Atmos. Chem. Phys., 6, 5193–5211, 2006 www.atmos-chem-phys.net/6/5193/2006/ Atmospheric © Author(s) 2006. This work is licensed Chemistry under a Creative Commons License. and Physics
From molecular clusters to nanoparticles: second-generation ion-mediated nucleation model
F. Yu Atmospheric Sciences Research Center, State University of New York, 251 Fuller Road, Albany, New York, 12203, USA Received: 16 January 2006 – Published in Atmos. Chem. Phys. Discuss.: 13 April 2006 Revised: 09 October 2006 – Accepted: 31 October 2006 – Published: 15 November 2006
Abstract. Ions, which are generated in the atmosphere by 1 Introduction galactic cosmic rays and other ionization sources, may play an important role in the formation of atmospheric aerosols. Atmospheric aerosols from both natural and anthropogenic In the paper, a new second-generation ion-mediated nucle- sources indirectly impact the Earth climate through the ef- ation (IMN) model is presented. The new model explicitly fect on the cloud formation and properties, and precipitation treats the evaporation of neutral and charged clusters and (e.g., Twomey, 1977; Charlson et al., 1992). Indirect ra- it describes the evolution of the size spectra and composi- diative forcing is poorly constrained in the existing climate tion of both charged and neutral clusters/particles ranging models and this represents the single greatest uncertainty from small clusters of few molecules to large particles of in assessing the climate change (Penner et al., 2001). An- several micrometers in diameter. Schemes used to calcu- other important issue is that the particles in the atmosphere late the evaporation coefficients for small neutral and charged can cause visibility degradation and adverse health effects. clusters are consistent with the experimental data within the Climatic, health and environmental impacts of atmospheric uncertainty range. The present IMN model, which is size-, particles depend strongly on the size spectra and composi- composition-, and type-resolved, is a powerful tool for inves- tions of aerosols in the Earth atmosphere. These proper- tigating the dominant mechanisms and key parameters con- ties are governed by a number of microphysical processes trolling the formation and subsequent growth of nanoparti- (e.g. nucleation, condensational growth and coagulation) tak- cles in the atmosphere. This model can be used to analyze ing place simultaneously. New particle formation has been simultaneous measurements of the ion-mobility spectra and observed in various locations in the lower troposphere (e.g., particle size distributions, which became available only re- Kulmala et al., 2004a). Some observations have indicated cently. General features of the spectra for ions smaller than that significant numbers of newly formed particles can grow the critical size, size-dependent fractions of charged nanopar- to the size of the cloud condensation nuclei (CCN) within ticles, and asymmetrical charging of freshly nucleated par- a day under favorable conditions (Kulmala, 2003; Stanier et ticles predicted by the new IMN model are consistent with al., 2004; Zhang et al., 2004a; Wehner et al., 2005; Laak- recent measurements. Results obtained using the second sonen et al., 2005; Stolzenburg et al., 2005). A clear and generation IMN model, in which the most recent thermo- insightful understanding of the mechanisms responsible for dynamic data for neutral and charged H2SO4-H2O clusters the formation of the atmospheric particles is critically impor- were used, suggest that ion-mediated nucleation of H2SO4- tant for quantitative assessment of the climate-related, health H2O can lead to a significant production of new particles in and environmental impacts of atmospheric aerosols. the lower atmosphere (including the boundary layer) under Binary homogeneous nucleation (BHN) of sulfuric acid favorable conditions. It has been shown that freshly nucle- and water has been considered for a long time as a dominant ated particles of few nanometers in size can grow by the con- mechanism of the new particle formation. However, it has densation of low volatile organic compounds to the size of been recently found that BHN theory can’t explain the ob- cloud condensation nuclei. In such cases, the chemical com- served nucleation events in the lower troposphere (e.g, We- position of nucleated particles larger than 10 nm is domi- ber et al, 1996; Clarke et al., 1998). Ternary homogeneous nated by organics. ∼ nucleation (THN) theory, which involves H2SO4,H2O and NH3 (e.g., Coffman and Hegg, 1995; Korhonen et al., 1999; Correspondence to: F. Yu Napari et al., 2002), and ion-mediated nucleation (H2SO4- ([email protected]) H2O-Ion) (Yu and Turco, 2000, 2001) have been proposed as
Published by Copernicus GmbH on behalf of the European Geosciences Union. 5194 F. Yu: Ion-mediated nucleation alternative mechanisms of the particle formation. The actual of derivations from measurements of small ion clusters, ab role of NH3 in the atmospheric nucleation remains unclear initio calculations, thermodynamic cycle, and some approx- because the difference between experimental results and pre- imations (adjustment of Gibbs free energy for neutral clus- dictions of THN is excessively large (Yu, 2006a). Prelim- ters calculated based on liquid droplet model, interpolation, inary simulations performed using a kinetically consistent etc.). Some uncertainties in the thermodynamic data used in THN model constrained using the experimental data indicate the model of Lovejoy et al. (2004) are expected. Lovejoy that the contribution of THN to the formation of new par- et al. (2004) stated that the nucleation of H2SO4 (and H2O) ticles in the boundary layer is negligible (Yu, 2006a). Other on negative ions does not generally explain the observed nu- recently proposed nucleation mechanisms include nucleation cleation events in the boundary layer. Recent observations of iodine species (O’Dowd et al., 2002) and organics com- of the overcharge of 3–5 nm particles show that ions are in- pounds (Zhang et al., 2004b). It may be possible that all the volved in the nucleation in the boundary layer (Laakso et al., above nucleation mechanisms contribute to the formation of 2004; Vana et al., 2006; Iiad et al., 2005). Sorokin et al. new particles in the atmosphere and that the atmospheric nu- (2006) reported laboratory investigation of positive and neg- cleation under different conditions may be dominated by dif- ative H2SO4-H2O cluster ions and they showed that small ferent nucleation mechanisms. The present paper is focused positive ions are markedly enriched in H2O and negative on the ion-mediated nucleation. ions are enriched in H2SO4 molecules. Sorokin et al. (2006) Yu and Turco (1997, 1998, 2000, 2001) developed a novel also developed an ion-cluster-aerosol kinetic model which approach to study the nucleation on ions. The new approach uses the thermochemistry data reported in Froyd and Love- is based on a kinetic model that explicitly solves the com- joy (2003a, b) and empirical correction terms suggested in plex interactions among ions, neutral and charged clusters Lovejoy et al. (2004). Sorokin et al. (2006) compared their of various sizes, vapor molecules, and pre-existing parti- model predictions with laboratory measurements but didn’t cles. Compared to homogeneous nucleation involving neu- discuss what their model will predict under ambient atmo- tral clusters, the nucleation on ions is favored because: (1) spheric conditions. The small charged clusters are much more stable thermody- In the last few years, we have made substantial progress namically; (2) Growth rate of small ion clusters is enhanced in understanding the molecular nature and thermodynam- by the dipole-charge interaction between charged clusters ics of small charged clusters (Nadykto et al. 2003, 2006; and strongly dipolar precursor molecules and, thus, ionic Nadykto and Yu, 2003; 2004; Yu, 2005a) and derived a mod- clusters grow faster than neutrals. Evolution of the size dis- ified Kelvin-Thomson (MKT) equation that accurately takes tributions of both charged and neutral clusters in the pres- into account the dipole-charge interactions (Yu, 2005a). The ence of ionization, neutralization, coagulation, and scaveng- thermodynamic data for small ion clusters derived from re- ing leads to a net flux of clusters crossing the critical size cent MKT equation are in much better agreement with ex- (i.e., nucleation). This mechanism is referred to as the ion- periments than those obtained using the classical Kelvin- mediated nucleation (IMN) (Yu and Turco, 2000). In recent Thomson equation (Yu, 2005a). We have also developed years there is a continuously growing interest to the nucle- a scheme to calculate the evaporation of H2SO4 molecules ation of H2SO4-H2O on ions (Yu, 2002; Carslaw et al., 2002; from neutral H2SO4-H2O clusters (Yu, 2005b, 2006b). This Eichkorn et al., 2002; Laakso et al., 2003; Lee et al., 2003; scheme, in which the most recent thermodynamic data for Harrison and Carslaw, 2003; Lovejoy et al., 2004; Wilhelm H2SO4-H2O binary system are used, explicitly includes the et al., 2004; Sorokin et al., 2006). The mobility distribution hydration effect and it predicts H2SO4-H2O homogeneous of charged clusters/particles measured with the ion mobil- nucleation rates within the uncertainty range of the experi- ity spectrometers (Tammet, 2006) provide useful information mental data (Yu, 2005b, 2006b). In this paper we present about the possible involvement of ions in the atmospheric a second-generation model of IMN, which treats the evap- nucleation (Horrak˜ et al., 1998; Tamm et al., 2001; Makel¨ a¨ oration of neutral/charged clusters explicitly using recently et al., 2003; Laakso et al., 2004; Vana et al., 2006; Iida et developed schemes. The model also takes into account the al., 2005). In the earlier version of the IMN model (Yu and difference in the composition and thermodynamics of small Turco, 1997, 2001), the compositions of neutral and charged positive and negative ions, and can be used to study the ef- clusters were assumed to be the same and the evaporation fect of the sign preference on the nucleation in the Earth of small clusters was accounted for using a simple adjust- atmosphere. In addition to a rigorous treatment of sulfuric ment to the condensation accommodation coefficients due to acid-water clusters, the condensation of organic species on the lack of thermodynamic data for the small clusters. This freshly nucleated particles has been included in the present quite rough approximation likely leads to significant uncer- model. Our model explicitly simulates the evolution of the tainties in predicted nucleation rates in the atmosphere. Re- size spectra and composition of neutral, positively charged cently, Lovejoy et al. (2004) developed a kinetic ion nucle- and negatively charged clusters. The model has a capability ation model, which explicitly treats the evaporation of small of analyzing the recent simultaneous ion mobility distribu- neutral and negatively charged clusters. The thermodynamic tion and particle charge state measurements. data used in their model were obtained via a combination
Atmos. Chem. Phys., 6, 5193–5211, 2006 www.atmos-chem-phys.net/6/5193/2006/ F. Yu: Ion-mediated nucleation 5195
Fig. 1. Schematical illustration of kinetic processes controlling the evolution of positively charged (H+AaWwXx), neutral (AaWwXx), and negatively charged (Y−AaWwXx) clusters/particles that are explicitly simulated in the size-, composition-, and type-resolved IMN model (see text for details). The model uses the discrete-sectional bin structure to represent the sizes of clusters/particles.
2 Ion mediated nucleation (IMN) model take into account the effect of core ion composition (see Sect. 2.3). In this study, we assume that the core of negative 2.1 The kinetic nucleation processes ions to be NO3−. However, during the nucleation events when [H2SO4(g)] is relatively high, the negative ions may be dom- inated by HSO core ions. The uncertainty in charge effect New particle formation is a dynamic process involving vari- 4− ) ous interactions among precursor gas molecules, small clus- associated with core ion sizes (NO3− versus HSO4− for small ters, and pre-existing particles. Figure 1 illustrates schemati- ions is smaller than the uncertainty in experimental data and is likely to be small for larger cluster ions (see Sect. 2.4). cally the evolution of positively charged (H+AaWwXx), neu- tral (AaWwXx), and negatively charged (Y−AaWwXx) clus- Compared to the neutral clusters, charged clusters have ters/droplets that is explicitly simulated in the new kinetic higher growth rates and lower evaporation rates as a result IMN model. Here A, W, and X represent the sulfuric acid of interaction between ions and polar or polarizable host va- (H2SO4), water (H2O), and other possible species (for ex- por molecules (Yu and Turco, 1997, 2001; Nadykto and Yu, ample, organics, NH3, etc.), respectively, while a, w, and x 2004; Yu, 2005a). Thus, charged clusters have a great growth refer to the number of A, W, and X molecules in the clus- advantage over the neutral ones that is very important for the ters/droplets, respectively. Y− is an abbreviation for the neg- nucleation. Size to which a charged cluster can grow de- ative core ion. The initial positive ions are assumed to be pends on the cluster growth rate that is largely determined H+Ww. The initial ions are generated by galactic cosmic by concentrations of precursor gases, evaporation coefficient, rays (GCRs) and by other sources (radioactive emanations, which is a function of the ambient temperature, radius and lightning, corona discharge, combustion, etc.). Measure- composition of clusters, the charge effect, and lifetime due ments of nature negative ion mass spectrum (Eisele and Tan- to the recombination, which is governed by concentrations ner, 1990) indicate the presence of NO3−, HSO4−, SO4NO2−, and size spectra of ions of the opposite sign. Recombina- SO4NO3−, malonate ion, etc. The negative ions are domi- tion of oppositely charged clusters is a major source of large nated by NO3−core ions at low sulfuric acid gas concentra- neutral clusters under typical conditions in the lower atmo- tion but are generally dominated by HSO4−core ions when sphere. Neutral clusters resulted from the recombination may sulfuric acid gas concentration is high. The modified Kelvin shrink due to evaporation if they are smaller than the critical Thomson equation used to calculate the charge effect con- size; however they may grow to larger size and finally be- siders the effect of the size of core ions but is not able to come “nucleated”, if they are bigger than the critical size. In www.atmos-chem-phys.net/6/5193/2006/ Atmos. Chem. Phys., 6, 5193–5211, 2006 5196 F. Yu: Ion-mediated nucleation
Negative, Model Positive, Calculated with thermodynamic data from Froyd (2002) Neutral, Model 2.2 Average compositions of clusters - Negative, Calculated with thermodynamic data from Froyd (2002) Positive, model T=295 K, RH=5% T=290 K, RH=95% 1 - - - - 1 H2SO4 (A) and H2O (W) are known to play an important 0.9 0.9 0.8 0.8 role in the particle formation in the atmosphere (Fiedler et - 0.7 0.7 - al., 2005; Kulmala et al., 2006). In a wide range of the at- 0.6 0.6 0.5 0.5 mospheric conditions, the specie dominating the growth of - AMF 0.4 AMF 0.4 - small clusters is H2SO4; however, organic species may dom- 0.3 Positive, obs., Wilhelm et al. (2004) 0.3 0.2 Negative, obs., Wilhelm et al. (2004) 0.2 inate the growth rate of nucleated nanoparticles (Kulmala et 0.1 Positive ion from Fig. 3 of 0.1 Wilhelm et al. (2004) al., 2004b). The contribution of H O to the nucleation re- 0 0 2 0 5 10 15 20 0 5 10 15 20 lates to the hydration of H2SO4 clusters (or, in the other a a words, modification of the composition of binary H2SO4 - T=250 K, RH=50% T=280 K, RH=70% 1 1 H2O clusters) that reduces the H2SO4 vapor pressure over 0.9 0.9 the binary H2SO4-H2O clusters and, hence, diminishes the 0.8 - - 0.8 - - evaporation of H SO from the clusters. NH (and/or some 0.7 - 0.7 2 4 3 0.6 0.6 - organic compounds) may also be involved in the nucleation 0.5 0.5
AMF 0.4 - AMF 0.4 - process because they may stabilize the cluster and reduce the 0.3 0.3 evaporation coefficient of H SO from clusters due to the 0.2 0.2 2 4 0.1 0.1 change in the cluster composition. Recent analysis of ex- 0 0 0 5 10 15 20 0 5 10 15 20 perimental study on ternary nucleation indicates that NH3 is a a unlikely able to stabilize the small H2SO4-H2O molecular 0 clusters, though the presence of NH3 may contribute to a sta- Fig. 2. Sulfuric acid mole fractions AMF+, AMF−, AMF as func- bility of larger clusters/droplets (Yu, 2006a). The possible tions of cluster sizes under 4 different atmospheric conditions (see involvement of NH and organics in the formation of pre- text for details). 3 critical clusters, which remains to be established, is out of the scope of the present study. addition to the condensation of neutral monomers, both neu- In the case of the nucleation in systems involving tral and charged clusters can grow by collecting smaller clus- H2SO4(A), H2O (W) and ions, which are of the primary in- ters and they may also be scavenged by larger pre-existing terest, the number concentration of water vapor molecules particles. The neutral particles can become charged by col- is much larger than that of H2SO4 vapor and ions. Neu- lecting small ions (ion attachment), while charged particles tral and charged sulfuric acid clusters of various sizes (in- may be neutralized by attachment of ions or clusters of the cluding monomers) can be considered to be in instanta- opposite sign. neous equilibrium with the water vapor, and their compo- In the present study, kinetic processes controlling the evo- sition (i.e., number of H2O molecules w in a cluster con- lution of neutral, positively charged, and negatively charged taining a H2SO4 molecules) can be approximated using the clusters/particles were explicitly simulated using the new average composition. In such a case, the nucleation process size-, composition-, and type- resolved IMN model, which is controlled by the growth/evaporation of clusters through has been built based on the earlier versions of aerosol micro- the uptake/evaporation of H2SO4 molecules and coagulation physics model originally developed by Turco and colleagues among clusters. Assumptions about the instantaneous equi- (Turco et al., 1979; Hamill et al., 1982; Toon et al., 1988; Ja- librium of H2SO4-H2O clusters with the water vapor and the cobson et al., 1994; Jacobson and Turco, 1995; Yu and Turco, dominating role of H2SO4 in nucleation are basic assump- 1998, 2001). tions in all the recently developed kinetic H2SO4-H2O nucle- The current model uses the discrete-sectional bin structure ation models (Yu and Turco, 1997, 1998, 2001; Yu, 2005b, to represent the size spectra of molecular clusters/particles. 2006b; Lovejoy et al., 2004). The bin sizes represent the dry sizes of clusters/particles and In the new IMN model, the average equilibrium composi- corresponding wet sizes are calculated based on the equilib- tions of neutral clusters are calculated using the liquid droplet rium of clusters/particles with the water vapor (Jacobson and approximation (Kelvin Equation). Measurements for both Turco, 1995). For small clusters, the dry volume of ith bin positive (H+AaWw) and negative (Y−AaWw) ionic clus- vi i*v1, where i is the bin index and v1 is the volume of ters indicate that their composition is quite different from = first bin (in this study v1 is the volume of H2SO4 molecule). that of the corresponding neutral clusters, when the clus- When i>id (id is set to be 30 in this study), vi = VRATi * ters are small (a< 5). However, the deviation disappears, th th ∼ vi 1, where VRATi is the volume ratio of i bin to (i-1) when clusters become large (a> 5) (Froyd, 2002; Wilhelm − ∼ bin. VRATi depends on i and increases gradually from (id et al., 2004). Small Y−AaWw ions have a strong pref- +1)/id to a maximum value of VRATmax (1.5 in this study) erence for A-ligands (i.e., higher A-ligand mole fraction), as i (>id ) increases. while small H+AaWw ions have a strong preference for W- ligands (i.e., lower A-ligand mole fraction). In the new IMN
Atmos. Chem. Phys., 6, 5193–5211, 2006 www.atmos-chem-phys.net/6/5193/2006/ F. Yu: Ion-mediated nucleation 5197 model, we parameterized the average A-ligand mole fraction - - a HSO4 (H2SO4)n ---> HSO 4 (H2SO4)n-1 + H2SO4 (AMF= a w ) for the positively charged (AMF+) and nega- + tively charged (AMF−) clusters as Data from Arnold et al., 1982 Data from Arnold and Qiu, 1984 , 0 h , 0 i Data from Froyd and Lovejoy, 2003 AMF+ −(a) AMF (a0) AMF+ −(1) AMF (a0) 25 = + − CKT Equation 2.5 - a0 a MKT Equ. with f = r0 /rn − , a < a0 (1) MKT Equ. with f - = 1 × a0 1 - 2 − MKT Equ. with f =(r0 /rn )
0 (kcal/mol) AMF+(a) AMF−(a) AMF (a), a a0 (2) 15
= = ≥ 0 n, n-1
0 G
where AMF (a) is the A-ligand mole fraction for neutral Δ clusters containing a H2SO4 molecules. In the above pa- rameterizations, it was assumed that charged clusters have (a) the same AMF as neutral ones at a a0. In this study, we use ≥ 5 a0=7 and AMF−(1)=1. AMF+(1) is calculated using ther- 110 modynamic data from Froyd and Lovejoy (2003a, b). n 0 Figure 2 shows AMF+, AMF−, AMF as functions of a under 4 different atmospheric conditions. The black dashed 0 - - lines are AMF calculated using the liquid droplet approxi- HSO4 (H2SO4)n(H2O)m --> HSO4 (H2SO4)n-1(H2O)m + H2SO4 mation as described in Yu (2005b, 2006b). The dot-dashed - m=0, MKT (f =r0 /rn) and dotted lines are AMF+and AMF− computed using pa- m=0, data (Floyd & Lovejoy, 2003b) - rameterizations described above. The pluses (“+”) and mi- m=1, MKT (f =r0 /rn) 25 m=1, data (Floyd & Lovejoy, 2003b) - nuses (“–”) refer to AMF+ and AMF− calculated using m=2, MKT (f =r0 /rn) m=2, data (Floyd & Lovejoy, 2003b) the step-wise water-ion clustering enthalpy and entropy data - m=3, MKT (f =r0 /rn) from Froyd and Lovejoy (2003a, b). In Fig. 2(a), the data m=3, data (Floyd & Lovejoy, 2003b) from Wilhelm et al. (2004) are also shown (Negative ions: (kcal/mol) filled circles; Positive ions: diamonds and triangles). Since 15 0 we found that the AMF+values shown in two figures (Fig. 6 n, n-1 G and Fig. 3) in Wilhelm et al. (2004) are different, both data Δ sets are shown in Fig. 2a. At temperature (T) of 295 K and relative humidity (RH) of 5%, the AMF+ values calculated (b) using Froyd and Lovejoy’s thermodynamic data are close to 5 the set of the data derived from ion mass spectra reported 110 in Wilhelm et al. (2004). However, the AMF− calculated n using thermodynamic data from Froyd and Lovejoy (2003a, b), which does not show the trend to approach AMF0as a Fig. 3. Step-wise Gibbs free energy changes under the stan- 0 increases, are quite different from those presented in Wil- dard condition (1Gn,n 1) for the evaporation of H2SO4 from (a) helm et al. (2004). At this point, it is hard to determine the − HSO4−(H2SO4)n and (b) HSO4−(H2SO4)n(H2O)m. The predic- reason for the difference and the uncertainty in the measure- tions based on traditional CKT equation (Holland and Castleman, ments. Our parameterization should be considered as an ap- 1982) are shown in Fig. 3a only. proximation which may contribute to the uncertainty in the predicted nucleation rates. More data are clearly needed to constrain the model and reduce the uncertainty. At high RH, pressure, etc.) were decided using the bulk liquid droplet ap- there exists difference between the parameterized hydration proximation. of a=1 clusters and the calucations based on experimental data. However, the difference shall have little effect on nu- 2.3 Differential equations cleation as the charge effect dominates the thermodynamics The evolution of three different types of clusters (as shown when clusters are very small (see Sect. 2.4). Figure 2 shows in Fig. 1) is described by the following set of the differential clearly that both AMF and AMF calculated using our own + − equations parameterizations are in reasonable agreement with those ob- served at low RH (Wilhelm et al., 2004) and those calcu- lated using the thermodynamic data from Froyd and Lovejoy (2003a, b) at high RH. At given AMFs, the properties of clus- ters/droplets (density, size, surface tension, saturation vapor www.atmos-chem-phys.net/6/5193/2006/ Atmos. Chem. Phys., 6, 5193–5211, 2006 5198 F. Yu: Ion-mediated nucleation
∂Ci,Y+ δY,Ynucl gi 1,i γi+ 1 Ci+ 1,Y gi,i 1 γi+ Ci,Y+ ∂t = + + + − − i 1 i i 1 i i i X− X 0 X− X X X 0 fj,k,iβj,k+ Cj,Y+ Nk fj,k,iηj,k+ Cj,Y+ Nk+ fj,k,iβj,k+ Nj+Ck,Y , i 1 (3) + j 0 k 1 + j 0 k 0 + j 0 k 1 ≥ ======imax imax imax ! X 0 X X , Ci,Y+ (1 fi,j,i)βi,j+ Nj (1 fi,j,i)ηi,j+ Nj+ αi,j+ −Nj− − j 1 − + j 0 − + j 0 = = =
imax imax imax ! ∂N0+ X 0 X X , Q γ N N β N η N α+ −N (4) ∂t 1+ 1+ 0+ i,j+ j i,j+ j+ 0,j j− = + − j 1 + j 0 + j 0 = = =
∂Ci,Y− δY,Ynucl gi 1,i γi− 1 Ci− 1,Y gi,i 1 γi− Ci,Y− ∂t = + + + − − i 1 i i 1 i i i X− X 0 X− X X X 0 fj,k,iβj,k− Cj,Y− Nk fj,k,iηj,k− Cj,Y− Nk− fj,k,iβj,k− Nj−Ck,Y , i 1 (5) + j 0 k 1 + j 0 k 0 + j 0 k 1 ≥ ======imax imax imax ! X 0 X X , Ci,Y− (1 fi,j,i)βi,j− Nj (1 fi,j,i)ηi,j− Nj− αi,j− +Nj+ − j 1 − + j 0 − + j 0 = = =
imax imax imax ! ∂N0− X 0 X X , Q γ N N β N η N α− +N (6) ∂t 1− 1− 0− i,j− j i,j− j− 0,j j+ = + − j 1 + j 0 + j 0 = = =
∂C0 i,Y 0 0 0 0 δY,Ynucl gi 1,i γi 1 Ci 1,Y gi,i 1 γi Ci,Y (7) ∂t = + + + − − i i 1 i i X X− 0 0 0 X X , fj,k,iβj,kNj Ck,Y fj,k,iαj,k+ −(Nj+Ck,Y− Cj,Y+ Nk−) + j 1 k 1 + j 0 k 0 + = = = = imax imax ! 0 X 0 0 X Ci,Y (1 fi,j,i)βi,j Nj (βj,i+ Nj+ βj,i− Nj−) , i 2 − j 1 − + j 0 + ≥ = =
i i ∂N 0 Xmax Xmax 1 P g γ 0 N 0 γ 0 N 0 (γ N γ N ) (8) ∂t 2,1 2 2 j j j+ j+ j− j− = + + j 2 + j 1 + = = imax imax ! 0 X 0 0 X N1 (1 f1,j,1)β1,j Nj (βj,+1Nj+ βj,−1Nj−) − j 1 − + j 0 + = =
In Eqs. (3)–(8), the superscripts “+”, “–”, “0” refer to bin j with positively charged, negatively charged, and neu- positively charged, negatively charged, and neutral clusters, tral clusters/particles in bin i, respectively. When j=1, βi,j+ , i, j, k C 0 respectively. Subscripts are the bin indexes. i,Y β− , β become the condensation coefficients of H2SO4 3 3 i,j i,j refers to the volume concentration (cm cm− ) of compo- monomers. ηj,k+ and ηj,k− are kernels of the coagulation nent Y (Y=A, W, or X) in the ith bin, while Ni is the num- 3 between charged clusters/particles from bin j with bin k ber concentration (cm− ) of cluster/particles in the bin i. , charged clusters/particles of the like sign. α+ − is the recom- In this study the nucleating species is A (i.e, Y = A). i,j nucl bination coefficient of positively charged clusters/particles γ is the cluster evaporation coefficient. β , β , β0 are i,j+ i,j− i,j in bin i with negatively charged clusters/particles in bin the coagulation kernels of the neutral clusters/particles in , j, while αi,j− + is the recombination coefficient of bin i
Atmos. Chem. Phys., 6, 5193–5211, 2006 www.atmos-chem-phys.net/6/5193/2006/ F. Yu: Ion-mediated nucleation 5199 negatively charged clusters/particles with positively charged H2SO4 vapor concentration over the surface of neutral clus- 0 clusters/particles in bin j. Due to the difference in the ter with radius ri (Yu, 2006b), composition (and mass) of small positively and negatively total ! , , ρ 2σ va charged clusters, α+ − is not equal to α− +for small clus- γ 0 β0 a,s i,j i,j i 1,i total exp 0 (13) ters (i orj< a0). imax is the maximum number of bins in the = ρa kT ri model. Q is the ionization rate and P is the production rate where ρtotal is the total number concentration of H SO of H SO molecules. T is the ambient temperature and k is a,s 2 4 2 4 molecules in the saturated vapor above a flat surface of a so- the Boltzmann’s constant. f is the volume fraction of in- j,k,i lution of the same composition as the cluster composition. termediate particles (volume=vj +vk) partitioned into bin i, total v1 ρa (=N1) is the total number concentration of sulfuric acid as defined in Jacobson et al. (1994). gi 1,i is the vi 1 vi monomers (free + hydrated) in the nucleating system. σ is + = + − volume fraction of intermediate particles of volume vi 1– the surface tension of the binary solution, and va is the acid v partitioned into bin i. δ accounts for the vol-+ 1,Y nucl Y,Y nucl partial molecular volume. The exponential term takes into ume (or mass) of nucleating species (i.e., H2SO4 monomers) account the Kelvin effect. evaporated from the clusters, and is defined as The evaporation coefficients for H2SO4 molecules escap- ing from charged clusters γ + and γ − are calculated using vi /vi 1, if Y Y i i + = nucl the following equation δY,Y (9) nucl = 1, if Y Y , nucl , 0+ − , , 6= γ + − γ CE+ − CE+ − (14) i = i × Thomson × Dipole The change in the volume concentration of organic com- , where γ 0+ −is the evaporation coefficients for neutral ponents (Y=organics) in clusters/particles due to the conden- i clusters of the same size and composition as that of charged sation and evaporation of organic species is calculated using 0 0 0 clusters. At i a0, γ +, γ − , and γ are same, how- the following formulas ≥ i i i ever, their values at i
Atmos. Chem. Phys., 6, 5193–5211, 2006 www.atmos-chem-phys.net/6/5193/2006/ F. Yu: Ion-mediated nucleation 5201
+ + H (H2O)w (H2SO4)s --> H (H2O)w (H2SO4)s-1 +H2SO4 T=270 K 35 (a) w=1 Data from Froyd (2002) 25 CKT Equation + MKT Equ. with f = - r0 /rn (kcal/mol)
0 15 n, n-1 G Δ
5 110 n 35 (b) w=2
Data from Froyd (2002) 25 CKT Equation + MKT Equ. with f = - r0 /rn (kcal/mol) 0 n, n-1 15 G Δ
5 110 n
35 (c) w=3
Data from Froyd (2002) 25 CKT Equation + (kcal/mol) MKT Equ. with f = - r0 /rn 0 n. n-1 15 G Δ
5 110 n
0 Fig. 4. Step-wise Gibbs free energy changes under the standard pressure (1Gn,n 1) for the evaporation of H2SO4 from − H+(H2O)w(H2SO4)n with (a) w=1, (b) w=2, and (c) w=3. Symbols refer to the data from Froyd (2002) and Froyd and Lovejoy (2003a). Solid and dotted lines are the predictions based on MKT equation with f r /rn and CKT equation, respectively. += − 0
Under the conditions given in Fig. 5, there is a nucleation ation rates. In the simulations presented in this section, we barrier for both positive and negative ions. The barrier peak assume a constant N1, T , RH, Q, and surface area of pre- for positive ions is located around i=7, while that for nega- existing particles (S), and solve Eqs. (3)–(8) to obtain the tive ions is located near i 3–4. The nucleation barriers for steady state cluster distribution and nucleation rate. At t=0, =∼ 0 both positive and negative ions vary with T , RH, and N1. only neutral monomers exist (N1 N1), and concentrations of all the other clusters (including= initial core ions) are set to be zero. The pre-existing particles with fixed surface area 3 Simulations and results serve as a sink for all clusters. The condensation of organics is not included in this part. 3.1 Evolution of clusters and nucleation rates Figure 6 shows the evolution of cluster size distribu- tions (dN/dlogDp) for two cases with different N1: (a- 6 3 7 3 The evolution of cluster/particle size distributions can be ob- 1,2,3) N1=5 10 cm− ; (b-1,2,3) N1=1.5 10 cm− . In × × 3 1 tained by solving the dynamic Eqs. (3)–(8). Many practical both cases, T 285 K, RH=75%, Q=5 ion-pairs cm− s− , =2 3 applications require information on the steady state nucle- and S=50 µm cm− . The inserted figures give the size www.atmos-chem-phys.net/6/5193/2006/ Atmos. Chem. Phys., 6, 5193–5211, 2006 5202 F. Yu: Ion-mediated nucleation
(a) Positive and neutral, T=285 K, RH=75% (b) Negative and neutral, T=285 K, RH=75% 2 2 10 10 + γ - γ i , f=r0/rn i , f=-r0/rn β + 7 3 β - N , N =107/cm3 i N1, N1=10 /cm i 1 1 1 γ 0 1 γ 0 10 i 10 i 0 7 3 β 0 7 3 β N , N =10 /cm i N1, N1=10 /cm i 1 1 - + 0 0 -1 γ (γ ) (no charge effect)
( ) (no charge effect) -1 i i - (s )
(s ) γ 0 0 i , f=1
i 10 10 - 2 i γ γ , f=(r /r )
γ i 0 n , 1 , 1 N -1 N -1 i, 1
10 i, 1
β 10 β
--2 --2 10 10
-3 -3 10 10 0 5 10 15 20 25 30 0 5 10 15 20 25 30 i i
7 3 Fig. 5. The growth rates and evaporation coefficients of charged clusters at T =285 K, RH=75%, and N1=10 /cm : (a) positive (βi,+1N1,γi+ 2 with f r /rn) and (b) negative (β− N , γ −with f =1, f r /rn, f =(r /rn) ). The evaporation coefficients and growth rates += − 0 i,1 1 i − −= 0 − 0 0 0 of neutral clusters (γi , βi,1N1) are given in both panels for the comparison. Note that the compositions of small charged/neutral clusters (containing less than 7 H2SO4molecules) are different. The dotted lines are the evaporation coefficients of neutral clusters having the same sizes and compositions as the charged ones.
7 6 distributions at four selected times. The diameter of neu- steady state values of JIMN are 1.5 10− , 4.5 10− , and 3 3 1 × × 3 1 tral critical clusters is 2.18 nm in the case (a) and 1.85 nm in 3.4 10− cm− s− for case (a) and 0.17, 0.54, 1.5 cm− s− × 2 the case (b). The evolution of positively charged, negatively for case (b) with f =(r0/rn) , f r0/rn, f =1, respec- − −= − charged, and neutral clusters can be clearly seen from Fig. 6. tively. In the given conditions, the uncertainty in f − leads Spectra of clusters smaller than 1.5 nm reach the steady to approximately one order of magnitude difference in JIMN state within 5 to 10 min. Due to the∼ existence of growth bar- in the case (b) and about four orders of magnitude differ- riers for both positive and negative ions (see Fig. 5), the con- ence in JIMN in the case (a). It appears that the uncertainty in centration of small positive ions peaks around 1 nm, while JIMN associated with f − is relatively small, when nucleation 3 1 that of the negative clusters peaks around 0.7 nm. This be- rate is large ( 1 cm s ) and becomes larger when JIMN ∼ − − havior of small positive and negative cluster ions is consis- is lower. In the simulations presented below f − r0/rn has tent with recent observations (Laakso et al., 2004; Vana et al., been used. = 2006). Only few clusters grow beyond 1.5 nm in case (a) due The steady state values of JIMN depend on T , RH,N1,Q, to the lower H2SO4 concentration. A significant number of and S. Figure 8 presents JIMN as a function of time under negative ions grow beyond 1.5 nm in case (b), however most nine different combinations of T , RH,N1,Q, andS. Here we of these ions were neutralized before approaching 3 nm in focus on the conditions, which are typical for lower tropo- size. There exists a clearly visible mode of neutral particles sphere (boundary layer). N1 and T are the two most impor- centering around 2–3 nm that resulted from the neutralization tant parameters controlling the particle formation. RH, Q, of charged clusters/particles. Nucleation of negative ions was and S affect the nucleation rates at a lesser degree. For high 8 3 found to be favorable in both cases. N1 (up to 10 cm− in polluted areas such as in the down- The nucleation rates in the second-generation IMN model wind of power plants), IMN can lead to a significant parti- (denoted as JIMN) are calculated based on the net fluxes of cle nucleation even if the ambient temperature T is 290 K. 7 3 ∼ particles across the critical size of neutral clusters (i i*), When N1 is 1.5 10 cm− , T =275 K can lead to high nu- = ∼ × 6 3 0 0 0 0 0 0 cleation rates at RH> 75%. When N1 is 5 10 cm− , JIMN βi,1N1 Ni γi Ni 1 βi,+1N1 Ni+ ∼ ∼ × = ∗ − ∗+ + ∗ T <275 K and RH above 60% lead to a noticeable nucleation 0 γ +N + β− N N − γ −N − (18) 3 1 i i 1 i,1 1 i i i 1 (>0.1 cm− s− ). − ∗+ + ∗ − ∗+ Figure 7 shows JIMN as a function of time corresponding to Based on the simulations performed using the second gen- the cases shown in Fig. 6. For each case, three curves corre- eration IMN we found that ion-mediated nucleation can lead sponding to three different f − (see Fig. 3) are given to show to a significant new particle formation in the lower atmo- the sensitivity of nucleation rates to the thermochemistry of sphere (including boundary layer) under favorable condi- the ion clustering. Our results show that JIMN initially in- tions. Our results are different from the predictions of the ion creases with time, however it reaches a steady-state value nucleation model of Lovejoy et al. (2004), which indicates after 45 min for case (a) and 15 min for case (b). The that the nucleation of H2SO4 (and H2O) on negative ions ∼ ∼
Atmos. Chem. Phys., 6, 5193–5211, 2006 www.atmos-chem-phys.net/6/5193/2006/ F. Yu: Ion-mediated nucleation 5203
Case (a): T285RH75A0.5E7S50Q5 Case (b): T285RH75A1.5E7S50Q5
2 2 5 5 ) 10 3 ) 10 (a-1) Positive (b-1) Positive 3 t= 1 min t= 60 min 4 100 4 100 10 t=120 min 8 10 t= 3 min 8 (#/cm P 6 (#/cm t= 10 min 6
P 3 3 t=120 min 10 4 10 4 2 10 2 10 t= 10 min
2 2 dN/dlogD dN/dlogD 1 t= 30 min 1 10 10 1 10 1 10 10 10 Diameter (nm) 8 Diameter (nm) 8 6 6 4
4 Diameter (nm) Diameter (nm)
2 2
1 1 8 8 6 6
0 20 40 60 80 100 120 0 20 40 60 80 100 120 time (minutes) time (minutes)
2 5 2 5 ) ) 10 10 (a-2) Negative 3 3 t= 60 min (b-2) Negative 100 4 t= 1 min 100 4 t=120 min 8 10 t= 3 min 8 10 (#/cm 6 (#/cm P P 6 10 3 t= 10 min 10 3 4 t=120 min 4 10 2 10 2 t= 10 min 2 t= 30 min dN/dlogD dN/dlogD 2 10 1 10 1 1 10 1 10 10 Diameter (nm) 10 Diameter (nm) 8 8 6 6 4 Diameter (nm) 4 Diameter (nm)
2 2
1 1 8 8 6 6
0 20 40 60 80 100 120 0 20 40 60 80 100 120 time (minutes) time (minutes)
2 2 5
5 ) 10 )
10 (a-3) Neutral 3 (b-3) Neutral 3 t= 1 min t= 60 min 100 4 100 4 t=120 min 8 10 t= 3 min 8 10 (#/cm (#/cm 6 t= 10 min P P 6 10 3 t=120 min 10 3 4 4 2 2 10 10 t= 10 min
2 2 dN/dlogD dN/dlogD t= 30 min 1 10 1 10 1 10 1 10 10 10 Diameter (nm) 8 Diameter (nm) 8 6 6 4
Diameter (nm) 4 Diameter (nm)
2 2
1 1 8 8 6 6
0 20 40 60 80 100 120 0 20 40 60 80 100 120 time (minutes) time (minutes)
0 2 4 6 8 10-2 10 10 10 10 10 dN/dlogDp (#/cm3)
Fig. 6. Evolution of the size distribution (dN/dlogDp) of positive, negative, and neutral clusters for two cases with different N1: (a-1,2,3) 6 3 7 3 3 1 2 3 N1=5 10 cm− ; (b-1,2,3)N1=1.5 x10 cm− . For both cases, T 285 K, RH=75%, Q=5 ion-pairs cm− s− , and S=50 µm cm− . The insert× in each panel gives the size distributions× at four selected times.= does not generally explain the observed nucleation events in by adding empirical terms to Thomson equation that the boundary layer (Modgil et al., 2005). The possible rea- decayed exponentially with cluster size, etc.). In our sons for this deviation are discussed below: model, the thermodynamical properties of ion clusters were calculated using modified Kelvin-Thomson equa- 1. The thermodynamics of ion clusters may be differ- tion, which explicitly takes into account dipole-charge ent. The ion-clustering thermodynamic data used in the interaction and is consistent with ion clustering exper- model by Lovejoy et al. (2004) were obtained via a com- iments for a variety of systems (see Figs. 3–4 in the bination of measurements of small ion clusters, ab initio present paper and Yu, 2005a). calculations, thermodynamic cycle, and approximations (extrapolation of data for small clusters to large clusters www.atmos-chem-phys.net/6/5193/2006/ Atmos. Chem. Phys., 6, 5193–5211, 2006 5204 F. Yu: Ion-mediated nucleation
T=285 K, RH=75%, Q= 5 ion-pairs/cm3s, S=50 μm2/cm3 2 10 7 3 [H2SO4]=1.5x10 /cm , f=1 1 7 3 [H2SO4]=1.5x10 /cm , f=r0/rn 10 7 3 2 [H2SO4]=1.5x10 /cm , f=(r0/rn) 0 10
-1 10 ) -1 s
-3 -2 10
-3 10 6 3 [H2SO4]=5x10 /cm , f=1 -4 6 3 [H2SO4]=5x10 /cm , f=r0/rn 10 6 3 2 [H2SO4]=5x10 /cm , f=(r0/rn) -5 10 Nucleation rate (cm Nucleation rate
-6 10
-7 10
-8 10 0 306090120 time (min)
Fig. 7. Ion-mediated nucleation rates as a function of time corresponding to the cases shown in Fig. 6. For each case, three curves corre- sponding to three different f − are given to show the sensitivity of nucleation rates to ion-clustering thermodynamic parameterizations.
3 10 T285RH75A1.5E7S50Q5 T275RH60A5.0E6S50Q5 2 10 T295RH95A5E7S10Q2 T290RH70A1E8S200Q10 T275RH75A1.5E7S50Q5 1 10
) 0
-1 10 s -3 -1 10
-2 10 CT285RH75A1.0E7S50Q5 CT275RH45A0.5E7S50Q5 -3 10 Nucleation rate (cm Nucleation rate -4 10 T290RH75A1.5E7S50Q5 T285RH75A5.0E6S50Q5 -5 10
-6 10 0 306090120 time (s)
Fig. 8. Ion-mediated nucleation rates as a function of time under nine different combinations of T , RH, N1, Q, and S. Read 7 3 2 3 T285RH75A1.5E7S50Q5 as the case with T of 285 K, RH of 75%, [H2SO4] (or N1) of 1.5 10 cm− , surface area of 50 µm /cm , 3 1 × and ionization rate of 5 ion-pairs cm− s− .
2. There exists some difference in the treatment of positive Fig. 6, which demonstrates the agreement between our ions/clusters. In the model of Lovejoy et al. (2004) pos- model results and recent field measurements (Laakso et itive ions are treated as a single species (initial ions con- al., 2004; Vana et al., 2006), the concentration of small taining no H2SO4) and they are not allowed to grow. In positive ions peaks around 1 nm that corresponds to a our model, clustering of positive ions and interaction of cluster containing 4 H2SO4 molecules. Assumption positive ions of different sizes with negative and neutral that all positive ions∼ are single species containing no clusters was explicitly resolved. As it has been shown in H2SO4 may influence the model predictions given by
Atmos. Chem. Phys., 6, 5193–5211, 2006 www.atmos-chem-phys.net/6/5193/2006/ F. Yu: Ion-mediated nucleation 5205
Lovejoy et al. (2004) in a number of ways. Here we found that organics appear to dominate the growth of nucle- would like to consider two main aspects. First, this as- ated particles in many observed nucleation and growth events sumption may cause the underestimation of the lifetime (Kulmala et al., 2004a, b). of negative ions due to recombination because the re- In Sect. 3.1, [H2SO4] was fixed and organics condensation combination coefficient between two ions decreases sig- was not considered. In this section, we study the evolution nificantly as the sizes of the recombining ions increase. of neutral and charged particles with a time-dependent con- Secondly, this assumption leads to the underestimation centration of H2SO4 and organics. We focus on the coupling of the sizes of neutrals resulted from the recombination between the nucleation and growth processes in the presence of charged clusters. Both aspects lead to an obvious and in the absence of organics. To take into account the di- under-prediction of the nucleation rates. urnal variations of precursor gas concentrations in the atmo- sphere, we parameterized [H2SO4] and [organics] as 3. The thermodynamic data used for H2SO4-H2O binary 2 system may be different. Lovejoy et al. (2004) used [H2SO4 [H2SO4max sin π(t 4)/12, 16 t 4 (19) the vapor pressures calculated with the On-Line Aerosol = − ≥ ≥ 0.5 organics organicsmax sin π(t 6)/12, 18 t 6 (20) Inorganics Model (Carslaw et al., 1995) and the pa- = − ≥ ≥ rameterizations of the density from Perry and Chilton where t is the local time (hour). [H SO ] (1973) and surface tension from Sabinina and Terpu- 2 4 max and [organics] are the peak concentrations of gow (1935). In order to make the nucleation rates pro- max [H SO ] and [organics], respectively. The mini- duced by their model consistent with the experimen- 2 4 mum concentrations of H SO and organics are as- tal results of Ball et al. (1999), Lovejoy et al. (2004) 2 4 sumed to be 5 105 cm 3 and 5 106 cm 3, respec- added empirical terms, 4exp(-a/5) and 5exp(-w/5) (units − − tively. The time-dependent× concentrations× of H SO of kcal/mol), to their liquid droplet Gibbs free energies 2 4 and organics with [H SO ] =1.5 107 cm 3 and associated with the addition of H SO and H O, re- 2 4 max − 2 4 2 [organics] =5 107 cm 3, which are× used to run the spectively, to (H SO ) (H2O) clusters. These terms max − 2 4 a w model, are shown× in Fig. 9. It is important to note that systematically decrease the bonding energies of H SO 2 4 [H SO ] and [organics] and their variations may be different and H O and reduce the nucleation rates (Lovejoy et 2 4 2 in different locations/days and Fig. 8 represents one of the al., 2004). While the empirical term may improve the possible scenarios. agreement of model predictions with experimental re- The evolutions of the size distribution of positively sults under the laboratory conditions, there is no physics charged, negatively charged, neutral, and total clus- behind the terms that will ensure their validity at other ters/particles with [H SO ] variations as described in Fig. 9 temperature. In our model, the saturation vapor pressure 2 4 are shown in Fig. 10: without (a-1,2,3,4) and with (b- over the binary system is calculated using the recent pa- 1,2,3,4) organics condensation. To focus our investigation rameterization of Taleb et al. (1996) with the pure acid on the effect of the precursor gas concentration, we as- saturation vapor pressure given by Noppel et al. (2002), sume a constant T of 280 K and RH of 50% during the and the bulk cluster density and surface tension are cal- period of the simulation. The organic species is assumed culated using the most recently updated parameteriza- to have a saturation pressure of 2.5 106 cm 3, molecular tions of Vehkamaki et al. (2002). No adjustments were − weight of 200 g/mol, density of 1.2 g× cm 3, and surface ten- made to these parameterizations. Our kinetic H SO - − 2 4 sion of 30 erg cm 2. The surface area of pre-existing parti- H O binary homogeneous nucleation (BHN) model pre- − 2 cles is 50 µm2 cm 3. The evolution of small clusters that dicts BHN rates within with the uncertainty range of the − lead, as∼ [H SO ] increases, to the nucleation and growth of laboratory measurements (Yu, 2005b, 2006b). The dif- 2 4 nanoparticles is demonstrated in Fig. 10. Under the con- ference in the thermodynamics of neutral clusters may dition studied here the concentration of small positive ions have significant impacts on the ion nucleation rates be- peaks around 1 nm, while that of negative ions peak around cause the thermodynamics of ionic clusters depends on 0.7 nm when [H SO ]> 2 106 cm 3. When [H SO ] is that of neutral ones (see for example Eq. 14) and the sta- 2 4 − 2 4 very low (<2 106 cm 3∼in× this case), initial core ions are bility of neutral clusters formed via the recombination is − most abundant.× In the atmosphere, other species (such as critically important. HNO3, NH3, organic compounds, etc) may also be involved 3.2 Nucleation coupled with growth in the formation of small ions, especially when [H2SO4] is low. A mode of negative ions between 1–3 nm is clearly vis- In the atmosphere, the nucleation and growth processes are ible during the nucleation period, while there is no such a coupled. The freshly nucleated particles are typically 2 nm mode in the size spectrum of the positive ions. The nucle- or smaller in size; however it has been frequently observed∼ ation on negative ions is obviously more favorable in such that these particles can grow to the sizes of cloud condensa- conditions. There exists a pool of neutral clusters/particles tion nuclei within a day (Kulmala, 2003; Stanier et al., 2004; smaller than 3 nm, which resulted from the recombination Zhang et al., 2004a; Wehner et al., 2005). It has also been of oppositely∼ charged cluster ions. Without the condensation www.atmos-chem-phys.net/6/5193/2006/ Atmos. Chem. Phys., 6, 5193–5211, 2006 5206 F. Yu: Ion-mediated nucleation
5e+07
[Organics] 4e+07 ) -3
3e+07
2e+07 [H2SO4]
gas concentration (cm gas concentration 1e+07
0 4 6 8 10 12 14 16 18 local time (hr)
7 Fig. 9. Time-dependent concentrations of H2SO4 and organics assumed in our simulations with [H2SO4]max=1.5 10 cm-3 and 7 3 5 3 × 6 3 [organics]max=5 10 cm− . The minimum concentrations of H2SO4 and organics are assumed to be 5 10 cm− and 5 10 cm− , re- spectively. × × ×
of organics, the specified [H2SO4] result in growth of the needed to reach the equilibrium may be longer than the clus- freshly nucleated particles to 10 nm. However, in the pres- ter/particle growth time. CFs of both positive and negative ence of organics (see Fig. 9) the∼ nucleated particles grow to can be readily calculated in our new IMN model, which sim- 30–80 nm. Due to the Kelvin effect, organics can condense ulates the size distributions of positive, negative, and neutral only if particles are larger than 3 nm in size. A small mode clusters/particles explicitly. of particles between 2 and 3 nm∼ in Fig. 10b-3 is a result of Figure 12 shows the evolution of CFs for the case corre- the evaporation of neutral clusters smaller than 2 nm (criti- sponding to Fig. 10b (with organics): (a) positive, (b) neg- cal size of neutral clusters around 2 nm) and the activation of ative. As can be seen from Fig. 12, there exists a minimum clusters larger than 3 nm by organics condensation. The acti- CF of 2–3% during the nucleation period. The diameter ∼ vation diameter for organics depends on the super-saturation (dm) of minimum CF is 2.5–7 nm for positive and 4–8 nm ratio and Kelvin effect and it may be as small as 2 nm un- for negative ions, respectively.∼ The minimum is formed∼ due der some conditions (Kerminen et al., 2004). The∼ obvious to the neutralization of nanoparticles nucleated on ions and gap in the number size distributions of positive and negative an increase in the charging probability with increasing par- ions/particles shown in Fig. 10b-1, 2 is associated with the ticle size. Another important feature is the charge asymme- activation of particles/cluster by organics and neutralization try for particles smaller than 4 nm. Particles from the size of charged nucleated particles. range between 2 and 4 nm are∼ significantly negatively over- In our model, the compositions of clusters /particles have charged (i.e., the charged fraction is much higher than that been resolved. Fig. 11 shows the evolution of particle mass in the equilibrium state) while they are only slightly posi- size distributions for the case corresponding to Fig. 10b: (a) tively overcharged. Most of the particles between 1.5–2 nm H2SO4, (b) Organics. The dry volume of initial pre-existing are negatively charged, while most of the particles between particles is assumed to be composed of 50% H2SO4 and 1–1.5 nm are positively charged. Under the specific condi- 50% organics. It may be seen clearly from Fig. 11 that or- tions simulated here, the nucleation on negative ions is pre- ganics contribute to the mass of particles larger than 3 nm. ferred. The existence of a minimum CF 4–6 nm (with CF ∼ Moreover, the composition of nucleated particles larger than of 2–3%) and charge asymmetry for particles smaller than ∼ 10 nm is dominated by the organics. 4 nm in size are consistent with the measurements (Vana et ∼ al.,∼ 2006). 3.3 Size-dependent charging state of nanoparticles during Our simulations indicate that while ions play an important nucleation/growth events role in the new particle formation, the nucleated particles loss their memory of ions (i.e., carrying a charge) after they grow The aerosol particles in the atmosphere generally have an to a certain size (dm) due to the recombination. The values of equilibrium charge distribution due to the diffusion of small dm depend on the concentrations of precursor gases, concen- ions to the particles. The equilibrium charged fraction (CF, trations and sizes of small ions, surface area of pre-existing concentration of positively or negatively charged particles particles, and ambient conditions (T , RH). Systematic inves- divided by total particle concentration in the size range) of tigation of CF distributions under a variety of atmospheric particles decreases as particle size decreases. The nucle- conditions will be carried out in the future. ation and growth events may disturb the equilibrium charge distribution of nanoparticles because a characteristic time
Atmos. Chem. Phys., 6, 5193–5211, 2006 www.atmos-chem-phys.net/6/5193/2006/ F. Yu: Ion-mediated nucleation 5207
(a) without organics (b) with organics 1000 1000 (a-1) Positive (b-1) Positive
100 100
10 10 Diameter (nm) Diameter (nm)
1 1
4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 18 1000 1000 (a-2) Negative (b-2) Negative
100 100
10 10 Diameter (nm) Diameter (nm)
1 1
4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 18 1000 1000 (a-3) Neutral (b-3) Neutral
100 100
10 10 Diameter (nm) Diameter (nm) 1 1
4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 18 1000 1000 (a-4) total (positive+negative+neutral) (b-4) total (positive+negative+neutral)
100 100
10 10 Diameter (nm) Diameter (nm)
1 1
4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 18 local time (hours) local time (hours)
0 1 2 3 4 10 10 10 10 10 105 dN/dlogDp (#/cm3 )
Fig. 10. The size distribution evolutions of positively charged, negatively charged, neutral, and total clusters/particles with [H2SO4] varia- tions as described in Fig. 9: (a) without organics condensation; (b) with organics condensation.
In recent years, advanced instruments to measure charged ions in the atmospheric nucleation. The observed (both neg- sub-nanometer and fine nanometer particles in the atmo- ative and positive) overcharge of particles smaller than 4– spheric air have been developed by Tammet (e.g., 2006) 5 nm clearly indicates that ions can lead to the nucleation∼ in and they have been employed in a number of the field stud- boundary layer atmosphere, that agrees well with our model ies (e.g, Laakso et al., 2004; Vana et al., 2006; Iida et al., prediction. Detailed comparisons of the observed evolutions 2005). Simultaneous measurements of the size distribution of the ion mobility and particle size spectrums during nucle- of charged and total particles during the nucleation events ation events (Laakso et al., 2004; Vana et al., 2006; Iida et al., give the charging fraction of freshly nucleated particles, and 2005) with the predictions of our model shall provide useful such measurements provide very useful information about insights about the mechanisms of new particle formation. the nucleation mechanisms in terms of the involvement of www.atmos-chem-phys.net/6/5193/2006/ Atmos. Chem. Phys., 6, 5193–5211, 2006 5208 F. Yu: Ion-mediated nucleation
1000 1000 (a) (b)
100 100
10 10 Diameter (nm) Diameter (nm)
1 1
4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 18 hour of day hour of day
-7 -4 -3 -2 0 10 10-6 10 -5 10 10 10 10-1 10 101 dM/dlogDp (microgram/m 3 )
Fig. 11. Evolution of particle mass size distributions for the case corresponding to Fig. 10b: (a) H2SO4, (b) Organics.
1000 1000 6 (a) positive 6 (b) negative 4 4 2 2 100 100 6 6 4 4 2 2 Diameter (nm) Diameter (nm) 10 10 6 6 4 4 2 2 1 1 4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 18 local time (hours) local time (hours)
0.1 0.3 1 310 30 100 Charged Fraction (%)
Fig. 12. Evolution of the fractions of the charged particles for the case corresponding to Fig. 10b (with organics): (a) positive, (b) negative.
4 Summary and discussion The fraction of positively and negatively charged particles as a function of particle sizes can be calculated using our new A clear and insightful understanding of the secondary aerosol model. formation in the atmosphere remains to be achieved. In The specific features of the spectra of small positive and recent years there is an increasing interest in the nucle- negative ions were successfully predicted by the new IMN ation involving ions. In this paper we present a new sec- model. The peak concentration of positive ions at 1 nm and ∼ ond generation ion-mediated nucleation model that treats the peak concentration of negative ions at 0.7 nm, as well as the ∼ evaporation of neutral/charged clusters explicitly and solves sign preference, were predicted by our new model in agree- the evolutions of the sizes and compositions of positively ment with the observations. Our results suggest that IMN charged, negatively charged, and neutral clusters/particles can lead to a significant new particle formation in the lower ranging from molecules to large particles of few micrometers atmosphere (including boundary layer) under favorable con- in size. Schemes to calculate the evaporation coefficients of ditions. Our results are different from predictions of Lovejoy small neutral and charged clusters were shown to be con- et al. (2004) which suggest that that the nucleation of H2SO4 sistent with experimental data. The new model explicitly (and H2O) on negative ions does not generally explain the accounts for the difference in the composition and thermo- observed nucleation events in the boundary layer. The possi- dynamics of small positive and negative ions. The second ble reasons for the difference include the different thermody- generation IMN model enables us to simulate in detail the namic data used for H2SO4-H2O binary system, the differ- evolution of small charged/neutral and the coupling of the ence in the treatment of positive ions/clusters, and different nucleation with growth. The condensation of low volatile or- thermochemistry of ion clustering. ganics and sulfuric acid on the nucleated particles were sim- Our simulations of charged particle fraction as a func- ulated and composition of the grown particles was obtained. tion of the particle size during nucleation and growth events
Atmos. Chem. Phys., 6, 5193–5211, 2006 www.atmos-chem-phys.net/6/5193/2006/ F. Yu: Ion-mediated nucleation 5209 indicate the existence of a minimum charging fraction at par- Clarke, A. D., Davis, D, Kapustin, V. N., et al.: Particle nucleation ticle size 2.5–7 nm for positive and 4–8 nm for negative in the tropical boundary layer and its coupling to marine sulfur ionic clusters.∼ The value of the minimum∼ CF is 2–3%. The sources, Science, 282, 89–92, 1998. minimum is due to the neutralization of nanoparticles∼ nucle- Coffman, D. J. and Hegg, D. A.: A preliminary study of the effect ated on ions and the increase of the charging probability with of ammonia on particle nucleation in the marine boundary layer, the particle size. The charge asymmetry for particles smaller J. Geophys. Res., 100, 7147–7160, 1995. Eichkorn, S., Wilhelm, S., Aufmhoff, H., Wohlfrom, K. 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