Growth of sulphuric acid nanoparticles under wet and dry conditions

New particle formation, which greatly influences the number concentrations and size distributions of an atmospheric aerosol, is often followed by a rapid growth of freshly formed particles. The initial growth of newly formed aerosol is the crucial process determining the fraction of nucleated particles growing to cloud condensation nuclei sizes, which have a significant influence on climate. In this study, we report the laboratory observations of the growth of nanoparticles produced by nucleation of H 2SO4 and water in a laminar flow tube at temperatures of 283, 293 and 303 K, under dry (a relative humidity of 1 %) and wet conditions (relative humidity of 30 %) and residence times of 30, 45, 60 and 90 s. The initial H2SO4 concentration spans the range from 2× 108 to 1.4× 1010 molecule cm−3 and the calculated wall losses of H2SO4 were assumed to be diffusion limited. The detected particle number concentrations, measured by the Ultrafine Condensation Particle Counter (UCPC) and Differential Mobility Particle Sizer (DMPS), were found to depend strongly on the residence time. Hygroscopic particle growth, presented by growth factors, was found to be in good agreement with the previously reported studies. The experimental growth rates ranged from 20 nm h −1 to 890 nm h−1 at relative humidity (RH) 1 % and from 7 nm h −1 to 980 nm h−1 at RH 30 % and were found to increase significantly with the increasing concentration of H 2SO4. Increases in the nucleation temperature had a slight enhancing effect on the growth rates under dry conditions. The influence of relative humidity on growth was not consistent – at lower H 2SO4 concentrations, the growth rates were higher under dry conditions while at H2SO4 concentrations greater than 1 × 109 molecule cm−3, the growth rates were higher under wet conditions. The growth rates show only a weak dependence on the residence time. The experimental observations were compared with predictions made using a numerical model, which investigates the growth of particles with three different extents of neutralization by ammonia, NH 3: (1) pure H2SO4 – H2O particles; (2) particles formed by ammonium bisulphate, (NH4)HSO4; (3) particles formed by ammonium sulphate, (NH4)2SO4. The highest growth rates were found for ammonium sulphate particles. Since the model accounting for the initial H2SO4 concentration predicted the experimental growth rates correctly, our results suggest that the commonly presumed diffusional wall losses of H 2SO4 in case of ong-lasting experiments are not so significant. We therefore assume that there are not only losses of H 2SO4 on the wall, but also a flux of H2SO4 molecules from the wall into the flow tube, the effect being more profound under dry conditions and at higher temperatures of the tube wall. Based on a comparison with the atmospheric observations, our results indicate that sulphuric acid alone cannot explain the growth rates of particles formed in the atmosphere. Published by Copernicus Publications on behalf of the European Geosciences Union. 6462 L. Skrabalova et al.: Growth of sulphuric acid nanoparticles under wet and dry conditions

Abstract.New particle formation, which greatly influences the number concentrations and size distributions of an atmospheric aerosol, is often followed by a rapid growth of freshly formed particles.The initial growth of newly formed aerosol is the crucial process determining the fraction of nucleated particles growing to cloud condensation nuclei sizes, which have a significant influence on climate.In this study, we report the laboratory observations of the growth of nanoparticles produced by nucleation of H 2 SO 4 and water in a laminar flow tube at temperatures of 283, 293 and 303 K, under dry (a relative humidity of 1 %) and wet conditions (relative humidity of 30 %) and residence times of 30, 45, 60 and 90 s.The initial H 2 SO 4 concentration spans the range from 2 × 10 8 to 1.4 × 10 10 molecule cm −3 and the calculated wall losses of H 2 SO 4 were assumed to be diffusion limited.The detected particle number concentrations, measured by the Ultrafine Condensation Particle Counter (UCPC) and Differential Mobility Particle Sizer (DMPS), were found to depend strongly on the residence time.Hygroscopic particle growth, presented by growth factors, was found to be in good agreement with the previously reported studies.The experimental growth rates ranged from 20 nm h −1 to 890 nm h −1 at relative humidity (RH) 1 % and from 7 nm h −1 to 980 nm h −1 at RH 30 % and were found to increase significantly with the increasing concentration of H 2 SO 4 .Increases in the nucleation temperature had a slight enhancing effect on the growth rates under dry conditions.The influence of relative humidity on growth was not consistent -at lower H 2 SO 4 concentrations, the growth rates were higher under dry conditions while at H 2 SO 4 concentrations greater than 1 × 10 9 molecule cm −3 , the growth rates were higher under wet conditions.The growth rates show only a weak dependence on the residence time.The experimental observations were compared with predictions made using a numerical model, which investigates the growth of particles with three different extents of neutralization by ammonia, NH 3 : (1) pure H 2 SO 4 -H 2 O particles; (2) particles formed by ammonium bisulphate, (NH 4 )HSO 4 ; (3) particles formed by ammonium sulphate, (NH 4 ) 2 SO 4 .The highest growth rates were found for ammonium sulphate particles.Since the model accounting for the initial H 2 SO 4 concentration predicted the experimental growth rates correctly, our results suggest that the commonly presumed diffusional wall losses of H 2 SO 4 in case of long-lasting experiments are not so significant.We therefore assume that there are not only losses of H 2 SO 4 on the wall, but also a flux of H 2 SO 4 molecules from the wall into the flow tube, the effect being more profound under dry conditions and at higher temperatures of the tube wall.Based on a comparison with the atmospheric observations, our results indicate that sulphuric acid alone cannot explain the growth rates of particles formed in the atmosphere.

Introduction
Aerosol particles influence the global radiative balance and climate directly by scattering and absorbing solar radiation and indirectly by acting as condensation cloud nuclei (Charlson et al., 1992).New particle formation through the photochemical reactions of gaseous species significantly influences the number concentrations and size distributions of atmospheric aerosol.Also, aerosol models suggest that atmospheric nucleation is very likely a major source of aerosol particles in the global atmosphere (Spracklen et al., 2006) and that it is also a significant source of cloud condensation nuclei (Spracklen et al., 2008;Merikanto et al., 2009).Several mechanisms of new particle formation have been proposed, including the binary homogeneous nucleation of water and sulphuric acid (Vehkamäki et al., 2002), ternary homogeneous nucleation of water, sulphuric acid and ammonia or amines (Ball et al., 1999;Korhonen et al., 1999;Benson et al., 2009;Berndt et al., 2010;Kirkby et al., 2011), ioninduced nucleation (Lee et al., 2003;Lovejoy et al., 2004;Yu et al., 2010;Kerminen et al., 2010;Hirsikko et al., 2011) and homogeneous nucleation involving iodine species (Kulmala, 2003;O'Dowd et al., 2002b).However, it still remains unclear which mechanism is dominant in the atmosphere (Kulmala et al., 2004b), mainly because the preferred new particle formation mechanism depends on the atmospheric conditions and geographical location.Our current inability to quantify new particle formation correctly results in huge uncertainties in the assessment of the direct and indirect effects of aerosols on climate change in the climatic models (Spracklen et al., 2006;Merikanto et al., 2009).
Atmospheric nucleation is often followed by a rapid growth of freshly formed particles.The initial growth of newly formed aerosol is the crucial process determining the fraction of nucleated particles growing to cloud condensation nuclei sizes (∼ 50 nm and larger) and hence subsequently participating in cloud formation processes (Dusek et al., 2006;Andreae and Rosenfeld, 2008;Kulmala and Kerminen, 2008).The majority of particle growth rates observed during atmospheric measurements lies in the range of 1-10 nm h −1 , indicating that it takes about 12-72 h before the nucleated particles grow to cloud condensation nuclei sizes (Kulmala and Kerminen, 2008).Many recent studies have suggested that sulphuric acid plays a key role in the atmospheric nucleation and subsequent growth of newly formed particles (Sipilä et al., 2010;Brus et al., 2011a;Kirkby et al., 2011).Growth rates based entirely on the condensation of sulphuric acid vapour greatly underestimate the growth rates observed in atmospheric measurements (Sihto et al., 2006;Nieminen et al., 2010), mainly because low-volatile organic species are responsible for up to 90 % of the observed growth (Mäkela et al., 2001;Smith et al., 2008).Although the growth of freshly formed particles has been intensively studied for a long time, the exact mechanism is still not well understood.
The processes governing the growth of particles in a nucleation-mode size range are condensation, selfcoagulation and coagulation scavenging (Leppä et al., 2011).After formation, the particles grow by multiple condensations of different organic and inorganic vapours (Kulmala, 2003).The condensation rate of different chemical species is influenced by the Kelvin effect, which increases the equilibrium vapour pressure with decreasing particle size and increasing molar volume of the condensing compound.According to the nano-Köhler theory (Kulmala et al., 2004a), the non-volatile and low-volatile compounds are responsible for the initial growth of freshly formed particles, and the condensation of more volatile components increases with increasing particle size (Zhang et al., 2004).Self-coagulation -coagulation between particles in the same size mode -increases the mean diameter and decreases the particle number concentration in this mode.Unless the number concentration of freshly formed particles is 1 × 10 6 cm −3 or higher, self-coagulation is only a minor contributor to the initial growth of nucleation-mode particles (Kulmala and Kerminen, 2008).The coagulation scavenging of nucleation-mode particles with pre-existing larger particles results in a decrease of the total particle number concentration and an increase of the diameter describing the whole aerosol population.The growth of nucleation-mode particles due to coagulation scavenging is thus only apparent because none of the particles in this mode grow larger (Leppä et al., 2011).
There are several methods to determine the particle growth rates from the atmospheric particle size distribution measurements.A data analysis method based on the fitting of the aerosol general dynamic equation to the particle size distributions has recently been introduced (Kuang et al., 2012).This approach enables, for the first time, the decoupling of the size and time dependence of particle growth rates.The growth rate of sub-3 nm particles can be determined from the time lag between the increase of the concentration of sulphuric acid and the particles in the sub-3 nm size range (Weber et al., 1997;Sihto et al., 2006).The maximum concentration method (Hirsikko et al., 2005) is based on investigating spectra from air ion spectrometer, in which the timing of maximum concentration in each size fraction is followed.Another method is based on the temporal evolution of the geometric mean diameters of the nucleation-mode particles, which are determined by fitting a log-normal function to the obtained particle size distributions.To determine the growth rate, a first-order polynomial is subsequently fitted to the geometric mean diameters of the nucleation mode during the new particle formation event (dal Maso et al., 2005).In laboratory studies, kinetic models or methods based on the temporal evolution of the geometric mean diameters of the measured particle size distributions are mainly used to determine the growth rates of particles formed during nucleation experiments (Young et al., 2008).
In this paper, we present the results of a laboratory study of the growth behaviour of sulphuric acid nanoparticles produced by nucleation of H 2 SO 4 and water under wet and dry conditions.A variety of experimental conditions have been studied to assess the effect of temperature, relative humidity, residence time and H 2 SO 4 concentration on the growth of freshly nucleated particles.The growth of the particles was calculated using a zero dimensional model, which was designed to simulate the processes governing the initial steps of particle growth and accounts for the condensation of sulphuric acid as well as the uptake of water and ammonia by the particles.Furthermore, three different extents of neutralization of the particles by ammonia and their growth were investigated: pure sulphuric acid-water particles, particles corresponding to an ammonium bisulphate solution and particles corresponding to an ammonium sulphate solution.The comparison of the particle growth rates determined from the different modifications of the model, as well as an analysis of the growth rates as a function of different experimental conditions is presented here.

Methods
The growth behaviour of sulphuric acid nanoparticles produced by the nucleation of sulphuric acid and water vapour was studied.The nucleation experiments were carried out in a laminar flow tube at the Finnish Meteorological Institute, Helsinki, Finland.The detailed description of the flow tube and the operational principle has been presented and discussed in detail by Brus et al. (2010) and Neitola et al. (2013).

Measurements and experimental set-up
The experimental set-up consists of four major parts -the saturator, mixing unit, a flow tube and particle detection device (Fig. 1).Sulphuric acid vapour was produced from a liquid reservoir by passing a stream of carrier gas through a saturator filled with high purity H 2 SO 4 (97 wt%, Baker Analyzed).The saturator was an iron cylinder (I.D. (inner diameter) 6 cm) with Teflon insert inside.It was placed horizontally and thermally controlled using a liquid circulating bath (Lauda RC6).The temperature of the saturator was measured with a probe (PT100) just above the liquid surface.Dry, purified and particle-free air served as the carrier gas in this study.The carrier gas flow was kept at the same temperature as the saturator in order to ensure stable temperature.
Another stream of the carrier gas was dry or saturated with water vapour by passing through a set of Nafion humidifiers (MH-050, Permapure, USA).Both streams were introduced into a mixing unit and then the mixed gas stream flowed through the tube, where particles nucleated and grew to detectable sizes.The flow tube was a 200 cm long vertical cylinder (I.D. 6 cm) made of stainless steel.The tube was thermally controlled with a liquid circulating bath (Lauda RC 6) to ensure stable temperature.At the outlet of the flow tube, the number concentrations of the produced particles were measured using an Ultrafine Condensation Particle Counter (UCPC, Model 3776, TSI Inc., USA).The same modification to UCPC TSI 3776 has been done previously, as described in Brus et al. (2010), to obtain a d 50 cut-off of 2.25 nm.The saturator temperature was increased from a nominal 39 • C up to 40 • C, and the condenser temperature was decreased from a nominal 10 • C down to 8 • C. At these new temperatures no homogenous nucleation was observed inside the counter.Particle size distributions were measured using a Differential Mobility Particle Sizer (DMPS) with a short HAUKE-type Differential Mobility Analyzer (DMA), a bipolar radioactive 63 Ni neutralizer and UCPC (Model 3025A, TSI Inc., USA).
The measurements were performed at relative humidities of ∼ 1 % and ∼ 30 %, presented here as dry and wet conditions respectively.The flow tube was kept at constant temperature during the measurements and the nucleation temperatures investigated were 283, 293 and 303 K.The relative humidity was measured by a humidity sensor (Vaisala HMI38) and temperature by a probe (PT100).Both lines of purified and particle-free air (saturator and mixing flow) were controlled by a mass flow rate controller to within ±3 % (MKS type) (Brus et al., 2010).The total gas flow inside the tube was maintained to provide four residence times in the tube: 30, 45, 60 and 90 s.
The temperature of the H 2 SO 4 saturator was increased stepwise in seven increments of 5 K during each measurement, resulting in a gradually growing concentration of sulphuric acid in the flow tube.In order to determine the number concentration of gas-phase H 2 SO 4 in the tube, the saturation vapour pressure of H 2 SO 4 in the saturator was calculated first using the following equation (Kulmala and Laaksonen, 1990): where p SA is the saturation vapour pressure (atm) of H 2 SO 4 at a temperature of T (K), p SA,0 is the saturation vapour pressure of H 2 SO 4 at the temperature T 0 = 360 K (Ayers et al., 1980), H v is the enthalpy of vaporization, T is the temperature of the saturator and T c is the critical temperature (T c = 905 K).Equation ( 1) is commonly used in studies of binary or ternary nucleation theories and in their parameterizations (Vehkamäki et al., 2002;Merikanto et al., 2007).Also, its ac- The wall losses of H 2 SO 4 in the flow tube were assumed to be a diffusion-controlled first-order rate process, which can be described by a simple equation given by Hanson and Eisele (2000): where [H 2 SO 4 ] 0 is the initial concentration of H 2 SO 4 , [H 2 SO 4 ] t is the concentration after time t and k is the rate constant given by the equation, where r is the radius of the flow tube and D is the RH-dependent diffusion coefficient of H 2 SO 4 (Hanson and Eisele, 2000).The diffusion coefficient D for dry conditions is D dry = 0.376 cm 2 s −1 and for wet conditions D wet = 0.319 cm 2 s −1 .In our experiment, k was 0.0381 s −1 for dry conditions and k was 0.0323 s −1 for wet conditions.In the work of Neitola et al. (2013), who used the same setup and comparable experimental conditions, the maximum condensational losses of sulphuric acid were estimated to be 1.4 %.Therefore condensational losses of sulphuric acid were neglected in further analysis in this study.
Although no measurement of the NH 3 concentration was done during the experiments, NH 3 is assumed to be present in the system (Brus et al., 2011a;Neitola et al., 2013).Since NH 3 and other chemical species are ubiquitous in the ambient environment, the presence of these compounds at low concentrations cannot be excluded in the case of laboratory measurements (e.g.Benson et al., 2011, Kirkby et al., 2011).The nucleated sulphuric acid nanoparticles in our experiments are thus partially neutralized to (NH 4 ) 2 SO 4 and (NH 4 )HSO 4 during the measurements.The extent of the partial neutralization depends on the particle size and relative humidity, and is highest for the smallest particles and highest relative humidities (Biskos et al., 2009).In our previous study with similar set-up (Neitola et al., 2013), the concentration of ammonia was measured with the MARGA system (ten Brink et al., 2007).The average NH 3 concentrations were 60 pptv under dry conditions and 126 pptv under wet conditions.These concentrations did not change with the increasing temperature of the saturator and thus the NH 3 is assumed to originate from the carrier gas and from the ultrapure water used to humidify the mixing flow.Similar results were already reported earlier by Benson et al. (2011).
The DMPS detected particles in the size range from 3 to 200 nm with a time resolution of 12 min.The uncertainties of the measured particle mode diameters were estimated to be 10 % based on a comparison of the DMPS used with a standard one (Wiedensohler et al., 2012).The raw DMPS data were inverted to yield the number size distributions of the formed particles.The charging efficiencies were calculated using the parameterization of Wiedensohler and Fissan (1991).The obtained number size distributions were then fitted with the log-normal distribution and the geometric mean diameter of the nucleation mode was determined.The particle growth rates were then obtained from the change of the modal geometric mean as a function of time.

Model description
The particle growth inside the laminar flow tube was simulated with a zero dimensional model that accounts for the condensation of sulphuric acid as well as uptake of water and ammonia by the particles.The former process was modelled dynamically by calculating the mass transfer rate of sulphuric acid onto the particles, I SA (molecule s −1 ), using the Fuchs-Sutugin equation (Fuchs and Sutugin, 1970): FS(α, Kn) = 1 + Kn Here d p is the particle diameter (m), D SA is the diffusion coefficient (m 2 s −1 ), α is the mass accommodation coefficient of sulphuric acid, C SA is the gas-phase concentration of sulphuric acid (molecule cm −3 ) and C SA,sat is the number concentration of sulphuric acid at the saturation vapour pressure (molecule cm −3 ).Moreover, FS (α, Kn) is the socalled Fuchs-Sutugin correction factor which accounts for non-continuum effects in the mass transfer, and c SA (ms −1 ) is the mean molecular speed of sulphuric acid molecules in the gas phase.Here the value of C SA was taken from the measurements, and C SA,sat was set as equal to zero, corresponding to the assumption that sulphuric acid behaves as a non-volatile vapour.This assumption is reasonable for systems that contain ammonia (e.g.Kulmala et al., 2000).Finally, the value of α was set as equal to unity based on the measurements conducted by Hanson (2005).
The uptake of the considered semi-volatile compounds, ammonia and water, was modelled as follows.First, since there were no direct measurements of the ammonia concentration levels in the system, we applied three different degrees of particle neutralization: (1) no ammonia was assumed to be taken up by the aerosols, (2) ammonia was assumed to condense along with sulphuric acid so that a 1 : 1 molar ratio was maintained between ammonia and sulphuric acid, corresponding thus to an ammonium bisulphate solution, and (3) two ammonia molecules were assumed to condense for each acid molecule which corresponds to an ammonium sulphate solution.The particles were assumed to be aqueous regardless of the relative humidity, and the particle water content was calculated as a function of the water activity (a w ) using the appropriate molality data found in the literature (Staples, 1981 for sulphuric acid; Tang and Munkelwitz, 1994 for ammonium-bisulphate and ammonium-sulphate).Here the water activity a w was calculated according to the relation a w = RH/Ke where RH is the relative humidity in the instrument and Ke is the Kelvin term (Seinfeld and Pandis, 1998).Finally, the particle surface tension and density were calculated using the model presented by Hyvärinen et al. (2005).
The initial particle diameter d init (corresponding to the median diameter obtained from fitting of DMPS size distributions obtained from measurement at the lowest temperature of the saturator) was taken from the measurements, and the initial chemical composition was set so that the particles were in equilibrium with respect to water and ammonia.The increase of the particle diameter as a function of the increasing sulphuric acid concentration (temperature of the saturator) was then simulated.Also, the particle size was increased after each time step by first converting the total particle mass (obtained as described above) to a corresponding volume and further to a diameter d p by assuming that the particles are spherical.At the end of the simulation, the "effective" growth rate of particles over the experiment, GR, was calculated as follows: where d p is the particle diameter at the end of the experiment and t exp is the residence time in the laminar flow tube.The applied time step was 0.1 s in all of the performed calculations.

Reproducibility of the measurements
The reproducibility of the performed measurements is illustrated in Figs.2a and b, which show the results of experiments at a temperature of 283 K, a residence time of 60 s and under dry conditions (RH ∼ 1 %), taken 1 day apart.The total particle concentrations as a function of the H 2 SO 4 concentration measured by DMPS for both experiments are presented in Fig. 2a.Except the first points, which show larger scatter and with a ratio of these concentrations of 1 : 1.17, the ratios of the remaining concentrations range from 1 : 1.01 to 1 : 1.07.The observed variation of the median particle diameters as a function of the initial H 2 SO 4 concentrations with standard deviations as error bars is shown in Fig. 2b.At the same temperature, relative humidity, residence time and comparable H 2 SO 4 concentrations, the maximum difference of single median particle diameters determined from both experiments was 0.6 nm, with most diameters varying by 0.3 or 0.4 nm.These results show that the measurements of the particle diameters and particle number concentrations were very reproducible.

Variation of particle number concentrations and particle size distributions
During each experiment the temperature of the saturator was increased in seven consecutive steps of 5 K every 2 h, resulting in a distinct increase of the H 2 SO 4 concentration in the gas phase and a subsequent significant rise of the particle number concentration.The stability of particle production was not achieved immediately; it took approximately 30 min to obtain a steady particle production.The first 30 min of every period of constant saturator temperature were therefore excluded from the analysis.The data from the DMPS were then averaged over the whole period analysed to receive a single data point characterizing each saturator temperature, and the data from the UCPC were averaged over two equal periods of 45 min to receive two data points.
The determined curves of the particle number concentration, as a function of the initial H 2 SO 4 concentration measured by both DMPS and UCPC at T = 293 K, RH ∼ 30 % and at residence times of 45, 60 and 90 s, are presented in Fig. 3.The total number concentrations determined from both instruments were found to be strongly dependent on the residence time of the gaseous mixture in the flow tube.The significance of residence time in nucleation measurements has been discussed in previous studies (Sipilä et al., 2010;Berndt et al., 2010).The results clearly show that the observed total number concentration is influenced by the growth process and the longer the residence time, the larger the fraction of nucleated particles grows beyond the detection limits of the UCPC and DMPS.For example, during the experiment performed at T = 293 K and RH ∼ 30 %, at a H 2 SO 4 concentration of 6.5 × 10 8 molecule cm −3 , the particle number concentration increases about one order of magnitude, from 3.2 × 10 3 ± 0.15 × 10 3 cm −3 at a residence time of 45 s to 3 × 10 4 ± 1.1 × 10 3 cm −3 at a residence time of 90 s.Absolutely no particles were detected during experiments performed at a residence time of 30 s, indicating that the nucleated particles were not able to grow to detectable sizes during the first 30 s of the experiments.The particle number concentrations at all residence times were rather stable at any H 2 SO 4 concentration (see Fig. 3).The total particle concentrations obtained from the DMPS measurements were slightly lower than the values detected with the standalone UCPC, which was due to the lower cut-off diameter (d 50 = 2.25 nm) of the stand-alone UCPC (Brus et al., 2010) and the upper limit (200 nm) of the DMPS which undercounts at higher sulphuric acid concentrations (Fig. 3).By comparing the measurements from both instruments, we received an almost linear relationship between the concentrations in most cases, which can be seen in Fig. 4. A visible decrease of the particle concentration at the temperature of the saturator, 295 K, corresponding to the H 2 SO 4 concentration of ∼ 3.5 × 10 9 molecule cm −3 recorded by UCPC, can be seen in Fig. 3.This artefact of the experimental set-up was observed when the temperature of the acid saturator was close to the temperature of the mixing unit (∼ 293 K), and this behaviour was also reported in our previous study with a very similar set-up (Neitola et al., 2013).The observed variation in the particle size distributions obtained from the inversion of the raw DMPS data from a single experiment -a measurement performed at a constant nucleation temperature of T = 283 K, a residence time of 60 s, an RH of ∼ 30 % and at different H 2 SO 4 concentrationsis presented in Fig. 5.The increasing total particle concentration and particle median diameter correspond with the increasing H 2 SO 4 concentration in the gaseous mixture.The values of the total number concentrations during all of the measurements ranged from 1.1 × 10 3 ± 0.17 × 10 3 cm −3 to 4.7 × 10 4 ± 1.2 × 10 3 cm −3 , and were generally higher during experiments performed at RH of ∼ 30 % and nucleation temperature of 303 K.The values of the median particle diameter ranged from 14.4 ± 0.1 nm to 39.8 ± 1.6 nm and particles grew larger at an RH of ∼ 30 % and at high H 2 SO 4 concentrations.

Growth of the particles under dry and wet conditions
The H 2 SO 4 -H 2 O nucleation was affected by the presence of impurities originating from ultra-pure water and carrier gas.
The enhancing effect of NH 3 on nucleation was observed in ) the laboratory experiments and was found to be stronger at low relative humidities (Berndt et al., 2010;Benson et al., 2011).The freshly formed H 2 SO 4 particles are partially neutralized to ammonium bisulphate, (NH 4 )HSO 4 , and ammonium sulphate, (NH 4 ) 2 SO 4 .For a fixed relative humidity, the hygroscopic growth of these particles was found to decrease with decreasing particle size owing to a greater degree of neutralization, since (NH 4 ) 2 SO 4 is less hygroscopic than H 2 SO 4 (Biskos et al., 2009).When considering the effect of water vapour on the particle growth, the hydration of H 2 SO 4 should be taken into account.The number of water molecules attached to an H 2 SO 4 molecule increases significantly with the growing relative humidity and the higher the relative humidity, the higher the growth rate due to the condensation of H 2 O on the particles (Nieminen at al., 2010).The variation of the particle diameters has the same pattern under both wet and dry conditions, which is illustrated in Fig. 6.Hygroscopic growth behaviour can be described with the so-called hygroscopic growth factor (GF), In this study, the dry diameters D p (dry) corresponds to the median particle diameters obtained from measurements performed at an RH of ∼ 1 %, and the wet diameters D p (wet) to the median particle diameters obtained from measurements at an RH of ∼ 30 %. Hygroscopic growth factors determined from measurements performed at T = 293 K ranged from 1.05 to 1.35 and at T = 303 K the values covered the range from 1.1 to 1.42.Our findings were then compared with the results from Biskos et al. (2010), who measured the hygroscopic growth of acidic sulphate nanoparticles over a wide range of relative humidities using the tandem DMA technique.At a relative humidity of ∼ 30 %, Biskos et al. (2010) reported for dry diameters from 7.5 nm to 36.1 nm, which are comparable with this study, growth factors from 1.18 to 1.3.The best agreement with our study was found for T = 303 K, since most GF values determined at this temperature were close to 1.25, which is illustrated in Fig. 7.At T = 293 K most GFs (growth factors) were around 1.1 and reached values above 1.2only at a residence time of 90 s and for H 2 SO 4 concentrations of 5 × 10 9 molecule cm −3 and higher (Fig. 7).The hygroscopic growth factors were not determined for T = 283 K, since the differences in the determined median particle diameters from measurements under wet and dry conditions at all residence times were so small that in most cases they fell within the uncertainty range of the measurements.A clear dependence of GFs on H 2 SO 4 concentration can be seen in Fig. 7.At the lowest applied H 2 SO 4 concentrations at 293 K, the GFs slightly decrease with increasing H 2 SO 4 while the opposite trend was observed at the concentration range above ∼ 3 × 10 9 molecule cm −3 .However, the GFs calculated from our model were not in good agreement with the experimental values, since it predicted higher GFs (∼ 15 % higher at T 293 K and ∼ 25 % higher at T 303 K) and also predicted different trend in GFs behaviour.
For this reason, it could not be explained if the trends in the GFs behaviour are real or spurious.The changing behaviour of the growth factors could be explained by a larger fraction of acidic and therefore more hygroscopic particles at higher H 2 SO 4 concentrations.

Wall losses of sulphuric acid
The initial concentrations of H 2 SO 4 , at which newly formed particles were detected during the experiments, covered the range from 1.8 × 10 8 to 1.4 × 10 10 molecule cm −3 .Previous nucleation experiments, conducted with H 2 SO 4 produced from a liquid reservoir, reported that nucleation occurred at an H 2 SO 4 concentration of ∼ 10 9 molecule cm −3 and higher (Wyslouzil et al., 1991;Viisanen et al., 1997;Ball et al., 1999;Zhang et al., 2004).The H 2 SO 4 molecules can attach to the inner surfaces of the flow tube during experiments, and in order to determine the residual concentration of H 2 SO 4 the corrections of the initial concentrations are necessary.The wall loss factor characterizing the diffusion losses of sulphuric acid on the walls of the tube is defined as follows: where [H 2 SO 4 ] 0 is the initial concentration of sulphuric acid in the flow tube determined from Eq. ( 1) and [H 2 SO 4 ] t is the concentration of sulphuric acid after time t.In this study, the time, t, was set as equal to half of the residence time of the gaseous mixture in the flow tube, and thus the concentration [H 2 SO 4 ] t corresponds approximately to the H 2 SO 4 concentration in the middle of the flow tube.This assumption was based on our previous studies where the nucleation zone was determined experimentally (Brus et al., 2010) and also verified by the computational fluid dynamics (CFD) model (Herrmann et al., 2010).It should be noted that the experimental set-up in the previous study was different from this worka furnace was used instead of saturator and thus temperature gradient was introduced at the beginning of the flow tube.The wall losses were determined according to Hanson and Eisele (2000) and the wall loss factors span the range from 1.9 to 4.8 under wet conditions and from 2.2 to 6.2 under dry conditions for a t from 22 to 45 s, calculated as half of the initial residence times.However, when using the calculated H 2 SO 4 concentrations corrected by WLFs (wall loss factors) as an input parameter in our model, the experimental values did not agree  2000) and a modified model, accounting for a system-specific wall loss coefficients (Brus et al., 2011b).
with the theoretical predictions.This can be seen from Fig. 8 which illustrates the variation of both the measured and calculated median particle diameters at an RH of ∼ 30 %, with T = 283 K and a residence time of 60 s.The model fails to capture the observed growth rates in all cases since it predicts significantly lower particle growth than that observed in experiments, and the deviations are more profound at an RH of ∼ 1 % and with high H 2 SO 4 concentrations.These results suggest that the H 2 SO 4 concentration corresponding to the middle of the flow tube is too low and does not describe the growth behaviour of the particles correctly.For this reason, the initial H 2 SO 4 concentration corresponding to the H 2 SO 4 concentration at the beginning of the flow tube was used as the input parameter for all the model calculations in the further analysis.
Although the particles are assumed to nucleate at the beginning of the flow tube in this study, the nucleation can also occur in some distance along the tube.The uncertainty of the calculated growth rates resulting from the nucleation zone location was estimated as the difference between growth rates calculated assuming nucleation at the beginning of the flow tube and growth rates assuming the nucleation occurring 50 cm from the beginning of the flow tube (the total length of the flow tube is 2 m).The calculated uncertainties are 7.5 % for residence time 45 s, 10 % for residence time 60 s and 15 % for residence time 90 s.The system-specific wall loss coefficients were used in these calculations (see explanation below).

The particle growth rates and model evaluation
The growth of freshly formed particles was calculated using the numerical model described in Sect.2.2.By including the initial H 2 SO 4 concentration determined from Eq. ( 1) in the model, we achieved much better agreement with the experimental data as compared to the results based on the H 2 SO 4 concentrations corrected for wall losses (Hanson and Eisele, 2000).In order to investigate this discrepancy, additional calculations were performed using the same model accounting for system-specific wall loss coefficients (0.0047 cm −1 for wet conditions and 0.0061 cm −1 for dry conditions) determined for the flow tube in our previous study (Brus et al., 2011b).A comparison of the experimental and numerical results is illustrated in Fig. 9, which shows the experiment conducted at T = 283 K, an RH of ∼ 30 % and a residence time of 60 s (compare with Fig. 8).As can be seen there, the calculations agree very well with the experimental data, despite the fact that the model slightly overestimates the growth rates at a residence time of 90 s, at all temperatures and under both wet and dry conditions (Fig. 10).Also using the system-specific wall loss coefficients provides much better agreement with experimental data compared to calculations based on wall loss coefficients according to Hanson and Eisele (2000) (see Fig. 8).The results may also be influenced by different carrier gases - Hanson and Eisele (2000) used nitrogen in their work, whereas in our studies particlefree and purified air was used as the carrier gas (the diffusion of H 2 SO 4 in air is slower compared to diffusion of H 2 SO 4 in nitrogen).
It should be noted that the model accounts only for H 2 SO 4 , water and ammonia while different impurities may have been present in our system in trace concentrations.Such Figure 10.The comparison of the experimental median particle diameters determined from a measurement conducted at T = 283 K, with an RH of ∼ 30 % and a residence time of 90 s, and the values predicted theoretically from a model using the initial H 2 SO 4 concentration without a correction for wall losses.As can be seen, the model overestimates the growth rates slightly in the case of experiments conducted at a residence time of 90 s.
compounds might have influenced the nucleation process and the subsequent growth of the freshly formed particles.The impurities (amines and other organics) were measured by MARGA in the same experimental set-up several times (see Neitola et al., 2013), and their levels were always below detection limits (for amines ∼ 100 pptv).In spite of that, we cannot rule out the presence of the impurities in the flow tube and their influence on growth dynamics.The assumed presence of ammonia and its role in the growth process is addressed in the model, accounting for three degrees of neutralization of formed particles by ammonia.Amines, more specifically alkylamines, which usually accompany ammonia in one order lower concentrations, can displace ammonia from ammonium sulfate and create alkylaminium sulfates (Zhang et al., 2012;Ge et al., 2011).Alkylaminium sulfates have comparable properties to ammonium sulfate and are even more stable in the particle phase; also, aerosol dynamics are very similar to that of ammonium sulphate and ammonium bisulphate (Qiu and Zhang, 2012).An indirect way to determine the H 2 SO 4 concentration in experimental devices is based on the measured growth rates of the freshly formed particles.The H 2 SO 4 concentrations in our study, derived solely from the growth rates determined experimentally and verified in our model, indicate that the commonly assumed wall losses of H 2 SO 4 on the inner surfaces calculated from Eq. ( 2) are not as significant in case of long-lasting experiments as previously believed.Using the system-specific wall loss coefficients in our model provides good agreement with experimental data, especially at lower acid concentrations.This indicates that in our experiments the sulphuric acid wall losses were substantially lower than predicted according to a commonly used expression from Hanson and Eisele (2000).We therefore speculate that due to close to wall-equilibrium conditions, the wall is not an infinite sink for H 2 SO 4 , but that there is also a flux of H 2 SO 4 from the wall to the flow tube.For example, in the study by Hanson and Eisele (2000), the wall of a laminar flow tube was found to be a significant source of H 2 SO 4 at an RH of < 0.5 %, and the concentration of H 2 SO 4 from the wall reached up to 3 × 10 8 molecule cm −3 .Another possible explanation for the discrepancy between the H 2 SO 4 concentrations calculated from Eq. ( 2) and that derived from our experimental growth rates might be the limited adsorption capacity of the wall.The wall becomes saturated with H 2 SO 4 during experiments, and therefore further adsorption of H 2 SO 4 molecules might be hindered after a certain time period.We estimated the "real" wall losses of H 2 SO 4 by matching the predicted and observed growth rates through tuning the initial H 2 SO 4 concentration in the model.Although the estimated wall losses were slightly scattered for different experimental conditions (RH, temperature and residence time), a reasonable agreement found for the experimental and modelled data yields an estimation of the wall losses: ∼ 10 % for a residence time of 45 s, ∼ 15 % for a residence time of 60 s and ∼ 25 % for a residence time of 90 s, corresponding to WLFs of 1.11, 1.18 and 1.33, respectively.
The experimental growth rates, determined from Eq. ( 7), range from 20 nm h −1 to 890 nm h −1 under dry conditions and from 7 nm h −1 to 980 nm h −1 under wet conditions.When analysing the dependence on the experimental conditions, the measured growth rates were found to increase with growing H 2 SO 4 concentration and increased almost linearly with increasing particle size.Also, increases in the nucleation temperature were found to have a slight enhancing effect on particle growth rates under dry conditions.At a very low RH, the wall is a source of H 2 SO 4 molecules and the flux is proportional to the H 2 SO 4 vapour pressure, which increases with rising temperature.The influence of the RH is not consistent -at lower H 2 SO 4 concentrations the growth rates were higher under dry conditions, at H 2 SO 4 concentrations of ∼ 1 × 10 9 molecule cm −3 and above, the growth rates were higher under wet conditions.This effect could be partially explained by the displacement reaction of alkylamines with ammonium sulphate to form alkylaminium sulphates.This reaction causes the transition from crystalline to an amorphous phase (Qui and Zhang, 2012), which enhances water uptake and consequently particle growth with increasing RH.The residence time was found to have a negligible effect on the measured growth rates.
The predicted growth rates, calculated from the model with the initial H 2 SO 4 concentration using Eq. ( 7), range from 7 nm h −1 to 1100 nm h −1 under dry conditions and from 15 nm h −1 to 1300 nm h −1 under wet conditions.Growth rates over 1000 nm h −1 were reached only at very high H 2 SO 4 concentrations of 8 × 10 9 molecule cm −3 and higher, and at a residence time of 90 s.Most growth rates span the range from ∼ 10 nm h −1 to ∼ 500 nm h −1 under dry conditions and from ∼ 15 nm h −1 to ∼ 400 nm h −1 under wet conditions.Our model considered three different numbers of NH 3 molecules taken up by each molecule of H 2 SO 4 during particle formation.All three tested degrees of neutralization provided results that are in good agreement with the experimental data and all of them capture the trends in the growth rate values in a similar manner (see Fig. 9).The highest growth rates were achieved for ammonium sulphate particles.The numerical results indicate that the presence of NH 3 enhances the growth of a freshly formed aerosol.
Equation ( 4) does not account for molecule size effects on the collision cross section nor the particle thermal speed effects on the relative collisional speeds which may impact the estimation of the growth rates of nanometre-sized particles (Lehtinen and Kulmala, 2003;Nieminen et al., 2010).We performed sensitivity calculations where Eqs.(4-6) were modified, as proposed by Lehtinen and Kulmala (2003), to address these issues.The enhancement of the calculated growth rates was ∼ 5 %, which improved the agreement between modelled and measured values at residence times 45 and 60 s, but also contributes to growth overestimation at residence time 90 s.
Figure 11 depicts the experimental growth rates under wet conditions, at a residence time of 90 s and at three nucleation temperatures and the atmospheric growth rates, obtained in Heidelberg and Hyytiälä during the Quantification of Aerosol Nucleation in the European Boundary Layer (QUEST) project (Fiedler et al., 2005), data obtained in Atlanta during the Atlanta Aerosol Nucleation and Real-time Characterization Experiment (ANARChE) study (Stolzenburg et al., 2005), data from Beijing during the Campaigns of Air Quality Research in Beijing and Surrounding Regions in 2008(CAREBeijing-2008) (Yue et al., 2010), data from Mace Head Monitoring Station during the Particle Formation and Fate in the Coastal Environment (PARFORCE) campaign (O'Dowd et al., 2002a) and data from Kent, Ohio (Erupe et al., 2010) are depicted for comparison.The theoretical predictions of the growth of ammonium sulphate particles under wet conditions (RH = 30 %) are also depicted.The best agreement with our data was found for sulphuric aciddriven growth rates from a study by Stolzenburg et al. (2005), who investigated the growth of particles containing ammonium sulphate, which is consistent with the chemical compositions of particles in our study.Most observed atmospheric growth rates correspond to substantially lower H 2 SO 4 concentrations, and our results thus show that in most cases sulphuric acid alone cannot explain the growth rates observed in the atmosphere.H 2 SO 4 is the main condensing vapour responsible for particle growth only in large urban areas, where it can contribute up to 60 % of the growth (H 2 SO 4 accounts for the 60 % of growth observed) (Stolzenburg et al., 2005;Yue et al., 2010).In order to explain the atmospheric growth rates, the condensation of additional chemical species is assumed, mainly organic compounds (Erupe et  (Fiedler et al., 2005), data obtained in Atlanta during the ANARChE study (Stolzenburg et al., 2005), data from Beijing during the CAREBeijing-2008 campaign (Yue et al., 2010), data from Mace Head during the PARFORCE campaign (O'Dowd et al., 2002) and data from Kent, Ohio (Erupe et al., 2010) are depicted for comparison.The line presents the theoretical predictions of the growth of ammonium sulphate particles at an RH of 30 %. al., 2010;Fiedler et al., 2010) and iodine species (O'Dowd et al., 2002b).
There are only a few previously reported values of particle growth rates from nucleation experiments.Young et al. (2008) have studied the binary nucleation of H 2 SO 4 and water at T = 288 K, RH from 11 % to 23 % and at initial H 2 SO 4 concentrations from 10 8 to 10 10 molecule cm −3 .The observed particle growth rates in their experiment ranged from 95 nm h −1 to 500 nm h −1 .Benson et al. (2008) measured the binary nucleation of H 2 SO 4 and water at T = 288 K, at RH from 10 % to 55 % and at H 2 SO 4 concentrations from 10 8 to 10 9 molecule cm −3 .The particle growth rates estimated from their measurements were roughly from 160 to 490 nm h −1 .The results of these studies are in good agreement with the growth rates determined from our experiments, as can be seen in Fig. 12.

Conclusions
The results of an experimental study of sulphuric acid nanoparticle growth under different conditions are presented here.The measurements were performed in a laminar flow tube at temperatures of 283, 293 K and 303 K, at RH of 1 % and 30 %, an initial H 2 SO 4 concentration from 2 × 10 8 to 1.4 × 10 10 molecule cm times.The number concentrations and size distributions of the newly formed particles were measured with a UCPC and a DMPS.The obtained size distributions were fitted with a log-normal distribution in order to determine the median particle diameter and the temporal variation of the median diameter was used to calculate the growth rate of the nucleation mode.The variation of the growth rates and their dependence on the experimental conditions were analysed.A comparison of the experimental values with the theoretical ones predicted from a model, considering the growth of particles with three different ammonia-to-sulphate ratios, was made.It was shown that our system can produce very reproducible results.A strong dependence of the number concentrations of newly formed particles on residence time was observed.The obtained growth rates were found to increase significantly with increasing H 2 SO 4 concentration.A slightly enhancing effect of increased RH on growth rates was observed at higher H 2 SO 4 concentrations, and a clear dependence of the growth rates on increasing nucleation temperature was recorded under dry conditions.The residence time was found to have a negligible effect on the growth rates.The modelled growth rates were highest for ammonium sulphate particles, indicating that NH 3 promotes particle growth under both wet and dry conditions.A comparison of our data with atmospheric measurements shows that growth rates based solely on the condensation of H 2 SO 4 significantly underestimate the growth rates observed in the atmosphere.A satisfactory agreement of our data with the growth rates determined from previous laboratory experimental studies was found.
The wall losses of H 2 SO 4 derived from experimental growth rates were found to be substantially lower than the diffusion limited values calculated according to Hanson and Eisele (2000).Our results indicate that the wall losses of H 2 SO 4 are not as great as is commonly presumed.Due to long-lasting experiments, the measurements are believed to be performed under close to wall-equilibrium conditions.We therefore speculate that the wall of the flow tube is not an infinite sink for H 2 SO 4 molecules, but that there is also a flux of H 2 SO 4 from the wall into the tube, which is more profound under dry conditions.The correct determination of the sulphuric acid concentration in nucleation measurements is a crucial factor for subsequent analysis and data interpretation.Our results show that neglecting the flux of H 2 SO 4 from the wall may cause a significant underestimation of the residual H 2 SO 4 concentration.More detailed measurements are needed to gain a better understanding of the processes influencing the H 2 SO 4 concentration in experimental devices and the role of sulphuric acid in the early stages of particle growth.

Figure 1 .
Figure 1.Schematic figure of the experimental set-up.

Figure 2 .
Figure2.The variation of the total particle concentrations determined from a DMPS from measurements performed at T = 283 K, with an RH of ∼ 1 % and a residence time of 60 s, taken 1 day apart.Fig.2b: the median particle diameters determined from measurements performed at T = 283 K, with an RH of ∼ 1 % and a residence time of 60 s, taken 1 day apart.The standard deviations of the median particle diameters are depicted as error bars.

Figure 3 .
Figure 3.The observed particle number concentrations at different residence times at T = 293 K and with an RH of ∼ 30 %.The solid symbols present the number concentrations determined by a DMPS and the open symbols are number concentrations determined by a UCPC.

Figure 4 .
Figure 4.An almost linear relationship was reached by a comparison of the particle number concentrations determined from a DMPS and a UCPC at different residence times, at T = 293 K and with the RH set at 30 %.

Figure 6 .
Figure6.The variation in the median particle diameters determined from measurements performed at T = 303 K, with a residence time of 60 s and at different RH.The standard deviations of the median particle diameters are depicted as error bars.

Figure 7 .
Figure 7.The growth factors as a function of the H 2 SO 4 concentration at T = 293 and T = 303 K at different residence times.

Figure 9 .
Figure9.The comparison of the experimental median particle diameters from a measurement conducted at T = 283 K, with an RH of ∼ 30 % and a residence time of 60 s, and the values predicted theoretically from a model using the initial H 2 SO 4 concentration without a correction for wall losses.

Figure 11 .
Figure11.The experimental growth rates obtained under wet conditions (RH = 30 %), with a residence time of 90 s and three nucleation temperatures of 283, 293 and 303 K.The atmospheric growth rates, obtained in Heidelberg and Hyytiälä during the QUEST project(Fiedler et al., 2005), data obtained in Atlanta during the ANARChE study(Stolzenburg et al., 2005), data from Beijing during the CAREBeijing-2008 campaign(Yue et al., 2010), data from Mace Head during the PARFORCE campaign(O'Dowd et al.,  2002)  and data from Kent, Ohio(Erupe et al., 2010) are depicted for comparison.The line presents the theoretical predictions of the growth of ammonium sulphate particles at an RH of 30 %.

Figure 12 .
Figure 12.The experimental growth rates determined from measurements conducted at an RH of 30 %, a residence time of 90 s and three nucleation temperatures are compared with the particle growth rates measured in the nucleation experiments made by Benson et al. (2008) at T = 288 K and Young et al. (2008) at T = 288 K.
The comparison of the experimental median particle diameters from a measurement conducted at T = 283 K, with an RH of ∼ 30 % and a residence time of 60 s, values predicted theoretically from a model using the H 2 SO 4 concentration corrected for wall losses, determined according toHanson and Eisele (