that can be kept at a constant tempera-

ture within 0.1 K precision. It offers the possibility to study

new particle formation under different ionization levels. Two

high-voltage electrode grids inside the chamber can effi-

ciently clear ions and charged particles from the chamber

within seconds, ensuring neutral conditions. When there is

no electric field in the chamber, galactic cosmic rays lead to

Atmos. Chem. Phys., 20, 7359–7372, 2020

https://doi.org/10.5194/acp-20-7359-2020

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

7361

an ion production rate of

∼

2–4 ion pairs cm

−

. Ion con-

centrations can also be elevated to upper tropospheric con-

ditions by the illumination of the chamber with a pion beam

from the CERN Proton Synchrotron. The dry air supply for

the chamber is provided by boil-off oxygen and boil-off ni-

trogen mixed at the atmospheric ratio of 79 : 21. This ensures

extremely low contaminant levels, especially from organics

and sulfuric acid. This was verified by a PTR3 proton transfer

reaction time-of-flight mass spectrometer (Breitenlechner et

al., 2017) and a nitrate chemical ionization atmospheric pres-

sure interface time-of-flight (nitrate CI-APi-ToF) mass spec-

trometer (Jokinen et al., 2012). The absence of any contam-

ination from amines was confirmed by measurements with

a water cluster CI-APi-ToF (Pfeifer et al., 2020), which did

not register dimethylamine mixing ratios above the detection

limit of 0.1 pptv.

We performed measurements of particle growth from sul-

furic acid and ammonia at either

20 or

◦

C with the rel-

ative humidity kept constant at either 38 % or 60 %. SO

(5 ppb), O

(

∼

120 ppb) and ammonia (varied between 3

and 1000 pptv) were injected into the chamber. The exper-

iments were initiated by homogeneous illumination of the

chamber at constant O

and SO

levels. The UV light of

four Hamamatsu UV lamps guided into the chamber with

fibre optics induced the photo-dissociation of O

and the

production of OH

q

radicals. Thus, SO

was oxidized, lead-

ing to the formation of sulfuric acid (varied between 10

and 10

−

). A typical experiment is shown in Fig. S1 in

the Supplement. Sulfuric acid monomer concentrations were

measured with the nitrate CI-APi-ToF. Calibration of the in-

strument’s response to sulfuric acid (Kürten et al., 2012) was

performed before and after the measurement campaign and

yielded comparable results. Compared with previous stud-

ies, the measurement of gas-phase NH

also significantly im-

proved due to the deployment of the calibrated water cluster

CI-APi-ToF. The protonated water cluster reagent ions selec-

tively ionize ammonia and amines at ambient pressure reach-

ing a detection limit of approximately 0.5 pptv for ammonia.

Particle growth was monitored using a differential mo-

bility analyser-train (DMA-train; Stolzenburg et al., 2017)

for the main size range from 1.8 to 8 nm. We also include

measurements from a Caltech nano-radial DMA (Brunelli

et al., 2009) with a custom-built diethylene glycol (DEG)

counter for sizes between 4 and 8 nm and a TSI Scanning

Mobility Particle Sizer (nano-SMPS; model 3936) for sizes

larger than 5 nm when investigating the size dependence of

the growth. For the growth of the charged fraction, we use a

neutral cluster and air ion spectrometer (NAIS; Manninen et

al., 2009). All four instruments use electrical mobility classi-

fication, and the measured mobility diameters are corrected

to mass diameters (Larriba et al., 2011) for the calculation of

collision kinetics. Compared with the scanning particle size

magnifier (see e.g. Lehtipalo et al., 2014), which was used in

Lehtipalo et al. (2016), these instruments that use direct mo-

bility analysis have less systematic uncertainty on the actual

size classification. The size ranges of both studies are also

not directly comparable. We show the measurements in the

lower size interval of the DMA-train (1.8–3.2 nm mobility

diameter) as well as the earlier results (size range between

1.5 and 2.5 nm mobility diameter) in Fig. S2.

Another difference between the instruments is the treat-

ment of the sample relative humidity. In the DMA-train, the

aerosol sheath flow is dried using silica gel, achieving a rela-

tive humidity measured at the sheath inlet of the DMA below

5 % for all experiments in this study. The nano-SMPS uses a

water trap to keep the relative humidity of the DMA sheath

flow below 20 % during the reported experiments. The Cal-

tech nano-radial DMA, the NAIS and the particle size magni-

fier used in Lehtipalo et al. (2016) do not deploy any humid-

ity conditioning for the sheath or sample flow, except for the

possible decrease in relative humidity as a result of a temper-

ature increase between the measurement device and chamber.

This effect occurred for all instruments to some extent, even

if the sampling lines were insulated. The effect of aerosol de-

hydration during the measurement is usually described by the

hygroscopic growth factor gf, relating the measured diameter

to the actual diameter

as follows:

From the measured aerosol size distributions, we inferred

particle growth rates using two complementary methods in

order to limit systematic biases in the analysis. In the first

method, particle growth rates were measured with the ap-

pearance time method, which requires a growing particle

population that can be clearly identified (Dada et al., 2020;

Lehtipalo et al., 2014; Stolzenburg et al., 2018). Figure S1d

demonstrates how the signal in each size channel is fitted

by an empirical sigmoidal shape curve estimating the time

at which 50 % of the maximum signal intensity is reached.

These appearance times are fitted with a linear function over

the size intervals from 1.8 to 3.2 and from 3.2 to 8 nm, with

the slope yielding an average growth rate over the interval

(shown in Fig. S1b). In the second method, we applied the

size- and time-resolving growth rate analysis method “IN-

SIDE” (INterpreting the change rate of the Size-Integrated

general Dynamic Equation; Pichelstorfer et al., 2018) to

cross-check our results. The INSIDE method uses the mea-

sured particle size distribution at a time

and simulates the

expected aerosol dynamics (coagulation, wall losses and di-

lution) until time

. By comparing this to the measured data

and evaluating the general dynamics equation, it in-

fers the condensational growth rate at specified diameters for

this time step. The time- and size-resolved growth rates for

each experiment were time-averaged for all sizes to yield a

statistically more robust result. Compared to the appearance

time method, INSIDE requires accurate absolute number size

distributions, whereas the appearance time method only de-

pends on the relative signal increase. However, INSIDE can

confirm the absence of systematic biases like changing pre-

cursor vapour concentrations or coagulation and wall loss ef-

fects. Therefore, a combined assessment with both methods

should yield a solid estimate of the observed growth rates.

https://doi.org/10.5194/acp-20-7359-2020

Atmos. Chem. Phys., 20, 7359–7372, 2020

7362

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

2.2 Growth model description

If the evaporation rates of the growing particles are effec-

tively zero due to the extremely low vapour pressure of the

condensing vapour, particle growth rates are limited by the

collision frequencies of vapour molecules with the growing

particles. Our description of particle growth follows the ap-

proach of Nieminen et al. (2010), which, in comparison to

the equations of mass transfer that can be found in e.g. Sein-

feld and Pandis (2016), include the non-negligible effect of

vapour molecular size using a collision frequency between

vapour and particle in analogy to coagulation theory (Lehti-

nen and Kulmala, 2003):

coll

(

)

[

]

coll

(

, d

)

π/

(1)

where

is the growing particle mass diameter,

and

are

the volume of the particle and vapour molecule respectively,

is the vapour monomer concentration and

coll

(

)

the kinetic collision frequency between particle and vapour.

Following Fuchs and Sutugin (1971), the collision frequency

for the transition regime is defined by

coll

(

)

(

)

(

)

(

377

)

(2)

where, according to Lehtinen and Kulmala (2003), the

Knudsen number (

) and mean free path (

) need to

be specified as

(

)

−

and

(

)

(

)

−

, which depend on the diameters

, the

masses

(within the calculation of the mean thermal ve-

locities

)

and the diffusion coefficients

of the col-

liding vapour molecules or particles respectively. Assuming

that the accommodation coefficient

is unity and relating the

volume

of the condensing monomer to its molecular mass

and (bulk) density

/ρ

, Eqs. (1) and (2) determine

the hard-sphere kinetic limit for particle growth.

We then additionally consider a collision enhancement of

neutral vapour monomers and particles due to attractive van

der Waals forces, where the collision frequency can be de-

scribed according to Sceats (1989):

coll

(

)





√

(

)

−

(

)





(3)

with the enhanced collision frequency for the continuum

regime described by

(

)

(

)

(4)

and the enhanced collision frequency for the kinetic regime

described by

(

)

(

)

(

)

∞

)

(5)

Equation (3) is designed such that it reaches the correct lim-

its of the free molecular and diffusion regime which is com-

parable to the approach of Fuchs and Sutugin (1971), i.e.

Eq. (2). However, it includes the collision enhancement fac-

tors

∞

)

and

)

. These factors can be linked to the at-

tractive potential of van der Waals forces. For the continuum

regime, this is done by solving the following integral:

(

)







∞

∫

(

)

(

)

exp

(

)







−

(6)

Here,

is the relative distance between the centres of the

two colliding entities, and

φ(x)

is the van der Waals potential

(Hamaker, 1937), which is expressed in terms of the vapour

and particle radii

(

)

=−

(

−

(

)

−

(

−

)

(

−

(

)

−

(

−

)

))

(7)

Chan and Mozurkewich (2001) provide a fit to the solution

of the numerically evaluated integral from Sceats (1989):

(

)

(

′

)

(

′

)

(8)

where

are the fit parameters, and

′

is the reduced

Hamaker constant, which relates to the Hamaker con-

stant

′

−

(

)

−

(Chan and

Mozurkewich, 2001; Hamaker, 1937). However, the mea-

surements of this study are conducted completely in the free

molecular regime; thus, the derivation of the continuum case

will not significantly affect our results. For the free molecular

regime enhancement factor

(

∞

)

, an overview of its rela-

tion to the Hamaker constant is given in Ouyang et al. (2012).

Chan and Mozurkewich (2001) also used a fit to the solution

from Sceats (1989) with the fit parameters

(

∞

)

√

′

√

′

(

′

)

(

′

)

(9)

In this study, we compare the results of Sceats (1989), who

used Brownian coagulation to describe the collisions, to the

simple ballistics approach of Fuchs and Sutugin (1965). In

that approach, the minimum distance

min

along the trajec-

tory of two colliding particles with impact parameter

Atmos. Chem. Phys., 20, 7359–7372, 2020

https://doi.org/10.5194/acp-20-7359-2020

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

7363

calculated from the conservation of angular momentum and

energy:

min

√

(

φ(x

min

)

μv

)

(10)

where

is the interaction potential,

is the reduced mass of

the colliding entities and

is their relative speed. The critical

impact parameter

crit

is obtained as the minimum value of

for which the minimum distance still takes a real value larger

than

(

)

. The enhancement factor is than related to the

critical impact parameter

crit

(

∞

)

crit

(

)

√

(11)

Note, that this approach is oversimplified, as the initial veloc-

ity of the colliding entities is assumed to be fixed but should

actually follow a (Maxwell–Boltzmann) distribution. How-

ever, Ouyang et al. (2012) concluded that the difference in

the derived Hamaker constant is almost negligible.

Using the description of an enhanced collision kernel, the

particle growth rates measured with the DMA-train can be

fitted with the Hamaker constant as the single free parameter

of the fit. As the theoretical growth rates are compared to

the appearance time growth rates, which are measured as a

time difference in signal appearance

over a certain size

interval

(ranging from

init

final

)

, a comparison with

experimental values requires the integration of Eq. (1):

(

init

final

)

(

final

−

init

)

final

∫

init

π/

coll

(

)

(12)

Equation (12) includes several properties of the condensing

vapour and the growing particles. Sulfuric acid molecules are

usually hydrated at typical ambient relative humidity. While

the thermodynamic model E-AIM (Extended Aerosol Inor-

ganics Model; Wexler et al., 2002) predicts an average of

two water molecules attached to a sulfuric acid monomer

at 298 K and 40 %–60 % relative humidity, quantum chem-

ical studies predict an average hydration of one to two water

molecules for these conditions (Henschel et al., 2014; Kurtén

et al., 2007; Temelso et al., 2012). Moreover, the hydra-

tion state of the particles in the chamber is also not directly

measured and might be altered during the sampling process,

which requires information on the hygroscopic growth factor

(see Sect. 2.1).

We examine the effect of hydration using three different

approaches. In the first naïve approach, we assume that no

dehydration occurs during measurement and that the parti-

cle sulfuric acid mass fraction is equal to the vapour mass

fraction, i.e.

, with

(assuming two water molecules attached to the sulfuric acid

monomer), where

and

are the molecular mass

of sulfuric acid and water respectively. In the second ap-

proach, we assume a dry measurement, and in this case the

growth of the measured dry particles is described by uptake

of sulfuric monomers only, i.e.

. However, for

the actual vapour and particle size used in the collision ker-

nel

coll

(

)

, the hydrated sizes are used. We again as-

sume an average hydration for the monomer with two water

molecules as above and an average hygroscopic growth fac-

tor of 1.25 for all particle sizes and RH values in our experi-

ments. The latter is an average value of the results of Biskos

et al. (2009) for highly acidic sulfuric acid sub-10 nm parti-

cles at 40 %–60 % relative humidity. In the third approach,

we consider that the extent of hydration might vary with

size and relative humidity. We use modelled composition

data from MABNAG (Model for Acid–Base chemistry in

Nanoparticle Growth; Yli-Juuti et al., 2013) in order to pre-

dict the sulfuric acid mass fraction

,T)

(see Fig. S4a)

and calculate the hygroscopic growth factor:

(

)

sol

(w(

),T

)

,T)

sol

(w(

,T),T)

)

(13)

where

sol

is a parametrization of the density of the sulfu-

ric acid–water solution (Myhre et al., 1998), and

,T)

and

)

are the mass fractions of sulfuric acid in

the growing and measured particles respectively. We follow

the considerations of Verheggen and Mozurkewich (2002) in

order to separate the growth by sulfuric acid addition and

water uptake by differentiating the hydrated particle volume

/(wρ

sol

)

. Both the numerator (particle sulfuric

acid mass

) and the denominator (sulfuric acid mass

fraction and solution density) depend on time. The addition

of sulfuric acid is again described in analogy to coagulation

theory, resulting in

coll

(

)

−

πd

d ln

(

wρ

)

coll

(

)

−

πd

d ln

(wρ)

(14)

Equation (14) contains a first term for the addition of pure

sulfuric acid and a second term for water uptake. It can be

solved for the particle growth rate

coll

(

)

(

)

(

)

(

d ln

(

wρ

)

(15)

In this case, we assume

, but we use the hy-

drated monomer diameter

in the collision kernel. For the

particles, we now use the hydrated size, i.e.

with

gf and

(

)

taken from the model. We compare the

MABNAG predictions in Fig. S4b with SAWNUC (Sulfuric

Acid Water Nucleation model; Ehrhart et al., 2016), which

https://doi.org/10.5194/acp-20-7359-2020

Atmos. Chem. Phys., 20, 7359–7372, 2020

7364

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

only takes sulfuric acid and water into account, whereas

MABNAG also includes ammonia. MABNAG predicts a sig-

nificantly lower water content at larger sizes (

5 nm), even

at 3 pptv ammonia. In addition, previous experiments in the

CLOUD chamber have suggested that even background level

ammonia has an influence on the hygroscopic growth factor

(Kim et al., 2016); this is similar to Biskos et al. (2009),

who also indicated some extent of neutralization for sub-

10 nm particles at low ammonia. Due to the presumably bet-

ter prediction of the particle hydration by MABNAG for sizes

larger than 2.5 nm, we choose the results from Fig. S4a, even

if they might overestimate the hydration at small sizes. We

have neglected the effect of ammonia addition on collisions

in all three approaches so far, but we test the assumption

and different vapour hydra-

tions in our systematic uncertainties estimate in Fig. S5. All

of the parameters for vapour and particles used for all ap-

proaches are summarized in Table S1 in the Supplement.

2.3 Global model description

We implement the results of our growth rate measurements

for sulfuric-acid-driven growth in a global model (Mann

et al., 2010; Mulcahy et al., 2018), which includes sulfu-

ric acid–water binary nucleation. However, the model does

not include ternary nucleation schemes (Dunne et al., 2016)

and pure biogenic nucleation (Gordon et al., 2016) and will,

therefore, underestimate the impact of nucleation on the

global aerosol and CCN budget. In the model, growth be-

tween the nucleation size and 3 nm is treated with the equa-

tion from Kerminen and Kulmala (2002), which gives the

fraction of particles surviving to 3 nm at a given growth and

loss rate. Here, as a baseline case, we use the geometric hard-

sphere kinetic growth rate based on bulk density (Eqs. 1–2)

and compare this to the collision-enhanced growth (Eqs. 3–

9). For larger sizes, aerosol growth in the model is calcu-

lated by solving the condensation equations. Therefore, no

direct growth parametrization can be altered, but as conden-

sational growth scales linearly with the diffusion coefficient

of the condensing vapour, we increased sulfuric acid diffu-

sion for condensation in the nucleation mode (2–10 nm) and

in the Aitken mode (10–100 nm). The enhancement factors

are derived for the median diameters of the modes (7.6 and

57 nm respectively) at the cloud-base level (1 km). However,

this constant factor of increase in the diffusion coefficient

(and, hence, flux onto particles) for all particles of the en-

tire mode might underestimate the impact of the collision

enhancement. Rapid growth is increasingly important for the

smallest particles, which actually have a higher collision en-

hancement than particles with the size of the mode median

diameters.

3 Results

3.1 Collision enhancement

Figure 1 shows the particle growth rates for two size inter-

vals (Fig. 1a, 1.8–3.2 nm mobility diameter; Fig. 1b, 3.2–

8.0 nm mobility diameter) versus the sulfuric acid monomer

concentration, which correlate linearly. No significant depen-

dence on temperature, ionization levels in the chamber or

the concentration of ammonia is evident. While the effect

of temperature expected from theory is small and cannot be

discerned within the statistical uncertainties of our measure-

ments (Nieminen et al., 2010), the insignificant influence of

ammonia and the ionization level on the growth rate differs

from previous findings (Lehtipalo et al., 2016).

We compare the measured growth rates from this study

with the results from Lehtipalo et al. (2016) in Fig. S2. In

contrast to our results, elevated ammonia (

∼

1000 pptv) led

to increased growth rates in that study. The major differ-

ence is the narrower size range for the growth rate mea-

surements (1.5–2.5 nm mobility diameter) due to different

instrumentation. For smaller sizes and at low ammonia, sul-

furic acid evaporation likely plays a role due to an increased

Kelvin term. The stabilizing effect of ammonia is certainly

relevant at the sizes of the nucleating clusters (Kirkby et

al., 2011). For our results, we confirm the absence of sig-

nificant evaporation rates above 2 nm using an independent

experiment presented in Fig. 2. This demonstrates that, in

the absence of gas-phase sulfuric acid, the coagulation- and

dilution-corrected loss rates of particles (

meas

tot

−

dil

−

avg

coag

)

over all sizes follow the expected size dependence of wall

losses which is inferred from the sulfuric acid monomer de-

cay. Evaporation would cause another term and would distort

the balance equation (also depending on the relative abun-

dances of the particles during the decay), causing a deviation

from the expected wall loss rate.

The insignificant effect of ammonia on growth (Fig. 1)

and the same high ratio (

100, Fig. S3a) between sulfuric

acid monomer and dimer concentrations for all experiments

point towards a negligible influence of clustering on our mea-

sured growth rates (Li and McMurry, 2018). Moreover, in

Fig. S3b, using a model including sulfuric acid/ammonia

clustering and evaporation, we show that no cluster contri-

bution is indeed expected, even at elevated ammonia concen-

trations (Kürten, 2019).

In the absence of evaporation and strong clustering, our

growth rate data provide a direct measurement of the con-

densational growth at the kinetic limit caused by sulfuric

acid monomers only. We find the measured growth rates

both with and without the addition of ammonia to be signif-

icantly above the geometric hard-sphere limit (Eqs. 1–2) of

kinetic condensation (Nieminen et al., 2010). For this com-

parison, we followed a naïve approach, assuming an aver-

age hydration of the monomer by two water molecules and

applied the resulting mass fraction to find the bulk density

Atmos. Chem. Phys., 20, 7359–7372, 2020

https://doi.org/10.5194/acp-20-7359-2020

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

7365

Figure 1.

Growth rates of nanoparticles in two size intervals ver-

sus the measured gas-phase sulfuric acid monomer concentration.

Panel

(a)

shows growth rates for the size interval between 1.8

and 3.2 nm (mobility diameter; 1.5–2.9 nm in mass diameter), and

panel

(b)

shows growth rates for the size interval between 3.2

and 8.0 nm (mobility diameter; 2.9–7.7 nm in mass diameter). The

colour code represents the measured NH

concentration during the

growth period. Squares are measurements at 20

◦

C, and circles are

measurements at 5

◦

C. Filled symbols represent runs under ambient

galactic cosmic ray ionization levels, and open symbols represent

runs under neutral conditions. Error bars for the data points repre-

sent the statistical uncertainty in the appearance time growth rate

measurements and the maximum variation of the sulfuric acid con-

centration during the growth period, also explaining the slight de-

viations from linearity at high sulfuric acid concentrations, where

stable conditions are not fully reached. The black line shows the ge-

ometric limit of kinetic condensation assuming the same hydration

for the condensing cluster and the measured particles (Nieminen et

al., 2010). The red solid line shows the fit of Eq. (12) to the data with

the Hamaker constant as the free parameter assuming a Brownian

coagulation model for the enhanced collision kernel (Sceats, 1989),

whereas the red dashed line uses a ballistics approach (Fuchs and

Sutugin, 1965).

(Myhre et al., 1998). The observed enhancement is simi-

lar to Lehtipalo et al. (2016) in the case where evaporation

was suppressed by ammonia (see Fig. S2). We also mea-

sure a growth rate enhancement for the larger size range

(Fig. 1b), which should be less sensitive to evaporation. The

faster growth rates might be due to an enhanced collision

frequency, which can be attributed to van der Waals forces,

either permanent dipole–(induced) dipole interactions be-

tween polar sulfuric acid molecules and particles or Lon-

Figure 2.

Measurement of zero sulfuric acid evaporation rates. The

total loss rates of sulfuric acid and ammonia particles (with the mo-

bility diameter shown on the

axis) were measured during a de-

cay experiment (5

◦

C, 60 % relative humidity, 1000 pptv NH

) by

switching off the UV lights after a particle growth stage, which

stops the production of sulfuric acid and, subsequently, nucleation

and growth. After sulfuric acid was reduced to the background level,

the exponential decay rate of the remaining particles in the cham-

ber was measured (

meas

tot

, blue circles), which was not possible for

the 1.8 nm channel due to low statistics. Decay of particles in the

chamber is dominated by wall loss, dilution loss and coagulation

loss to other particles. Particle loss rates are corrected for an aver-

aged coagulation loss during the decay (

avg

coag

) to all particles larger

than

and for the dilution loss (

dil

; turquoise circles). They agree

well with the expected wall loss rate

wall

(

)

wall

√

)

(red dashed line) with

wall

0077 s

−

inferred from an

independent sulfuric acid decay experiment in the absence of a par-

ticle sink, where the mobility diameter is assumed to be 0.82 nm

(Ehrhart et al., 2016; turquoise diamond). This suggests that there

is negligible evaporation from the sulfuric acid particles above ca.

2 nm under the above-mentioned experimental conditions, which

would introduce another term that disturbs the balance equation at

each size. As all of our growth rate measurements, independent of

the ammonia concentration and temperature, fall on the same line

(see Fig. 1), this also points towards negligible evaporation effects

at reduced ammonia levels (below 10 pptv) and up to 20

◦

don dispersion forces (London, 1937). The magnitude of

the enhancement is described by the Hamaker constant

(Hamaker, 1937), which we use as the single free parame-

ter to fit a collision-enhanced kinetic limit. For the Brown-

ian coagulation model linking the Hamaker constant to the

collision kernel, i.e. Eqs. (3)–(9) (Sceats, 1989), we find

(

stat

))

−

J. If we apply a ballistics ap-

proach in the free molecular regime (Fuchs and Sutugin,

1965; Ouyang et al., 2012), we derive a slightly higher value

−

J, but both yield comparable values to

previous results (Chan and Mozurkewich, 2001; McMurry,

1980).

An enhancement due to charge–dipole interactions be-

tween the polar sulfuric acid monomers and charged particles

is not significant in our total (neutral plus charged particle)

growth rate measurements (as shown in Fig. 1), where we ob-

https://doi.org/10.5194/acp-20-7359-2020

Atmos. Chem. Phys., 20, 7359–7372, 2020

7366

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

Figure 3.

The effect of charge on growth. Measured growth rates

of 1.8–3.2 nm (mobility diameter) particles and ions in experiments

with ammonia above 25 pptv. The DMA-train measures both neutral

and charged particles (diamonds), whereas the NAIS

−

(Man-

ninen et al., 2009) measures purely charged particles (triangles).

Both the positively and negatively charged particle population have

a faster apparent growth rate than the total particle population due

to an enhanced collision rate from charge–dipole interactions. We

measure a multiplicative charge enhancement factor of 1.45 in this

size range with a combined fit to both polarities (red dotted line),

which is consistent with estimates from average dipole orientation

theory (Nadykto and Yu, 2003). At galactic cosmic rays ionization

levels in the chamber, the charged fraction of the growing particles

in the size range from 1.8 to 3.2 nm (mobility diameter) is between

5 % and 25 %. This is demonstrated by the colour code which in-

dicates the integrated total or ion number concentration over the

growth rate size interval averaged during the growth period. There-

fore, the fit of the appearance time for the total particle population

is affected on a minor level by the small, earlier appearing charged

fraction.

serve no difference between growth rates under neutral and

galactic cosmic ray ionization levels. From average dipole

orientation theory (Su and Bowers, 1973), a small enhance-

ment is expected in the collision frequency for charged parti-

cles above 2 nm (Nadykto and Yu, 2003), which should affect

the growth rate (Laakso et al., 2003; Lehtipalo et al., 2016).

We find an enhancement factor of 1.45 by comparing the to-

tal to the ion growth rate (as shown in Fig. 3), which is in

good agreement with theory. However, the total growth rate

is influenced on a minor level by faster ion growth because,

at the representative galactic cosmic ray ionization levels and

sulfuric acid concentrations in our experiments, most (more

than 75 %) of the growing particles are neutral (see Fig. 3).

However, the effects of ion condensation and charge–dipole

enhancement might be stronger at lower sulfuric acid con-

centrations (Svensmark et al., 2017).

3.2 Size dependence and hydration effects

Condensational growth at the geometric kinetic limit predicts

increasing growth rates with decreasing particle sizes due to

the non-negligible effect of vapour molecule size on the col-

lision cross section (Nieminen et al., 2010), which has not

yet been shown experimentally. Furthermore, the collision

enhancement due to van der Waals forces and the collision

enhancement due to charge–dipole interactions also depend

on the comparative size of the condensing vapour and the

growing particle. Figure 4a illustrates the theoretical predic-

tions of the size dependence of the collision rate of sulfuric

acid monomers with larger particles, including van der Waals

forces and charge–dipole interactions. The enhancement fac-

tor compared to the hard-sphere kinetic limit is shown for

both the Brownian coagulation model (Sceats, 1989) and the

ballistics approach (Fuchs and Sutugin, 1965), which is 2.1

and 2.3 for the free molecular regime respectively, and is

comparable to previous experimental results (Kürten et al.,

2014; Lehtipalo et al., 2016) and quantum chemical calcula-

tions (Halonen et al., 2019).

In addition to the approach for calculating the kinetic en-

hancement factor, the description of particle hydration might

also play a crucial role. Until now, we have used the naïve

assumption that vapour and particle hydration are the same

and that particles are measured at their hydrated size. How-

ever, during sampling the measured particles are potentially

dried. To investigate the effect of particle hydration, we use

the DMA-train data from Fig. 1 to fit the collision enhance-

ment for two alternative approaches: one approach where we

assume that particles are measured dry and one approach

where we separate the uptake of water and sulfuric acid con-

densation (Verheggen and Mozurkewich, 2002) using mod-

elled particle composition data from SAWNUC (Ehrhart et

al., 2016) or MABNAG (Yli-Juuti et al., 2013). We compare

the predictions for the size dependence of all approaches with

the measured growth rates of all instruments normalized to

a sulfuric acid concentration of 10

−

in Fig. 4b. In ad-

dition, we show the growth rates using the time- and size-

resolving growth rate analysis method INSIDE (Pichelstorfer

et al., 2018), which agrees with the appearance time method,

demonstrating a minor systematic bias in our growth rate de-

termination. All approaches reproduce the size dependence

at an acceptable level (

larger than 0.87). The separa-

tion approach yields higher growth rates at the smallest sizes

due to the overestimation of hydration by MABNAG below

2.5 nm. However, for SAWNUC composition data, which

presumably describe the cluster hydration better, the

only 0.66 and does not reproduce the observed size depen-

dence. This is possibly caused by the overly high hydration

assumed for larger sizes. Thus, the simple dry measurement

approach might be a good approximation for the predictions

of both MABNAG and SAWNUC for the size range of inter-

est (see Fig. S4b). We estimate the systematic uncertainty of

the results in Fig. S5, including the effects of different vapour

hydration, ammonia addition and sulfuric acid measurement

uncertainty. All approaches overlap largely within their sys-

tematic uncertainties with

(

−

(

syst

)

−

J as

the best estimate of a combined assessment (assuming the

Brownian coagulation model). We also give a first-order ap-

Atmos. Chem. Phys., 20, 7359–7372, 2020

https://doi.org/10.5194/acp-20-7359-2020

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

7367

Figure 4.

The size dependence of sulfuric acid growth.

Panel

(a)

shows the theoretical collision rate of hydrated sulfuric

acid vapour molecules (

) with particles of

a certain mass diameter. The black line represents the hard-sphere

limit, the red solid line also includes a collision enhancement due

to van der Waals forces based on the approach of Sceats (1989;

−

J), and the red dashed line is based on the approach

of Fuchs and Sutugin (1965;

−

J). The red dotted

line additionally includes charge–dipole interactions based on av-

erage dipole orientation theory. The blue lines show the enhance-

ment factor of a single attractive force compared to the hard-sphere

limit. Panel

(b)

shows the measured size dependence of growth rates

normalized to a sulfuric acid concentration of 10

−

. The solid

blue line shows the growth rates inferred using the INSIDE method.

Filled boxes represent the appearance time growth rates from the

DMA-train used to fit the Hamaker constant. Empty boxes represent

the appearance time growth rates from other instruments, includ-

ing the results from Lehtipalo et al. (2016) with high (

100 pptv)

concentrations. The boxes indicate the median and the 50 %

interquartile range of the data, whereas the whiskers represent the

90 % quantile. The small red error bars indicate the

−

33 %/

50 %

systematic uncertainty in the sulfuric acid measurement. We show

the size dependence of three different approaches for particle hy-

groscopicity: the naïve approach (solid turquoise line), assuming

the same hydration for vapour and particle; the dry measurement

approach (solid light green line), assuming that the DMA-train mea-

sures completely dehydrated particles; and the separation approach

(solid yellow line), assuming that available composition data from

MABNAG can disentangle water uptake from sulfuric acid conden-

sation. The separation approach using SAWNUC composition data

is also shown as a dashed yellow line.

proximation for our measured growth rates and their size de-

pendence for the conditions in our experiments:

(

nm h

−

)

[

(

)

−

]

[

(

−

)

−

]

(16)

3.3 Global implications

The observed steep increase of the growth rates with de-

creasing size shows that the collision enhancement due to

van der Waals forces is especially important for the small-

est particles. As these are the most vulnerable for losses

to pre-existing aerosols, their survival probability in the

atmosphere is directly affected, altering the CCN budget

(Pierce and Adams, 2007) or promoting NPF in urban en-

vironments (Kulmala et al., 2017). In order to test the ef-

fects of collision enhancement on sulfuric acid growth on

a global scale, we use the atmosphere-only configuration of

the United Kingdom Earth System Model (UKESM1; Mulc-

ahy et al., 2018; Walters et al., 2019) which includes the

GLOMAP (Global Model of Aerosol Processes) aerosol mi-

crophysics module describing nucleation and growth (Mann

et al., 2010). Figure 5 illustrates the global model results

comparing the baseline case (no collision enhancement) with

a collision enhancement simulation (with enhancement fac-

tors of 2.2, 1.8 and 1.3 for the cluster, nucleation and Aitken

modes respectively) for the present-day atmosphere. The ab-

solute particle number concentrations averaged over all lon-

gitudes are shown in Fig. 5a, indicating changes of more

than 50 %, especially at high altitudes (

10 km; Fig. 5b)

where most aerosol particles originate from pure sulfuric-

acid-driven NPF. The importance of the nucleation process

and, therefore, the growth rate enhancement is lower at lower

altitudes and in the Northern Hemisphere, which is mainly

due to the higher condensation sink and the restriction of

the model to sulfuric acid–water binary nucleation. However,

the significant enhancement of sulfuric-acid-driven nanopar-

ticle growth in the upper troposphere may be important in

quantifying sources of stratospheric aerosols and cirrus CCN

(Brock et al., 1995; Deshler, 2008) and needs to be accounted

for in future model development.

4 Discussion

Understanding nanoparticle growth driven by sulfuric acid

is extremely important for modelling the present-day atmo-

sphere. Our measured growth rates cover a wide range of

representative atmospheric conditions below 20

◦

C and re-

veal that sulfuric acid growth proceeds faster than the ge-

ometric hard-sphere kinetic limit. These faster growth rates

in the cluster size range could be partially responsible for

the occurrence of NPF in polluted environments (Kulmala

et al., 2017). Our results suggest that this collision enhance-

ment due to van der Waals forces can be more important

https://doi.org/10.5194/acp-20-7359-2020

Atmos. Chem. Phys., 20, 7359–7372, 2020

7368

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

Figure 5.

Increased global aerosol number concentrations due to collision enhancement. Results from a global modelling study of the

present-day atmosphere. Panel

(a)

shows the relative change in the total aerosol number concentration (particles larger 3 nm) averaged over

all longitudes in a vertical profile if collision enhancement is considered in sulfuric acid growth. Panel

(b)

shows the relative increase at an

altitude of 15 km on a global scale where the effects are most significant. Higher relative changes would also be expected at lower altitudes

if the model is adjusted for ternary sulfuric acid–water–ammonia nucleation.

than charge–dipole interactions or base stabilization by am-

monia for sizes larger than 2 nm. However, a better knowl-

edge of the chemical composition of the condensing vapour

and growing sub-10 nm particles could further improve our

understanding of molecular collision rates. For smaller sizes,

the evaporation of sulfuric acid and charge effects need to be

considered, but the size range covered by our measurements

is sufficient for the global model used, which nucleates par-

ticles at 1.7 nm. We find significantly increased upper tropo-

spheric aerosol concentrations, but the global impact of van

der Waals forces in nanoparticle growth might be even higher

due to the model limitations to binary sulfuric acid–water nu-

cleation. Therefore, our results should be considered in fu-

ture model development, especially when discussing the im-

portance of changing sulfuric acid levels due to the reduced

anthropogenic emissions of SO

. Moreover, our parametriza-

tion of pure sulfuric acid growth rates will help to identify the

contribution of other co-condensing vapours in ambient and

laboratory experiments to growth, as they set a new baseline

for the kinetic condensation of sulfuric acid. Several simpli-

fications have often been applied to kinetic particle growth,

including hard-sphere collision based on bulk density and the

omission of vapour size in the collision cross section; our re-

sults provide clear experimental verification that these sim-

plifications are no longer fit for increasingly accurate mea-

surements at these tiny yet critical sizes.

Data availability.

All of the datasets presented in this paper are

available from the corresponding author upon reasonable request.

Supplement.

The supplement related to this article is available on-

line at: https://doi.org/10.5194/acp-20-7359-2020-supplement.

Author contributions.

DS, MSim, AK, KL, HF, XH, SBri, MX,

RB, AB, SBrä, LCM, DC, BC, AD, JDo, JDu, IEH, LF, LGC, MH,

CK, WK, HL, CPL, ML, ZL, VM, HEM, TM, EP, JP, MP, MPR,

SScho, SSchu, JS, MSip, GS, YS, YJT, AT, ACW, MW, YW, SKW,

DW, PJW, YW, QY, MZW, UB, JC, RCF, RV, JK and PMW pre-

pared the CLOUD facility or measuring instruments. DS, MSim,

AR, KL, XH, SBri, MX, AA, RB, AB, LB, SBrä, LCM, DC, LD,

AD, JDu, IEH, HF, LF, LGC, MH, CK, TKK, WK, HL, CPL, ML,

ZL, HEM, RM, TM, WN, EP, JP, MPR, BR, SSchu, GS, CT, YJT,

AT, MVP, ACW, MW, SKW, DW, PJW, YW, QY and MZW col-

lected the data. DS, MSim, AR, HG, TN, LP, LD, HF, SE, MH, CK,

ACW and SKW analysed the data. DS, MS, AR, AK, KL, TN, XH,

MX, JDo, JDu, IEH, TKK, TP, MPR, MSip, UB, KSC, JC, NMD,

RCF, AH, MK, JL, RV, JK and PMW were involved in the scien-

tific discussion and the interpretation of the data. DS, AK, KL, HG,

NMD, JK and PMW wrote the paper.

Competing interests.

The authors declare that they have no conflict

of interest.

Special issue statement.

This article is part of the special issue

“The CERN CLOUD experiment (ACP/AMT inter-journal SI)”. It

is not associated with a conference.

Acknowledgements.

We thank CERN for supporting CLOUD with

technical and financial resources and for providing a particle

beam from the CERN Proton Synchrotron. We are also grate-

ful to Patrick Carrie, Louis-Philippe De Menezes, Jonathan Du-

mollard, Katja Ivanova, Francisco Josa, Timo Keber, Ilia Krasin,

Robert Kristic, Abdelmajid Laassiri, Osman Maksumov, Ben-

jamin Marichy, Herve Martinati, Robert Sitals, Albin Wasem,

Sergey Vitaljevich Mizin and Mats Wilhelmsson for their contri-

butions to the experiment.

Atmos. Chem. Phys., 20, 7359–7372, 2020

https://doi.org/10.5194/acp-20-7359-2020

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

7369

Financial support.

This research has received funding from

the European Commission Seventh Framework Programme

and the European Union’s Horizon 2020 programme (Marie

Skłodowska-Curie action no. 764991 “CLOUD-MOTION”;

MC-COFUND grant no. 665779 and ERC projects nos. 616075

“NANODYNAMITE”

and

714621

“GASPARCON”),

the

German Federal Ministry of Education and Research (grant

no. 01LK1601A “CLOUD-16”), the Swiss National Science

Foundation

(project

nos.

200020_152907,

20FI20_159851,

200021_169090, 200020_172602 and 20FI20_172622), the

Academy of Finland (project nos. 296628, 299574, 307331 and

310682), the Austrian Science Fund (FWF; project nos. J-3951,

P27295-N20 and J-4241), the Portuguese Foundation for Science

and Technology (FCT; project no. CERN/FIS-COM/0014/2017),

the U.S. National Science Foundation (grant nos. AGS-1649147,

AGS-1801280, AGS-1602086 and AGS-1801329). Open access

funding was provided by University of Vienna.

Review statement.

This paper was edited by Jonathan Abbatt and

reviewed by David R. Hanson and two anonymous referees.

References

Biskos, G., Buseck, P. R., and Martin, S. T.: Hygroscopic growth

of nucleation-mode acidic sulfate particles, J. Aerosol Sci., 40,

338–347, https://doi.org/10.1016/j.jaerosci.2008.12.003, 2009.

Breitenlechner, M., Fischer, L., Hainer, M., Heinritzi, M., Curtius,

J., and Hansel, A.: PTR3: An Instrument for Studying the Lifecy-

cle of Reactive Organic Carbon in the Atmosphere, Anal. Chem.,

89, 5824–5831, https://doi.org/10.1021/acs.analchem.6b05110,

2017.

Brock, C. A., Hamill, P., Wilson, J. C., Jonsson, H. H., and Chan,

K. R.: Particle Formation in the Upper Tropical Troposphere:

A Source of Nuclei for the Stratospheric Aerosol, Science,

270, 1650–1653, https://doi.org/10.1126/science.270.5242.1650,

1995.

Brunelli, N. A., Flagan, R. C., and Giapis, K. P.: Ra-

dial Differential Mobility Analyzer for One Nanome-

ter Particle Classification, Aerosol Sci. Tech., 43, 53–59,

https://doi.org/10.1080/02786820802464302, 2009.

Bzdek, B. R., Horan, A. J., Pennington, M. R., DePalma, J. W.,

Zhao, J., Jen, C. N., Hanson, D. R., Smith, J. N., McMurry, P. H.,

and Johnston, M. V: Quantitative and time-resolved nanoparticle

composition measurements during new particle formation, Fara-

day Discuss., 165, 25–43, https://doi.org/10.1039/C3FD00039G,

2013.

Chan, T. W. and Mozurkewich, M.: Measurement of the co-

agulation rate constant for sulfuric acid particles as a func-

tion of particle size using tandem differential mobility analy-

sis, J. Aerosol Sci., 32, 321–339, https://doi.org/10.1016/S0021-

8502(00)00081-1, 2001.

Dada, L., Lehtipalo, K., Kontkanen, J., Nieminen, T., Baalbaki,

R., Ahonen, L., Duplissy, J., Yan, C., Chu, B., Petäjä, T.,

Lehtinen, K., Kerminen, V.-M., Kulmala, M., and Kangaslu-

oma, J.: Formation and growth of sub-3-nm aerosol parti-

cles in experimental chambers, Nat. Protoc., 15, 1013–1040,

https://doi.org/10.1038/s41596-019-0274-z, 2020.

Deshler,

T.:

review

global

stratospheric

aerosol:

Measurements,

importance,

life

cycle,

and

local

stratospheric

aerosol,

Atmos.

Res.,

90,

223–232,

https://doi.org/10.1016/j.atmosres.2008.03.016, 2008.

Dunne, E. M., Gordon, H., Kürten, A., Almeida, J., Duplissy,

J., Williamson, C., Ortega, I. K., Pringle, K. J., Adamov, A.,

Baltensperger, U., Barmet, P., Benduhn, F., Bianchi, F., Breit-

enlechner, M., Clarke, A., Curtius, J., Dommen, J., Donahue,

N. M., Ehrhart, S., Flagan, R. C., Franchin, A., Guida, R.,

Hakala, J., Hansel, A., Heinritzi, M., Jokinen, T., Kangasluoma,

J., Kirkby, J., Kulmala, M., Kupc, A., Lawler, M. J., Lehti-

palo, K., Makhmutov, V., Mann, G., Mathot, S., Merikanto,

J., Miettinen, P., Nenes, A., Onnela, A., Rap, A., Reddington,

C. L. S., Riccobono, F., Richards, N. A. D., Rissanen, M. P.,

Rondo, L., Sarnela, N., Schobesberger, S., Sengupta, K., Simon,

M., Sipilä, M., Smith, J. N., Stozkhov, Y., Tomé, A., Tröstl,

J., Wagner, P. E., Wimmer, D., Winkler, P. M., Worsnop, D.

R., and Carslaw, K. S.: Global atmospheric particle formation

from CERN CLOUD measurements, Science, 354, 1119–1124,

https://doi.org/10.1126/science.aaf2649, 2016.

Duplissy, J., Merikanto, J., Franchin, A., Tsagkogeorgas, G., Kan-

gasluoma, J., Wimmer, D., Vuollekoski, H., Schobesberger,

S., Lehtipalo, K., Flagan, R. C., Brus, D., Donahue, N. M.,

Vehkamäki, H., Almeida, J., Amorim, A., Barmet, P., Bianchi,

F., Breitenlechner, M., Dunne, E. M., Guida, R., Henschel, H.,

Junninen, H., Kirkby, J., Kürten, A., Kupc, A., Määttänen, A.,

Makhmutov, V., Mathot, S., Nieminen, T., Onnela, A., Pra-

plan, A. P., Riccobono, F., Rondo, L., Steiner, G., Tome, A.,

Walther, H., Baltensperger, U., Carslaw, K. S., Dommen, J.,

Hansel, A., Petäjä, T., Sipilä, M., Stratmann, F., Vrtala, A., Wag-

ner, P. E., Worsnop, D. R., Curtius, J., and Kulmala, M.: Ef-

fect of ions on sulfuric acid-water binary particle formation: 2.

Experimental data and comparison with QC-normalized classi-

cal nucleation theory, J. Geophys. Res.-Atmos., 121, 1752–1775,

https://doi.org/10.1002/2015JD023539, 2016.

Ehrhart, S., Ickes, L., Almeida, J., Amorim, A., Barmet, P.,

Bianchi, F., Dommen, J., Dunne, E. M., Duplissy, J., Franchin,

A., Kangasluoma, J., Kirkby, J., Kürten, A., Kupc, A., Lehti-

palo, K., Nieminen, T., Riccobono, F., Rondo, L., Schobes-

berger, S., Steiner, G., Tomé, A., Wimmer, D., Baltensperger,

U., Wagner, P. E., and Curtius, J.: Comparison of the

SAWNUC model with CLOUD measurements of sulphuric acid-

water nucleation, J. Geophys. Res.-Atmos., 121, 12401–12414,

https://doi.org/10.1002/2015JD023723, 2016.

Fuchs, N. A. and Sutugin, A. G.: Coagulation rate of

highly dispersed aerosols, J. Colloid Sci., 20, 492–500,

https://doi.org/10.1016/0095-8522(65)90031-0, 1965.

Fuchs, N. A. and Sutugin, A. G.: High dispersed aerosols, in: Topics

in Current Aerosol Research (Part 2), edited by: Hidy, G. M. and

Brock, J. R., 1–200, Pergamon, New York, 1971.

Gordon, H., Sengupta, K., Rap, A., Duplissy, J., Frege, C.,

Williamson, C., Heinritzi, M., Simon, M., Yan, C., Almeida,

J., Tröstl, J., Nieminen, T., Ortega, I. K., Wagner, R., Dunne,

E. M., Adamov, A., Amorim, A., Bernhammer, A.-K., Bianchi,

F., Breitenlechner, M., Brilke, S., Chen, X., Craven, J. S., Dias,

A., Ehrhart, S., Fischer, L., Flagan, R. C., Franchin, A., Fuchs,

C., Guida, R., Hakala, J., Hoyle, C. R., Jokinen, T., Junninen,

H., Kangasluoma, J., Kim, J., Kirkby, J., Krapf, M., Kürten,

A., Laaksonen, A., Lehtipalo, K., Makhmutov, V., Mathot, S.,

https://doi.org/10.5194/acp-20-7359-2020

Atmos. Chem. Phys., 20, 7359–7372, 2020

7370

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

Molteni, U., Monks, S. A., Onnela, A., Peräkylä, O., Piel, F.,

Petäjä, T., Praplan, A. P., Pringle, K. J., Richards, N. A. D.,

Rissanen, M. P., Rondo, L., Sarnela, N., Schobesberger, S.,

Scott, C. E., Seinfeld, J. H., Sharma, S., Sipilä, M., Steiner,

G., Stozhkov, Y., Stratmann, F., Tomé, A., Virtanen, A., Vogel,

A. L., Wagner, A. C., Wagner, P. E., Weingartner, E., Wim-

mer, D., Winkler, P. M., Ye, P., Zhang, X., Hansel, A., Dom-

men, J., Donahue, N. M., Worsnop, D. R., Baltensperger, U.,

Kulmala, M., Curtius, J., and Carslaw, K. S.: Reduced anthro-

pogenic aerosol radiative forcing caused by biogenic new par-

ticle formation, P. Natl. Acad. Sci. USA, 113, 12053–12058,

https://doi.org/10.1073/pnas.1602360113, 2016.

Gordon, H., Kirkby, J., Baltensperger, U., Bianchi, F., Breit-

enlechner, M., Curtius, J., Dias, A., Dommen, J., Donahue,

N. M., Dunne, E. M., Duplissy, J., Ehrhart, S., Flagan, R.

C., Frege, C., Fuchs, C., Hansel, A., Hoyle, C. R., Kul-

mala, M., Kürten, A., Lehtipalo, K., Makhmutov, V., Molteni,

U., Rissanen, M. P., Stozkhov, Y., Tröstl, J., Tsagkogeor-

gas, G., Wagner, R., Williamson, C., Wimmer, D., Winkler,

P. M., Yan, C., and Carslaw, K. S.: Causes and importance

of new particle formation in the present-day and preindus-

trial atmospheres, J. Geophys. Res.-Atmos., 122, 8739–8760,

https://doi.org/10.1002/2017JD026844, 2017.

Guo, S., Hu, M., Zamora, M. L., Peng, J., Shang, D., Zheng,

J., Du, Z., Wu, Z., Shao, M., Zeng, L., Molina, M. J.,

and Zhang, R.: Elucidating severe urban haze formation

in China, P. Natl. Acad. Sci. USA, 111, 17373–17378,

https://doi.org/10.1073/pnas.1419604111, 2014.

Halonen, R., Zapadinsky, E., Kurtén, T., Vehkamäki, H., and Reis-

chl, B.: Rate enhancement in collisions of sulfuric acid molecules

due to long-range intermolecular forces, Atmos. Chem. Phys.,

19, 13355–13366, https://doi.org/10.5194/acp-19-13355-2019,

2019.

Hamaker, H. C.: The London–van der Waals attraction

between

spherical

particles,

Physica,

1058–1072,

https://doi.org/10.1016/S0031-8914(37)80203-7, 1937.

Henschel, H., Navarro, J. C. A., Yli-Juuti, T., Kupiainen-Määttä,

O., Olenius, T., Ortega, I. K., Clegg, S. L., Kurtén, T., Riip-

inen, I., and Vehkamäki, H.: Hydration of Atmospherically Rel-

evant Molecular Clusters: Computational Chemistry and Clas-

sical Thermodynamics, J. Phys. Chem. A, 118, 2599–2611,

https://doi.org/10.1021/jp500712y, 2014.

Jen, C. N., McMurry, P. H., and Hanson, D. R.: Stabilization of

sulfuric acid dimers by ammonia, methylamine, dimethylamine,

and trimethylamine, J. Geophys. Res.-Atmos., 119, 7502–7514,

https://doi.org/10.1002/2014JD021592, 2014.

Jokinen, T., Sipilä, M., Junninen, H., Ehn, M., Lönn, G., Hakala,

J., Petäjä, T., Mauldin III, R. L., Kulmala, M., and Worsnop,

D. R.: Atmospheric sulphuric acid and neutral cluster measure-

ments using CI-APi-TOF, Atmos. Chem. Phys., 12, 4117–4125,

https://doi.org/10.5194/acp-12-4117-2012, 2012.

Jokinen, T., Sipilä, M., Kontkanen, J., Vakkari, V., Tisler, P., Du-

plissy, E., and Junninen, H.: Ion-induced sulfuric acid – ammo-

nia nucleation drives particle formation in coastal Antarctica, Sci.

Adv., 4, eaat9744, https://doi.org/10.1126/sciadv.aat9744, 2018.

Kangasluoma, J. and Kontkanen, J.: On the sources of uncertainty

in the sub-3nm particle concentration measurement, J. Aerosol

Sci., 112, 34–51, https://doi.org/10.1016/j.jaerosci.2017.07.002,

2017.

Kerminen, V.-M. and Kulmala, M.: Analytical formulae connect-

ing the “real” and the “apparent” nucleation rate and the nu-

clei number concentration for atmospheric nucleation events,

J. Aerosol Sci., 33, 609–622, https://doi.org/10.1016/S0021-

8502(01)00194-X, 2002.

Kim, J., Ahlm, L., Yli-Juuti, T., Lawler, M., Keskinen, H., Tröstl,

J., Schobesberger, S., Duplissy, J., Amorim, A., Bianchi, F., Don-

ahue, N. M., Flagan, R. C., Hakala, J., Heinritzi, M., Jokinen, T.,

Kürten, A., Laaksonen, A., Lehtipalo, K., Miettinen, P., Petäjä,

T., Rissanen, M. P., Rondo, L., Sengupta, K., Simon, M., Tomé,

A., Williamson, C., Wimmer, D., Winkler, P. M., Ehrhart, S., Ye,

P., Kirkby, J., Curtius, J., Baltensperger, U., Kulmala, M., Lehti-

nen, K. E. J., Smith, J. N., Riipinen, I., and Virtanen, A.: Hy-

groscopicity of nanoparticles produced from homogeneous nu-

cleation in the CLOUD experiments, Atmos. Chem. Phys., 16,

293–304, https://doi.org/10.5194/acp-16-293-2016, 2016.

Kirkby, J., Curtius, J., Almeida, J., Dunne, E., Duplissy, J., Ehrhart,

S., Franchin, A., Gagné, S., Ickes, L., Kürten, A., Kupc, A., Met-

zger, A., Riccobono, F., Rondo, L., Schobesberger, S., Tsagko-

georgas, G., Wimmer, D., Amorim, A., Bianchi, F., Breitenlech-

ner, M., David, A., Dommen, J., Downard, A., Ehn, M., Fla-

gan, R. C., Haider, S., Hansel, A., Hauser, D., Jud, W., Junni-

nen, H., Kreissl, F., Kvashin, A., Laaksonen, A., Lehtipalo, K.,

Lima, J., Lovejoy, E. R., Makhmutov, V., Mathot, S., Mikkilä, J.,

Minginette, P., Mogo, S., Nieminen, T., Onnela, A., Pereira, P.,

Petäjä, T., Schnitzhofer, R., Seinfeld, J. H., Sipilä, M., Stozhkov,

Y., Stratmann, F., Tomé, A., Vanhanen, J., Viisanen, Y., Vrtala,

A., Wagner, P. E., Walther, H., Weingartner, E., Wex, H., Win-

kler, P. M., Carslaw, K. S., Worsnop, D. R., Baltensperger, U.,

and Kulmala, M.: Role of sulphuric acid, ammonia and galac-

tic cosmic rays in atmospheric aerosol nucleation, Nature, 476,

429–433, https://doi.org/10.1038/nature10343, 2011.

Kontkanen, J., Olenius, T., Lehtipalo, K., Vehkamäki, H., Kul-

mala, M., and Lehtinen, K. E. J.: Growth of atmospheric clus-

ters involving cluster–cluster collisions: comparison of differ-

ent growth rate methods, Atmos. Chem. Phys., 16, 5545–5560,

https://doi.org/10.5194/acp-16-5545-2016, 2016.

Kuang, C., Riipinen, I., Sihto, S.-L., Kulmala, M., McCormick, A.

V., and McMurry, P. H.: An improved criterion for new par-

ticle formation in diverse atmospheric environments, Atmos.

Chem. Phys., 10, 8469–8480, https://doi.org/10.5194/acp-10-

8469-2010, 2010.

Kulmala, M., Kontkanen, J., Junninen, H., Lehtipalo, K., Manni-

nen, H. E., Nieminen, T., Petäjä, T., Sipilä M., M., Schobes-

berger, S., Rantala, P., Franchin, A., Jokinen, T., Järvinen, E.,

Äijälä, M., Kangasluoma, J., Hakala, J., Aalto, P. P., Paasonen,

P., Mikkilä, J., Vanhanen, J., Aalto, J., Hakola, H., Makkonen,

U., Ruuskanen, T., Mauldin, R. L., Duplissy, J., Vehkamäki, H.,

Bäck, J., Kortelainen, A., Riipinen, I., Kurtén, T., Johnston, M.

V, Smith, J. N., Ehn, M., Mentel, T. F., Lehtinen, K. E. J., Laak-

sonen, A., Kerminen, V.-M., and Worsnop, D. R.: Direct Obser-

vations of Atmospheric Aerosol Nucleation, Science, 339, 943–

946, https://doi.org/10.1126/science.1227385, 2013.

Kulmala, M., Kerminen, V.-M., Petäjä, T., Ding, A. J., and Wang,

L.: Atmospheric gas-to-particle conversion: why NPF events

are observed in megacities?, Faraday Discuss., 200, 271–288,

https://doi.org/10.1039/C6FD00257A, 2017.

Kürten, A.: New particle formation from sulfuric acid and

ammonia: nucleation and growth model based on thermo-

Atmos. Chem. Phys., 20, 7359–7372, 2020

https://doi.org/10.5194/acp-20-7359-2020

D. Stolzenburg et al.: Enhanced growth rate of atmospheric particles from sulfuric acid

7371

dynamics derived from CLOUD measurements for a wide

range of conditions, Atmos. Chem. Phys., 19, 5033–5050,

https://doi.org/10.5194/acp-19-5033-2019, 2019.

Kürten, A., Rondo, L., Ehrhart, S., and Curtius, J.: Calibration of

a Chemical Ionization Mass Spectrometer for the Measurement

of Gaseous Sulfuric Acid, J. Phys. Chem. A, 116, 6375–6386,

https://doi.org/10.1021/jp212123n, 2012.

Kürten, A., Jokinen, T., Simon, M., Sipilä, M., Sarnela, N., Jun-

ninen, H., Adamov, A., Almeida, J., Amorim, A., Bianchi, F.,

Breitenlechner, M., Dommen, J., Donahue, N. M., Duplissy, J.,

Ehrhart, S., Flagan, R. C., Franchin, A., Hakala, J., Hansel, A.,

Heinritzi, M., Hutterli, M., Kangasluoma, J., Kirkby, J., Laakso-

nen, A., Lehtipalo, K., Leiminger, M., Makhmutov, V., Mathot,

S., Onnela, A., Petäjä, T., Praplan, A. P., Riccobono, F., Rissa-

nen, M. P., Rondo, L., Schobesberger, S., Seinfeld, J. H., Steiner,

G., Tomé, A., Tröstl, J., Winkler, P. M., Williamson, C., Wim-

mer, D., Ye, P., Baltensperger, U., Carslaw, K. S., Kulmala, M.,

Worsnop, D. R., and Curtius, J.: Neutral molecular cluster forma-

tion of sulfuric acid–dimethylamine observed in real time under

atmospheric conditions, P. Natl. Acad. Sci. USA, 111, 15019–

15024, https://doi.org/10.1073/pnas.1404853111, 2014.

Kurtén, T., Noppel, M., Vehkamäki, H., Salonen, M., and Kulmala,

M.: Quantum chemical studies of hydrate formation of H

and HSO

−

, Boreal Environ. Res., 12, 431–453, 2007.

Laakso, L., Kulmala, M., and Lehtinen, K. E. J.: Effect

of condensation rate enhancement factor on 3-nm (diam-

eter) particle formation in binary ion-induced and homo-

geneous nucleation, J. Geophys. Res.-Atmos., 108, 4574,

https://doi.org/10.1029/2003JD003432, 2003.

Larriba, C., Hogan Jr., C. J., Attoui, M., Borrajo, R., Garcia,

J. F., and de la Mora, J. F.: The Mobility–Volume Rela-

tionship below 3.0 nm Examined by Tandem Mobility–

Mass Measurement, Aerosol Sci. Tech., 45, 453–467,

https://doi.org/10.1080/02786826.2010.546820, 2011.

Lehtinen, K. E. J. and Kulmala, M.: A model for particle formation

and growth in the atmosphere with molecular resolution in size,

Atmos. Chem. Phys., 3, 251–257, https://doi.org/10.5194/acp-3-

251-2003, 2003.

Lehtipalo, K., Leppä, J., Kontkanen, J., Kangasluoma, J., Franchin,

A., Wimmer, D., Schobesberger, S., Junninen, H., Petäjä, T.,

Sipilä, M., Mikkilä, J., Vanhanen, J., Worsnop, D. R., and Kul-

mala, M.: Methods for determining particle size distribution and

growth rates between 1 and 3 nm using the Particle Size Magni-

fier, Boreal Environ. Res., 19, 215–236, 2014.

Lehtipalo, K., Rondo, L., Kontkanen, J., Schobesberger, S., Jokinen,

T., Sarnela, N., Kürten, A., Ehrhart, S., Franchin, A., Nieminen,

T., Riccobono, F., Sipilä, M., Yli-Juuti, T., Duplissy, J., Adamov,

A., Ahlm, L., Almeida, J., Amorim, A., Bianchi, F., Breitenlech-

ner, M., Dommen, J., Downard, A. J., Dunne, E. M., Flagan, R.

C., Guida, R., Hakala, J., Hansel, A., Jud, W., Kangasluoma, J.,

Kerminen, V.-M., Keskinen, H., Kim, J., Kirkby, J., Kupc, A.,

Kupiainen-Määttä, O., Laaksonen, A., Lawler, M. J., Leiminger,

M., Mathot, S., Olenius, T., Ortega, I. K., Onnela, A., Petäjä,

T., Praplan, A., Rissanen, M. P., Ruuskanen, T., Santos, F. D.,

Schallhart, S., Schnitzhofer, R., Simon, M., Smith, J. N., Tröstl,

J., Tsagkogeorgas, G., Tomé, A., Vaattovaara, P., Vehkamäki,

H., Vrtala, A. E., Wagner, P. E., Williamson, C., Wimmer, D.,

Winkler, P. M., Virtanen, A., Donahue, N. M., Carslaw, K. S.,

Baltensperger, U., Riipinen, I., Curtius, J., Worsnop, D. R., and

Kulmala, M.: The effect of acid–base clustering and ions on the

growth of atmospheric nano-particles, Nat. Commun., 7, 11594,

https://doi.org/10.1038/ncomms11594, 2016.

Lehtipalo, K., Yan, C., Dada, L., Bianchi, F., Xiao, M., Wagner,

R., Stolzenburg, D., Ahonen, L. R., Amorim, A., Baccarini, A.,

Bauer, P. S., Baumgartner, B., Bergen, A., Bernhammer, A.-K.,

Breitenlechner, M., Brilke, S., Buchholz, A., Mazon, S. B., Chen,

D., Chen, X., Dias, A., Dommen, J., Draper, D. C., Duplissy,

J., Ehn, M., Finkenzeller, H., Fischer, L., Frege, C., Fuchs, C.,

Garmash, O., Gordon, H., Hakala, J., He, X., Heikkinen, L.,

Heinritzi, M., Helm, J. C., Hofbauer, V., Hoyle, C. R., Joki-

nen, T., Kangasluoma, J., Kerminen, V.-M., Kim, C., Kirkby, J.,

Kontkanen, J., Kürten, A., Lawler, M. J., Mai, H., Mathot, S.,

Mauldin, R. L., Molteni, U., Nichman, L., Nie, W., Nieminen,

T., Ojdanic, A., Onnela, A., Passananti, M., Petäjä, T., Piel, F.,

Pospisilova, V., Quéléver, L. L. J., Rissanen, M. P., Rose, C.,

Sarnela, N., Schallhart, S., Schuchmann, S., Sengupta, K., Si-

mon, M., Sipilä, M., Tauber, C., Tomé, A., Tröstl, J., Väisänen,

O., Vogel, A. L., Volkamer, R., Wagner, A. C., Wang, M., Weitz,

L., Wimmer, D., Ye, P., Ylisirniö, A., Zha, Q., Carslaw, K. S.,

Curtius, J., Donahue, N. M., Flagan, R. C., Hansel, A., Riip-

inen, I., Virtanen, A., Winkler, P. M., Baltensperger, U., Kulmala,

M., and Worsnop, D. R.: Multicomponent new particle formation

from sulfuric acid, ammonia, and biogenic vapors, Sci. Adv., 4,

eaau5363, https://doi.org/10.1126/sciadv.aau5363, 2018.

Li, C. and McMurry, P. H.: Errors in nanoparticle growth

rates inferred from measurements in chemically react-

ing aerosol systems, Atmos. Chem. Phys., 18, 8979–8993,

https://doi.org/10.5194/acp-18-8979-2018, 2018.

London, F.: The general theory of molecular forces, Trans. Faraday

Soc., 33, 8b–26, https://doi.org/10.1039/TF937330008B, 1937.

Mann, G. W., Carslaw, K. S., Spracklen, D. V., Ridley, D. A.,

Manktelow, P. T., Chipperfield, M. P., Pickering, S. J., and

Johnson, C. E.: Description and evaluation of GLOMAP-mode:

a modal global aerosol microphysics model for the UKCA

composition-climate model, Geosci. Model Dev., 3, 519–551,

https://doi.org/10.5194/gmd-3-519-2010, 2010.

Manninen, H. E., Petäjä, T., Asmi, E., Riipinen, I., Nieminen, T.,

Mikkilä, J., Hõrrak, U., Mirme, A., Mirme, S., Laakso, L., Ker-

minen, V.-M., and Kulmala, M.: Long-term field measurements

of charged and neutral clusters using Neutral cluster and Air Ion

Spectrometer (NAIS), Boreal Environ. Res, 14, 591–605, 2009.

McMurry, P. H.: Photochemical aerosol formation from SO

: A the-

oretical analysis of smog chamber data, J. Colloid Interf. Sci., 78,

513–527, https://doi.org/10.1016/0021-9797(80)90589-5, 1980.

Mulcahy, J. P., Jones, C., Sellar, A., Johnson, B., Boutle, I. A.,

Jones, A., Andrews, T., Rumbold, S. T., Mollard, J., Bel-

louin, N., Johnson, C. E., and Williams, K. D.: Improved

Aerosol Processes and Effective Radiative Forcing in HadGEM3

and UKESM1, J. Adv. Model Earth Sy., 10, 2786–2805,

https://doi.org/10.1029/2018MS001464, 2018.

Myhre, C. E. L., Nielsen, C. J., and Saastad, O. W.: Density and Sur-

face Tension of Aqueous H

at Low Temperature, J. Chem.

Eng. Data, 43, 617–622, https://doi.org/10.1021/je980013g,

1998.

Nadykto, A. B. and Yu, F.: Uptake of neutral polar vapor

molecules by charged clusters/particles: Enhancement due to

dipole-charge interaction, J. Geophys. Res.-Atmos., 108, 4717,

https://doi.org/10.1029/2003JD003664, 2003.

https://doi.org/10.5194/acp-20-7359-2020

Atmos. Chem. Phys., 20, 7359–7372, 2020