Estimating of neutral nanoparticles according to measurements of intermediate ions

Estimating of

neutral nanoparticles according to

measurements of intermediate ions

Hyytiälä 20130611 Hannes.Tammet@ut.ee

Kaupo Komsaare & Urmas Hõrrak University of Tartu

Estimating of

neutral nanoparticles according to

measurements of

intermediate ions

The presentation is based on a published paper:

Aim of the presentation is to explain

the concept of RCGP and one special figure

Symbol Quantity Unit

n(d) Size distribution of particle concentration dN / dd cm^–3nm^–1 n₁(d) Size distribution of + or – particle concentration dN₁ / dd cm^–3nm^–1

NB: n(d) = n₀(d) + 2 n₁(d)

GR(d) Growth rate nm s^–1

GF(d) Growth flux (or apparent nucleation rate J ) GR(d) × n(d) cm^–3s^–1

GP(d) Growth product GF(d) dt cm^–3

N_1(3–7) Concentration of charged particles of one polarity

in diameter range of 3–7 nm cm^–3

N_1(3–7) Upper limit of N_1(3–7) cm^–3

w(t, N_1(3–7)) Condition function if (N_1(3–7)(t) < N_1(3–7) ) then 1 else 0 GP_w(d, N_1(3–7)) Conditional growth product w(t, N_1(3–7)) GF(d) dt cm^–3 RCGP(d, N_1(3–7)) Relative Contribution to Growth Product GP_w(d, N_1(3–7)) / GP(d)

0 = neutral 1 = charged (one polarity)

The figure will suggest that the burst events in Tartu generate about 1/3 of new particles

in diameter range of 3…7 nm and about 2/3 of new particles are generated during

quiet periods of NPF.

WARNING: the special figure is based on very rough approximations and the conclusion above is rather a hypothesis.

Why 3…7 nm?

PR EV IEW

Relative Contribution to the Growth Product

REPLACEMENT FOR INTRODUCTION:

fragments of the published paper

STATEMENTS:

High concentrations of intermediate ions appear

during burst events of NPF, which typically last a few hours. The quiet periods between the events can last for weeks.

During quiet periods the old burst-generated

nanoparticles are grown to larger sizes, coagulated with large particles or deposited. However,

intermediate ions are still found in the air during the long pauses between the NPF events

which indicates that

atmospheric aerosol nucleation is continuous .

Theoretical model is based on general equations copied from:

Iida, K., Stolzenburg, M. R., McMurry, P. H., and Smith, J. N.:

Estimating nanoparticle growth rates from size-dependent charged fractions: Analysis of new particle formation events in Mexico City, J. Geophys. Res., 113, D05207, 2008.

NB: we assume steady state, no time dependence

 

) ( ) ( )

( ) ( 2

) ( ) ( ) 2

( ) ( GR

0 0

0 0

1 0 1

0

c d n d c d n d S d n d

dd

d n d d





  

 ^{GR ( ) ( )}  _{( ) ( ) ( ) ( ) ( ) ( )}

1 1

1 1

0 1 0

1

c d n d c d n d S d n d

dd

d n d d





  

Concentration of small ions

Attachment coefficient

Sink on background aerosol particles Index 0 marks neutrals and

1 marks the charged particles of one polarity + or –

Growth

flux Attachment

coefficients

Empiric data is acquired from the paper:

Tammet, H., Komsaare, K., and Hõrrak, U.:

Intermediate Ions in the Atmosphere, Atmos. Res., In Press, http://dx.doi.org/10.1016/j.atmosres.2012.09.009, 2012.

2 3 4 5 6

1 2 3 4 5 6 7

d (nm) positive ions

approximation negative ions

n

( d ) ( cm

n m

)

Empiric equations are acquired from the paper:

Tammet, H. and Kulmala, M.:

Empiric equations of coagulation sink of fine nanoparticles on background aerosol optimized for boreal zone,

Boreal Environ. Res., should appear in Press 2013.

1 - 3 6

6 . 1 500

0 50

10 cm s

) nm 1

/ (

45 . ) 1

( 

d d N

S

) ) (

2 nm

1 / (

4 nm

1 /

5 . 1 1

)

(

1

S d

d d d

S

 





 





 





Concentration of particles in range of 50…500 nm (typical values 1000 cm^–3

at Hyytiälä and 2000 cm^–3 in Tartu)

dd d dn d

d c d n

c

d S

d d c

n

( )

) ( ) GR

) ( (

) ( )

) (

(

0 1 1

0

1

0 1

 

  



 

) ( ) ( )

( ) ( )

( ) ) (

( ) ( GR

1 1

1 1

0 1 0

1

c d n d c d n d S d n d

dd

d n d d





  

The second general equation was:

Let’s assume that

 GR

is a constant,

 N

is known,

 n

(d) is known.

In this case

Unfortunately, the value of GR

is still unknown.

Size distributions of neutral nanoparticles n₀(d) in case of the near-median distribution of intermediate ions in Tartu and

N_50–500 = 2000 cm^–3 as calculated for the trial values of charged nanoparticle growth rate GR₁:

We assumed that GR

(d) may differ from GR

.

Now the first general equation is transformed into a linear differential equation for GR

(d):

This equation can be integrated when an initial

value GR

(d

) at an arbitrary diameter d

is known.

It is assumed that a possible dependence of the growth rate on the particle charge fades with an increase in particle size.

Thus a hypothesis GR

(7 nm) = GR

seems to be an acceptable initial condition.

) ( )

( ) 2

( ) ) (

( 2

) ( ) GR (

) ( 1 )

( GR

0 0

0 1 1

0 0 0

0

c d S d

d n

d d n

c dd d

d dn d

n dd

d d







  

Growth rate of neutral nanoparticles GR₀(d) in case of the near-median distribution of intermediate ions in Tartu and N_50–500 = 2000 cm^–3 calculated at the assumption

GR₀(7 nm) = GR₁

for trial values of charged nanoparticle growth rate GR₁

INTUITIVE UNREALISTIC UNREALISTIC

The growth flux GF or apparent nucleation rate J estimated for the near-median distribution of intermediate air ions in Tartu assuming GR₀(3 nm) = GR₀(7 nm) = GR₁ and N_50–500 = 2000 cm^–3

GF or J (cm^–3 s^–1)

GR  2 nm h

GF(d) = GR

(d)n

(d) + 2GR

(d)n

(d) ≈ GR (n

(d) + 2n

(d))

 consider all 7647 individual hourly size distributions available in the reference dataset of

intermediate air ion measurements in Tartu,

 estimate for every hour (?) the growth flux,

 calculate the growth product for hours

when the concentration of intermediate ions does not exceed certain limit,

 calculate Relative Contribution to Growth Product as function of the limit of intermediate ion concentration,

 draw a diagram of cumulative distribution function

of intermediate ion concentration (CDF) together with a diagram of Relative Contribution to Growth Product (RCGP),

PLAN of extra calculations:

Remark about technique:

The long term average size distribution of intermediate ions was approximated with a sophisticated 4-parameter curve in the

ACPD paper. This is not reasonable when considering the

one-hour measurements and limiting the size range with 3–7 nm.

A convenient parameterization is

Here we have only 2 parameters and easy way to estimate the concentration in the limited size range of 3–7 nm:

) exp(

)

1

( d a bd

n 

 

 ^{ }





7 7 3

3

exp( ) exp( 7 b ) exp( 3 b )

b dd a

bd a

N

Relative Contribution to Growth Product

CONCLUSION

The figure suggests that the burst events

in Tartu generate less than half of new particles in diameter range of 3…7 nm and

most of new particles are generated during quiet periods of NPF.

WARNING: the figure is based on very rough approximations and the statement above is still problematic.

TO DO:

► Improve the theoretical model, ► acquire data of simultaneous ion and aerosol measurements, ► consider alternative criteria

for discrimination of NPF event situations.

Thank you !