Free Energy Evaluation of Cavity Formation in Metastable Liquid Based on Stochastic Thermodynamics.

Nucleation is a fundamental and general process at the initial stage of first-order phase transition. Although various models based on the classical nucleation theory (CNT) have been proposed to explain the energetics and kinetics of nucleation, detailed understanding at nanoscale is still required. Here, in view of the homogeneous bubble nucleation, we focus on cavity formation, in which evaluation of the size dependence of free energy change is the key issue. We propose the application of a formula in stochastic thermodynamics, the Jarzynski equality, for data analysis of molecular dynamics (MD) simulation to evaluate the free energy of cavity formation. As a test case, we performed a series of MD simulations with a Lennard-Jones (LJ) fluid system. By applying an external spherical force field to equilibrated LJ liquid, we evaluated the free energy change during cavity growth as the Jarzynski's ensemble average of required works. A fairly smooth free energy curve was obtained as a function of bubble radius in metastable liquid of mildly negative pressure conditions.

Simultaneous Water Sorption and Crystallization in ASDs 2: Modeling Long-Term Stabilities.

The physical stability of amorphous solid dispersions (ASDs) is a major topic in the formulation research of oral dosage forms. To minimize the effort of investigating the long-term stability using cost- and time-consuming experiments, we developed a thermodynamic and kinetic modeling framework to predict and understand the crystallization kinetics of ASDs during long-term storage below the glass transition. Since crystallization of the active phrarmaceutical ingredients (APIs) in ASDs largely depends on the amount of water absorbed by the ASDs, water-sorption kinetics and API-crystallization kinetics were considered simultaneously. The developed modeling approach allows prediction of the time evolution of viscosity, supersaturation, and crystallinity as a function of drug load, relative humidity, and temperature. It was applied and evaluated against two-year-lasting crystallization experiments of ASDs containing nifedipine and copovidone or HPMCAS measured in part I of this work. We could show that the proposed modeling approach is able to describe the interplay between water sorption and API crystallization and to predict long-term stabilities of ASDs just based on short-term measurements. Most importantly, it enables explaining and understanding the reasons for different and sometimes even unexpected crystallization behaviors of ASDs.

Nucleation of Pitting and Evolution of Stripping on Lithium-Metal Anodes.

The stripping reaction of lithium (Li) will greatly impact the cyclability and safety of Li-metal batteries. However, Li pits' nucleation and growth, the origin of uneven stripping, are still poorly understood. In this study, we analyze the nucleation mechanism of Li pits and their morphology evolution with a large population and electrode area (>0.45 cm2). We elucidate the dependence of the pit size and density on the current density and overpotential, which are aligned with classical nucleation theory. With a confocal laser scanning microscope, we reveal the preferential stripping on certain crystal grains and a new stripping mode between pure pitting and stripping without pitting. Descriptors like circularity and the aspect ratio (R) of the pit radius to depth are used to quantify the evolution of Li pits in three dimensions. As the pits grow, growth predominates along the through-planedirection, surpassing the expanding rate in the in-plane direction. After analyzing more than 1000 pits at each condition, we validate that the overpotential is inversely related to the pit radius and exponentially related to the rate of nucleation. With this established nucleation-overpotential relationship, we can better understand and predict the evolution of the surface area and roughness of Li electrodes under different stripping conditions. The knowledge and methodology developed in this work will significantly benefit Li-metal batteries' charging/discharging profile design and the assessment of large-scale Li-metal foils.

Growth Synchronization and Size Control in Magic-Sized Semiconductor Nanocrystals.

"Magic-sized" nanocrystals (MSNCs) grow in discrete jumps between a series of specific sizes. Consequently, MSNCs have been explored as an alternative route to uniform semiconductor particles, potentially with atomic precision. However, because the growth mechanism has been poorly understood, the best strategies to control MSNC syntheses and obtain desired sizes are unknown. Experiments have found that common parameters, such as growth time and temperature, have limited utility. Here, we theoretically and experimentally investigate reactant supersaturation as a tool to control MSNC growth. We compare direct synthesis of CdSe MSNCs with ripening of isolated MSNCs or their mixtures. Surprisingly, we find that MSNCs readily synchronize to the same growth trajectory, even starting from distinct initial conditions, explaining the robustness of MSNC growth. Further, by understanding the synchronization mechanism, we demonstrate methods to control the final MSNC size. These results deepen our knowledge of MSNCs and indicate strategies to tailor their growth.

Numerical and Experimental Study of Gas Phase Nanoparticle Synthesis Using NanoDOME.

Nowadays, with the rocketing of computational power, advanced numerical tools, and parallel computing, multi-scale simulations are becoming applied more and more to complex multi-physics industrial processes. One of the several challenging processes to be numerically modelled is gas phase nanoparticle synthesis. In an applied industrial scenario, the possibility to correctly estimate the geometric properties of the mesoscopic entities population (e.g., their size distribution) and to more precisely control the results is a crucial step to improve the quality and efficiency of the production. The "NanoDOME" project (2015-2018) aims to be an efficient and functional computational service to be applied in such processes. NanoDOME has also been refactored and upscaled during the H2020 Project "SimDOME". To prove its reliability, we present here an integrated study between experimental data and NanoDOME's predictions. The main goal is to finely investigate the effect of a reactor's thermodynamic conditions on the thermophysical history of mesoscopic entities along the computational domain. To achieve this goal, the production of silver nanoparticles has been assessed for five cases with different experimental operative conditions of the reactor. The time evolution and final size distribution of nanoparticles have been simulated with NanoDOME by exploiting the method of moments and population balance model. The validation is performed by comparing NanoDOME's calculations with the experimental data.

Fe(II)-Catalyzed Transformation of Ferrihydrite with Different Degrees of Crystallinity.

Natural occurring ferrihydrite (Fh) nanoparticles have varying degrees of crystallinity, but how Fh crystallinity affects its transformation behavior remains elusive. Here, we investigated the Fe(II)-catalyzed transformation of Fh with different degrees of crystallinity (i.e., Fh-2h, Fh-12h, and Fh-85C). X-ray diffraction patterns of Fh-2h, Fh-12h, and Fh-85C exhibited two, five, and six diffraction peaks, respectively, indicating the order of crystallinity: Fh-2h < Fh-12h < Fh-85C. Fh with the lower crystallinity has a higher redox potential, corresponding to the faster Fe(II)-Fh interfacial electron transfer and Fe(III)labile production. With the increase of initial Fe(II) concentration ([Fe(II)aq]int.) from 0.2 to 5.0 mM, the transformation pathways of Fh-2h and Fh-12h change from Fh → lepidocrocite (Lp) → goethite (Gt) to Fh → Gt, but that of Fh-85C switches from Fh → Gt to Fh → magnetite (Mt). The changes are rationalized using a computational model that quantitatively describes the relationship between the free energies of formation for starting Fh and nucleation barriers of competing product phases. Gt particles from the Fh-2h transformation exhibit a broader width distribution than those from Fh-12h and Fh-85C. Uncommon hexagonal Mt nanoplates are formed from the Fh-85C transformation at [Fe(II)aq]int.= 5.0 mM. The findings are crucial to comprehensively understand the environmental behavior of Fh and other associated elements.

Which Surface Is More Scaling Resistant? A Closer Look at Nucleation Theories for Heterogeneous Gypsum Nucleation in Aqueous Solutions.

Developing engineered surfaces with scaling resistance is an effective means to inhibit surface-mediated mineral scaling in various industries including desalination. However, contrasting results have been reported on the relationship between scaling potential and surface hydrophilicity. In this study, we combine a theoretical analysis with experimental investigation to clarify the effect of surface wetting property on heterogeneous gypsum (CaSO4·2H2O) formation on surfaces immersed in aqueous solutions. Theoretical prediction derived from classical nucleation theory (CNT) indicates that an increase of surface hydrophobicity reduces scaling potential, which contrasts our experimental results that more hydrophilic surfaces are less prone to gypsum scaling. We further consider the possibility of nonclassical pathway of gypsum nucleation, which proceeds by the aggregation of precursor clusters of CaSO4. Accordingly, we investigate the affinity of CaSO4 to substrate surfaces of varied wetting properties via calculating the total free energy of interaction, with the results perfectly predicting experimental observations of surface scaling propensity. This indicates that the interactions between precursor clusters of CaSO4 and substrate surfaces might play an important role in regulating heterogeneous gypsum formation. Our findings provide evidence that CNT might not be applicable to describing gypsum scaling in aqueous solutions. The fundamental insights we reveal on gypsum scaling mechanisms have the potential to guide rational design of scaling-resistant engineered surfaces.

Cavity nucleation in single-component homogeneous amorphous solids under negative pressure.

Understanding the cavity formation and cavity growth mechanisms in solids has fundamental and applied importance for the correct determination of their exploitation capabilities and mechanical characteristics. In this work, we present the molecular dynamics simulation results for the process of homogeneous formation of nanosized cavities in a single-component amorphous metallic alloy. To identify cavities of various shapes and sizes, an original method has been developed, which is based on filling cavities by virtual particles (balls) of the same diameter. By means of the mean first-passage time analysis, it was shown that the cavity formation in an amorphous metallic melt is the activation-type process. This process can be described in terms of the classical nucleation theory, which is usually applied to the case of first order phase transitions. Activation energy, critical size and nucleation rate of cavities are calculated, the values of which are comparable with those for the case of crystal nucleation in amorphous systems.

Crystal Nucleation and Growth of Inorganic Ionic Materials from Aqueous Solution: Selected Recent Developments, and Implications.

In this review article, selected, latest theoretical, and experimental developments in the field of nucleation and crystal growth of inorganic materials from aqueous solution are highlighted, with a focus on literature after 2015 and on non-classical pathways. A key point is to emphasize the so far underappreciated role of water and solvent entropy in crystallization at all stages from solution speciation through to the final crystal. While drawing on examples from current inorganic materials where non-classical behavior has been proposed, the potential of these approaches to be adapted to a wide-range of systems is also discussed, while considering the broader implications of the current re-assessment of pathways for crystallization. Various techniques that are suitable for the exploration of crystallization pathways in aqueous solution, from nucleation to crystal growth are summarized, and a flow chart for the assignment of specific theories based on experimental observations is proposed.

Understanding the Importance of Labile Fe(III) during Fe(II)-Catalyzed Transformation of Metastable Iron Oxyhydroxides.

Transformation of metastable Fe(III) oxyhydroxides is a prominent process in natural environments and can be significantly accelerated by the coexisting aqueous Fe(II) (Fe(II)aq). Recent evidence points to the solution mass transfer of labile Fe(III) (Fe(III)labile) as the primary intermediate species of general importance. However, a mechanistic aspect that remains unclear is the dependence of phase outcomes on the identity of the metastable Fe(III) oxyhydroxide precursor. Here, we compared the coupled evolution of Fe(II) species, solid phases, and Fe(III)labile throughout the Fe(II)-catalyzed transformation of lepidocrocite (Lp) versus ferrihydrite (Fh) at equal Fe(III) mass loadings with 0.2-1.0 mM Fe(II)aq at pH = 7.0. Similar to Fh, the conversion of Lp to product phases occurs by a dissolution-reprecipitation mechanism mediated by Fe(III)labile that seeds the nucleation of products. Though for Fh we observed a transformation to goethite (Gt), accompanied by the transient emergence and decline of Lp, for initial Lp we observed magnetite (Mt) as the main product. A linear correlation between the formation rate of Mt and the effective supersaturation in terms of Fe(III)labile concentration shows that Fe(II)-induced transformation of Lp into Mt is governed by the classical nucleation theory. When Lp is replaced by equimolar Gt, Mt formation is suppressed by opening a lower barrier pathway to Gt by heterogeneous nucleation and growth on the added Gt seeds. The collective findings add to the mechanistic understanding of factors governing phase selections that impact iron bioavailability, system redox potential, and the fate and transport of coupled elements.

Cavity Nucleation and Growth in Nickel-Based Alloys during Creep.

The number of fossil fueled power plants in electricity generation is still rising, making improvements to their efficiency essential. The development of new materials to withstand the higher service temperatures and pressures of newer, more efficient power plants is greatly aided by physics-based models, which can simulate the microstructural processes leading to their eventual failure. In this work, such a model is developed from classical nucleation theory and diffusion driven growth from vacancy condensation. This model predicts the shape and distribution of cavities which nucleate almost exclusively at grain boundaries during high temperature creep. Cavity radii, number density and phase fraction are validated quantitively against specimens of nickel-based alloys (617 and 625) tested at 700 °C and stresses between 160 and 185 MPa. The model's results agree well with the experimental results. However, they fail to represent the complex interlinking of cavities which occurs in tertiary creep.

Classical and Nonclassical Nucleation and Growth Mechanisms for Nanoparticle Formation.

All solid materials are created via nucleation. In this evolutionary process, nuclei form in solution or at interfaces, expand by monomeric growth and oriented attachment, and undergo phase transformation. Nucleation determines the location and size of nuclei, whereas growth controls the size, shape, and aggregation of newly formed nanoparticles. These physical properties of nanoparticles can affect their functionalities, reactivities, and porosities, as well as their fate and transport. Recent advances in nanoscale analytical technologies allow in situ real-time observations, enabling us to uncover the molecular nature of nuclei and the critical controlling factors for nucleation and growth. Although a single theory cannot yet fully explain such evolving processes, we have started to better understand how both classical andnonclassical theories can work together, and we have begun to recognize the importance of connecting these theories. This review discusses the recent convergence of knowledge about the nucleation and growth of nanoparticles.

Crystal Nucleation and Growth in Cross-Linked Poly(ε-caprolactone) (PCL).

The crystal nucleation and overall crystallization kinetics of cross-linked poly(ε-caprolactone) was studied experimentally by fast scanning calorimetry in a wide temperature range. With an increasing degree of cross-linking, both the nucleation and crystallization half-times increase. Concurrently, the glass transition range shifts to higher temperatures. In contrast, the temperatures of the maximum nucleation and the overall crystallization rates remain the same, independent of the degree of cross-linking. The cold crystallization peak temperature generally increases as a function of heating rate, reaching an asymptotic value near the temperature of the maximum growth rate. A theoretical interpretation of these results is given in terms of classical nucleation theory. In addition, it is shown that the average distance between the nearest cross-links is smaller than the estimated lamellae thickness, which indicates the inclusion of cross-links in the crystalline phase of the polymer.

Nucleation of melt: From fundamentals to dispersed systems.

The most evident aspects of a first order transition of a system from an old to a new phase, are the presence of a discontinuity at the interface between both phases and the thermal effects related to the latent heat exchanged with the surrounding environment. These effects are the result of a sequence of events promoted by thermodynamic conditions persisting over the equilibrium in a metastable state. The breakdown of metastability is promoted by infinitesimal energy fluctuations resulting in the germination of clusters of the new phase that can grow to a critical size (nucleus) and then develop or vanish. Examples of these sequences are common in various technological fields such as combustion, food processing, pharmaceutical manufacturing, condensation, and phase change heat transfer, etc. This work aims to highlight a logical path that leads the readers from the fundamental phenomenology to the most intricated aspects of the nucleation within dispersed systems such as oil-in-water emulsions. Differences between the homogeneous and heterogeneous mechanisms are, under the light of the Classical Nucleation Theory (CNT), presented in bulk and confined systems until defining a minimum confinement size. By collecting insights coming from a rich scientific literature mostly focused on the stability of emulsified systems, the discussion is then on the aspects related to the surface related mechanisms. Two main aspects are then considered: a) the wettability of the nucleating cluster by the surrounding melt; b) the affinity between the adsorbed layer, where a surfactant is located, and the oil melt phase (mainly n-alkanes and triacylglycerols with different moieties). In cases where nucleation is dominating over the dewetting of the nucleus, the contact angle can be considered as a constant value. The affinity in terms of molecular features between the surfactant and the oil phase can promote the template effect. Several factors seem to play a role in this interaction such as the thermal characteristics of the surfactant and comparable dimensions between the molecule (or fractions) of the dispersed compound and the tail of the surfactant.

Brief Overview of Ice Nucleation.

The nucleation of ice is vital in cloud physics and impacts on a broad range of matters from the cryopreservation of food, tissues, organs, and stem cells to the prevention of icing on aircraft wings, bridge cables, wind turbines, and other structures. Ice nucleation thus has broad implications in medicine, food engineering, mineralogy, biology, and other fields. Nowadays, the growing threat of global warming has led to intense research activities on the feasibility of artificially modifying clouds to shift the Earth's radiation balance. For these reasons, nucleation of ice has been extensively studied over many decades and rightfully so. It is thus not quite possible to cover the whole subject of ice nucleation in a single review. Rather, this feature article provides a brief overview of ice nucleation that focuses on several major outstanding fundamental issues. The author's wish is to aid early researchers in ice nucleation and those who wish to get into the field of ice nucleation from other disciplines by concisely summarizing the outstanding issues in this important field. Two unresolved challenges stood out from the review, namely the lack of a molecular-level picture of ice nucleation at an interface and the limitations of classical nucleation theory.

Dynamic Surface Tension Enhances the Stability of Nanobubbles in Xylem Sap.

Air seeded nanobubbles have recently been observed within tree sap under negative pressure. They are stabilized by an as yet unidentified process, although some embolize their vessels in extreme circumstances. Current literature suggests that a varying surface tension helps bubbles survive, but few direct measurements of this quantity have been made. Here, we present calculations of dynamic surface tension for two biologically relevant lipids using molecular dynamics simulations. We find that glycolipid monolayers resist expansion proportionally to the rate of expansion. Their surface tension increases with the tension applied, in a similar way to the viscosity of a non-Newtonian fluid. In contrast, a prototypical phospholipid was equally resistant to all applied tensions, suggesting that the fate of a given nanobubble is dependent on its surface composition. By incorporating our results into a Classical Nucleation Theory (CNT) framework, we predict nanobubble stability with respect to embolism. We find that the metastable radius of glycolipid coated nanobubbles is approximately 35 nm, and that embolism is in this case unlikely when the external pressure is less negative than -1.5 MPa.

Two-step crystallization and solid-solid transitions in binary colloidal mixtures.

Crystallization is fundamental to materials science and is central to a variety of applications, ranging from the fabrication of silicon wafers for microelectronics to the determination of protein structures. The basic picture is that a crystal nucleates from a homogeneous fluid by a spontaneous fluctuation that kicks the system over a single free-energy barrier. However, it is becoming apparent that nucleation is often more complicated than this simple picture and, instead, can proceed via multiple transformations of metastable structures along the pathway to the thermodynamic minimum. In this article, we observe, characterize, and model crystallization pathways using DNA-coated colloids. We use optical microscopy to investigate the crystallization of a binary colloidal mixture with single-particle resolution. We observe classical one-step pathways and nonclassical two-step pathways that proceed via a solid-solid transformation of a crystal intermediate. We also use enhanced sampling to compute the free-energy landscapes corresponding to our experiments and show that both one- and two-step pathways are driven by thermodynamics alone. Specifically, the two-step solid-solid transition is governed by a competition between two different crystal phases with free energies that depend on the crystal size. These results extend our understanding of available pathways to crystallization, by showing that size-dependent thermodynamic forces can produce pathways with multiple crystal phases that interconvert without free-energy barriers and could provide approaches to controlling the self-assembly of materials made from colloids.

Self-Confined Nucleation of Iron Oxide Nanoparticles in a Nanostructured Amorphous Precursor.

Crystallization from solution is commonly described by classical nucleation theory, although this ignores that crystals often form via disordered nanostructures. As an alternative, the classical theory remains widely used in a "multistep" variant, where the intermediate nanostructures merely introduce additional thermodynamic parameters. However, this variant still requires validation by experiments addressing indeed proper time and spatial scales (millisecond, nanometer). Here, we used in situ X-ray scattering to determine the mechanism of magnetite crystallization and, in particular, how nucleation propagates at the nanometer scale within amorphous precursors. We find that the self-confinement by an amorphous precursor slows down crystal growth by 2 orders of magnitude once the crystal size reaches the amorphous particle size (∼3 nm). Thus, not only the thermodynamic properties of transient amorphous nanostructures but also their spatial distribution determine crystal nucleation.

On the mechanism of solid-state phase transitions in molecular crystals - the role of cooperative motion in (quasi)racemic linear amino acids.

During single-crystal-to-single-crystal (SCSC) phase transitions, a polymorph of a compound can transform to a more stable form while remaining in the solid state. By understanding the mechanism of these transitions, strategies can be developed to control this phenomenon. This is particularly important in the pharmaceutical industry, but also relevant for other industries such as the food and agrochemical industries. Although extensive literature exists on SCSC phase transitions in inorganic crystals, it is unclear whether their classications and mechanisms translate to molecular crystals, with weaker interactions and more steric hindrance. A comparitive study of SCSC phase transitions in aliphatic linear-chain amino acid crystals, both racemates and quasi-racemates, is presented. A total of 34 transitions are considered and most are classified according to their structural change during the transition. Transitions without torsional changes show very different characteristics, such as transition temperature, enthalpy and free energy, compared with transitions that involve torsional changes. These differences can be rationalized using classical nucleation theory and in terms of a difference in mechanism; torsional changes occur in a molecule-by-molecule fashion, whereas transitions without torsional changes involve cooperative motion with multiple molecules at the same time.

Fast-freezing kinetics inside a droplet impacting on a cold surface.

Freezing or solidification of impacting droplets is omnipresent in nature and technology, be it a rain droplet falling on a supercooled surface; in inkjet printing, where often molten wax is used; in additive manufacturing or metal-production processes; or in extreme ultraviolet lithography (EUV) for the chip production, where molten tin is used to generate the EUV radiation. For many of these industrial applications, a detailed understanding of the solidification process is essential. Here, by adopting an optical technique in the context of freezing-namely, total-internal reflection (TIR)-we elucidate the freezing kinetics during the solidification of a droplet while it impacts on an undercooled surface. We show that at sufficiently high undercooling, a peculiar freezing morphology exists that involves sequential advection of frozen fronts from the center of the droplet to its boundaries. This phenomenon is examined by combining elements of classical nucleation theory to the large-scale hydrodynamics on the droplet scale, bringing together two subfields which traditionally have been quite separated. Furthermore, we report a self-peeling phenomenon of a frozen splat that is driven by the existence of a transient crystalline state during solidification.