Hannes.Tammet@ut.ee Laboratory of Environmental Physics Institute of Physics, University of Tartu

1. 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 Hannes.Tammet@ut.ee Laboratory of Environmental PhysicsInstitute of Physics, University of Tartu

2. Tammet H. and Kulmala M.: Simulation tool for atmospheric aerosol nucleation bursts, J. Aerosol Sci., 36: 173–196, 2005. 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. 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. Sources of knowledge about growth and charging of nanoparticles

3. Long quiet periodsmay 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.

4. Extra noise as in BSMA, lowest contour of 100 cm–3 Measurement with SIGMA, noise from BSMA

5. Extra noise as in BSMA, lowest contour of 20 cm–3 Measurement with SIGMA, noise from BSMA

6. Measurement with SIGMA, lowest contour of 20 cm–3 Measurement with SIGMA without extra noise

7. Air inlet NOISE(10 min cycles) WORSE HALF OF MEASUREMENTS Sheathair filter Inlet gate BETTER HALF OF MEASUREMENTS Sheathair filter Attracting electrodes Attracting electrodes Air ion trajectory Repelling electrode Repelling electrode Repelling electrode Repelling electrode Shield electrode Shield electrode Electrometric filter for positive ions Electrometric filter for negative ions Filter batteries Filter batteries Air outlet through multi-orifice plate Low noise instrument SIGMA: 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

8. Charged nanoparticles are air ions

9. Particles and cluster ions Quantum retardation of sticking: internal enegy levels of a cluster will not be excited and the impact is elastic-specular Ion orparticle Molecule orgrowth unit

10. CLUSTER PARTICLE 1.5 or 1.6 nm Particle or molecular cluster ? to grow, or not to grow ? does not grow,molecules will bounce back grows,molecules will stick

11. 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.

12. Extra comment: Assumption: all surfaces are awayLaw of balance:genesis = destruction Flux of ionsto particles

13. do d number concentrationof particlesin diameterrangeof 0...d, cm–3, N(d)– dd = GR(d) dt dN = n dd = n GR dt density of concentration distribution, cm–3nm–1 →dN / dt = GRn – –growth rate, nm s–1, diameter crossing rate,– apparent nucleation rate,transit rate, cm–3s–1 Particle growth through a diameter margin Symbols: c – concentration of small ions, cm–3 d – particle diameter (d = dp), nm, J = GRn (a well known equation) NB: particle growth rate may essentially differ from the population growth rate.

14. Extrasource d db= d + h/2 da = d –h/2 Inflow Outflow Leakage Particle growth through a diameter interval (analog: classic problem about water tank and pipes) (GDE : Inflow + Extrasource – Outflow – Leakage = Increment) Steady state balance: Inflow + Extrasource – Outflow – Leakage = 0orOutflow = Inflow + Extrasource – Leakage

15. Extrasource d db= d + h/2 da = d –h/2 Inflow Outflow Leakage relative depletion rate orsink of particles s–1,(incl. CoagSas a component) – InflowJ(da) = GR(da)n(da), OutflowJ(db) = GR(db)n(db), Leakage = , Extrasource = Equation of steady state balance Charging state = CST General steady state balance equation (integral form): Outflow = Inflow + Extrasource – Leakage

16. substitute n with J/GR: calculate derivative: Equation (4) in Lehtinen et al. (2007): Differences: different notations of sink and two simplificationsE = 0 & additional components of sink are neglected,dependence of GR on d is not pointed out. Comparison with Lehtinen et al. (2007) Balance equation: Substitute GR n with J, assume E = 0, consider da = const & db = argument:

17. 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 Nbkgcan 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 nanoparticlesSbkg0 = K0(d, dbkg) NbkgSink of charged nanoparticlesSbkg1 = K1(d, dbkg) NbkgDifference is small and neglecting of the charge would not induce large errors.

18. TWO TWO ONE ONE b1 b0 + + + – 0 b0 b1 – – Charging and discharging of particles ion-to-neutral-particle attachment coefficient(a special case of coagulation coefficient). ion-to-opposite-charged-particle attachment coefficientor the recombination coefficient

19. 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

20. 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)cn1(d) The ion attachment source of charged particles of one polarity is E1(d) = β0(d)cn0(d) E0is usually a minor component in the balance of neutral particles whileE1is an important component in the balance of charged particles. If the rate ion-induced nucleation is zero, then all charged nanoparticles are comingfrom the extrasource.

21. The first mean value theorem states for any continuous Y = Y(d): A small step can be made using the midpoint rule and few iterations: Numerical solving of balance equations da db da db da db da d Step by step: da db da db da db GR or n can be computed step by step moving upwards or downwards

22. Abbreviations: , , , etc. Itemized numerical model of steady state growth of nanometer particles Equations: Example of a specific problem: Given – nucleation rates J0 and J1or values of distribution functionsn0 and n1 at first diameter, and growth rates GR0 at all sizes. Find –values of distribution functions n0 and n1 at all diameters.

23. 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.

24. dN1/dd : cm–3nm–1(average of 16240 records of both + and– intermediate ions) noise OK N d : nm 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.

25. 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 0.402 2.0 4.48 2.85 0.686 2.5 3.11 3.74 0.693 3.0 2.33 3.73 0.679 3.5 1.82 3.55 0.680 4.0 1.47 3.54 0.693 4.5 1.22 3.55 0.711 5.0 1.03 3.56 0.751 5.5 0.88 3.59 0.770 6.0 0.76 3.64 0.790 6.5 0.67 3.70 0.809 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. d : nm

26. 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 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

27. Assume and iterate 2…5 times: Automated fitting of intermediate ion measurements Given: measurements of intermediate ionsn1 (d)on a set of diameters(d1, d2,…, dm)

28. 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 CST 1.5 7.38 0.401 2.0 4.48 0.682 2.5 3.11 0.686 3.0 2.33 0.669 3.5 1.82 0.668 4.0 1.47 0.678 4.5 1.22 0.692 5.0 1.03 0.728 5.5 0.88 0.742 6.0 0.76 0.758 6.5 0.67 0.772 GR : nm h–1 WARNING: the solution is ambiguous. Different assumptions aboutJ0andJ1 are possible d : nm

29. 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)

30. Effect of guess about J0(1.5 nm)while requiredrelation isGR0(3 nm) = GR0(7 nm) (fitting the test distribution)

31. Sink, growth rate and transit rate compared with Lehtinen et al. (2007) S : 1/h,GR0 : nm/hJ0(d) : cm–3s–1 d : nm

32. 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–1is 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.

33. Thank You Thank You for Attention