Hannes.Tammet@ut.eeLaboratory of Environmental Physics

Institute of Physics, University of Tartu

Quiet nucleation of atmospheric aerosol

and intermediate ions

Quiet nucleation of atmospheric aerosol

and intermediate ions

15th Finnish-Estonian air ion and atmospheric aerosol workshop

Hyytiälä 20110524

Sources of knowledge about growth and charging of nanoparticles

Kerminen, V.-M., and Kulmala, M.: Analytical formulae connecting the “real” and the “apparent” nucleation rate and the nuclei number concentration for atmospheric nucleation events, J. Aerosol Sci., 33, 609–622, 2002.

Tammet H. and Kulmala M.: Simulation tool for atmospheric aerosol nucleation bursts, J. Aerosol Sci., 36: 173–196, 2005.

Verheggen, B. and Mozurkewich, M.:An inverse modeling procedure to determine particle growth and nucleation rates from measured aerosol size distributions, Atmos. Chem. Phys., 6, 2927–2942, 2006.

Long quiet periods may happen between burst events. The particles of secondary aerosol are mortal and would disappear when no supply. How they are regenerated?

Many research papers are written about burst events of atmospheric aerosol nucleation. Not so much about nucleation during quiet periods between the burst events. Why?

A reason: concentration of intermediate ions sufficiently exceeds the noise level of common instrumentsonly during burst events.

Extra noise as in BSMA, lowest contour of 100 cm–3

Measurement with SIGMA, noise from BSMA

Extra noise as in BSMA, lowest contour of 20 cm–3

Measurement with SIGMA, noise from BSMA

Measurement with SIGMA, lowest contour of 20 cm–3

Measurement with SIGMA without extra noise

Low noise instrumentSIGMA:Tammet, H. (2011) Symmetric inclined grid

mobility analyzer for the measurement of charged clusters and fine nanoparticles in atmospheric air. Aerosol Sci. Technol., 45, 468–479. http://dx.doi.org/10.1080/02786826.2010.546818

Air inlet

Air outlet through multi-orifice plate

Repelling electrode

Attracting electrodes

Sheathair filter

Repelling electrode

Sheathair filter

Attracting electrodes

Repelling electrode

Shield electrode

Inlet gate

Air ion trajectory

Electrometric filter for

positive ionsFilter

batteries

Electrometric filter

for negative ionsFilter

batteries

Shield electrode

Repelling electrode

WORSE HALF OF MEASUREMENTS

BETTER HALF OF MEASUREMENTS

NOISE(10 min cycles)

Charged nanoparticles are air ions

Particles and cluster ions

Ion orparticle

Molecule orgrowth unit

Quantum retardation of sticking: internal enegy levels of a cluster will not be excited and the impact

is elastic-specular

Particle or molecular cluster ?

to grow, or not to grow ?

does not grow,molecules will bounce back

grows,molecules will

stick

1.5 or 1.6 nm

CLUSTER PARTICLE

Introduction to modeling

An aim is to make the mathematical model easy to understand. GDE is not used and equations will be derived from scratch.

Empiric information is coming from measurements of intermediate ions. Quiet periods are characterized by very low concentration of nanoparticles and nearly steady state of aerosol parameters. This allows to accept assumptions:

the size range is restricted with d = 1.5 – 7.5 nm,

the nanoparticles can be neutral or singly charged,

attachment flux of ions does not depend on polarity,

nanoparticle-nanoparticle coagulation is insignificant,

all processes are in the steady state.

Extra comment:

ccNcccI

NcccI00

0

0

Assumption: all surfaces are away

Law of balance: genesis = destruction

Flux of ionsto particles

Particle growth through a diameter margin

dd = GR(d) dt

do

d

J = GR n

Symbols:

diameter crossing rate,

– apparent nucleation rate, transit rate, cm–3s–1 dt

dNdJ )(

→ dN / dt = GR n dN = n dd = n GR dt

d – particle diameter (d = dp), nm,

ddddN

dn)(

)( density of concentration distribution, cm–3nm–1–

dtdd

dGR )( – growth rate, nm s–1,

N(d) – number concentration of particles in diameter

range of 0...d, cm–3,

(a well known equation)

NB: particle growth rate may essentially differ from the population growth rate.

c – concentration of small ions, cm–3

Particle growth through a diameter interval

da = d – h/2 db = d + h/2

Inflow Leakage Outflow

d

Extrasource

(analog: classic problem about water tank and pipes)

Steady state balance:

Inflow + Extrasource – Outflow – Leakage = 0or

Outflow = Inflow + Extrasource – Leakage

(GDE : Inflow + Extrasource – Outflow – Leakage = Increment)

Equation of steady state balance

Inflow J(da) = GR(da) n(da), Outflow J(db) = GR(db) n(db),

Leakage = , Extrasource = b

a

d

ddddndS )()(

b

a

d

ddddE )(

b

a

b

a

d

d

d

daabb dddndSdddEdndGRdndGR )()()()()()()(

General steady state balance equation (integral form):

da = d – h/2 db = d + h/2

Inflow Leakage Outflow

d

Extrasource

Outflow = Inflow + Extrasource – Leakage

dtddn

dndS

)()(

1)(

relative depletion rate or

sink of particles s–1,(incl. CoagS as a component)

– Charging state = CST

Comparison with Lehtinen et al. (2007)

b

a

b

a

d

d

d

daabb dddndSdddEdndGRdndGR )()()()()()()(

Balance equation:

Substitute GR n with J, assume E = 0,

consider da = const & db = argument:

d

constdddndSconstdJ )()()(

Equation (4) in Lehtinen et al. (2007): JGR

dCoagS

dddJ p

p

)(

Differences: different notations of sink and two simplifications

E = 0 & additional components of sink are neglected,

dependence of GR on d is not pointed out.

substitute n with J/GR:

)()(

)()(dJ

dGRdS

ddddJ )()(

)(dndS

ddddJ

calculate derivative:

Sink of nanoparticleson background aerosol

The background aerosol can be replaced with an amount of monodisperse particles in simple numerical models. The diameter of particles is assumed dbkg = 200 nm that is close to the maximum in the distribution of coagulation sink. The concentration Nbkg can be roughly estimated according to the sink of small ions. The coagulation sink is calculated as

Sbkg = K(d, dbkg) Nbkg

The coagulation coefficient K (d, dbkg) depends on the nanoparticle

charge and the sink could be specified according to the charge.

Notations: neutral nanoparticles – index 0, charged nanoparticles – index 1.

Sink of neutral nanoparticles Sbkg0 = K0(d, dbkg) Nbkg

Sink of charged nanoparticles Sbkg1 = K1(d, dbkg) Nbkg

Difference is small and neglecting of the charge would not induce large errors.

Charging and discharging of particles

0 +–

+

–

+

– 10

1 0

ion-to-neutral-particle attachment coefficient

(a special case of coagulation coefficient).

ion-to-opposite-charged-particle attachment coefficient

or the recombination coefficient

TWOTWOONEONE

Sink of nanoparticlesdue to the small air ions

When a neutral particle encounters a small air ion then it converts to a charged particle and number of neutral particles is decreased. We expect concentrations of positive and negative ions c equal and the sink is

Sion0 = 2 βo(d) c

A charged particle can be neutralized with an ion of opposite polarity. The sink of charged nanoparticles on small ions is

Sion1 = β1(d) c

Extrasource of nanoparticles

Some amount of neutral particles appear as a result of recombination the charged nanoparticles of the same size with small ions of opposite polarity:

E0(d) = 2 β1(d) c n1(d)

The ion attachment source of charged particles of one polarity is

E1(d) = β0(d) c n0(d)

E0 is usually a minor component in the balance of neutral particles while

E1 is an important component in the balance of charged particles.

If the rate ion-induced nucleation is zero, then all charged

nanoparticles are coming from the extrasource.

Numerical solving of balance equations

b

a

b

a

d

d

d

daabb dddndSdddEdndGRdndGR )()()()()()()(

babaabab

d

dddddddYdddY

b

a

where))(()(

2

)()()( ba

ab

dYdYdY

A small step can be made using the midpoint rule and few iterations:

)()()1 ab dYdY

ba dd )... 3, 2,

The first mean value theorem states for any continuous Y = Y(d):

da db da da dadb db

da da dadb db db

dStep by step:

GR or n can be computed step by step moving upwards or downwards

ab ddh )(11 bb dGRG )(00 aa dGRG Abbreviations:

, , , etc.

Itemized numerical model of steady state growth of nanometer particles

hncShcnnGnG abababbkgababaabb 000110000 )2(2

hncShcnnGnG abababbkgababaabb 111001111 )(

Equations:

Example of a specific problem:

Given – nucleation rates J0 and J1 or values of distribution functions

n0 and n1 at first diameter, and growth rates GR0 at all sizes.

Find – values of distribution functions n0 and n1 at all diameters.

),(),( 0110 ddKGddKG uu

Two degrees of freedom

Growth rates or values of a distribution function can be computed

step by step starting form four initial values of G0, G1, n0, and n1.

If the distribution of intermediate ions is measured then one initial

value (n1) is known. The ratio G0/G1 is always known and the

number of unknown initial values is reduced to two. These two

may be presented by G0 and n0 at some point or by any pair of

parameters that are unambigyosly related with G0 and n0.

Some examples of necessary initial information: growth rate at a certain size and a nucleation rate, growth rates at two different sizes, ratio of growth rates for two sizes and a nucleation rate. ratio of growth rates for two sizes

and value of n0 at a certain size.

Test datacharacteristic of quiet nucleation

Measurements with the SIGMA in the city of Tartu (April 2010 – February 2011) were sorted by the instrumental noise and the worse half of data was deleted. Next the data were sorted by concentration of intermediate ions and the half of measurements with high concentration was deleted. Remained 16240 five-minute records are expected to belong to the quiet phase of nucleation. 0

5

10

15

20

25

1.5 2.5 3.5 4.5 5.5 6.5

d : nm

dN1/dd : cm–3nm–1

(average of 16240 records of both + and – intermediate ions)

N

noise

OK

Fitting the measurements by means of the numerical model

J0 = 5.0 cm–3s–1, J1 = 0.00133 cm–3s–1,dbkg = 200 nm, Nbkg = 2224 cm–3.

nm Sbkg:1/h GR CST 1.5 7.38 1.26 0.4022.0 4.48 2.85 0.6862.5 3.11 3.74 0.6933.0 2.33 3.73 0.6793.5 1.82 3.55 0.6804.0 1.47 3.54 0.6934.5 1.22 3.55 0.7115.0 1.03 3.56 0.7515.5 0.88 3.59 0.7706.0 0.76 3.64 0.7906.5 0.67 3.70 0.809

0

5

10

15

20

25

1.5 2.5 3.5 4.5 5.5 6.5

Measurement

Model

d : nm

dN/dd : cm–3nm–1

(average of + and – ions)

Nbkg is estimated according to the small ion depletion. J0 and J1 are

chosen by method of trial and error.

NB: the method does not provide unambiguous results.

Alternative approach Use any numeric model of nanometer aerosol dynamics, decide steady state conditions, adjust growth parameters, and integrate over a long period at least of few hours

0

5

10

15

20

25

1.5 2.5 3.5 4.5 5.5 6.5

Measurement

Simulator

Example (simulation tool)J0= 13 cm-3s-1, J1 = 0.07 cm-3s-1

d = 1.5 2.5 4.5 6.5 nm GR = 0.8 3.6 3.5 3.8 nm/h

dN1/dd : cm–3nm–1

d : nm

Automated fitting of intermediate ion measurements

Given: measurements of intermediate ions n1 (d)

on a set of diameters (d1, d2,…, dm)

Assume and iterate 2…5 times: abab nnnn 1100 /

hncShncnGn

G abbkgabaab

b 11100111

1 )(1

11

00 ),(

),(G

ddK

ddKG

u

u

hncShcnGnG

n abbkgabaab

b 00011000

0 )2(21

2 ,

211

100

0ba

abba

ab

nnn

nnn

Fitting the measurements adjusting the growth rate

J0 = 5 cm–3s–1, J1 = 0.013 cm–3s–1,dbkg = 200 nm, Nbkg = 2224 cm–3.

nm Sb:1/h CST1.5 7.38 0.4012.0 4.48 0.6822.5 3.11 0.6863.0 2.33 0.6693.5 1.82 0.6684.0 1.47 0.6784.5 1.22 0.6925.0 1.03 0.7285.5 0.88 0.7426.0 0.76 0.7586.5 0.67 0.772 0

1

2

3

4

1.5 2.5 3.5 4.5 5.5 6.5

d : nm

GR : nm h–1

WARNING: the solution is ambiguous. Different

assumptions about

J0 and J1 are possible

0

1

2

3

4

5

6

1 2 3 4 5 6 7

d : nm

Est

imat

ed g

row

th r

ate,

nm

/h

J=1.5

J=2.3

J=3.5

J=5

J=6.2

J=8

J=9

J=10.2

J=11

Restrictions on the free parameters(when fitting the test distribution)

PRIOR INFORMATION?

ANALOG OFREGULARIZATION?

3 variants of GR0(d1)3 variants of J0(d1)

3 variants of GR0(d1)3 variants of J0(d1)

0.25

0.35

0.45

0.55

0.65

0.75

0 5 10 15

J 0 (1.5 nm) : cm-3s-1

J0(3nm)

G0(3nm)/10

Effect of guess about J0(1.5 nm)while required relation is GR0(3 nm) = GR0(7 nm)

(fitting the test distribution)

Sink, growth rate and transit rate compared with Lehtinen et al. (2007)

0

1

2

3

4

5

6

7

1.5 2.5 3.5 4.5 5.5 6.5

Sink:1/h

GR0:nm/h

J0, present model

J0, fixed KKL

J0, sliding KKL

d : nm

S : 1/h,GR0 : nm/h

J0(d) : cm–3s–1

Conclusions

SIGMA provides low-noise measurements of intermediate ions.

The integral equation of steady state balance derived in a straigth- forward way enables to design correct numerical algorithms with ease.

Measurement of intermediate ions is not sufficient to get unambiguous solution of balance equation. Additionally the values of two scalar parameters are required. Some combinations are: growth rate at a certain size and a value of n for neutral particles, growth rates at two different sizes, ratio of growth rates at two different sizes and a nucleation rate.

The nucleation of 3 nm neutral particles at Tartu about J = 0.5 cm–3s–1

is considerable contribution into the atmospheric aerosol generation.

The nucleation rate of 3 nm charged particles at Tartu about 0.002…0.005 cm–3s–1 indicates the minor contribution of ion-induced nucleation during periods of quiet nucleation.

The growth rate of fine nanometer particles during quiet phase of aerosol nucleation at Tartu is estimated about 3…9 nm/h.

for Attention

Thank YouThank You