Beyond Köhler theory

Molecular dynamics simulations as a tool for atmospheric science

Thomas Hede

ii

Beyond Köhler theory – Molecular dynamics simulations as a tool for atmospheric science

Doctoral Thesis

Thomas Hede

Cover image: Cis-pinonic acid and fluoranthene in aggregate and at the surface of a water

cluster. Water molecules omitted for clarity.

©Thomas Hede, Stockholm University 2013

ISBN 978-91-7447-619-4

Printed in Sweden by US-AB, Stockholm 2013

Distributor: Department of Meteorology, Stockholm University

iii

To Angelica, Martin and Miranda.

iv

v

List of papers

The thesis consists of an introduction and the following papers:

I Li, X., Hede, T., Tu, Y., Leck, C., and Ågren, H. (2010) Sur-

face-active cis-pinonic acid in atmospheric droplets: a mo-

lecular dynamics study. J. Phys. Chem. Lett., 1 (4), 769-773.

II Hede, T., Li, X., Leck, C., Tu, Y., and Ågren, H. (2011)

Model HULIS compounds in nanoaerosol clusters; investiga-

tions of surface tension and aggregate formation using mo-

lecular dynamics simulations. Atmos. Chem. Phys., 11, 6549-

6557, doi:10.5194/acp-11-6549-2011.

III Hede, T., Leck, C., Sun, L., Tu, Y., and Ågren, H. (accepted)

A theoretical study revealing the promotion of light absorbing

carbon particles solubilisation by natural surfactants in

nanosized water droplets. J. Atmos. Sci. Lett.

IV Li, X. Hede, T., Tu, Y., Leck, C., and Ågren, H. (2011) Gly-

cine in aerosol water droplets: a critical assessment of Köhler

theory by predicting surface tension from molecular dynamics

simulations. Atmos. Chem. Phys., 11, 519-527,

doi:10.5194/acp-11-519-2011.

V Li, X., Hede, T., Tu, Y., Leck, C., and Ågren, H. (manu-

script) Cloud droplet activation mechanisms of amino acid

aerosol particles: insight from molecular dynamics simula-

tions. submitted to Tellus B.

Reprints are made with the permission of the publishers.

vi

Author´s contributions:

Papers I-V are the result of a collaboration between the department of mete-

orology, Stockholm university (Caroline Leck and Thomas Hede), and the

department of theoretical chemistry and biology, Royal institute of technol-

ogy, KTH, (Hans Ågren, Yaoquan Tu, Xin Li and Lu Sun) and the contribu-

tions lie within the field of respective expertise. Scientific discussions con-

cern all participating authors of the papers I-V respectively.

The initial idea of a collaboration concerning computer simulations of aero-

sol droplets by Caroline Leck and Hans Ågren, further developments and

implementations of the simulation approach by Yaoquan Tu and Thomas

Hede.

The idea of paper I by Caroline Leck, Thomas Hede, Yaoquan Tu and Hans

Ågren and the concept mainly by Thomas Hede. The MD simulations and

the code for surface tension calculations by Xin Li. Writing of major parts of

paper I by Xin Li. Writing of atmospheric related content by Thomas Hede.

Paper II is an extension of paper I, refined concept and idea by Thomas

Hede. Simulations and data collection and analysis by Thomas Hede with

assistance by Yaoquan Tu. Major parts of paper II was written by Thomas

Hede under supervision by Caroline Leck.

Idea and concept of paper III by Thomas Hede. Simulations carried out by

Thomas Hede, force fields constructed by Lu Sun. Data analysis and major

part written by Thomas Hede under supervision by Caroline Leck.

Idea and concept of paper IV by Caroline Leck. Simulations and calculations

by Xin Li. Major part of paper IV written by Xin Li. Writing of atmospheric

related content by Caroline Leck and Thomas Hede.

Idea and concept of paper V by Caroline Leck. Simulations and calculations

by Xin Li. Major part of paper V written by Xin Li. Writing of atmospheric

related content by Thomas Hede and Caroline Leck. Major revisions of the

manuscript by Thomas Hede, Caroline Leck and Xin Li.

vii

Papers not included in this thesis:

Sun, L., Li, X., Hede, T., Tu, Y., Leck, C., and Ågren, H. (2012) Molecular

dynamics simulations of the surface tension of salt solutions and clusters. J.

Phys. Chem. B, 3198-3204, doi:10.1021/jp209178s.

Hede, T., Sun, L., Leck, C., Tu, Y., and Ågren, H. (manuscript) Investiga-

tions of natural surfactants and sea salt in nanosized water droplets using

molecular dynamics simulations.

Hede, T., Murugan, A., Leck, C., Kongsted, J., and Ågren, H. (manuscript)

Light absorption of carbon particles in nanoaerosol clusters calculated using

computer simulations.

Hede, T., Claesson, J., and Leck, C. (manuscript) Enhanced feedback

mechanism of the forests-aerosol-climate system.

Hede, T. (2011) Moln, molekyler och miljöundervisning. Forskning om

Undervisning och Lärande, 7, 39-43.

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Abstract

In this thesis, the results from molecular dynamics (MD) simulations of

nanoaerosol clusters are discussed. The connecting link of these studies is

the Köhler theory, which is the theory of condensational growth and activa-

tion of cloud droplets to form clouds. By investigating parameters such as

the surface tension, state of mixture and morphology of nanoaerosol parti-

cles, conclusions can be drawn to improve the Köhler theory to include the

effects of organic compounds previously unaccounted for.

For the terrestrial environment, the simulations show that the natural surfac-

tant cis-pinonic acid, an oxidation product evaporated from boreal trees,

spontaneously accumulates at the surface of nanoaerosol clusters and thereby

reduces the surface tension. The surface tension depression is related to the

concentration of the surfactant and the size of the clusters. Surface tension is

an important parameter of the Köhler theory. A decrease of the surface ten-

sion can lower the critical water vapour supersaturation needed for cloud

droplet activation, giving rise to more, but smaller cloud droplets (Twomey

effect) which in turn could change the optical properties of the cloud. It was

also shown that the three organic surfactants, being model compounds for so

called Humic-like substances (HULIS) have the ability to form aggregates

inside the nanoaerosol clusters. These HULIS aggregates can also promote

the solubilization of hydrophobic organic carbon in the form of fluoranthene,

enabling soot taking part in cloud drop formation.

Dissolved intermediately surface-active free amino acids were shown to be

of some relevance for cloud formation over remote marine areas. The MD

simulations showed differences between the interacting forces for spherical

and planar interfaces of amino acids solutions.

This thesis has emphasized the surface-active properties of organic com-

pounds, including model HULIS and amino acids and their effect on surface

tension and molecular orientation including aggregate formation in

nanoaerosol clusters and their activation to form droplets. This thesis shows

that the Köhler equation does not fully satisfactory describe the condensa-

tional growth of nano-sized droplets containing organic surfactants. Differ-

ent approaches are suggested as revisions of the Köhler theory.

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Contents

1. Introduction ....................................................................................... 12 1.1. The climate issue of concern ...................................................................... 12 1.2. Köhler theory and organic constituents .................................................... 14 1.3. The role of surfactants in Köhler theory ................................................... 16 1.4. The method of molecular dynamics simulations ..................................... 18

2. Köhler theory .................................................................................... 20 2.1. Classic Köhler theory ................................................................................... 20

2.1.1. Supersaturation .................................................................................. 20 2.1.2. The components of Köhler theory ................................................... 21 2.1.3. Surface tension ................................................................................... 22

2.2. Modified Köhler equation ............................................................................. 23 2.2.1. Szyszkowski equation ....................................................................... 24

3. MD simulations ................................................................................. 26 3.1. Brief history of MD simulations .................................................................. 26 3.2. Basic concepts ............................................................................................... 27

3.2.1. Computer model ................................................................................. 27 3.2.2. Force field ............................................................................................ 27 3.2.3. Ions ....................................................................................................... 28 3.2.4. Periodic boundary conditions ........................................................... 29 3.2.5. Simulation procedure ........................................................................ 29

3.3. MD simulations applied to atmospheric science ...................................... 31

4. A glimpse beyond Köhler theory ................................................... 35 4.1. Theoretical approaches ................................................................................ 35

4.1.1. Nano-Köhler ........................................................................................ 35 4.1.2. κ-Köhler ............................................................................................... 36 4.1.3. Adsorption activation theory ............................................................ 37

4.2. Experimental approaches ............................................................................ 38 4.2.1. Water activity...................................................................................... 39 4.2.2. Amorphous particles .......................................................................... 40

5. Results ................................................................................................ 42 5.1. Paper I ............................................................................................................ 42 5.2. Paper II .......................................................................................................... 45 5.3. Paper III ........................................................................................................ 47

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5.4. Paper IV ......................................................................................................... 48 5.5. Paper V ........................................................................................................... 49

6. Outlook ............................................................................................... 51

7. Acknowledgements .......................................................................... 53

8. References ......................................................................................... 55

xi

Abbreviations

ALA

BET

CCN

CG

CPA

DFAA

GCM

GLY

GROMACS

H-TDMA

HULIS

KTA

KTH

LINCS

LJP

LPJ

LPS

MD

MET

OPLS

PAD

PAH

PAL

PBC

PHE

RH

RND

SDS

SER

SOA

SPC/E

SSC

Alanine

Brunauer Emmet and Teller

Cloud Condensation Nuclei

Conjugate Gradient

Cis-Pinonic Acid

Dissolved Free Amino Acids

General Circulation Model

Glycine

Groenigen Machine for Chemical Simulations

Hygroscopic Tandem Differential Mobility Analyzer

Humic-like Substances

Köhler Theory Analysis

Kungliga Tekniska Högskolan

Linear Constraint Solver

Lennard-Jones Potential

Lund-Potsdam-Jena

Lipopolysaccharide

Molecular Dynamics

Methionine

Optimized Potentials for Liquid Simulations

Pinic Acid

Polycyclic Aromatic Hydrocarbons

Pinone Aldehyde

Periodic Boundary Conditions

Phenylalanine

Relative Humidity

Radial Number Density

Sodium Dodecyl Sulphate

Seronine

Secondary Organic Aerosol

Extended Single Point Charge

Slightly Soluble Compounds

VAL Valine

12

1. Introduction

1.1. The climate issue of concern

We live in times of change. "Most of the observed increase in global average

temperatures since the mid-20th century is very likely due to the observed

increase in anthropogenic greenhouse gas concentrations" (IPCC, 2007). The

increase in global average temperatures is a threat to mankind for several

reasons – flooding, extreme temperature, hurricanes and drought will proba-

bly become more common. Changes in the climate have occurred before,

and often this has induced periods of starvation, poverty and war. It is even

considered that the fall of the Roman Empire was due to effects from chang-

es in the climate (Bϋntgen et. al, 2011). How, when and where future climate

change may occur cannot be determined exactly, but a projection can be

made using simulations of the future climate based on so called GCM’s

(General Circulation Models). However, the GCM’s are limited by the accu-

racy and detail of the representation of the various processes and compo-

nents of planet Earth. One such difficulty is the representation of clouds

(IPCC, 2007).

Clouds can feedback on climate in two ways. Both feedback mechanisms are

not fully understood and thus have a high degree of uncertainty embedded.

The positive feedback relates to that clouds absorb outgoing longwave radia-

tion, especially since clouds are colder than the surface, and thereby act as

warming greenhouse effect. A warmer climate evapourates more water and

more clouds could potentially form. But, our best knowledge today cannot

say for certain that more clouds would form. And even if it would, there is

much uncertainty in what types of clouds that would form. Deep convection

types of clouds have no net effect on the climate, whereas low and high

clouds have a cooling and warming effect respectively (Wallace and Hobbs,

2006). The negative feedback is that if a warmer climate produces more

clouds, then the planetary albedo will increase since clouds reflect more

sunshine and thereby cool the surface. However, high clouds, like cirrus,

warm the surface (Wallace and Hobbs, 2006), so the cloud feedback is high-

ly uncertain, but 10-50% amplification is proposed (IPCC, 2007). Another

This thesis is a further development of my licentiate thesis entitled “Cloud

formation and Molecular Dynamics simulations” (ISBN 978-91-633-8699-2)

from the year 2011.

13

factor to be taken into account is how clouds are treated in the GCM’s. The

accuracy of the climate projections will depend on the size of each grid box

(the resolution) in the model (Figure 1).

Figure 1. Although grid boxes in GCM´s have become smaller, they still are

much larger than the average cloud (IPCC, 2007).

Although, the grid resolution has increased rapidly recent years (IPCC,

2007), there is still need for an improved parameterization of clouds (de-

scription as functions of resolved scale parameters in the model), since they

are “too small” to be explicitly described in a climate model. This means that

a simplification of reality must be introduced, and different schemes with

different accuracy will be used (Peixoto and Oort, 1992). Clouds cannot form unless there is a high relative humidity and presence of

cloud condensation nuclei (CCN), which is the number of aerosol particles

available for uptake or condensation of water vapour. Aerosols will be re-

ferred to as particles dispersed in the air. Aerosols can be divided into two

main groups dependent on the origin of the source; primary aerosols are

emitted directly at the surface of the Earth and can typically consist of natu-

rally wind induced mineral dust from deserts and soils, sea salts and organic

material from wave braking and bubble bursting processes (Blanchard, 1963;

Blanchard and Woodcock, 1957) or from anthropogenic sources such as

biomass burning and pollution. Secondary aerosols form through gas-to-

particle conversion in the atmosphere. It involves chemical reactions, often

including photo- and radical chemistry. Secondary aerosols can also be of

either inorganic or organic composition. Aerosols interact with the climate in

14

mainly two ways; a direct effect which concerns absorption and scattering of

the incoming solar radiation, and an indirect effect that allows an increase of

CCN for more, but smaller cloud droplets to form, changing the optical

properties of the cloud to become more white and reflective (Twomey,

1977). Both the direct and the indirect effect (cloud albedo effect) of aero-

sols have a cooling impact on the climate system, but the uncertainties

accompanied with the estimates done are severe, see Figure 2 (IPCC, 2007).

Figure 2. Radiative forcing of climate (IPCC, 2007). The cloud albedo effect

is the largest negative radiative forcing, but also the far most uncertain.

1.2. Köhler theory and organic constituents

Köhler theory is widely used for describing cloud droplet activation and

growth and it is discussed in detail in section 2. In brief Köhler theory was

developed by the Swedish meteorologist Hilding Köhler (1936). Köhler the-

ory describes the condensational growth of a particle. Condensation of water

vapour is promoted by high relative humidity and a favorable solute. Köhler

theory is based on thermodynamics and is made up by a term related to the

solute, the Rault term, and one term related to the curvature of the droplet,

the Kelvin term. The underlying assumption of the theory is that the CCN

population is made up only from inorganic salts from marine and continental

areas. Over ocean it has generally been assumed that particles derived from

bubble production (Blanchard, 1963; Blanchard and Woodcock, 1957) dur-

ing wave breaking at high wind regimes would be composed of sea salt and

could thus contribute a significant fraction of the primary marine CCN popu-

15

lation (O'Dowd et al., 1999; Smith, 2007). However, a controversial issue in

the composition of primary organic aerosol has been the absence of sea salt

observed over the central Arctic Ocean and at lower latitudes in airborne

particles in sizes <200 nm diameter (Ayers and Gras, 1991; Leck et al.,

2002; Pósfai et al., 2003; Bigg and Leck, 2008), as compared with the organ-

ic aerosol (primary and/or secondary) experimentally produced or sampled

above temperate waters that range from 20-98% sea salt by mass (O’Dowd

et al. 2004, Lewis et al. 2004; Facchini et al. 2008, Keene et al. 2007, Rus-

sell et al. 2010) to 100% in particles even as small as 10 nm in diameter

(Clarke et al., 2003). Over both the ocean and continental areas, more recent

knowledge has shown the presence of organic constituents internally or ex-

ternally mixed as a part of the CCN population (e.g. Novakov and Penner,

1993; Shulman et al., 1996; Facchini et al., 1999; Rodhe, 1999; O’Dowd,

2002; Leck and Bigg, 2005a,b). State of mixture describes the way different

constitutes of the aerosol particle are mixed. It can be an external mixing

that is heterogenic with respect to the species that it consist of, or it can be an

internal mixing, where the different constitutes are homogenously mixed in

a solid or a liquid phase, see Figure 3.

Figure 3. Schematic picture of a) externally mixed and in b) internally mixed

aerosol particles.

Other factors such as particle morphology will also be of importance for

cloud droplet activation. To improve the representation of clouds in GCM’s

we obviously need further understanding on how the chemistry of the aero-

sol multiphase system does influence formation and evolution of the cloud

droplet population. One group of organic molecules that potentially could

play an important role in cloud activation goes under the name surfactants.

They have the ability to depress surface tension of water by disturbing the

hydrogen bonding network at the surface of a cloud droplet (Sorjamaa et al.,

16

2004), or may form amorphous states (Virtanen et. al, 2010) that in turn may

allow other organic constituents to dissolve and form more complex multi-

phase systems. All this together could severely change the conditions for

cloud droplet activation, since water condensation is enhanced by lowering

of the droplet´s surface tension (Chakraborty and Zachariah, 2008). Effects

of this kind are not taken into account by the original Köhler theory and

might necessitate modification of the same.

1.3. The role of surfactants in Köhler theory

Surfactants affect the surface tension, the state of mixture and morphology

of CCN, potentially making them more efficient in cloud droplet activation.

Figure 4 illustrates schematically the surfactant constituents in focus in this

Thesis.

Figure 4. Schematic illustration of the categories of surfactants studied in

this Thesis and their sources.

The physical and chemical properties of surfactants are depending on the

fact that they are amphiphilic, which means that one part of the molecule is

solvable in water and one part of the molecule prefer to solve in hydrocar-

17

bons, like oil or fat. Since water vapour does not contain hydrocarbons, sur-

factant molecules are forced to undergo two types of adjustments to be able

to act as CCN and “dissolve” in a water droplet. The two types of adjust-

ments are: a) accumulation at the surface or b) self-assembly into micelle-

like aggregates. Figure 5 shows these two types of adjustments.

Figure 5. Surfactant properties in water droplets.

Often when discussing micelles, the surfactants that form the micelles are

of the type made up by a long (12-18 carbons usually) hydrophobic “tail”

with a hydrophilic, polar or charged, “head” group containing for instance

sulphur or nitrogen atoms. A typical such amphiphilic surfactant is sodium

dodecyl sulphate (SDS). SDS is synthetic and often used as a model for sur-

factants like fatty acids. It is a strong detergent. SDS forms regular, spherical

micelles. A micelle contains about 80 SDS molecules.

Humic-like substances (HULIS) serves as one category of very efficient

surfactants. Commonly used model HULIS surfactants are; cis-pinonic acid

(CPA), pinic acid (PAD) and pinonaldehyde (PAL). These HULIS com-

pounds originate from boreal forests, where the trees are evaporating the

organic compound α-pinene. In addition, a minor contribution of α-pinene

could be expected from blooming algae in the oceans (Yassaa et al., 2008;

Luo and Yu, 2010). In the lower troposphere α-pinene will undergo photo-

chemical oxidation to yield CPA, PAD and PAL.

18

One other group of moderately efficient surfactants is amino acids. Amino

acids are the building blocks of the proteins that exist in all living organisms

over both land and oceans. In sea water dissolved free amino acids (DFAA)

are abundant and they accumulate easily in the surface microlayer (<100µm

thick surface film of the ocean) due to surface active properties. A mixture

of several DFAA, sea salt and various other components has been found in

aerosol particles in the marine boundary layer. Several types of L-amino

acids were identified, including alanine, arganine, glycine, phenylalanine,

proline, serine, and valine (Mace et al., 2003a-c; Wedyan and Preston, 2008;

Zhang and Anastasio, 2003; Malder et al., 2004).

1.4. The method of molecular dynamics simulations

To be able to study small clusters of water and surface active components in

order to measure changes in surface tension, laboratory experiments are in

general difficult, and at times even not possible to conduct. However, a

model system that describes how models of molecules interact, simulated in

a computer would be challenging but still appropriate for this type of appli-

cation. This is possible using Molecular Dynamics (MD) simulations. There

are several advantages using this approach:

Molecules can be followed individually through the simulation.

Time-scale is on the picosecond level, which is favorable to study molec-

ular interactions.

Features such as such as radial density, surface tension and order parame-

ter could be calculated.

Several physical properties may be investigated, such as temperature and

pressure.

However, there are some drawbacks that must be considered:

The force field that is a representation of the molecular interactions is an

approximation.

Chemical reactions cannot be considered.

Certain simplifications must be introduced, such as rigid molecules and

cut-off of ionic interactions.

MD simulations are presently capable to handle two component systems,

but in reality CCN is a mixture of chemical compounds that may poten-

tially interact. To model such systems are still a challenge for the MD

technique.

19

We use MD simulations conducted with the GROMACS (Groenigen Ma-

chine for Chemical Simulations) program package (van der Spoel et al.,

2005; Hess et al., 2008). Further information about the MD simulation tech-

nique can be found in Chapter 3.

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2. Köhler theory

As cloud formation cannot be treated explicitly in GCM’s they have to be

expressed as functions of the variables in the model as they appear on the

large scale – the resolved scale (larger than ~ 100 km and time scales of

longer than hours). Such parametric descriptions of physical and chemical

processes are based on theory and empirical evidence and require large

amounts of data both in formulation and in testing. As mentioned above

Köhler theory is commonly used as a parametric description of cloud for-

mation in GCM’s. The theory can be viewed as a predictive tool to calculate

under what conditions water vapour actually may condensate and later form

cloud droplets. Köhler theory was developed in the thirties by the Swedish

meteorologist Hilding Köhler (1936). In those days it was believed that wa-

ter vapour condensates on CCN made up by inorganic material from sea-

spray or mineral dust from land only.

2.1. Classic Köhler theory

2.1.1. Supersaturation

In a pure air and water vapour mix, without airborne aerosols available for

uptake of water vapour (CCN), the water vapour must be far above 100%

relative humidity (RH) in order to condensate and form droplets. What de-

termines the level of 100% RH depends on the pressure and temperature of

the air. The level above 100% RH is called water vapour supersaturation.

The equation, describing this, is as follows:

(2.0)

(S) is the water vapour supersaturation needed for drop growth and (d) is the

diameter of the growing droplet. (A) represents the Kelvin term and (B) is

representing the Rault term, described more in detail in the next section.

21

In order to form the cloud droplets that make up clouds, there is a need to

lower the point where water vapour condensation is possible (the so called

critical water vapour supersaturation), since the levels high above 100% RH

is not present in the troposphere. The critical water vapour saturation ratios

(Sc) vs. a flat surface and the corresponding aerosol critical radius or diame-

ter (rc, dc) is the minimum saturation ratio that is required for the correspond-

ing droplet to grow theoretically to infinity. If the droplet has grown to r,d >

rc,dc, it is called an activated droplet. All droplets that have a critical satura-

tion ratio Sc < S can thus be activated.

2.1.2. The components of Köhler theory

The Rault term of the Köhler equation tells us that solutes lower the critical

super saturation (since (B) in eq 2.0 is subtracted from the super saturation).

(2.1)

Here, (mS) is the mass of the solute, (MS) is the molar weight of the solute

and (MW) is the molecular weight of water.

The other term, the Kelvin term (A), of the Köhler equation (eq 2.0) de-

scribes the extra super saturation needed to form a droplet that has a spheri-

cal curvature, rather than over a plane surface.

(2.2)

(σ) is the surface tension. For pure water the value is 72.8 mNm-1

. (MW) is

the molar weight of water. (ρW) is the density of water. (R) is the general gas

constant 8.31 J K-1

mol -1

and (T) is the temperature.

The Köhler equation can be calculated and the result is a Köhler curve, see

Figure 6.

22

Figure 6. Example of a Köhler curve.

2.1.3. Surface tension

Differences between the energies of molecules located at the surface and in

the bulk phase manifest themselves as surface tension (Evans and

Wennerström, 1999). Surface tension is the main reason that boats can float,

so surface tension is a macroscopic feature The origin of surface tension,

however, is microscopic. In water, hydrogen bonding between water mole-

cules increases the surface tension. Water molecules in the bulk phase in the

interior of the droplet is bonded in any direction, whereas water molecules

on the surface lack bonding outwards and is therefore pulled inwards. This

minimizes the surface area. A spherical droplet is the most favorable shape

according to the Young-Laplace equation (Young, 1805; Laplace, 1806):

(2.3)

(Δp) is the pressure difference across the fluid interface, (γ) is the surface

tension and (H) is the mean curvature.

23

2.2. Modified Köhler equation

In order to improve the Köhler theory for applications of mixed chemical

composition including organic compounds, modifications of the original

Köhler equation have been suggested. Shulman et. al. (1996) use an alternate

form to calculate Köhler curves for a mixture of sulfate salts (sulf) and

slightly soluble compounds (ssc), for instance CPA:

(2.4)

where é is the equilibrium vapour pressure of water over a solution droplet

of a given radius, (r), relative to the water vapour pressure over a plane sur-

face of water, (es). (ρ) is the solution density, (k) is the Boltzmann constant,

(Ф) is the osmotic coefficient of the aqueous solution, (vdssc) is the number of

ions into which a SSC dissociates when dissolved, (mSSC) is the total mass of

SSC, (msulf) is the mass of the sulfate salt, (MSSC) is the molecular weight of

the SSC, and (Msulf) is the molecular weight of the sulfate salt. (Xdssc) is a

function of SSC solubility and sulfate concentration. If Xdssc=0, the Köhler

curve takes the standard form. If (Xdssc) monotonically increases up to unity

as the droplet grows, there may be two maxima, see Figure 7.

24

Figure 7. Example calculated using eq. 2.4 of Köhler curves for the two

component system of CPA and ammonium sulfate.

2.2.1. Szyszkowski equation

The Köhler equation given in (1.2) uses however a constant value of surface

tension independent of droplet diameter. This means that the effect of disso-

lution during droplet growth is not considered. To make the Köhler theory as

relevant as possible for atmospheric conditions, the effect of the concentra-

tion of the dissolved organic surfactant on cloud drop activation and growth

has to be taken into account. An attempt to account for this is to introduce

the empirical relationship developed by Szyszkowski in the year 1908.

Sometimes the isotherm is mentioned as the Szyszkowski-Langmuir equa-

tion (Langmuir, 1916) and it has later been improved (Meissner and

Michaels, 1949; Facchini, 1999):

(2.5)

Here, (C) is the concentration of the dissolved surfactant, (D) is a constant,

and (E) is a constant specific for each compound. The Szyszkowski-

Langmuir equation is developed specifically for bulk solutions, so the use of

the equation for droplets may be different for the surface to bulk distribution

10-1

100

101

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

wet diameter m

supers

atu

ation %

Köhler curves - Ammonium sulfate, cis-pinonic acid m=6e-16

m=4e-16

m=6e-16

m=8e-16

m=6e-16 without ssc

fraction SSC dissolved

25

of surfactants, discussed by Sorjamaa et al. (2004). Sorjamaa et al. suggest

that the Rault term is not counteracted enough by the reduction of the surface

tension in the Kelvin term. However, there are also other reported results

that show that this effect is not highly pronounced (Schwier et al., 2012).

When using the Szyszkowski equation 2.5 to account for a variable surface

tension, the Köhler equation takes on the form (Li et. al, 1998):

(2.6)

(A0) is the Kelvin term and (σ(r)) is the surface tension according to the

Szyszkowski equation as a function of radius of the droplet. Using this ex-

pression, modified Köhler curves can be calculated.

26

3. MD simulations

3.1. Brief history of MD simulations

The concept of studying the motions of atoms interacting with each other

was tried using rubber balls and sticks as a model, but this task was of course

impossible to carry out. Instead, the use of computers became possible as

computers developed and was available for non-military use in the middle of

the 20th century (Li, 2011). Metropolis et al. (1953) introduced the Monte-

Carlo method for solving physical equations. Here, random numbers are

used in the calculations, but the definition and creation of random numbers

are actually not simple. Later, the first MD simulation was carried out for a

hard sphere system (Alder and Wainwright, 1958). MD simulations of solid

and gaseous phase, being considered as more simple systems than for the

liquid phase were carried out first (Gibson et al., 1960; Rahman, 1964). MD

simulation of water was reported by Rahman and Stillinger in 1971. Only a

few years later, MD simulation of proteins was published in Nature (Levitt

and Warshel, 1975). Since then, several different applications in a wide field

of science have been simulated.

For atmospheric science, the approach is a new tool. Nijmeijer et al. (1992),

Zakharov et al. (1998), and Chakraborty and Zachariah (2008) have used

MD to determine surface tension for water clusters. However, these studies

are limited to water and fatty acids.

MD simulations are capable of generating trajectories of individual atoms in

both water molecules that make up the clusters and in surfactant molecules

that are dissolved inside. The clusters are in the size range of less than 10 nm

in diameter and thereby being representative for the nucleation mode. We

denote the clusters nanoaerosols since they are dispersed in air. By employ-

ing a force field in the MD simulation, molecular interactions can be studied

that would be not be possible today to achieve in a laboratory. Since

nanoaerosols are about 10 nm of diameter or less, only MD simulation

would be the method to investigate molecular behavior such as aggregation

formation, that otherwise only could be determined indirect and without

detail information about the conformations. Even though MD simulations

are a model framework for understanding of small scale resolution process-

27

es, one must keep in mind that results still are simplifications of a more com-

complex nature.

3.2. Basic concepts

3.2.1. Computer model

MD simulation is a numerical technique to generate molecular trajectory

by solving the Newton's equations of motion, where the interaction between

molecules is defined by the force field. As the simulation runs, the coordi-

nates of the atoms are saved frame by frame for subsequent analysis.

In our case we use the GROMACS (Groenigen Machine for Chemical Simu-

lations) software package (Hess et al. 2005; Spoel et al., 2008) to carry out

the simulations. The snapshots are saved with a time interval of 1 picose-

cond. The saved snapshots can be displayed continuously to make a movie

showing the motions of the molecules during the simulation, and statistical

analysis of the trajectory is able to give insights into the physical properties

as well as microscopic details. The duration of a typical MD simulation is

about 1 ns, but to be able to study processes like aggregate formation, a

longer, up to 10 ns, simulation must be conducted in order to ensure the sta-

bility of the aggregates.

MD simulations are computer resource consuming, and even utilizing super-

computers like the Ekman supercomputer, a simulation of 8 ns will run for

almost a month.

3.2.2. Force field

In a MD simulation, the forces between atoms are described by a force field.

The force field is the sum of all the interaction potentials. It can be described

by:

V = Vbonds + Vangle + Vtorsions + Vimpropers + Vnon-bonded

(3.0)

The first four terms are the intramolecular potential of atoms separated by up

to three covalent bonds. For non-bonded atoms separated by more than three

covalent bonds or located on different molecules, the term (Vnon-bonded) is

used:

28

Vnon-bonded =

(3.1)

The first two terms of the (Vnon-bonded) are the Lennard-Jones Potential (LJP);

the first term is short range interaction and the second term is long range van

der Waal interactions. Figure 8 show the LJP.

Figure 8. LJP (picture from Wickipedia, 2011).

The third term is the Coulomb interaction depending on the electrostatic

interaction between particles of different charge.

The force field employed is Optimized Potentials for Liquid Simulations

(OPLS) (Jorgensen, 1996). The force field parameters are described in a

computer file that the GROMACS software read as input data when initiat-

ing the simulations.

3.2.3. Ions

When simulating ions, special attention must be taken to the charges of the

ions. There are different ways of representing these charges and the use of

different force fields. One such force field is the polarizable force field. This

force field is more computational demanding. However, the use of a conven-

bondednon

ji

r

qq

r

C

r

C

0

6

6

12

12

4

29

tional force field can be carried out, since a recent study by Lu Sun et al.

(2012) showed that calculated surface tensions are not greatly affected by the

choice of force field.

The so called cut-off radius is also an important parameter when simulating

ions. Since electrostatic interactions are long range there must be a limit

where no calculations are carried out. The length from the charged ion to this

limit is the so called cut-off. In the study by Lu Sun et al. (2012) we show

that the optimum cut-off is 1.5 nm.

3.2.4. Periodic boundary conditions

Periodic boundary conditions (PBC) were used. PBC mean that if a molecule

or atom moves out of the simulation box, an equivalent molecule or atom

appears on the opposite side of the box. Therefore no atoms are lost and the

system seems infinite in space, see Figure 9.

Figure 9. PBC - The PBC are valid in all three dimensions.

3.2.5. Simulation procedure

To conduct MD simulations, you first need to construct a system that de-

scribes the system under study. The system can be of different kind, but

when we are discussing systems, we mean clusters of water molecules mixed

with organic molecules and in some cases additionally mixed with ions. The

build-up of the systems and the sequential steps of the simulation process is

illustrated in Figure 10 a-c.

30

Figure 10. The simulation procedure.

By using the GROMACS utility genbox we insert molecules that we like to

simulate randomly into a box of given size (Figure 10a). The coordinates and

type of each atom is represented in a computer file. We can insert other types

of molecules or ions the same way. Next step is to use genbox to insert water

molecules. We fill the box with water molecules and then edit the computer

file by deleting surplus water molecules so that the right amount is added

(Figure 10b). The SPC/E (extended simple point charge) water model

(Berendsen et al., 1987) was employed, with the two O-H bond lengths con-

strained at 1.0 Å by the LINCS (linear constraint solver) algorithm (Hess et

al., 1997; Hess, 2008). For the systems including ions, we use a convention-

al, non-polarizable force field.

By enlarging the simulation box 6 nm in each direction, we create a cluster

that will negligibly interact with the mirror image due to PBC. We center the

system inside the box so that box-formed system is completely surrounded

with void. The system is simulated using the GROMACS utilities steep

(steepest descend) and CG (conjugate gradient) to minimize the energy of

the system. This means that any molecules too close to each other are rear-

ranged. An equilibration simulation for about 1-2 ns converts the box-

formed cluster into a spherical nanoaerosol cluster (Figure 10c).

The simulation is divided into parts that each is 1 ns long. This is because of

two reasons. The first reason is that the simulations are time consuming. The

resource used was the Ekman super computer, and we use eight parallel

nodes. The time limit for these kinds of jobs is set to 10080 minutes, that is

one week, and 1 ns of simulation takes more than five days. The other reason

for dividing the simulation into 1 ns sequences is that the computer file that

is produced is very large (approximately 400 Mb per ns), and the data is

updated continuously on the Ekman server. When running several jobs in

31

parallel, to avoid exceeding the limit of storage and thereby aborting the

jobs, data must be transferred or deleted in sequences.

After a few (between four and eight) nanoseconds of simulations, a one na-

nosecond simulation produces a trajectory that is used for the calculations of

parameters of interest. The algorithm used for the calculations of surface

tension is based on the paper by Zakharov et al. (1997) and the program used

for the reading of the trajectory files and the calculation of surface tension

was written by Dr. Xin Li at the department of theoretical chemistry, Royal

institute of technology (KTH) in Stockholm.

3.3. MD simulations applied to atmospheric science

MD simulations have not been used for atmospheric research applications

until recently. In 2008, Chakraborty et. al conducted MD simulations for a

nano aerosol system containing lauric acid as a coating, but otherwise there

is no previous publication in the field of atmospheric science, even though

water clusters have been simulated before (Nijmeijer et. al, 1992; Zhakarov

et. al, 1997; Zhakarov et. al, 1998). We have investigated the possibility to

use MD simulations to shed new light upon the molecular processes in the

aerosol size range below 10 nm in diameter with extrapolations up to the 100

nm diameter size range typical of ambient CCN. Several properties, like

surface tension and radial density may be studied and as computer resources

are developing, more complex system may be considered. In this way, we

perform novel studies that open up for future research using MD simulations

as a tool for aerosol science.

As pointed out above, MD simulations are well suited for investigations of

molecular systems that are difficult to study using conventional experimental

methods. There may be several conditions where the method of MD simula-

tions is to prefer, such as the study of small systems. Even though electron

microscope can resolve images of nanometer size, this is a two-dimensional

picture. MD simulations can provide the possibility to view a system over

time and in three dimensions and in addition to this, every position of all the

atoms in the system are available in the trajectory file. This is highly useful

for studies of nucleation processes where a few up to hundreds of molecules

form new particles. New particle formation is a hot topic in aerosol science,

but the experimental methods used to study new particle formation are few.

MD simulations are therefore an excellent tool to shed light upon the interac-

tion between the nucleating molecules. The physical properties of such small

systems cannot be measured using conventional experiments. We study sur-

face tension calculated for droplets of nanometer size. Other types of physi-

32

cal properties, like the activity of water and solutes, would be interesting to

calculate from MD simulations, and although this type of calculations have

been conducted for small and simple systems like sodium chloride

(Lyubartsev and Laaksonen, 1997) the challenge to compute the activity for

organic molecules is far more great. The uncertainties accompanying the

data would be far too high for the method to be of value.

An important property of CCN is the state of mixture. When collecting sam-

ples of ambient air in order to determine the chemical properties of the aero-

sol particles experimentally, there is simply very difficult or not even possi-

ble to detect the low masses present, ranging ca, 10-15

– 10-18

gram. Gas- and

High Pressure Liquid Chromatography coupled with Mass Spectrometry is a

good choice that would give good information about the chemical composi-

tion of the sample, but the information on morphology and state of mixture

is completely lost. If the particles are collected with an impactor, the size

distribution of the aerosol sample may be determined, but the information on

the state of mixture is lost. Experiments using impactors in a new way have

been of help with determining the state of aerosol particles. By using the

bounce, that normally is an undesired side effect, Virtanen et al. (2010) were

able to show that SOA particles are in a glassy, amorphous, solid state.

The bottom line is that the state of which aerosol particles find themselves in

the ambient air is sensitive to handle, whereby investigations of this is very

difficult to conduct. MD simulations, however, can model different composi-

tions of molecules. SOA can change the state of mixture of light absorbing

carbon particles (soot) and also enhance the light absorption (Saathoff et al.,

2003). To study this in detail and to investigate the morphology would be

practically impossible without the use of MD simulations.

During the last three years, the research group that I am part of has tried the

MD simulations technique as a tool for atmospheric science and we have

achieved results that now are published in highly esteemed scientific jour-

nals. Still, there are numerous ways of continuing and developing the work.

Computer simulations have a broad variety of applications that reach from

quantum computations of a few molecules to coarse grained simulations of

large molecular systems. Quantum calculations are being performed at KTH

to evaluate the light absorption and the scattering of light of the light absorb-

ing carbon particles with and without the “coating” of CPA. We have also

seen preliminary results from other research groups at Stockholm university

using MD simulations to estimate the water accommodation of both planar

and spherical surfaces. For future we hope that the MD technique could be

applied to larger systems, which would enable a direct simulation of the

activation of cloud droplets.

33

The applications mentioned above for MD simulations are all related to in-

vestigations of cloud droplets and aerosol particles. The diameter of a CCN

at the point of activation is typically 100 nm, and this size of a cluster is too

large to handle in an MD simulation because of the large number of compu-

tations. In a near future maybe this would be feasible, but not for the mo-

ment.

We chose to simulate clusters of about 10 nm in diameter and study the

properties acquired for these systems. Surface tension is dependent both on

size and concentration of solutes, we have seen that the aggregation of model

HULIS compounds appear only in clusters larger than 5000 water molecules

and the surface tension is affected differently for planar surfaces than for

spherical surfaces. Therefore the size range of a few nm up to 10 nm in di-

ameter gives much information on the molecular behavior of the properties

we study such as surface tension and aggregate formation. This information

is of great importance, not only to understand nano-sized aerosols, but the

information can be extrapolated and applied also to larger systems such as

CCN at the point of activation. We suggest two types of extrapolation of the

surface tension:

The first one is to use the Szyszkowski parameters determined by the MD

simulations to predict the concentration dependency of the surface tension.

By using MD simulations, any compound that have an effect on surface ten-

sion can be investigated, and the Szyszkowski parameters can be deter-

mined. In this Thesis we determine the Szyszkowski parameters for two

previously undetermined compounds. By comparing with experimental data,

we can be confident to have a good agreement.

The second one is extrapolation with a quadratic polynomial with a relation

between the surface tension and the inverse of the droplet radius. By interpo-

lating the surface tensions of the nano-sized systems and the limiting planar

surface, the Aitken mode particles with larger sizes could be covered and the

Köhler equation could be improved by incorporating surface tension correc-

tions.

Other types of processes that are important for atmospheric science could

also be simulated with the use of the MD approach. Processes at the inter-

face between ambient air and water have been considered in this thesis, and

there are similar conditions regarding the sea surface where several process-

es of importance to atmospheric science are prominent, like bubble bursting,

where amphiphilic compounds from marine algae are inserted into the tropo-

sphere. The uppermost layer (microlayer) of the oceans accumulates surface-

34

active compounds, mostly lipopolysaccharides (LPS) from marine algae.

LPS make up a colloidal mixture with inorganic ions, and the different com-

positions could be modeled using MD simulations. There is only the imagi-

nation that sets the limit for the use of MD simulations as a tool for atmos-

pheric science.

35

4. A glimpse beyond Köhler theory

The knowledge on water vapour condensational growth of particles is in-

creasing and developing as new experimental techniques are becoming

available, new findings on the chemistry of the aerosol multiphase are re-

ported and new theoretical frameworks are being used. Since Köhler intro-

duced his theory, vast advances have been made. In this section we see a

glimpse beyond classical Köhler theory.

4.1. Theoretical approaches

This thesis confirms that Köhler theory is inadequate for describing the con-

densational growth of nano-sized droplets containing organic surfactants.

The need to revise the Köhler theory is imminent and many researchers are

accepting the challenge. Since the paper by Sorjamaa et al. (2004) where the

role of surfactants in Köhler theory was reconsidered, there are new theoreti-

cal approaches reported recently in the literature dealing with aspects of the

Köhler theory. Here, I give examples of three such theoretical approaches,

namely nano-Köhler, κ-Köhler and adsorption theory. The purpose is to give

an insight to the modifications that are recently proposed, not to find the

solution to the problem, but to introduce these new theoretical approaches.

Lately is also mentioned the so called Köhler theory analysis (KTA) in a few

articles (Asa-Awuku et al., 2007; Padró et al., 2007; Asa-Awuku et al.,

2010) though this type of analysis is not a further development of the Köhler

theory, rather it uses Köhler theory to derive properties of CCN such as av-

erage molar volume. Therefore, KTA will not be included here.

4.1.1. Nano-Köhler

Nano-Köhler theory (Kulmala et al., 2004) describes a thermodynamic equi-

librium between a nano-size cluster, water and an organic compound that is

fully soluble in water, i.e., it does not form a separate solid phase. Organic

and inorganic compounds in the clusters form a single aqueous solution. It is

assumed that ammonium bisulphate (bs) is formed from ammonia and gase-

ous sulphuric acid reacting 1:1 (Kulmala et al., 2000). The thermodynamic

36

phase equilibrium for water-soluble organic vapour (ov) is determined by the

equation (Laaksonen et al., 1998):

(4.0)

Where (χov) is the molar fraction in the solution and (γov) is the water activity

coefficient. The Kelvin term is (aov) and (dc) is the diameter.

The activity coefficient can be calculated with the equation:

(4.1)

Where (a) and (b) are van Laar coefficients, -190 and 100 respectively.

The surface tension used in the Kelvin term can be calculated using:

(4.2)

Where (σbs) and (σov) are the surface tensions of water-ammonium bi-

sulphate solution and the organic compound respectively. The pa-

rameters c = 0.3 and d = 0.8 are dimensionless.

4.1.2. κ-Köhler

κ-Köhler theory (Petters and Kreidenweis, 2007) is a development of previ-

ously used representations of solute hygroscopicity in the Köhler equation.

κ-Köhler theory is a one-parameter model, where the hygroscopicity pa-

rameter, (κ), represents a measure of aerosol water uptake and CCN activity.

Values of (κ) for specific compounds, or for mixtures, can be determined

experimentally. Fitted values of (κ) for individual components may be com-

bined to represent the hygroscopic behaviour of mixed aerosols of known

composition. It is suggested that the reduction in surface tension at activation produced by

organic surfactants is too low to compensate the impact on the Raoult term

(Fuentes et al., 2011; Irwin et al., 2010), but this statement leads to a differ-

ence between measured and calculated CCN activity when applied to ambi-

ent conditions. The distribution between surface and bulk can be seen as

micelle formation exist in equilibrium with, rather than competing with, a

surface monolayer (Schwier et al., 2012).

37

The use of a hygroscopicity parameter, (κ), for characterizing the relative

hygroscopicities of individual aerosol constituents, known mixtures, and

complex atmospheric aerosols models the composition-dependence of the

solution water activity. Combined with the Kelvin term into κ-Köhler theory,

it determines the equilibrium water vapour saturation ratio, (S), over an

aqueous droplet.

(4.3)

Where D3=6(Vs+Vw)/π and Dd

3=6Vs/π. Vs is the volume of the dry particu-

late matter and (Vw) is the volume of the water.

As with traditional Köhler theory, the maximum in S(D) computed for a

specified initial dry particle size and composition (expressed by κ) deter-

mines the particle’s critical supersaturation (sc) for activation to a cloud

droplet (Petters and Kreidenweis, 2007).

4.1.3. Adsorption activation theory

Adsorption of water on wettable surfaces can dominate over hygroscopic

uptake, leading to adsorption theory replacing Köhler theory (Ovadnevaite et

al., 2011; Kumar et al., 2011). This can be used for hydrophobic or colloidal

mixtures even though the adsorption activation theory is developed for dust

particles.

The adsorbed amount of water can be described with surface coverage, (Θ),

the quote of the adsorbed water molecules and the water molecules in a

monolayer. The Frumkin adsorption isotherm (Damaskin, 1973) can be used

for a monolayer as described in detail by Shchekin et al (1995):

(4.4)

Where c is concentration, (KF) is the equilibrium constant and α is the inter-

action parameter. The interaction parameter describes the interaction energy

of the adsorbed surfactant molecules. If (α) is positive it corresponds to net

repulsive interaction which may occur between charged head-groups. If (α)

is negative it corresponds to attractive forces between the tail groups of the

surfactant being stronger. If α = 0, the Frumkin isotherm is equal to the

Langmuir isotherm (Langmuir, 1916).

Brunauer, Emmet and Teller (BET) is an isotherm for a multilayer adsorp-

tion model (Brunauer et al., 1938; Sorjamaa and Laaksonen, 2007).

38

(4.5)

Where (S) is the saturation ratio of gas and (c) is a constant related to the

heat of adsorption. BET assumes that average heat of adsorption equals the

heat of condensation from the second layer upwards (Sorjamaa and

Laaksonen, 2007). The difference between the traditional Köhler curves and

the BET isotherm is shown in Figure 11.

Figure 11. Köhler curves for a 100 nm dry particle assuming full solubility (tradi-tional Köhler theory, solid and dotted line) and adsorption (BET isotherm with parameter c=2, dashed line). Picture from Sorjamaa and Laaksonen (2007).

4.2. Experimental approaches

Since a great number of studies are published and the major part of these

studies is using an experimental approach, there would be difficult to men-

tion them all. Therefore, two topics have been selected in this overview to

shed some light on the progress of the experimental work that can contribute

to the development of Köhler theory.

39

4.2.1. Water activity

Water activity is a well known parameter and a part of the Rault term in the

Köhler equation. This parameter must be parameterized, especially for mix-

tures of compounds, both inorganic and organic. This is done in the experi-

mental study by Svenningsson et al. (2006). The effect of water vapour on

aerosol particles was studied at different RH: at subsaturation using a hygro-

scopic tandem differential mobility analyzer (H-TDMA) and at supersatura-

tion using a CCN spectrometer. The mixtures used are listed in Table 1.

Table 1. The content of mixtures A-D.

Mixture Content Weight %

A Ammonium Sulfate 30

Levoglucosan 18

Succinic Acid 27

Fulvic Acid 25

B Ammonium Sulfate 50

Sodium Chloride 30

Succinic Acid 10

Fulvic Acid 10

C Levoglucosan 20

Succinic Acid 40

Fulvic Acid 40

D Ammonium Nitrate 35

Ammonium Sulfate 35

Levoglucosan 6

Succinic Acid 12

Fulvic Acid 12

40

The Maclaurin expansion of the Rault term as a function of molality using a

constant value for the van´t Hoff factor is shown in Equation (4.6).

(4.6)

There is the use of the same notation as in the Köhler equation (Equation

2.1). The Rault term is then paramterized accordingly:

(4.7)

The parameters are listed for the different mixtures in Table 2.

Table 2. Parameters in the polynomial fit.

Mixture a1 a2 a3 a4 a5

A -0.0148 -4.71*10-3

1.23*10-3

-1.23*10-4

4.32*10-6

B -0.0151 -1.70*10-3

2.08*10-4

-9.62*10-6

1.54*10-7

C -7.80*10-3

9.93*10-5

-9.69*10-7

4.58*10-9

N/A

D -1.91*10-2

-7.19*10-5

4.08*10-5

1.95*10-6

2.94*10-8

The results show that the model matches with the measurements within

0.05% of supersaturation for most of the compounds, even though it has a

general tendency to overestimate it (Svenningsson et al., 2006).

4.2.2. Amorphous particles

It was shown by Murry (2008), using a powder X-ray diffractometer, and

Zobrist et al. (2008), using a differential scanning calorimeter, that atmos-

pherically relevant organic solutions can form glassy states at low tempera-

tures, implying the significance for ice nuclei in the upper troposphere. The

amorphous solid state of aerosol particles is discussed by Mikhailov et al.

(2009). They used H-TDMA to characterize the hydration and dehydration

of crystalline ammonium sulfate, amorphous oxalic acid and amorphous

levoglucosan particles and one of the major conclusions is that solid amor-

phous phases may be important also at ambient temperatures in the lower

atmosphere. Virtanen et al. (2010) used two scanning mobility particle sizers

and one electrical low-pressure impactor to investigate the bounce of aerosol

particles, and thereby determining that biogenic SOA particles can be in an

amporphous solid state, see Figure 12.

41

Figure 12. a) Biogenic SOA show a high bounce factor, implying that they

are in an amorphous solid state. b) Solid particles bounce. c) Liquid parti-

cles adhere to the surface. Virtanen et al. (2010)

This shows the need to rethink the traditional views of the kinetics and ther-

modynamics of SOA transformations in the atmosphere.

42

5. Results

Here is presented a summary of papers I-V.

5.1. Paper I

Surface-active cis-pinonic acid in atmospheric droplets: A molecular

dynamics study

In this paper, published in the Journal of physical chemistry letters, we simu-

lated water clusters of 1000, 2000 and 5000 water molecules containing up

to 243 molecules of CPA. The CPA molecules spontaneously accumulated

on the surface of the nanoaerosol clusters, whereby the calculated surface

tension was depressed according to the Szyszkowski equation. A decrease of

surface tension facilitates water vapour condensation onto the nanoaerosol

cluster, according to Köhler theory. This promotes droplet growth, which in

turn have an impact on the properties of clouds that are forming such as re-

flectivity (albedo). Figure 13 shows where CPA is a part of the cloud and

Figure 14 shows CPA molecules (bluish) located at the surface of the cloud

droplet.

43

Figure 13. Cis-pinonic acid in atmospheric droplets.

Figure 14. CPA molecules (blue) accumulated on the surface of the

nanoaerosol cluster.

44

The calculated values for surface tensions from the MD simulations com-

pared well with experimental data (Shulman et al., 1996). The MD simula-

tions also showed that the calculated surface tensions were dependent not

only on the concentrations of the surfactant CPA, but also on the size of the

clusters due to curvature effect. The partitioning of CPA molecules between

the bulk and the surface is important to consider and difficult for the Köhler

equation in its present form to take into account.

45

5.2. Paper II

Model HULIS in nanoaerosol clusters – investigations of surface tension

and aggregate formation using molecular dynamics simulations

Paper II, published in Atmospheric Chemistry and Physics, continued the

work from paper I, now with simulations of clusters of 10000 water mole-

cules, also containing compounds similar to CPA, namely PAD and PAL.

We calculated the surface tension depression and determined the

Szyszkowski parameters for all three compounds, where PAD and PAL was

previously undetermined. The simulations revealed that aggregates formed

for higher concentrations, which has not been observed before. The

formation of aggregates is supported by an experimental study by Virtanen

et al. (2010). One aggregate is shown in Figure 15. The radial number

density (RND) is shown in Figure 16.

Figure 15. 162 CPA system; cross-section picture. Water molecules are

omitted for clarity.

46

Figure 16. RND showing two main peaks at 1.1 and 4.2 nm. The green line

is the RND for the 162 CPA system multiplied with a factor of 10.

The formation of aggregates is important for the understanding of the state

of mixture in aerosols containing various organic compounds.

0

10

20

30

40

50

0 1 2 3 4 5 6

Rad

ial n

um

ber

den

sity

(n

m^-

3)

Radius (nm)

water

162 CPA

162 CPA * 10

47

5.3. Paper III

A theoretical study revealing the promotion of light absorbing carbon

particles solubilization by natural surfactants in nanosized water drop-

lets

In paper III, accepted for publication in Atmospheric Science Letters, we

show with MD simulation that a hydrophobic compound not solvable in

water, fluoranthene, can be solubilized in the aggregates formed by CPA.

The fluoranthene molecules also show a change of orientation when mixed

with CPA. From being orientated flat or paired up at the surface of a pure

water cluster, the fluoranthene molecules was upended when mixed with

CPA at the surface of the cluster, see Figure 17.

Figure 17. Molecules of fluoranthene (green) are solubilized by CPA mole-

cules at the surface. Fluoranthene molecules are upended to minimize the

contact with water. Water molecules are omitted for clarity.

This can help to explain how soot is aged during transport in the troposphere

and taken up in cloud droplets.

48

5.4. Paper IV

Glycine in aerosol water droplets: a critical assessment of Köhler theory

by predicting surface tension from molecular dynamics simulations.

Paper IV, published in Atmospheric Chemistry and Physics, investigates

how the DFAA glycine affects the surface tension of nanoaerosol clusters. A

comparison between pure water clusters and water clusters containing gly-

cine show differences in surface tensions. A quadratic polynomial is fitted to

the Köhler equation and there is a small correction. This method show how

results obtained for nanometer sizes can be applied to activated cloud drop-

lets.

This paper describes the procedure for calculation of surface tensions in

spherical clusters.

49

5.5. Paper V

Cloud droplet activation mechanisms of amino acid aerosol particles:

insight from molecular dynamics simulations

Paper V discusses surface active properties of amino acids in nanoaerosol

clusters. Six examined amino acids are categorized according to their

hydrophility. The effect on surface tension is explained from a molecular

point of view and the orientations of the different amino acids are investigat-

ed. We show that the hydrophobic amino acids Methionine and Phenylala-

nine accumulate at the surface of the nanoaerosol clusters, see Figure 19.

Figure 19. Amino acids orientation in nanoaerosol clusters. SER – Seronine,

GLY – Glycine, ALA – Alanine, VAL – Valine, MET – Methionine, PHE –

Phenylalanine.

Phenylalanine even arranged in an ordered manner at the surface, see Figure

20.

50

Figure 20. Phenylalanine molecules ordered at the surface of the

nanoaerosol cluster. Hydrogen bonds are marked out.

One hypothesis states that the exposure to the ambient air at the interface

subjects the amino acids to possible oxidation and degradation.

51

6. Outlook

Since the method, MD simulations, is carried out using computers, the limit-

ing factor is the computer power used. The super computer used for the sim-

ulations in this thesis is very powerful compared to a PC working station

today, 2013. However, the development of computer hardware is very fast,

and from a historical perspective, super computers used for scientific work

may seem ridiculous twenty years later, see Figures 21 and 22.

Therefore, the future is bright for MD simulations as a tool for modeling the

formation and growth of aerosol particles and the process of cloud droplet

activation. The simulation time needed is approximately proportional to the

square of the size of the system simulated. Time is then reduced as the com-

puter speed becoming higher and higher.

There are other aspects of aerosols that are important for the understanding

of the aerosol-cloud-climate system such as light absorption and scattering.

These properties of both aerosols and clouds are of major importance for

determining the impact on global warming. We have begun to conduct cal-

culations of these properties using quantum computations. The systems we

use are similar to those reported in paper III. Preliminary results show that

Figure 21. ENIAC – the first su-

percomputer (University of Neva-

da Las Vegas, 2010)

Figure 22. Ekman – one of the

thirty fastest supercomputers in

the world (Stockholm university,

2010).

52

organic carbon in the form of CPA can change the absorption of soot-like

molecules (Fluoranthene). This implies that the aging of soot affect the ab-

sorbing potential and thereby the contribution to global warming.

A new approach to the understanding of aerosol-cloud-climate system is

started using the dynamic vegetation model LPJ (Lund-Potsdam-Jena)

(Smith et al., 2001; Sitch et al., 2003) for modeling the growth of pine for-

ests as a result of global warming and increased concentrations of carbon

dioxide in the atmosphere. Pine forests evaporate organic vapours that can

transform into CCN and affect the cloud formation, especially in the Arctic.

53

7. Acknowledgements

I would like to thank my supervisor Professor Caroline Leck for introducing

me to atmospheric science in a most excellent way. Her knowledge of the

field and good advice has been invaluable. We often have the same opinion

which I suspect depends on the fact that we are both teachers.

I sincerely thank my assistant supervisor Professor emeritus Henning Rodhe.

It is inspiring to work with a person that has contributed so much to the field

of atmospheric science.

I greatly thank my collaborators at the department for theoretical chemistry

and biology, KTH Royal institute of technology; Professor Hans Ågren,

associate Professor Yaoquan Tu, Doctor Xin Li and Lu Sun. The project has

been very fruitful thanks to you. You are very experienced and professional,

and the sharing of ideas and work has been easy. I thank you especially for

introducing me to GROMACS molecular dynamics.

I take this opportunity to thank all personnel at MISU, the department of

meteorology at Stockholm University. The friendly atmosphere has contrib-

uted significantly to a good working effort. I wish to thank my room-mate

Jenny Hieronymus and her husband and my colleague Magnus Hieronymus

for your friendship, lunchtime discussions and for inviting me and my family

to your wedding. I want to thank Evelyne Hamacher-Barth, Jonas Claesson

and Marcus Löfverström for all the conversations and good laughs. I also

want to thank all the members of the CM-group for interesting contributions

and for buns, cakes, ice-cream and such.

I want to thank my relatives; Mom and dad - I know you always want the

best for me and I appreciate it (even though it may not always show), my

brother Ronnie - I know I can count on you, and you have a great taste in

films and music, Margareta “Maggan” Wästfelt - you are a great support to

me and my family, especially during the last periods of bad health, Torsten

and Sandra Wästfelt - I hope we can get to know each other further, Holger

Rundström - you are very kind and you have shown real dedication to my

work, may also the memory of Ulla be with us, grandpa Martin and grandma

Ketty - if there is a heaven, I know you are there.

54

I want to thank my friends; Erik Pettersson - you are like a brother to me, I

wish you and your wife Anna a wonderful life together, thank you both for

inviting me and my family to your wedding, Marcus Sjödin - ever since the

chemistry classes we have been the best of friends and I hope for many more

years with bad jokes and other types of fun, Calle, Karin and Alice Ekstrand

- through good times, through bad times, I hope for the first in the future,

you are always welcome to Kungsängen and to Engelsfors. All you friends

that I have not mentioned here deserve gratitude and I hope you take credit

for it!

I want to thank all the teachers I have had, from the kindergarten to univer-

sity and to the system of education that made this journey possible.

Finally, I want to send my gratitude and love to my family; Angelica, Martin

and Miranda! I dedicate this thesis to you. You are everything to me!

55

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