Nucleation Temperature Research Articles

HUB: a method to model and extract the distribution of ice nucleation temperatures from drop-freezing experiments

Abstract. The heterogeneous nucleation of ice is an important atmospheric process facilitated by a wide range of aerosols. Drop-freezing experiments are key for the determination of the ice nucleation activity of biotic and abiotic ice nucleators (INs). The results of these experiments are reported as the fraction of frozen droplets fice(T) as a function of decreasing temperature and the corresponding cumulative freezing spectra Nm(T) computed using Gabor Vali's methodology. The differential freezing spectrum nm(T) is an approximant to the underlying distribution of heterogeneous ice nucleation temperatures Pu(T) that represents the characteristic freezing temperatures of all INs in the sample. However, Nm(T) can be noisy, resulting in a differential form nm(T) that is challenging to interpret. Furthermore, there is no rigorous statistical analysis of how many droplets and dilutions are needed to obtain a well-converged nm(T) that represents the underlying distribution Pu(T). Here, we present the HUB (heterogeneous underlying-based) method and associated Python codes that model (HUB-forward code) and interpret (HUB-backward code) the results of drop-freezing experiments. HUB-forward predicts fice(T) and Nm(T) from a proposed distribution Pu(T) of IN temperatures, allowing its users to test hypotheses regarding the role of subpopulations of nuclei in freezing spectra and providing a guide for a more efficient collection of freezing data. HUB-backward uses a stochastic optimization method to compute nm(T) from either Nm(T) or fice(T). The differential spectrum computed with HUB-backward is an analytical function that can be used to reveal and characterize the underlying number of IN subpopulations of complex biological samples (e.g., ice-nucleating bacteria, fungi, pollen) and to quantify the dependence of these subpopulations on environmental variables. By delivering a way to compute the differential spectrum from drop-freezing data, and vice versa, the HUB-forward and HUB-backward codes provide a hub to connect experiments and interpretative physical quantities that can be analyzed with kinetic models and nucleation theory.

Multi-scale analysis for solidification of phase change materials (PCMs): Experiments and modeling

We present a multi-scale solidification framework for pure substances using laboratory experiments and mathematical modeling. The multi-scale phenomena of solidification are experimentally captured by the state-of-the-art thermal control chamber and optical devices. In particular, the transient temperature over five solidification stages is observed under various cooling rates, while the nucleation site and crystal evolution are photographed and further processed via image analysis. A unified mathematical model is also developed to quantitatively examine the solidification process at three scales: (i) the supercooling, freezing, and subcooling stages with a time-dependent boundary at the macroscale are analytically solved by Duhamel’s theorem and perturbation method; (ii) the two-dimensional (2D) dendritic growth at the mesoscale is computed by the Allen-Cahn equation through phase field modeling; and (iii) the heterogeneous nucleation at the microscale is numerically simulated. The results demonstrated that the experimental data and modeling were in close agreement with the freezing curve, nucleation temperature, nucleation time, 2D crystal evolution, and freezing time.

A theoretical model on unfrozen water content in soils and verification

Phase transition of pore water is a fundamental reason for frost heave in cold regions. Therefore, studying the variation in unfrozen water content is of great significance for understanding the freezing process of pore water and revealing the freezing mechanism in soils. In this study, a prediction model for unfrozen water content was established based on a probabilistic ice-forming model. To determine the heterogeneous nucleation rate, which is the key variation in the probabilistic model, the relationship between the water film thickness and temperature variation in the soil was characterized based on the improved premelting theory. In this process, the equivalent particle size and density of impurities on the surface of the particles were determined by introducing the particle size distribution curve and average accumulation mode of the particles. Based on the heterogeneous nucleation mechanism of ice crystals and the variation in the water film, a relationship between the heterogeneous nucleation rate and temperature was established. Subsequently, a method for calculating the equivalent contact angle related to pore water in soils was presented. The results showed that the heterogeneous nucleation rate and equivalent contact angle are positively and negatively correlated with the equivalent particle size at the same temperature, respectively, and the angle decreases with increasing solution concentration. Furthermore, the experimental data of 10 different soils showed that the variation in water content obtained by our model was in good agreement with the experimental values, particularly during the stage of rapid water phase change. The study developed an effective correlation among heterogeneous nucleation rate and equivalent contact angle of pore water and physical properties of soil, by combining crystallization theory and premelting theory, which provided a new way to explain water freezing and predict unfrozen water content in soils.

Effect of the Freezing Step on Primary Drying Experiments and Simulation of Lyophilization Processes

Lyophilization is a widely used preservation method for thermosensitive products. It consists of three process steps: freezing, primary and secondary drying. One of the major drawbacks is the long processing time. The main optimization effort was put into the primary drying phase since it is usually the longest phase. However, the freezing step is of immense importance for process efficiency and product quality. The lack of control during freezing comprises a challenge for process design and tech transfer. In this study, four different freezing steps (shelf-ramped freezing with and without holding step, precooled shelves and an ice fog method for controlled nucleation) are used and their impact on primary drying experiments and simulations is shown. Only the ice fog method is able to control the nucleation temperature leading to low dry layer resistances with low deviations. During the primary drying simulations, the control of the nucleation temperature drastically increases the precision and accuracy of the product temperature prediction. For optimal primary drying design and model predictive control, the nucleation temperature is strongly recommended to be controlled inside a Process Analytical Technology (PAT) concept to achieve reliable and reproducible process conditions.

Supercooled Liquid Ga Stretchable Electronics

AbstractBy controlling the properties of its medium, supercooled liquid Ga (SLGa) based stretchable remains stretchable at −22 °C, i.e., 52 °C below its thermodynamic melting point of Ga. Thus far, our oldest deposited SLGa circuit and film have remained liquids for 2 years at room temperature. The study investigates the crystallization of SLGa triggered by the surface energy of nucleation agents, temperature, circuit cross‐section, and mechanical impact. Based on these parameters, a method is presented to integrate electronic components with SLGa circuits without compromising its supercooling effect. Further, the large stiffness variation induced by phase transition is demonstrated in different applications. For the desired stiffness variation, the crystallization rate can be controlled by varying the temperature and cross‐section area. Finally, spray‐printing an ink of microscale SLGa microscale particles can conformally pattern Ga on a rough surface, e.g., to fabricate a stretchable array of SLGa microelectrodes. A smart patch with stretchable SLGa electrode arrays records human electrocardiogram signals in cold water and does not stain the skin after use. Its low and stable impedance in water will enable novel applications in wearable electronics.

Elucidating the Impact of Thermodynamic Hydrate Inhibitors and Kinetic Hydrate Inhibitors on a Complex System of Natural Gas Hydrates: Application in Flow Assurance

To alleviate the hydrate blockage risk in oil and gas pipelines/production facilities, thermodynamic hydrate inhibitors (THIs) and kinetic hydrate inhibitors (KHIs) are the frequently used additives/chemicals. While these additives are highly effective, the impact of low dosage of THIs (under inhibited systems) and performance of KHIs at high water cut and/or high subcooling is not well understood. In this work, a high-pressure visual stirred tank reactor was employed to investigate the impact of THIs and KHIs on the kinetics of the complex hydrates of natural gas mixtures (CH4/C2H6/C3H8) and cyclopentane at high water-cut and high subcooling (∼21 °C). Various concentrations of a THI, mono-ethylene glycol (MEG) with a dosage ranging from 0.1 to 25 wt %, and multiple KHIs (polyvinylpyrrolidone (PVP k-30, PVP k-90), caprolactam, butyl glycol ether (BGE), and polyglycerin with 0.1 wt % dosage) were evaluated for hydrate formation kinetics, onset hydrate formation/nucleation temperature, and morphological changes. Gas uptake results reveal that hydrate blockage risk is higher at low MEG content (0.1 to 10 wt %) compared to the baseline, while a significant reduction in gas uptake was observed for the high MEG content trials (20–25 wt %). With 20 and 25 wt % MEG, the hydrate nucleation temperature was reduced by 10–12 °C compared to the baseline. In context to KHIs impact, 0.1 wt % BGE and caprolactam promoted the nucleation temperature and the rate of hydrate formation/gas uptake. However, PVPs not only reduced the gas uptake kinetics but also lessened the hydrate nucleation temperature by 6–8 °C compared to the baseline data. Our results may offer new insights into optimizing hydrate inhibitors dosage to diminish the risk of hydrate blockage in subsea pipelines.

Thermochemical behaviour, solidification, thermal stability and oxidation of Al-Mg2Si composites: An experimental and thermodynamic study

Effects of Mg and Si (Mg2Si) concentration on the thermochemical behaviour, solidification, thermal stability and oxidation of Al-Mg2Si composites have been investigated. Thermochemical behaviour, solidification characteristics and solid-liquid phase transformation of the composites have been simulated using FactSage™ 7.3 software and differential scanning calorimetry (DSC) heating and cooling curve analysis. The thermal stability of the composites has been investigated through thermogravimetric analysis (TGA) analysis. The oxides formation in Al-Mg2Si composites has been explored by FESEM-EDX analysis. In the hypoeutectic Al-Mg2Si composites, the α-Al nucleation temperature decreases with the increase in Mg2Si concentration, but in the hypereutectic composites, it increases with the increase in Mg2Si concentration in the composites. The reaction starting temperature between Mg and Si in molten composite increases with the increase in Mg2Si concentration. The Mg2Si solid-liquid transition initiation temperature decreases with the increase in Mg2Si concentration in the Al-Mg2Si composites. The Mg2Si acts as a barrier for the oxidation of Al up to the melting temperature of the composites which results in an improvement in the thermal stability of Al. Al2O3, MgO, SiO2, MgAl2O4 and AlFeMgOSi are the common oxides of Al-Mg2Si composites. With the increase in Mg2Si concentration, the Al2O3 and MgO oxides formation decreases and SiO2 and MgAl2O4 oxides formation increases in the Al-Mg2Si composites.

Homogeneous water nucleation in argon, nitrogen, and nitrous oxide as carrier gases.

Experimental results for homogeneous nucleation of water droplets in the presence of argon, nitrogen, and, for the first time, nitrous oxide as carrier gases are reported. The main objective of the study was to investigate the effects of different carrier gases on the nucleation rate. These gases differ in the number of atoms comprising the molecule, which affects the expansion ratio required to reach the target nucleation temperature. The experiments cover nucleation temperatures from 220 to 260K, nucleation pressures from 40 to 73kPa, supersaturations of 6.5-20, and nucleation rates ranging from about 4 × 105 to 4 × 109cm-3s-1. The new data obtained with a modernized expansion chamber utilizing the nucleation pulse method show good agreement with the available literature data. Another important point of our work is the application of real gas corrections to calculate the nucleation temperature and supersaturation. The results show that the influence of carrier gases on nucleation rate in the investigated pressure range is modest (less than a factor of 7), while without the real gas correction, the apparent effect of carrier gas is significant, with differences as high as a factor of 90.

Effect of Gold Tailing Addition on the Mechanical Properties and Microstructure of Foam Ceramics

Tailings, with their low utilisation rate and value, pose an urgent problem that needs to be solved. This study focused on foam ceramics and glass granules, which were prepared using gold tailings as the main raw materials, and the prepared microcrystalline foam ceramics were investigated. The optimum sample (S6) of foam ceramics consists of 77 wt% of gold tailings, 6 wt% of talc, 9 wt% of bentonite, 2 wt% of calcite, 0.9 wt% of foaming agent and 0.6% of water reducer. The optimum foaming temperature is 1190 °C, and the holding time is 60 min. The compressive strength and bulk density of the samples are 7.4 MPa and 396.4 kg/m3; nucleation temperature, crystallisation temperature, and crystallisation activation energy of glass particles are 700 °C ± 50 °C, 1100 °C ± 50 °C, and 1572 kJ/mol, respectively. Microanalysis results showed that the crystal phases of foam ceramics were mainly quartz, calcium silicate, and aluminium silicate, and crystallinity increases with increasing gold tailing content. Wollastonite appeared in the crystalline phase of microcrystalline foam ceramics. When the glass granule addition reached 30% (2–3 samples), the compressive strength was increased by 19% (8.81 MPa), and the pore size distribution was more uniform.

Synergistic effects of Mn and B on iron-rich intermetallic modification of recycled Al alloy

Individual manganese (Mn) modification cannot prevent the formation of coarse and blocky Iron-rich phases in recycled Al–Si alloys. In the present work, scanning/transmission electron microscopy (SEM/TEM), thermodynamic calculations, and synchrotron X-ray imaging were comprehensively applied to reveal the synergistic effect of Mn and B (boron) on Iron-rich phase formation in Al–Si–Fe alloys during solidification. The results showed that with addition of Mn and B, the morphology of Iron-rich phase translated from the coarse primary into a uniform and hollow-shaped multibranched Chinese-script morphology. An appropriate boron amount significantly reduced the initial nucleation temperature of the primary Iron-rich phase and increased the number of nucleation cites. The TEM results show that there was no obvious orientations relationship between the AlB2 and α-Al15(MnFe)3Si2 phases. The main modification mechanism is that B was adsorbed on the oxide film surface, which hindered the formation of the Iron-rich phase at high temperature. This Mn + B compound modification method provides an alternative way to enhance the mechanical properties of recycled Al–Si alloys in industry.

Effect of thermal fluctuations in the fill tube on deuterium-tritium ice layering in an inertial confinement fusion target

Laser nuclear fusion is extremely demanding on the quality of deuterium-tritium (D-T) ice in the capsule, and obtaining high quality d-T ice requires a combination of crystal growth and β-layering. The fill tube of the capsule not only serves as the injection function, but also plugs the fill tube after d-T fuel rapid-freezing to isolate the inside and outside of the capsule, and the shape of the fill tube is also helpful for seed crystal nucleation. In this paper, the effect of the fill tube on the processes of seed crystal nucleation, crystal growth, β-layering and rapid temperature drop before ignition is investigated. The thermal fluctuations and material exchange that can be brought about by a fill tube that is too thick to be completely plugged by d-T ice, but this has an important role in our understanding of the layering process and crystallization mechanism of d-T ice inside the capsule. We also found remedial methods to overcome the adverse effects of the fill tube and were able to obtain a d-T ice layer that basically met the requirements, which laid a good foundation for subsequent research on the d-T ice layering process.

Supercool subtleties of cosmological phase transitions

We investigate rarely explored details of supercooled cosmological first-order phase transitions at the electroweak scale, which may lead to strong gravitational wave signals or explain the cosmic baryon asymmetry. The nucleation temperature is often used in phase transition analyses, and is defined through the nucleation condition: on average one bubble has nucleated per Hubble volume. We argue that the nucleation temperature is neither a fundamental nor essential quantity in phase transition analysis. We illustrate scenarios where a transition can complete without satisfying the nucleation condition, and conversely where the nucleation condition is satisfied but the transition does not complete. We also find that simple nucleation heuristics, which are defined to approximate the nucleation temperature, break down for strong supercooling. Thus, studies that rely on the nucleation temperature — approximated or otherwise — may misclassify the completion of a transition. Further, we find that the nucleation temperature decouples from the progress of the transition for strong supercooling. We advocate use of the percolation temperature as a reference temperature for gravitational wave production, because the percolation temperature is directly connected to transition progress and the collision of bubbles. Finally, we provide model-independent bounds on the bubble wall velocity that allow one to predict whether a transition completes based only on knowledge of the bounce action curve. We apply our methods to find empirical bounds on the bubble wall velocity for which the physical volume of the false vacuum decreases during the transition. We verify the accuracy of our predictions using benchmarks from a high temperature expansion of the Standard Model and from the real scalar singlet model.

Identification of ultrastructural and biochemical cuticular markers influencing temperature of ice nucleation in selected genotypes of corn.

Corn is an economically important yet frost-sensitive crop, injured at the moment of ice nucleation. However, the influence of autumn temperatures on subsequent ice nucleation temperature is unknown. A 10-day chilling treatment under phytotron conditions ("mild", 18/6°C) or ("extreme", 10/5°C) generated no-visible damage but induced changes in the cuticle of the four genotypes in this study. The putatively more cold hardy Genotypes 884 and 959 leaves nucleated at colder temperatures compared to the more sensitive Genotypes 675 and 275. After chilling treatment, all four genotypes displayed warmer ice nucleation temperatures, with Genotype 884 expressing the largest shift to warmer nucleation temperatures. Cuticular hydrophobicity reduced while cuticular thickness remained unchanged under the chilling treatment. By contrast, under five-week field conditions, cuticle thickness increased in all genotypes, with Genotype 256 expressing a significantly thinner cuticle. FTIR spectroscopy revealed increases in the spectral regions of cuticular lipids in all genotypes after phytotron chilling treatment, while those spectral regions decreased under field conditions. A total of 142 molecular compounds were detected, with 28 compounds significantly induced under either phytotron or field conditions. Of these, seven compounds were induced under both conditions (Alkanes C31-C33, Ester C44, C46, β-amyrin, and triterpene). While clear differential responses were observed, chilling conditions preceding a frost modified physical and biochemical properties of the leaf cuticle under both phytotron and field conditions indicating this response is dynamic and could be a factor in selecting corn genotypes better adapted to avoiding frost with lower ice nucleation temperature.

Approximations for the nucleation temperature of water

The previously developed experimental methodologies for determining the nucleation temperatures of water at atmospheric pressure are critically reviewed and further developed. Particular attention is focused on the methodology, in which a special approach that regulates the details of the setup of the experiments and the procedure for translating primary data into required liquid temperatures at the onset of boiling is set out. It is pointed out that following the latter methodology, either partially or fully, leads to a prediction of higher nucleation temperatures of water at atmospheric pressure compared with most previous predictions of this temperature in the range of heating rates (T˙) 106K/s to 109K/s. New approximations for the nucleation temperature as a function of the heating rate are suggested in the ranges 102K/s to 104K/s and 106K/s to 109K/s, based on the amended and revised experimental data. These approximations are expected to have a wide range of applications, including in the analysis of timing of puffing/micro-explosion in composite water/fuel droplets, inkjet printing, Nano/Micro electro-mechanical systems (N/MEMS), and in the nuclear and medical industries.

Anisotropic gravitational waves induced by hypermagnetic fields during the electroweak phase transition epoch

We study the anisotropies of gravitational waves induced by weak hypermagnetic fields which are randomly distributed and oriented during the electroweak phase transition in the early universe. The theory setup of this study is the standard model plus a real singlet scalar field, which can produce the needed strongly first order electroweak phase transition. Then we investigate how the hypermagnetic fields can convert to magnetic fields and we compute the departure of energy difference between the symmetric phase and the broken phase when the magnetic fields are turned on. It is found that the presence of the hypermagnetic fields can increase the Euclidean action, thus can decrease nucleation temperature, which can lead to a supercool plasma. We point out that the hypermagnetic field can enhance the gravitational wave production from a first order electroweak phase transition and the inhomogeneity of primordial hypermagnetic field can lead to anisotropies of gravitational waves. By examining three well-motivated distribution of hypermagnetic fields, we calculate the corresponding angular power spectra of stochastic gravitational wave background and find they can be significantly larger than the contributions of the Sachs-Wolfe effects and integrated Sachs-Wolfe effects. Our results show that the anisotropies of gravitational wave could provide a novel probe to the primordial hypermagnetic field in the electroweak phase transition epoch.

Real-time observation of the freezing stage of the mannitol solution using high-resolution optical microscopy

Vacuum freeze-drying has been expanding its influence in many fields, and the freezing stage is of utmost importance for the freeze-drying process. However, the limited understanding of the freezing stage has posed a major challenge for developing the vacuum freeze-drying process. An experimental setup was designed and employed in this paper to experimentally investigate the freezing stage of the mannitol solution. The cooling rate and solute mass fraction are chosen as the key freezing parameters. The nucleation temperature, the morphology and velocity of the freezing front, the morphology and size distribution of the ice crystals at the combination of different freezing conditions were studied. The results show that the nucleation temperature (supercooling degree) distribution could be better described by the Gauss distribution. The morphology of the freezing front is more strongly affected by the cooling rate compared with the mass fraction. In addition, the morphology of ice crystals also exhibits differences under different freezing conditions. The average size decreases with the increase of the cooling rate, while the uniformity of particle size distribution increases when increasing the cooling rate. The research could help deepen the understanding of the freezing stage in a qualitative way, and provide a reference for the theoretical research.

Freeze-Drying of Pharmaceuticals in Vials Nested in a Rack System—Part I: Freezing Behaviour

The distribution of biopharmaceuticals often requires either ultra-cold conditions or lyophilisation. In both cases, the drug product is frozen and, thus, exposed to similar stress conditions, which can be detrimental to its quality. However, these stresses can be inhibited or mitigated by a suitable formulation and/or an appropriate freezing design. This paper addresses how the key freezing parameters, i.e., ice nucleation temperature and cooling rate, impact the freezing behaviour of a sucrose-based formulation. The analysis included two loading configurations, vials directly resting on the shelf and nested in a rack system. The loading configuration affected the product freezing rate and the ice nucleation temperature distribution, resulting in larger ice crystals in the case of vials nested in a rack system. SEM micrographs and specific surface area measurements confirmed the different product morphology. Eventually, the different product morphology impacted the bioactivity recovery of lactate dehydrogenase.

Low-temperature preparation of α-Al2O3 with the assistance of seeding a novel hydroxyl aluminum oxalate

α-Al2O3 with outstanding physical and chemical properties makes it an excellent feedstock to prepare advanced ceramics, but its preparation at low temperature still remains a challenging task. Herein, hydroxyl aluminum oxalate (HAO) with an average particle size of 196 nm was successfully prepared by solvothermal reactions using 40 vol% ethanol aqueous solution (EAS) at 200 °C for 2.5 h. Meanwhile, HAO acting as seed was introduced into Al(OH)3 modified with oxalic acid (AHOD) for the first time. The results demonstrated that α-Al2O3 can be obtained by seeding 5% HAO at 900 °C and the initial nucleation temperature was as low as 780 °C. The morphologic evolution mechanism of obtained α-Al2O3 was proposed. Kinetic analysis displayed that the activation energy of γ-Al2O3 to α-Al2O3 after seeding 5% HAO was 197.01 kJ/mol.

How Does Diurnal and Nocturnal Warming Affect the Freezing Resistance of Antarctic Vascular Plants?

The Antarctic Peninsula has rapidly warmed up in past decades, and global warming has exhibited an asymmetric trend; therefore, it is interesting to understand whether nocturnal or diurnal warming is the most relevant for plant cold deacclimation. This study aimed to evaluate the effect of diurnal and nocturnal warming on Antarctic vascular plant's freezing resistance under laboratory conditions. This was studied by measuring the lethal temperature for 50% of tissue (LT50), ice nucleation temperature (INT), and freezing point (FP) on Deschampsia antarctica and Colobanthus quitensis plants. Additionally, soluble carbohydrates content and dehydrin levels were analyzed during nocturnal and diurnal temperatures increase. Nocturnal warming led to a 7 °C increase in the LT50 of D. antarctica and reduced dehydrin-like peptide expression. Meanwhile, C. quitensis warmed plants reduce their LT50 to about 3.6 °C. Both species reduce their sucrose content by more than 28% in warming treatments. Therefore, nocturnal warming leads to cold deacclimation in both plant species, while C. quitensis plants are also cold-deacclimated upon warm days. This suggests that even when the remaining freezing resistance of both species allows them to tolerate summer freezing events, C. quitensis can reach its boundaries of freezing vulnerability in the near future if warming in the Antarctic Peninsula progress.

The Role of Bismuth as Trace Element on the Solidification Path and Microstructure of Na‐Modified AlSi7Mg Alloys

The effects of Bi content as a trace element on the microstructure and the solidification path of A356.2 alloy have been investigated. The alloys containing different Bi levels (0, 20, and 200 ppm) have been modified by sodium. The experimental alloys have been thermally analyzed by using the two‐thermocouple method. Metallographic and image analysis techniques have been used to quantitatively examine the microstructural changes occurring at different Bi and Na concentrations. The results indicate how the presence of Bi as a trace element affects the eutectic structure. Upon increasing the Bi level, the nucleation and growth temperatures of eutectic Si raise, and the eutectic Si particles appear coarser in Na‐modified alloys. The EBSD analyses show that the crystallographic orientation between eutectic Al and surrounding primary Al dendrites becomes identical in Na‐modified Bi‐containing alloy. Furthermore, an irregular Bi + (Mg,Na)3Bi2 eutectic is formed prior to the precipitation of the eutectic Si, thus reducing the efficiency of Na addition to fully modify the eutectic Si.