Growth of nanometer particles during weak stationary formation of atmospheric aerosol

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KL-parameterization of atmospheric aerosol size distribution

Hannes.Tammet@ut.ee

University of Tartu, Institute of Physics

Growth of nanometer particles during weak stationary formation

of atmospheric aerosol

ACKNOWLEDGMENTS:

This research was in part supported by the Estonian Science Foundation through grant 8342 and the Estonian Research Council Project SF0180043s08.

Special thanks to Kaupo Komsaare, Urmas Hõrrak, Marko Vana, and Markku Kulmala for help with data. (The presentation is compiled from fragments of the poster)

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1. INTRODUCTION 1.1. Motivation

Intermediate atmospheric ions (charged fine nanometer particles between 1.5–7.5 nm) are thoroughly studied during burst events of new particle formation when high concentrations

ensure strong signal in mobility analyzers. The new instrument SIGMA (Tammet, 2011) offers a

standard deviation of noise about five times less than the BSMA and makes measurements during quiet periods possible.

We have a dataset of measurements for about one year

(Hõrrak et al., 2011; Tammet et al., 2012) and wish to understand

what is possible to conclude about new particle formation

during quiet periods between burst events. An additional aim is to

explain intermediate ion balance with a simple and intelligible model.

The mathematical approach is an alternative for recent studies

(Leppä et al., 2011; Gagné et al., 2012) and the equations will be derived from scratch while

including only unavoidable components.

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1.2. Simplifications

The probability of having two elementary charges on an intermediate atmospheric ion is negligibly low. The

attachment coefficient of an opposite charged small ion to a 7.5 nm intermediate ion is about 1.2×10

^–6

cm

³

s

^–1

and the typical concentration of small air ions is about 500

cm

^–3

. It follows characteristic time of recombination less than half an hour. Quiet periods of aerosol formation

typically last many hours and the steady state model

seems to be an acceptable tool in the present study. Key simplifications are:

 chemical composition and internal structure of nanoparticles

are not discussed,

 nanoparticles are considered as neutral or singly charged spheres,

 the nanoparticle-nanoparticle coagulation is neglected,

 background aerosol particles are assumed to be in equilibrium charging state,

 parameters of positive and negative ions are expected to be equal,

 all processes are assumed to be in the steady state.

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1.3. Symbols

d is the diameter of a nanometer particle and d_bkg is the diameter of a particle of background aerosol.

n(d) = dN(d) / dd, where N(d) is the number concentration of particles, which diameter does not exceed d.

Neutral particles are marked with index 0 and charged particles of one polarity with index 1.

Correspondingly, the distributions of neutral, charged and total particles are n₀(d), n₁(d), and

n_total(d) = n₀(d) + 2 n₁(d).

GR(d) = dd / dt is the growth rate of an individual particle. Sometimes the growth rate is measured by the

growth of the population mean diameter. This would lead to a different quantity. The growth rate

of singly charged particles (an average of two polarities) GR₁ may considerably exceed GR₀ due

to their ability to entrap different growth units depending on the electric charge of the growing particle.

GF(d) = GR(d) × n(d) is the growth flux of particles through the diameter d.

β(d) is the attachment coefficient of small ions to a nanometer particle.

c is the concentration of small ions of one polarity. The small ions are not in the focus in the following

discussion and their concentrations appear only in combination with an attachment coefficient.

Ionization and recombination of small ions are symmetric. Thus and the effect of

small ions in the steady state aerosol balance appears to be nearly polarity- symmetric.

S_bkg0(d) and S_bkg1(d) are coagulation sinks of neutral and charged nanometer particles on

the pre-existing background aerosol.





 

₀c ₀c

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2. EQUATIONS

Let us consider a size section (d

_a

… d

_b

) and fraction concentrations

The components of particle flux into the section are:



d^d_a^b

n ( d ) dd

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Polarity-asymmetric equations

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2. EQUATIONS

Let us consider a size section (d

_a

… d

_b

) and fraction concentrations

The components of particle flux into the section are:



d^d_a^b

n ( d ) dd

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In the steady state, the sum of all five component fluxes should be zero.

This requirement leads to the balance equations

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a

= quant

ile

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N50:

d

_bkg

= 50…500 nm

Responsible for 86% of

coagulation sink

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4. DISCUSSION 4.1. Problems

The distribution of intermediate ions n

₁

(d) is expected to be known as a result of measurements. However, general

differential equations still contain three unknown functions

GR

₀

(d), GR

₁

(d), n

₀

(d) and don’t provide unambiguous solutions without attaching some external information. We have no

measurement-based external information and the following discussion is limited with analysis of certain hypothesis-based problems. All examples are presented for the distribution n

₁

(d) corresponding to the situation around the lower quartile of

intermediate ion concentration and expressed with approximation at a = 2. Other fixed presumptions are

p = 1013 mb, T = 0 C, c = 500 cm

^–3

. The coagulation sink will be

calculated according to approximations at selected values of

N50. Some of the hypothetic situations under consideration are

intentionally far of reality, and some seem to be plausible.

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4.2. Perfect neutral growth and perfect charged growth

If the particles grow only in the neutral state then GR

₁

(d) = 0 and Equation (2b) allows one to express

independent of GR

₀

(d). In the reverse extreme situation, the particles grow only in the charged state, GR

₀

(d) = 0, and Equation (2a) proceeds in

independent of GR

₁

(d). The effective factors are concentrations of small ions and background aerosol particles. A set of

hypothetical diagrams is shown in Figure.

) ) (

(

) ( )

) (

( ₁

0 1 1

0 n d

d c

d S

d d c

n ^bkg





 

) ) (

( )

( 2

) ( ) 2

( ₁

0 0

0 1 n d

d S

d c

d d c

n

 bkg



 

Comment:

We could get the same

assuming that:

GR

₁

(d) = const

& n

₁

(d) = const

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1

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4.3. Simple kinetic growth

The electric charge of a nanometer particle may assist with entrapping growth units (e.g. gas molecules or small clusters) from some

distance. The simplest approximation of the effective capture cross- section is π(d + d

₊

)2 / 4, where d

₊