Overview of the CLOUD facility

The CLOUD experiment at CERN is designed to study the effects of cosmic rays on aerosols, cloud droplets and ice particles, under precisely controlled laboratory conditions. The 3-m-diameter stainless-steel CLOUD chamber and its gas system have been built to the highest technical standards of cleanliness and performance. The CLOUD chamber is periodically cleaned by rinsing the walls with ultra-pure water, followed by heating to 373 K and flushing at a high rate with humidified synthetic air and elevated ozone (several parts per million by volume). Contaminant levels of condensable vapours are in the sub-p.p.t.v. range. The high cleanliness of the chamber, together with its large volume (26.1 m3) and highly stable operating conditions, allows particle formation to be studied under atmospheric conditions at nucleation rates between about 0.001 cm−3 s−1 and 100 cm−3 s−1. The loss rate of condensable vapours and particles onto the chamber walls is comparable to the ambient condensation sink of the pristine boundary layer.

Ion production in the chamber can be controlled using an internal electric clearing field (which creates an ion-free environment), GCRs or an adjustable π+ beam9,33 from the CERN Proton Synchrotron. The π+ beam is de-focused to a transverse size of about 1.5 m × 1.5 m when it passes through the CLOUD chamber. With the electric field set to zero, the equilibrium ion-pair concentration in the chamber due to GCRs is around 700 cm−3. With the π+ beam, this can be increased to any value up to about 3,000 cm−3. Hence, ion concentrations corresponding to any altitude in the troposphere can be generated in the CLOUD chamber.

The experiment has precise control of the trace vapours inside the chamber and also of the environmental temperature between 300 K and 203 K. Uniform mixing is achieved with magnetically coupled stainless-steel fans mounted at the top and bottom of the chamber. The characteristic gas mixing time in the chamber is a few minutes, depending on the fan speeds. Photochemical processes are initiated by illumination with an ultraviolet fibre-optic system, providing highly stable gas-phase reactions with a precise start time. The contents of the chamber are continuously analysed by instruments connected to sampling probes that project into the chamber. The sampling analysers are tailored for each experimental campaign, but typically comprise around 30–35 instruments, of which up to 10 are mass spectrometers.

Summary of analysing instruments

For the results reported here, the analysing instruments attached to the chamber included a chemical ionization mass spectrometer (CIMS) for H 2 SO 4 concentration34; an atmospheric pressure interface time-of-flight (APi-TOF; Aerodyne Research Inc. and Tofwerk AG)35 mass spectrometer for molecular composition of positively or negatively charged ions and clusters; two chemical ionization atmospheric pressure interface time-of-flight (CI-APi-TOF; Aerodyne Research Inc. and Tofwerk AG)36,37 mass spectrometers for molecular composition and concentration of neutral gas-phase H 2 SO 4 and HOMs; a proton transfer reaction time-of-flight (PTR-TOF; Ionicon Analytik GmbH)38 mass spectrometer for organic vapours; a neutral cluster and air ion spectrometer (NAIS; Airel Ltd)39 for concentrations of positive ions, negative ions and charged clusters in the range 1–40 nm; a nano-radial differential mobility analyser (nRDMA)40 and a nano scanning mobility particle sizer (nano-SMPS) for particle size spectra; and several condensation particle counters (CPCs) with 50% detection efficiency thresholds between 1 nm and 4 nm: two Airmodus A09 particle size magnifiers, PSM41, (one fixed-threshold and the other scanning), two diethylene glycol CPCs, DEG-CPC42,43, a butanol TSI 3776 CPC and a water TSI 3786 CPC (TSI Inc.).

Additional gas analysers included dew-point sensors (EdgeTech), sulfur dioxide (Thermo Fisher Scientific, Inc. 42i-TLE) and ozone (Thermo Environmental Instruments TEI 49C). For certain tests, HONO vapour was supplied to the chamber and photolysed with ultraviolet light to produce OH· in the absence of O 3 . The gaseous HONO was generated by continual mixing of H 2 SO 4 with NaNO 2 (ref. 44) in a specially designed stainless-steel reactor, and then steadily flowed into the chamber. The HONO analyser involved a specially designed probe that passed samples of air from the chamber through a solution of H 2 SO 4 and sulfanilamide, which was then analysed online with a long path absorption photometer (LOPAP)45.

Determination of the nucleation and growth rates

The nucleation rates (in cm–3 s–1) were measured under neutral (J n ), ground-level GCR (J gcr ) and π+ beam (J π ) conditions. Neutral nucleation rates are measured with the clearing field electrodes set to ±30 kV, which establishes an electric field of about 20 kV m−1 in the chamber. This completely suppresses ion-induced nucleation because, under these conditions, small ions or molecular clusters are swept from the chamber in about 1 s. Because all of the nucleation and growth processes under consideration take place on substantially longer timescales, neutral nucleation rates can be measured with zero background from ion-induced nucleation. For GCR and π+ beam conditions, the electric field was set to zero, leading to equilibrium ion-pair concentrations around 700 cm−3 and 3,000 cm−3, respectively. The nucleation rate J n measures the neutral rate alone, whereas J gcr and J π measure the sum of the neutral and ion-induced nucleation rates, J n + J iin .

The nucleation rates reported here were obtained primarily with the Airmodus scanning PSM at 1.8-nm threshold (PSM1.8) and the TSI 3776 CPC (CPC2.5), nominally 2.5-nm threshold, but measured at 3.2-nm threshold with WO x particles46. The nucleation rates J 1.7 are determined at 1.7-nm mobility diameter (1.4-nm mass diameter), at which size a particle is normally considered to be above its critical size and, therefore, thermodynamically stable. The critical size corresponds to the cluster size at which the evaporation and growth rates are equal. It varies with temperature, chemical species, charge and vapour concentrations, and may even be absent when evaporation rates are highly suppressed, such as for sulfuric acid–dimethylamine clusters10,37. Our measurements indicate that the smallest neutral HOM clusters are relatively unstable; therefore, 1.7 nm, which is equivalent to around 5 HOM monomer units, is a reasonable size at which to derive the experimental nucleation rates.

AEROCLOUD model

To determine nucleation rates at 1.7 nm, the time-dependent particle concentrations measured with the PSM1.8 and CPC2.5 are fitted with a simplified numerical model (AEROCLOUD) that treats particle nucleation and growth kinetically at the molecular level. The model uses HOM monomer, HOM dimer and H 2 SO 4 production rates derived from the CI-APi-TOF experimental data. The measured HOM production rates are scaled by a factor of 1.8 to match the observed particle appearance times and growth rates. This scaling results in good agreement of the model with the experimental data over the full experimental range of HOM concentrations. The scaling factor is within the systematic measurement uncertainty of the CI-APi-TOF, and could arise if a nitrate CI-APi-TOF does not detect all the HOMs that contribute to particle growth.

Primary ions from GCRs are generated in the model at the known rate of q = 1.7 ion pairs per cubic centimetre per second. A fixed parameter of the model, f c , accounts for the charge sign asymmetry due to differences in the diffusional loss rates of positive and negative primary ions to the chamber walls:

The parameter f c is determined by the experimentally measured positive and negative ion concentrations in the NAIS to have the value 0.52.

Molecules and particles collide kinetically, and cluster with each other. The model uses a reduced clustering probability (termed a ‘sticking probability’ below) to account for unstable small clusters, rather than allowing clusters to evaporate once they have formed. This greatly increases the speed of the computation. If the particle formed by a collision exceeds a certain size (corresponding to around 1.7-nm mobility diameter for pure biogenic clusters; see below), then it is assumed to be effectively stable and subsequently grows at near the kinetic limit. The particle growth rate between the PSM1.8 and CPC2.5 is therefore implicitly treated in the model essentially as kinetically limited growth by particle coagulation plus HOM and H 2 SO 4 vapour condensation. Particles grow through size bins that are linearly spaced for small sizes and logarithmically spaced from about 2 nm to a maximum size of 400 nm. The time-steps for clustering processes range from 0.9 s to 10 s, depending on the conditions of the experimental run under analysis. The time-step is 10 s for all other processes (for example, updates of gas concentrations, high-voltage clearing-field changes, fan changes, and particle losses due to dilution of the chamber contents or diffusion to the walls). The density of the pure HOM clusters is fixed at 1.3 g cm−3, and at 1.85 g cm−3 for a pure H 2 SO 4 cluster.

For neutral–neutral collisions, the number of particles in size bins 1 and 2 that coagulate in a time interval Δt to produce a particle of mass m 12 is:

where K 00 is the neutral–neutral collision kernel, n 1 , n 2 and n 12 are the particle number concentrations, and V 12 is the van der Waals enhancement factor (see below). The neutral–neutral sticking probability for pure biogenic particles, , is:

where C B and S B are free parameters. The parameter C B effectively defines the threshold mass of stable clusters because the sticking probability when C B = m 12 , whereas the parameter S B controls the sharpness of the threshold. The sticking probability for collisions where at least one particle is mainly sulfuric acid is similarly defined as:

where C A and S A are free parameters.

The neutral–neutral collision kernel, K 00 , in equation (1) is the Fuchs form of the Brownian coagulation coefficient47,48. The van der Waals enhancement factor is the modification to Fuchs theory due to Sceats49, as described in ref. 50, for a Knudsen number in the kinetic (free molecular) regime. The enhancement factor is:

where the reduced Hamaker constant, A′, is:

where r 1,2 are the particle radii, A = 6.4 × 10−20 J (the Hamaker constant for sulfuric acid50), b 0 = 0.0151, b 1 = −0.186, b 2 = −0.0163, k is the Boltzmann constant and T is temperature. The same Hamaker constant is used for both sulfuric acid and HOMs because it does not noticeably change the model predictions.

Ions and charged clusters collide according to a similar expression as equation (1):

where E is an enhancement factor to obtain the charged collision kernels (described below). The sticking probability for collisions between a neutral particle and a charged particle, , is:

where is a free parameter and C = C B or C A for biogenic or acid particles, respectively. Ion–ion recombination results in a neutral particle, which may evaporate at small sizes. The model allows partial evaporation of such recombination particles; in this case the cluster divides into monomers and the mass is conserved. The probability of cluster survival after ion–ion recombination, , is:

where C +− is a free parameter. A power of unity (S +− = 1) is used because the data do not constrain this parameter well.

To obtain the charged collision kernels, the neutral–neutral collision kernel is multiplied by size-dependent enhancement factors, E:

where K are the collision kernels and the subscripts refer to the charge of the colliding particles. The charged collision kernels in equation (2) are obtained from ref. 51, which refers to sulfuric acid particles. Because biogenic particles may have different neutral–charged collision kernels, their enhancement factor is left free in the fit:

where f 0+,0− is a free parameter.

Ions, monomers, clusters and larger particles are continually lost by diffusion to the walls and by dilution of the chamber contents with fresh gas mixture. The dilution lifetime is near 3 h (10−4 s−1), depending on the total sampling rate of all instruments attached to the chamber. The wall loss rate is 1.8 × 10−3 s−1 for H 2 SO 4 monomers, and decreases with increasing cluster or molecule diameter as 1/d. The same scaling law is used to obtain the wall loss rate for HOMs; that is, it is assumed that HOMs and particles that collide with the walls are irreversibly lost. For experimental runs for which there is a pre-existing population of particles in the chamber at the start of a run due to incomplete cleaning of the chamber, losses to this coagulation sink are accounted for by inserting the initial size distribution into the size bins of the model.

To determine the nucleation rates, the five free parameters of the model (S B , S A , S 0+,0− , f 0+,0− and C +− ) are fitted to the experimental particle concentrations in the PSM1.8 and CPC2.5 versus time. For example, for neutral pure biogenic runs, only one free parameter (S B ) is involved in the fit. The value of S B ranges from 12 to 14, S A from 4 to 6, S 0+,0− from 0.1 to 1.0, f 0+,0− is near 4 and C +− is near 10,000 Th. The parameters C B , C A , S +− and f c were determined by a global fit to all runs in the dataset and then subsequently fixed at these values. The fitted threshold masses for C B and C A are around 1,300 Th and 700 Th, respectively. The parameter S +− is set to 1.0 and f c is set to 0.52. The time development of the particle number concentrations in both counters throughout all of the nucleation events in our dataset is well reproduced by the model (an example is shown in Extended Data Fig. 4b).

After fitting the data with the model, the nucleation rate J 1.7 is determined as the number of particles that grow to a mobility diameter of 1.7 nm or larger in any time-step, divided by the time increment. In each nucleation run at fixed conditions, the time t max is determined at which J 1.7 is maximum; the value of J 1.7 for that run is then calculated as the mean measurement over the interval (t max ± 300 s).

There are three major advantages of using a data-driven kinetic model to determine nucleation rates rather than making direct measurements with the PSM1.8 or CPC2.5 data. First, it avoids the need for time derivatives of the data, which are subject to large errors at low counting rates. Second, particle growth rates are determined by kinetics and properly account for growth due to collisions both with monomers and with other particles. The model treatment of the data therefore avoids the exponential sensitivity on experimental growth rates that occurs with other methods52,53,54,55. Experimental growth rates are determined from particle counter rise times and have relatively large uncertainties in the 1–3-nm size range. Finally, the model requires consistency between the PSM1.8 and CPC2.5 so the formation rates are experimentally constrained both near the 1.7-nm threshold size and near 3 nm.

Verification of the model nucleation rates

We performed extensive cross-checks of the nucleation rates obtained with the model by calculating the nucleation rates independently in two additional ways: (1) direct measurements at 1.8 nm using the scanning PSM and (2) CPC2.5 measurements that are stepwise-corrected to 1.7-nm threshold size. Within their experimental uncertainties, the nucleation rates obtained by both these methods agree well with the values obtained with the AEROCLOUD kinetic model.

The stepwise-corrected method is described in detail in ref. 55, but a brief summary is provided here. The nucleation rates are derived from the rate of change of the formation rates, dN CPC /dt, where N CPC is the particle number concentration measured with the CPC2.5 above its detection threshold, d th . The formation rate is corrected in two sequential steps for particle losses to chamber walls, dilution and coagulation: (1) particle losses above d th and (2) particle losses during growth from 1.7 nm to d th . The dilution and wall loss rates are the same as in the kinetic model. To calculate the coagulation rate, the particles are divided into size bins and then the loss rate in each bin i is computed by summing the size-dependent collision (coagulation-loss) rate of the particles in bin i with those in all other bins. The total coagulation loss rate is then the sum of the particle loss rates in each bin i.

Correcting for particle losses during growth from 1.7 nm to d th (item (2) above) requires knowledge of the particle growth rate. This is experimentally determined with several instruments, for example, from the appearance times measured in the scanning PSM56, which detects particles over a range of threshold diameters between 1 nm and 2.5 nm. The growth rates were also measured over different size ranges with several other instruments, including a fixed-threshold PSM, two DEG-CPCs, a TSI 3776 CPC, an APi-TOF, an NAIS, an nRDMA and a nano-SMPS. The experimental growth rates are parameterized because they cannot be measured sufficiently precisely at each point in time during all events. To determine the nucleation rate at 1.7 nm from the corrected formation rate at d th , the size interval is divided into m log-normally spaced bins, dlog(D p ), chosen to match the spacing of the SMPS bins at larger sizes. The residence time of a particle in each bin is δt = δd i /(growth rate), where δd i is the size of bin i. Starting with the measured particle distribution above d th , the size distribution and formation rate is then extended towards 1.7 nm in a stepwise process. In the first step, using the known loss rates due to the chamber walls, dilution and coagulation, as well as the time δt, the concentration in the largest new bin is calculated, as well as the formation rate into this bin. Using this concentration, the size distribution is updated and the process is repeated until, after m steps, the smallest size bin at 1.7 nm is reached, where the nucleation rate is determined.

The NAIS

The neutral cluster and air ion spectrometer (NAIS)57 measures the size distributions of positively and negatively charged particles, and also of total (charged plus neutral) particles, between mobility-equivalent diameters of 0.75 nm and 45 nm. Because the instrument includes two mobility analysers operating in parallel, positive and negative spectra are obtained simultaneously, each with 21 electrometers. Taking into account the internal diffusion losses, the mobility distribution is then calculated in 28 size bins from the measured electrometer currents.

The instrument operates sequentially in three modes: ion, particle and offset mode (one cycle takes 150 s). The aerosol sample first passes through a preconditioning section containing a discharger, an electric filter, a charger and a second electric filter (post-filter). The charger and discharger are corona needles of opposite polarities. In ion mode, the preconditioning unit is switched off and the sample passes through unaffected. In this way, the mobility analysers measure only ions and charged particles from the CLOUD chamber. In particle mode—which was not used for the results reported here—both chargers are switched on and so neutral particles from the CLOUD chamber can be classified. The post-filters improve the measurements by removing residual ions from the charger. In offset mode, the dischargers and corresponding filters are switched on. The sample is charged to the opposite polarity as the subsequent analyser and so no detectable particles can enter. In this way, the noise levels and possible parasitic currents are measured to provide corrections for the preceding ion and particle measurement.

After preconditioning, the aerosol sample is classified in two cylindrical mobility analysers. The central electrode consists of several sections, each at a different fixed electric potential. The particles enter the analysers through a circular slit near the central electrode and are collected at the 21 outer electrodes where they transfer their charge to the connected electrometer and the resulting current is measured. The analysers operate at a sheath flow rate of 60 l min−1. Filtered excess air serves as sheath gas to ensure conditions similar to the sample flow. The data inversion that converts the measured electrometer currents to particle concentrations is based on model calculations simulating trajectories of particles with different mobilities, and on calibration measurements of the internal losses. The performance of the NAIS for ion-mobility (size) and concentration measurements is described in refs 58, 59.

The APi-TOF mass spectrometer

The atmospheric pressure interface time-of-flight (APi-TOF) mass spectrometer14 measures the mass-to-charge ratio of positive or negative ions with an inlet at atmospheric pressure. The first stage of the instrument consists of an atmospheric pressure interface (APi) section where ions are focused and guided by two quadrupoles and an ion lens through three chambers at progressively lower pressures down to 10−4 mbar. The second stage of the instrument is a time-of-flight (TOF) mass spectrometer at 10−6 mbar.

The APi-TOF was connected to the CLOUD chamber via a 1″ (21.7-mm inner diameter) sampling probe shared with the NAIS. A Y-splitter divided the total flow of 20 l min−1 equally between the two instruments. The sample flow for the APi-TOF was 0.8 l min−1, with the remainder being discarded.

The APi-TOF measurements were made during GCR and π+ beam runs; that is, the ions were charged by GCRs or charged pions traversing the CLOUD chamber. Because the APi-TOF can measure only one polarity at a time, positive and negative ions were measured in different runs. Different instrument settings were used during the campaigns to optimize detection in the low- or high-mass regions of the spectrum. The data were analysed with tof Tools35, developed by the University of Helsinki. The tool is implemented in MATLAB and allows complete processing of TOF data: averaging, mass calibration, baseline detection, peak fitting and high-resolution analysis.

The CI-APi-TOF mass spectrometer

Two nitrate chemical ionization atmospheric pressure interface time-of-flight (CI-APi-TOF) mass spectrometers were used to measure neutral sulfuric acid and HOMs. The instruments were operated by the University of Frankfurt (UFRA-CI) and the University of Helsinki (UHEL-CI); differences between the two instruments are indicated in this section by adding the UHEL-CI characteristics in parentheses after those of the UFRA-CI. The CI-APi-TOF has been described previously36,37. The sample air from the CLOUD chamber was drawn in through a 1/2″ stainless steel tube at flow rate of 9 l min−1 (10 l min−1). An electrostatic filter was installed in front of each instrument to remove ions and charged clusters formed in the chamber. The geometry of both ion sources follows the design of ref. 60, but a corona charger34 (X-ray generator) is used for ion generation. Dry air with nitric acid vapour is flushed over the ionizer to generate ions. The ions are guided into the sample flow with an electric field, where they react with sulfuric acid and HOMs. The reaction time is approximately 50 ms (200 ms) before the ions enter the APi section through a pinhole with a diameter of 350 μm (300 μm). The APi section consists of three consecutive differentially pumped chambers where the pressure is progressively reduced and the ions are focused by two sets of quadrupoles and an ion lens system. The mass-to-charge ratios, m/z, of the ions that pass through these chambers are measured by a time-of-flight (TOF) mass spectrometer (Tofwerk AG).

The voltage settings in the APi-TOF section influence the mass-dependent transmission efficiency. The transmission curves were determined in a series of calibration measurements in which various perfluorinated acid vapours of different m/z were passed into the instrument in sufficient amounts to saturate all the primary ions. In this way, a constant ion signal could be generated at each m/z and so the transmission efficiency could be determined relative to that of the primary ions mass range. The UFRA-CI operated at the same voltage settings for the entire data collection period; the UHEL-CI was operated in a switching mode between two voltage settings optimized for low and high m/z, respectively.

The raw data were analysed with the MATLAB tofTools package35. The mass scale is calibrated to an accuracy of better than 10 p.p.m. using a two-parameter fit. The concentration of sulfuric acid is calculated from the ratio of bisulfate ion counting rates (in s−1) relative to primary ions as follows:

The factor corrects for losses in the sampling line from the CLOUD chamber. The calibration coefficient, C, is determined by connecting the CI-APi-TOF to a well-characterized H 2 SO 4 generator61. The value of C depends on the voltage settings in the APi-TOF section and was determined to be 6.5 × 109 cm−3 (1.2 × 1010 cm−3 and 2.8 × 109 cm−3 for the high and low m/z settings, respectively), with an uncertainty of +50%/−33%. The H 2 SO 4 detection limit is 5 × 104 cm−3 or slightly lower.

The concentration of a HOM at m/z = i is calculated as follows:

Here, is the background-subtracted counting rate of the HOM. Background levels were measured by sampling air from the clean CLOUD chamber without any α-pinene present. The factor T i is the mass-dependent transmission efficiency. The calibration coefficient, C, is the same as that obtained for sulfuric acid because HOMs and sulfuric acid were shown to have similar molecular collision rates with the nitrate ions16. Furthermore, the binding of with highly oxidized HOMs is found in the present study to be strong, so clustering should proceed at near the kinetic limit, as it does for with sulfuric acid. The factor corrects for losses in the sampling line from the CLOUD chamber. The values were determined for E 1 and E 2 separately, using experimentally determined diffusion coefficients, as and .

The HOM monomers, E 1 , are the background-subtracted sum of the peaks in the m/z band 235–424 Th; the HOM dimers, E 2 , are the corresponding sum for 425–625 Th. Instrumental contamination peaks are excluded from the band summation, as are peaks assigned to the RO 2 · radical (C 10 H 15 O 6,8,10,12 , which correspond to m/z = 293 Th, 325 Th, 357 Th and 389 Th). Total HOMs is defined as the sum RO 2 · + E 1 + E 2 .

HOM yields

The HOM yields from either ozonolysis or OH· chemistry were calculated by assuming equal production and loss rates during steady-state16:

where the yield, γ Ox , is the fraction of α-pinene (AP) oxidation reactions leading to HOM formation, and ‘Ox’ signifies O 3 or OH·. The values of the rate constants (in cm3 per molecule per second) at 278 K for oxidation of α-pinene are and k AP + OH· = 5.84 × 10−11, from the International Union of Pure and Applied Chemistry (IUPAC)62 (the α-pinene + O 3 rate constant is updated on the IUPAC website at http://iupac.pole-ether.fr/htdocs/datasheets/pdf/Ox_VOC8_O3_apinene.pdf). The HOM wall loss rate was determined to be 1.1 × 10−3 s−1, assuming they are irreversibly lost. An additional loss is due to dilution of the chamber contents by makeup gases (0.1 × 10−3 s−1). The total loss rates for HOMs is then k loss = 1.2 × 10−3 s−1.

During the experiments involving pure OH· chemistry, nitrous acid (HONO) concentrations ranging from 0.5 p.p.b.v. to 3 p.p.b.v. were photolysed by ultraviolet radiation from the fibre optic system to produce OH·. This led to a small contamination of NO in the chamber, which may potentially influence the HOM yield. The OH· concentrations in the CLOUD chamber were estimated using the PTR-TOF measurements of the difference of the α-pinene concentrations with no OH· present (ultraviolet off) and OH· present (ultraviolet on at different intensities). The decrease in α-pinene was due to only OH· reactions, because no O 3 was present in the chamber during these experiments. The accuracy for [OH·] is estimated to be ±30% (1σ) including uncertainties in α-pinene measurements and reaction rate constant, which leads to a systematic scale uncertainty on the HOM production rate, k AP + OH· [AP][OH·], of ±40% (1σ). However, run-to-run uncertainties contribute substantially to the overall uncertainty as indicated by the error bars in Extended Data Fig. 2.

The SO 2 -CIMS

The SO 2 chemical ionization mass spectrometer (SO 2 -CIMS) uses primary ions to convert SO 2 to , which is then measured in a quadrupole mass spectrometer with an APi interface (Georgia Tech). The general design of the ion source is shown in ref. 60, but the primary ions are generated with a corona discharge34. The corona needle holder was modified so that CO 2 , O 2 and Ar are fed directly over the corona discharge. In this way, direct contact between the N 2 sheath flow and the discharge needle is avoided, which leads to a reduced contamination by and maximizes the ratio of to . The reaction scheme for the ionization of SO 2 to can be found in ref. 63. The use of a dry N 2 buffer flow in front of the pinhole of the mass spectrometer evaporates associated water molecules from ions, and so sulfur dioxide is detected in the mass spectrum at m/z = 112 Th ( ).

The SO 2 concentration (in p.p.t.v.) is calculated from the ion count rates, R m/z , as follows:

where R 112 corresponds to the background-corrected ion count rate of and R 60 is the ion count rate of the primary ion . The calibration factor C S was obtained by periodically calibrating the instrument with a SO 2 gas standard (Carbagas AG) during the campaign. During a calibration, the gas standard was diluted with ultraclean humidified air at 38% relative humidity (the same as that supplied to the CLOUD chamber) to achieve a range of different SO 2 mixing ratios between 12 p.p.t.v. and 11 p.p.b.v. The calibration factor was found to be 1.3 × 105 p.p.t.v., with an estimated uncertainty of ±11%. The error includes uncertainties in the flow rates during a calibration and in the gas standard concentration, as well as statistical uncertainties. However, we also observed that temperature changes in the experimental hall where the experiments were conducted led to a drift in the background signal when no SO 2 was applied to the CIMS. This effect contributes to the overall uncertainty and mainly affects the measurement at low SO 2 levels (<100 p.p.t.v.), with lower precision in this concentration range. For example, at 30 p.p.t.v. SO 2 , the estimated uncertainty is ±23%, but it becomes progressively smaller with higher SO 2 levels, reaching ±13% above 100 p.p.t.v. SO 2 . The detection limit of the instrument is 15 p.p.t.v. SO 2 .

Experimental errors

To determine J 1.7 , the measured particle concentrations in the PSM1.8 and CPC2.5 versus time are fitted with the AEROCLOUD model (see above). The nucleation rate error, σ J , has three main components. The dominant error at slow growth rates is due to uncertainties in the PSM1.8 and CPC2.5 detection thresholds for HOM particles64. The threshold error components are first determined numerically for each nucleation measurement by performing additional AEROCLOUD fits after shifting the PSM1.8 particle detection threshold by +0.2/−0.1 nm and the CPC2.5 threshold by ±0.4 nm. This provides four fractional J 1.7 errors which are then averaged for each counter to provide a mean fractional uncertainty, σ psm and σ cpc , respectively. The total error due to detection threshold uncertainties, σ thr , for the combined fit to the PSM1.8 and CPC2.5 data is then:

The total fractional J 1.7 error, σ J , is then obtained by adding σ thr in quadrature with an experimental error due to run-to-run reproducibility under nominally identical chamber conditions, σ exp , and an error to account for model approximations, σ model :

where σ exp = 30% and σ model = 50%.

The concentration of O 3 is measured with a calibrated instrument and is known to ±10%. The α-pinene concentration in the PTR-TOF is known to ±10%. As discussed above, the uncertainty on SO 2 is ±13% above 150 p.p.t.v., increasing at lower values to ±23% at 30 p.p.t.v.

For CI-APi-TOF measurements, the run-to-run experimental uncertainties are ±10% for [H 2 SO 4 ] and ±20% for [HOM]. However, there is a larger overall systematic error that scales all measurements by the same amount. The systematic scale uncertainty for [H 2 SO 4 ] is estimated to be +50%/−33%. This estimate is based on a comparison of [H 2 SO 4 ] measurements with a CIMS and a calibrated H 2 SO 4 generator61. The systematic uncertainties for [HOM] have the following sources and fractional errors (1σ): sulfuric acid calibration (50%), charging efficiency of HOMs in the ion source (25%), mass dependent transmission efficiency (50%) and sampling line losses (20%). This results in an overall systematic scale uncertainty for [HOM] of +80%/−45%. The uncertainty in the HOM yield from ozonolysis or hydroxyl chemistry is estimated by adding the [HOM] uncertainty in quadrature with the errors for α-pinene (10%), O 3 (10%), OH· (30%), HOM wall loss rate (6%) and rate constants (35% for the α-pinene O 3 reaction and 20% for the α-pinene OH· reaction). This results in a mean estimated uncertainty in HOM yield for either ozonolysis or hydroxyl chemistry of +100%/−60%.

Quantum chemical calculations

To estimate the characteristic binding energies and evaporation rates expected for ELVOC clusters, we chose C 10 H 14 O 7 (molecular weight of 246) to represent the ELVOC monomer, E 1 , and C 20 H 30 O 14 (molecular weight of 494) to represent the covalently bound ELVOC dimer, E 2 . Their formation mechanism and structures are shown in Extended Data Figs 3 and 7. To evaluate the effect of charge on the formation of ELVOC clusters, we studied initial molecular clusters of E 1 and E 2 that are either neutral or else include an ion of the type , , or (Extended Data Table 1).

We calculated formation Gibbs free energies at 278 K, ΔG 278 K , of different clusters with the MO62X functional65 and the 6-31+G(d) basis set66 using the Gaussian09 program67. The formation Gibbs free energy can be related to evaporation rate as described in refs 68, 69. In previous works10,15, we used the method proposed in ref. 68 for calculating the formation free energy of different clusters. However, this method is too computationally demanding for the large clusters of the present study. The MO62X functional has been shown to be well suited to the study of atmospheric clusters70. Ref. 70 has shown how reducing the basis set from the largest Pople basis set available (6-311++G(3df,3pd)) to the basis set used in this work (6-31+G(d)) leads to differences in the calculated formation free energies below 1 kcal mol−1. Therefore, MO62X/6-31+(d) is a good alternative to the B3RICC2 method68 when studying large clusters. We confirmed this by comparing the formation free energies previously calculated15 using the B3RICC2 method with those calculated here using the MO62X/6-31+G(d) method. The differences were found to be below 2 kcal mol−1.

Parameterization of the pure biogenic nucleation rate

We parameterized the experimentally measured pure biogenic nucleation rates in a form suitable for global aerosol models. The neutral and ion-induced pure biogenic nucleation rates (in cm−3 s−1) are parameterized as:

where [n ± ] = [n + ] = [n − ] is the small-ion concentration of either sign. Expressions for [HOM] and [n ± ] are given in equations (7) and (10) below, respectively. The parameters a n are determined from fits to the data in Fig. 3 and have the values a 1 = 0.04001, a 2 = 1.848, a 3 = 0.001366, a 4 = 1.566 and a 5 = 0.1863, with [HOM] expressed in units of 107 cm−3. The parameterized rates are shown by the curves in Fig. 3. The R2 value of the fit is 0.97. The terms a 1–4 describe simple power laws, whereas the term a 5 accounts for the steepening of the nucleation rate at low HOM concentrations. The nucleation rates are assumed to be independent of temperature, except for the effect of rate constants (equation (6) below), because the experimental measurements exist at only a single temperature.

The HOM concentration in equation (4) is determined from its production and loss rates:

where MT represents total monoterpenes. The IUPAC62 reaction rate constants (in cm3 per molecule per second) for oxidation of α-pinene by ozone and hydroxyl radicals are, respectively:

where T (in K) is the temperature (the α-pinene+O 3 rate constant is updated on the IUPAC website at http://iupac.pole-ether.fr/htdocs/datasheets/pdf/Ox_VOC8_O3_apinene.pdf). The HOM yields in each ozone–monoterpene and hydroxyl–monoterpene reaction are and , respectively. The parameter k HOM is the HOM loss rate or, equivalently, the atmospheric condensation sink, CS (in s−1). The condensation sink is determined assuming the diffusion characteristics of a typical α-pinene oxidation product (see appendix A1 of ref. 71). Assuming steady-state in equation (5), the HOM concentration becomes:

where the HOM yield from ozonolysis is , and from reaction with the hydroxyl radical is (Extended Data Fig. 2). The HOM yield from ozonolysis is determined from CLOUD measurements in the presence of a hydroxyl scavenger (0.1% H 2 ). The HOM yield from reaction with hydroxyl radicals is determined from CLOUD measurements in the absence of ozone, and where photolysed HONO provides the OH· source. Therefore, the experimental measurement of hydroxyl-initiated oxidation is made in the presence of NO x , as occurs in the atmosphere.

The small-ion concentration in equation (4) is calculated from the steady-state solution of the ion balance equation:

where q (in cm−3 s−1) is the ion-pair production rate and α is the ion–ion recombination coefficient (in cm3 s−1). The factor of 2 in equation (4) accounts for nucleation from positive and negative ions. For the CLOUD GCR data, q = 1.7 cm−3 s−1. Terrestrial radioactivity such as radon contributes additional ionization in the boundary layer over land masses72. The ion loss rate, k i , is due to the condensation sink, CS, and ion-induced nucleation:

where J iin /(2[n ± ]) is given by equation (4) and the steady-state concentration of small ions is, from equation (8):