Homogeneous Nucleation Limit Research Articles

The limit of macroscopic homogeneous ice nucleation at the nanoscale.

Nucleation in small volumes of water has garnered renewed interest due to the relevance of pore condensation and freezing under conditions of low partial pressures of water, such as in the upper troposphere. Molecular simulations can in principle provide insight on this process at the molecular scale that is challenging to achieve experimentally. However, there are discrepancies in the literature as to whether the rate in confined systems is enhanced or suppressed relative to bulk water at the same temperature and pressure. In this study, we investigate the extent to which the size of the critical nucleus and the rate at which it grows in thin films of water are affected by the thickness of the film. Our results suggest that nucleation remains bulk-like in films that are barely large enough accommodate a critical nucleus. This conclusion seems robust to the presence of physical confining boundaries. We also discuss the difficulties in unambiguously determining homogeneous nucleation rates in nanoscale systems, owing to the challenges in defining the volume. Our results suggest any impact on a film's thickness on the rate is largely inconsequential for present day experiments.

Spinodal limits of supercooled liquid Al deduced from configuration heredity of crystal clusters

Whether one-component supercooled liquid encounters a spinodal limit at a sufficiently low temperature has been a controversial issue. To explore the homogeneous nucleation limit (HNL) in liquid Al, a series of molecular dynamics simulations have been performed, and a unique technique able to distinguish the critical nucleus from various embryos has been adopted to measure the crystal nucleation time τN of supercooled liquids and evaluate the nucleation energy barrier ΔEcri∗ in isothermal crystallization. The estimated kinetic spinodal (i.e., HNL) temperature Tks and thermodynamic spinodal temperature Tts are 0.51 Tm and 0.45 Tm, respectively. At the HNL, the nucleation energy barrier ΔEcri∗ is discovered to be very small, and a critical slowdown behavior is also observed near Tks. A careful analysis for the Stokes-Einstein (SE) relation reveals the temperature TSE of SE relation breakdown is only 0.02 Tm higher than Tks, and the occurrence of HNL is not affected by whether the SE relation breaks down or not. These results are consistent with previous reports. To some extent, the small gap between TSE and Tks can be attributed to a weak glass formation ability of liquid Al.

Water above the spinodal.

The liquid spinodal has long been discussed alongside the elusive liquid-liquid critical point hidden behind the limit of homogeneous nucleation. This has inspired numerous scenarios that attempt to explain water anomalies. Despite recent breakthrough experiments doubting several of those scenarios, we lacked a tool to localize the spinodal and the liquid-liquid critical point. We constructed a unique equation of state combining Speedy's well known expansion and the liquid-liquid critical point to remove that deficit and to review these explanations. For the first time, the proposed equation of state independently depicts the spinodal in the presence of the liquid-liquid critical point and demonstrates that the explanation for water anomalies based on the reentrance of the spinodal is not valid; this feature (reentrance of the spinodal) was predicted because the density surface is curved by the presence of the second critical point. However, the critical point alone is not sufficient to explain the shape of the density surface of water. In the new equation, hydrogen bond cooperativity is important to force the critical point to exist outside of zero temperature. Together with the recent discovery of a compressibility maximum behind the homogeneous nucleation limit at positive pressure, the findings argue in favor of excluding all explanations for water anomalies except for the existence of the liquid-liquid critical point at positive pressure. Finally, an extensive study of heat capacity demonstrated profound disagreement between the two major experimental heat capacity datasets and identified the more accurate dataset.

CO2 condensation onto alkanes: unconventional cases of heterogeneous nucleation.

The classical picture invoked for heterogeneous nucleation is frequently that of a liquid condensing onto an immiscible solid particle. Here, we examine heterogeneous nucleation of CO2 onto particles comprised of n-pentane or n-hexane under conditions where CO2 should be a solid and the seed particles may be liquid or solid. Although CO2 condensed under all but one of the six conditions investigated, these experiments do not easily fit into the framework of standard heterogeneous nucleation experiments. Rather they explore unconventional regimes of heterogeneous nucleation in which the state of the seed particle may both affect whether deposition can proceed, and, in turn, be influenced by the presence of the condensing species. The work complements the earlier work of Tanimura et al. [RSC Adv., 2015, 5, 105537-105550] that investigated CO2 condensation onto ice nanoparticles, by using seed particles comprised of non-polar compounds that form and freeze under conditions where CO2 is already supersaturated with respect to the solid ice. In some cases, the conditions for seed formation approach the limit of homogeneous CO2 nucleation. Vibrational spectroscopy measurements help pinpoint where CO2 starts to condense. Furthermore, these IR measurements suggest that the n-alkanes never freeze in the presence of CO2, even if the temperatures are well below those required for them to freeze when CO2 is absent. Over the temperature range 65 < T/K < 140, the conditions corresponding to the onset of CO2 heterogeneous nucleation on pre-existing seed particle almost all lie very close to the extrapolated vapor-liquid equilibrium line of CO2 for a broad range of seed materials.

X-ray emission spectroscopy of bulk liquid water in "no-man's land".

The structure of bulk liquid water was recently probed by x-ray scattering below the temperature limit of homogeneous nucleation (TH) of ∼232 K [J. A. Sellberg et al., Nature 510, 381-384 (2014)]. Here, we utilize a similar approach to study the structure of bulk liquid water below TH using oxygen K-edge x-ray emission spectroscopy (XES). Based on previous XES experiments [T. Tokushima et al., Chem. Phys. Lett. 460, 387-400 (2008)] at higher temperatures, we expected the ratio of the 1b1' and 1b1″ peaks associated with the lone-pair orbital in water to change strongly upon deep supercooling as the coordination of the hydrogen (H-) bonds becomes tetrahedral. In contrast, we observed only minor changes in the lone-pair spectral region, challenging an interpretation in terms of two interconverting species. A number of alternative hypotheses to explain the results are put forward and discussed. Although the spectra can be explained by various contributions from these hypotheses, we here emphasize the interpretation that the line shape of each component changes dramatically when approaching lower temperatures, where, in particular, the peak assigned to the proposed disordered component would become more symmetrical as vibrational interference becomes more important.

Deeply-cooled water under strong confinement: neutron scattering investigations and the liquid–liquid critical point hypothesis

We present an overview of recent experimental investigations into the properties of strongly-confined water below the bulk freezing temperature. Under strong confinement, the crystallization of water is completely suppressed and the behavior of the confined liquid state can be measured at temperatures and pressures that are inaccessible to the bulk liquid. We focus on two phenomena that have recently been discovered in strongly confined water: the density minimum and the fragile-to-strong dynamic crossover. All experimental results seem to indicate that confined water undergoes a unique kind of transition below the bulk homogeneous nucleation limit. Much of the recent work on deeply-cooled water under strong confinement has been motivated by the liquid-liquid critical point (LLCP) hypothesis. We discuss this hypothesis in the context of the various experimental findings.

How safe is to safely enter in the water no-man's land?

Salt solvation and confinement can be efficiently used to supercool aqueous samples to temperatures well below the homogeneous nucleation limit of pure water. Does it imply that the behavior of water in regions of the thermodynamic space not experimentally accessible may be inferred from that of salty or confined water? Neutron diffraction and broad band dielectric spectroscopy are used to discuss this issue, and put into evidence advantages and risks of a straightforward extrapolation.

Heterogeneous freezing of water droplets containing kaolinite particles

Abstract. Clouds composed of both ice particles and supercooled liquid water droplets exist at temperatures above ~236 K. These mixed phase clouds, which strongly impact climate, are very sensitive to the presence of solid particles that can catalyse freezing. In this paper we describe experiments to determine the conditions at which the clay mineral kaolinite nucleates ice when immersed within water droplets. These are the first immersion mode experiments in which the ice nucleating ability of kaolinite has been determined as a function of clay surface area, cooling rate and also at constant temperatures. Water droplets containing a known amount of clay mineral were supported on a hydrophobic surface and cooled at rates of between 0.8 and 10 K min−1 or held at constant sub-zero temperatures. The time and temperature at which individual 10–50 μm diameter droplets froze were determined by optical microscopy. For a cooling rate of 10 K min−1, the median nucleation temperature of 10–40 μm diameter droplets increased from close to the homogeneous nucleation limit (236 K) to 240.8 ± 0.6 K as the concentration of kaolinite in the droplets was increased from 0.005 wt% to 1 wt%. This data shows that the probability of freezing scales with surface area of the kaolinite inclusions. We also show that at a constant temperature the number of liquid droplets decreases exponentially as they freeze over time. The constant cooling rate experiments are consistent with the stochastic, singular and modified singular descriptions of heterogeneous nucleation; however, freezing during cooling and at constant temperature can be reconciled best with the stochastic approach. We report temperature dependent nucleation rate coefficients (nucleation events per unit time per unit area) for kaolinite and present a general parameterisation for immersion nucleation which may be suitable for cloud modelling once nucleation by other important ice nucleating species is quantified in the future.

Lower limit of homogeneous nucleation boiling explosion for water

In this paper, the lower limit for the occurrence of homogeneous nucleation boiling explosion during water heating at atmospheric pressure has been determined by applying a new theoretical model proposed by the authors. Two different cases of water heating have been considered for the study of homogeneous nucleation boiling explosion. In one case, the liquid on the surface is linearly heated at a rate of 10 K/s to 10 9 K/s. In another case, the liquid suddenly contacts with a high temperature surface such as in case of quenching with impinging jet or droplet. With the assumption of liquid boiling without any cavity or surface effect, the liquid temperature limit at which homogeneous boiling explosion occurs essentially corresponds to a value of 302 °C even though the surface is heated very slowly. On the other hand, during water contact with hot surfaces, the occurrence of the homogeneous boiling explosion within a characteristic time period of 1 ms is obtained at a maximum liquid temperature of 303 °C for a limiting steady state boundary temperature of about 304 °C. From the definition of the steady-state interface boundary temperature of two 1-D semi-infinite body contact problem, the lower limiting surface temperatures for the occurrence of the homogeneous nucleation boiling explosion have been determined for water contact with various solid surfaces at different initial liquid temperatures ranging from 0 °C to 100 °C. The effects of the parametric variation in the boundary heating conditions on various characteristics of the homogeneous boiling explosion such as liquid temperature and time of boiling explosion, heat-flux across the liquid–vapor interface at the boiling explosion, etc. are determined and compared with other results reported in the literature.

More accurate X-ray scattering data of deeply supercooled bulk liquid water

Deeply supercooled water droplets held containerless in an acoustic levitator are investigated with high-energy X-ray scattering. The temperature dependence of the X-ray structure function is found to be nonlinear. Comparison with two popular computer models reveals that structural changes are predicted too abrupt by the TIP5P-E model, while the rate of change predicted by TIP4P-Ew is in much better agreement with experiment. The abrupt structural changes, predicted by the TIP5P-E model to occur in the temperature range between 260 and 240 K as water approaches the homogeneous nucleation limit, are unrealistic. Both models underestimate the distance between neighbouring oxygen atoms and overestimate the sharpness of the OO distance distribution.

Homogeneous bubble nucleation limit of mercury under the normal working conditions of the planned European spallation neutron source

In spallation neutron sources, liquid mercury is the subject of big thermal and pressure shocks, upon adsorbing the proton beam. These changes can cause unstable bubbles in the liquid, which can damage the structural material. While there are methods to deal with the pressure shock, the local temperature shock cannot be avoided. In our paper we calculated the work of the critical cluster formation (i.e. for mercury micro-bubbles) together with the rate of their formation (nucleation rate). It is shown that the homogeneous nucleation rates are very low even after adsorbing several proton pulses, therefore the probability of temperature induced homogeneous bubble nucleation is negligible.

Crystal Nucleation in a Supercooled Liquid with Glassy Dynamics

In simulations of supercooled, high-density liquid silica we study a range of temperature T in which we find both crystal nucleation as well as the characteristic dynamics of a glass forming liquid, including a breakdown of the Stokes-Einstein relation. We find that the liquid cannot be observed below a homogeneous nucleation limit (HNL) at which the liquid crystallizes faster than it can equilibrate. We show that the HNL would occur at lower T, and perhaps not at all, if the Stokes-Einstein relation were obeyed, and hence that glassy dynamics plays a central role in setting a crystallization limit on the liquid state in this case. We also explore the relation of the HNL to the Kauzmann temperature, and test for spinodal-like effects near the HNL.

Freezing and Melting of Water Confined in Silica Nanopores

In nanosized pores, liquid water can be thermodynamically stable down to temperatures well below the limit of homogeneous nucleation of bulk water ( approximately 235 K). Studies of water in such pores therefore offer an opportunity to reveal the anomalous behavior of deeply supercooled water. Herein we focus on recent studies of the limits of freezing and melting of water in the cylindrical pores of ordered mesoporous silicas with pore diameters in the range of 2-10 nm, based on vapor sorption measurements, calorimetric studies, NMR spectroscopy and cryoporometry, and neutron diffraction studies.

Glass-Formers and Viscous Liquid Slowdown since David Turnbull: Enduring Puzzles and New Twists

AbstractTo Turnbull's study of the kinetic problem of nucleation and growth of crystals, we add the further enquiry into what lies behind the slow nucleation kinetics of glass-formers. Our answer to this question leads to the proposal of conditions in which a pure liquid metal, monatomic and elemental, can be vitrified. Using the case of high-pressure liquid germanium, we give electron microscope evidence for the validity of our thinking.On the question of how liquids behave when crystals do not form, Turnbull pioneered the study of glass transitions in metallic alloys, measuring the heat capacity change at the glass transition Tg for the first time, and developing with Cohen the free volume model for the temperature dependence of liquid transport properties approaching Tg. We extend the phenomenological picture to include networks where free volume does not play a role and reveal a pattern of behavior that provides for a classification of glass-formers (from “strong” to “fragile”). Where Turnbull studied supercooled liquid metals and P4 to the homogeneous nucleation limit using small droplets, we studied supercooled water in capillaries and emulsions to the homogeneous nucleation limit near −40°C. We discuss the puzzling divergences observed that are now seen as part of a cooperative transition that leads to very untypical glass-transition behavior at lower temperatures (when crystallization is bypassed by hyperquenching). Finally, we show how our interpretation of water behavior can be seen as a bridge between the behavior of the “strong” (network) liquids of classical glass science (e.g., SiO2) and the “fragile” behavior of typical molecular glass-formers. The link is made using a “Gaussian excitations” model by Matyushov and the author in which the spike in heat capacity for water is pushed by cooperativity (disorder stabilization of excitations) into a first-order transition to the ground state, at a temperature typically below Tg. In exceptional cases like triphenyl phosphite, this liquid-to-glass first-order transition lies above Tg and can be studied in detail.

Limit of superheat in uniformly heated fluid

The homogeneous nucleation limit is investigated in pure liquid subject to intense uniform heating at constant pressure. The energy equation is solved in conjunction with a new non-equilibrium vapor formation model in order to predict the maximum attainable liquid superheat as a function of the heating rate. It is shown that for uniformly heated liquids, conditions related to the local temperature in a critical vapor embryo and to the local heat consumption for vapor generation on the homogeneous fluctuation centers, must be satisfied simultaneously in order to initiate explosive boiling. The effect of heating rate on the maximum attainable superheat temperature could be as high as 10 K.

Aqueous Oxygen Near the Homogeneous Nucleation Limit of Water: Stabilization With Submicron Capillaries

Previous studies have demonstrated that the metastability threshold of aqueous oxygen (AO) is inversely dependent on the internal diameter of capillary tubes used to deliver it into blood. The hypothesis was tested herein that significantly higher thresholds are attainable with capillaries having markedly smaller dimensions (submicron) than those previously studied. Water was equilibrated with oxygen over a 0.3- to 0.7-k bar range. Inert gases (argon, helium) facilitated studies at pressures to 2.5 k bar. An argon-ion laser was used to visualize fluorescein in the liquid effluent from silica capillaries that were tapered at the distal end to a submicron internal diameter (0.5 +/- 0.3 microns). During infusion of the fluorescent effluent into host water at 21 degrees C and atmospheric pressure, integrity of the effluent and lack of microbubbles were monitored by videomicroscopy. No microbubbles were noted at AO concentrations ranging from 7.5 to 12.8 ml O2/g (0.34 to 0.68 k bar, respectively) or in the aqueous argon effluent at concentrations to 14 ml Ar/g (0.75 k bar). For aqueous helium, effluent nucleation was not observed at a mean concentration of 13 +/- 3 ml He/g (2.0 +/- 0.5 k bar), with an upper value of 15.2 ml He/g (2.4 k bar). The data represent the highest values of the tensile strength of water ever observed and approximate its theoretical homogeneous nucleation limit. Thus, remarkably high metastable concentrations of AO and other gases are attainable with the use of submicron capillaries.

Curvature effect on the physical boundary of metastable states in liquids

The physical boundary of metastable states, the kinetic spinodal, is introduced as a locus where the lifetime of metastable state becomes shorter than a relaxation time to local equilibrium. The theory does not contain any adjustable parameters. If the surface tension is known, the kinetic spinodal is completely determined by the equation of state only. The curvature effect on the surface tension and nucleation barrier is considered and a general, curvature-corrected, equation for the kinetic spinodal is developed. The theory was tested against experimental data for the homogeneous nucleation limit of superheated, stretched, and supercooled water. In all cases, good agreement between theoretical predictions and experimental data was achieved. We find that in water, the Tolman length is negative and the curvature effect increases the surface tension and the nucleation barrier. The glass transition in supercooled water is also discussed. The high-temperature limit for glassy states is introduced as a second root of the kinetic equation in supercooled fluids.

Physical Limit of Stability in Supercooled Liquids

The kinetic spinodal (KS) in supercooled liquids, similar to the KS in superheated and stretched liquids, has been introduced as a locus where the mean time of formation of a critical nucleus becomes shorter than a relaxation time to local equilibrium. If the surface tension of the solid–liquid interface is known, the kinetic spinodal is completely determined by the equation of state of the supercooled liquid. The theory was tested against experimental data for the surface tension and the homogeneous nucleation limit for supercooled water. Reasonably good agreement between theoretical predictions and experimental data was observed. A prediction of the high-temperature limit for glass transitions is also discussed.

Pressure and power generation during explosive vaporization on a thin-film microheater

When a liquid is superheated above its boiling point to temperatures near or at the homogeneous nucleation limit, the energy released could create a so-called explosive vaporization, if a significant fraction of this energy is manifested in the form of vapor expansion. In this study, a thin-film microheater (100 μm×110 μm) was placed on the underside of a water layer. The surface temperature of the heater was rapidly (6 μs) raised electrically, well above the boiling point of water. As a result, rapid vaporization took place. Due to its rapid growth, the vapor volume performs mechanical work on its surrounding and emits acoustic pressure waves. By measuring the acoustic emission from an expanding volume, the dynamic growth of the vapor microlayer is reconstructed where a linear expansion velocity up to 17 m/s was reached. Using the Rayleigh–Plesset equation, an absolute pressure inside the vapor volume of 7 bar was calculated from the data of the acoustic pressure measurement. The amount of extractable mechanical energy produced from the explosive expansion of a vapor microlayer on a thin-film microheater surface, its rate of production, and the energy conversion efficiency was also quantified in this work.

Flashing Inception in Water During Rapid Decompression

A phenomenological model is presented for predicting the thermodynamic conditions at the onset of flashing in liquid undergoing a static or flow depressurization transient. It is shown that at extremely high rates of decompression (pulse expansion), a liquid may reach the homogeneous nucleation limit of superheat before appreciable phase transition occurs. A criterion for pulse expansion is derived by an asymptotic solution of the mass and energy equations in conjunction with the equation for spontaneous bubble nucleation and growth near the flashing inception point. The effect of impurities and dissolved gases is considered by an empirically defined heterogeneous nucleation coefficient. The model predicts the minimum pressure at the flashing point with a probable error of less than 11 percent, using 83 experimental data points.