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The formation of secondary ice in clouds, that is, ice particles that are created at temperatures above the limit for homogeneous freezing without the direct involvement of a heterogeneous ice nucleus, is one of the longest-standing puzzles in cloud physics. Here, we present comprehensive laboratory investigations on the formation of small ice particles upon the freezing of drizzle-sized cloud droplets levitated in an electrodynamic balance. Four different categories of secondary ice formation (bubble bursting, jetting, cracking, and breakup) could be detected, and their respective frequencies of occurrence as a function of temperature and droplet size are given. We find that bubble bursting occurs more often than droplet splitting. While we do not observe the shattering of droplets into many large fragments, we find that the average number of small secondary ice particles released during freezing is strongly dependent on droplet size and may well exceed unity for droplets larger than 300 μm in diameter. This leaves droplet fragmentation as an important secondary ice process effective at temperatures around −10°C in clouds where large drizzle droplets are present.

Ice formation on aerosol particles is a process of crucial importance to Earth’s climate and the environmental sciences, but it is not understood at the molecular level. This is partly because the nature of active sites, local surface features where ice growth commences, is still unclear. Here we report direct electron-microscopic observations of deposition growth of aligned ice crystals on feldspar, an atmospherically important component of mineral dust. Our molecular-scale computer simulations indicate that this alignment arises from the preferential nucleation of prismatic crystal planes of ice on high-energy (100) surface planes of feldspar. The microscopic patches of (100) surface, exposed at surface defects such as steps, cracks, and cavities, are thought to be responsible for the high ice nucleation efficacy of potassium (K)–feldspar particles.

Water activity (aw) and interfacial energy or surface tension (σ) are key thermodynamic parameters to describe the hygroscopic growth of atmospheric aerosol particles and their ability to serve as cloud condensation nuclei (CCN), thus influencing the hydrological cycle and climate. Due to size effects and complex mixing states, however, these parameters are not well constrained for nanoparticles composed of organic and inorganic compounds in aqueous solution. In this study, we determined aw and σ by differential Köhler analysis (DKA) of hygroscopic growth measurement data for aerosol particles smaller than 100 nm composed of aqueous ammonium sulfate (AS), D-glucose (Gl), and their mixtures. High-precision measurements of hygroscopic growth were performed at relative humidities (denoted RH) ranging from 2.0 % to 99.6 % with a high-humidity tandem differential mobility analyzer (HHTDMA) in three complementary modes of operation: hydration, dehydration, and restructuring. The restructuring mode (hydration followed by dehydration) enabled the transformation of initially irregular particles into compact globules and the determination of mass equivalent diameters. The HHTDMA-derived growth factors complemented by DKA allows for determination of water activity and surface tension from dilute to highly supersaturated aqueous solutions that are not accessible with other methods. Thus, for mixed AS / Gl nanoparticles with mass ratios of 4:1 and 1:1, the upper limit of solute mass fraction (Xs) was 0.92 and 0.98, respectively. For pure AS and Gl, the DKA-derived aw is in good agreement with electrodynamic balance and bulk measurement data. For AS particles, our aw data also agree well with the Extended Aerosol Inorganics Model (E-AIM III) over the entire concentration range. In contrast, the UNIFAC model as a part of AIOMFAC (Zuend et al., 2011) was found to overestimate aw in aqueous Gl particles, which can be attributed to unaccounted intermolecular interactions. For mixed AS and Gl nanoparticles, we observed a non-monotonic concentration dependence of the surface tension that does not follow the predictions by modeling approaches constructed for mixed inorganic/organic systems. Thus, AS / Gl particles with a 1:1 mass ratio exhibited a strong decrease of σ with increasing solute mass fraction, a minimum value of 56.5 mN m−1 at Xs≈0.5, and a reverse trend of increasing σ at higher concentrations. We suggest that D-glucose molecules surrounded by ammonium sulfate ions tend to associate, forming non-polar aggregates, which lowers the surface tension at the air–droplet interface. We analyzed the uncertainty in the DKA-derived water activity and surface tension, related to the instrumental errors as well as to the morphology of the nanoparticles and their phase state. Our studies have shown that under optimal modes of operation of HHTDMA for moderate aqueous concentrations, the uncertainty in aw and σ does not exceed 0.2 %–0.4 % and 3 %–4 %, respectively, but it increases by an order of magnitude in the case of highly concentrated nanodroplet solutions.

Mixed-phase clouds are essential for Earth’s weather and climate system. Ice multiplication via secondary ice production (SIP) is thought to be responsible for the observed strong increase in ice particle number concentration in mixed-phase clouds. In this study, we focus on the rime splintering also known as the Hallett–Mossop (HM) process, which still lacks physical and quantitative understanding. We report on an experimental study of rime splintering conducted in a newly developed setup under conditions representing convective mixed-phase clouds in the temperature range of −4 to −10 °C. The riming process was observed with high-speed video microscopy and infrared thermography, while potential secondary ice (SI) particles in the super-micron size range were detected by a custom-built ice counter. Contrary to earlier HM experiments, where up to several hundreds of SI particles per milligram of rime were found at −5 °C, we found no evidence of productive SIP, which fundamentally questions the importance of rime splintering. Further, we could exclude two potential mechanisms suggested to be the explanation for rime splintering: the freezing of droplets upon glancing contact with the rimer and the fragmentation of spherically freezing droplets on the rimer surface. The break-off of sublimating fragile rime spires was observed to produce very few SI particles, which is insufficient to explain the large numbers of ice particles reported in earlier studies. In the transition regime between wet and dry growth, in analogy to phenomena of the deformation of drizzle droplets upon freezing, we also observed the formation of spikes on the rimer surface, which might be a source of SIP.

Disparities between the measured concentrations of ice-nucleating particles (INPs) and in-cloud ice crystal number concentrations (ICNCs) have led to the hypothesis that mechanisms other than primary nucleation form ice in the atmosphere. Here, we model three of these secondary production mechanisms – rime splintering, frozen droplet shattering, and ice–ice collisional breakup – with a six-hydrometeor-class parcel model. We perform three sets of simulations to understand temporal evolution of ice hydrometeor number (Nice), thermodynamic limitations, and the impact of parametric uncertainty when secondary production is active. Output is assessed in terms of the number of primarily nucleated ice crystals that must exist before secondary production initiates (NINP(lim)) as well as the ICNC enhancement from secondary production and the timing of a 100-fold enhancement. Nice evolution can be understood in terms of collision-based nonlinearity and the “phasedness” of the process, i.e., whether it involves ice hydrometeors, liquid ones, or both. Ice–ice collisional breakup is the only process for which a meaningful NINP(lim) exists (0.002 up to 0.15 L−1). For droplet shattering and rime splintering, a warm enough cloud base temperature and modest updraft are the more important criteria for initiation. The low values of NINP(lim) here suggest that, under appropriate thermodynamic conditions for secondary ice production, perturbations in cloud concentration nuclei concentrations are more influential in mixed-phase partitioning than those in INP concentrations.

In recent years, sea spray as well as the biological material it contains has received increased attention as a source of ice-nucleating particles (INPs). Such INPs may play a role in remote marine regions, where other sources of INPs are scarce or absent. In the Arctic, these INPs can influence water–ice partitioning in low-level clouds and thereby the cloud lifetime, with consequences for the surface energy budget, sea ice formation and melt, and climate. Marine aerosol is of a diverse nature, so identifying sources of INPs is challenging. One fraction of marine bioaerosol (phytoplankton and their exudates) has been a particular focus of marine INP research. In our study we attempt to address three main questions. Firstly, we compare the ice-nucleating ability of two common phytoplankton species with Arctic seawater microlayer samples using the same instrumentation to see if these phytoplankton species produce ice-nucleating material with sufficient activity to account for the ice nucleation observed in Arctic microlayer samples. We present the first measurements of the ice-nucleating ability of two predominant phytoplankton species: Melosira arctica, a common Arctic diatom species, and Skeletonema marinoi, a ubiquitous diatom species across oceans worldwide. To determine the potential effect of nutrient conditions and characteristics of the algal culture, such as the amount of organic carbon associated with algal cells, on the ice nucleation activity, Skeletonema marinoi was grown under different nutrient regimes. From comparison of the ice nucleation data of the algal cultures to those obtained from a range of sea surface microlayer (SML) samples obtained during three different field expeditions to the Arctic (ACCACIA, NETCARE, and ASCOS), we found that they were not as ice active as the investigated microlayer samples, although these diatoms do produce ice-nucleating material. Secondly, to improve our understanding of local Arctic marine sources as atmospheric INPs we applied two aerosolization techniques to analyse the ice-nucleating ability of aerosolized microlayer and algal samples. The aerosols were generated either by direct nebulization of the undiluted bulk solutions or by the addition of the samples to a sea spray simulation chamber filled with artificial seawater. The latter method generates aerosol particles using a plunging jet to mimic the process of oceanic wave breaking. We observed that the aerosols produced using this approach can be ice active, indicating that the ice-nucleating material in seawater can indeed transfer to the aerosol phase. Thirdly, we attempted to measure ice nucleation activity across the entire temperature range relevant for mixed-phase clouds using a suite of ice nucleation measurement techniques – an expansion cloud chamber, a continuous-flow diffusion chamber, and a cold stage. In order to compare the measurements made using the different instruments, we have normalized the data in relation to the mass of salt present in the nascent sea spray aerosol. At temperatures above 248 K some of the SML samples were very effective at nucleating ice, but there was substantial variability between the different samples. In contrast, there was much less variability between samples below 248 K. We discuss our results in the context of aerosol–cloud interactions in the Arctic with a focus on furthering our understanding of which INP types may be important in the Arctic atmosphere.

Feldspar is an important constituent of airborne mineral dust. Some alkali feldspars exhibit particularly high ice nucleation (IN) activity. This has been related to structural similarities of the ice (101‾0) prism planes and the (100) planes of alkali feldspar. Here the effect of generating feldspar surfaces with close to (100) orientation by means of chemically induced fracturing on the IN activity of alkali feldspar was investigated experimentally. To this end, gem-quality K-rich alkali feldspar was shifted towards more Na-rich compositions by cation exchange with an NaCl–KCl salt melt at 850 ∘C. By this procedure, a system of parallel cracks with an orientation close to the (100) plane of the feldspar was induced. Droplet-freezing assay experiments performed on grain mounts of the cation-exchanged alkali feldspars revealed an increase in the overall density of ice-nucleating active site (INAS) density with respect to the untreated feldspar. In addition, annealing at 550 ∘C subsequent to primary cation exchange further enhanced the INAS density and led to IN activity at exceptionally high temperatures. Although very efficient in experiment, fracturing by cation exchange with an alkali halide salt is unlikely to be of relevance in the conditioning of alkali feldspars in nature. However, parting planes with similar orientation as the chemically induced cracks may be generated in lamellar microstructures resulting from the exsolution of initially homogeneous alkali feldspar, a widespread phenomenon in natural alkali feldspar known as perthite formation. Perthitic alkali feldspars indeed show the highest IN activity. We tentatively ascribe this phenomenon to the preferential exposure of feldspar crystal surfaces oriented sub-parallel to (100).

We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert–Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information.

In this paper, we consider the thermal bath Lindblad master equation to describe the quantum nonunitary dynamics of quantum states in a multi-mode bosonic system. For the two-mode bosonic system interacting with an environment, we analyse how both the coupling between the modes and the coupling with the environment characterised by the frequency and the relaxation rate vectors affect dynamics of the entanglement. We discuss how the revivals of entanglement can be induced by the dynamic coupling between the different modes. For the system, initially prepared in a two-mode squeezed state, we find the logarithmic negativity as defined by the magnitude and orientation of the frequency and the relaxation rate vectors. We show that, in the regime of finite-time disentanglement, reorientation of the relaxation rate vector may significantly increase the time of disentanglement.

We study the photon statistics of a single-mode sub-Poissonian light propagating in the lossy thermal bosonic channel with fluctuating transmittance which can be regarded as a temperature-dependent model of the turbulent atmosphere. By assuming that the variance of the transmittance can be expressed in terms of the fluctuation strength parameter we show that the photon statistics of the light remains sub-Poissonian provided the averaged transmittance exceeds its critical value. The critical transmittance is analytically computed as a function of the input states’ parameters, temperature, and the fluctuation strength. The results are applied to study special cases of the one-mode squeezed states and the odd optical Shr¨odinger cats.