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Doctoral Thesis

Thermodynamic Properties and Nucleation Processes of UpperTropospheric and Lower Stratospheric Aerosol Particles

Author(s): Knopf, Daniel A.

Publication Date: 2003

Permanent Link: https://doi.org/10.3929/ethz-a-004555208

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Diss. ETH No. 15103

Thermodynamic Properties and Nucleation

Processes of Upper Tropospheric and Lower

Stratospheric Aerosol Particles

A dissertation submitted to the

SWISS FEDERAL INSTITUTE OF TECHNOLOGY

ZURICH

for the degree of

Doctor of Natural Sciences

presented byDANIEL A. KNOPF

Dipl. Phys.born 1. May 1973

citizen of Germany

accepted on the recommendation of

Prof. Thomas Peter, examiner

Prof. Ulrich Schurath, co-examiner

Dr. Thomas Koop, co-examiner

2003

1

Zusammenfassung

Atmosphärische Aerosolteilchen unterhegen thermodynamischen und kinetischen Prozessen

durch die Wechselwirkung mit ihrer Umwelt. Diese Prozesse beinhalten unter an¬

derem Änderungen in ihrer Zusammensetzung durch die Aufnahme von Gasmolekülen und

Phasenübergänge, die durch Kristallbildung hervorgerufen werden. Eine atmosphärische Re¬

gion von besonderer Bedeutung, ist die obere Troposphäre/untere Stratosphäre (OT/US), in

der Aerosolteilchen an der Wolkenbildung und an heterogenen Reaktionen beteiligt sind. Diese

Prozesse sind für die Ozonchemie, die Strahlungswechselwirkung und die Dehydratation von

Luft beim Durchqueren der Tropopause von grosser Bedeutung. In dieser Arbeit wurden La¬

borexperimente mit Hilfe von optischer Mikroskopie in Kombination mit Raman-Spektroskopie

durchgeführt, die Relevanz für Aerosolprozesse in der OT/US besitzen.

Die Dissoziationsreaktion des Hydrogensulfations, HSOJ ?=± SO|~ + H+, wird in wässrigen

H2S04-Lösungen in einem Konzentrationsbereich von 0.54-15.23 mol kg-1 und einem Tempe¬

raturbereich von 180-330 K unter Verwendung der Raman-Spektroskopie untersucht. Alle unter¬

suchten H2S04-Lösungen zeigen einen kontinuierlichen Anstieg des Dissoziationsgrads von HSOJ

mit abnehmender Temperatur. Dies steht im Widerspruch zu Vorhersagen thermodynamischer

Modelle wässriger H2S04-Lösungen. Ein Pitzer Ionen-Wechselwirkungsmodell wird eingesetzt,

um eine thermodynamische Dissoziationskonstante des Hydrogensulfations, Kn(T), abzuleiten,

die thermodynamisch konsistent ist und mit den experimentellen Daten übereinstimmt. Die

neue Parameterisierung von Ku(T) ist gültig von 180 K bis 473 K. Im typischen Temperaturbe¬

reich der OT/US zeigen Berechnungen des Ionen-Wechselwirkungsmodells deutliche Abweichun¬

gen der Aktivitätskoeffizienten, der Wasseraktivitäten, der Wasserdampfdrücke und der HCl

Löslichkeiten zu bestehenden thermodynamischen Modellen von H2SO4/H2O Lösungen.

Die Zirrus-Eiswolkenbildung wird durch Messungen der oberen Grenzen des homogenen Eis-

nukleationsratenkoeffizienten und des pseudo-heterogenen Eisnukleationsratenkoeffizienten in

wässrigen (NRi)2S04 Tropfen untersucht. Für Temperaturen von 215 K ergeben die Experi¬

mente Ratenkoeffizienten von 106 cm-3 s_1 bzw. 3.2-102 cm-2 s~1. Diese Eisnukleationsraten-

koeffizienten sind kleiner als die durch Infrarotspektroskopie an strömenden Aerosolpartikeln

(AFT-IR: Aerosol Flow Tube-Infrared Spectroscopy) bestimmten Werte, sind aber im Ein¬

klang mit in Emulsions- und anderen optischen Mikroskop-Experimenten gewonnen Raten¬

koeffizienten. Es wird vermutet, dass die Gründe für die widersprüchlichen Datensätze in der

Aufarbeitung der experimentellen Daten liegen.

Die Bildung Polarer Stratosphärenwolken wird theoretisch und experimentell erforscht, in¬

dem homogene und pseudo-heterogene Nukleationsratenkoeffizienten von NAD und NAT

in HNO3/H2O und HN03/H2S04/H20-Lösungströpfchen untersucht werden. Die unter

stratosphärischen Bedingungen in flüssigen Tröpfchen gemessenen oberen Grenzen der homo¬

genen Nukleationsratenkoeffizienten von NAD und NAT sind 2-10-5 cm-3 s_1 und 8-10~2

cm-3 s-1. Die oberen Grenzen der pseudo-heterogenen Nukleationsratenkoeffizienten von NAD

und NAT betragen 1.5-10-6 cm-2 s-1 und 9-10~4 cm-2 s_1. Diese experimentell bestimmten

Nukleationsratenkoeffizienten sind bis zu 8 Grössenordnungen kleiner als Ratenkoeffizienten

berechnet durch eine Nukleationsparameterisierung, die in einer kürzlich veröffentlichten De-

nitrifizierungsstudie zur Anwendung kam. Die hier vorgestellten Nukleationsratenkoeffizienten

11

ergeben unter stratosphärischen Bedingungen Bildungsraten der aus Salpetersäure Hydraten

bestehenden Teilchen von maximal 3-10-10 cm-3 (Luft) h-1 und 6-10-6 cm-3 (Luft) h_1 für die

homogene und pseudo-heterogene Nukleation. Diese Produktionsraten sind zu gering, um die

kürzlich beobachteten Teilchenanzahlen grosser salpetersäurehaltiger Teilchen zu erklären und

reichen deshalb nicht aus, die daraus folgende Denitrifizierung des arktischen polaren Wirbels

zu beschreiben.

m

Abstract

Atmospheric aerosol particles are subject to thermodynamic and kinetic processes through inter¬

action with their environment. Such processes involve, among others, composition changes due

to uptake of gas phase molecules and liquid-to-solid phase transitions induced by crystal nucle¬

ation. An atmospheric region of particular interest is the upper troposphere/lower stratosphere

(UT/LS), where aerosol particles are involved in cloud formation and heterogeneous reactions,

which are important for ozone chemistry, radiation, and the dehydration of air crossing the

tropopause. In this work, laboratory experiments, employing optical microscopy combined with

Raman spectroscopy, have been performed to study aerosol processes relevant to the UT/LS.

The dissociation reaction of the bisulfate ion, HSO4 ^ SO2- + H+, is investigated in aqueous

H2SO4 solutions with concentrations of 0.54-15.23 mol kg-1 in the temperature range of 180-326

K using Raman spectroscopy. All investigated H2SO4 solutions show a continuous increase in

the degree of dissociation of HSOJ with decreasing temperature, in contrast to predictions from

thermodynamic models of aqueous H2SO4 solutions. A Pitzer ion interaction model is used to

derive a thermodynamically consistent formulation of the thermodynamic dissociation constant

of the bisulfate ion, Kn(T), that is in agreement with the experimental data. The new formula¬

tion of Ku(T) is valid from 180 K to 473 K. Calculations with the ion interaction model reveal

considerable differences in ion activity coefficients, water activities, water vapor pressure, and

HCl solubilities, when compared to existing thermodynamic models of H2SO4/H2O solutions,

in particular at temperatures typical for the UT/LS.Cirrus ice cloud formation is studied by measuring upper limits of the homogeneous and pseudo-

heterogeneous ice nucleation rate coefficients in aqueous (NHj)2S04 droplets. At temperatures

of about 215 K, the experiments reveal values of these rate coefficients that are smaller than ~106

cm-3 s_1 and ~3.2-102 cm-2 s-1, respectively. These values are smaller than the nucleation

rate coefficients obtained by AFT-IR (Aerosol Flowtube-Infrared) spectroscopy studies, but are

in agreement with emulsion studies and other optical microscope experiments. The reasons for

the discrepancies between the different data sets cannot be resolved but are suspected to have

their origin in the evaluation procedures of the experimental data.

Polar Stratospheric Cloud formation is studied by investigating, both theoretically and experi¬

mentally, the homogeneous nucleation and pseudo-heterogeneous nucleation of NAD and NAT

in HNO3/H2O and HNO3/H2SO4/H2O solution droplets. For polar stratospheric conditions,

the upper limits of the homogeneous nucleation rate coefficients of NAD and NAT in liquid

aerosols derived from the experiments are 210-5 cm-3 s_1 and 810-2 cm-3 s_1, respectively.

The upper limits of the pseudo-heterogeneous nucleation rate coefficients of NAD and NAT are

1.5-10-6 cm-2 s-1 and 9-10-4 cm-2 s_1, respectively. These experimentally derived nucleation

rate coefficients are lower by up to 8 orders of magnitude than values in recently published nu¬

cleation parameterizations used in denitrification studies. From the nucleation rate coefficients

presented here, maximum hourly production rates of nitric acid hydrate particles at strato¬

spheric conditions are calculated which yield about 3-10-10 cm"3 (air) h_1 and 610-6 cm~3

(air) h_1 for homogeneous and pseudo-heterogenous nucleation, respectively. These production

rates are too low to explain the number densities of large nitric acid containing particles recently

observed in the Arctic stratosphere and, therefore, are insufficient to account for the subsequent

IV

stratospheric denitrification of the Arctic polar vortex.

Contents

1 Introduction 1

1.1 Aerosols in the atmosphere 1

1.1.1 Particulate matter 1

1.1.2 The atmosphere 3

1.1.3 Aerosols in the UT/LS 3

1.2 Relevance of atmospheric aerosols 7

1.2.1 Climate forcing 7

1.2.2 Heterogeneous chemistry 9

1.3 Processes in UT/LS aerosols 10

1.3.1 Thermodynamic processes11

1.3.2 Kinetic processes11

1.4 Objectives of this PhD thesis 12

2 Theory 13

2.1 Thermodynamic processes in UT/LS aerosol 13

2.1.1 The Gibbs free energy13

2.1.2 Chemical potential of solutions 14

2.1.3 Henry's law constant 15

2.1.4 Water activity 16

2.1.5 Phase diagram of H2S04/H20 16

v

vi

2.1.6 Phase diagram of (NH4)2S04/H20 17

2.1.7 Phase diagram of HN03/H20 18

2.2 Kinetic processes in UT/LS aerosol 20

2.2.1 Classical nucleation theory 20

2.2.2 Surface nucleation 23

2.3 Raman spectroscopy 24

2.3.1 Classical derivation of the Raman effect 26

3 Experimental 29

3.1 Sample preparation 29

3.2 Sample cell 31

3.3 Hydrophobic coating 31

3.4 Experimental setup 32

3.5 Experimental procedure 34

4 Thermodynamic processes in UT/LS aerosol particles 35

4.1 Abstract 39

4.2 Introduction 39

4.3 Experimental Section 40

4.4 Results and Discussion 42

4.4.1 Analysis of Experimental Data 43

4.4.2 Results of the Pitzer Ion Interaction Model 49

4.5 Atmospheric Implications 53

4.6 Conclusions 56

4.7 Appendix 56

4.7.1 Tables 56

4.7.2 Derivation of the thermodynamic dissociation constant of HSOJ 61

4.7.3 Extended Pitzer Ion Interaction Model 62

Contents vii

4.8 HCl solubility in H2S04/H20 solutions 67

4.9 Analysis of H2SO4/H2O Raman spectra 69

4.10 Analysis of (NH4)2S04/H20 Raman spectra 75

4.11 The ferroelectric phase transition of (NH4)2S04 77

5 Kinetic processes in UT/LS aerosol particles 83

5.1 Abstract 87

5.2 Introduction 87

5.3 Nucleation formulation analysis 88

5.4 Experimental 90

5.5 Results and discussion 94

5.6 Conclusions 98

5.7 Pseudo-heterogeneous nucleation of PSCs 101

5.8 Homogeneous ice nucleation in (NH4)2S04/H20 droplets 107

6 Final remarks 113

6.1 Summary and conclusion 113

6.2 Outlook 116

A Experimental 119

A.l Electrical circuit for the operation of the inkjet-cartridge 119

B Raman spectroscopy 121

B.l Assignments of the normal vibrations of the investigated Raman spectra 121

C Heterogeneous chemistry 125

D Nucleation rate coefficients and production rates 127

D.l Derivation of upper nucleation limits 127

D.2 Derivation of stratospheric production rates of NAD and NAT 128

VlllContents

E Parametrizations of NAD and NAT nucleation mechanisms 131

E.l Homogeneous nucleation parametrization of NAD and NAT 131

E.2 Pseudo-heterogeneous nucleation activation energies of NAD and NAT 132

List of Figures 133

Bibliography 137

Acknowledgements 149

Chapter 1

Introduction

1.1 Aerosols in the atmosphere

1.1.1 Particulate matter

Aerosols are defined as relatively stable suspensions of solid or liquid particles in a gas (Finlayson-

Pitts and Pitts, 2000). Atmospheric aerosols consists of particles and particulate matter with

diameters of ~0.002-100 fim.

The particles arise from natural sources like sea spray and volcanos, but also from anthropogenic

activities such as combustion of fuels. Aerosol particles can be emitted directly (primary aerosol)

into the atmosphere or can be formed in the atmosphere by gas-to-particle conversion processes

(secondary aerosol). The airborne particles can change their size and composition due to several

interaction processes, such as condensation and evaporation of vapor species, coagulation with

other aerosol particles, and chemical reactions. In an environment supersaturated with respect

to water the particles also can become activated into cloud droplets.

Figure 1.1 shows a typical aerosol size distribution. Whitby and Sverdrup (1980) suggested

that three distinct aerosol size modes exist: Particles larger than 2.5 /im are identified as coarse

particles and those with diameters smaller than 2.5 /xm are called fine particles. Most of the

aerosol mass and aerosol number belongs to this fine particle mode. This mode can be further

devided into the accumulation range (0.08 /im to 1-2 /im) and the transient or Aitken range

(0.01-0.08 /im). In recent years the technology for measuring very small particles has advanced,

so a fourth size mode could be identified known as ultra fine particles, which describe aerosol

particles with diameters smaller than 0.01 /im. Figure 1.1 also shows the main atmospheric

aerosol formation mechanisms, leading to the different particle size modes. These formation

mechanisms involve the chemical conversion of gases to low volatile gases, the condensation of

hot vapor to particulate matter occurring during combustion, and non-chemical processes such

as wind blown dust and sea spray. Homogeneous nucleation plays a fundamental role in the

formation processes of aerosol particles. These particles can grow in diameter by coagulation

until they reach sizes corresponding to the Aitken mode and accumulation mode. The two

1

2 CHAPTER 1. INTRODUCTION

Chemical conversion

of gases to low

volatility vapors

Chemical conversion

of gases to low

volatility vapors

Wind blown dust

+

Emissions

Sea Spray+

Volcanos

+

Plant particles

Particle diameter (urn)

„ „

Transient nucleiUltra fine or Aitken nuclei

particles__

| range->+*- -*+*-

Accumulation

range

fine particles -

Mechanicallygeneratedaerosol range

Coarse particles -

Figure 1.1: Sketch of atmospheric aerosol formation mechanisms and corresponding four mode aerosol

size distribution (Finlayson-Pitts and Pitts, 2000). This graph was adapted from Whitby and Sverdrup

(1980) whose original hypothesis consist only of a three mode aerosol size distribution which is indicated

as solid line.

main mechanisms which axe responsible for the removal of atmospheric aerosol particles are

dry deposition and wet deposition. The first applies mainly to coarse particles which sediment

due to gravitational forces. The latter is the main loss process for particles belonging to the

accumulation size mode due to the scavenging by raindrops (washout).Table 1.1 shows average values for mass and composition of typical tropospheric aerosols. A

significant fraction of the aerosol is due to anthropogenic origin. The particles contain sulfate,

ammonium, nitrate, and a large fraction of elemental and organic carbon. Elemental carbon

(soot, graphite) is directly emitted by combustion processes. Organic carbon can be emitted

directly or forms by condensation of low volatile organic gases such as polycychc aromatic

hydrocarbons (PAHs).

1.1. Aerosols in the atmosphere 3

Table 1.1: Moss concentration and composition of tropospheric aerosols (Heintzenberg, 1989). The

composition is given in percentage.

Region Mass [/xg m 3] C (elemental) C (organic) NH+ NO3 SOl"

Remote 4.8 0.3 11 7 3 22

Nonurban continental 15 5 24 11 4 37

Urban 32 9 31 8 6 28

In the free troposphere above about 6 km height the average mass concentration of the particles

is about 1 /ig m-3. At lower altitudes the mass concentration can vary from 0.7 /ig m-3 in

remote continental sites to 150 /ig m-3 in desert regions (Jaenicke, 1993). An average aerosol

number density of about 300 cm-3 is observed in the well-mixed troposphere above 6 km height.

Higher particle number concentrations of up to 3104 cm-3 can be found in remote continental

areas at lower altitudes (Jaenicke, 1993).

1.1.2 The atmosphere

Figure 1.2 shows the pressure and temperature of the standard atmosphere as a function of

altitude. The pressure decreases exponentially with altitude. As a rule of thumb, the pressure

decreases by a factor oftwo over 5 km in height. Temperature decreases with altitude throughout

the troposphere up to the tropopause, where the temperature experiences a minimum. The

height of the tropopause is defined by the lowest altitude level where the temperature decreases

by less than two kelvin per kilometer (WMO, 1992). The temperature of the tropopause can be

as low as 180 K. The height of the tropopause changes with latitude and season, ranging from

8 km at the poles up to 16-17 km in the tropics. While temperatures in the lower stratosphere

are generally warmer than at the tropopause it can be as low as 180 K in the polar regions, a

prerequisite for the formation of Polar Stratospheric Clouds (PSCs). The temperature in the

stratosphere rises with altitude until a temperature maximum is reached at the stratopause.

The gray shaded region in Fig. 1.2 indicates the part of the atmosphere which is called Upper

Troposphere/Lower Stratosphere (UT/LS). It is the region of the atmosphere between ~10-25

km, which is one of the coldest parts of the atmosphere. This thesis focuses on aerosol particles

and their interactions with the surrounding environment in this part of the atmosphere.

1.1.3 Aerosols in the UT/LS

The chemical composition of aerosol particles in the UT/LS can vary significantly. It is

generally agreed that aerosol in the upper troposphere are usually sulfate particles with a

varying degree of neutralization ranging from sulfuric acid to ammonium sulfate (Martin, 2000;

Colberg, 2002). Additional components such as nitrates and organics have been also found in

upper tropospheric aerosols (Murphy et al., 1998).


<B133

1C-3 10"2 10'1 1 10 102

00

I 1 1 I 1

Thermosphère /

/

90 /

1

j Mesopause

80 - \

70

60

50

-

X. Mésosphère XI®*.

X Stratopause

\ ;

40 \ /

Stratosphere \ /

30 / \

20

/ x/ xi X.

10

TrofopHtise \ X.\ XN X

01 I I I

Troposphere v^

1 1 I 1 1 1 I I 1 h I I I 1

100 200 300

Temperature (K)

Figure 1.2: The pressure and temperature ofthe standard atmosphere are plotted as afunction of altitude

(adapted from Finlayson-Pitts and Pitts (2000)). The different parts of the atmosphere are indicated. The

gray shaded area is defined as the upper troposphere/lower stratosphere.

Since the 1970's it has been known that stratospheric aerosol particles consist of sulfuric acid and

water (Junge and Manson, 1961). The source for the H2SO4 in the globally distributed strato¬

spheric background aerosol is the oxidation of carbonyl sulfide (OCS). This is oxidized to SO2

which further reacts with OH to finally form H2SO4. H2SO4 nucleates to form aerosol particles.

Another important source for stratospheric H2SO4 axe major volcanic eruptions. Because of its

very low vapor pressure, the stratospheric background aerosol consists predominantly of sulfate

as was recently confirmed by laser ionization mass spectrometry, see Fig. 1.3. During this field

measurements only in a few percent of the particles was sulfate not the dominant compound

(Murphy et al., 1998).Stratospheric background aerosol particles act as precursor for the formation of PSCs. The latter

have been observed since 1870 (Stanford and Davis, 1974). During winter time PSCs form in the

polar regions at an altitude of 15-30 km, when the temperature drops below ~198 K. Usually

PSCs persist longer over the Antarctic region since the polar vortex is dynamically more stable

than that over the Arctic pole and, therefore, the temperatures remain longer cold enough for

PSC formation (Schoeberl and Hartmann, 1991). PSCs consist mainly of ternary mixtures of

1.1. Aerosols in the atmosphere 5

0.3

|o.2m

0.1

0.0

OH"

1»8«$©7#o6?219 km; 31°M

(M37K

MS04"

HSO,

20

SOjT 804"

^-4-

rrso/

40 60 80

Ion mass/charge

100 100

Figure 1.3: Negative ion mass spectra of individual sampled aerosol particles in the lower stratosphere

Murphy et al. (1998).

Table 1.2: PSC properties. Adapted from Turco et al. (1989).

Type la Type lb Type II

T threshold < 198 K > 187 K < 187 K

composition H2SO4/HNO3/H2O STS H2O + traces

diameter > 1 /im 0.5-1 /im 5-100 /im

phase crystalline liquid ice

H2SO4, HNO3, and H2O. Table 1.2 presents typical properties ofPSC particles such as existence

temperature, composition, diameter, and the kind of phase. There are three forms of PSC par¬

ticles. Type I PSCs contain signifant amounts of HNO3, whereas type II PSCs consist mainly of

water ice. PSCs of type I axe further divided into type la and lb. Laboratory experiments sug¬

gested that PSCs of type la consist of crystalline NAT (nitric acid trihydrate) which is the most

stable nitric acid hydrate under stratospheric conditions (Hanson and Mauersberger, 1988a).

Worsnop et al. (1993) showed in laboratory experiments that also crystalline NAD (nitric acid

dihydrate) could exist in PSCs. Type lb PSCs are composed of supercooled ternary solutions

(STS). First suggestions of their existence were based on model calculations. Figure 1.4 repre¬

sents the volume density of PSCs measured in the Airborne Arctic Stratospheric Experiment

1989 (AASE) by Dye et al. (1992) and the thermodynamic equilibrium model calculations of

Carslaw et al. (1994).

Figure 1.4 shows that neither aqueous H2SO4 nor NAT particles can explain the measured

volume densities. The model calculations indicate that in this field measurements STS aerosols


10

gm

E

10.1

0,01185 190 195 200 205 210

T/K

Figure 1.4: The dots represent particle volumes measured by Dye et al. (1992). The lines indicate

model calculations of Carslaw et al. (1994). The thick solid line represents model calculations assuming

the growth of liquid STS particles by Hi 0 and HNO3 uptake. The dashed line corresponds to a model

simulation taking into account the NAT deposition on frozen particles. The dotted line shows the growth

of binary liquid H2SO4/H2O by H2O uptake. The model calculations were performed at 55 mbar for 5

ppmv H2O, lOppbv HNO3, and 0.5 ppbv H2SO4. The thin solid lines indicate a sensitivity study assuming

5 and 15 ppbv gas-phase HNO3, respectively. The NAT saturation temperature for 10 ppbv HNO3 (196.2

K) and the frost point (188.9 K) are also displayed.

were sampled. The model calculations in Fig. 1.4 are performed with a Pitzer ion interaction

model (Carslaw et al., 1995a). In the meantime in situ composition measurements of PSC

particles have confirmed that PSC particles can consist of STS or NAT particles (Schreiner

et al., 1999; Voigt et al., 2000).At temperatures below the frost point Type II, PSCs can form. Due to the large amount

of available water vapor these PSC particles can grow to diameters up to 100 /im. Type la

particles are typically larger than type lb aerosols, since only a few particles nucleate NAT

which subsequently deplete the available gaseous HNO3. The liquid type lb particles grow

simultaneously, thereby distributing the gaseous HNO3 amount to a larger number of particles.

Therefore, their size is smaller than that of type la PSCs.

If HNO3 containing particles grow to particle sizes larger than 2 /im in diameter, they can

sediment to lower altitudes due to gravitational forces. This process can lead to a significant

removal of HNO3 from the stratosphere and is known as stratospheric denitrification (Seinfeld

and Pandis, 1998). At lower altitudes and, hence, higher temperatures, the particles evaporate

and HNO3 is released again into the gas phase. The removal of HNO3 is crucial for stratospheric

gas-phase chemistry since NO2 (NO2 is a photolysis product of HNO3) converts the ozone

destroying gas CIO into the unreactive reservoir species CIONO2 (Seinfeld and Pandis, 1998).

A still unresolved question is the observation of large HNO3 containing particles up to 15 /im

in diameter with number densities of about 10-4 cm-3 during the Arctic winter of 1999/2000

(ICE) (NAT)

Ll Li I

1.2. Relevance of atmospheric aerosols 7

(Fahey et al., 2001). Such large HNO3 containing particles can have a major impact on the

denitrification of the stratosphere. Tabazadeh et al. (2001) proposed that the observed number

densities of the large particles can be explained by homogeneous nucleation of NAD and NAT

in STS particles. In contrast, Knopf et al. (2002) derived NAD and NAT production rates from

laboratory experiments showing that homogeneous nucleation rates in STS particles are too

small to explain stratospheric denitrification. Thus, other formation processes of the observed

large particles must be involved, such as heterogeneous nucleation of NAT onto PSC type II

particles (Waibel et al., 1999) or the proposed mother cloud/NAT-rock mechanism (Fueglistaler

et al., 2002). A very recent suggestion of Tabazadeh et al. (2002a) follows the idea of a pseudo-

heterogeneous nucleation mechanism of NAD and NAT in STS particles. These suggestions will

be discussed in more detail later in this thesis.

1.2 Relevance of atmospheric aerosols

1.2.1 Climate forcing

The Earth's climate is controlled by the energy balance between the incoming solar radiation

and the emission of long-wave radiation from the Earth-atmosphere system into space. 30 % of

the incoming solar radiation is scattered back to space due to the Earth's albedo. The latter is

strongly influenced by the presence of aerosols and clouds. A major proportion of the radiation

emitted by the Earth into space is absorbed by greenhouse gases, aerosols, and clouds, thereby

warming the atmosphere.A measure of any perturbation in the radiative energy budget of the Earth's climate system is

given by the term "radiative forcing". The definition for radiative forcing given here is adapted

from the Intergovernmental Panel on Climate Change (Houghton et al., 2001): uThe change in

radiative forcing of the surface-troposphere system due to the perturbation in the amount of or

the newly introduction of an agent in the atmosphere, respectively, is defined as the change in

net (downward minus upward energy flux) irradiance (incoming solar radiation plus outgoing

long-wave radiation in units W m~2) at the tropopause after allowing for stratospheric temper¬

atures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and

state held fixed at the unperturbed values".

The aerosol effect on radiative forcing can be divided into the direct and the indirect aerosol

effect. The direct effect describes the interactions of the aerosol with radiation. The indirect

effect takes into account the ability of aerosol particles to serve as cloud condensation nuclei

(CCN) or ice nuclei (IN) thereby changing the optical properties of clouds. Figure 1.5 sum¬

marizes the anticipated radiative forcing of various substances by IPCC. The scientific level of

understanding for the particular processes is also indicated (Houghton et al., 2001). Here we

will focus on the effects related to aerosols. Sulfate containing aerosols and particles generated

by biomass burning have a negative radiative forcing, i. e. they contribute to a cooling of the

atmosphere. The influence of mineral dust particles is not clear yet. They can contribute to

either cooling or heating. Aerosols containing black carbon emitted from fossil fuel burning axe

expected to heat the atmosphere, since these particles are strong absorbers. Aerosols containing


| -2

Hatocarbons

CH«

Aerosols

CO,

Tropoapnericozone

Blackcarbon irom

fossilfuel

burning

MineralDust

-cçrStratasphariç

ozone

îi «-*-»—nnT [ * ^pl"^ Organic 11 carbon ri*»«,«

Organiccarbon

fuel

burning

Blomass

owning

Aviation-induced

,*

N

Contrails cirrus

Tn.CD

Solar

Aaissaf

indlwctsi set

Land-

(afcedo)only

High Med. Med. Low VeryLow

Verytow

Very VeryLow Low

VeryLow

VaryLow

VeryLow

VsryLow

Leva of Scientific Understanding

Figure 1.5: The effect on radiative forcing is shown for various atmospheric radiatively active agents.

The level of scientific understanding is also indicated for the presented processes (Houghton et al., 2001).

organic carbon are assumed to cool the atmosphere. The scientific level of understanding of

these processes is in general low to very low.

It is assumed that changes in cloud properties induced by aerosol particles contribute negatively

to radiative forcing. However, because of the large uncertainties involved no forcing value was

assigned by IPCC and only a range is given, indicated by the error bars in Fig. 1.5. In the follow¬

ing sections the influence of aerosols on the direct and indirect aerosol effects will be discussed

in further detail.

Direct aerosol effect

The aerosol particles in the atmosphere interact with the incoming solar radiation by scattering

and absorption. Therefore, the particles affect the radiation budget of the Earth-atmosphere

system. The main uncertainties in quantifying this direct aerosol effect are accurate estimates

in the determination of the primary aerosol sources (Houghton et al., 2001). Secondary aerosol

species also have uncertainties both in the sources of the precursor gases and in the atmospheric

processes that convert some of those gases to aerosol particles.

The optical interaction of aerosols with solar radiation depends on the phase and radius of

the particles. Due to the temperature and relative humidity changes in the atmosphere, aerosol

particles are forced to take up or to release water and, hence, change their diameters accordingly.

Therefore, particle radius and phase are crucial for the optical properties of the aerosols, i.

1.2. Relevance of atmospheric aerosols 9

e. wether the particles have a net positive or negative effect on radiative forcing. As long

as the particles are liquid or partially liquid the change in particle volume due to changes

in atmospheric conditions can be calculated using thermodynamic models such as Pitzer ion

interaction models. The optical properties of the liquid aerosol will change significantly, when a

crystalline phase forms in the particles. The nucleation of a new phase is a kinetic process and,

therefore, cannot be predicted by thermodynamic models. Hence, the atmospheric conditions

at which crystalline phases nucleate in aqueous droplets must be determined by laboratory

experiments. The experimentally derived nucleation rates can then be applied to radiation

models to obtain an estimate of the radiative forcing.

Indirect aerosol effect

The indirect aerosol effect links various processes such as the ability of aerosol particles to serve

as CCN and IN with the resulting radiative forcing due to clouds. In the lower troposphere the

indirect aerosol effect combines two individual effects:

First, anthropogenic emissions increase the number of aerosols which can act as CCN. Therefore,

the number of cloud droplets is increased and the cloud droplet size distribution is shifted to

lower diameters. This leads to an increases of the optical depth of the cloud, enhancing the

cloud albedo (Twomey, 1974).The second effect refers to the lower precipitation efficiency and the increased thickness of clouds

due to the reduction in cloud droplet size and the increase of cloud droplet number density, re¬

spectively (Albrecht, 1989; Pincus and Baker, 1994).In the upper troposphere cirrus ice clouds form due the low temperatures in this part of the

atmosphere. Although the role of cirrus ice clouds on climate is not yet quantified, ice formation

by homogeneous nucleation of aerosol particles is believed to have an impact on the global ra¬

diative forcing (Houghton et al., 2001). Several Global Circulation Models (GCM) studies have

supported the expected influence of ice formation from supercooled water on global radiative

forcing (Senior and Mitchell, 1993; Fowler and Randall, 1996). Lohmann and Feichter (1997)

performed a sensitivity modelling study showing a globally averaged cloud forcing of +16.9 W

m-2 obtained by allowing only ice in clouds with a temperature below 273 K compared to clouds

containing only water droplets for temperatures above 238 K. Therefore, even small changes of

the ice content in the clouds can have a significant impact on the global radiative forcing.

Current models still suffer from uncertainties in the parameterization of the microphysical for¬

mation mechanisms of ice particles in high-altitude clouds (Jensen et al., 1994a,b). One way to

significantly improve this situation axe detailed laboratory experiments on ice nucleation pro¬

cesses in aerosols. These experimental data are required to develop microphysical nucleation

models such as the one recently presented by Koop et al. (2000) for homogeneous ice nucleation.

1.2.2 Heterogeneous chemistry

Atmospheric trace gases can react heterogeneously on aerosol particle surfaces and subsequently

homogeneously within the particle volume. The most prominent example of the importance of


heterogeneous reactions on aerosols is the Antarctic Ozone hole. The large Ozone losses during

the Antarctic spring time can be explained only by including heterogeneous reactions on the

surface of PSCs (Solomon et al., 1986; Ravishankara and Sheperd, 1999). The heterogeneous

reactions activate chlorine from its reservoir species (HCl and CIONO2) into CI2, which then

is photolyzed into two chlorine atoms in eaxly spring. These chlorine radicals can react with

O3, thereby destroying a large amount of the ozone within a short time period. There axe four

important heterogeneous reactions on PSCs:

HCI + CIONO2 - CI2 + HNO3 (1.1)

HC1 + N205 -» CINO2 + HNO3. (1.2)

CIONO2 + H2O -* HOCI + HNO3 (1.3)

HC1 + HOC1 -» CI2 + H2O (1.4)

Reaction 1.1 was shown to be a two-step process: CIONO2 hydrolyzes on the surface of the par¬

ticle forming HOC1 (see Reaction 1.3), which subsequently reacts homogeneously with dissolved

HCl to CI2 (see reaction 1.4) (Hanson and Ravishankara, 1991, 1993; Abbatt et al., 1992).

Also, cirrus ice clouds have the potential to serve as a surface for heterogeneous reactions in¬

volving chlorine activation (Borrmann et al., 1997b). During AASE II the research aircraft

ER-2 measured a positive correlation between aerosol surface and CIO concentrations within

cirrus clouds (Borrmann et al., 1997a). Model simulations of a 3-D chemical transport model

including typical heterogeneous reactions on ice surfaces also confirm the correlation between

the occurrence of subvisible ice clouds and measured CIO concentrations (Bregman et al., 2002).

Due to the their major atmospheric impact, the heterogeneous reactions of CIONO2 and N2O5

with HCl and H2O were intensively investigated in numerous laboratory experiments (see e. g.

Hanson and Ravishankara, 1992, 1993; Williams and Golden, 1993; Elrod et al., 1995; Hanson,

1998; Zhang et al., 1993a; Robinson et al., 1998). The experimental data show that heteroge¬

neous reactions involving HCl tend to be fast on solid surfaces such as ice, NAT, and Sulfuric

Acid Tetrahydrate (SAT) and also on liquid aerosol surfaces consisting of binary H2SO4/H2O

or ternary H2SO4/HNO3/H2O solutions.

The reaction rates of heterogeneous reactions depend on the uptake ability of gaseous molecules

onto/into the solid and liquid particles. The solubility of trace gases into liquid aerosol parti¬

cles under atmospheric conditions is expressed by the Henry's law constant, which is usually

predicted for systems such as H2S04/H20, H2SO4/HNO3/H2O, and NH3/H2SO4/H2O using

Pitzer ion interaction models.

1.3 Processes in UT/LS aerosols

In the UT/LS the aerosol is exposed to temperatures down to 180 K and relative humidities

with respect to ice of 10-150 % (Gierens et al., 1999; Jensen et al., 1994a,b; Heymsfield et al.,

1998). The influence of the aerosols on the environment involves, among others, radiative

forcing by particles, cloud formation, and heterogeneous chemistry on the particle surface. These

interactions can only be understood and quantified through the knowledge of the physical and

1.3. Processes in UT/LS aerosols 11

chemical aerosol properties. In the UT/LS the aerosol particles are often composed of inorganic

water soluble species such as H2SO4, NH3, and HNO3. These substances dissociate in the

aqueous solutions, thereby forming ions. Hence, in most cases UT/LS aerosols can be considered

to consist of aqueous electrolytic solutions.

1.3.1 Thermodynamic processes

The theory of Debye and Hückel (1923a,b), describing the ionic forces within aqueous elec¬

trolytes, paved the way for the invention of thermodynamic models of electrolytes based on

the ion interaction (Pitzer) equations (Pitzer, 1991). The functionality of these models requires

accurate thermodynamic data sets of the investigated systems over a large temperature and con¬

centration range. These models can be used to predict thermodynamic properties of aqueous

solution aerosol particles under atmospheric conditions. These properties involve the speciation

of the various ions within the solution or the change in water vapor pressure and water activity

of the solution with temperature and concentration. The two most important parameters de¬

termining the concentration of solutes in aqueous atmospheric aerosol particles are temperature

and relative humidity. When an aerosol particle is in equihbrium with its environment, the

gas phase relative humidity is equal to the liquid phase water activity, which in turn can be

calculated using Pitzer models.

Heterogeneous chemistry is also affected by the thermodynamic properties because it depends

strongly on the solubihty of the involved gases. The solubihty of a trace gas into an aqueous

solution changes with temperature and relative humidity, and under equilibrium conditions sol¬

ubilities can be predicted using Pitzer models. Liquid aqueous UT/LS aerosol particles can also

experience a large degree of supercooling, i. e. they are metastable with respect to crystalline

phases. The composition in this supercooled temperature regime and the change in speciation,

water activity, and solubihty with changing environmental conditions, can be obtained by Pitzer

models. However, the available data to constrain Pitzer models at the low temperatures that

can occur in the UT/LS is very limited. Therefore, experimental investigations of thermody¬

namic aerosol properties at very low temperatures will improve the predictions of the particle

characteristics and interactions in the UT/LS region.

1.3.2 Kinetic processes

Due to large fluctuations in atmospheric conditions, the aerosol particles in the UT/LS expe¬

rience phase changes. An increase in relative humidity can drive a solid particle to become

an aqueous aerosol particle (deliquescence). Decreasing relative humidity can lead to solidifica¬

tion of an aqueous particle (efflorescence). Under certain atmospheric conditions ice or certain

hydrates nucleate in an aqueous solution, thereby forming cirrus ice clouds or PSC particles,

respectively. In the UT/LS region two types of clouds are dominant: Cirrus ice clouds in the

upper troposphere and PSCs in the lower stratosphere. Cirrus ice cloud formation is assumed to

occur, at least in part, due to homogeneous ice nucleation of aqueous H2SO4 and (NH4)2S04 so¬

lutions (Houghton et al., 2001; Martin, 2000). PSC formation requires the nucleation of ice and


of nitric acid hydrates from supercooled ternary HNO3/H2SO4/H2O solutions (Peter, 1997).

Nucleation of a crystalline phase in an aqueous solution droplet is a process whose kinetics,

though dependent on thermodynamic properties, cannot be described by the laws of thermody¬

namics, but has to be measured in laboratory experiments or in situ in the atmosphere.

1.4 Objectives of this PhD thesis

In this Ph.D. thesis thermodynamic and kinetic processes will be studied in aerosol particles of

the UT/LS region of the atmosphere.

The investigation of thermodynamic processes of UT/LS aerosols, such as the changes in water

activity and in solubility of involved trace gases due to changes in the atmospheric conditions,

requires the knowledge of the thermodynamic properties of the investigated aqueous aerosol par¬

ticles at low temperatures. Experimentally derived thermodynamic data sets of aqueous solution

droplets obtained at low temperatures will be applied to constrain thermodynamic models of the

investigated systems. The improved thermodynamic models will yield more accurate predictions

of the thermodynamic properties of UT/LS aerosols and, therefore, a better understanding of

the interactions of the particles with their environment.

Kinetic processes in UT/LS aerosol particles such as PSC and cirrus ice cloud formation will

be investigated by employing nucleation experiments. In the context of PSC formation the ob¬

servation of large nitric acid containing particles will be addressed by measuring experimentally

homogeneous nucleation rate coefficients of NAD and NAT in aqueous HNO3 and HNO3/H2SO4

droplets under stratospheric conditions. Recently suggested theoretical parameterizations of ho¬

mogeneous and pseudo-heterogeneous nucleation mechanisms of NAD and NAT in STS aerosols

will be verified theoretically and experimentally by applying the nucleation data sets of NAD

and NAT derived in this work.

The influence of high altitude cirrus ice clouds on the globally radiative forcing will be followed up

by the investigation of the ice formation mechanisms in these altitudes. Therefore, homogeneous

ice nucleation rate coefficients will be derived experimentally in aqueous (NH4)2S04 particles.

The experimentally obtained data set will allow the comparison with ice nucleation data de¬

rived by other experimental methods and the verification of a possible pseudo-heterogeneous

nucleation pathway.

Chapter 2

Theory

In section 2.1 thermodynamic principles axe presented which axe necessary to describe thermo¬

dynamic processes such as gas-phase to liquid-phase interactions for varying temperatures and

compositions of the investigated solutions. The phase diagrams of the aqueous systems studied

in this work wiU be shown. In section 2.2 kinetic principles are discussed, i. e. the formation of a

critical nucleus in a supersaturated environment leading to crystalhzation of the solution. A brief

derivation of the Classical Nucleation Theory (CNT) will be given. The pseudo-heterogeneous

nucleation mechanism, i. e. nucleation induced at the surface of a droplet, recently suggested by

Tabazadeh et al. (2002a,b) and Djikaev et al. (2002) will be presented. The last section deals

with the theoretical background of Raman spectroscopy which is one of the main investigating

tool of this thesis.

2.1 Thermodynamic processes in UT/LS aerosol

2.1.1 The Gibbs free energy

From the first and second law of thermodynamics the Gibbs free energy, G, of a system is defined

as (Atkins, 1994):G = U +pV-TS, (2.1)

where U is the internal energy of the system, p and V its pressure and volume, respectively,

and S is the entropy of the system. T is absolute temperature. The study of atmospheric

processes is facilitated by the introduction of the Gibbs free energy since the variables p and T

axe convenient to obtain. Using the Gibbs free energy one can define the chemical potential for

a species i in a solution, /ij, for constant T, p, and constant moles of additional other solution

species, nv as:

*-(£) ,(2-2)

13

14 CHAPTER 2. THEORY

where nt is the number of moles of species i. From this the general equation

k

G = Y,ßtnt, (2.3)î=i

can be derived. The total Gibbs free energy of a system is the sum of all single chemical potentials

weighted by the corresponding number of moles. The second law of thermodynamics states that

the entropy of a system in an adiabatic (dQ = 0) enclosure increases for an irreversible process

and remains constant in a reversible one. This is expressed as dS > 0. This corresponds to

dG < 0 or that a system will tend to decrease its Gibbs free energy for any process to occur

spontaneously.

2.1.2 Chemical potential of solutions

A solution is defined as ideal if the chemical potential of every component is a hnear function

of the logarithm of its aqueous mole fraction, xt, according to the relation (Seinfeld and Pandis,

1998):Ht = l4(T,p) + RTIn x%, (2.4)

where /i* is the chemical potential of the pure species (xt = 1) under the same pressure and

temperature as the solution under discussion. R is the universal gas constant. When the partial

pressures of the components vary linearly with xt, i. e.

x, = h ,(2.5)

the solution is called ideal. pt is the vapor pressure of species i over the solution and p° is the

vapor pressure over the pure component i. Equation 2.5 is a form of Raoult's law, which for

real solutions usually holds only in the dilute concentration range.

Atmospheric aerosols are usually concentrated aqueous solutions that deviate significantly from

ideality. The deviation from ideality is described by introducing the activity coefficient, 7,, and,

thus, the chemical potential is given as (Seinfeld and Pandis, 1998):

Ai, = /i:(T,p) + Ärin(7,*a:t). (2.6)

The activity coefficient is a function of p, T, and x%. For an ideal solution 7* = 1. /i* is defined

as the chemical potential at the hypothetical state for which 7* — 1 and x% — 1. The product

of activity coefficient and mole fraction, 7*x4, is called activity, al.

An often used concentration scale is molahty, mt, defined as moles of solute i per kilogram of

solvent given in units mol kg-1. On the molahty scale the chemical potential, /i,, is defined as

IM = n\{T,p) + RThiat, (2.7)

where at = 7»^-. /4 is the value of the chemical potential asm,-*1 and ^ —* 1, i. e. when m, =

mt = 1 mol kg-1. In this case the hypothetical state of ideality corresponds to a concentration

of 1 mol kg-1.

2.1. Thermodynamic processes in UT/LS aerosol 15

2.1.3 Henry's law constant

The distribution of a species between the gas and aqueous phase is described by the Henry's law

constant, Hx, often given in units mol atm-1. Hx for a particular species X is the equilibrium

constant for the reaction

X(g) ^ X(aq) Hx = [XU/px, (2-8)

where [X]aq is the concentration of species X in the solution and px is its partial pressure. For

a real solution the activity of the species X, ax, is used instead of [X]. The effective Henry'slaw constant, H^, (given in units mol l-1 atm-1) takes into account further reaction of X in

the liquid phase (Seinfeld and Pandis, 1998). The solution of gaseous HCl will be given as an

example. The first step is the hydrolysis of HCl into the aqueous solution, the second step is

the dissociation of HCl:

HCl(g) ^ HCl(aq) (2.9)

HCl(aq) ^ Cr + H+. (2.10)

The equihbrium constant for the above reactions are:

i*HC. =^ (2-11)PHC1

Kdis = âiSSi, (2.12)ÛHC1

where i^dis is the thermodynamic dissociation constant of HCl. Since anci = #hciPhci Eq. 2.12

can be written as

tfdis = f^^. (2-13)iiHClPHCl

Therefore, the amount of dissociated HCl is given by

-Kdis-ffHClPHCl foiA\aa- =

. (2.14)

aH+

The total amount of dissolved gaseous HCl, afja, can be obtained by

aHCi = «HCi + aci- (2-15)

= #hci-Phci(i +—) (2-16)

Equation 2.16 shows similarity to the definition of the Henry's law constant. Therefore, one can

define the effective Henry's law constant as

tfSci = HHa(l + —). (2-17)

Equation 2.17 indicates that the solubility of gaseous HCl depends also on the amount of H+ in

the solution.


2.1A Water activity

In a given air parcel the water content is not affected by transport of water vapor to the condensed

water of the aerosols due to the large water amount in the gas phase compared to the liquid

water in the aerosol phase. Considering the equilibrium

H20(g) ^ H20(aq)

and using the criterion for thermodynamic equilibrium between the gas phase and aqueous phase

(AtH20(g) = AtH20(aq)) the water activity, Ow, can be written as:

pw RH, .

aw =

^=

IÖÖ' (2-18)

where pw is the water vapor pressure of the solution and p% is the saturation vapor pressure of

the pure liquid at the same conditions. RH is the relative humidity given in percent and is equal

to aw. Thus, for each RH the water activity for any aqueous aerosol solution is fixed as long as

equilibrium conditions axe maintained.

2.1.5 Phase diagram of H2S04/H20

Junge (1961) discovered a layer of stratospheric aerosols which consists mainly of liquid

H2SO4/H2O particles. Since the vapor pressure of sulfuric acid of about 10~15-10-20 mbar is

very low it can be dealt as a non-volatile substance in the troposphere and lower stratosphere.The upper bound of the stratospheric aerosol layer is defined by the complete evaporation of the

aerosol particles due to higher temperatures (250 K) and lower water partial pressures (Carslawet al., 1997). In lower regions of the atmosphere other gaseous species exist such as ammonia

which are taken up by the liquid H2SO4/H2O particles to form ternary solutions or solids.

Figure 2.1 shows the phase diagram for aqueous sulfuric acid in the weight percent scale taken

from Gable et al. (1950). This phase diagram was corroborated by various thermodynamicmodels and measurements (Tabazadeh et al., 1994; Carslaw et al., 1995a; Luo et al., 1995;

Clegg and Brimblecombe, 1995; Middlebrook et al., 1993; Zhang et al., 1993b). The followingsolid phases can be identified in the phase diagram:

H2SO4 - H20: The Sulfuric Acid Monohydrate (SAM) is thermodynamically stable in the

temperature range of 220-250 K. Koop et al. (1997b) strongly suggest that aqueous H2SO4

does not nucleate as SAM due to low nucleation rates.

H2S04 • 2 H20 and H2S04 • 3 H20: The Sulfuric Acid Dihydrate (SAD) and the Sulfuric

Acid Trihydrate (SATr) which do not play a significant role in the stratosphere due to very low

nucleation rates (Koop et al., 1997b).


ouu

280 /\ )

rture[K]

i\>

ro

o

o

.ICE \

/ SAM W,

\ v-2i

Q.

V /sat vy7 /

jk H2S04

| 22° \ J SATr SAD

200y^SAH

180 -

300

280

260

- 240

220

200

180

0 10 20 30 40 50 60 70 80 90 100

H2S04 [Wt%]

Figure 2.1: The binary phase diagram of aqueous H2SO4 is shown (Gable et al., 1950). The solid lines

correspond to the melting curves of the indicated solids ice, SAH, SAT, SATr, SAD, and SAM.

H2SO4 • 4 H2O: The Sulfuric Acid Tetrahydrate (SAT) is under stratospheric conditions the

most important hydrate. Although it is supersaturated at temperatures below 240 K it forms

rarely, since its nucleation rate is very low (Koop et al., 1995, 1997b).

H2SO4 • 6.5 H2O: The Sulfuric Acid Hemihexahydrate (SAH) has a lower existence temper¬

ature than SAT. Since SAT will form more readily than SAH as temperatures decreases, the

nucleation of SAH will occur very rarely.

2.1.6 Phase diagram of (NH4)2S04/H20

Gaseous ammonia, NH3, is immediately taken up by liquid H2SO4/H2O particles in which it

reacts to form the ammonium ion, NHJ" (Swartz et al., 1999). In the case of aqueous (NÜ4)2S04the vapor pressure of NH3 is very low, similar to the vapor pressure of H2SO4. Therefore, it

can be assumed that NH3 is also a non-volatile substance under most atmospheric conditions.

Figure 2.2 shows the phase diagram of aqueous (NHi)2S04 in the weight percent scale. The

phase diagram indicates that solid (NH4)2S04 could be thermodynamically stable in a wide

temperature and concentration range.


300

290

5f 280

s"

«j 270

CDQ.

E

H- 260

250

2400 10 20 30 40 50 60 70 80 90 100

(NH4)2S04 [Wt%]

Figure 2.2: The phase diagram of aqueous (NH^SO^ is shown. The solid lines correspond to the

melting curves of the indicated solids ice and (NH^SO^.

2.1.7 Phase diagram of HN03/H20

Due to the importance of HNO3 in PSC formation the binary HN03/H20-system has been

investigated intensively in the recent years (Hanson and Mauersberger, 1988a,b; Worsnop et al.,

1993; Carslaw et al., 1995a; Massucci et al., 1999; Beyer and Hansen, 2002). Since the vapor

pressure of HNO3 is much higher than the one of H2SO4, no binary HNO3/H2O aerosols exist

under stratospheric equilibrium conditions. Below 196 K HNO3 is taken up by H2SO4/H2Oaerosols forming ternary solution particles. Under non-equihbrium conditions, induced by rapid

temperature changes which can occur in lee wave situations, quasi-binary HNO3/H2O aerosols

with only traces of H2SO4 can form due to a large uptake of HNO3 (Meilinger et al., 1995).

Figure 2.3 shows the phase diagram of aqueous HNO3 in weight percent scale. The followingsolid phases can be found in the binary HN03/H20-system:

HNO3 • H20: The Nitric Acid Monohydrate (NAM). Hanson and Mauersberger (1988a,b) and

Worsnop et al. (1993) show by vapor pressure measurements that the vapor pressure ofNAM is

higher than the stratospheric partial pressures of HNO3. Therefore, NAM does not exist under

stratospheric conditions.

t——1——r ouu

290

(NH4)2S04

(solid)

280

270

260

250

'---'--'-' OAfi


300

280

gr 260

"fi

g3 240

<DQ.

E<»r- 220

200

1800 10 20 30 40 50 60 70 80 90 100

HN03 [Wt%]

Figure 2.3: The phase diagram of aqueous HNO3 is shown. The solid lines correspond to the melting

curves of the indicated solids ice, NAT, NAD, and NAM.

HNO3 • 2 H20: The Nitric Acid Dihydrate (NAD). Worsnop et al. (1993) present first

thermodynamic data of NAD. The authors also state that NAD has a potentially lower

nucleation barrier than NAT, i. e. NAD nucleation is favored over nitric acid trihydrate (NAT)formation. Therefore, under stratospheric conditions NAD is always metastable with respect

to NAT. Ji and Petit (1993) investigated the binary HN03/H20-system using Differential

Scanning Calorimetry (DSC). These authors give a melting point of NAD of about 232.7 K.

A newer study of the binary HN03/H20-system by Beyer and Hansen (2002) presents a 2 K

higher melting point for NAD. Tsias et al. (1997) showed theoretically, that NAD can form in

highly HNO3 concentrated (~58 wt%) non-equilibrium solution droplets during strong warming

events in mountain wave PSCs.

HNO3 • 3 H20: The Nitric Acid Trihydrate (NAT). Hanson and Mauersberger (1988a) showed

that this hydrate is the stable form of condensed phase HNO3 under stratospheric conditions

above the ice frost point. The saturation temperature is about 196 K at stratospheric conditions,

i. e. at 50 mbar ambient pressure, 5 ppmv H2O, 10 ppbv HNO3, and 0.5 ppbv H2SO4.

ICE '

NAT \

"

NAD

ham\J J ,

HNO3"

ouu

280

260

240

- 220

- 200


2.2 Kinetic processes in UT/LS aerosol

Aerosol particles experience phase transitions due to changes in atmospheric conditions, i. e.

temperature and RH variation. A pure liquid aerosol particle has a defined melting point. If

the ambient temperature decreases below the melting temperature, the solid phase is thermo¬

dynamically preferred. Since the nucleation process and, therefore, the phase transition, is a

kinetic process, an aerosol particle can remain liquid, although the temperature is lower than its

melting point. Under these conditions the liquid particle is in a supercooled state, i. e. the liquidis supersaturated with respect to its solid, but nucleation is kinetically hindered. In the case of

pure water a supersaturated state exists when the vapor pressure of the liquid is higher than

the vapor pressure of its solid phase at the same conditions. Temperature can be decreased and

supersaturation in the supercooled liquid can be increased until a critical number of molecules

in the liquid phase form a critical cluster, which is the definition of the nucleation process. In

most cases crystallization of the whole liquid follows immediately after the nucleation occurs.

The nucleation process depends crucially on the supersaturation of the liquid phase with respect

to its solid phase. Nucleation theory can be used to obtain the critical size of the cluster, to

calculate supersaturations required for nucleation, and to derive nucleation rate coefficients. The

latter define the expected start of the crystallization process for given atmospheric conditions

and aerosol particle size.

The following sections deal with the derivation of the nucleation processes which occur in super¬

saturated aerosol droplets. The first section presents classical nucleation theory (CNT), in which

the nucleation rate scales with the volume of the investigated particle. The second section deals

with a newly proposed pseudo-heterogeneous nucleation mechanism (Tabazadeh et al., 2002a,b;

Djikaev et al., 2002), which assumes that nucleation is induced at the surface of the particle.

Thus, the derived nucleation rates scale with the surface of the particle.

2.2.1 Classical nucleation theory

Here, the classical nucleation theory is briefly presented. There axe two common approachesto derive CNT: the kinetic approach and the constrained equilibrium approach (Seinfeld and

Pandis, 1998). The first develops CNT by determining the rates of collision of monomers, i. e.

monomers sticking together and forming a critical cluster in the liquid, and the rates of hittingand disengaging monomers within the liquid. From these processes, a nucleation rate coefficient

is obtained. The constrained equihbrium approach treats the formation of a critical cluster by

determining its Gibbs free energy of formation, which also allows to derive a nucleation rate

coefficient. In this section CNT will be described using the constrained equilibrium approach.

Homogeneous nucleation occurs exclusively in a supersaturated environment. In the case of a

pure liquid X, e. g. water, the liquid phase activity of X corresponds to the saturation ratio S:

liq

* = &• (2-19)Px

2.2. Kinetic processes in UT/LS aerosol 21

where p£ is the vapor pressure of the pure liquid and p1 is the vapor pressure of its solid at

the same conditions. When a liquid is saturated with respect to its solid then 5 = 1.

Homogeneous nucleation depends on the transfer of molecules from the liquid to the solid phase,

i. e. the increase of the number of molecules to a critical cluster size. If 5 is sufficiently large, this

critical cluster size will be exceeded and a new phase starts growing. A transfer of i molecules

from the liquid phase forms an i-zner cluster of radius r. The corresponding change in the Gibbs

free energy is

AGi = (ßsoi - imq)i + 4irasoir2 , (2.20)

where /isoj and nuq are the chemical potentials of the solid and liquid phase, respectively. asoi is

the surface tension between the solid and liquid phase and r is the radius of the critical cluster.

The first term in Eq. 2.20 describes the Gibbs free energy of the transfer of a molecule to the

cluster and the second specifies the Gibbs free energy of forming an interface. The number of

molecules in the solid, i, can be obtained by

« =^

= ^, ("I)

where Vsoi is the volume of the critical cluster and vsoi is the volume of one i-mer in the solid.

The difference in the chemical potentials can be expressed with respect to the corresponding

vapor pressures:

mq-»soi = kTmS (2.22)

= *ThÄ, (2.23)Px

where k is the Boltzman's constant. The Gibbs free energy change of i-mer formation can now

be written using Eq. 2.23 and Eq. 2.21 within Eq. 2.20 as

a ^ 24irkTlnS o

,nnA\

AGi = 4ivasolr2 - r3. (2.24)

3 Vs0l

The first term describes the Gibbs free energy increase due to the formation of a surface of the

critical cluster. The second term is the Gibbs free energy decrease due to the transfer of molecules

from the liquid to the solid phase. This equation assumes that the critical cluster has the same

properties as the bulk. Typically this is known as capillarity approximation (Seinfeld and Pandis,

1998; Defay and Prigogine, 1966). Also, the surface tension, asoi, is not known for such a small

critical nucleus. It is only known for some pure substances at the melting temperature of the

bulk crystal, whereas nucleation occurs at lower temperatures in the supersaturated regime.

These two assumptions are still a controversial subject in the formulation of CNT.

Figure 2.4 gives an example for AG as a function of r for different values of 5. In a subsaturated

environment (5 < 1) the Gibbs free energy increases with increasing cluster size r due to the

formation of a surface. For supersaturated conditions (5 > 1) AG increases initially with r due

to the formation of a surface but is compensated at a critical cluster size r* by the decrease of

AG due to the formation of the solid. This critical i-mer radius can be derived by

r* =

2asolVso1(2.25)


\ /s<i

<

AG/

/S,>1

/ ^^ !^

AO,* ^^\^\\|

1 \ \1 ! \Ste>S,\

r2*

Figure 2.4: The Gibbs free energy difference due to the formation of a critical cluster as function of

saturation ratio S and critical cluster size, r*.

The Gibbs free energy at r* is obtained by substitution of Eq. 2.25 in Eq. 2.24, which yields

*_

16tt vfo-3solAG ~

~MJfcTln5)2-(2-26>

Thus, an increase in 5 decreases the Gibbs free energy barrier, AG*, and the critical i-mer

radius, r* (Eq. 2.25), i. e. less molecules for the formation of the critical cluster are necessary

(see Fig. 2.4). If the nucleus is smaller than r* it will dissociate at once because of the increase

of AG. If the critical cluster reaches the size r* nucleation will start, because of the continuous

decrease of AG with an additional i-mer. Therefore, the nucleation barrier depends on the Gibbs

free energy for the formation of a critical cluster, AG*, and on the necessary energy to transfer

molecules to the cluster. Thus, the activation energy can be written as given by Turnbull and

Fisher (1949):

AGact(T) = AG*(T) + AGdi/(T), (2.27)

where AGdif is the molar Gibbs free energy of activation for diffusion of molecules across the

liquid-solid boundary. From this, the homogeneous nucleation rate coefficient in units cm-3 s-1

can be derived:

AGactÇr)-kTJhorn = nuq—exp

RT(2.28)

where n^ is the molecular number density of the species and h is the Plank's constant. Although

osoi and AGdif are not known, AGact can be obtained by

AGact(T) _ JnJhomnliqh

„jiKJ-

(2.29)

2.2. Kinetic processes in UT/LS aerosol 23

using experimentally derived //«„„-values.

CNT has the advantage that it is convenient to apply to experimental data due to the simple

underlying mathematical expressions. The disadvantage of CNT is the assumption that the

critical cluster behaves like the bulk. Therefore, CNT uses o~soi and AGdif which are obtained

from macroscopic samples. These quantities are often not available (MacKenzie, 1997).

2.2.2 Surface nucleation

Djikaev et al. (2002) and Tabazadeh et al. (2002a,b) propose a new idea of the nucleation

mechanism of aerosol particles. The authors claim to have found evidence that nucleation

starts at the droplet surface, i. e. at the air-solution interface (Djikaev et al., 2002; Tabazadeh

et al., 2002a,b). Here, the arguments for this pseudo-heterogeneous phase transformation or

surface-induced nucleation, suggested by the authors are presented and the derivation of the

pseudo-heterogeneous nucleation rate coefficients are shown.

fp liq ^svap

a- a"sol

Figure 2.5: Sketch of a liquid (liq) that rests on its solid (sol) and is surrounded by its vapor (vap).

The three interfaces are vapor-solid (vs), liquid-solid (Is), vapor-liquid (vl). The corresponding surface

tensions are avs, au, and avi, respectively.

Figure 2.5 shows a liquid droplet sitting on its solid for an one-component system. aV3, ats, ovi

correspond to the surface tensions of the vapor-solid, liquid-solid, and vapor-liquid interfaces,

respectively. The contact angle, 6, is defined as

=, (2.30)

&vl

which is also known as Young's relation (Pruppacher and Klett, 1997). For 6 > 0° one follows

from Eq. 2.30, that:

Ovs < °~vl + o~ls • (2-31)

Equation 2.31 indicates the condition of partial wetting of a solid by its liquid.

Figure 2.6 shows a crystal forming at the surface of its liquid. If we use Young's relation on the

facet of the crystal which is in contact with the vapor phase we obtain the same inequality given

by Eq. 2.31. Therefore, surface nucleation would be favored if at least one of the facets of the


vap

Figure 2.6: Sketch of a crystal nucleus (sol) that forms at the surface of its liquid (liq). The facet in

contact with the vapor (vap) is indicated by a dashed line. The solid lines represent the contact of the

crystal with its liquid. The corresponding surface tensions are avs, ois, av\ similar to Fig. 2.5. This

figure is adapted from Djikaev et al. (2002) and Tabazadeh et al. (2002a).

crystal is only partially wettable by its own melt. The authors (Djikaev et al., 2002; Tabazadeh

et al., 2002a,b) state that Eq. 2.31 is the pre-requisite for the occurrence of surface-induced

nucleation.

Equation 2.28 gives an expression for the derivation of the homogeneous rate coefficient within

the volume of a liquid. Tabazadeh et al. (2002a) present a similar relation for the pseudo-

heterogeneous nucleation rate coefficient of a nucleus on the droplet surface:

hornKT

kTNs— exp

h

&Gsact(T)RT

(2.32)

where Ns is the total number of molecules per unit surface of the liquid. The authors relate the

surface-based to volume-based homogeneous nucleation rate coefficients in the following way:

Jhom — Wt/St) Jfiom > (2.33)

where Vt is the total aerosol volume and St is the total surface area of an observed aerosol

ensemble. A monodisperse distribution of droplets yields the following relation:

Tshorn (r/3)JL». (2.34)

where r is the droplet radius.

From these presented equations one can easily convert the experimentally derived volume-based

Jftom-values into surface-based Jôm-values.

2.3 Raman spectroscopy

The Raman effect in liquids was discovered in 1928 by Raman and Krishnan (1928). Almost

simultaneously Landsberg and Mandelstam (1928) observed the Raman effect in crystals. The¬

oretically, the Raman effect was already 1923 predicted by Smekal (1923). Placzek (1934)

2.3. Raman spectroscopy 25

developed a semi-quantum mechanical theory of the Raman effect. It abandons the quantum

mechanical treatment of the light, but regards the molecule energies in a quantum mechanical

way. This theory still holds for most of the common Raman spectroscopic applications.

The Raman effect is an inelastic scattering process of two photons. If a photon with energy, Erj

e| s,

/?v0 hvi

i

hv0 hvi

Figure 2.7: Term diagram of the inelastic scattering process. On the left hand side the Stokes scattering

process is shown and on the right hand side the Anti-Stokes scattering process is shown (Schrader, 1995).

= Iivq, hits a molecule the elastic scattering process, i. e. Rayleigh-scattering, which emits the

same energy quantum, Erj, as the incoming photon, has the highest probability to occur. The

inelastic scattering process, i. e. the Raman-scattering, where an exchange of vibrational energy

takes place, has a much lower probability. The Raman-scattering process emits the energy quan¬

tum of hvQ =f hvs- Figure 2.7 shows the principle of Raman scattering. At ambient temperature

most molecules occupy their vibrational ground state at No. By absorbing the energy quanta

hvQ, the molecules reach an excited state. These molecules emit energy quanta hu^, which is

lower by hi>s than the incoming energy quanta, leaving the molecules in an excited state (Ng)little higher than their vibrational ground state (No). If the excited molecules have emitted the

energy quanta of hi>o the molecules would have reached again their ground vibrational state.

This process would correspond to Rayleigh-scattering. The emittance of the energy quantum

hVft is called Stokes-Raman scattering, since Stokes postulated in 1852 that the light produced

by fluorescence has always a longer wavelength than the excitation wavelength. Therefore, the

energy of the Stokes-Raman intensity line can be written as

Er — huR — hvo — hvs (2.35)

According to Boltzmann's law, even at ambient temperature there is still a small number of

molecules in the vibrationally excited state, Ns. If an energy quantum of hvo hits the already

excited molecules they reach a higher excited state and can emit the energy quanta hv^ to reach

their vibrational ground state. This transition is called Anti-Stokes-Raman-scattering, because

it exhibits a larger frequency and, hence, a higher amount of energy than the corresponding

Stokes-Raman-scattering and Rayleigh-scattering, respectively. The energy quanta of the Anti-


Stokes-Raman intensity fine is

Eft = huR — hvQ + hus (2.36)

Figure 2.8 shows the intensity distribution of the Rayleigh-scattering process (at zô), the Stokes-

line (at v^), and the Anti-Stokes-line (at u^). Since the highest probability is obtained for the

elastic scattering process, the Rayleigh-line is the most pronounced signal. The Anti-Stokes-

line is the lowest signal, since at ambient temperature, the number of molecules in the excited

state are much lower than the number of molecules in the vibrational ground state. Since the

occupation of the vibrational ground and excited states depend on the temperature-dependentBoltzmann factor, the temperature can be obtained from the ratio of the Anti-Stokes-line and

Stokes-line.

Stokes

— vs —

Anti-Stokes* vs

Vr v0 Vr

Figure 2.8: The intensity distribution in a Raman spectrum as function of frequency and scattering

process. From left to right: Stokes-scattering, Rayleigh-scattering, and Anti-Stokes-scattering (Schrader,

1995).

A change in the excitation wavelength will change the resulting Raman spectrum. Also, impuri¬

ties inside the sample can cause fluorescence which can strongly perturb the Raman spectrum.

The reason for this is the relatively small Raman-scattering cross section compared to the elastic

Rayleigh scattering cross section. Therefore, highly monochromatic and powerful light sources

axe needed for Raman spectroscopy. Optical niters of high quality are also necessary to cut

off the Rayleigh scattered light, whose intensity can be up to a factor of 106 higher than the

scattered Raman light.

2.3.1 Classical derivation of the Raman effect

The following derivation of the Raman effect is given by Kiefer et al. (1995) and Schrader (1995)which is based on the semi-quantum mechanical theory of Placzek (1934).The classical approach of light scattering is based on the idea that a dipole moment in a liquid is

induced by the electromagnetic field of fight. This dipole moment oscillates with the frequency of

the incoming electromagnetic field. Therefore, the oscillating dipole moment can be considered

as a source for the emittance of electromagnetic radiation. This secondary emitted radiation is

2.3. Raman spectroscopy 27

distributed over an angle of 4n. The incoming electromagnetic field consists of a magnetic part

and an electric part. The latter one will be considered in this derivation. The incoming electric

field, E, oscillates with the frequency, vq, and can be expressed as:

Ê = Éo- cos(27ri/0t), (2.37)

where Eq is the amplitude of the electric field. E induces a dipole moment, ß, of

ß = a-E, (2.38)

where a is the polarizability of the molecule. From Eq. 2.37 and Eq. 2.38 one follows

ß = a-EQ- cos(27ri/0t). (2.39)

The polarizability, a, is a tensor which projects one component of the vector E to produce

the corresponding component of ß. a depends on the molecule symmetry and also on inter¬

nal molecule vibrations. The flexibility of electrons and nuclei in a molecule depends on their

mutual distance. If this distance is small, an external field has only a small influence on the

positions of the electrons and nuclei, and a large influence, if their distance is large. Therefore,

the polarizability of a molecule can be modulated by the vibration of the incoming light. The

emitted radiation depends also on the polarizability and, hence, on the vibration. If the excita¬

tion wavelength deviates significantly from the resonance wavelength of the molecule, a can be

expanded in a Taylor series with respect to the normal coordinates qk at its equilibrium position

qk = 0 and aborted after the hnear element. (The assumption of an expansion of a in a Taylor

series is the main point of Placzek's theory (Placzek, 1934), since the Schrödinger equation, i.

e. the quantum mechanical treatment, cannot be solved for all wave functions of this scattering

problem.) The expansion in a Taylor series yields:

3Q-/ ,~ v

Oij = «auk = 0) + £ ^ qk, (2.40)fc=1

\ °Qk J qk=Q

where aiij(qk = 0) is the polarizability in the equilibrium position. Q is the number of the atoms,

3Q — / is the number of normal vibrations. / depends on the molecular geometry, e. g. / = 5 for

a linear molecule and / = 6 for a non-linear molecule. In the case of small molecule vibrations

the normal coordinates qk can be approximated by a harmonic oscillation:

qk = qkO- cos(2irukt), (2.41)

where gô is the amplitude of the fcth oscillation and vk is the frequency of the fcth oscillation.

From equations 2.39-2.41 one obtains

M

k v%A,=o'<x(qk = 0) + Y] ( -£— 1 qko • cos(27Ti/fci) Ê0cos(2nvot). (2.42)


Applying trigonometrical transformation yields

ß = a(qk = 0) • Êq cos(27ti/o*) +%

v'

Rayleigh — scattering

qk0Êo cos(27r(z/fco - vo)t) +9fe=0

Stokes — Raman — scattering

qk0Ê0 cos(27r(i/fe0 + ô)*) • (2.43)9fc=0

Anti — Stokes — Raman — scattering

The fraction of the emitted light can be identified. Light with the frequency of vq corresponds to

Rayleigh-scattering and fight with the frequency of Vko — vq and ukQ + vq corresponds to Stokes-

and Anti-Stokes-Raman-scattering, respectively. Equation 2.43 indicates that Raman scattering

only occurs when the polarizability a changes during an oscillation through the equilibrium

position, i. e.

(£)*" <

Therefore, a molecular vibration can be observed in the Raman spectrum only if there is a

modulation of the molecular polarizability by the vibration. From this, one can conclude which

molecules are Raman-active and which molecules axe Raman-inactive.

l^p/dcA

2-MaJ

Chapter 3

Experimental

All experiments performed in this work have made use of droplet samples. The following sections

describe all necessary steps to generate a droplet sample which is used in the Raman spectro¬

scopic measurements and nucleation experiments. This includes the preparation of the aqueous

solutions, the droplet production, the sample holder (i. e. the droplet cell), and the experimental

setup. In the last section of this chapter the typical experimental procedures are illustrated.

3.1 Sample preparation

The solutions investigated in this work are mixtures of H2SO4/H2O, (NH4)2S04/H20,

HNO3/H2O, and HNO3/H2SO4/H2O. The H2S04 and HNO3 containing solutions were

prepared from stock solutions which were titrated against 1 M NaOH. The (NHi)2S04 solutions

were prepared from solid (NH4)2S04 and Milhpore water (Resistivity > 18.2 Mfi-cm). In

addition, the solutions were filtered through a 0.2 /im pore size membrane to exclude insoluble

impurities.These solution were used to produce two types of droplet samples. On the one hand relatively

large droplets with diameters of about 0.4-1.5 mm, and on the other hand small droplets

with diameters of about 10-50 /im. The whole droplet production was performed inside a

laminar flow clean bench to minimize the contamination with dust particles. The large droplets

were produced using a micropipette. The small droplets were generated by an atomizer or an

inkjet-cartridge:

Figure 3.1 shows a homemade atomizer made of glass, since acidic solutions (H2SO4/H2O, or

(NHi)2S04/H20 solutions with typical concentrations of about 20 wt%) are used within the

droplet production. Gaseous nitrogen with a pressure of about 0.4 bar flows over a nozzle,

thereby, drawing the aqueous solution through the capillary and creating numerous droplets

with a mean diameter of about 0.7 /im (Knopf et al., 2001). The second vessel serves as a

precipitation reservoir for larger drops. The particles will be deposited onto a hydrophobicallycoated glass plate. This plate, 13 mm in diameter, is immersed for a few seconds in the aerosol

29

30 CHAPTER 3. EXPERIMENTAL

flow. The resulting droplet diameters can be changed by varying the nitrogen pressure, the

concentration of the aqueous solution, and the contact time of aerosol and plate. The higher the

amount of the non-volatile substances in the solution the larger the diameter of the droplets for

a given relative humidity. This method generates a high number density of deposited particles

with average diameters between 5-200 /im.

œrosolsproy

reservoir \X

nozzle

=4-aerosol drain

quartz

plate

aerosol

generator

Figure 3.1: Sketch of the atomizer.

A lower number density of deposited droplets - or even single droplets - are obtained by the

operation of a modified Hewlett-Packard inkjet-cartridge. The setup is shown in Fig. 3.2. The

plate is placed on a micrometer stage. A few millimeters above this stage the inkjet-cartridgeis fixed. By adjusting the micrometer stage and by operating the pulse generator in single

pulse mode defined droplet arrays can be generated. Furthermore, the inkjet-cartridge can be

run in a 100 Hz mode, hence, producing many more droplets. Preferentially, very dilute acidic

inkjet-cartridge

aerosol

quartz plate

micrometer stage

Figure 3.2: Sketch of the single droplet generator using an inkjet-cartridge.

3.2. Sample cell 31

solutions (up to a maximum of 5 wt%) are used within the inkjet-cartridge, due to the danger of

solubilization of the inkjet-cartridge surfaces. The inkjet-cartridge produces droplets of about 58

/im in diameter (Diiwel, 2003), whose diameters can be changed by varying the concentration of

the solution for a given relative humidity. The electric circuit to operate such an inkjet-cartridge

is given in appendix A.l.

3.2 Sample cell

An o-ring or a Teflon washer (for the large droplets) or an aluminum foil (for the small droplets)treated with high-vacuum-grease served as a spacer for a second quartz plate, which sealed

the droplets against ambient air. Model calculations have been performed which show that

the amount of gas-phase water inside the small cell is negligible compared to the liquid-phase

water of the droplets. Therefore, no concentration changes inside the droplets occur due to

evaporation and condensation of gas-phase water from the droplet cell to the droplets. Hence,

the composition of the droplets in the presented experiments remains fixed. This kind of

sample, consisting of two glass plates separated by a spacer will be called aerosol cell or droplet

cell in the remaining parts of the thesis.

The investigation of the ferroelectric phase transition of solid (NrLi)2S04 requires a different

sample preparation. A very diluted aqueous (NH4)2S04 solution was spread out on the the

quartz plate. The plate was placed on the temperature stage and was warmed to about 330 K,

thus, evaporating the liquid water. A thin layer of solid polycrystalline (NH4)2S04 remained

on the plate. Afterwards, the cell was sealed by an aluminum foil and a second quartz plate to

avoid water uptake from the ambient air.

3.3 Hydrophobic coating

The droplets were deposited on a hydrophobically coated glass or quartz (Herasil) plate. Herasil

quartz plates were used for Raman spectroscopic measurements due to the large transmission

efficiency of about 92 % in a wavelength range of 300-1000 nm, which coincides with the exci¬

tation wavelength used in the presented experiments. The effect of the surface on the droplets

can be minimized by coating the glass surface with a hydrophobic substrate. In this work three

different substrates were tested for the production of a hydrophobic coating:

1. Silanization Solution I: 5 % Dimethlydichlorosilane in heptanefrom Fluka BioChemika

2. Aqua Sil: Organosilane concentrate

from Hampton Research

3. OTS: Octadecyltrichlorosilanefrom Aldrich

The glass plates were purified by immersion into Caro's acid (prepared from a 2.5/1 mole ratio


of H2SO4/H2O2 using 93 wt% H2S04 and 35 wt% H202) for a period of one day.

In the case of Silanization Solution I the formation of the substrate occurred via gas-phase

reaction. The dry plates rest in a closed container for two days which is flooded by gaseous

Dimethlydichlorosilane. Afterwards, they were flushed with water and dried.

The preparation with Aquqa Sil was as follows: 1 ml of Aqua Sil was dissolved in 100 ml water

(Milhpore water, Resistivity > 18.2 Mfi-cm). The plates were dipped for a few seconds into the

solution and then flushed with water.

In the case of OTS a 1 mmol solution of OTS in chloroform was prepared. Then, the plates

were brought for a few seconds into contact with the solution and then flushed with water.

The quality of the hydrophobic coating was determined by placing a droplet with known volume

on the coated glass plate and measuring the droplet diameter. The more the diameter of the

placed droplet approached the diameter of a sphere with similar volume, the higher the quality

of the hydrophobic coating. Another quality test of the hydrophobic coating was performed by

investigating the homogeneous nucleation of pure water droplets. The quality of the hydropho¬

bic coating was considered to be good when pure water droplets reached the expected degree of

supercooling with respect to their size (Pruppacher and Klett, 1997), hence, indicating that no

heterogeneous nucleation due to the contact with the substrate occurred.

The highest quality of the hydrophobic coating was achieved by using the Silanization Solu¬

tion I, followed by OTS and Aqua Sil. Therefore, all glass/quartz plates used in the presented

experiments were treated by the Silanization Solution I.

3.4 Experimental setup

Figure 3.3 shows the experimental setup. It consists of two main parts: a Confocal Raman

Microscope (Jobin Yvon, model: Labram) and a homemade temperature stage.

The Confocal Raman Microscope allows the visual observation of phase transitions of the

droplets. The instrument is equipped with several objectives with a magnification of 10, 50, and

100. Raman spectra of the droplets can also be recorded. The Raman microscope is equipped

with a Nd:YAG-laser which is operated at a wavelength of 532 nm and has a maximum power

of 100 mW for illumination. The laser power can be changed by inserting filters with different

optical densities. The light backscattered from the sample is passed onto a grating of 1800

mm-1 and focused on the CCD detector of the spectrograph. This yields a spectral resolution

of about 2-4 cm-1 within the observed range of 500-4000 cm-1.

Figure 3.4 shows a sketch of the temperature stage. Cooling of the temperature stage is

achieved through the evaporation of liquid nitrogen and the counterheating is generated by a

heating foil. Liquid nitrogen enters the small chamber below a heating foil and a copper plate.

The liquid N2 evaporates and, hence, cools the whole temperature stage. Gaseous nitrogen

leaves the temperature stage through a valve and is pumped away by a membrane pump. By

adjusting the orifice of the valve the amount of pumped gaseous N2 is controlled and, thus,

the cooling capacity. The droplet cell is placed inside the depression of the copper plate. A

resistance temperature sensor (Pt 100) is fixed onto the copper plate close to the droplet cell.

The whole temperature stage is surrounded by a box which is flushed with gaseous nitrogen

3.4. Experimental setup 33

laser

video

analysis

spectrographCCD detector

^532 nm

microscope

temperature stagear

grating:1800 g/mm

droplet cell

Figure 3.3: Sketch of the experimental setup.

to prevent ice condensation on the droplet cell and the apparatus. The heating foil and

the temperature sensor axe connected with a low temperature controller (LTC-11, Neocera).The LTC-11 allows to maintain a constant temperature or to perform definite temperature

ramps of the cooling stage. The LTC-11 is controlled by a Windows-based computer using

Hewlett-Packard Visual Engineering Environment (HP VEE) which is a graphical programming

language optimized for instrument control (Helsel, 1995). The complete experimental run

including a serial of heating and cooling ramp can be set. Experiment time and actual droplet

temperature are transferred to the computer and saved on harddisk every 0.1 seconds. This

data is also displayed on the monitor during the experiment using a Videotext overlay module

(Engineering, 2001). The temperature stage is able to vary the temperature of the sample

in a range of 160-350 K. The temperature of the sample is measured by the Pt 100 sensor

whose linear resistance/temperature response was confirmed by measuring the melting points,

Tm, of heptane (TTO=182.55 K), octane (Tm=216.35 K), decane (Tm=243.45 K), dodecane

(Tm=263.5 K), and water (Tm=273.15 K). These substances were put into the droplet cell

and the melting points were determined using a heating rate of 1 K/min. The statistical mean

of 10 melting point measurements were used for the calibration. As expected the calibration

data reveals a hnear relationship between the measured resistance and the temperature. The

calibration error was obtained by error propagation law analysis of the data and the fit function.

The temperature accuracy of the homemade temperature stage is better than ±0.1 K. A

dynamic calibration was also performed, i. e. the change of nucleation temperature of the above

mentioned substances (heptane, octane, decane, dodecane, water) was investigated by variation

of the cooling rate. The freezing temperatures show no deviation for cooling rates in the range

of 1-20 K/min. Most experiments were performed with a cooling rate of maximum 10 K/min.


objective

heating foilPt-100

shielding box

evaporation chamberniiài

copper plate

light source

Figure 3.4: Sketch of the temperature stage.

3.5 Experimental procedure

Two different types of experiments were performed in this study: the record of temperature-

dependent Raman spectra and nucleation experiments.The first kind of experiment was performed in the following way: At a fixed temperature a

Raman spectrum was recorded. Afterwards, the sample was either cooled or heated with a

rate of 10 K/min to a new temperature 5-10 K lower or higher, respectively, than the previous

temperature. As the temperature was reached a new Raman spectrum was recorded.

The experimental procedure for the nucleation experiments was performed in the following way:

A cooling ramp with a maximum cooling rate of 10 K/min was conducted until the nucleation of

all droplets had occurred. The whole experimental run is recorded on a video tape. The actual

temperature of the droplets and the experimental time is displayed on the monitor and on the

video tape. The tapes were analyzed ex post, i. e. the droplet diameters and, hence, the volume

and the surfaces of the droplets, the nucleation temperature, and the cooling rate were noticed

for further analysis.

Chapter 4

Thermodynamic processes in UT/LSaerosol particles

This chapter presents an investigation of the ionic speciation in aqueous H2SO4 under thermo¬

dynamic equilibrium conditions and relevant atmospheric temperatures. The dissociation of the

bisulfate ion, HSOJ, is analyzed using Raman spectroscopy. The dissociation data obtained at

low temperature is implemented into a Pitzer model to derive a more consistent thermodynamic

model of the H2S04/H20-system. This leads to the derivation of a new thermodynamic disso¬

ciation constant of the bisulfate ion for a temperature range of 180 K to 473 K. Sections 4.1

to 4.7 axe identical to the publication "Thermodynamic Dissociation Constant of the Bisulfate

Ion from Raman and Ion Interaction Modeling Studies of Aqueous Sulfuric Acid at Low Tem¬

peratures" reproduced with permission from the Journal of Physical Chemistry Part A, 107,

4322-4332. Unpublished work copyright 2003 American Chemical Society.Section 4.8 describes in further detail the changes of HCl solubility in aqueous H2SO4 aerosol

particles due to implementation of the new thermodynamic dissociation constant of the bisulfate

ion.

The last three sections of this chapter present further analysis of H2SO4/H2O and (NH4)2S04Raman spectra. This involves the effects of temperature and water uptake on the composition

and phase of the investigated solutions.

35

36 CHAPTER 4. THERMODYNAMIC PROCESSES

Seite Leer /

Blank leaf

37

Thermodynamic Dissociation Constant of the Bisulfate Ion from Raman

and Ion Interaction Modeling Studies of Aqueous Sulfuric Acid at Low

Temperatures

D. A. Knopf*, B. P. Luo, U. K. Krieger, and Thomas Koop

Institute for Atmospheric and Chmate Science, Swiss Federal Institute of Technology, Hongger-

berg HPP, 8093 Zurich, Switzerland

* To whom correspondence should be addressed. Email: [email protected].

Reproduced with permission from the Journal of Physical Chemistry Part

A, 2003. Unpublished work copyright 2003 American Chemical Society.


Seite Leer /Blank leaf

4.1. Abstract 39

4.1 Abstract

The dissociation reaction of the bisulfate ion, HSOJ ^ SO4- + H+, is investigated in aqueous

H2SO4 solutions with concentrations of 0.54-15.23 mol kg-1 in the temperature range of 180-

326 K using Raman spectroscopy. All investigated H2SO4 solutions show a continuous increase

in the degree of dissociation of HSOJ with decreasing temperature, in contrast to predictionsfrom thermodynamic models of aqueous H2SO4 solutions. A Pitzer ion interaction model is

used to derive a thermodynamically consistent formulation of the thermodynamic dissociation

constant of the bisulfate ion, Ku(T), that is in agreement with the experimental data. The

new formulation of Ku(T) is valid from 180 K to 473 K. All ion interaction parameters and the

corresponding parametrizations of the Pitzer ion interaction model are presented. Calculations

with this model reveal significant differences in ion activity coefficients, water activities, water

vapor pressure, and HCl solubilities, when compared to existing thermodynamic models of

H2SO4/H2O solutions, in particular at lower temperatures.

4.2 Introduction

Aqueous sulfuric acid (H2SO4) is one of the most important mineral acids in chemical industries

(Donovan and Salamone, 1983). Because of this, its thermodynamic properties such as partial

pressures as well as osmotic and activity coefficients were intensively studied over the past

decades (Rard et al., 1976; Staples, 1981; Bolsaitis and Elliott, 1990; Zeleznik, 1991). In the

atmosphere, sulfuric acid affects many properties of ambient aerosols. Stratospheric backgroundaerosols consists of highly concentrated aqueous sulfuric acid droplets (Junge and Manson, 1961;

Hamill and Toon, 1991). Tropospheric aerosols can contain mixtures of various inorganic and

organic species but H2SO4 is often a major component (Murphy et al., 1998). Furthermore, the

solubihty of volatile gases such as HCl and NH3 in liquid aerosols depends on the concentration

of dissolved H+-ions (Luo et al., 1994; Swartz et al., 1999) which, in turn, depends on the degree

of dissociation of H2SO4. The dissociation of H2SO4 is a two-step process:

H2S04 ^ HS04+H+ (I)

HSO4 ^ SO|- + H+ (II)

It has been shown that the dissociation of H2SO4 is essentially complete for concentrations

up to 40 mol kg-1 at temperatures between 273 K and 323 K (Young et al., 1959). These

measurements further suggest that full dissociation occurs also at lower temperatures at these

concentrations. On the other hand, the dissociation of the bisulfate ion, HSO4 , depends strongly

on temperature (Young et al., 1959; Chen and Irish, 1971; Dawson et al., 1986; Dickson et al.,

1990; Tomikawa and Kanno, 1998). The thermodynamic dissociation constant of the HSOj-ion,

K\\(T), is defined by the activities of the particular ions (see Appendix 4.7.2 for a full derivation

oftfii(r)):

aH+(T)ao02-(T)*n(T) =

n S%, (4.1)


mn+ (T)mS02- (T) 7h+ (r)7s02- (T)

»»hsoj-O' 7hso4-C0Q(T) • 7(D, (4.3)

where aî7 m*, and ji denote the activity, molahty, and activity coefficient of ion i (i = H+,

SO^-, HSOJ) in equilibrium, m) is by definition 1 mol kg-1, and Q(T) and -){T) are the molal

dissociation quotient and activity coefficient product, respectively.

Knowledge of Kn(T) is a prerequisite for the description of the thermodynamic properties of

a multicomponent system containing H2SO4, such as the NH3/H2SO4/H2O system at atmo¬

spheric temperatures («180-300 K). However, there are only few experimental studies of the

properties of aqueous H2SO4 at low temperatures Zhang et al. (1993b); Massucci et al. (1996);Das et al. (1997); Tomikawa and Kanno (1998). Therefore, thermodynamic solution models axe

employed to predict ion activity coefficients and ion concentrations in aqueous solutions at low

temperatures in a consistent way. One widely used model of this kind is the aerosol inorganics

model (AIM) (Clegg et al., 1998) which is based on the Pitzer ion interaction approach (Pitzer,

1991). Since low-temperature data on the dissociation of sulfuric acid are not available, the

formulation of the thermodynamic dissociation constant Ku(T) that has been implemented in

the AIM model (Clegg et al., 1994, 1998), is the one taken from Dickson et al. (1990), who

derived Kii(T) from measurements in the temperature range of 298-523 K.

One way to experimentally investigate the dissociation of the bisulfate ion is Raman spec¬

troscopy. Raman data of aqueous H2SO4 solutions in the temperature range of 278-328 K

Young et al. (1959) axe available but the only existing Raman study at temperatures below

273 K focused on H2SO4/H2O solutions in the glassy state and investigated the dissociation

of the bisulfate ion in more detail only for a solution 4.37 mol kg-1 in concentration to 233 K

Tomikawa and Kanno (1998).In this paper we present new experimental data on the degree of dissociation of the bisulfate

ion in sulfuric acid solutions derived from Raman spectroscopic measurements at concentrations

of 0.54-15.23 mol kg-1 and temperatures of 180-326 K. We use a Pitzer ion interaction model

(Pitzer, 1991) to derive a thermodynamically consistent formulation of K\\(T) which is in agree¬

ment with the experimental data. The ion activity coefficients, 7H+, and 7so2-, 7^+ •

7So2- >

and water activity, aw, for selected H2SO4 solutions are calculated using the new formulation of

Kji(T). These results axe compared to values derived by the AIM model of (Clegg et al., 1998).

4.3 Experimental Section

Figure 4.1 shows the experimental setup. Raman spectra of aqueous droplets axe obtained using

a confocal Raman microscope (Jobin Yvon, model: Labram) operated with a Nd:YAG-laser at

a wavelength of 532 nm and a power of 25-100 mW for illumination. The backscattered light is

passed onto a grating (1800 mm-1) and focused on the CCD detector of the spectrograph. The

resulting spectral resolution is about 2-4 cm-1 within the observed range of 500-4000 cm-1.

A homemade temperature stage is attached to the microscope table. The temperature of the

stage can be varied between 180 and 326 K. The temperature was measured using a resistance

4.3. Experimental Section 41

0

video

analysis

laserspectrographCCD detector

\ I

532 nm

microscope

x_ -7

grating:1800 g/mm

droplet cell

I-JJMtemperafure stage


temperature sensor (Pt 100) whose linear resistance/temperature response was confirmed by

measuring the melting points of heptane, octane, decane, dodecane, and water. Phase changes

(i.e. freezing or melting) are observed visually with the microscope part of the setup.

Table 4.1 shows the composition of the investigated solutions of H2SO4/H2O and

(NH4)2S04/H20. The H2SO4 solutions were prepared from stock solutions which were

titrated against 1 M NaOH. The (NH4)2S04 solutions were prepared from solid

(NH4)2S04 and Milhpore water (Resistivity > 18.2 Mfi-cm). In addition, the solutions were

filtered through a 0.2 /im pore size membrane. The volume of the droplets varied between 0.5

and 10 /xL (diameters of about 0.1-0.26 cm). The droplets were deposited with a micropipet on

a silanized (hydrophobic) quartz plate inside a laminar flow clean bench. Either an O-ring or

a Teflon washer treated with high-vacuum grease served as a spacer for a second quartz plate,

which sealed the droplets against ambient air. Afterward the droplet cell was placed on the

temperature stage.A typical experiment started by taking a Raman spectrum at room temperature. Subsequently,

the droplet was either cooled or heated in temperature steps of 5-10 K (at a rate of 10 K min-1)and a new Raman spectrum was taken at each temperature.

To exclude any possible bias in the temperature and composition of the droplet due to the en¬

ergy transfer from the laser light, a sensitivity study was performed. At a fixed temperature of

298 K, Raman spectra were recorded, in which a droplet was exposed to different illumination

times and laser intensities. Figure 4.2 shows 12 Raman spectra of a H2SO4/H2O droplet 10

fiL in volume with a concentration of 4.37 mol kg-1. Six of the 12 Raman spectra were taken

with a laser power of 100 mW and varying laser excitation times between 1 s and 1 h. The

other 6 Raman spectra were recorded with a laser power of 25 mW and varying illumination

times from 1 s to 2 h. The Raman spectra are indistinguishable from each other, showing that

the energy transfer from the laser into the droplets has no significant influence on the droplet


1.2

1.0

0.8

0.6

0.4

0.2

0.0)0

Raman shift [cm"1]

Figure 4.2: Raman spectra of an aqueous H2SO4, droplet 10 ßL in volume with a concentration of 4-37

mol kg-1 at room temperature. Twelve Raman spectra are shown for which the laser excitation time

varies between 1 s and 2 h. Six of the 12 Raman spectra were taken with a laser power of 25 m W. The

other six Raman spectra were taken with a laser power of 100 mW. The Raman spectra are normalized

to the ^(SO^-) vibration band.

composition or temperature, which would have been seen as a change in the vibration band ratio

ui(S02~)/ui(H.SO^) (see below). The influence of the laser light on droplet temperature was

also checked by measuring melting temperatures of aqueous nitric acid droplets while they were

excited by the laser Knopf et al. (2002). The experimentally obtained melting temperatures

were in agreement with literature data (Carslaw et al., 1995a) within 1 K, which also indicates

that no significant change in composition occurred.

4.4 Results and Discussion

To determine the ion activity product, 7(T), in an aqueous H2SO4 solution measured values

of Q(T) and data on Ku(T) are required. In the following, we present the analysis of the

experimental data and derive a new formulation of K\\(T) using a Pitzer ion interaction model

Pitzer (1991).

1.2

0.0

T 1 " •—1——1—•—1——r

•«i(HS041

"1<S04*)

- l__i l_ _< I L. _• L.

500 600 700 800 900 1000 1100 1200 1300 14(

4.4. Results and Discussion 43

4.4.1 Analysis of Experimental Data

Raman spectroscopy can be used for a quantitative analysis of ion speciation if the vibration

bands of the individual species can be identified. The assignment of the various S04_, HSOJ,and H30+ vibration bands according to Querry et al. (1974) and Cox et al. (1981) are indicated

in Fig. 4.2. We chose the integrated line intensities of the vibration bands i/i(S04_) at 980

cm-1 and ^(HSOJ) at 1040 cm-1 to obtain the corresponding molal ratio of rag02-/mHSO-

(Dawson et al., 1986; Tomikawa and Kanno, 1998), where m denotes the molahty of the particular

ion. The integrated line intensities, Iu, were obtained by simultaneously fitting a Lorentzian

function to each peak in the 800-1300 cm-1 interval. The line intensities are proportional to

the concentration of the respective ion i:

F(i)=m(i).r(i), (4.4)

where m(i) is the molal concentration and Jv(i) is the molal scattering coefficient of ion i. Jv(i)

depends on the Raman scattering cross section of the ion, cru(i), and on instrumental properties,

-înstr:

r(i) = o-l'(i)-AiBStT. (4.5)

The molal ratio of SO|_ and HSOJ can be derived from the measured integrated fine intensities

in the following way:

m(SOl-)mQHSOj)

Therefore, the conversion of an intensity ratio into a molal ratio depends only on the ratio of

the Raman scattering cross sections of the particular ions. Equations 4.6 and 4.8 show that for

one particular experiment the ratio of <jv can be substituted by the ratio of the corresponding

Jv, because Amstr cancels out. This requires that av(i) or likewise Jv{i) are constant in the

investigated concentration and temperature range.

Dawson et al. (1986) investigated the temperature and concentration dependence of J980(SO4_)and J1040(USO^) using sodium sulfate and ammonium bisulfate solutions. They found both

molal scattering coefficients to be constant within 1 o error in the temperature range of

298.15-523.15 K and for concentrations of 0.514-2.25 mol kg-1. Hayes et al. (1984) also found

that J980(SO4-) is temperature and concentration independent in the temperature range of

298.15-358.15 K in (NH4)2S04/H20 solutions with concentrations of 0.53-3.14 mol kg-1.Here, we investigate the temperature and concentration dependence of J980(SO|~) at lower

temperatures and higher concentrations than those of the studies mentioned above. The

line intensities of the vibration bands vi(SOl~), ^(SO^-), and ^(SO^-) obtained from

jl040(HgOr) 7980(302-)

J980(S02-)'

/1040(HSO4)

<71040(HSO4-)Ainstr J«»(SO?-)<7980(SOl-)Ainstr

'

/1040(HSO4-)

a1040(HSQr) 7980(302-)

CT980(SO|-) 71040(HSO4 )'


0.9

X

0.3

c3

r» 0.25

m

Pm 0.2

£•COcCD

0.15

0.05

0.0

I I I I • I I

(a)

"i(S04^

KrfstV)^so/-)

500 600 700 800 900 1000 1100 1200

Raman shift [cm*1]

0.25

0.15

0.05

500 600 700 800 900 1000 1100 1200

Raman shift [cm"1]

Figure 4.3: Raman spectra of (NH^foSO^/Ô droplets. Panel (a) shows 10 Raman spectra of a droplet

0.5 fiL in volume and with a concentration of 0.99 mol kg"1 for temperatures between 245 K and 285 K

every 5-10 K. Panel (b) shows 12 Raman spectra of a droplet 1 fiL in volume and with a concentration

of 5.35 mol kg~r for temperatures between 220 K and 296 K every 5-10 K. The Raman spectra are

normalized to the ui(SOl~) vibration band.

Raman spectra of (NH4)2S04/H20 droplets with concentrations of 0.99-5.35 mol kg-1 and at

temperatures of 220-296 K were analyzed. Figure 4.3 displays 10 Raman spectra of a 0.99 mol

kg-1 (NH4)2S04/H20 solution at temperatures between 245 and 285 K and 14 spectra of a 5.35

mol kg-1 (NH4)2S04/H20 solution at temperatures between 220 and 296 K. The ^(SO?-)and 1/4 (SO4-) bands show no change in intensity when compared to the normalized i/i(S04 )vibration band over the investigated temperature and concentration ranges. We conclude

that J980(SO*-) and, thus, also <t980(SO|~) are constant at temperatures of 220-296 K for

concentrations up to 5.35 mol kg-1. Assuming this also to be the case for J1040(HSO4~), we can

use the measured molal scattering coefficients by Dawson et al. (1986) to obtain the ratio of the

Raman scattering cross sections: a^,/ct98^_ = J980(SO|")/J1040hso: so^

(HSO4) = 1.035±0.024.

The small relative difference between the Raman scattering cross sections of 0.035 indicates that

the excitation of the SO|~ and HSO4 stretching vibrations are very similar. This gives further

support for the above assumption that J1040(HSO4~) is independent of temperature and concen¬

tration, just as in the case of the investigated J980(SO|~) band discussed above and in Figure 4.3.

Figure 4.4 shows the phase diagram of the H2SO4/H2O system (Gable et al., 1950). The tem¬

perature and concentration ranges of solutions that were investigated by Raman spectroscopy in


6 8 10 12 14 16 18 20

mHaso4 [mol kg"1]

Figure 4.4: Phase diagram of H2SO4/H2O (Gable et al, 1950). Solid lines represent the melting

curves of several crystalline solids of H2SO4/H2 0. SAH: sulfuric acid hemihexahydrate; SAT: sulfuric

acid tetrahydrate; SATr: sulfuric acid trihydrate. The dashed lines indicate the temperatures and concen¬

trations where Raman experiments have been performed.

this study are indicated by the dashed fines. The experimental data axe limited to the tempera¬

ture range where the droplets remained liquid. As seen in Figure 4.44, the measurements could

be extended well into the supercooled regime. Figure 4.5 shows Raman spectra of a H2SO4/H2O

droplet with a concentration of 2.55 mol kg-1 at different temperatures. The spectra are nor¬

malized to the ^(SO^-) vibration band and reveal a strong decrease in the intensity of the

^(HSOJ) vibration band at low temperatures. We conclude that the concentration of HSO4decreases with decreasing temperature. The dashed line corresponds to a Raman spectrum of a

frozen droplet. The peak at about 3100 cm-1 indicates the presence of ice. We also investigated

the ratio, R, of the integrated line intensities of the SO|~~ and HSO4 vibration bands in the

range of 800-1300 cm-1 (with a negligible intensity stemming from the U2(H.sO+) vibration

band) and the integrated line intensities of the ï/i(H20) and ^3(^0) vibration bands in the


CO

c

cd

!o

COc

CD

290 K

n(HS04)i/,(S04a)

500 1000 1500 2000 2500 3000 3500 4000

Raman shift [cm"1]

Figure 4.5: Raman spectra of a H2SO4/H2O droplet 0.5 ßL in volume and with a concentration of

2.55 mol kg~l. Spectra are shown from 290 K in 10 K steps until freezing occurs (228 K). The dashed

line corresponds to a Raman spectrum of the frozen H2SO4/H2O droplet. Individual spectra are shifted

vertically for better visibility. The Raman spectra are normalized to the i>i(S04~) vibration band.

range of 2500-4000 cm-1, that is

1300

£ /"(SOI") + /"(HSOJ) + J"(H30+)R =

i/=800

4000

E J*(H20)i/=2500

(4.9)

We found R to be constant for a particular solution concentration over the investigated temper¬

ature range within an experimental uncertainty of about 10%, indicating that no concentration

changes due to water evaporation or condensation occurred during the cooling of the droplets.

Figure 4.6 shows the mS02- /mBSO- ratio obtained from our Raman measurements for 0.54-

15.23 mol kg-1 H2SO4 solutions at temperatures of 180-326 K. The experimental data (open

squares) show a continuous increase of the "^so2_/mHSO~ rati° wîth decreasing temperature

for all investigated concentrations. Tomikawa and Kanno (1998) present results which show


2.0

1.5

1.0

0.5

0.0

OCOI

E 12

-~» 9

<% 6

O o

CO d

E o

10

8

6

4

2

0

4

3

2

1

0

1.5

1.0

0.5

0.0

180 200 220 240 260 280 300 320

—I 1 —i 1 1 —

• Œ m

0.54 mol kg'1

• S S

*1.13 mol kg"1

H 1.5

1.0

0.5

0.0

• «S g I g

3

2

-|1

T T T• • 2.55 mol kg'1

"ra„••i g

9Bet t T

4.37 mol kg

• • • •

H—i—i

+

• • S* O* a A.

,—I—, | ? f f» f» Mip»iP»p

6.79 mol kg"1

r * r r r ? y m « s i t » t

9.84 mol kg

f • r ' f ? r f r t ? 9 1 »ff15.23 mol kg'1J

js_^ e_£ e t e

Q] Q,m"m œ nm m m m rj

-C t S « — «* •»

2.0

180 200 220 240 260 280 300 320

Temperature [K]

o

5

4

3

2

1

0

12

9

6

3

0

10

8

6

4

2

0

4

3

2

1

0

1.5

1.0

0.5

0.0

Figure 4.6: Ratios o/mS02-/mHSO- m H2SO4/H2O solutions with concentrations of 0.54-15.23 mol

kg-1 as function of temperature. Open squares with error bars indicate the data obtained from our Raman

spectra. Circles represent values derived using the AIM model (Clegg et al, 1998). Diamonds show data

of a Raman study by Tomikawa and Kanno (1998). Note the different scales for each concentration.

full dissociation at even lower temperatures for aqueous H2SO4 solutions with concentrations of

4.37-15.23 mol kg-1 in the glassy state (about 143-158 K). Our Raman data for the 4.37 mol

kg-1 H2SO4 solution axe in very good agreement with the data by Tomikawa and Kanno (1998)for the same concentration (diamonds in Figure 4.6). In contrast, the "^go2-/rnHSO_ ra*i°s

predicted by the AIM model (Clegg et al., 1998) are much smaller than our measurements and


exhibit a maximum for all concentrations at about 180-240 K. In addition, for concentrations

greater than 6.79 mol kg-1, the model predictions deviate significantly from the experimental

data even at room temperature.

From the wS02-/mHS0- ratios the degree of dissociation of the HSOJ ion, c*HSO-, can be

calculated:

aHso:

ms02

m"

ms02

m.

1 +mS02

-l

m-r

(4.10)

where m^ is the total HS04 molahty before dissociation (Note 1). Figure 4.7 shows a

HSO.hso;

4 6 8 10 12

mH2so4 [mol kg"1]

16

Figure 4.7: Degree of dissociation of the HSO^ ion versus the solution H2SO4 molality. Diamonds,

squares, and circles with corresponding error bars represent experimentally derived data at 190, 230, and

290 K, respectively. The dotted lines indicate the values predicted by the AIM model (Clegg et al, 1998).

The solid lines show values calculated by the Pitzer ion interaction model using K\\(T) derived in this

study.

derived from our experimental data (symbols) as a function of mH2so4 for temperatures of 190,

230, and 290 K. The dotted lines correspond to values predicted by the AIM model (Clegget al., 1998). The solid lines represent aHSO- values calculated by our Pitzer model (see below).

There is a large discrepancy between the experimentally derived data and the AIM values, in

particular at low temperatures and high concentrations.


One possible explanation for the observed discrepancy between the AIM model and the experi¬

mental data could be an inaccurate parametrization of the thermodynamic dissociation constant

of HSOJ, Kn(T), in the model of Clegg et al. (1998) at lower temperatures. The experimental

data used to derive the formulation of Kn(T) were limited to a temperature range of 298-523 K

(Dickson et al., 1990). Nevertheless, this formulation had been adopted in the AIM model for

temperatures down to 180 K. For these reasons we will investigate the temperature dependence

of K\\(T) in more detail in the following section.

4.4.2 Results of the Pitzer Ion Interaction Model

We have used an extended Pitzer ion interaction model (Pitzer, 1991) to calculate ion activity

coefficients and Kn(T) for the H2SO4/H2O system at low temperatures. It is based on the

molality concentration scale and is valid up to concentrations of 40 mol kg-1. A detailed de¬

scription of the working equations is given in the Appendix.For a consistent calculation of the activity coefficients of the various ions (7h+ , 7so2_ > Thso- ) a*

low temperatures, the dissociation of HSOJ has to be considered. Thus, the temperature depen¬

dent second thermodynamic dissociation constant, Ku(T), must be known for the investigated

temperature range. In Figure 4.8, In K\\{T) is plotted as a function of inverse temperature. The

dotted fine shows the formulation of K\\{T) given by Clegg et al. (1994), which is also imple¬

mented in the AIM model (Clegg et al., 1998; Note 2). This formulation was originally derived

by Dickson et al. (1990) for the temperature range of 298-523 K. Some of the high temperature

data of K\\ of Marshall and Jones (1966) and Dickson et al. (1990) are also plotted as diamonds

in Figure 4.8. The dissociation of HSO4 at room and higher temperature is an exothermic

reaction. Extrapolation of the formulation of Ku(T) of Dickson et al. (1990) to low temper¬

atures in the AIM model (Clegg et al., 1998) suggests that the exothermic reaction changes

to an endothermic reaction at around 233 K. From K\\(T) the corresponding standard Gibbs

free energy, AGn(T), enthalpy, AH^T), and entropy, AS^T), of the dissociation reaction of

HSO4 (HSO4 -s. SO^_ + H+) can be derived:

AG^(T) = -RTlnKn(T) (4.11)

A/4(T) = -R*h*°Çl (4.12)d^

AS,(T) _ A^(T)-Ao;,(T)| (413)

where T is temperature and R is the universal gas constant. The dotted lines in Figure 4.9

show AGjj(T), Ai?jj(T), and A5n(T) for the dissociation reaction of the bisulfate ion using the

formulation of -Kn(T) of Clegg et al. (1994). AG\X has a minimum at about 220 K with increasing

values at lower temperatures. Also, A.ffn and ASjj increase with decreasing temperature over

the entire temperature range. ASjj at 298.15 K is about -110 J K_1mol-1 (Lide, 1998), which

is in agreement with the formulation of Kn(T) of Clegg et al. (1994). However, the increase in

A5jj at very low temperature contradicts the Nernst heat theorem (Nernst, 1906; Berry et al.,


T[K]400 333.3 285.7 250 222.2 200 181.8

-2.0

-2.5

-3.0

-3.5

-4.0

^-4.5ç

-5.0

-5.5

-6.0

-6.5

-7.00.0025 0.003 0.0035 0.004 0.0045 0.005 0.0055

T"1 [K"1]

Figure 4.8: In K\\ plotted as a function of inverse temperature. The dotted line corresponds to the

formulation given by Clegg et al. (1994). The solid line represents K\\ derived in this study. Dashed lines

represent the results of a sensitivity study (see text for details). Open squares show Kn(T)-values using

the measured <*HSO- and the activity coefficients derived by our Pitzer model. Diamonds show some of

the high-temperature data of Ku from Marshall and Jones (1966) and Dickson et al. (1990).

2000), which says that AS for any reaction vanishes as temperature approaches 0 K; that is

linvr—o AS = 0.

In the following, we use a Pitzer ion interaction model (Pitzer, 1991) to determine a formulation

of K\\(T) which is consistent with the experimental data and with thermodynamics. Several

data sets were implemented in the Pitzer ion interaction model to obtain the new formulation

of Ku(T): the data of ojhso- obtained in this study; data of electromotive force experiments

(Harned and Hamer, 1935); enthalpies and heat capacities of H2SO4/H2O (Giauque et al., 1960);

and dissociation constants in the temperature range of 323-473 K (Marshall and Jones, 1966;

Dickson et al., 1990). Because each of these data sets consists of a different number of data

points, the data were weighted such that each data set had equal weight in the overall fit.

The enthalpy of the dissociation reaction of HSO4 , A.ffn(T), was fitted within the Pitzer ion


Ö 50

E

X

<-50

-100

600 k

O

E 400

-5 200 k

<°

-200

-—h

(b)

H——r- H——I-

(c)

50

-50

-100

600

400

200

0

-200

100 150 200 250 300 350 400 450 500

Temperature [K]

Figure 4.9: (a) Gibbs free energy for the dissociation reaction of the bisulfate, AG'n, as a function of

temperature, (b, and c) Corresponding reaction enthalpy, AHU, and entropy, ASjj, respectively. The

dotted lines show results using the formulation ofKn(T) by Clegg et al. (1994). The solid lines represent

results using the formulation of Ku(T) derived in this study. The dashed lines indicate the temperature

range where experimental data are available.

interaction model by11 dco dcp,

Afl£(D = AflS + 4(T - T0) + ^(T2 + T02) - ^T0T, (4.14)

1c° must be changed to Ac£. Due to reasons of copyright the correction will not be implemented.


where To is 298.15 K, Aüjj is the enthalpy of the dissociation reaction at To, c0, is the heat

capacity of the solution at To, and dcp/dT describes its temperature dependence. We performed

several model runs to derive a new formulation of Kn(T) at low temperatures. To achieve

thermodynamic consistence, we were forced to treat the dissociation as an exothermic reaction in

the temperature range of 165-473 K in our fitting procedure (i. e. Aüjj < 0 for this temperature

range). The final results (the parameters for the Pitzer equations and Ku(T)) axe both consistent

with all the experimental data and the Nernst heat theorem (Nernst, 1906; Berry et al., 2000).The formulation for Ku(T) derived in this study is shown as the solid line in Figure 4.8. The

dashed lines in Figure 4.8 indicate the results of a sensitivity study. They represent fits which

were constrained to Aiïjj < 0 down to 120 K and to 180 K, respectively. The two curves

(dashed lines) differ only slightly from the best fit (solid line), indicating that the formulation

of K\i(T) is rather insensitive to the choice of temperature range where Aiïjj is assumed to

be negative. The open squares in Figure 4.8 were derived, using the measured Q;Hso- an(i *ne

activity coefficients of the Pitzer model used in the present study. The obtained Ku(T) values

match the fit, showing that our Pitzer model works in a consistent way. The solid lines in Figure

4.9 show AGjj, Aüj'j, and ASjj calculated using the formulation of Kn(T) derived in this study.

AGjj decreases with decreasing temperature, and A/ïjj and A5jj approach zero with decreasing

temperature (in the range of available data), in agreement with the Nernst heat theorem (Nernst,

1906; Berry et al., 2000). It should be noted that, when our new dissociation data are included,

the Pitzer model can be tuned to reproduce all experimental data even with Ki\(T) fixed to the

formulation of Clegg et al. (1994). This is achieved by adjusting the ion activity coefficients in

the aqueous solutions. However, although the resulting model parametrization is consistent with

all experimental data, it contradicts the Nernst heat theorem (Nernst, 1906; Berry et al., 2000).

Furthermore, we expect that also the AIM will reproduce all experimental data in agreement

with the Nernst heat theorem when our new dissociation data and the newly derived K\\{T) are

implemented. Values for our newly derived Ku(T) (solid fine in Figure 4.8) can be calculated

from the following equation using the parameters given in table 4.2. Ku was calculated by

integrating eq 4.12 and using eq 4.14 for A/ïjj:2

lnÄ-n(T) = lnirj0i(r0)-/TAi4(r)4 (4.15)

- in*?,- [(Atf8-<$r0 + I^)(I- i)

-K-înL-l^T-n)} (4.16)

The above formulation can be used in the temperature range of 180-473 K.

With the newly derived formulation for Ku(T) our Pitzer ion interaction model can be used to

predict the degree of dissociation, a°<?_. Comparisons between the modeled a„°^_ and the

experimentally obtained data are given in Table 4.3 and Figure 4.7. Also shown in Table 4.3

are values for the activity coefficient product, 7(T), which were calculated from eq 4.3 using the

Äll(T)-values from Eq. 4.16 together with Q(T)-values obtained directly from the experimental

2In Eq. 4.15 and Eq. 4.16 ^ is missing in front of the integral and the big bracket. Due to reasons of copyright

the correction is not implemented.

4.5. Atmospheric Implications 53

data.

Figure 4.10 and 4.11 show calculated ion activity coefficients, 7h+, 7so2_> a3X^- 7h+'

^SO2-' an(^

water activities, aw, for a 1.13 mol kg-1 and a 9.84 mol kg-1 H2SO4/H2O solution, respectively.

The solid lines correspond to values calculated with our Pitzer model using the new Ku(T)-

formulation; the dotted lines are calculated using the AIM model (Clegg et al., 1998). Significant

differences between the two models exist for all parameters, in particular at low temperatures.

Note that the difference in <zw for the 9.84 mol kg-1 solution is about 10 % at 180 K. This

may be due to the larger HSO4 dissociation and, thus, larger ionic strength in our model at

low temperatures. Also note, that the activity coefficients between the two models also differ

strongly, for example in the case of 7SQ2- in Figure 4.11b by up to 2 orders of magnitude.

4.5 Atmospheric Implications

Relative humidity and temperature can vary over a large range in the atmosphere; for exam¬

ple temperatures can be as low as 180 K in the polar stratosphere and tropical tropopause.

Stratospheric aerosols can consist of highly concentrated H2SO4/H2O droplets (Junge and

Manson, 1961; Hamill and Toon, 1991) at dry conditions. Under these conditions the exper¬

imental data obtained in this work show a significantly higher dissociation for the reaction

HSOJ ^ SO|_ + H+ than was assumed in previous model calculations. This also has im¬

plications for other thermodynamic properties of aqueous H2SO4 solutions. The water vapor

pressure, Ph20> of a H2SO4/H2O solution depends on the water activity of the solution, <zw:

PH2o(T) = av,(T)p0H2O(T), (4.17)

where Ph2q is the water vapor pressure over pure water at the same temperature. Because

we calculate lower water activities at low temperatures than the AIM does, our results imply

slightly lower water vapor pressures of sulfuric acid aerosols under stratospheric conditions.

In addition, the new binary interaction parameters for H2SO4/H2O obtained by our Pitzer

model can serve as input parameters for the derivation of ternary interaction parameters in

aqueous solutions such as the NH3/H2SO4/H2O and HCI/H2SO4/H2O systems, which axe com¬

mon in aerosols of the troposphere and stratosphere. Furthermore, the solubility of trace gases

in H2SO4/H2O solutions such as HCl and NH3 is affected (Luo et al., 1994; Swartz et al., 1999).The larger dissociation constant leads to higher H+ concentrations in H2SO4/H2O solutions

and, therefore, to lower HCl solubilities/Henry's law constants when compared to AIM results

(Carslaw et al., 1995a). Over the concentration range of 4.3-15.23 mol kg-1 and at tempera¬

tures between 180 and 300 K, the maximum difference between our model and the AIM (Carslawet al., 1995a) is about a factor of 3. We note that Carslaw et al. (1995a) show in their Figure

13 that data from vapor pressure measurements (Hanson and Ravishankara, 1993; Zhang et al.,

1993a) fall below their model predictions, while data from uptake experiments (Hanson and

Ravishankara, 1993; Williams and Golden, 1993; Elrod et al., 1995) are closer to predictions.

Later Hanson (1998) reexamined their earlier data which are still below but closer to the predic¬

tions than before. Unfortunately, the scatter between the different data sets (and experimental


333.3

?»

10"4

3

?101

O* 10","2 -

?

10-°

s

0.975

0.97

3 0.965(0

0.96

0.955

0.95

285.7

T[K]250 222.2 200

-r

181.8

_i_

(a)

(b)"-

(c)

(d)

10"'4

3

10-8

7

6

5

10'

5

10-°

5

0.975

0.97

0.965

0.96

0.955

0.95

0.003 0.0035 0.004 0.0045

r1 [K-1]

0.005 0.0055

Figure 4.10: Activity coefficients 7H+, 7so2-> 7h+"

7so2~ an^ flw °f a ^-^ mo' ^_1 H2SO4/H2O

solution plotted as a function of inverse temperature. The solid lines are calculated by the Pitzer model

using Ku(T) derived in this study. The dotted lines are predictions from the AIM model by Clegg et al.

(1998).

methods) is large and, thus, does not allow us to conclude which of the model predictions is

closer to real solubilities at this stage.

4.5. Atmospheric Implications 55

285.7

T[K]250 222.2 181.8

0.003 0.0035 0.004 0.0045

r1 [K-1]

Figure 4.11: Activity coefficients 7h+, 7go2-> 7h+'

7so2~ an^ flw °f a 9-&4 mo^ ^g_1 H2SO4/H2O

solution plotted as a function of inverse temperature. The solid lines are calculated by the Pitzer model

using Ku(T) derived in this study. The dotted lines are predictions from the AIM model by Clegg et al

(1998).


4.6 Conclusions

The dissociation of the bisulfate ion (HSOJ ^ SO2- + H+) has been studied in a temperature

range of 180-326 K in H2SO4 solutions with concentrations of 0.54-15.23 mol kg-1 using Raman

spectroscopy. The experimental results show a continuous increase in the degree of dissociation

of HSOJ with decreasing temperatures within the investigated concentration and temperature

range. Our results disagree with predictions from the thermodynamic model AIM (Clegg et al.,

1998), which underestimates the degree of dissociation of HSOJ for high H2SO4 concentrations

and low temperatures by up to a factor of 5. This is most likely due to the implementation of a

thermodynamic dissociation constant in the AIM, that is at odds with the Nernst heat theorem.

Therefore, we have employed a Pitzer ion interaction model to obtain a new thermodynamically

consistent formulation of the thermodynamic dissociation constant, Kjj(T), that is in agreement

with experimental data. The new formulation of -Kn(T) is valid from 180 to 473 K. In the

model, consistency with thermodynamics can be achieved only by assuming that the dissociation

reaction is exothermic over the entire temperature range. Results from our model indicate that

ion activity coefficients can differ by up to 2 orders of magnitude, water activities and vapor

pressures by up to 10%, and HCl solubilities by up to a factor 3 when compared to results from

the AIM (Clegg et al., 1998; Carslaw et al., 1995a).We recommend that future thermodynamic investigations of multicomponent aqueous solutions

containing H2SO4 use the new formulation of K\i(T) for a correct description of the dissociation

reaction of the bisulfate ion.

4.7 Appendix

4.7.1 Tables

Table 4.3: Experimental Data and Modeling Results for the

Investigated Aqueous H2SO4 solutions"

T H2S04 «hso4- «SS- lnQ ln7

[K] [mol kg"1]321.0 0.54 0.22 0.20 -1.667 -3.507

316.0 0.54 0.22 0.22 -1.657 -3.379

311.0 0.54 0.19 0.23 -1.864 -3.033

306.0 0.54 0.23 0.25 -1.620 -3.140

297.1 0.54 0.30 0.29 -1.182 -3.344

290.4 0.54 0.34 0.32 -1.014 -3.337

280.5 0.54 0.38 0.37 -0.787 -3.318

270.7 0.54 0.46 0.42 -0.424 -3.444

260.8 0.54 0.46 0.48 -0.384 -3.258

251.0 0.54 0.53 0.54 -0.079 -3.350

241.0 0.54 0.59 0.60 0.185 -3.413

Table 4.3: (continued)

T H2S04 aHSo4- agg_ InQ In 7

[K] [mol kg"1]*

289.4 1.13 0.37 0.37 -0.077 -4.251

279.4 1.13 0.42 0.42 0.135 -4.212

269.6 1.13 0.48 0.48 0.418 -4.261

259.8 1.13 0.54 0.54 0.696 -4.315

254.9 1.13 0.59 0.57 0.937 -4.448

249.9 1.13 0.60 0.60 1.019 -4.427

240.1 1.13 0.68 0.66 1.401 -4.611

290.8 2.55 0.42 0.41 0.962 -5.325

280.1 2.55 0.46 0.47 1.144 -5.239

270.1 2.55 0.51 0.52 1.398 -5.253

260.8 2.55 0.57 0.58 1.690 -5.332

251.2 2.55 0.64 0.64 1.989 -5.423

246.1 2.55 0.67 0.68 2.145 -5.474

240.1 2.55 0.70 0.71 2.304 -5.513

236.1 2.55 0.73 0.74 2.457 -5.589

233.0 2.55 0.75 0.75 2.565 -5.643

231.0 2.55 0.75 0.77 2.615 -5.656

325.9 4.37 0.34 0.33 1.093 -6.407

320.8 4.37 0.34 0.34 1.112 -6.283

315.9 4.37 0.35 0.35 1.156 -6.189

310.9 4.37 0.36 0.36 1.208 -6.103

306.0 4.37 0.37 0.38 1.276 -6.037

301.0 4.37 0.39 0.39 1.344 -5.973

297.4 4.37 0.40 0.40 1.397 -5.931

289.7 4.37 0.40 0.43 1.398 -5.733

279.9 4.37 0.47 0.47 1.748 -5.837

269.8 4.37 0.52 0.52 1.982 -5.830

259.8 4.37 0.58 0.58 2.250 -5.869

249.7 4.37 0.64 0.64 2.522 -5.926

239.9 4.37 0.70 0.70 2.844 -6.050

230.0 4.37 0.76 0.75 3.195 -6.218

219.7 4.37 0.83 0.81 3.665 -6.515

209.5 4.37 0.85 0.85 3.867 -6.568

199.7 4.37 0.89 0.89 4.219 -6.797

190.0 4.37 0.92 0.91 4.540 -7.021

289.9 6.79 0.41 0.41 1.909 -6.249

279.1 6.79 0.45 0.44 2.082 -6.151

269.6 6.79 0.49 0.48 2.280 -6.124

259.8 6.79 0.53 0.52 2.473 -6.093

249.9 6.79 0.58 0.57 2.703 -6.110

8OI11Ia>

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4.7. Appendix 59

Table 4.3: (continued)

T EtfÖl «Hsor«ï£- toQ kTÏ

[K] [mol kg"1]HSOJ "hSO

4

221.0 15.23 0.47 0.47 2.994 -5.865

211.2 15.23 0.51 0.51 3.170 -5.893

201.3 15.23 0.55 0.55 3.355 -5.951

191.3 15.23 0.59 0.60 3.546 -6.039

181.5 15.23 0.64 0.64 3.771 -6.190

"The first two columns indicate the temperature and concentration of the H2SO4 solutions.

aHSO-: experimentally obtained degree of dissociation (see eq 4.10); off^L- is the degree of

dissociation calculated from our Pitzer model using the new Än(T)-formulation; Q is the molal

equilibrium quotient (see eq 4.3); 7 is the activity coefficient product (see eq 4.3).


Table 4.1: Composition and Volume of the Investigated Aqueous Droplets.

H2so4 (NH4)2S04 Volume

[mol kg-1] [mol kg-1] [10-3cm3]

0.54 0 10

1.13 0 0.5

2.55 0 0.5

4.37 0 0.5

6.79 0 0.5

9.84 0 10

15.23 0 10

0 0.99 0.5

0 1.95 0.5

0 3.17 0.5

0 3.88 1

0 5.35 1

Table 4.2: Fit Parameters to Derive \nKu{T) Using Eq 4.I6.

K AHn/R [K] %/R &/R [K"1]

1.0576 lO-2 -2231.620793 -24.7273 -0.11967

Numerical check: lnü:(273K) = -3.954.

4.7. Appendix 61

Table 4.4: Temperature Dependent Parameters (p) and Temperature Independent Parameters (aca, u)Ca>

b) of the Ion Interaction Model?.

p X AHn/R [K] cl/R S/Ä IK"1]0(0)^H+,HS07

-0.12672773 122.83352564 0.79298257 4.49770xlO-3

3{1)MH+,HS07

1.43843400 140.47112887 -15.44397569 -0.49178043

c(0)H+.HS07

1.08965 xlO"3 -1.36879879 -9.58811 xlO-3 -2.78 xlO-6

c(1)H+.HS07

0.31617615 4.38280351 -0.50421020 2.74165 xlO-3

/3(0)PH+,S02-

0.12485773 9.86603452 -0.59448781 -6.1367X10-4

tf(1)

PH+,S02--0.46260131 358.49482175 17.75619395 5.849624xl0~2

CH+,S02"5.10014X10-3 -3.21170454 -1.264739xl0~2 -4.46 xlO-6

CH+,S02--0.27604369 83.11418947 4.55227587 6.408755xl0-2

^H+,HS07: 1.2 ^H+,so2_: 1.2

Cl,H+,HS07: 0.91291829 WH+,S02-: 1.91623572

aH+,HS07: 2.0 aH+,S02_: 2.0

"Units are as follows: ßej and /%, in kg mol 1; cid and c)J in kg2 mol 2; atca, ^ca, and bCl

in kg1/2 mol-1/2; the temperature dependent parameters are calculated in the following way:

p = lnx + (AFj0i-c°ro + è^T2)(i-^)-(^-^ro)ln^-i^(r-To).

4.7.2 Derivation of the thermodynamic dissociation constant of HS04

The chemical potentials ß% (i = H+, SO2, HS04 ) of the species involved in the dissociation

reaction HSOJ ^ SO|" + H+ can be written as:

ßt(T) = ßl(T) + RT In at(T) (4.18)

where ß\ is the standard chemical potential of the species 1, that is the chemical potential in a

hypothetical 1 mol kg-1 aqueous solution with ideal properties. The activity, at, of each species

is the product of its activity coefficient, 7,, and its molality mt, such that at(T) = li(T)m^ '.

ml is by definition 1 mol kg-1.In chemical equilibrium, the Gibbs free energy for the dissociation reaction is

AGn(T) = /iSO2-(T) + MH+(T)-/iHSO7(T) = 0- (4.19)

Replacing ß% from eqs 4.18 and 4.12 into eq 4.19 yields the temperature dependent thermody¬

namic dissociation constant of HSO4 , Kn(T):

Kn(T)mS02- (T) • mH+ (T) \ /7soJ- (T) • 7h+ (T)

'

mhso; -(T)-mt 7hso7(T)

(4.20)


Equation 4.20 shows that in order to derive Kn(T) not only dissociation data are required, but

also knowledge of the activity coefficients of the involved ions.

4.7.3 Extended Pitzer Ion Interaction Model

The Gibbs free energy of an aqueous electrolyte solution can be written as

G 1

WvRT RT«0*w - a*1) + J2m^ ~ /4) (4.21)

= Qlnow-I- y^mjlnai, (4.22)i

where R is the universal gas constant, T is the temperature, ww is the mass of the solvent (1

kg of water), Q is number of moles in one kilogram of water (55.51 mol), and mi, ßi, ß], and ai

are defined as above.

For an ideal solution, the activity coefficient 7» = 1 and, thus, the Gibbs free energy of an ideal

solution becomes

Qideal

wZrt= mna^ + ^milnî). (4.23)

Since the excess Gibbs free energy is the difference between the Gibbs free energies of a real and

an ideal solution, one finds using eqs 4.22 and 4.23

G G G(424)

wwRT wwRT wwRT

= n(ln a* - Ino^ + ^mi In7i. (4.25)i

Instead of water activity, the osmotic coefficient, $, is often used in thermodynamic treatments

and is defined as

$ = --^-lnaw. (4.26)

To derive the water activity in the ideal solution, d^0,1, the Gibbs-Duhem relation is applied to

eq 4.23:

fid In a**"* + Y^mdm (^) = 0, (4.27)i

and integration yields

= "è?"1*- (4-28)In a***'

4.7. Appendix 63

Thus, eq 4.25 can be written as

Gex

WwRT= ^m,(l-$ + ln7,). (4.29)

The water activity, Ow, and the activity coefficients, % (i = H+, S04_, HSO4 ), can be derived

from the following derivatives of the excess Gibbs free energy:

i / piCex \

Using eqs 4.26, 4.28, and 4.30 the expression for the osmotic coefficient can be written as:

,_! _

' J-(*q. (4.32)

The statistical mechanics of electrolytic solutions suggest that Gex can be expressed in terms

of a virial expansion in concentration (Pitzer, 1991). In our model the three-body interaction

(H+, SO|", HSO4 ) and the interaction between HSOJ and SO2- axe neglected and, therefore,

Gex can be written as:

/~<ex

—— ~ /(/) +Vmcma (2Bca(I) + ZCÎ)) , (4.33)ca

where m, is the molality of the ith ion (i = a or c, i. e. anion or cation, respectively). Z is

given by Z = ^2tml \ z% |, where zt is the charge of the ith ion. /(J) is the Debye-Hückel

term, representing the long-range electrostatic interaction, and Bca(I) and Cca(I) describe the

short-range interactions in binary solutions. fîca(7) is the two body interaction term (one cation

interacts with one anion) and Cca(I) is the three body interaction term (two identical ions

interact with one other ion: era, aac). AU given parameters depend on temperature and on the

molal ionic strength, /, which is given by i" = 1/2 £^ mtz%.According to eq 4.31 the activity coefficient of a cation or an anion can be derived by taking the

derivatives from eq 4.33:

In 7c = z^F + J2ma(2Bca + ZCca), (4.34)a

In 7a = 22F + ^mc(2Bca + ZCco), (4.35)c

where the summations run over cations (c) and anions (a). The quantity F includes derivatives

of the long-range electrostatic interaction term, /, and of B and C with respect to the ionic

strength I:

F=lf' + Yl mc«(B'ca + ^C'ca) (4-36)


According to eq 4.32 the osmotic coefficient is calculated from the derivative of eq 4.33 with

respect to u;w:

$-1 = -,

where

If*[I) + £ m°m° [ß-(J) + ZCcaV)] (4.37)

f*W = ^(If'(I)-f(I)), (4-38)

B%(I) = BM + IB'Î), (4.39)

Ct{I) = Cca(/) + ^(/). (4.40)

The differential equations 4.38-4.40 are solved numerically using the foUowing analytical func¬

tions fitted to available data sets:

f*W = -jL£-r> (4-41)1+6/2

Bcl(I) = ßW+ßtte-^, (4.42)

Ccl(I) = cM + cUe-»^, (4.43)

where A^ is the temperature dependent Debye-Hückel parameter given by Pitzer (Pitzer, 1991),and ßca, , ßca , Cca ,

and CcJ are temperature dependent fit parameters, and b, a, and u are

temperature independent fit parameters. Note, that the parameters Cca and cca represent the

average of the two different three-body interactions caa and cca, which cannot be separated

numerically. The analytical functions /* and I?*, in eqs 4.41 and 4.42 axe chosen according to

Pitzer (Pitzer, 1991) to yield the best fit to the data of a large number of aqueous solutions. We

chose 0%, also to depend on the ionic strength. The parameters of our Pitzer ion interaction

model are given in table 4.4.

The solutions of the differential equations 4.38, 4.39, and 4.40 give /(/), Bca{I), Cca(I), and

their corresponding derivatives. These functions axe required to calculate Ow using eq 4.37 or to

derive the activity coefficients employing eqs 4.34 and 4.35.

4.7. Appendix 65

Here ends the publication:

Thermodynamic Dissociation Constant of the Bisulfate Ion from Raman

and Ion Interaction Modeling Studies of Aqueous Sulfuric Acid at Low

Temperatures

D. A. Knopf*, B. P. Luo, U. K. Krieger, and Thomas Koop

Institute for Atmospheric and Climate Science, Swiss Federal Institute of Technology, Hongger-

berg HPP, 8093 Zurich, Switzerland


Reproduced with permission from the Journal of Physical Chemistry Part

A, 2003. Unpublished work copyright 2003 American Chemical Society.


w©iL© L@©r /

Blank leaf

4.8. HCl solubility in H2S04/H20 solutions 67

4.8 HCl solubility in H2S04/H20 solutions

The newly derived thermodynamic dissociation constant has an effect on the calculated the

amount of H+ in aqueous H2SO4 solutions. The H+ concentration in solution has an impact

on the solubility of trace gases into liquid H2SO4/H2O (see section 2.1.3). A change in sol¬

ubihty, expressed by the effective Henry's law constant, #£, corresponds to a change of the

heterogeneous reaction rate coefficient (see appendix C). Here, the solubihty of HCl, H^cv into

H2SO4/H2O solution is discussed in further detail.

Figure 4.12 shows HCl solubilities derived from model predictions and experimental studies for

four different aqueous H2SO4 solutions. At low temperatures the predictions of the Pitzer model

of this study coincides with the ones of the AIM model (Clegg et al., 1998) only in the case

of a H2SO4 solution 5.5 mol kg-1 in concentration. The solubilities shown in Fig. 4.12 for the

other H2SO4 solutions derived by the Pitzer model in this study axe up to a factor of three

lower than the predictions of the AIM model (Clegg et al., 1998) over the entire temperature

range. The experimental data of Zhang et al. (1993a) axe also up to a factor of three lower than

the AIM predictions. The experimentally obtained data coincides with the predictions of the

Pitzer model of this study in the case of a 8.35 mol kg-1 H2SO4 solution. But for an aqueous

H2SO4 solution 10.2 mol kg-1 in concentration the experimentally obtained data is closer to the

predictions of the AIM model (Clegg et al., 1998). In the case of a H2SO4 solution 15.23 mol

kg-1 in concentration most of the experimentally obtained data points correspond to the AIM

model except the data of Zhang et al. (1993a) which agrees with the solubility values derived in

this study.

The vapor pressure measurements of HCl over mixtures of HCl in aqueous H2SO4 result in an

absolute determination of #hC1 whereas in reactive uptake experiments the value H^cl-^D{is obtained. Therefore, an accurate determination of the solubility from reactive uptake

experiments requires the knowledge of the liquid-phase diffusion coefficient, D\. D\ is a function

of viscosity, which itself depends strongly on temperature (Williams and Long, 1995). The

uncertainty in D\ could be a possible explanation for the scatter within the experimental data

derived by reactive uptake experiments (Hanson and Ravishankara, 1993; Williams and Golden,

1993; Elrod et al., 1995; Hanson, 1998; Robinson et al., 1998) and, hence, their deviations

from the models. Carslaw et al. (1995a) expect an uncertainty in the experimentally obtained

solubihty values of a factor of three due to an uncertainty in the viscosity of up to a factor of

10.

As discussed by Elrod et al. (1995) the measurements of Zhang et al. (1993a) probably suffered

from instrument calibration errors. The tendency of lower solubilities of Zhang et al. (1993a)

compared to the AIM predictions is similar to the solubihty values derived by the Pitzer model

of this work. The solubility values of this study and Zhang et al. (1993a) even coincide for the

H2SO4 solution with a concentration of 15.23 mol kg-1.At this point, it cannot be concluded which of the two models is more accurate in predictingthe HCl uptake by aqueous H2SO4 aerosols. The scatter within the experimental data sets and

the alternating agreement of the experimentally obtained solubilities with both models does

not allow a final decision. However, it should be noted that the Pitzer model presented in this

work is thermodynamically more consistent than AIM.


Temperature [K] Temperature [K].180 200 220 240 260 280 300 180 200 220 240 260 280 300

10 I i —r——i—>—i—>—i ' r——i—>—i i i—> i 110

10

"E 109CO

L_ 10'

10

,8 -

o

E io7

o

.x 10'

X

10'

,6

,5

10*

-i—>—i—>—i

5.5 mol kg"1 .

\ \'

* V* \.

«

* V.* V.* \r.* X.* X.* X. AIM

/^*!Zhang et al.xOx>. Pitzer model

data * ^Cv. /* X^'t

*^^*.*^%

^.-

10.2 mol kg'1.

8.35 mol kg".

i i

i

L - - -

10"

10°

1180 200 220 240 260 280 300 180 200 220 240 260 280 300

Temperature [K] Temperature [K]

Figure 4.12: HCl solubilities for the indicated concentrations are shown as a function of temperature.

The dotted line represent HHCl predictions of the AIM model (Carslaw et al, 1995a). The dashed line

shows solubility data given by Zhang et al (1993a). The solid line is calculated by the Pitzer model of

this study using the newly derived Ku(T). The open circles represent solubility values derived by vapor

measurements. The solid symbols represent solubility values obtained by reactive uptake measurements.

In the case of the H2SO4 solutions 5.5, 8.35, and 10.2 mol kg-1 in concentration the following denotation

is applied: o Hanson and Ravishankara (1993); • Hanson (1998); Williams and Golden (1993);Elrod et al (1995). In the case of the 15.23 mol kg~1 H2SO4 solution the following denotation is applied:

• Hanson and Ravishankara (1993) ( data of a 15.1 mol kg-1 H2SO4 solution); Williams and Golden

(1993).

4.9. Analysis of H2SO4/H2O Raman spectra 69

Because HCl and HBr have similar molecular properties, one would expect lower solubility

predictions in aqueous H2SO4 solutions for HBr, when using the newly derived H2SO4/H2Ointeraction parameters within a ternary H2S04/HBr/H20 Pitzer model. The original AIM

model (Carslaw et al., 1995a) derived higher HBr solubility predictions than the experimentallyobtained HBr solubility data (Abbatt, 1995; Abbatt and Nowak, 1997; Williams and Long,

1995; Kleffmann et al., 2000). Therefore, Massucci et al. (1999) revised the original AIM

model (Carslaw et al., 1995a) in order to get a better agreement with the experimentallyobtained data. However, the solubihty values derived by vapor pressure measurements are still

a little lower than the predictions of the revised AIM model (Massucci et al., 1999). Therefore,

the newly derived thermodynamic constant should be implemented within the AIM model

(Massucci et al., 1999) to reanalyze HBr solubilities, possibly leading to a better agreement

with experimental data.

If the HCl solubility is indeed a factor of up to three lower than assumed in previous studies

(Carslaw et al., 1995a) this will have consequences also for the heterogeneous reaction rate coeffi¬

cient of HCl on aqueous H2SO4 particles. The heterogeneous reaction rate coefficient will change

linearly with a change in the effective Henry's law constant (see appendix C, Eq. C.I). A lower

solubility of HCl results in a lower reaction probability of HCl with CIONO2 on aqueous H2SO4

aerosol particles and, therefore, leads to a lower amount of activated CI2. Becker et al. (1998)have shown that the high ozone loss rates at the end of January in the Arctic obtained by the

MATCH analysis (von der Gathen et al., 1995), cannot be simulated with their photochemicalbox model. This model includes 11 heterogeneous reactions on NAT and ice, 3 reactions on SAT,and 8 reactions on H2SO4/HNO3/H2O solutions, all based on the analytical expressions of the

predictions of the AIM model (Carslaw et al., 1995b,a). Sensitivity studies of ozone loss rates

within the model of Becker et al. (1998) show no strong dependence on details of the heteroge¬

neous chemistry, i. e. particle formation, temperature dependence, and the negligence of chlorine

deactivation. However, a sensitivity study with respect to heterogeneous reaction rates was not

performed. The HCl solubilities derived in this study imply lower heterogeneous reaction rates

and, thus, even lower chlorine activation will be obtained in the box model calculations. This

will enhance the deviations between box model simulations and the MATCH-analysis in Becker

et al. (1998). Therefore, it can be concluded that there must be other reasons than wrong

HCl solubilities for the observed differences such as additional chemical reactions or dynamicalinfluences like exchange of stratospheric and tropospheric air masses.

4.9 Analysis of H2SO4/H2O Raman spectra

In this section Raman spectra of H2SO4/H2O as a function of temperature and concentration

will be discussed.

The temperature dependence of liquid-phase Raman spectra is shown in Fig. 4.13 for a

H2SO4/H2O solution with a concentration of 6.79 mol kg-1. It can be seen that the inten¬

sity of the i/i(HS04 ) vibration band decreases with decreasing temperature due to the increase


t—|—i—|—i—|—i—|—i—i——r

"i(HSO„")

^^-^'-

-

-: i i ^-i

500 1000 1500 2000 2500 3000 3500 4000

Raman shift [cm'1]

Figure 4.13: Raman spectra of a H2SO4/H2O droplet 0.5 ßL in volume and a concentration of 6.79

mol kg~l. Spectra are shown from 290 K in 10 K steps. Individual spectra are shifted vertically for better

visibility. The Raman spectra are normalized to the ui(SÖ4~) vibration band.

of the dissociation of the bisulfate ion (see previous sections). The shapes of the vi(H2O) and

1/3(^0) vibration bands change with decreasing temperature due to the reorientation of the

hydrogen bonds between the water molecules. In the literature the reasons for the change in

the shape of the water vibration bands is still discussed. In pure water it is assumed that the

v\(H2O) and 1/3(^0) vibration bands change due to temperature dependent intra- and inter-

molecular coupling and Fermi resonances (Ratcliffe and Irish, 1982; Zhelyaskov et al., 1988).Since in the presented study an aqueous acidic solution is considered the explanation for the

change in the water vibration bands is more complex and, thus, will not be discussed in this

work. The Raman spectra which are taken at temperatures lower than 220 K are supercooledwith respect to SAH and SAT.

The instrumental setup can also be used to record Raman spectra of small droplets with a

diameter of about 50 /uu. Figure 4.14 shows Raman spectra of a H2SO4/H2O droplet with a

concentration of 3.04 mol kg-1 at different temperatures which is similar to the Raman spectra

of Fig. 4.5. A comparison between the two sets of Raman spectra shown in figures 4.5 and 4.14

cannot be performed quantitatively, since the H2SO4 concentration of the solutions differs about

0.5 mol kg-1. But the similar quality of both Raman spectra indicates that even spectra taken

from small droplets can be used for a quantitative analysis.


1—1—1—1——!—1—1—1—1—if—r

Figure 4.14: Raman spectra of a H2SO4/H2O droplet with a volume of 6.5-10~b ßl and a concentration

of 3.04 mol kg~l. Spectra are shown from 290 K in 10 K steps until freezing occurs (190 K). The dashed

line corresponds to a Raman spectrum of the frozen H2SO4/H2O droplet. Individual spectra are shifted

vertically for better visibility. The Raman spectra are normalized to the v\ (SO4- ) vibration band.

Figure 4.15 shows liquid-phase Raman spectra of a H2SO4/H2O droplet at 250 K for varying

H2SO4 concentrations. As the concentration increases, the amount of HSOJ increases too as

indicated by the rise of the ^(HSOJ) vibration band at about 1050 cm-1. The increase in con¬

centration can also be seen in a strong decrease in the vibration bands corresponding to water

in the range of 2800-3700 cm-1. Note that the Raman spectra of solutions with concentrations

of 0.54-2.55 mol kg-1 were supercooled with respect to ice.

The line intensity area of a particular vibration band is proportional to the molecular number

of the species in the solution. Thus, for a quantitative analysis of the concentration of a species

in solution the line intensity areas must be obtained. This is done by simultaneously fitting

Lorentzian functions to the peaks. Figure 4.16 shows such a multiple Lorentzian fit to a Raman

spectrum. It can be seen that the characteristic vibration bands of the corresponding molecules

can be determined easily.The various Raman spectra recorded as a function of temperature and concentration can be used

to derive a relation between the Raman spectra and the corresponding H2SO4 concentrations.

This has been done by defining R, the ratio of the integrated line intensities of the SO|" and

HSO4 vibration bands in the range of 800-1300 cm-1 (with a negligible intensity stemming from


500 1000 1500 2000 2500 3000 3500 4000

500 1000 1500 2000 2500 3000

Raman shift [cm"1]

3500 4000

Figure 4.15: Liquid-phase Raman spectra of H2SO4/H2O droplets 0.5 ßl in volume and varying concen¬

trations given in molality at 250 K. The spectrum of the solution with a concentration of 0.54 m°l kg-1is recorded at 260 K. Individual spectra are shifted vertically for better visibility. The Raman spectra are

normalized to the î>i(S04~) vibration band at 980 cmT1.


1

-i(S042-) , -

Bc3

-

co

-1—»

JO

-

(0c

.",(HS041

-

1a ^(S048) .

/ VH ^(hso;>V4(HS04-) / / \

/: •. .• \ *s(HsO J .

700 800 900 1000 1100 1200 1300 1400

Raman shift [cm1]

Figure 4.16: Raman spectrum of a H2SO4/H2O droplet 0.5 ßl in volume and a concentration of 6.79

mol kg"1 at 230.5 K. The dotted lines show the Lorentzian functions, which are used to fit the single

vibration bands of the spectrum.

the i*2(H30+) vibration band) and the integrated line intensities of the v\(H.20) and 1/3(^0)vibration bands in the range of 2500-4000 cm-1:

R =

1300

£ /"(SOl") + /"(HSOJ) + /"(H30+)^=800

4000

£ ^(H2o)i/=2500

(4.44)

Figure 4.17 shows R as function of temperature and concentration. R is constant for a par¬

ticular solution concentration over the investigated temperature range within the experimental

uncertainty of about 10 %.

Kamenz (1999) performed Raman spectroscopic measurements of aqueous H2SO4 bulk samples.

He derived a relation between the H2SO4 concentration and the Raman spectrum, expressed as

a weighted ratio, Ryj. The ratio Ry, is derived by the integrated line intensities of the SO|_ and

HSOJ vibration bands in the range of 800-1300 cm-1, Is, and the integrated line intensities of

the i/i(H.20) and 1/3(^0) vibration bands in the range of 2500-4000 cm-1, Ih, each multiplied


0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

180 200 220 240 260 280 300

I

320 3400.7

I

niiiiiiiïnïiiHminium

0.6

0.5

0.4

0.3

0.2

0.1

0.0180 200 220 240 260 280 300 320 340

Temperature [K]

Figure 4.17: R is plotted as function of temperature for various H2SO4 concentrations. From bottom

to top: 0.54, 1.13, 2.55, 6.79, 9.84, 15.23 mol kg-1.

with their corresponding molar masses:

'IsulfRw

98 L

98 • Is + 18 • Ih' (4.45)

where Isuif — 98 • Is and Is = 98/s + 18//,. Kamenz (1999) studied Rw as a function of

concentration for a temperature of 285 K. The R-values of this study have been converted to

iî^-values in order to compare the data of Kamenz (1999) with those of this study. Figure

4.18 shows Rw as function of molal concentration. The i^-values derived by Kamenz (1999)and the i^-values obtained in this study agree within the experimental uncertainty3 Since the

data of Kamenz (1999) were obtained only at 285 K the i^-values derived in this study in

the temperature range of 180-324 K provide a significant improvement. Therefore, the analysis

of the relation between Raman spectrum and H2SO4 concentration has been expanded to this

temperature range by fitting the experimental data to Eq. 4.45.

The ratio Ru, for a given solution concentration can be obtained from the following function:

Rvim) = 0.17478(±0.00988) • mO-53359(±o.028i4)j (4.46)

3This and the fact that R is independent of temperature for each concentration (see Pig. 4.17) indicates that

no concentration changes have occurred in the investigated droplets during the cooling experiments.

4.10. Analysis of (WH4J2SO4/H2O Raman spectra 75

Concentration [mol kg ]

Figure 4.18: Rw, the weighted ratio of SO\~ containing molecules to the sum of SO\~ containing

molecules and water molecules, is plotted as function of concentration. The squares with corresponding

error bars are R^,-values derived in this study obtained in a temperature range of 180-324 K. The triangles

represent data of Kamenz (1999) valid for a temperature of 285 K. The solid line represents a fit of the

Rw-values derived in this study.

where m is the H2SO4 concentration in mol kg-1. The derivation of the H2SO4 concentration

from a Raman spectrum of a solution of unknown concentration can be obtained using the

following function, which is the inverse function of Eq. 4.46:

miRu,) = 27.05586(±1.2436) • ^93228(^.09104) > (4.47)

The error in concentration associated with Eq. 4.47 is about 7.5 %. This value was determined

by analyzing the fitting procedure with a Gauss error propagation law.

4.10 Analysis of (NH4)2S04/H20 Raman spectra

Figure 4.19 shows Raman spectra of an aqueous (NH4)2SÜ4 droplet with a concentration of

5.35 mol kg-1 for varying temperatures. The measurements reach well into the temperature

regime which is supercooled with respect to solid (NH4)2S04 and ice (see Fig. 2.2). Below

253 K the droplet is slightly higher supersaturated with respect to solid (NHi)2S04 than with

respect to ice. The Raman spectrum at a temperature of 226 K is still a spectrum of liquid


500 1000 1500 2000 2500 3000 3500 4000

Raman shift [cm"1]

Figure 4.19: Raman spectra of a fiVHt^504/02 0 droplet 1.0 ßl in volume and a concentration of 5.35

mol kg-1. Spectra are shown from 296 K in 10 K steps until freezing occurs (216 K). Individual spectra

are shifted vertically for better visibility. The Raman spectra are normalized to the ^(SO^-) vibration

band.

(NH4)2S04/H20. At a temperature of 216 K the strong signal of ice can be observed in the

spectrum. In addition, the shift of the ^(SO^-) normal vibration to lower wavenumbers, the

splitting up of the ^(SO^-) normal vibration, and the decrease in band width of the ^(SOf-)normal vibration indicates the possible formation of solid (NH4)2S04. This indication will be

discussed in further detail in the next section. From the presented Raman spectra it cannot be

concluded which solid phase, ice or (NH4)2S04, nucleated first.

The variation of the integrated fine intensities corresponding to the SO4- ion with temperature

is not as pronounced as in the case for aqueous H2SO4 solutions. The reason for this is the

complete dissolution of (NH4)2S04 into NH^ and SO|" by the reaction (NH4)2S04 <=* 2 NHj+ SO4-. This is corroborated by the Raman spectra which show no signal of HSOJ.Figure 4.20 shows liquid-phase Raman spectra of (NH4)2S04/H20 droplets at 250 K for varying

concentrations. The change in concentration due to water uptake can only be seen in an increase

of the normal vibration of water {y\(H.20) and uz{ß.iO)).

4.11. The ferroelectric phase transition of CJVH4J2SO4 77

500 1000 1500 2000 2500 3000 3500 4000

'E

CO

^—»

!o>_

COc

4-»

c

5.35_-—-\

3.88 /-^"^X

,

3.17 ^--*\

.

1.95 / \

0.99 / \

. n r

500 1000 1500 2000 2500 3000 3500 4000

Raman shift [cm"1]

Figure 4.20: Liquid-phase Raman spectra of (NH4)2S04/H20 droplets 0.5-1 ßl in volume and varying

concentrations given in molality at 250 K. Individual spectra are shifted vertically for better visibility.

The Raman spectra are normalized to the ^(SO^-) vibration band at 980 cm"1.

4.11 The ferroelectric phase transition of (NH^SC^

Sofid (NH4)2S04 belongs to the group of ferroelectric substances. The characteristic property

of these substances is the distribution of the electric dipole moments in at least two sublattices


(I, II). Below a critical temperature, the Curie temperature, Tc, the structural symmetry in a

ferroelectrical crystal is lowered leading to an appearance of a spontaneous electrical polariza¬

tion of the crystal. These polar properties axe lost above Tc in the so-called paraelectric phase.

Since the electrical polarization changes during the phase transition, the dielectric constant also

alters significantly at Tc.

(NH4)2S04 undergoes a structural phase transition at 223 K associated with a change in space

group from D^/Pnam in the paraelectric phase to C\vIPna2\ in the ferroelectric phase. Sev¬

eral models have been proposed to describe the microscopic mechanism of the transition in the

crystal. Up to now there is a discussion in the literature about the microphysical mechanism

of the phase transition and, also, wether it is a first or second order phase transition. Below,

three commonly discussed models will be presented and their strengths and weaknesses will be

indicated.

O'Reilly and Tsang (1967a) suggested that the ferroelectricity of (NHi)2S04 is due to a dis¬

tortion of NH4 ions and that the transition results from an ordering of the distorted ions with

respect to the mirror plane of the crystal. But such order could not be confirmed by nuclear

magnetic resonance experiments (Miller et al., 1962) and neutron diffraction measurements

(Schlemper and Hamilton, 1966). Furthermore, this order-disorder type mechanism is not able

to explain other features of the phase transition.

An alternative model is that of Sawada and Takagi (1975) who proposed a phase transition of

displacive type. This model attributes the net spontaneous polarization to the shifts of the two

NH4 ions and the SO4- ion along the c-axis from the equilibrium positions in the paraelectric

phase. The basic idea of this model is that a mixed mode of translational and rotational vibra¬

tions of the ions is responsible for the displacement of the NH4 ions. However, an experimental

verification of these vibrations has not been observed in any kind of vibrational spectra (Jainet al., 1973; Iqbal and Christoe, 1976b; Petzelt et al., 1974) and the validity of the basic idea

was also criticized (Jain and Bist, 1974).The third approach was proposed by Jain et al. (1986) and Bajpai and Jain (1987) who de¬

scribe the phase transition as one of a molecular distortion type. This mechanism can take

place only in crystals that have at least one molecular unit and it occurs mainly as a result of

the change in the structure and symmetry of molecular unit(s) rather than in their positions or

orientation. Jain et al. (1986) showed that the distortion in the SO4- ion triggers the transition

and, therefore, can serve as an order parameter for the transition. The external vibration modes

(lattice vibrations) of SO4- and the translational and vibrational modes of NH4" can be found at

frequencies lower than 450 cm-1. This frequency range was investigated by Iqbal and Christoe

(1976a), Iqbal and Christoe (1976b), and Unruh et al. (1978) who corroborate the important

role of the SO|" ions for this phase transition. This model accounts for many properties of the

crystal, including the dielectric anomaly and the heat of the transition which is in agreement

with measured values of Shomate (1945), Hoshino et al. (1958), and Higashigaki and Chihara

(1981). At Tc the SO|" ion undergoes a sudden change in its internal structure, whereas the

NH4 ions do not change significantly at Tc, but undergo a continuous change in a region ± 10

K around Tc. The specific isobaric heat capacity of (NH4)2S04 is shown as line A in Fig. 4.21

(Shomate, 1945). The heat capacity shows the characteristics of a lambda phase transition. This

kind of transition is often assigned to a second order phase transition in ferroelectric substances

due to an order-disorder mechanism. But in the case of (NH4)2S04 it is believed that the fer-

4.11. The ferroelectric phase transition of (NH4)2SÖ4 79

roelectric phase transition is of first order type (Hoshino et al., 1958; Jain et al., 1973; O'Reilly

and Tsang, 1967b). The increase of the specific heat capacity with temperature approaching Tc

(see Fig. 4.21) is due to the slight reorientation of the NHj ions. At Tc the sudden distortion

of the S04_ ions leads to an infinite value of the specific heat capacity which corresponds to a

first order phase transition. Since a deuteration of the NHj-group does not change the Curie

temperature of the phase transition, this further supports that the ferroelectric phase transition

is of first order type (Hoshino et al., 1958; Jain et al., 1973; O'Reilly and Tsang, 1967b).

160

ia>

8 80

40

0

100 200 300

Temperature [KJ

Figure 4.21: The specific isobaric heat capacity is plotted as a function of temperature (Shomate, 1945).

A: (NH4)2S04; B: NH4Al(S04)2; C: NHiAl(S04)2 H20.

Torrie et al. (1972) derived the Raman-active and infrared-active vibration modes for the param¬

agnetic and ferroelectric phase of solid (NH4)2S04 from Raman spectroscopic and infrared spec¬

troscopic measurements. Here it will be focused on the Raman spectroscopic measurements.

Figure 4.22 and 4.23 show the investigated Raman vibration bands of the SO4- molecule in

(NH4)2S04 obtained in the current work. These bands reveal significant changes when going

from the paraelectric to the ferroelectric phase: The ^(SO^-) vibration band shifts to lower

wave numbers at the transition temperature. The ^(SO^-) vibration band is fourfold degen¬

erated in the liquid phase (see appendix B.l). In the solid paraelectric phase the ^(SO^-)vibration band is twofold degenerated but within the ferroelectric phase the degeneration is

completely cancelled (see Fig. 4.23) which is in agreement with the quoted vibration modes of

Torrie et al. (1972). Table 4.5 compares the given positions of the vibration modes of Torrie

et al. (1972) with the positions measured in this study. Both experimental data sets agree within

the experimental uncertainty. In this work, the reorientation of the NH|(I) and NH^(II) ions

could not be investigated since the low frequency range was not experimentally analyzed.

"T~7

'

I

%--

fJL

„ _

T

l J&' y^? i


<

'

*N

«T \ \.

*-*

'c : 1 \

3

^ / / - I(01-*~»

2 i&_

Ä

£-(0c<D I4-»

_C

940 950 960 970 980 990

Raman shift [cm"1]

1000

Figure 4.22: The shift in the line intensity of v\ (SO\~) during the ferroelectric transition is shown.

The solid lines correspond to the vi(SO\~) normal vibration in the paraelectric phase (T > 223 K) and

the dotted lines represent the vi(SO\~) normal vibration in the ferroelectric phase (T < 223 K).

Conclusion

The Raman spectra obtained in this study confirm the abrupt molecular distortion of the SO4-ions at Tc. These observations support the model by Jain et al. (1973, 1986), who also sug¬

gested that the phase transition is triggered by the SO4- ions. Therefore, it can be concluded

that the phase transition is of the molecular distortion type (Jain et al., 1986). Due to the

pronounced role of the SO4- ions at Tc and the infinite value of the isobaric heat capacity at

Tc it can also be assumed that the ferroelectric phase transition is a first order transition. In

this study the ferroelectric phase transition was observed to occur at 223.1±0.1 K. Furthermore,

the temperature hysteresis of the phase transition was found to be smaller than 0.3 K which is

in agreement with studies of Hoshino et al. (1958) and Iqbal and Christoe (1976b). Thus, the

ferroelectric phase transition is not kinetically inhibited. This makes the transition an ideal "in

situ" temperature calibration point for spectroscopic aerosol experiments.

4.11. The ferroelectric phase transition of (IVH4J2SO4 81

«

.

<n

c'

3

Î» m

re

«-»

/r '^ \re // % / *

A

// v ' * ' \^ -

CO if£- ifCD 1/ ,

Ç\ \

•\>

1 1—

""

1020 1040 1060 1080 1100 1120 1140 1160 1180

Raman shift [cm"1]

Figure 4.23: The splitting of the doublett of the vs(SO\~) vibration band during the ferroelectric tran¬

sition is shown. The solid lines correspond to the 1/3 (SO\~) normal vibrations in the paraelectric phase

(T > 223 K) and the dotted lines represent the vz(SO\~) normal vibrations in the ferroelectric phase (T

< 223 K).

Table 4.5: Raman frequencies of the SO\~ ion in solid fJVÏÏJ)2S04 at 223.1 K (paraelectric phase)

and at 223 K (ferroelectric phase). Vibration, character, maximum position determined by Torrie et al.

(1972) and maximum position derived in this work are presented.

normal vibration character max. position

V [cm-1]Torrie et al. (1972)

max. position

V [cm-1]this work

paraelectric v\ Ai 977 ±2 972 ±4

phase vz F2 1062 ± 10 1061 ± 4

vz F2 1106 ± 10 1090 ± 4

ferroelectric v\ Ai 972 ±2 970 ±4

phase vz F2 1043 ± 10 1053 ± 4

vz F2 1077 ± 10 1083 ± 4

vz F2 1124 ± 10 1115 ±4

vz F2 1147 ± 10 1138 ± 4

Seite Leer /

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Chapter 5

Kinetic processes in UT/LS aerosol

particles

This chapter presents the results of studies on atmospheric kinetic processes: the nucleation

of solid phases in liquid stratospheric aerosol particles and the nucleation of ice in aque¬

ous (NH4)2S04 aerosols. A theoretical and experimental analysis of the derivation of homo¬

geneous nucleation rate coefficients of NAD and NAT from binary HNO3/H2O and ternary

HNO3/H2SO4/H2O solutions is given. Sections 5.1 to 5.6 are identical to the publication "Ho¬

mogeneous nucleation of NAD and NAT in liquid stratospheric aerosols: insufficient to explain

denitrification" published in Atmospheric Chemistry and Physics, 2, 207-214, 2002. Section 5.7

deals with a newly proposed pseudo-heterogeneous nucleation mechanism, i. e. the nucleation is

induced at the surface of the particle (Tabazadeh et al., 2002a,b; Djikaev et al., 2002). There¬

fore, the experimentally derived volume-based nucleation data will be reanalyzed with respect to

surface-induced nucleation. The last section discusses results of homogeneous ice nucleation ex¬

periments on aqueous (NHi)2S04 solutions. The experimental data of this work are comparedto homogeneous ice nucleation rate coefficients obtained by a different experimental method.

The newly proposed pseudo-heterogeneous nucleation mechanism will also be considered in the

analysis of the ice nucleation data.

83

84 CHAPTER 5. KINETIC PROCESSES

Seite Leer /

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85

Homogeneous nucleation of NAD and NAT in liquid stratospheric aerosols:

insufficient to explain denitrification

D. A. Knopf*, T. Koop, B. P. Luo, U. G. Weers, and T. Peter

Institute for Atmospheric and Climate Science, Swiss Federal Institute of Technology,

Honggerberg HPP, 8093 Zurich, Switzerland


Published in Atmospheric Chemistry and Physics, 2, 207-214, 2002.


Seite Leer /

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5.1. Abstract 87

5.1 Abstract

The nucleation of NAD and NAT from HN03/H20 and HNO3/H2SO4/H2O solution droplets

is investigated both theoretically and experimentally with respect to the formation of polar

stratospheric clouds (PSCs). Our analysis shows that homogeneous NAD and NAT nucleation

from liquid aerosols is insufficient to explain the number densities of large nitric acid containing

particles recently observed in the Arctic stratosphere. This conclusion is based on new droplet

freezing experiments employing optical microscopy combined with Raman spectroscopy. The

homogeneous nucleation rate coefficients of NAD and NAT in liquid aerosols under polar strato¬

spheric conditions derived from the experiments axe < 2 x 10-5 cm-3s-1 and < 8 x 10~2

cm-3s-1, respectively. These nucleation rate coefficients are smaller by orders of magnitude

than the value of ~ 103 cm-3 s-1 used in a recent denitrification modelling study that is based

on a linear extrapolation of laboratory nucleation data to stratospheric conditions (Tabazadehet al., Science, 291, 2591-2594, 2001). We show that this hnear extrapolation is in disagree¬

ment with thermodynamics and with experimental data and, therefore, must not be used in

microphysical models of PSCs. Our analysis of the experimental data yields maximum hourly

production rates of nitric acid hydrate particles per cm3 of air of about 3 x 10-10 cm-3(air) h-1

under polar stratospheric conditions. Assuming PSC particle production to proceed at this rate

for two months we arrive at particle number densities of < 5 x 10-7 cm-3, much smaller than

the value of ~ 10-4 cm-3 reported in recent field observations. In addition, the nitric acid

hydrate production rate inferred from our data is much smaller than that required to reproducethe observed denitrification in the modelling study mentioned above. This clearly shows that

homogeneous nucleation of NAD and NAT from liquid supercooled ternary solution aerosols

cannot explain the observed polar denitrification.

5.2 Introduction

Polar stratospheric cloud (PSC) particles activate chlorine from reservoir to reactive species

by heterogeneous reactions on their surfaces. Field measurements have shown that PSCs can

be composed of liquid supercooled ternary solutions (STS) and nitric acid trihydrate (NAT)

(Schreiner et al., 1999; Voigt et al., 2000). In addition, nitric acid dihydrate (NAD) has been

suggested to exist in PSCs based on laboratory experiments (Worsnop et al., 1993). Large

HN03-containing PSC particles can lead to significant denitrification of the polar stratosphere

by sedimentation (Fahey et al., 2001). However, the mechanisms of how such large particles

come about have not yet been established (Tolbert and Toon, 2001). It has been suggested that

large nitric acid hydrate particles leading to denitrification could be produced by homogeneous

nucleation of NAD and NAT from liquid STS (Tabazadeh et al., 2001), based on an extrapolation

of laboratory aerosol nucleation data (Salcedo et al., 2001) to stratospheric conditions. However,

the employed extrapolation is in disagreement with bulk nucleation experiments performed at

stratospheric conditions (Koop et al., 1997b). For example, according to the nucleation formula¬

tion an aqueous ternary solution of 41.2 wt% HNO3 and 3.9 wt% H2SO4 and 1 cm3 in volume is

predicted to freeze at 249.0 K. In contrast, in experiments such samples did not freeze down to


temperatures of 190 K (Koop et al., 1995). Also, the formulation is in disagreement with aerosol

experiments of aqueous nitric acid solutions (Bertram and Sloan, 1998b,a; Bertram et al., 2000a;

Salcedo et al., 2001). To resolve these inconsistencies we investigate here the nucleation kinetics

of NAD and NAT in liquid binary HN03/H20 and ternary HNO3/H2SO4/H2O solutions both

theoretically and experimentally. First, we reexamine the physics of the nitric acid hydrate

nucleation formulation used by Tabazadeh et al. (2001). Second, we present new experimentaldata on NAD and NAT nucleation from STS droplets under stratospheric conditions. Third,

we use these data together with previously published data sets to deduce upper limits of ho¬

mogeneous nucleation rate coefficients of NAD and NAT. Finally, from the inferred nucleation

rate coefficients we derive maximum production rates of sofid nitric acid particles under polar

stratospheric conditions.

5.3 Nucleation formulation analysis

Salcedo et al. (2001) and Tabazadeh et al. (2001) have employed classical nucleation theory to

describe the experimentally observed homogeneous nucleation rate coefficients, Jhom-, of nitric

acid hydrates (NAX; X = D or T):

Jhom(T) = n-Hq f — j exp-AGact(T)

RT(5.1)

where nuq is the HNO3 molecular number density in the liquid, R is the universal gas constant,

k is the Boltzmann constant, and h is the Planck constant. AGact is the activation energy

required to form a critical cluster in the solution. According to classical nucleation theory this

activation energy depends on the saturation ratio of the respective nitric acid hydrate («Snax):

AGact(T) = yTra3 (T)Vsoi

[RTln(SNAX)AGdif (T) (5.2)

Here, asi is the interfacial tension between the solid and liquid phase, vsoi is the molar volume

of NAX in the critical cluster, and AGdif is the HNO3 diffusion activation energy across the

boundary between the cluster and the solution. Since measured values for crsi and AGdif are not

available (MacKenzie, 1997), AGact can be determined from experimentally observed nucleation

rate coefficients by solving Eq. 5.1 for AGad,:

AGact(T) = -RT Inh Jhom(T)kT ring

(5.3)

Figure 5.1 shows values of AGact in aqueous nitric acid solutions as plotted by Salcedo et al.

(2001) as function of the NAD and NAT saturation ratio derived from their experimental data

using Eq. (5.3). The laboratory data reveal a hnear relationship between AGact and Snax

(solid lines in Fig. 5.1) in the experimentally observed range of saturation ratios (Snad=11_

30, 5nat=52-107). Since stratospheric saturation ratios (shaded areas in Fig. 5.1) are much

smaller than the experimentally investigated range, Tabazadeh et al. (2001) used a linear ex¬

trapolation (dotted lines in Fig. 5.1) to infer AGact-values for NAD and NAT at stratospheric

5.3. Nucleation formulation analysis 89

200

190

^ 180

170

160

40

T-1 35

o

1 30

D

1 25

J 20

<

15

^f

-

10 20 30 0 30 60 90 120

'NAD 'NAT

Figure 5.1: AGact as function of the NAD and NAT saturation ratios derived from laboratory nucleation

data using Eq. (5.3) (Salcedo et al, 2001). All data points were derived from experiments with droplets

consisting of binary aqueous nitric acid solutions of varying composition, (a): : 57 wt%, 60 wt%, and

64 wt% HNOz Salcedo et al (2001); : 64 wt% HN03 (Bertram and Sloan, 1998b). (b): ; 54 wt%

HNO3 (Salcedo et al., 2001); : 54 wt% HNO3 (Bertram and Sloan, 1998a). The color coding indicates at

which temperature the data were obtained. The shaded regions indicate typical NAD and NAT saturation

ratios at polar stratospheric conditions. The solid lines show the linear relationship between AGact and

Snax observed by Salcedo et al (2001), and the dotted lines are the linear extrapolations to stratospheric

conditions used in Tabazadeh et al (2001).

conditions. However, applying such an extrapolation is physically unreasonable because accord¬

ing to Eq. (5.2), AGact increases towards infinity for -Snax approaching unity. In contrast, the

linear extrapolation leads to a AGoct-value of about 30 kcal mol-1 in each case. Note, that an

underestimation of AGact by 1 kcal mol-1 increases the corresponding homogeneous nucleation

rate coefficient by a factor of 14. Therefore, the Hnear extrapolation underestimates AGact and,

consequently, largely overestimates the homogeneous nucleation rate coefficient at low satura¬

tion ratios. In Fig. 5.2 we elucidate the effects of the hnear extrapolation on the homogeneous

nucleation rate coefficients of NAD and NAT in aqueous nitric acid solutions. The nucleation

formulation produces finite nucleation rate coefficients along the NAD and NAT melting point

curves (where Snax=1) an(l does so even for values of -Snax < 1 (not shown in Fig. 5.2). This is

thermodynamically impossible for any spontaneous process, since the formation of an unstable

crystal (similar to nucleating ice above 273.15 K) would lead to an increase of the total Gibbs

free energy of the system. This nucleation formulation produces unrealistically high nucleation

rate coefficients of about 108 cm-3 s-1 at the top of the NAD and NAT melting curves (dark

yellow region at T — 230 K in Fig. 5.2a and T = 250 K in Fig. 5.2b) in disagreement with

numerous experimental studies (Anthony et al., 1997; Koop et al., 1997b; Bertram and Sloan,

1998b,a; Bertram et al., 2000a; Salcedo et al., 2001). In addition, at stratospheric tempera¬

tures (180-200 K) and saturation ratios (between the solid and dotted lines in Fig. 5.2) the

homogeneous nucleation rate coefficient increases with temperature. This behavior is due to the


OT

10

10

15

11

E 107ifL 3^

10°E° 1

-f 10_1

10-5

260ICE \ »»w~V°)

240 V.

_\NAM

*T 220

/ NAD^tr—

200

'/ i1

180 !/ A

ICE NAT,

0 20 40 60 80 0

HN03 [wt%]

20 40 60 80

HNO3 [wt%]

Figure 5.2: Homogeneous nucleation rate coefficients of NAD (a) and NAT (b) in binary HNO3/H2O

solutions as function of temperature and concentration using the formulation of Tabazadeh et al (2001).

Solid lines show the melting point curves of the different solid phases (S = 1). The regions between dotted

and solid lines indicate typical polar stratospheric temperatures (< 200 K) and saturation ratios (< 4- 7

for NAD and < 23.5 for NAT). Black asterisks correspond to the experimental data shown in Fig. 5.1.

fact that in the formulation AGact depends solely on SnaX) independently of the temperature

(Tabazadeh et al., 2001, note 21). Only in the proximity of the experimental data (black aster¬

isks in Fig. 5.2) a reasonable temperature and concentration dependency of Jhom is observed. We

conclude that the linear relationship between AGact and Snax should not be used outside the

range of available experimental data and, therefore, should not be extrapolated to stratosphericconditions.

5.4 Experimental

Freezing experiments with HNO3/H2O and HNO3/H2SO4/H2O droplets were performed in or¬

der to determine homogeneous nucleation rate coefficients of NAD and NAT at stratospheric

saturation ratios. We chose to investigate large droplets (0.12-0.27 cm in diameter) because

smaller droplets (2 x 10-5-8.5 x 10-3 cm in diameter) do not freeze at stratospheric tempera¬

tures and saturation ratios (Anthony et al., 1997; Bertram and Sloan, 1998b,a; Bertram et al.,

2000a; Salcedo et al., 2001). The droplets were deposited with a micropipette on a hydrophobi-

cally coated quartz plate inside a laminar flow clean bench. Either a Teflon plate or an o-ring,

each covered by a thin layer of high-vacuum-grease, served as a spacer for a second quartz plate

which sealed the droplets against ambient air. The inner diameter of the spacer depended on

the investigated droplet volume and varied between 0.3-0.6 cm and the spacer thickness ranged

between 0.125-0.175 cm. The total volume of the cell was about 8.8 x 10~3-5 x 10-2 cm3. The

volume of the droplets varied between 10-3-10-2 cm3. Therefore, even at room temperature the

5.4. Expérimental 91

number of water and HNO3 molecules in the gas phase of the cell is neghgible when compared

to the number of condensed water and HNO3 molecules in the droplets. Hence, the composition

of the droplets stays constant during a freezing experiment. The preparation of the droplet cell

took about 15 s. The number of molecules which may evaporate during that time is neghgible

to the total number of molecules in the condensed phase. This was confirmed by checking the

melting points of the droplets after freezing which were found to be in agreement with the phase

diagram. After sealing the droplets against ambient air with a second plate, the droplet cell

was placed on a temperature stage attached to a Confocal Raman Microscope (see Fig. 5.3). In

video

analysis

laser

_^

532 nm

microscope

spectrographCCD detector

temperature stage

grating:1800 g/mm

aerosol cell


this setup the droplets' temperature can be varied between 170-295 K. The temperature was

calibrated by measuring the melting points of heptane (182.55 K), octane (216.35 K), decane

(243.45 K), dodecane (263.5 K), and water (273.15 K) in the cell. Phase changes (i.e. freezing or

melting) are observed visually with the microscope part of the setup. In addition, the crystalline

solids formed upon freezing were identified by Raman spectroscopy using a Nd:YAG-laser at a

wavelength of 532 nm for illumination. The backscattered light is reflected onto a grating (1800

mm-1) and focused on the CCD detector of the spectrograph. The resulting spectral resolution

is about 2-4 cm-1 within the observed range of 500-4500 cm-1. Figure 5.4 shows Raman spec¬

tra of droplets (10-2 cm3) with an HNOs:H20 mole ratio of 1:2 and 1:3 corresponding to the

stoichiometry of NAD and NAT, respectively. In each case the spectra were recorded during a

cooling cycle (red spectra) and a warming cycle (blue spectra) at about the same temperature.

To avoid any possible temperature bias the droplets were not illuminated by laser fight duringthe course of the freezing experiments reported below. Spectra were taken only after the droplets

were frozen.

Table 1 shows the composition, volume, total number of different performed experiments, and

total number of individual droplets. The droplets were prepared from stock solutions which


-i 1 r

HN03:H201:2 (a):

yy

hquid/\ 211 K.

JL

500 1000 1500 2000 2500 3000 3500 4000

0.95

co

c3

2

CO

x

0.3

0.25 -

0.2

500

T 1 1 •"

HN03:H201:3

- 1 -

(b>:

jf

liquid » 211 K

frozen

1000 1500 2000 2500 3000 3500 4000

Raman shift [cm"1]

Figure 5.4: Raman spectra of droplets with a volume of 10~2 cm3, (a): Red line: spectrum of a liquid

droplet with a HNO3.H2O mole ratio of 1:2 at 211 K; blue line: spectrum of a frozen droplet at 212

K. (b): Red line: spectrum of a liquid droplet with a HNO3.H2O mole ratio of 1:3 at 211 K; blue line:

spectrum of a frozen droplet at 211 K. The spectra are normalized with respect to the ui(NO^) vibration

band at ~1040 cmT1.

5.4. Experimental 93

Table 5.1: Composition, volume, total number ofperformed experiments, and total number of individual

droplets. The symbols refer to the ones in Fig. 5

Solution HN03 H2SO4 H20 Volume Symbol #Exp. # Drop.

[wt%] [wt%] [wt%] [10-3cm-3]1 63.6 0 36.4 5-10 X 16 16

2 53.8 0 46.2 1-10 + 28 28

3 32.2 13.8 54.0 10 * 22 5

4 38.3 7.6 54.1 10 • 16 4

were titrated against a 1 M NaOH solution. In an experimental run the droplets were cooled

at a rate of dT/dt = —10 Kmin-1 until nucleation occurred. The ternary solution droplets

(solution 3 and 4, Table 5.1) did not freeze above 178 K during such runs. Hence, the tem¬

perature in these experiments was decreased stepwise (by 5-10 K) keeping the temperature

constant for several minutes after each step. All experiments were recorded on tape together

with the experimental time and droplet temperature. The video tapes were analyzed after¬

wards to determine the number of nucleation events, n, as a function of time and temperature.

The upper limit of the homogeneous nucleation rate coefficient J^ can be derived from the

experimental data using the following formula:

n*

«CCO =

£y,.t,(D' (5"4)

i

where tt(T) = fT' [dT"/dt)~ldT' is the time interval that the ith droplet with volume Vt re¬

mained liquid between T and T*. T* is either the nucleation temperature of the droplet or

the lowest investigated temperature, and (dT/dt)t is the cooling rate applied in the particular

experiment, n* is the upper fiducial limit of n determined by Poisson statistics at a confidence

level of 0.999 (Koop et al., 1997b) - i.e., if the experiments were repeated an infinite number of

times the observed number of nucleation events will be smaller than n* in 99.9 % of the cases.

Equation (5.4) yields a conservative (i.e. the highest possible) Jhom-vahie, which is in agreementwith the experimental data.

In detail, Eq. (5.4) is conservative for the following reasons: First, the time interval, U(T), that

a droplet stays liquid below T is always smaller than the time interval it would stay liquid at

T (assuming that Jhom monotonically increases with decreasing temperature in the investigated

temperature range). Second, instead of using the actual number of nucleation events, n, we

employed n*, which represents a conservative value for n because n* > n in all cases. Third,

it cannot be ruled out that heterogeneous nucleation of NAD and NAT occurred in the large

droplets. Even in this case, the observed nucleation rate is always an upper limit for the ho¬

mogeneous nucleation rate, independently of whether heterogeneous nucleation occurred or not.

All experimental data were analyzed using Eq. (5.4). The derived Jj^-values were used to

calculate lower limits of the activation energy, AG^, according to Eq. (5.3).


5.5 Results and discussion

In Fig. 5.5 the resulting AGact-values axe shown as function of temperature and saturation

ratio. The different symbols in Fig. 5.5 correspond to those in Table 5.1. In addition, we have

reanalyzed published bulk experiments (Koop et al., 1995, 1997b) to determine the upper hmit

for Jhom. according to J^îT) = n*/(V t) ,where n* is the same as above, V is the volume

of the solution, and t is the time the solution remained liquid at temperature T (Koop et al.,

1997b). The corresponding AG^-values were obtained using Eq. (5.3) and axe shown as open

symbols in Fig. 5.5. The solid symbols in Fig. 5.5 represent the same data as in Fig. 5.1.

Furthermore, we have added the aerosol nucleation data by Bertram et al. (2000a). We note,

that we have used a nucleation rate coefficient of J — 4.4 x 109 cm-3 s-1 for these data, slightly

lower than the one in the original publication (A.K. Bertram, personal communication). Figure

5.5 clearly reveals that the newly derived AGacrvalues are significantly higher than the hnear

extrapolation formulation at stratospheric conditions. Since our data points axe lower limits of

AGact (thus, upper limits of Jhom) the actual values of AGact are likely to be even higher than

those shown in Fig. 5.5. Clearly, the hnear extrapolation used in Tabazadeh et al. (2001) is not

in agreement with our new droplet data nor with bulk experiments published previously. In the

following, we use the combined experimental data (Koop et al., 1995,1997b; Bertram and Sloan,

1998b,a; Bertram et al., 2000a; Salcedo et al., 2001, and this work) to derive upper homogeneous

nucleation rate coefficients of NAD and NAT at stratospheric conditions. Figure 5.7a shows the

composition and corresponding NAD and NAT saturation ratios of STS droplets at 50 mbar

(approx. 20 km altitude) for mixing ratios of 5 ppmv H2O, 10 ppbv HNO3, and 0.5 ppbv H2SO4

(Carslaw et al., 1994). In Fig. 5.7b, NAD and NAT nucleation rate coefficients axe shown for

the conditions displayed in panel (a). In the region of highest saturation ratios (shaded region

in Fig. 5.7) circles and squares represent maximum nucleation rate coefficients derived from

experimental data as follows: In Fig. 5.5 for one temperature (e.g. 191.5 K) all data points are

selected by color, and then interpolated as function of saturation ratio using 5nax read off Fig.

5.7a. From the AGoct-value obtained in this way we derive J^, using Eq. (5.1). Blue and red

arrows mark the temperature where 5nad—1 and 5nat=1j respectively, i.e. where the nucleation

rate coefficients must decrease to zero. Solid lines in Fig. 5.7b represent homogeneous nucleation

rate coefficients calculated using the formulation of Tabazadeh et al. (2001). Figure 5.7c shows

the corresponding NAD and NAT particle production rates for the conditions displayed in panel

(a) using the nucleation rate coefficients shown in panel (b). Solid lines axe calculated with the

equations given by Tabazadeh et al. (2001) taking into account that the total aerosol volume

increases with decreasing temperature (Carslaw et al., 1994). Stars are values taken directly

from Fig. 1 in Tabazadeh et al. (2001). The circles and squares represent the production rates

calculated using the experimentally derived upper nucleation rate coefficients shown in Fig.

5.7b. Figure 5.7c reveals that the maxima of the resulting production rates of the formulation

by Tabazadeh et al. (2001) (solid lines) are too large by a factor of 108 for NAD and 104 for

NAT when compared to the experimentally derived production rates.

5.5. Results and discussion 95

200

190

^ 180

170

160

oo

o<3

o

E

"5o

0 10 20 30 0 30 60 90 120

'NAD

40

K «

(a')

35

»Y^ê*

-

30

•

-..*

-

25 -... *-

°NAT

(b')

t#A

% ^&A*\x

^fefc:*.* -

**

4 8 12 0 10 20 30 40

SNAD SNAT


data using Eq. 5.3. Large droplet data: x : 63.6 wt% HN03; +: 53.8 wt% HN03; *: 32.2 wt% HNO3 and

13.8 wt% H2SO4; •: 38.3 wt% HNO3 and 7.6 wt% H2S04 (all this work). Bulk solution data: A: binary

HNO3/H2O solutions of varying composition (Koop et al, 1997b). O: ternary HNO3/H2SO4/H2O solu¬

tions of varying composition (Koop et al, 1995, 1997b). Aerosol data: (a): : 57 wt%, 60 wt%, and 64

wt% HNO3 (Salcedo et al, 2001); : 64 wt% HN03 (Bertram and Sloan, 1998b); A: binary HN03/H20

aerosol of varying composition (Bertram et al., 2000a). (b): : 54 wt% HNO3 (Salcedo et al, 2001);

: 54 wt% HNO3 (Bertram and Sloan, 1998a). The color coding indicates at which temperature the

data were obtained. The solid lines indicate the linear relationship between AGact and Snax observed by

Salcedo et al (2001), and the dotted lines are the linear extrapolations to stratospheric conditions used

in Tabazadeh et al (2001). (a') and (b') show an enlarged view of the top left corner of panels (a) and

(b), respectively.


Correction of Fig. 5.5:1

200

190

^ 180

170

160

ou

oo

<l

40

35

l (a)

30:

25""-\kj.

n""^Snê

20 ^V,15

0 10 20 30 0

°NAD

40

(a')

35

a\^

-

30

r- ^\.

-

75 -•-. "V

30 60 90 120

^NAT

II (b1)

;^„"

i i

*.

4 8

°NAD

12 0 10 20 30 40

'NAT


data using Eq. 5.3. Large droplet data: x: 63.6 wt% HN03; +: 53.8 wt% HN03; *: 32.2 wt% HN03 and

13.8 wt% H2SO4; •: 38.3 wt% HN03 and 7.6 wt% H2S04 (all this work). Bulk solution data: A: binary

HNO3/H2O solutions of varying composition (Koop et al, 1997b). O: ternary HNO3/H2SO4/H2O solu¬

tions of varying composition (Koop et al, 1995, 1997b). Aerosol data: (a): : 57 wt%, 60 wt%, and 64

wt% HNO3 (Salcedo et al, 2001); : 64 wt% HNO3 (Bertram and Sloan, 1998b); A: binary HN03/H20

aerosol of varying composition (Bertram et al, 2000a). (b): : 54 wt% HNO3 (Salcedo et al, 2001);

: 54 wt% HNO3 (Bertram and Sloan, 1998a). The color coding indicates at which temperature the

data were obtained. The solid lines indicate the linear relationship between AGact o,nd Snax observed by

Salcedo et al (2001), and the dotted lines are the linear extrapolations to stratospheric conditions used

in Tabazadeh et al. (2001). (a') and (b') show an enlarged view of the top left corner of panels (a) and

(b), respectively.

1In the original figure 5.5a the nucleation data of the aqueous 63.6wt% HNO3 droplets are missing.

5.5. Results and discussion 97

S -1

5 10°

to

o3

10s I* *

Ij

103 ; i i i i i i t lui»» i| i i i \ | i

'

'°"U ' " » - i —i L i i—l

186 187 188 189 190 191 192 193 194 195

Temperature [K]

10'

196

Figure 5.7: (a) The composition (green and orange lines) and the saturation ratios (red and blue lines)

of STS aerosols as a function of temperature at 50 mbar with 5 ppmv H2O, 10 ppbv HNO3, and 0.5 ppbv

H2SO4 (Carslaw et al, 1994). The shaded region indicates the temperature range where the S^p^x-values

have their maximum, (b): Upper limits for the nucleation rate coefficients of NAD (squares) and NAT

(circles) in STS droplets, derived from experimental data for the conditions shown in panel (a). For

comparison, solid lines indicate the homogeneous nucleation rate coefficient in STS droplets for the same

conditions calculated using the formulation of Tabazadeh et al (2001). (c): Hourly production rates of

NAD and NATparticles (squares and circles, respectively) per cm3 of air derivedfrom the nucleation rate

coefficients shown in panel (b). The increase of the total aerosol volume with decreasing temperature was

taken into account (Carslaw et al, 1994). Also shown as solid lines are the NAD and NAT production

rates for the same conditions calculated using the formulation of Tabazadeh et al (2001). Stars show

values for similar conditions taken directly from Fig. 1 of Tabazadeh et al. (2001). (We note that we can

reproduce the stars by assuming a constant total aerosol volume of 5.9 x 10~12 cm3.) Arrows in (b) and

(c) mark the temperature where the saturation ratio of NAD (blue) and NAT (red) equals one.


5.6 Conclusions

Salcedo et al. (2001) have investigated the nucleation of NAD and NAT from binary aqueous

nitric acid droplets. We consider their experimental data to be sound and the observed linear

relationship between the activation energy, AGaCi, and the respective nitric acid hydrate

saturation ratio, £nax> to be valid in the experimentally observed range of saturation ratios

(5nad=H-30, S'nat=:52-107). However, the theoretical arguments and experimental data

presented above show that the linear relationship between AGact and -Snax is not valid

at stratospheric saturation ratios. Therefore, the linear relationship must not be used in

microphysical models of PSCs.

The analysis of experimental data presented above shows homogeneous NAD and NAT nucle¬

ation rate coefficients to be exceedingly low (< 2 x 10-5 cm-3 s-1 and < 8 x 10-2 cm-3 s-1, re¬

spectively) in STS aerosols under polar stratospheric conditions, in agreement with earlier studies

(Koop et al., 1995, 1997b). These nucleation rate coefficients are smaller by orders of magnitudethan those used in a recent modelling study of stratospheric denitrification (Tabazadeh et al.,

2001). In that study, it was asserted that homogeneous NAD and NAT nucleation from STS

aerosols is sufficient to explain the denitrification observed in the Arctic and Antarctic strato¬

sphere. NAT particle number densities that are in agreement with recent field observations (~10~4 cm-3, (Fahey et al., 2001)) were obtained by converting all NAD particles into NAT parti¬

cles in the simulation. This was achieved by adding the NAD and NAT homogeneous nucleation

rate coefficients. The corresponding particle production rates were about ~ 10-5 cm-3 (air) h-1.

In contrast, using the upper limits for the particle production rates (Fig. 5.7c) derived in this

study and assuming the maximum saturation ratios to persist for two months, we arrive at par¬

ticle number densities of ~ 5 x 10-7 cm-3, much smaller than reported by Fahey et al. (2001).

Furthermore, Tabazadeh et al. (2001) state that NAT particle production rates smaller than ~

10-5 cm-3(air) h-1 are unimportant to denitrification. Even if we combine the NAD and NAT

production rates of Fig. 5.7c the maximum possible value in agreement with the laboratory data

is only ~ 3xl0-10 cm-3(air)h-1. This clearly shows that homogeneous nucleation of NAD

and NAT from liquid supercooled ternary solution aerosols cannot explain the observed polar

denitrification. Therefore, other NAD/NAT formation mechanisms such as heterogeneous NAT

nucleation on ice particles are required to explain polar denitrification (Waibel et al., 1999).

5.6. Conclusions 99

Here ends the publication:

Homogeneous nucleation of NAD and NAT in liquid stratospheric aerosols:

insufficient to explain denitrification

D. A. Knopf*, T. Koop, B. P. Luo, U. G. Weers, and T. Peter

Institute for Atmospheric and Climate Science, Swiss Federal Institute of Technology,

Honggerberg HPP, 8093 Zurich, Switzerland


Published in Atmospheric Chemistry and Physics, 2, 207-214, 2002.


Seite Leer /

Blank leaf

5.7. Pseudo-heterogeneous nucleation of PSCs 101

5.7 Pseudo-heterogeneous nucleation of PSCs

Tabazadeh et al. (2002a) claim to have found evidence that pseudo-heterogeneous nucleation

occurs in laboratory nucleation experiments. Therefore, the experimental data shown in section

5.5 are reanalyzed with respect to a potential surface-induced nucleation pathway. In section

2.2.2 the derivation of the surface-based homogeneous nucleation rate coefficient, J/fom, and

the conversion of the volume-based homogeneous nucleation rate coefficient, J)^, into Jhsom is

given. Before reanalyzing the experimentally obtained nucleation data shown in the previous

1015

10" Iw

CM

I

o

10-3

10

10*

-15

260

240

220

200

180

0 20 40 60 80 0 20 40 60 80

HN03 [wt%] HN03 [wt%]

Figure 5.8: The surface-based homogeneous nucleation rate coefficients of NAD (a) and NAT (b) in

binary HNO3/H2 O solutions as a function of temperature and concentration using the formulation of

Tabazadeh et al. (2002a) taken from Knopf et al (2003) The solid lines indicate the melting point

curves of the different solid phases (S = 1). The regions between dotted and solid lines represent typical

polar stratospheric temperatures (< 200 K) and saturation ratios (< 4-7 for NAD and < 23.5 for NAT).

sections (see Fig. 5.7), the parameterization of the pseudo-heterogeneous nucleation of NAD

and NAT given by Tabazadeh et al. (2002a) will be discussed.

Tabazadeh et al. (2002a) give AGÂD and AGf£AT as a function of temperature and HNO3

mole fraction inside the droplets (see appendix E.2). The surface-based homogeneous nucleation

rate coefficient can be derived from Eq. 2.32 using AGÂD and AGfÂT . Figure 5.8 shows

surface-based homogeneous nucleation rate coefficients of NAD (panel a) and NAT (panel b) in

binary HNO3/H2O solutions as a function of temperature and concentration (Knöpfet al., 2003)based on the formulations of Tabazadeh et al. (2002a). The derived JÂD and JÂT-valuesshow a physically unreasonable behavior: As S approaches unity, i. e. the melting curve (solidlines in Fig. 5.8), the surface-based nucleation formulation of Tabazadeh et al. (2002a) predicts

high jfÂD and JÂT-values. This is at odds with CNT, since for S approaching unity AG*d

increases towards infinity (see Eq. 2.26). Hence, Jhgm and Jh'om -values must vanish when

the concentration approaches the melting curves in Fig. 5.8. Furthermore, the temperature

dependence of Jhom at about 60 wt% HNO3 is unusually small, indicating that J^^changes only by three orders of magnitude over a temperature range of 65 K, which seems


unlikely. More importantly, the increase in the surface-based nucleation rate coefficient with

increasing HNO3 concentration contradicts nucleation experiments showing that no freezing

occurs between 72 and 75 wt% (Bertram et al., 2000a). Hence, it must be concluded that

the current parameterization for pseudo-heterogeneous nucleation of NAD and NAT given by

Tabazadeh et al. (2002a) has severe deficiencies.

In the following a reanalysis of the experimentally obtained nucleation data of this work with

respect to a pseudo-heterogeneous nucleation mechanism is presented. The surface-based

homogeneous nucleation rate coefficients derived from these data will be compared to the

nucleation rate coefficients given by Tabazadeh et al. (2002a).If nucleation starts at the surface of a particle it must be assured that the molecular surface

layer is not contaminated by foreign (e. g. organic) molecules (Tabazadeh, 2003). The present

analysis is performed under the assumption that the droplet surface, i. e. the vapor-liquid

interface, is not contaminated by external species. This assumption is based on the following

arguments. A droplet of 10 ul in volume contains about 2-1014 molecular surface sites and

about 3-1021 molecules in the volume. Therefore, about 1014 molecules are needed to occupy

the surface layer. Even surface active species dissolve into the aqueous phase (Jungwirth, 2003).

Using mass spectroscopy Middlebrook et al. (1997) detect 0.02 wt% of organic contaminants

in 0.2 /mi particles in a laboratory environment. These impurities were assigned to organic

substances such as formaldehyde, ethylene, acetylene and butane, which have solubilities in

water of about 0.001-0.01 % (Howard and Meylan, 1997). Formaldehyde is very soluble in

water (Saxena and Hildemann, 1996) and, therefore, will be distributed in the volume of

the droplets rather than at their surface. From the solubilities and the molecule number

in a droplet of 10 ul in volume it can be concluded that at least 3-1017 organic molecules

can be dissolved in the volume. In equilibrium, the organic molecules will be distributed

equally throughout the droplet, hence, only a fraction of the organic molecules will be sitting

on the droplet surface. Assuming 0.1 ppbv of organics in the gas phase and a 7 of 0.1

(Middlebrook et al., 1997), the flux of organics impinging on the droplet (r = 0.13 cm)with subsequent dissolution within the liquid is about 1011 s-1. Therefore, it would take

more than 106 s to dissolve the 3-1017 organic molecules. Based on the above arguments, it

is assumed in the following section that the droplet surfaces of this study can be treated as clean.

The solid line in Fig. 5.9 represents Jhom in a solution with a HNO3 mole fraction of 0.333

(Tabazadeh et al., 2002a). The surface-based homogeneous nucleation rate coefficients derived

from experiments presented above (dotted lines) are upper limits (see appendix D.l), i. e.

the surface-based homogeneous nucleation rate coefficient is expected to be even lower. The

filled circles represent reanalyzed bulk sample experiments of Koop et al. (1997b), where the

vapor-liquid interface was taken as the surface area. In the investigated temperature range the

difference between the surface-based homogeneous nucleation rate coefficients derived from the

experiments of this work and the surface-based homogeneous nucleation rate coefficients derived

from the formulation of Tabazadeh et al. (2002a) is at least four orders of magnitude. There¬

fore, jfÂD obtained by using AGf;fAD of Tabazadeh et al. (2002a) strongly overestimates


(0

CM

"E£

3=0)O

O

to

rr

c

g's©

o3

170 180 190 200 210 220 230

Temperature [K]

Figure 5.9: The solid line shows the surface-based homogeneous nucleation rate coefficients of NAD in a

solution with a HNO3 mole fraction of 0.333 derived using the formulations of Tabazadeh et al. (2002a).

The vertical bars encompass the temperature range of the experimental data used by Tabazadeh et al.

(2002a) to derive the parameterization. The dotted line represents NAD nucleation data of large droplets

from a solution with a mole fraction of 0.333. The filled circles represent binary HNO3/H2O solutions

with a mole fraction of 0.333 taken from Koop et al. (1997b)

the surface-based homogeneous nucleation rate coefficient with respect to the surface-based

homogeneous nucleation rate coefficients derived from the experiments of this work.

The solid and dotted lines in Fig. 5.10 represent the surface-based homogeneous nucleation rate

coefficients of NAD in a solution with a HNO3 mole fraction of 0.246 (Tabazadeh et al., 2002a)and the upper limits of the surface-based homogeneous nucleation rate coefficients derived from

experiments of this study. Reanalyzed bulk experiments are also shown (Koop et al., 1997b),which are in agreement with the nucleation rate coefficients derived in this work. Above a

temperature of 195 K the modelled nucleation rates overestimate the experimentally obtained

nucleation rate coefficients by up to four orders of magnitude. In this temperature range the

nucleation formulation of Tabazadeh et al. (2002a) is not able to simulate the Jhom -values

derived from experiments of this work. Below 190 K the experimentally obtained nucleation

rate coefficients increase strongly with temperature and approaches the Jham -values derived

by using the formulations of Tabazadeh et al. (2002a). Since the data derived in experiments

are only upper limits of the homogeneous nucleation rate coefficient, the difference between

both data sets could be even larger.The solid and dotted line in Fig. 5.11 represent the surface-based homogeneous nucleation rate

coefficients for NAT in a solution with a HNO3 mole fraction of 0.246 given by Tabazadeh

et al. (2002a) and the Jhom -values obtained in experiments. The reanalyzed bulk experiments


105

104

103

102

10

1

lO"1

lO"2

'U160 170 180 190200 210 220 230 24^°

Temperature [K]

Figure 5.10: The solid line shows surface-based homogeneous nucleation rate coefficients of NAD m a


The vertical bars envelop the temperature range of the experimental data used by Tabazadeh et al (2002a)

to derive the parameterization. The dotted line represents NAD nucleation data of large droplets from a

solution with a mole fraction of 0.246. The filled circles represent binary HNO3/H2O solutions with a

mole fraction of 0.246 taken from Koop et al. (1997b)

ci -\j Ann

(Koop et al., 1997b) are in agreement with the Jhom -values obtained in this work. Since the

9 NAT 9 NATdotted line represents upper limits of Jhom there is no contradiction between Jf^,m -values

C MAT

derived by using the formulations of Tabazadeh et al. (2002a) and Jhom -values derived from

the experiments of this study. However, as shown in Fig. 5.8 the surface-based nucleation model

suffers from an erroneous temperature and concentration dependence. Hence, the coincidence*7 NAT

of the Jfrem -values obtained by the parameterization of Tabazadeh et al. (2002a) and the

ç MAT1

^hom ~values derived from the experiments of this study at ~185 K is only by chance.

Figure 5.12a shows the composition and corresponding NAD and NAT saturation ratios of

STS droplets at 50 mbar (approx. 20 km altitude) for mixing ratios of 5 ppmv H2O, 10

ppbv HNO3, and 0.5 ppbv H2S04 (Carslaw et al., 1994). In Fig. 5.12b, NAD and NAT

surface-based nucleation rate coefficients axe shown for the conditions displayed in panel (a).These surface-based homogeneous nucleation rate coefficients are analyzed as explained in

section 5.4, but the volume of the zth droplet, K, in Eq. 5.4 was substituted by the surface

of the ith droplet, St. In the region of highest saturation ratios (shaded region in Fig. 5.12)arrows represent the range of the upper limits of surface-based nucleation rate coefficients

derived from volume-based nucleation rate coefficients of Fig. 5.7 using Eq. 2.34. The radii

of the investigated aqueous HNO3 droplets vary between ~3-10~5-0.248 cm. Hence, for

each upper limit of the volume-based homogeneous nucleation rate coefficient two values for


160 170 180 190 200 210 220 230

Temperature [K]

240

Figure 5.11: The solid line shows surface-based homogeneous nucleation rate coefficients of NAT in a


The horizontal bars encompass the temperature range of the experimental data used by Tabazadeh et al.

(2002a) to derive the parameterization. The dotted line represents NAT nucleation data of large droplets

from a solution with a mole fraction of 0.246. The filled circles represent binary HNO3/H2O solutions

with a mole fraction of 0.246 taken from Koop et al. (1997b)

the surface-based nucleation rate coefficient are derived corresponding to the minimum and

maximum radius (upper and lower end of the arrows in Fig. 5.12). Figure 5.12c shows the

production rates per cm3 air and hour derived from the surface-based nucleation rate coefficients

given in panel (b). The particle volume per cm3 air was taken from Carslaw et al. (1994). An

average aerosol number density of about 10 cm-1 was taken and the corresponding total surface

was calculated assuming monodisperse aerosol droplets.The maximum surface-based nucleation rate coefficients and production rates of NAD given

by Tabazadeh et al. (2002a) (blue solid lines in Fig. 5.12) are about 7 orders of magnitude

larger than the corresponding data derived from experiments of this work (highest values of

blue arrows in Fig. 5.12). This could be expected due to the large differences in the nucleation

rate coefficients shown in Fig. 5.9 and 5.10. The production rate of NAD derived in this

study is about 10~9 cm-3 h-1 and, therefore, too low to account for the observed particlenumber densities of 10~4 cm-3 of large nitric acid containing particles (Fahey et al., 2001).The maximum surface-based nucleation rate coefficients and production rates of NAT given

by Tabazadeh et al. (2002a) agree quite well since the modelled surface-based nucleation rate

coefficients and the experimentally derived upper limits of the nucleation rate coefficients do

not contradict each other as shown in Fig. 5.11. However, this agreement is only by accident,

because Fig. 5.8b indicates that the surface-based nucleation rate coefficients derived by the


186 187 188 189 190 191 192 193 194 195 196

25

20

15

10

5

10

10'

103

105

107

102

lO"4

106

186 187 188 189 190 191 192 193 194 195 196

Temperature [K]

Figure 5.12: (a) The composition (green and orange lines) and the saturation ratios (red and blue

lines) of STS aerosols as a function of temperature at 50 mbar with 5 ppmv H2O, 10 ppbv HNO3, and

0.5 ppbv H2SO4 (Carslaw et al., 1994). The shaded region indicates the temperature range where the

SjsiAX-values have their maximum, (b): The both-way ending blue and red arrows represent upper limits

for the surface-based nucleation rate coefficients of NAD and NAT in STS droplets, respectively, derived

from experimental data for the conditions shown w panel (a). The range of the Jôm-values is due to

the different aerosol radii of the various nucleation data sets. For comparison, solid lines indicate the

surface-based homogeneous nucleation rate coefficient in STS droplets for the same conditions calculated

using the formulation of Tabazadeh et al (2002a) (c): Hourly production rates of NAD and NAT

particles (blue arrows and red arrows, respectively) per err? of air derivedfrom the surface-based nucleation

rate coefficients shown in panel (b) The total aerosol surface as a function of temperature was taken

into account (Carslaw et aL, 1994). An average particle number density of 10 cm~3 was assumed. Also

shown as solid lines are the NAD and NAT production rates for the same conditions calculated using the

formulation of Tabazadeh et al. (2002a). Small arrows in (b) and (c) mark the temperature where the

saturation ratio of NAD (blue) and NAT (red) equals one.

t' r^

5.8. Homogeneous ice nucleation in (HH4J2SO4/JT2O droplets 107

formulation of Tabazadeh et al. (2002a) exhibit an unreasonable temperature and concentration

dependency. Here, a maximum NAT production rate of about 2-10-6 cm-3 h_1 is derived.

Microphysical sensitivity studies show that an hourly production rate below 10-5 cm-3 h_1

has no significant influence on the overall stratospheric particle number density of nitric acid

containing particles (Tabazadeh et al., 2001, 2002a; Mann et al., 2002). Hence, also the NAT

production rate is too low to account for the observed particle number density of large nitric

acid containing particles. Furthermore, it must also be considered that the production rates

derived here are only upper limits and, hence, the production rate in the atmosphere could be

much lower.

Conclusion

It has been shown that the new parameterization of surface-based AGa^ and AGn^ given

by Tabazadeh et al. (2002a) does not lead to a physically reasonable behavior of the surface-based

homogeneous nucleation rate coefficients. The paxameterizations also suggest that nucleation

of NAD occurs in highly concentrated HNO3 solutions which, however, is not corroborated by

experiments (Bertram et al., 2000a). Furthermore, the modelled J-values show unreasonable

temperature dependence, e. g. when approaching the melting points of the respective solid. The

parameterization of Tabazadeh et al. (2002a) for a pseudo-heterogeneous nucleation is not capa¬

ble to describe the data set obtained in this work and Bertram et al. (2000a) and the nucleation

data sets of Salcedo et al. (2001), Bertram and Sloan (1998b), and Bertram and Sloan (1998a).The surface-based production rates derived experimentally in this work from droplets under

stratospheric conditions are up to 7 orders of magnitude lower than the predicted ones. These

production rates are too low to explain the observed particle number density of large nitric acid

containing particles of about 10~4 cm-3 (Fahey et al., 2001) and, hence, the subsequent den¬

itrification of the polar vortex. Furthermore, from the experimentally obtained surface-based

homogeneous nucleation rate coefficients it cannot be concluded that a pseudo-heterogeneous

phase transition occurred at all in the present experiments.

Since the volume-based homogeneous nucleation mechanism and the proposed pseudo-

heterogeneous nucleation mechanism are not able to explain the particle number densities of

the observed large nitric acid containing particles, other formation mechanisms must exist, such

as heterogeneous NAT nucleation on ice particles (Waibel et al., 1999).

5.8 Homogeneous ice nucleation in (NH^SC^/tÔ droplets

In this section the results of homogeneous ice nucleation experiments with aqueous (NH4)2S04

droplets are discussed. The experimentally obtained homogeneous ice nucleation rate coeffi¬

cients are compared to experimentally derived homogeneous ice nucleation rate coefficients of

Hung et al. (2002), JHung- Hung et al. (2002) and Hung and Martin (2001) tried to derive

a single formulation for the homogeneous ice nucleation rate coefficient using nucleation data


sets obtained from several different techniques, including optical microscopy (OM) (Bertramet al., 2000b) (similar to the technique presented here), differential scanning calorimetry (DSC)

(Bertram et al., 2000b), continuous flow thermal diffusion chamber (CFD) (Chen et al., 2000),and several aerosol flow tube studies employing infrared spectroscopy for the detection of ice

nucleation (AFT-IR) (Prenni et al., 2001; Czizco and Abbatt, 1999; Chelf and Martin, 2001).After a reexamination of the results of Hung and Martin (2001) by Hung et al. (2002), the

authors conclude that Chelf and Martin (2001) studied an aerosol containing both crystalline

and aqueous particles. The crystalline phase of (NH4)2S04 is detected by a change in the in¬

frared spectrum due to the ferroelectric phase transition (see section 4.11). The existence of

crystalline particles shifts the spectroscopically derived composition of the aerosol to higher con¬

centrations, which has been corrected by Hung et al. (2002). Since the freezing temperatures of

the (NH4)2S04 aerosol derived by Chelf and Martin (2001) are in agreement with the freezing

temperatures measured by Czizco and Abbatt (1999), Hung et al. (2002) suggest that also the

aerosol of Czizco and Abbatt (1999) consists of a mixture of crystalline and aqueous particles

and, thus, must be corrected in composition. In the spectra of Prenni et al. (2001) a signal of

the ferroelectric phase transition is absent, thus, it can be assumed that the particles nucleated

homogeneously. Prenni et al. (2001) set the composition of the aerosol particles by passing

the aerosol through a conditioning flow tube, in which the particles were in equilibrium with

the ice-coated tube walls. The nucleation data of Prenni et al. (2001) corresponds closer to

the J-values obtained by OM, DSC, and CFD experiments. If the temperature of the aerosol

particles of Prenni et al. (2001) is determined using the features of the IR spectrum, similar

to the procedure described by Hung et al. (2002), the freezing temperatures come closer to the

freezing values of Hung et al. (2002). A more difficult task is the reconciliation of AFT-IR, OM,

DSC, and CFD measurements. Hung et al. (2002) are not able to find a common J-function

which describes the J-values obtained by the different experimental methods. Therefore, in this

study further experiments were performed employing the OM-technique to measure additional

J-values. The possibility of a pseudo-heterogeneous nucleation mechanism will be considered

in the analysis. Volume-based Jffun9-values of Hung et al. (2002), J#uns, and J^TO-values of

this study, and the corresponding surface-based JHung-values of Hung et al. (2002), JHung, and

J^^-values of this study will be compared to each other.

Figure 5.13 shows volume-based Jûnp-values of Hung et al. (2002) and upper limits of Jômderived in this study. The experimentally derived freezing points and J^^-values of this work

axe in agreement with the freezing points and Jôm-values presented in Bertram et al. (2000b).The upper limits derived in this work imply that the "true" J^^-values for a defined (NH4)2S04mole fraction are smaller than those of the corresponding dashed line. Figure 5.13 indicates that

an agreement between AFT-IR and OM-technique is obtained only for low (NH4)2S04 mole frac¬

tions (below 0.02). (NH4)2S04 solutions with higher mole fractions (above 0.02) disagree.

Since Hung et al. (2002) cannot explain the discrepancies between the different data sets, pseudo-

heterogeneous nucleation was taken into account in the present analysis as a possible nucleation

pathway (Tabazadeh et al., 2002a,b). In this reanalysis of the ice nucleation data of aqueous

(NH4)2S04 droplets derived from the experiments of this work it was assumed that the droplet

surface is not contaminated by external species (see discussion in section 5.7). The J^m-valuesderived by Hung et al. (2002) and the J^j-values obtained in this study are reanalyzed with

5.8. Homogeneous ice nucleation in (JVH4J2SO4/IÎ2O droplets 109

11

10

<o

E ' 0.070

1

F 8 "

10x:

-3 1

01

\

O 7

6

T I I I

0.11

205 210 215 220 225 230 235 240

Temperature [K]

Figure 5.13: The solid line indicate volume-based homogeneous nucleation rate coefficients by Hung

et al (2002). The (NH4)2SOi mole fractions which correspond to the J-values are plotted besides the

lines. The data for XHNO3 = 0 (1. e. pure water) are taken from the model of Tabazadeh et al. (2000). The

dashed lines represent upper limits of the volume-based homogeneous nucleation rate coefficients obtained

in this study.

respect to surface-induced nucleation using Eq. 2.34. A mean diameter of 300 nm and about

40 /im for the droplet radii of Hung et al. (2002) and of this work, respectively, were chosen.

Figure 5.14 shows surface-based homogeneous nucleation rate coefficients of Hung et al. (2002),

Jfiungi and ^fom"vames derived in this study for different (NH4)2S04 mole fractions. J-¬values obtained in this work again represent upper limits of the nucleation rate coefficient (see

Fig. 5.13). As in the volume-based case there is no contradiction between the values of JHung

and Jhsom-values of this study for low mole fractions (below a mole fraction of 0.02). In the

case of a mole fraction of 0.07 both data sets are in agreement for temperatures higher than

218 K. For lower temperatures there is still a discrepancy between the measured nucleation rate

coefficients.

The difference between the data sets could have their origin in the following possible reasons.

First, it appears that the freezing points of higher concentrated particles of Hung et al. (2002)were obtained at warmer temperatures when compared to the nucleation rate coefficients derived

in the OM experiments (Bertram et al., 2000b), DSC measurements (Bertram et al., 2000b),and the freezing points of this study. As Hung et al. (2002) state that using the spectroscopic

features of the AFT-IR spectra of Prenni et al. (2001) to obtain the freezing temperatures, i.


205 210 215 220 225 230 235 240

Temperature [K]

Figure 5.14: The solid line indicate surface-based homogeneous nucleation rate coefficients by Hung

et al (2002). The (NH4)2SÛ4 mole fractions which correspond to the J-values are plotted besides the

lines. The data for xhno3 = 0 (i. e. pure water) are taken from the model of Tabazadeh et al. (2000). The

dashed lines represent upper limits of the surface-based homogeneous nucleation rate coefficients obtained

m this study.

e. the procedure given by Hung et al. (2002), the freezing temperatures of Prenni et al. (2001)

come closer to the data of Hung et al. (2002). Therefore, the difference in freezing temperatures

could lie in a temperature bias due to the temperature retrieval procedure given by Hung et al.

(2002).Second, an erroneous droplet composition could be the reason for the difference in the data sets.

The deconvolution of the aerosol composition from infrared-spectra is a difficult task. The com¬

position of the particles used in the OM-techniques axe determined by measuring their melting

points. The melting points of the particles can be easily detected visually with the microscope

and, therefore, are measured directly without complicated algorithms.

Third, Hung et al. (2002) have taken into account that the aerosol used in the AFT-IR ex¬

periments consist of solid and aqueous (NH4)2S04 particles. A small fraction of these solid

particles can nucleate ice heterogeneously. These few ice particles can deplete the surrounding

gas phase water partial pressure thereby growing into large particles with significant ice signal

in the infrared spectra. Hence, heterogeneous ice nucleation leads to larger J-values at higher

temperatures.

5.8. Homogeneous ice nucleation in (NHi^SOi/RÔ droplets 111

Conclusion

The volume-based homogeneous ice nucleation rate coefficients derived in this work axe in agree¬

ment with a previous study of Bertram et al. (2000b) which also employed the OM-technique.

The differences between the data sets obtained using the OM-technique (this study, Bertram

et al. (2000b)) and the AFT-IR-technique ((Czizco and Abbatt, 1999; Chen et al., 2000; Prenni

et al., 2001; Chelf and Martin, 2001; Hung and Martin, 2001; Hung et al., 2002) was further

consolidated in the range of higher (NH4)2S04 mole fractions. It has also been shown that

pseudo-heterogeneous nucleation cannot explain the differences between the data sets of both

methods. There is no evidence that surface-induced nucleation has occurred at all in the ex¬

periments. Therefore, the causes for these discrepancies still remain speculative. The reasons

could be a false temperature and composition determination within the AFT-IR experiments.

Also, heterogeneous ice nucleation in the mixed (NH4)2S04 aerosol could have occurred. Further

experiments with the ability to cover a larger range of homogeneous nucleation rate coefficients

axe necessary to answer the remaining ambiguities.

Seite Leer /

Blank leaf

Chapter 6

Final remarks

6.1 Summary and conclusion

During the course of this thesis thermodynamic properties of and kinetic processes in aqueous

solutions were investigated. The main topics included:

• the dissociation of the bisulfate ion in H2SO4/H2O solutions,

• the nucleation of NAD and NAT in HN03/H20 and HNO3/H2SO4/H2O solutions,

• the nucleation of ice in (NH4)2S04/H20 solutions.

The experimental temperatures and concentrations were chosen such that they represent the

conditions experienced by aerosol droplets in the UT/LS. For these purposes an experimental

setup has been built to investigate aerosol properties optically and by Raman spectroscopy. A

temperature stage was constructed and adapted to a Confocal Raman Microscope. The stage

allows an accurate adjustment of the temperature of the investigated aerosol droplets from 180

to 330 K. Furthermore, a sample preparation procedure was developed for the production of

droplets in the 5 /xm-1.5 mm size range. Finally, Raman spectroscopy has been proved to be

a sensitive tool for the quantitative investigation of composition changes in aqueous droplets

with diameters of 50 /xm-1.5 mm.

Thermodynamic properties

The dissociation of the bisulfate ion (HSO4 ^ SO4- + H+) has been studied in aqueous H2SO4

solutions. For this purpose, Raman spectra of aqueous H2SO4 and (NH4)2S04 droplets with

concentration of 0.54-15.23 mol kg-1 and 0.99-5.35 mol kg-1, respectively, were recorded in a

113

114 CHAPTER 6. FINAL REMARKS

temperature range of 180-326 K. The experimentally derived degree of dissociation of HSOJincreases with decreasing temperature for all investigated aqueous H2SO4 solutions. This is in

contrast to the widely used atmospheric thermodynamic model AIM (Clegg et al., 1998), which

underestimates the degree of dissociation by up to a factor of 5. The experimentally obtained

low-temperature data of the dissociation of the bisulfate ion was implemented in a Pitzer ion

interaction model of the H2S04/H20-system. This Pitzer ion interaction model was used to

derive a new formulation of the thermodynamic dissociation constant for the bisulfate ion in

the temperature range of 180-473 K. The thermodynamic dissociation constant derived in this

work is shown to be thermodynamically consistent with the Nernst heat theorem, in contrast

to the dissociation constant used in AIM.

Relevant atmospheric properties of the aerosol particles such as water activity and trace gas

solubility are affected by the newly derived thermodynamic dissociation constant of the HSO4ion. For 1.13-15.23 mol kg-1 H2SO4/H2O solutions the Pitzer model presented in this study

predicts water activities up to 10 % lower than the corresponding values derived with the AIM

model (Clegg et al., 1998). Predicted activity coefficients differ by up to 2 orders of magnitudewhen compared to the ones obtained from the AIM model. Heterogeneous reaction rates in

H2SO4/H2O depend on the solubility of the involved trace gases. Predicted HCl solubilities

axe up to 3 orders of magnitude lower when compared to the solubilities derived with the AIM

model (Carslaw et al., 1995a). Lower HCl solubilities and, hence, decreased heterogeneousreaction rates result in lower chlorine activation.

Kinetic processes

PSC formation mechanisms were studied both theoretically and experimentally by analyzingnucleation parameterizations given in literature and by measuring upper limits of the homo¬

geneous nucleation rate coefficients of NAD and NAT in aqueous HNO3 and HNO3/H2SO4droplets. The main focus of the present study was to investigate possible formation processes

of large nitric acid containing particles observed in particle number densities of 10-4 cm-3 in

the lower stratosphere in the winter 1999/2000 (Fahey et al., 2001). These large particles lead

to a strong denitrification of the polar stratosphere, which inhibits the deactivation of ozone

destroying agents. Tabazadeh et al. (2001) suggested that homogeneous nucleation of NAD

and NAT in STS aerosols is sufficiently fast to obtain large nitric acid containing particles in

number densities of 10-4 cm-3. Knopf et al. (2002) have shown that the parameterization used

in Tabazadeh et al. (2001) yields unreasonable homogeneous nucleation rate coefficients under

stratospheric conditions. Therefore, this parameterization must not be used in microphysicalaerosol models which are applied to stratospheric conditions (Knopf et al., 2002). In contrast

to the parameterization, the experimentally derived homogeneous nucleation rate coefficients of

NAD and NAT are exceedingly low (< 2-10-5 cm_3s_1 and < 8-10-2 cm_3s_1, respectively) in

STS aerosols under polar stratospheric conditions. This is in agreement with earlier nucleation

studies of NAD and NAT in aqueous binary HNO3 and ternary HNO3/H2SO4 bulk solutions

(Koop et al., 1995, 1997b). The experimentally derived upper limits of NAD and NAT

homogeneous nucleation rate coefficients yield maximum hourly particle production rates of

6.1. Summary and conclusion 115

~3-10~10 cm_3(air)h-1 under stratospheric conditions. Thus, the production rates used in

the microphysical modelling study of stratospheric denitrification of Tabazadeh et al. (2001)axe 5 orders of magnitude too high. If maximum saturation ratios axe assumed to persist for

two months, the experimentally derived production rates yield particle number densities of

~5-10-7 cm-3, which are much smaller than the reported values by Fahey et al. (2001). The

experimental nucleation data of this PhD thesis clearly show that homogeneous nucleation

pathway cannot be responsible for the occurrence of large nitric acid containing particles in

particle number densities of 10-4 cm-3.

More recently, Tabazadeh et al. (2002a) and Djikaev et al. (2002) suggested a pseudo-

heterogeneous nucleation mechanism, (i. e. the nucleation is induced at the aerosol surface,)which may lead to the observed particle number densities of large nitric acid containing particlesof 10-4 cm-3. The pseudo-heterogeneous parameterization of Tabazadeh et al. (2002a) yieldsNAD production rates of about ~5-10-2 cm_3(air) h_1 in the polar stratosphere. This NAD

production rate is sufficient to obtain the observed particle number densities of 10~4 cm-3.

However, the present study has shown that the pseudo-heterogeneous parameterization is

at odds with classical nucleation theory and experimentally obtained data. Therefore, the

stratospheric pseudo-heterogeneous nucleation rate coefficients derived from the parameteri¬zation of Tabazadeh et al. (2002a) must not be used in microphysical modelling studies. The

experimentally obtained surface-based nucleation rates of NAD and NAT of this work are up to

7 orders of magnitude lower than the values derived by the parameterization of Tabazadeh et al.

(2002a). The experimentally derived hourly surface-based production rates of NAD and NAT

axe <10-9 cm_3(air) h_1 and <2-10-6 cm_3(air) h-1, respectively. Microphysical sensitivitystudies show that production rates below ~10-5 cm-3 (air) h_1 do not have a significantinfluence on the overall stratospheric particle number densities of nitric acid containing particles

(Tabazadeh et al., 2001, 2002a; Mann et al., 2002). Therefore, the experimentally derived

surface-based production rates exclude the pseudo-heterogeneous nucleation pathway as a

formation mechanism of the large nitric acid containing particles observed in particle number

densities of 10~4 cm-3 (Fahey et al., 2001).The theoretical and experimental analysis of the homogeneous and pseudo-heterogeneousnucleation mechanism indicate that neither nucleation mechanisms can explain the observation

of the particle number densities of the large nitric acid containing particles and the subsequentdenitrification of the polar vortex. Hence, other nucleation mechanisms must be responsible,for example heterogeneous nucleation of NAT on ice particles as suggested by Waibel et al.

(1999). Another recently proposed formation mechanism is the mother cloud/NAT-rockmechanism of Fueglistaler et al. (2002). This mechanism suggests that type la PSCs can serve

as mother clouds for the formation of the large nitric acid containing particles. Individual NAT

particles at the cloud base fall into lower stratospheric layers undepleted in gas phase HNO3

and, thus, rapidly accelerate due to a positive feedback between their growth and sedimentation.

Cirrus ice cloud formation was investigated by measuring upper limits of the homogeneous ice

nucleation rate coefficients in aqueous (NH4)2S04 droplets. At upper tropospheric conditions,for example at 215 K, the experimentally derived upper limits of the homogeneous ice nucleation

rate coefficients of this work are lower than ~106 cm-3 s_1 for an aqueous (NH4)2S04 droplet


with a (NH4)2S04 mole fraction of 0.07. The nucleation data derived in this work are in

agreement with experimentally derived homogeneous ice nucleation rate coefficients of Bertram

et al. (2000b), but disagree with experimentally obtained data of AFT-IR studies (Czizco and

Abbatt, 1999; Chelf and Martin, 2001; Prenni et al., 2001; Hung and Martin, 2001) for higher

(NH4)2S04 mole fractions. At temperatures lower than 225 K and (NEÏ4)2S04 mole fractions

higher than 0.05 the microscope experiments yield significantly lower homogeneous ice nucleation

rate coefficients when compared to those obtained by the AFT-IR studies. The newly derived

upper limits of the homogeneous ice nucleation rate coefficients of this work does not lead to

a reconciliation of the different data sets. The difference must be due to the experimental and

theoretical retrieval procedures. The analysis of ice nucleation in aqueous (NH4)2S04 droplets

with respect to a pseudo-heterogeneous nucleation pathway does not reconcile the nucleation

data of the microscope and AFT-IR experiments either. The discrepancy at temperatures lower

than 225 K and (NH4)2SÛ4 mole fractions larger than 0.05 remains.

6.2 Outlook

The results of the investigations of thermodynamic and kinetic processes performed in this work

raise a number o open questions and topics which should be investigated in the future.

Thermodynamic processes

Pitzer modellingIn the context of thermodynamic processes in aqueous aerosol particles the thermodynamic dis¬

sociation constant derived in this work should be implemented in ternary NH3/H2SO4/H2O and

HNO3/H2SO4/H2O Pitzer ion interaction models. Predictions of the water activity and NH3

solubility in NH3/H2SO4/H2O solutions may experience significant changes due to the newlyderived binary interaction parameters of H2SO4/H2O. The changes in the solution properties

may be important for upper tropospheric aerosols with respect to homogeneous and heteroge¬

neous nucleation as a pathway for cirrus ice cloud formation and heterogeneous reactions. STS

aerosols consist of HNO3/H2SO4/H2O solutions. The influence of the newly derived thermody¬namic dissociation constant on HNO3, H2O, and HCl uptake should be investigated. This may

have further implications on nucleation of NAD and NAT in STS aerosols due to slight changesin the aerosol composition at stratospheric conditions.

It has been recognized that bromine may be responsible for 25 % of the ozone destruction

(WMO, 1998). Therefore, solubilities of HBr in H2S04/H20 and HNO3/H2SO4/H2O dropletsshould be calculated using the modified Pitzer ion interaction model. The predicted solubilities

should be compared with experimental data (Abbatt, 1995; Abbatt and Nowak, 1997; Williams

and Long, 1995; Kleffmann et al., 2000).

6.2. Outlook 117

Kinetic processes

Formation mechanisms of PSCs

The formation mechanism of observed large nitric acid containing particles with number

densities of 10-4 cm-3 is still unresolved. Recently, it was suggested that pseudo-heterogeneousnucleation might be a suitable nucleation pathway for the observed large nitric acid containing

particles. In a recent discussion (Tabazadeh, 2003) it was claimed that pseudo-heterogeneousnucleation cannot be investigated in laboratory environment due to contamination of the

employed aerosol particles. To resolve the influences of surface contamination of the particleson the measured nucleation rate coefficients, nucleation rate coefficients derived from purposelycontaminated particles should be compared to those from clean particles. Furthermore,nucleation rate coefficients of particles varying widely in volume and in surface area should be

measured to determine the dominant nucleation mechanism.

Heterogeneous nucleation mechanisms of NAD and NAT should be investigated experimentally.

Heterogeneous nuclei such as meteoritic material (Murphy et al., 1998) should be introduced

into binary and ternary HNO3/H2O and H2SO4/HNO3/H2O solutions to determine nucleation

rate coefficients (Biermann et al., 1996). Also, the gas-to-solid nucleation of NAD, NAT, and

ice (deposition mode) should be further investigated to derive corresponding heterogeneousnucleation rate coefficients. Raman spectroscopy could be used to identify the solid phasewhich forms on the nuclei. The measured heterogeneous nucleation rate coefficients togetherwith data on the prevalence of the investigated nuclei could be used to derive stratospheric

production rates that can be evaluated with respect to the observed particle number densities

of NAT in the stratosphere.

Pseudo-heterogeneous nucleation

If pseudo-heterogeneous nucleation occurs, the surface enrichment of solution species should be

studied as a function of droplet radius. Stuart and Berne (1999) investigated the propensity of

chlorine molecules as a function of droplet curvature. A similar molecular dynamics study should

be performed for typical particle compositions of UT/LS aerosol such as NH3/H2SO4/H2O and

HNO3/H2SO4/H2O. This could increase our understanding on which molecules may initiate or

inhibit the nucleation on the surface of atmospheric aerosol droplets.

Organics

Murphy et al. (1998) have shown that aerosol particles in the upper troposphere usuallycontain also a fraction of organic compounds. These organics may influence homogeneous and

heterogeneous nucleation mechanisms of solid phases. This should be investigated by nucleation

experiments employing aerosol droplets which are doped with organics.

Heterogeneous nucleation

Because there axe only few studies of heterogeneous ice nucleation in concentrated inorganic


solutions (Zuberi et al., 2002) further systems such as aqueous (NH4)3H(S04)2, NH4HSO4,

and NH4NO3 solutions should be investigated. Since heterogeneous ice nucleation can occur

on solid nuclei immersed in liquid aerosols (immersion mode) or on solid particles from the gas

phase directly (deposition mode) both formation pathways should be studied in the experiments.

Homogeneous ice nucleation

The discrepancies of the homogeneous ice nucleation rate coefficients in (NH4)2S04/H20solutions derived by optical microscopy experiments and AFT-IR experiments shows the

importance to build a technique which is capable of measuring a wide range of homoge¬

neous nucleation rate coefficients. Such a setup would be able to reconcile the different

data sets available in the literature (Bertram et al., 2000b; Chen et al., 2000; Prenni et al.,

2001; Czizco and Abbatt, 1999; Chelf and Martin, 2001; Hung and Martin, 2001, and this work).

Appendix A

Experimental

A.l Electrical circuit for the operation of the inkjet-cartridge

Single droplets are generated by an inkjet-cartridge (Hewlett Packard, Model HP 51604). A

sketch of the structure and functionality is given in Fig. A.l. The functionality of the inkjet-

cartridge is based on a thermo-electrical principle. A resistor wire heats strongly the liquid

for a short moment. A gas bubble forms and pushes a definite amount of liquid through the

nozzle. The inkjet-cartridge is operated by a positive square pulse signal of about 23 V and

A nozzle

F"

j surfaceInk-

" ' '

1channel

u1circuit path

1 silicium-

resistorsubstrafe

Bdroplet

gas bubble H

Figure A.l: Sketch of the working principle of the inkjet-cartridge. Panel A shows the internal structure

of the inkjet-cartridge. Panel B shows the inkjet-cartridge in operation. This figure was adapted from

Düwel (2003).

119

120 APPENDIX A. EXPERIMENTAL

0-30 V

0-3 A

0-10 V

APM

PF

4I Osn.

PF

Figure A.2: Sketch of the electric circuit used for the operation of the inkjet-cartridge. The first part of

the circuit is the source, followed by the amplification and the signal inversion.

6 /xs in duration. Figure A.2 shows the electric circuit needed to drive the inkjet-cartridge. A

pulse generator is used for the production of a square pulse of 10 V height and 6 ßs duration.

This signal has to be amplified to 23 V. Since the load resistor of the inkjet-cartridge is about

65 Cl a power supply with a minimum of 25 V and 0.4 A is necessary. A homemade power

supply yielding up to 30 V and up to 3 A is used. The amplification circuit consist of a n-

channel Power Metal-Oxide-Semiconductor Field-Effect-Transistor(BUZll) and a resistor, R,

of 100 Q. Then follows the inverter, which transforms the incoming negative pulse signal to

a positive pulse signal. The inversion is done using a p-channel (MTP12P10) and a n-channel

(MTP12N10) Power Field-Effect-Transistor. Parallel to the inkjet-cartridge an oscilloscope is

applied to monitor the resulting pulse signal. The pulse generator can be operated in single

pulse mode, hence, generating single droplets. The operation of the inkjet-cartridge with pulse

frequencies of up to 100 Hz is also possible producing higher droplet numbers.

Appendix B

Raman spectroscopy

B.l Assignments of the normal vibrations of the investigatedRaman spectra

The number and the symmetry species (also called irreducible representations) of the normal

vibrations depend on the point group of the molecule or the molecule fragment. A detailed dis¬

cussion about point groups and their significance for the selection rules of the normal vibrations

can be found in Engelke (1985) and Schrader (1995). All assignments in the following tables

are taken from the work of Querry et al. (1974) and Cox et al. (1981). The assignments of the

vibration modes can be derived unambiguously by polarization measurements of IR and Raman

spectra. The following abbreviations for the characterization of the normal vibrations were used:

v. stretching vibration

Ö: bending vibration

Indices:

s: symmetricas: antisymmetricd: degenerate

The SO4- ion and the NH4 ion have a tetrahedral structure and belong to the point group T^

with the symmetry species IA1+IE+2F2. All normal vibrations are Raman-active, whereas

the vibrations of the symmetry species F2 are IR-active.

The HSOJ ion has a pyramidal structure and belongs to the point group C3„. This yields the

symmetry species 3Ai+3E. All normal vibrations are Raman-active and IR-active.

The H2O molecule belongs to the point group C2^. This yields 2A1+B2 symmetry species for

a molecule consisting of three atoms. All normal vibrations are Raman and IR-active. In the

121

S024- ion NHJ ion

v [cm-1] v [cm-1]

Vs 980 3033

Od 451 1685

Vd 1105 3134

Öd 613 1397

122 APPENDIX B. RAMAN SPECTROSCOPY

Vibration, symmetry species, mode, and maximum position of the SO4 ion and NH4 ion.

normal vibration symmetry species vibration mode maximum position maximum position

v\ Ai

V2 E

vz F2

Vj Fj2

Vibration, symmetry species, mode, and maximum position of the HSOJ ion.

normal vibration symmetry species vibration mode maximum position

v [cm-1]

vi Ai vs 1047

v2 E bas 417

1/3 Ai v 1341

Vz E Vas 1230

v4 Ai os 885

v4 E ôs 593

Vibration, symmetry species, mode, and maximum position of the H2O molecule.


v [cm-1]

1/1 Ai us 3219

v2 Ai b~s 1640

vz Bi v_as3445

liquid phase appears an additional intermolecular vibration, vr,, at 590 cm-1 due to hydrogen

bonding (Querry et al., 1974).

The H30+ ion belongs to the point group C3,,. This yields 3Ai+3E symmetry species for a

molecule consisting of four atoms. All normal vibrations are Raman-active and IR-active.

The H2SO4 molecule has a tetrahedral structure and belongs to the point group 02^. This yields

the symmetry species 4Ai-|-A2+2Bi-r-2B2. All normal vibrations are Raman and IR-active.

B.l. Assignments of the normal vibrations of the investigated Raman spectra 123

Vibration, symmetry species, mode, and maximum position of the HsO+ molecule.


V [cm-1]

vi Ai v3 2650-3380

V2 Ai Ss 1134

vz E vd 2650-3380

V4 E Sd 1670

Vibration, symmetry species, and maximum position of the H2SO4 molecule.

normal vibration symmetry species maximum position

v [cm-1]

V! Ai 905

1*2 Ai 381

v2 A2 417

1/3 Ai 1140

v3 Bi 1190

1/3 B2 1370

V4 Ai 741

1/4 Bi 564

v4 B2 965

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Appendix C

Heterogeneous chemistry

The uptake of a gas into a liquid followed by reaction involves a number of physical as well as

chemical processes (Finlayson-Pitts and Pitts, 2000):1. The transport of the gas to the surface, which is determined by the gas-phase diffusion

coefficient, Dg.2. The uptake at the interface, controlled by the mass accommodation coefficient, a.

3. The diffusion into the bulk, which depends on the liquid diffusion coefficient, Di.

4. The chemical reaction in the bulk.

Assuming a fast gas transport, high solubility, and fast reaction, the following diffuso-reactive

uptake coefficient can be obtained (Hanson and Ravishankara, 1993; Finlayson-Pitts and Pitts,

2000):

- = - + ?-—, (CI)7 a 4JRTJJ*v/ÂF

where R is the universal gas constant, T is absolute temperature, v is the mean thermal velocity

of the gas-phase molecules at T, H* is the effective Henry's law constant, and A;1 = /^[X]^ is

the pseudo-first-order loss rate coefficient for the reaction of [Y] with [X] in the liquid. Thus,

for a particular value of a, Eq. C.l indicates that the reaction in the bulk of the aerosol scales

linearly with H*.

125

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Appendix D

Nucleation rate coefficients and

production rates

D.l Derivation of upper nucleation limits

This section is based mainly on the work of Koop et al. (1997b). Since nucleation is a stochas¬

tic process, similar to radioactive decay, one can give an expectation value for the number of

nucleation events which should occur within a given sample number and particular observation

time. Due to the stochastic nature of nucleation the successful formation of a critical nucleus

does not depend on the previous trials. Also, different nucleation processes are independent of

each other. An experiment must be repeated several times, or, alternatively, a large number of

equal samples must be observed simultaneously to obtain statistical information (Koop et al.,

1997b).For a large number of molecules, m, in a sample or droplet, the probability, P, to observe k

nucleation events can be expressed by a Poisson distribution:

Pfc(f) = ^~e_mP' (D-1}

where p is the probability that a molecule becomes the center of a critical cluster. For small p

the nucleation rate for the whole sample can be introduced asw = mp/t within the observation

time, t. If we assume ntot equal samples and nuq is the number of samples which have not

nucleated within a specific time, t, the probability of observing k nucleation events within t is

Pk{t) = M!e-- ^jom i ln

ntot

k\"

ntotk\ V" lnhq(t)\.'

The total observation time in an experiment consists of the time, for which each droplet stays

liquid, £hg,i, and the time after which individual droplets nucleate, tnuCtt.

nhq nnuc

Hot = / jHXq% + y

jtnuCil , \D.oJ

i=0 »=0

127

128 APPENDIX D. NUCLEATION RATE COEFFICIENTS AND PRODUCTION RATES

where nnuc is the number of droplets, that nucleate after times tnuCti. It is found that nnuc =

Li)ttat. If we assume higher or lower values of oj (i. e. the uncertainty in w) than the measured

w-value, the probability of the occurrence of nnuc nucleation events is never zero. Therefore, an

upper fiducial limit, uup, can be given such that less than n\fuc nucleation events occur with a

given probability x (x is also called "confidence level"), if ujup was the true nucleation rate:

OO nnuc i . \k

x= £ Pfe(W = l-e-^-£^fp-. (D.4)

==fl,nuc+l fc—U

Even if no nucleation events occurred during the experiments, an upper limit, nn%c, of possible

nucleation events due to the statistical uncertainty in u can be given:

<L = wupttot = In (j~^j • (D-5)

Equation D.5 yields for zero observed nucleation events, nnXuc = 0, an upper limit of the number

of nucleation events of nffuc = 6.908 for a confidence level of 0.999. In other words, if the

experiment would be repeated an infinite number of times the maximum number of observable

nucleation events are smaller than n^„c within a probability of 0.999. For ntfuc > 0, Eq. D.4

must be solved numerically. Values for n\fuc for given nnXuc are presented in Table D.I.

Using these upper limits for the number of nucleation events in the analysis of the experimental

data leads to upper limits of the nucleation rates. These upper limits of the nucleation rate can be

understood as the most conservative values for the determined nucleation rates, i. e. the highest

estimation of a particular nucleation rate. The "true" nucleation rate is expected to be even

lower, since the upper limit of the nucleation rate includes also possible heterogeneous nucleation

processes, which have a lower nucleation barrier and, hence, nucleate at higher temperatures.

The upper limit of J can be used to derive lower limits of AG1^ using Eq. 2.29. But these

AGatf'-values cannot be used to derive quantitative values of the Gibbs free energy of activation

for diffusion or the surface tensions using Eq. 2.26 and 2.27, since the AG^-values do not

represent the "true" activation values of the solution.

D.2 Derivation of stratospheric production rates of NAD and

NAT

Here, a more detailed description of the analysis of the data presented in Fig. 5.7 of Knopf et al.

(2002) is given:The experimentally derived data analyzed as described in section 5.4 and all available different

nucleation data sets (Koop et al., 1995,1997a; Bertram and Sloan, 1998b,a; Bertram et al., 2000a;

Salcedo et al., 2001) plotted in Fig. 5.5 are used within this evaluation. For each temperature

all available data on AGact were gathered and the highest value for each saturation ratio was

used to derive AGact as a function of the NAD or NAT saturation ratio. The stratospheric

saturation ratio corresponding to the temperature was taken according to Fig. 5.7a. This yields

the lowest value of Jj^. This procedure was repeated for all plotted temperatures for which

D.2. Derivation of stratospheric production rates of NAD and NAT 129

Table D.l: Upper and lower fiducial limits for selected numbers of nucleation events, nnUC, at a confi¬

dence Level of x = 0.999 as calculated using Poisson statistics (Koop et al, 1997b).

UlowHot nnuc ûpHot

nda 0 6.908

0.001 1 9.233

0.045 2 11.229

0.191 3 13.062

0.429 4 14.794

0.739 5 16.455

1.107 6 18.062

1.520 7 19.626

1.971 8 21.156

2.452 9 22.657

2.961 10 24.134

5.794 15 31.244

8.958 20 38.042

12.337 25 44.636

15.869 30 51.083

19.518 35 57.418

23.260 40 63.662

27.078 45 69.833

30.959 50 75.942

38.878 60 88.007

46.963 70 99.909

55.180 80 111.682

63.506 90 123.348

71.921 100 134.924

159.130 200 247.675

433.739 500 573.028

a, not defined.

several nucleation data sets were available. The corresponding production rates shown in Fig.

5.7c were obtained by multiplying the aerosol volume density given by Carslaw et al. (1994) and

the time of one hour with the homogeneous nucleation rate coefficients shown in Fig. 5.7b.

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Appendix E

Parametrizations of NAD and NAT

nucleation mechanisms

E.l Homogeneous nucleation parametrization ofNAD and NAT

Here, the parameterizations used by Tabazadeh et al. (2001) are given to obtain Fig. 5.2 of

Knopf et al. (2002). The laboratory nucleation rates of Bertram and Sloan (1998b), Bertram

and Sloan (1998a), and Salcedo et al. (2001) are parameterized in the below given way by

Tabazadeh et al. (2001). The nucleation activation energies are given by (Salcedo et al., 2001),but were extrapolated to stratospheric saturation ratios by Tabazadeh et al. (2001). In the case

of NAD the following formulations were used:

AG£Ad((Snad) = (28.8 ±0.2)-(0.37 ±0.01)5nad. (E.l)

The homogeneous nucleation rate coefficients can be derived by

Jnat = 1-138 -nrVTrSexp-AGNAD

RT(E.2)

where r is the radius of the aerosol particle, which is assumed to be about 0.82 /mi.

In the case of NAT nucleation Tabazadeh et al. (2001) gives the following expressions including

the nucleation activation energy derived by Salcedo et al. (2001):

AG^T(SNAT) = (30.9 ±0.3)-(0.14 ±0.0004)5nat, (E.3)

which is used to derive homogeneous NAT nucleation rate coefficients by

Jnat = 9.269 • 103VTr3exp-AGâd

RT(E.4)

131

132APPEJVDJX E. PARAMETRIZATIONS OF NAD AND NAT NUCLEATION MECHANISMS

E.2 Pseudo-heterogeneous nucleation activation energies of

NAD and NAT

The following parametrizations are given by Tabazadeh et al. (2002a) to obtain the pseudo-

heterogeneous nucleation rate coefficients of NAD and NAT shown in Fig. 5.8. The activation

energy for the nucleation of NAD on the surface of a binary HNO3/H2O solution is given by:

^GÎaAD(xnN03,T) = 11.5593 + 0.0804214T

- (71.5133 - 0.256724 T) XHNO3, (E.5)

where xhno<< is the mole fraction of the solution and T is the temperature in Kelvin. SinceC WAT

AGact was onry obtained for a mole fraction value of 0.246, the concentration dependence of

AGact (XHN03)T) is used to obtain a concentration dependence of AG^ (xhno3>T):

AGact (XHN03,T) =

AGg,NAD(0 246 r)AGact (zHN03,T), (E.6)

where AG^NAD(0.246, T) is given by

AGf£AT(0.246, T) = -45.2429 + 0.364844 T. (E.7)

These nucleation activation energies can be used to calculate surface-based homogeneous nucle¬

ation rate coefficients of NAD and NAT by using Eq. 2.32.

List of Figures

1.1 Aerosol formation mechanisms and aerosol size distribution 2

1.2 Sketch of the standard atmosphere 4

1.3 Composition of aerosol particles of the lower stratosphere 5

1.4 Volume density of PSC particles as function of temperature 6

1.5 Radiative forcing of atmospheric agents (IPCC) 8

2.1 Phase diagram of H2S04/H20 17

2.2 Phase diagram of (NH4)2S04/H20 18

2.3 Phase diagram of HN03/H20 19

2.4 Gibbs free energy for the formation of a critical cluster 22

2.5 Surface tensions of a liquid sitting on its solid 23

2.6 Nucleation of a solid at the surface of its liquid 24

2.7 Term diagram of the Raman scattering process 25

2.8 Intensity distribution within a Raman spectrum 26

3.1 Sketch of the atomizer 30

3.2 Sketch of the single droplet generator using an inkjet-cartridge 30

3.3 Sketch of the experimental setup 33

3.4 Sketch of the temperature stage 34


4.2 Laser influence on Raman spectra 42

133

134 List of Figures

4.3 Raman spectra of (NH4)2S04/H20 droplets 0.99 and 5.35 mol kg1 in concentration 44

4.4 Phase diagram of H2S04/H20 45

4.5 Temperature dependent Raman spectra of a H2SO4/H2O droplet 2.55 mol kg-1in concentration 46

4.6 Ratios of mS02-/mHS0- in H2SO4/H2O solutions 47

4.7 Degree of dissociation of the HSOJ ion 48

4.8 The thermodynamic dissociation constant of the HSOJ ion 50

4.9 Gibbs free energy, reaction enthalpy, and reaction entropy of the dissociation of

HSOJ 51

4.10 Activity coefficients and water activity of a 1.13 mol kg-1 H2SO4/H2O solution .54

4.11 Activity coefficients and water activity of a 9.84 mol kg-1 H2SO4/H2O solution .55

4.12 HCl solubilities of H2SO4 solutions 5.5, 8.35, 10.2, and 15.32 mol kg-1 in concen¬

tration 68



4.15 Concentration dependent Raman spectra of H2SO4/H2O droplets 72

4.16 Lorentzian fit functions 73

4.17 Ratio R as a function of temperature 74

4.18 Ratio Rw as a function of concentration 75

4.19 Temperature dependent Raman spectra of a (NH4)2S04/H20 droplet 5.35 mol

kg-1 in concentration 76

4.20 Concentration dependent (NH4)2S04/H20 Raman spectra 77

4.21 Heat capacity of the ferroelectric phase transition 79

4.22 Effect of the ferroelectric phase transition on the î(S04~) normal vibration ... 80

4.23 Effect of the ferroelectric phase transition on the 1^3 (SO^-) normal vibrations . .81

5.1 AGact of NAD and NAT as a function of saturation ratio 89

List of Figures 135

5.2 Homogeneous nucleation rate coefficients of NAD and NAT using the formulations

of Tabazadeh et al. (2001) 90


5.4 Raman spectra of HNO3/H2O droplets 92

5.5 AGact-values of this work as a function of the NAD and NAT saturation ratios .95

5.6 AGact-values of this work as a function of the NAD and NAT saturation ratios .96

5.7 Composition, homogeneous nucleation rate coefficients, and production rates of

STS aerosols 97

5.8 Pseudo-heterogeneous NAD and NAT nucleation rate coefficients as a function of

temperature and concentration 101

5.9 Surface-based homogeneous nucleation rate coefficients of NAD in a solution with

a HNO3 mole fraction of 0.333 103

5.10 Surface-based homogeneous nucleation rate coefficients of NAD in a solution with


5.11 Surface-based homogeneous nucleation rate coefficients of NAT in a solution with


5.12 Composition, surface-based homogeneous nucleation rate coefficients, and corre¬

sponding production rates of STS aerosols 106

5.13 Homogeneous nucleation rate coefficients in (NH4)2S04 droplets 109

5.14 Surface-based homogeneous nucleation rate coefficients in (NH4)2S04 droplets . .110

A.l Sketch of inkjet-cartridge 119

A.2 Electric circuit to operate inkjet-cartridge 120

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Acknowledgements

The development of a Ph.D. student and his doctoral thesis is not possible without the great

support of his colleagues, friends, and family. Here I want to thank all people who participated

directly and indirectly in this Ph.D. doctoral thesis.

I thank

• Thomas Peter to have offered to me the possibihty to join his group at the ETH Zürich.

I appreciated your comments and advices. You established a wonderful mood within your

group where it is a pleasure to work.

• Thomas Koop, alias "Köpi", (alias "ice cream killer") for a wonderful scientific and amica¬

ble relationship. I had fun working with you and I learned very much from you. Certified:

one of the best tutors you can get!

• Ulrich Schurath being the co-examiner of my Ph.D. thesis and coming to Zürich to hold

the PhD defense.

• Beiping Luo, who is able to treat a fish and chicken in a wok as fast as a fortran code.

Beiping, thanks for your cooperation, unlimited ideas, and your humor.

• Uwe G. Weers, formerly known as the python, now alias "Notfallaufnahme" in M 8.1, for

technically support, friendship, and much inspiration.

• Dominik W. Brunner, alias "Chefpathologe" of M 8.1, for not becoming crazy and leaving

our office, good spirit, Badminton-colleague, and dynamical input (PV will be always with

you).

• Uh K. Krieger, specialist for Grisons nut pie, for all the good experimental ideas and

feedbacks.

• Bernhard Zobrist, alias "Chefarzt" of M 8.1, for good vibes, experimental support, and

friendship.

• Christina Colberg, for showing a physicist how Raman spectra can be interpreted, friend¬

ship, good time, and Badminton-colleague (well thought, poorly played!).

149

• Christian Braun, alias "the Hacker", for digital connections within the experiment, soft¬

ware support, friendship, and some beers.

• Peter Isler, for technical support (which was often necessary in a few minutes), for good

techno vibrations, and snowboard support.

• Claudia Marcolli, for showing a physicist what organics all can do.

• Michaela Hegglin, alias "Micca", for good vibes, yogurt, and friendship.

• Marc Wüest, the Plüsch- and Schümlipflümli-specialist, for fastest and most patient IT-

support, friendship, and humor.

• Ruedi Lüthi, for the technical, computer hardware, and infrastructure support.

• Hans Hirter, master of IT-support, for connection between the computers I used.

• Edwin Hausammann, for the technical support. If you have been in our group already two

years ago, I would have had to write two more chapters in my PhD thesis!

• Thomas Huthwelker, alias "Huthi, the man who had the shortest stay in the States" for

always being open for discussions, much experimental input, and ideas.

• Bruno Nussberger, the man with the smooth hands, for developing all the glass apparatus.

• Daniel Lüthi, for Sun/email support.

• Raphael Schefold, for good vibes, and for support in institutional politics.

• Petra Forney, for taking over some of the administration.

• Eva Choffat, for administrative advice and speaking consequently Swiss German.

• all other Ph.D. students for an enjoyable mood.

• all skating and snowboarding people I know (especially Chris Eggers) giving me the right

balance for a successful Ph.D. thesis.

• all the bar people at the skiing region Jochpass, Engelberg, Switzerland, for enjoyable

weekends (Schümlipflümli).

• Ursula, Jose, Barbara, and Michi Sogo for making me feel home in Switzerland from the

beginning on of the Ph.D. thesis.

• my whole family for supporting me the last years and giving me the freedom in choosing

my personal development.

150

Curriculum Vitae

Daniel Alexander Knopf

Education and University Career

2000-2003 Ph.D. doctoral thesis at the Institute for Atmospheric and Climate

Sciences. Swiss Federal Institute of Technology (ETH) Zurich, Switzerland.

Title: Thermodynamic Properties and Nucleation Processes

of Upper Tropospheric and Lower Stratospheric Aerosol Particles.

1998-1999 Diploma thesis in atmospheric physics, at the Max-Planck-Institute

for Nuclear Physics, Division Atmospheric Science, Heidelberg, Germany.

Title: Calibration of an Aerosol Beam Mass Spectrometer

with definite Sulfuric Acid Water Aerosols.

1997-1998 During Graduation/Diploma thesis:

Spanish study at the Ruprecht-Karls-University of Heidelberg, Germany.

1997 Graduated in physics at the Ruprecht-Karls-University of Heidelberg.

Elective subjects: environmental physics and economics.

1996 Certificate for "Interdisciplinary Supplementary Studies in

Environmental Sciences", Ruprecht-Karls-University of Heidelberg.

1992 Begin of physics studies at the Ruprecht-Karls-University of Heidelberg.

1983-1992 Graduate of the Hebel-Grammer-School in Schwetzingen, Germany.

Professional Career

2000-2003 Teaching assistance at the Institute for Atmospheric

and Climate Sciences, ETH Zurich, Switzerland.

1999 Scientific assistant responsible for the "AIDA-Aerosol-Project"

at the Max-Planck-Institute for Nuclear Physics, Heidelberg, Germany.

1998-1999 Scientific assistant at the Max-Planck-Institute for Nuclear Physics,

Heidelberg, responsible for the operation of particle accelerators.

1995-1997 Scientific assistant at SAP Corporation, Walldorf, Germany.

Responsible for the installation, configuration, and error finding

in the software and hardware field of complex TCP/IP networks.

1992-1996 Working student employed for the controlling of computerized metal

processing machines at Vögele Corporation, Mannheim, Germany.

1991-1994 Snowboard teacher.

1991-1992 Coach of a table-tennis team.

Languages

German: mother tongue. English fluent in spoken and written. Spanish and French: flu¬

ent/advanced. Italian: basic.

Publications

Peer-Reviewed Articles

• Knopf, D. A., Luo B. P., Krieger, U. K., Koop, T.: Thermodynamic Dissociation Constant

of the Bisulfate Ion from Raman and Ion Interaction Modeling Studies of Aqueous Sulfuric

Acid at Low Temperatures, J. Phys. Chem. A, 107, 4322-4332, 2003.

• Knopf, D. A., Luo B. P., Krieger, U. K., Koop, T., Peter, T.: Homogeneous nucleation

of NAD and NAT in liquid stratospheric aerosols: insufficient to explain denitrification,

Atmos. Chem. Phys., 2, 207-214, 2002.

• Knopf, D. A., Zink, P., Schreiner J., Mauersberger, K.: Cahbration of an Aerosol Com¬

position Mass Spectrometer with Sulfuric Acid Water Aerosol, Aerosol Sei. Technol, 35,

924-928, 2001.

• Schreiner J., Voigt, C, Zink, P., Kohlmann, A., Knopf, D., Weisser, C, Budz, P., Mauers¬

berger, K.: A Mass Spectrometer System for Analysis of Polar Stratospheric Aerosols,

Rev. Sei. Inst, 73, 446-452, 2002.

• Zink P., Knopf, D. A., Schreiner, J., Mauersberger, K., Möhler, O., Saathof, H., Seifert, M.,

Tiède, R., Schurath, U.: Cryo-chamber simulation of stratospheric H2SO4/H2O particles:

Composition analysis and model comparison, Geophys. Res. Lett., 11, Vol. 29, 46-1-46-4,

2002.

Conference Proceedings and Extended Abstracts

• Knopf, D. A., Luo B. P., Krieger, U. K., Koop, T., Peter, T.: Experimental and Theo¬

retical Analysis with Respect to Surface-Induced Nucleation, Madrid, European Aerosol

Conference 2003, J. Aerosol Science, 2003, accepted.

• Knopf, D. A., Luo B. P., Krieger, U. K., Koop, T.: The Thermodynamic Dissociation

Constant of HSOJ at Atmospheric Conditions, Madrid, European Aerosol Conference

2003, J. Aerosol Science, 2003, accepted.

• Knopf, D. A., Koop, T., Weers, U. G., Krieger, U. K., Peter, T.: Investigation of Ice Nucle¬

ation in Liquid Aerosols Using Raman Microscopy, Leipzig, European Aerosol Conference

2001, J. Aerosol Science, 32, Suppl. 1, 283-284, 2001.

• Möhler, O., Bunz, H., Saathoff, H., Schäfer, S., Seifert, M., Tiède, R., Schurath, U., Knopf,

D., Schreiner, J., Voigt, C, Zink, P., Mauersberger, K.: The Potential of the AIDA Aerosol

Chamber for Investigating PSC Formation and Freezing Mechanisms. BAD TOLZ, Work¬

shop 'Mesoscale Processes in the Stratosphere' (9.11.-11.11.1998) proceedings. Air Pollu¬

tion Report 69, Office for Official Publications of European Communities, Luxembourg,

1999, 171-174.

• Zink, P., Knopf, D., Schreiner, J., Voigt, C, Mauersberger, K., Bunz, H., Möhler, O.,

Saathoff, H., Seifert, M., Tiède, R., Schurath, U.: Growth of Aerosol Particles under

Stratospheric Conditions - Experiments inside the AIDA Aerosol Chamber. BAD TOLZ,

Workshop 'Mesoscale Processes in the Stratosphere' (9.11.-11.11.1998) proceedings. Air

Pollution Report 69, Office for Official Publications of European Communities, Luxem¬

bourg, 1999, 281-284.

Ph.D. Thesis and Diploma Thesis

• Knopf, D. A., Thermodynamic Properties and Nucleation Processes of Upper Tropospheric

and Lower Stratospheric Aerosol Particles, Ph.D. thesis 15103, ETH Zurich, Switzerland,

2003.

• Knopf, D., Kalibration eines Aerosolstrahlmassenspektrometers mit definierten Schwe¬

felsäure-Wasser-Aerosolen, Diploma thesis, Ruprecht-Karls-University of Heidelberg, Ger¬

many, 1999.

Invited Talks

• Thermodynamic Properties and Nucleation Processes of UT/LS Aerosol Particles, Uni¬

versity of British Columbia, Chemistry Department, Vancouver, Canada, 20th of May

2003.

• Equilibrium and Non-equilibrium Processes in Aqueous Aerosols of the UT/LS, Institute

for Meteorology and Climatology, Research Center Karlsruhe, Karlsruhe, Germany, 17th

of March 2003.

• Equilibrium and Non-equilibrium Processes in Aqueous Aerosols of the UT/LS, Max-

Planck Institute for Nuclear Physics, Division Atmospheric Science, Heidelberg, Germany,

18th of March 2003.

Oral and Poster Presentations at Conferences

2002 Conference of the European Geophysical Society, Nice, France.

2001 American Geophysical Union, San Francisco, USA.

2001 Visit of the international and interdisciplinary ETH summer school

"Cortona-Week" for Ph.D. students, Cortona, Italy.

2001 European Aerosol Conference, Leipzig, Germany.

1999 Bunsen-Conference of the German Chemical Society, Dortmund, Germany.

1998 Conference of the German Physical Society in Regensburg, Germany.

1996 Conference "Economy-Energy-Entropy-Ecology",

organized by the European Physical Society, Geneva, Switzerland.

Documents

Rights / License: Research Collection In Copyright - Non … · 2020. 5. 7. · Prof. Ulrich Schurath, co-examiner Dr. ThomasKoop, co-examiner 2003. 1 Zusammenfassung Atmosphärische