Predictions Of Classical Nucleation Theory Research Articles

Analysis of the self-consistency of nucleation in the diffuse interface limit of binary alloy phase field models

This paper examines the process of nucleation in phase field (PF) models, with the aim of elucidating how the use of diffuse interfaces often employed for quantitative modelling of solidification affects nucleation rates and distribution statistics in relation to the predictions of classical nucleation theory. Nucleation is simulated through the use of noise in a quantitative binary alloy PF model using different interface widths. Our results reveal that the rate of nucleation in the PF model is found to be strongly dependent on the scale of the interface width and the numerical discretization, but that careful control of these quantities offers the possibility of a consistent interpretation of nucleation rate. The paper ends by assessing some of the practical merits of seeded versus noise-induced nucleation in PF modelling in the diffuse-interface limit, while also emphasizing how nucleation in this limit is fundamentally flawed from a quantitative perspective.

Size-Independent Nucleation and Growth Model of Potassium Sulfate from Supersaturated Solution Produced by Stirred Crystallization.

This paper explores the kinetics of the crystallization of potassium sulfate in a stirred bed crystallizer through experimental investigation. Employing classical nucleation theory, the homogeneous and heterogeneous nucleation mechanisms of potassium sulfate were investigated. The induction time and critical nucleation parameters, including the surface tension (γ), critical nucleation radius (r*), critical nucleation free energy (ΔG*), and critical nucleation molecule number (i*), were meticulously determined under varying temperatures and supersaturation ratios. The experimental findings revealed that as the temperature and supersaturation ratio increased, the induction time, critical nucleation free energy, critical nucleation radius, and critical molecule number decreased whereas the nucleation rate increased. The crystalline shape remains relatively unaltered with respect to temperature and supersaturation ratio, yet the particle size (D10, D50, D90) increases as the supersaturation and temperature increase. The variations in the measured nucleation parameters align well with the predictions of classical nucleation theory. Furthermore, the kinetic equations of crystal nucleation and the growth rate in a stirred crystallization system were fitted using population balance equations. The results demonstrate that the growth rate increases with increasing supersaturation and stirring rates. Additionally, the effects of the parameters in the nucleation rate equation suggested that the suspension density exerted the greatest influence, followed by the supersaturation ratio and stirring rate. This extensive research provides invaluable theoretical guidance for optimizing the crystallization process and designing industrial crystallizers.

Spatiotemporal Mapping of Hole Nucleation and Growth during Block Copolymer Terracing with High-Speed Atomic Force Microscopy.

As a platform for investigating two-dimensional phase separation, we track the structural evolution of block copolymer thin films during thermal annealing with environmentally controlled atomic force microscopy (AFM). Upon thermal annealing, block copolymer films with incommensurate thickness separate into a terraced morphology decorated with holes. With in situ imaging at 200 °C, we follow the continuous progression of terrace formation in a single region of a cylinder-forming poly(styrene-block-methyl methacrylate) thin film, beginning with the disordered morphology on an unpatterned silicon substrate and continuing through nucleation and coarsening stages. Topographic AFM imaging with nanoscale resolution simultaneously captures ensemble hole growth statistics while locally tracking polymer diffusion through measurements of the film thickness. At early times, we observe homogeneous hole nucleation and isotropic growth, with kinetics following the predictions of classical nucleation theory. At later times, however, we find anomalous hole growth which arises due to the combination of Ostwald ripening and coalescence mechanisms. In each case, our real-space observations highlight the importance of hole interactions for determining coarsening kinetics, mediated either through the interconnected phase for Ostwald ripening or through binary collision events for coalescence.

Hydroxide films on mica form charge-stabilized microphases that circumvent nucleation barriers.

Crystal nucleation is facilitated by transient, nanoscale fluctuations that are extraordinarily difficult to observe. Here, we use high-speed atomic force microscopy to directly observe the growth of an aluminum hydroxide film from an aqueous solution and characterize the dynamically fluctuating nanostructures that precede its formation. Nanoscale cluster distributions and fluctuation dynamics show many similarities to the predictions of classical nucleation theory, but the cluster energy landscape deviates from classical expectations. Kinetic Monte Carlo simulations show that these deviations can arise from electrostatic interactions between the clusters and the underlying substrate, which drive microphase separation to create a nanostructured surface phase. This phase can evolve seamlessly from a low-coverage state of fluctuating clusters into a high-coverage nanostructured network, allowing the film to grow without having to overcome classical nucleation barriers.

Freezing of few nanometers water droplets

Water-ice transformation of few nm nanodroplets plays a critical role in nature including climate change, microphysics of clouds, survival mechanism of animals in cold environments, and a broad spectrum of technologies. In most of these scenarios, water-ice transformation occurs in a heterogenous mode where nanodroplets are in contact with another medium. Despite computational efforts, experimental probing of this transformation at few nm scales remains unresolved. Here, we report direct probing of water-ice transformation down to 2 nm scale and the length-scale dependence of transformation temperature through two independent metrologies. The transformation temperature shows a sharp length dependence in nanodroplets smaller than 10 nm and for 2 nm droplet, this temperature falls below the homogenous bulk nucleation limit. Contrary to nucleation on curved rigid solid surfaces, ice formation on soft interfaces (omnipresent in nature) can deform the interface leading to suppression of ice nucleation. For soft interfaces, ice nucleation temperature depends on surface modulus. Considering the interfacial deformation, the findings are in good agreement with predictions of classical nucleation theory. This understanding contributes to a greater knowledge of natural phenomena and rational design of anti-icing systems for aviation, wind energy and infrastructures and even cryopreservation systems.

Ultrafast dynamics of acoustic vaporization and payload release of phase-shift emulsions

Acoustic droplet vaporization (ADV) is the phase-transitioning of perfluorocarbon emulsions via focused ultrasound. ADV has been utilized in many biomedical applications. For drug delivery and tissue regeneration, we developed composite hydrogel scaffolds, termed acoustically responsive scaffolds (ARSs), which here contained fluorescently labeled monodispersed emulsions (Ø: 12.3 ± 0.8 μm). Using ultra-high speed microscopy, we investigated the dynamics of ADV (2.5 MHz, P-: 6 MPa, pulse length: 6μs) in ARSs containing emulsions with perfluoropentane, perfluorohexane, and perfluorooctane. Vaporization and growth dynamics were studied in micro- to millisecond time scales at frame rates up to 10 Mfps. During ADV, the generated bubbles expanded 4.8-, 2.8-, and 2-fold greater than the initial diameter of the perfluoropentane, perfluorohexane, and perfluorooctane emulsions, respectively. Stable bubbles formed from ADV in perfluoropentane and perfluorohexane, though growth rates post-ADV were significantly different. Bubbles recondensed within perfluorooctane emulsions, which exhibited a 20% decrease in diameter following five repeated ADV events. Stable or transient bubble formation was further compared with classical nucleation theory predictions. Additionally, we compared the release dynamics of fluorescently labeled payloads from the emulsions. The results provide physical insight enabling the modulation of bubble dynamics with ADV and hence release kinetics, which can be used for therapeutic applications.

Heterogeneous bubble nucleation dynamics

Abstract

Synthesis of Zinc-Sulfate Nano Particles and Detection of Their Induction Time, Nucleation Rate and Interfacial Tension

The production of zinc sulfate is important both medically and agriculturally. If zinc sulfate is produced without agglomeration at the nanoscale, its absorption in the body is more and faster. In this research, the induction time parameter is assessed for nucleation of zinc sulfate nanoparticles at room temperature and various supersaturations using acetone (as anti-solvent) in the presence of sodium dodecyl sulfate surfactant (SDS). The nucleation mechanism of zinc sulfate nanoparticles altered from primary to secondary by adding SDS surfactant in solution. The morphology of the zinc sulfate nanoparticles was analyzed by a Scanning Electron Microscope (SEM) and Transmission Electron Microscopy (TEM) tests. The TEM results revealed that the size of the nanoparticles is between 30 and 35 nm in the presence of SDS surfactant. The experimental data proved that the induction time reduces and improves with increasing supersaturation and SDS concentration, respectively. Meanwhile, the nucleation rate increases with the decrease in the interfacial tension of the zinc sulfate particles. The experimental results were also compared with the predictions of classical nucleation theory and the results proved good agreement between them.

Experimental measurement of the diamond nucleation landscape reveals classical and nonclassical features

Nucleation is a core scientific concept that describes the formation of new phases and materials. While classical nucleation theory is applied across wide-ranging fields, nucleation energy landscapes have never been directly measured at the atomic level, and experiments suggest that nucleation rates often greatly exceed the predictions of classical nucleation theory. Multistep nucleation via metastable states could explain unexpectedly rapid nucleation in many contexts, yet experimental energy landscapes supporting such mechanisms are scarce, particularly at nanoscale dimensions. In this work, we measured the nucleation energy landscape of diamond during chemical vapor deposition, using a series of diamondoid molecules as atomically defined protonuclei. We find that 26-carbon atom clusters, which do not contain a single bulk atom, are postcritical nuclei and measure the nucleation barrier to be more than four orders of magnitude smaller than prior bulk estimations. These data support both classical and nonclassical concepts for multistep nucleation and growth during the gas-phase synthesis of diamond and other semiconductors. More broadly, these measurements provide experimental evidence that agrees with recent conceptual proposals of multistep nucleation pathways with metastable molecular precursors in diverse processes, ranging from cloud formation to protein crystallization, and nanoparticle synthesis.

Classical nucleation theory in the phase-field crystal model.

A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.

Protic additives determine the pathway of CdSe nanocrystal growth.

The formation of semiconductor nanocrystals by hot-injection synthesis follows complex reaction mechanisms that are not yet fully understood. In particular the occurrence of intermediate species indicated by sharp, stationary spectral lines poses an important deviation from the predictions of classical nucleation theory. We show that trace amounts of water and other protic additives strongly impact the structure of these reaction intermediates, forming either coordination polymers under dry conditions or small clusters in the presence of moisture. These intermediates bind monomer during the initial nucleation phase. The structure of the intermediate determines the monomer release rate, either continuously or in a rapid dissolution event, and hence controls the reaction kinetics. From this we propose a kinetic model that allows us to predict secondary nucleation events. By directing the type of intermediate formed, protic additives provide a lever to manipulate this equilibrium and control nanocrystal synthesis in a rational fashion.

Communication: Relationship between local structure and the stability of water in hydrophobic confinement.

Liquid water confined between nanoscale hydrophobic objects can become metastable with respect to its vapor at nanoscale separations. While the separations are only several molecular diameters, macroscopic theories are often invoked to interpret the thermodynamics and kinetics of water under confinement. We perform detailed rate and free energy calculations via molecular simulations in order to assess the dependence of the rate of evaporation, free energy barriers, and free energy differences between confined liquid and vapor upon object separation and compare them to the relevant macroscopic theories. At small enough separations, the rate of evaporation appears to deviate significantly from the predictions of classical nucleation theory, and we attribute such deviations to changes in the structure of the confined liquid film. However, the free energy difference between the confined liquid and vapor phases agrees quantitatively with macroscopic theory, and the free energy barrier to condensation displays qualitative agreement. Overall, the present work suggests that theories attempting to capture the kinetic behavior of nanoscale systems should incorporate structural details rather than treating it as a continuum.

Atomistic insight into the non-classical nucleation mechanism during solidification in Ni.

Nucleation is a key step during crystallization, but a complete understanding of the fundamental atomistic processes remains elusive. We investigate the mechanism of nucleation during solidification in nickel for various undercoolings using transition path sampling simulations. The temperature dependence of the free energy barriers and rate constants that we obtain is consistent with the predictions of classical nucleation theory and experiments. However, our analysis of the transition path ensemble reveals a mechanism that deviates from the classical picture of nucleation: the growing solid clusters have predominantly non-spherical shapes and consist of face-centered-cubic and random hexagonal-close-packed coordinated atoms surrounded by a cloud of prestructured liquid. The nucleation initiates in regions of supercooled liquid that are characterized by a high orientational order with structural features that predetermine the polymorph selection. These results provide atomistic insight not only into the nucleation mechanism of nickel but also into the role of the preordered liquid regions as precursors for crystallization.

Dynamic scaling of island size distribution in submonolayer one-dimensional growth

The dynamic scaling of the island size distribution (ISD) in the submonolayer growth regime of low-dimensional nanostructured systems is a long standing problem in epitaxial growth. In this study, kinetic Monte Carlo simulations of a realistic atomistic lattice-gas model describing the one-dimensional nucleation and growth of Al on Si(100):2×1 were performed to investigate the scaling behavior under varied growth conditions. Consistent with previous predictions, our results show that the shape of the scaled island size distribution can be altered by controlling the temperature and the C-defect density. The shifts in the scaled ISD are opposite to each other with temperature depending on the density of C-defects. For low C-defect density, a shift from a monomodal to a monotonically decreasing distribution as temperature increases is observed. We attribute the monomodal distribution to enhanced nucleation and aggregation whereas a monotonically decreasing distribution is attributed to restricted aggregation with defects playing only a minor role. At higher C-defect density, we show that the scaled ISD shift is from a monotonically decreasing to a monomodal distribution with increasing temperature. We argue that the reversal of the shift is due to competing effects introduced by high C-defect concentration. In addition, results show that the ISD is generally insensitive to flux variations and that at a high coverage regime the shift in the scaling behavior vanishes. Lastly, we posit that the shift in the scaled ISD indicates the departure of the island density's temperature dependence from predictions of classical nucleation theory.

Microscopic Mechanism and Kinetics of Ice Formation at Complex Interfaces: Zooming in on Kaolinite

Most ice in nature forms because of impurities which boost the exceedingly low nucleation rate of pure supercooled water. However, the microscopic details of ice nucleation on these substances remain largely unknown. Here, we have unraveled the molecular mechanism and the kinetics of ice formation on kaolinite, a clay mineral playing a key role in climate science. We find that the formation of ice at strong supercooling in the presence of this clay is about 20 orders of magnitude faster than homogeneous freezing. The critical nucleus is substantially smaller than that found for homogeneous nucleation and, in contrast to the predictions of classical nucleation theory (CNT), it has a strong two-dimensional character. Nonetheless, we show that CNT describes correctly the formation of ice at this complex interface. Kaolinite also promotes the exclusive nucleation of hexagonal ice, as opposed to homogeneous freezing where a mixture of cubic and hexagonal polytypes is observed.

Optimization of crystal nucleation close to a metastable fluid-fluid phase transition.

The presence of a metastable fluid-fluid critical point is thought to dramatically influence the crystallization pathway, increasing the nucleation rate by many orders of magnitude over the predictions of classical nucleation theory. We use molecular dynamics simulations to study the kinetics of crystallization in the vicinity of this metastable critical point and throughout the metastable fluid-fluid phase diagram. To quantitatively understand how the fluid-fluid phase separation affects the crystal nucleation, we evaluate accurately the kinetics and reconstruct the thermodynamic free-energy landscape of crystal formation. Contrary to expectations, we find no special advantage of the proximity of the metastable critical point on the crystallization rates. However, we find that the ultrafast formation of a dense liquid phase causes the crystallization to accelerate both near the metastable critical point and almost everywhere below the fluid-fluid spinodal line. These results unveil three different scenarios for crystallization that could guide the optimization of the process in experiments

Molecular dynamics simulation of vapour-liquid nucleation of water with constant energy

The paper describes molecular dynamics study of nucleation of water in NVE ensemble. The numerical simulation was performed with the DL_POLY. The metastable steam consisting of 10976 water molecules with TIP4P/2005 potential was driven on the desired energy level by a simulation at constant temperature, and then the nucleation at constant energy was studied for several tens of nanoseconds, which was sufficient for clusters to evolve at hundred molecules size. The results were compared with the previously published results and the classical nucleation theory predictions.

Nanoscale Dynamics in Ultrathin Liquids Visualized with TEM

Nanoscale imaging of frozen aqueous specimens and solid materials with transmission electron microscopes (TEM) has revolutionized our understanding in biological and material sciences. However, there is an ample number of important problems in life and physical sciences that occur only in liquid environments. Therefore, there is an incredible advantage of being able to image nanoscale processes directly in liquids [1-3]. I will describe our recent work on development of platform for imaging soft materials and biological samples in liquids using TEM [4-6]. We use this platform to study liquid properties at nanoscale. Here we show that the properties of fluid at nanoscale dominated by its interfacial interaction with the solid substrate surface and drastically differ from the expected bulk behavior. For example, the diffusive movement and rotation of nanocrystals within liquid nanodroplets are severely dampened when compared with macroscopic fluids. We will describe dynamic processes in nanoscale fluids such as condensation of nanodroplets and flow of nanodroplets. Imaging nanoscale fluids also enabled us to observe nanocrystal nucleation through nanocluster aggregation that differs from predictions of classical nucleation theory. We observe that crystals form amorphous aggregates.

The spatial-temporal characteristics of type I collagen-based extracellular matrix.

Type I collagen abounds in mammalian extracellular matrix (ECM) and is crucial to many biophysical processes. While previous studies have mostly focused on bulk averaged properties, here we provide a comprehensive and quantitative spatial-temporal characterization of the microstructure of type I collagen-based ECM as the gelation temperature varies. The structural characteristics including the density and nematic correlation functions are obtained by analyzing confocal images of collagen gels prepared at a wide range of gelation temperatures (from 16 °C to 36 °C). As temperature increases, the gel microstructure varies from a "bundled" network with strong orientational correlation between the fibers to an isotropic homogeneous network with no significant orientational correlation, as manifested by the decaying of length scales in the correlation functions. We develop a kinetic Monte-Carlo collagen growth model to better understand how ECM microstructure depends on various environmental or kinetic factors. We show that the nucleation rate, growth rate, and an effective hydrodynamic alignment of collagen fibers fully determines the spatiotemporal fluctuations of the density and orientational order of collagen gel microstructure. Also the temperature dependence of the growth rate and nucleation rate follow the prediction of classical nucleation theory.

Quasi-equilibrium size distribution of subcritical nuclei in amorphous phase change AgIn-Sb2Te

We investigate the effect of low temperature annealing or of extended storage at room temperature on the subsequent nucleation behavior of amorphous AgIn-incorporated Sb2Te (AIST), a material for phase change memories. Time-resolved reflectivity measurements during pulsed laser crystallization reveal the rates of solid-phase transformation, while fluctuation transmission electron microscopy detects the nanoscale order in the amorphous phase prior to crystallization. The nanoscale order is postulated to consist of subcritical nuclei that coarsen upon annealing at temperatures ranging from 25 °C (for months) or 100 °C (for hours). Samples that have been annealed remain fully amorphous as evaluated by conventional diffraction experiments. Shorter nucleation times are consistently associated with the observation of increased nanoscale order. The effect of annealing is observed to saturate: there is no further reduction in nucleation time or increase in nanoscale order for annealing at 100 °C beyond three hours. This result supports the general prediction of classical nucleation theory that the size distribution of subcritical nuclei increases from the as-deposited state to a quasi-equilibrium.