Ion-induced nucleation of pure biogenic particles.

Atmospheric aerosols and their effect on clouds are thought to be important for anthropogenic radiative forcing of the climate, yet remain poorly understood. Globally, around half of cloud condensation nuclei originate from nucleation of atmospheric vapours. It is thought that sulfuric acid is essential to initiate most particle formation in the atmosphere, and that ions have a relatively minor role. Some laboratory studies, however, have reported organic particle formation without the intentional addition of sulfuric acid, although contamination could not be excluded. Here we present evidence for the formation of aerosol particles from highly oxidized biogenic vapours in the absence of sulfuric acid in a large chamber under atmospheric conditions. The highly oxygenated molecules (HOMs) are produced by ozonolysis of α-pinene. We find that ions from Galactic cosmic rays increase the nucleation rate by one to two orders of magnitude compared with neutral nucleation. Our experimental findings are supported by quantum chemical calculations of the cluster binding energies of representative HOMs. Ion-induced nucleation of pure organic particles constitutes a potentially widespread source of aerosol particles in terrestrial environments with low sulfuric acid pollution.

The role of low-volatility organic compounds in initial particle growth in the atmosphere.

About half of present-day cloud condensation nuclei originate from atmospheric nucleation, frequently appearing as a burst of new particles near midday. Atmospheric observations show that the growth rate of new particles often accelerates when the diameter of the particles is between one and ten nanometres. In this critical size range, new particles are most likely to be lost by coagulation with pre-existing particles, thereby failing to form new cloud condensation nuclei that are typically 50 to 100 nanometres across. Sulfuric acid vapour is often involved in nucleation but is too scarce to explain most subsequent growth, leaving organic vapours as the most plausible alternative, at least in the planetary boundary layer. Although recent studies predict that low-volatility organic vapours contribute during initial growth, direct evidence has been lacking. The accelerating growth may result from increased photolytic production of condensable organic species in the afternoon, and the presence of a possible Kelvin (curvature) effect, which inhibits organic vapour condensation on the smallest particles (the nano-Köhler theory), has so far remained ambiguous. Here we present experiments performed in a large chamber under atmospheric conditions that investigate the role of organic vapours in the initial growth of nucleated organic particles in the absence of inorganic acids and bases such as sulfuric acid or ammonia and amines, respectively. Using data from the same set of experiments, it has been shown that organic vapours alone can drive nucleation. We focus on the growth of nucleated particles and find that the organic vapours that drive initial growth have extremely low volatilities (saturation concentration less than 10(-4.5) micrograms per cubic metre). As the particles increase in size and the Kelvin barrier falls, subsequent growth is primarily due to more abundant organic vapours of slightly higher volatility (saturation concentrations of 10(-4.5) to 10(-0.5) micrograms per cubic metre). We present a particle growth model that quantitatively reproduces our measurements. Furthermore, we implement a parameterization of the first steps of growth in a global aerosol model and find that concentrations of atmospheric cloud concentration nuclei can change substantially in response, that is, by up to 50 per cent in comparison with previously assumed growth rate parameterizations.

Coronavirus Disease 2019 Patients in Earlier Stages Exhaled Millions of Severe Acute Respiratory Syndrome Coronavirus 2 Per Hour.

Coronavirus disease 2019 (COVID-19) patients exhaled millions of severe acute respiratory syndrome coronavirus 2 RNA copies per hour, which plays an important role in COVID-19 transmission. Exhaled breath had a higher positive rate (26.9%, n = 52) than surface (5.4%, n = 242) and air (3.8%, n = 26) samples.

Breath-, air- and surface-borne SARS-CoV-2 in hospitals.

The COVID-19 pandemic has brought an unprecedented crisis to the global health sector. When discharging COVID-19 patients in accordance with throat or nasal swab protocols using RT-PCR, the potential risk of reintroducing the infection source to humans and the environment must be resolved. Here, 14 patients including 10 COVID-19 subjects were recruited; exhaled breath condensate (EBC), air samples and surface swabs were collected and analyzed for SARS-CoV-2 using reverse transcription-polymerase chain reaction (RT-PCR) in four hospitals with applied natural ventilation and disinfection practices in Wuhan. Here we discovered that 22.2% of COVID-19 patients (n = 9), who were ready for hospital discharge based on current guidelines, had SARS-CoV-2 in their exhaled breath (~105 RNA copies/m3). Although fewer surface swabs (3.1%, n = 318) tested positive, medical equipment such as face shield frequently contacted/used by healthcare workers and the work shift floor were contaminated by SARS-CoV-2 (3-8 viruses/cm2). Three of the air samples (n = 44) including those collected using a robot-assisted sampler were detected positive by a digital PCR with a concentration level of 9-219 viruses/m3. RT-PCR diagnosis using throat swab specimens had a failure rate of more than 22% in safely discharging COVID-19 patients who were otherwise still exhaling the SARS-CoV-2 by a rate of estimated ~1400 RNA copies per minute into the air. Direct surface contact might not represent a major transmission route, and lower positive rate of air sample (6.8%) was likely due to natural ventilation (1.6-3.3 m/s) and regular disinfection practices. While there is a critical need for strengthening hospital discharge standards in preventing re-emergence of COVID-19 spread, use of breath sample as a supplement specimen could further guard the hospital discharge to ensure the safety of the public and minimize the pandemic re-emergence risk.

Molecular understanding of sulphuric acid-amine particle nucleation in the atmosphere.

Nucleation of aerosol particles from trace atmospheric vapours is thought to provide up to half of global cloud condensation nuclei. Aerosols can cause a net cooling of climate by scattering sunlight and by leading to smaller but more numerous cloud droplets, which makes clouds brighter and extends their lifetimes. Atmospheric aerosols derived from human activities are thought to have compensated for a large fraction of the warming caused by greenhouse gases. However, despite its importance for climate, atmospheric nucleation is poorly understood. Recently, it has been shown that sulphuric acid and ammonia cannot explain particle formation rates observed in the lower atmosphere. It is thought that amines may enhance nucleation, but until now there has been no direct evidence for amine ternary nucleation under atmospheric conditions. Here we use the CLOUD (Cosmics Leaving OUtdoor Droplets) chamber at CERN and find that dimethylamine above three parts per trillion by volume can enhance particle formation rates more than 1,000-fold compared with ammonia, sufficient to account for the particle formation rates observed in the atmosphere. Molecular analysis of the clusters reveals that the faster nucleation is explained by a base-stabilization mechanism involving acid-amine pairs, which strongly decrease evaporation. The ion-induced contribution is generally small, reflecting the high stability of sulphuric acid-dimethylamine clusters and indicating that galactic cosmic rays exert only a small influence on their formation, except at low overall formation rates. Our experimental measurements are well reproduced by a dynamical model based on quantum chemical calculations of binding energies of molecular clusters, without any fitted parameters. These results show that, in regions of the atmosphere near amine sources, both amines and sulphur dioxide should be considered when assessing the impact of anthropogenic activities on particle formation.

Reduced anthropogenic aerosol radiative forcing caused by biogenic new particle formation.

The magnitude of aerosol radiative forcing caused by anthropogenic emissions depends on the baseline state of the atmosphere under pristine preindustrial conditions. Measurements show that particle formation in atmospheric conditions can occur solely from biogenic vapors. Here, we evaluate the potential effect of this source of particles on preindustrial cloud condensation nuclei (CCN) concentrations and aerosol-cloud radiative forcing over the industrial period. Model simulations show that the pure biogenic particle formation mechanism has a much larger relative effect on CCN concentrations in the preindustrial atmosphere than in the present atmosphere because of the lower aerosol concentrations. Consequently, preindustrial cloud albedo is increased more than under present day conditions, and therefore the cooling forcing of anthropogenic aerosols is reduced. The mechanism increases CCN concentrations by 20-100% over a large fraction of the preindustrial lower atmosphere, and the magnitude of annual global mean radiative forcing caused by changes of cloud albedo since 1750 is reduced by [Formula: see text] (27%) to [Formula: see text] Model uncertainties, relatively slow formation rates, and limited available ambient measurements make it difficult to establish the significance of a mechanism that has its dominant effect under preindustrial conditions. Our simulations predict more particle formation in the Amazon than is observed. However, the first observation of pure organic nucleation has now been reported for the free troposphere. Given the potentially significant effect on anthropogenic forcing, effort should be made to better understand such naturally driven aerosol processes.

Formation and evolution of molecular products in α-pinene secondary organic aerosol.

Much of our understanding of atmospheric secondary organic aerosol (SOA) formation from volatile organic compounds derives from laboratory chamber measurements, including mass yield and elemental composition. These measurements alone are insufficient to identify the chemical mechanisms of SOA production. We present here a comprehensive dataset on the molecular identity, abundance, and kinetics of α-pinene SOA, a canonical system that has received much attention owing to its importance as an organic aerosol source in the pristine atmosphere. Identified organic species account for ∼58-72% of the α-pinene SOA mass, and are characterized as semivolatile/low-volatility monomers and extremely low volatility dimers, which exhibit comparable oxidation states yet different functionalities. Features of the α-pinene SOA formation process are revealed for the first time, to our knowledge, from the dynamics of individual particle-phase components. Although monomeric products dominate the overall aerosol mass, rapid production of dimers plays a key role in initiating particle growth. Continuous production of monomers is observed after the parent α-pinene is consumed, which cannot be explained solely by gas-phase photochemical production. Additionally, distinct responses of monomers and dimers to α-pinene oxidation by ozone vs. hydroxyl radicals, temperature, and relative humidity are observed. Gas-phase radical combination reactions together with condensed phase rearrangement of labile molecules potentially explain the newly characterized SOA features, thereby opening up further avenues for understanding formation and evolution mechanisms of α-pinene SOA.

Role of sulphuric acid, ammonia and galactic cosmic rays in atmospheric aerosol nucleation.

Atmospheric aerosols exert an important influence on climate through their effects on stratiform cloud albedo and lifetime and the invigoration of convective storms. Model calculations suggest that almost half of the global cloud condensation nuclei in the atmospheric boundary layer may originate from the nucleation of aerosols from trace condensable vapours, although the sensitivity of the number of cloud condensation nuclei to changes of nucleation rate may be small. Despite extensive research, fundamental questions remain about the nucleation rate of sulphuric acid particles and the mechanisms responsible, including the roles of galactic cosmic rays and other chemical species such as ammonia. Here we present the first results from the CLOUD experiment at CERN. We find that atmospherically relevant ammonia mixing ratios of 100 parts per trillion by volume, or less, increase the nucleation rate of sulphuric acid particles more than 100-1,000-fold. Time-resolved molecular measurements reveal that nucleation proceeds by a base-stabilization mechanism involving the stepwise accretion of ammonia molecules. Ions increase the nucleation rate by an additional factor of between two and more than ten at ground-level galactic-cosmic-ray intensities, provided that the nucleation rate lies below the limiting ion-pair production rate. We find that ion-induced binary nucleation of H(2)SO(4)-H(2)O can occur in the mid-troposphere but is negligible in the boundary layer. However, even with the large enhancements in rate due to ammonia and ions, atmospheric concentrations of ammonia and sulphuric acid are insufficient to account for observed boundary-layer nucleation.

Neutral molecular cluster formation of sulfuric acid-dimethylamine observed in real time under atmospheric conditions.

For atmospheric sulfuric acid (SA) concentrations the presence of dimethylamine (DMA) at mixing ratios of several parts per trillion by volume can explain observed boundary layer new particle formation rates. However, the concentration and molecular composition of the neutral (uncharged) clusters have not been reported so far due to the lack of suitable instrumentation. Here we report on experiments from the Cosmics Leaving Outdoor Droplets chamber at the European Organization for Nuclear Research revealing the formation of neutral particles containing up to 14 SA and 16 DMA molecules, corresponding to a mobility diameter of about 2 nm, under atmospherically relevant conditions. These measurements bridge the gap between the molecular and particle perspectives of nucleation, revealing the fundamental processes involved in particle formation and growth. The neutral clusters are found to form at or close to the kinetic limit where particle formation is limited only by the collision rate of SA molecules. Even though the neutral particles are stable against evaporation from the SA dimer onward, the formation rates of particles at 1.7-nm size, which contain about 10 SA molecules, are up to 4 orders of magnitude smaller compared with those of the dimer due to coagulation and wall loss of particles before they reach 1.7 nm in diameter. This demonstrates that neither the atmospheric particle formation rate nor its dependence on SA can simply be interpreted in terms of cluster evaporation or the molecular composition of a critical nucleus.

Real-Time Studies of Iron Oxalate-Mediated Oxidation of Glycolaldehyde as a Model for Photochemical Aging of Aqueous Tropospheric Aerosols.

The complexation of iron(III) with oxalic acid in aqueous solution yields a strongly absorbing chromophore that undergoes efficient photodissociation to give iron(II) and the carbon dioxide anion radical. Importantly, iron(III) oxalate complexes absorb near-UV radiation (λ > 350 nm), providing a potentially powerful source of oxidants in aqueous tropospheric chemistry. Although this photochemical system has been studied extensively, the mechanistic details associated with its role in the oxidation of dissolved organic matter within aqueous aerosol remain largely unknown. This study utilizes glycolaldehyde as a model organic species to examine the oxidation pathways and evolution of organic aerosol initiated by the photodissociation of aqueous iron(III) oxalate complexes. Hanging droplets (radius 1 mm) containing iron(III), oxalic acid, glycolaldehyde, and ammonium sulfate (pH ∼3) are exposed to irradiation at 365 nm and sampled at discrete time points utilizing field-induced droplet ionization mass spectrometry (FIDI-MS). Glycolaldehyde is found to undergo rapid oxidation to form glyoxal, glycolic acid, and glyoxylic acid, but the formation of high molecular weight oligomers is not observed. For comparison, particle-phase experiments conducted in a laboratory chamber explore the reactive uptake of gas-phase glycolaldehyde onto aqueous seed aerosol containing iron and oxalic acid. The presence of iron oxalate in seed aerosol is found to inhibit aerosol growth. These results suggest that photodissociation of iron(III) oxalate can lead to the formation of volatile oxidation products in tropospheric aqueous aerosols.

Worldwide data sets constrain the water vapor uptake coefficient in cloud formation.

Cloud droplet formation depends on the condensation of water vapor on ambient aerosols, the rate of which is strongly affected by the kinetics of water uptake as expressed by the condensation (or mass accommodation) coefficient, αc. Estimates of αc for droplet growth from activation of ambient particles vary considerably and represent a critical source of uncertainty in estimates of global cloud droplet distributions and the aerosol indirect forcing of climate. We present an analysis of 10 globally relevant data sets of cloud condensation nuclei to constrain the value of αc for ambient aerosol. We find that rapid activation kinetics (αc > 0.1) is uniformly prevalent. This finding resolves a long-standing issue in cloud physics, as the uncertainty in water vapor accommodation on droplets is considerably less than previously thought.

Molecular understanding of atmospheric particle formation from sulfuric acid and large oxidized organic molecules.

Atmospheric aerosols formed by nucleation of vapors affect radiative forcing and therefore climate. However, the underlying mechanisms of nucleation remain unclear, particularly the involvement of organic compounds. Here, we present high-resolution mass spectra of ion clusters observed during new particle formation experiments performed at the Cosmics Leaving Outdoor Droplets chamber at the European Organization for Nuclear Research. The experiments involved sulfuric acid vapor and different stabilizing species, including ammonia and dimethylamine, as well as oxidation products of pinanediol, a surrogate for organic vapors formed from monoterpenes. A striking resemblance is revealed between the mass spectra from the chamber experiments with oxidized organics and ambient data obtained during new particle formation events at the Hyytiälä boreal forest research station. We observe that large oxidized organic compounds, arising from the oxidation of monoterpenes, cluster directly with single sulfuric acid molecules and then form growing clusters of one to three sulfuric acid molecules plus one to four oxidized organics. Most of these organic compounds retain 10 carbon atoms, and some of them are remarkably highly oxidized (oxygen-to-carbon ratios up to 1.2). The average degree of oxygenation of the organic compounds decreases while the clusters are growing. Our measurements therefore connect oxidized organics directly, and in detail, with the very first steps of new particle formation and their growth between 1 and 2 nm in a controlled environment. Thus, they confirm that oxidized organics are involved in both the formation and growth of particles under ambient conditions.

On-chip integrated differential optical microring refractive index sensing platform based on a laminar flow scheme.

We propose an on-chip integrated differential optical microring refractive index sensing platform which leverages laminar flow conditions. Close spacing between a sensing and a reference resonator, and sharing the same microfluidic channel allows the two resonators to experience similar environmental disturbances, such as temperature fluctuations and fluidic-induced transients, achieving reliable and sensitive sensing performance. We obtain a noise floor of 80.0 MHz (0.3 pm) and a bulk refractive index sensitivity of 17.0 THz per refractive index unit (RIU) (64.2 nm/RIU), achieving a limit of detection of 1.4×10(-5) RIU in a 30 min and an 8°C window.

Under What Conditions Can Equilibrium Gas-Particle Partitioning Be Expected to Hold in the Atmosphere?

The prevailing treatment of secondary organic aerosol formation in atmospheric models is based on the assumption of instantaneous gas-particle equilibrium for the condensing species, yet compelling experimental evidence indicates that organic aerosols can exhibit the properties of highly viscous, semisolid particles, for which gas-particle equilibrium may be achieved slowly. The approach to gas-particle equilibrium partitioning is controlled by gas-phase diffusion, interfacial transport, and particle-phase diffusion. Here we evaluate the controlling processes and the time scale to achieve gas-particle equilibrium as a function of the volatility of the condensing species, its surface accommodation coefficient, and its particle-phase diffusivity. For particles in the size range of typical atmospheric organic aerosols (∼50-500 nm), the time scale to establish gas-particle equilibrium is generally governed either by interfacial accommodation or particle-phase diffusion. The rate of approach to equilibrium varies, depending on whether the bulk vapor concentration is constant, typical of an open system, or decreasing as a result of condensation into the particles, typical of a closed system.

Insight into acid-base nucleation experiments by comparison of the chemical composition of positive, negative, and neutral clusters.

We investigated the nucleation of sulfuric acid together with two bases (ammonia and dimethylamine), at the CLOUD chamber at CERN. The chemical composition of positive, negative, and neutral clusters was studied using three Atmospheric Pressure interface-Time Of Flight (APi-TOF) mass spectrometers: two were operated in positive and negative mode to detect the chamber ions, while the third was equipped with a nitrate ion chemical ionization source allowing detection of neutral clusters. Taking into account the possible fragmentation that can happen during the charging of the ions or within the first stage of the mass spectrometer, the cluster formation proceeded via essentially one-to-one acid-base addition for all of the clusters, independent of the type of the base. For the positive clusters, the charge is carried by one excess protonated base, while for the negative clusters it is carried by a deprotonated acid; the same is true for the neutral clusters after these have been ionized. During the experiments involving sulfuric acid and dimethylamine, it was possible to study the appearance time for all the clusters (positive, negative, and neutral). It appeared that, after the formation of the clusters containing three molecules of sulfuric acid, the clusters grow at a similar speed, independent of their charge. The growth rate is then probably limited by the arrival rate of sulfuric acid or cluster-cluster collision.

High sensitivity nanoparticle detection using optical microcavities.

We demonstrate a highly sensitive nanoparticle and virus detection method by using a thermal-stabilized reference interferometer in conjunction with an ultrahigh-Q microcavity. Sensitivity is sufficient to resolve shifts caused by binding of individual nanobeads in solution down to a record radius of 12.5 nm, a size approaching that of single protein molecules. A histogram of wavelength shift versus nanoparticle radius shows that particle size can be inferred from shift maxima. Additionally, the signal-to-noise ratio for detection of Influenza A virus is enhanced to 381 from the previously reported 31. The method does not use feedback stabilization of the probe laser. It is also observed that the conjunction of particle-induced backscatter and optical-path-induced shifts can be used to enhance detection signal-to-noise.

Assessing the importance of nitric acid and ammonia for particle growth in the polluted boundary layer.

Aerosols formed and grown by gas-to-particle processes are a major contributor to smog and haze in megacities, despite the competition between growth and loss rates. Rapid growth rates from ammonium nitrate formation have the potential to sustain particle number in typical urban polluted conditions. This process requires supersaturation of gas-phase ammonia and nitric acid with respect to ammonium nitrate saturation ratios. Urban environments are inhomogeneous. In the troposphere, vertical mixing is fast, and aerosols may experience rapidly changing temperatures. In areas close to sources of pollution, gas-phase concentrations can also be highly variable. In this work we present results from nucleation experiments at -10 °C and 5 °C in the CLOUD chamber at CERN. We verify, using a kinetic model, how long supersaturation is likely to be sustained under urban conditions with temperature and concentration inhomogeneities, and the impact it may have on the particle size distribution. We show that rapid and strong temperature changes of 1 °C min-1 are needed to cause rapid growth of nanoparticles through ammonium nitrate formation. Furthermore, inhomogeneous emissions of ammonia in cities may also cause rapid growth of particles.

Temperature, humidity, and ionisation effect of iodine oxoacid nucleation.

Iodine oxoacids are recognised for their significant contribution to the formation of new particles in marine and polar atmospheres. Nevertheless, to incorporate the iodine oxoacid nucleation mechanism into global simulations, it is essential to comprehend how this mechanism varies under various atmospheric conditions. In this study, we combined measurements from the CLOUD (Cosmic Leaving OUtdoor Droplets) chamber at CERN and simulations with a kinetic model to investigate the impact of temperature, ionisation, and humidity on iodine oxoacid nucleation. Our findings reveal that ion-induced particle formation rates remain largely unaffected by changes in temperature. However, neutral particle formation rates experience a significant increase when the temperature drops from +10 °C to -10 °C. Running the kinetic model with varying ionisation rates demonstrates that the particle formation rate only increases with a higher ionisation rate when the iodic acid concentration exceeds 1.5 × 107 cm-3, a concentration rarely reached in pristine marine atmospheres. Consequently, our simulations suggest that, despite higher ionisation rates, the charged cluster nucleation pathway of iodic acid is unlikely to be enhanced in the upper troposphere by higher ionisation rates. Instead, the neutral nucleation channel is likely to be the dominant channel in that region. Notably, the iodine oxoacid nucleation mechanism remains unaffected by changes in relative humidity from 2% to 80%. However, under unrealistically dry conditions (below 0.008% RH at +10 °C), iodine oxides (I2O4 and I2O5) significantly enhance formation rates. Therefore, we conclude that iodine oxoacid nucleation is the dominant nucleation mechanism for iodine nucleation in the marine and polar boundary layer atmosphere.

Ion mobility-mass spectrometry with a radial opposed migration ion and aerosol classifier (ROMIAC).

The first application of a novel differential mobility analyzer, the radial opposed migration ion and aerosol classifier (ROMIAC), is demonstrated. The ROMIAC uses antiparallel forces from an electric field and a cross-flow gas to both scan ion mobilities and continuously transmit target mobility ions with 100% duty cycle. In the ROMIAC, diffusive losses are minimized, and resolution of ions, with collisional cross-sections of 200-2000 Å(2), is achieved near the nondispersive resolution of ~20. Higher resolution is theoretically possible with greater cross-flow rates. The ROMIAC was coupled to a linear trap quadrupole mass spectrometer and used to classify electrosprayed C2-C12 tetra-alkyl ammonium ions, bradykinin, angiotensin I, angiotensin II, bovine ubiquitin, and two pairs of model peptide isomers. Instrument and mobility calibrations of the ROMIAC show that it exhibits linear responses to changes in electrode potential, making the ROMIAC suitable for mobility and cross-section measurements. The high resolution of the ROMIAC facilitates separation of isobaric isomeric peptides. Monitoring distinct dissociation pathways associated with peptide isomers fully resolves overlapping peaks in the ion mobility data. The ability of the ROMIAC to operate at atmospheric pressure and serve as a front-end analyzer to continuously transmit ions with a particular mobility facilitates extensive studies of target molecules using a variety of mass spectrometric methods.

On the mixing and evaporation of secondary organic aerosol components.

The physical state and chemical composition of an organic aerosol affect its degree of mixing and its interactions with condensing species. We present here a laboratory chamber procedure for studying the effect of the mixing of organic aerosol components on particle evaporation. The procedure is applied to the formation of secondary organic aerosol (SOA) from α-pinene and toluene photooxidation. SOA evaporation is induced by heating the chamber aerosol from room temperature (25 °C) to 42 °C over 7 h and detected by a shift in the peak diameter of the SOA size distribution. With this protocol, α-pinene SOA is found to be more volatile than toluene SOA. When SOA is formed from the two precursors sequentially, the evaporation behavior of the SOA most closely resembles that of SOA from the second parent hydrocarbon, suggesting that the structure of the mixed SOA resembles a core of SOA from the initial precursor coated by a layer of SOA from the second precursor. Such a core-and-shell configuration of the organic aerosol phases implies limited mixing of the SOA from the two precursors on the time scale of the experiments, consistent with a high viscosity of at least one of the phases.