Laboratory of Environmental Physics Institute of Physics, University of Tartu Quiet nucleation of atmospheric aerosol and intermediate ions 15th Finnish-Estonian air ion and atmospheric aerosol workshop Hyytiälä

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, Tammet H. and Kulmala M.: Simulation tool for atmospheric aerosol nucleation bursts, J. Aerosol Sci., 36: 173–196, 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 instruments only 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 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– Air inlet Air outlet through multi-orifice plate Repelling electrode Attracting electrodes Sheath air filter Repelling electrode Sheath air filter Attracting electrodes Repelling electrode Shield electrode Inlet gate Air ion trajectory Electrometric filter for positive ions Filter batteries Electrometric filter for negative ions Filter 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 or particle Molecule or growth 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: Assumption: all surfaces are away Law of balance: genesis = destruction Flux of ions to particles

Particle growth through a diameter margin dd = GR(d) dt dodo d J = GR n Symbols: diameter crossing rate, – apparent nucleation rate, transit rate, cm –3 s –1 → dN / dt = GR n dN = n dd = n GR dt d – particle diameter (d = d p ), nm, density of concentration distribution, cm –3 nm –1 – – growth rate, nm s –1, N(d) –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 d a = d – h/2 d b = d + h/2 Inflow Leakage Outflow d Extrasource (analog: classic problem about water tank and pipes) Steady state balance: Inflow + Extrasource – Outflow – Leakage = 0 or Outflow = Inflow + Extrasource – Leakage (GDE : Inflow + Extrasource – Outflow – Leakage = Increment)

Equation of steady state balance Inflow J(d a ) = GR(d a ) n(d a ), Outflow J(d b ) = GR(d b ) n(d b ), Leakage =, Extrasource = General steady state balance equation (integral form): d a = d – h/2 d b = d + h/2 Inflow Leakage Outflow d Extrasource Outflow = Inflow + Extrasource – Leakage relative depletion rate or sink of particles s –1, (incl. CoagS as a component) – Charging state = CST

Comparison with Lehtinen et al. (2007) Balance equation: Substitute GR n with J, assume E = 0, consider d a = const & d b = argument: Equation (4) in Lehtinen et al. (2007): 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 : calculate derivative:

Sink of nanoparticles on background aerosol The background aerosol can be replaced with an amount of monodisperse particles in simple numerical models. The diameter of particles is assumed d bkg = 200 nm that is close to the maximum in the distribution of coagulation sink. The concentration N bkg can be roughly estimated according to the sink of small ions. The coagulation sink is calculated as S bkg = K(d, d bkg ) N bkg The coagulation coefficient K (d, d bkg ) 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 S bkg0 = K 0 (d, d bkg ) N bkg Sink of charged nanoparticles S bkg1 = K 1 (d, d bkg ) N bkg Difference is small and neglecting of the charge would not induce large errors.

Charging and discharging of particles 0 + – + – + – 11 00 11 00 ion-to-neutral-particle attachment coefficient (a special case of coagulation coefficient). ion-to-opposite-charged-particle attachment coefficient or the recombination coefficient TWO ONE

Sink of nanoparticles due 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 S ion0 = 2 β o (d) c A charged particle can be neutralized with an ion of opposite polarity. The sink of charged nanoparticles on small ions is S ion1 = β 1 (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: E 0 (d) = 2 β 1 (d) c n 1 (d) The ion attachment source of charged particles of one polarity is E 1 (d) = β 0 (d) c n 0 (d) E 0 is usually a minor component in the balance of neutral particles while E 1 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 A small step can be made using the midpoint rule and few iterations: The first mean value theorem states for any continuous Y = Y(d) : dada dbdb dada dada dada dbdb dbdb dada dada dada dbdb dbdb dbdb d Step by step: GR or n can be computed step by step moving upwards or downwards

Abbreviations:,,, etc. Itemized numerical model of steady state growth of nanometer particles Equations: Example of a specific problem: Given – nucleation rates J 0 and J 1 or values of distribution functions n 0 and n 1 at first diameter, and growth rates GR 0 at all sizes. Find – values of distribution functions n 0 and n 1 at all diameters.

Two degrees of freedom Growth rates or values of a distribution function can be computed step by step starting form four initial values of G 0, G 1, n 0, and n 1. If the distribution of intermediate ions is measured then one initial value (n 1 ) is known. The ratio G 0 /G 1 is always known and the number of unknown initial values is reduced to two. These two may be presented by G 0 and n 0 at some point or by any pair of parameters that are unambigyosly related with G 0 and n 0. 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 n 0 at a certain size.

Test data characteristic 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 five-minute records are expected to belong to the quiet phase of nucleation. d : nm dN 1 /dd : cm –3 nm –1 (average of records of both + and – intermediate ions) N noise OK

Fitting the measurements by means of the numerical model J 0 = 5.0 cm –3 s –1, J 1 = cm –3 s –1, d bkg = 200 nm, N bkg = 2224 cm –3. nm S bkg :1/h GR CST d : nm dN/dd : cm –3 nm –1 (average of + and – ions) N bkg is estimated according to the small ion depletion. J 0 and J 1 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 Example (simulation tool) J 0 = 13 cm -3 s -1, J 1 = 0.07 cm -3 s -1 d = nm GR = nm/h dN 1 /dd : cm –3 nm –1 d : nm

Automated fitting of intermediate ion measurements Given: measurements of intermediate ions n 1 (d) on a set of diameters ( d 1, d 2,…, d m ) Assume and iterate 2…5 times:

Fitting the measurements adjusting the growth rate J 0 = 5 cm –3 s –1, J 1 = cm –3 s –1, d bkg = 200 nm, N bkg = 2224 cm –3. nm Sb:1/h CST d : nm GR : nm h –1 WARNING: the solution is ambiguous. Different assumptions about J 0 and J 1 are possible

Restrictions on the free parameters (when fitting the test distribution) PRIOR INFORMATION? ANALOG OF REGULARIZATION? 3 variants of GR 0 (d 1 ) 3 variants of J 0 (d 1 )

Effect of guess about J 0 (1.5 nm) while required relation is GR 0 (3 nm) = GR 0 (7 nm) (fitting the test distribution)

Sink, growth rate and transit rate compared with Lehtinen et al. (2007) d : nm S : 1/h, GR 0 : nm/h J 0 (d) : cm –3 s –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 –3 s –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 –3 s –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.

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