Picture Of Nucleation Research Articles

Early stages of covalent organic framework formation imaged in operando

Covalent organic frameworks (COFs) are a functional material class able to harness, convert and store energy. However, after almost 20 years of research, there are no coherent prediction rules for their synthesis conditions. This is partly because of an incomplete picture of nucleation and growth at the early stages of formation. Here we use the optical technique interferometric scattering microscopy (iSCAT)1–3 for in operando studies of COF polymerization and framework formation. We observe liquid–liquid phase separation, pointing to the existence of structured solvents in the form of surfactant-free (micro)emulsions in conventional COF synthesis. Our findings show that the role of solvents extends beyond solubility to being kinetic modulators by compartmentation of reactants and catalyst. Taking advantage of these observations, we develop a synthesis protocol for COFs using room temperature instead of elevated temperatures. This work connects framework synthesis with liquid phase diagrams and thereby enables an active design of the reaction environment, emphasizing that visualization of chemical reactions by means of light-scattering-based techniques can be a powerful approach for advancing rational materials synthesis.

Rate theory of gas-liquid nucleation: Quest for the elusive quantitative accuracy.

The task of a first principles theoretical calculation of the rate of gas-liquid nucleation has remained largely incomplete despite the existence of reliable results from unbiased simulation studies at large supersaturation. Although the classical nucleation theory formulated by Becker-Doring-Zeldovich about a century ago provides an elegant, widely used picture of nucleation in a first-order phase transition, the theory finds difficulties in predicting the rate accurately, especially in the case of gas-to-liquid nucleation. Here, we use a multiple-order parameter description to construct the nucleation free energy surface needed to calculate the nucleation rate. A multidimensional non-Markovian (MDNM) rate theory formulation that generalizes Langer's well-known nucleation theory by using the Grote-Hynes MDNM treatment is used to obtain the rate of barrier crossing. We find good agreement of the theory with the rate obtained by direct unbiased molecular dynamics simulations-the latter is feasible at large supersaturation, S. The theory gives an experimentally strong dependence of the rate of nucleation on supersaturation, S. Interestingly, we find a strong influence of the frequency-dependent friction coefficient at the barrier top. This arises from multiple recrossings of the barrier surface. We find that a Markovian theory, such as Langer's formulation, fails to capture the rate quantitatively. In addition, the multidimensional transition state theory expression performs poorly, revealing the underlying role of the friction coefficient.

Anomalous Vapor and Ice Nucleation in Water at Negative Pressures: A Classical Density Functional Theory Study.

In contrast to the abundance of work on the anomalous behavior of water, the relationship between the water's thermodynamic anomalies and kinetics of phase transition from metastable water is relatively unexplored. In this work, we have employed classical density functional theory to provide a unified and coherent picture of nucleation (both vapor and ice) from metastable water at negative pressure conditions. Our results suggest a peculiar nonmonotonic temperature dependence of vapor-liquid surface tension at temperatures where vapor-liquid coexistence is metastable with respect to the ice phase. The vapor nucleation barrier on isochoric cooling also shows a nonmonotonic temperature dependence. We further report that, for low density isochores, the temperature of the minimum vapor nucleation barrier does not coincide with the temperature of maximum density (TMD) where metastability is maximum. The difference between the and the TMD, however, decreases with increasing the density of the isochore. The vapor nucleation barrier along isobars shows an interesting crossover behavior in the vicinity of the Widom line on lowering the temperature. Our results on the ice nucleation suggest an anomalous retracing behavior of the nucleation barrier along isotherms at negative pressures and theoretically validate the recent findings that the reentrant ice(Ih)-liquid coexistence line can induce a drastic change in the kinetics of ice nucleation. Thus, this study establishes a direct connection between the metastable water's thermodynamic anomalies and the (vapor and ice) nucleation kinetics. In addition, this study provides deeper insights into the origin of the isothermal compressibility maximum on isochoric cooling.

Vapor nucleation paths in lyophobic nanopores

.In recent years, technologies revolving around the use of lyophobic nanopores gained considerable attention in both fundamental and applied research. Owing to the enormous internal surface area, heterogeneous lyophobic systems (HLS), constituted by a nanoporous lyophobic material and a non-wetting liquid, are promising candidates for the efficient storage or dissipation of mechanical energy. These diverse applications both rely on the forced intrusion and extrusion of the non-wetting liquid inside the pores; the behavior of HLS for storage or dissipation depends on the hysteresis between these two processes, which, in turn, are determined by the microscopic details of the system. It is easy to understand that molecular simulations provide an unmatched tool for understanding phenomena at these scales. In this contribution we use advanced atomistic simulation techniques in order to study the nucleation of vapor bubbles inside lyophobic mesopores. The use of the string method in collective variables allows us to overcome the computational challenges associated with the activated nature of the phenomenon, rendering a detailed picture of nucleation in confinement. In particular, this rare event method efficiently searches for the most probable nucleation path(s) in otherwise intractable, high-dimensional free-energy landscapes. Results reveal the existence of several independent nucleation paths associated with different free-energy barriers. In particular, there is a family of asymmetric transition paths, in which a bubble forms at one of the walls; the other family involves the formation of axisymmetric bubbles with an annulus shape. The computed free-energy profiles reveal that the asymmetric path is significantly more probable than the symmetric one, while the exact position where the asymmetric bubble forms is less relevant for the free energetics of the process. A comparison of the atomistic results with continuum models is also presented, showing how, for simple liquids in mesoporous materials of characteristic size of ca. 4nm, the nanoscale effects reported for smaller pores have a minor role. The atomistic estimates for the nucleation free-energy barrier are in qualitative accord with those that can be obtained using a macroscopic, capillary-based nucleation theory.Graphical abstract

Continuous Transformations of the Nucleation Mechanism in the Undercooled State

Studies on nucleation have relied for many decades on the classical nucleation theory. Within that picture, thermal fluctuations govern the formation of critically sized, homogeneous nuclei of the newly developing phase. At the same time, structural inhomogeneities or impurities or extrinsic substrates such as surfaces or container walls can favor the formation of a critical-sized nucleus, leading to so-called heterogeneous nucleation. Specifically, according to this theoretical framework, a kinetic nucleation transition between heterogeneous and homogeneous is predicted to happen at a critical cooling rate. This underlying picture of nucleation has been applied since the development of classical nucleation theory, but this transition has rarely been observed experimentally for simple metallic systems. Now, with the development of fast scanning chip calorimetry and careful selection of a model alloy, we have been able to experimentally map the kinetic transition between these two fundamental modes of nucl...

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.

Nucleation in atomic, molecular, and colloidal systems

Abstract

Analysis of necking in high speed experiments by stereocorrelation

Tensile tests with Hopkinson bars are monitored with high speed cameras to extract 3D displacement fields and the corresponding strain fields by resorting to stereocorrelation. The aim of the experiments is to analyze the onset and development of necking for various strain rates and samples. Various challenges have to be dealt with, namely small definition of the pictures, large displacements that occur during the experiment, and the need for good spatial resolutions to capture the strain levels within the neck. In order to address all these issues, pre-correction techniques are used to allow for the required stability and accuracy of the analysis.Eight experiments on cylinders and parallelepipeds at different loading rates are analyzed. Either single or multiple neck inceptions were observed, irrespective of the mean strain rate, supporting a random nucleation picture rather than a deterministic result of the constitutive law. Local strains up to about 600% were measured. In the case of multiple necking, a selection leading to the growth of a dominant one is observed, in agreement with Mott's theory of an “unloading wave” emanating from neck inception. A propagation speed of this wave can be estimated from the analysis and is shown to agree with the theoretical prediction.

The thermodynamics of calcite nucleation at organic interfaces: Classical vs. non-classical pathways

Nucleation in the natural world often occurs in the presence of organic interfaces. In mineralized tissues, a range of macromolecular matrices are found in contact with inorganic phases and are believed to direct mineral formation. In geochemical settings, mineral surfaces, which are often covered with organic or biological films, surround the volume within which nucleation occurs. In the classical picture of nucleation, the presence of such interfaces is expected to have a profound effect on nucleation rates, simply because they can reduce the interfacial free energy, which controls the height of the thermodynamic barrier to nucleation of the solid phase. However, the recent discovery of a nearly monodisperse population of calcium carbonate clusters—so called pre-nucleation clusters—and the many observations of amorphous precursor phases have called into question the applicability of classical descriptions. Here we use in situ observations of nucleation on organothiol self-assembled monolayers (SAMs) to explore the energetics and pathways of calcite nucleation at organic interfaces. We find that carboxyl SAM-directed nucleation is described well in purely classical terms through a reduction in the thermodynamic barrier due to decreased interfacial free energy. Moreover, the differences in nucleation kinetics on odd and even chain-length carboxyl SAMs are attributable to relative differences in these energies. These differences arise from varying degrees of SAM order related to oxygen-oxygen interactions between SAM headgroups. In addition, amorphous particles formed prior to or during crystal nucleation do not grow and are not observed to act as precursors to the crystalline phase. Instead, calcite appears to nucleate independently. These results imply that the recently proposed model of calcite formation as a non-classical process, one which proceeds via aggregation of stable pre-nucleation clusters that form an amorphous precursor from which the crystalline phase emerges, is not applicable to template-directed nucleation on carboxyl SAMs and does not provide a universal description of calcite formation.

Nucleation of Crystals from Solution: Classical and Two-Step Models

Crystallization is vital to many processes occurring in nature and in the chemical, pharmaceutical, and food industries. Notably, crystallization is an attractive isolation step for manufacturing because this single process combines both particle formation and purification. Almost all of the products based on fine chemicals, such as dyes, explosives, and photographic materials, require crystallization in their manufacture, and more than 90% of all pharmaceutical products contain bioactive drug substances and excipients in the crystalline solid state. Hence control over the crystallization process allows manufacturers to obtain products with desired and reproducible properties. We judge the quality of a crystalline product based on four main properties: size, purity, morphology, and crystal structure. The pharmaceutical industry in particular requires production of the desired crystal form (polymorph) to assure the bioavailability and stability of the drug substance. In solution crystallization, nucleation plays a decisive role in determining the crystal structure and size distribution. Therefore, understanding the fundamentals of nucleation is crucial to achieve control over these properties. Because of its analytical simplicity, researchers have widely applied classical nucleation theory to solution crystallization. However, a number of differences between theoretical predictions and experimental results suggest that nucleation of solids from solution does not proceed via the classical pathway but follows more complex routes. In this Account, we discuss the shortcomings of classical nucleation theory and review studies contributing to the development of the modern two-step model. In the two-step model that was initially proposed for protein crystallization, a sufficient-sized cluster of solute molecules forms first, followed by reorganization of that cluster into an ordered structure. In recent experimental and theoretical studies, we and other researchers have demonstrated the applicability of the two-step mechanism to both macromolecules and small organic molecules, suggesting that this mechanism may underlie most crystallization processes from solutions. Because we have observed an increase in the organization time of appropriate lattice structures with greater molecular complexity, we propose that organization is the rate-determining step. Further development of a clearer picture of nucleation may help determine the optimum conditions necessary for the effective organization within the clusters. In addition, greater understanding of these processes may lead to the design of auxiliaries that can increase the rate of nucleation and avoid the formation of undesired solid forms, allowing researchers to obtain the final product in a timely and reproducible manner.

CRYSTALLIZATION KINETICS OF SYNDIOTACTIC POLYPROPYLENE STUDIED BY TIME-DEPENDENT LIGHT ATTENUATION

Crystallization kinetics of syndiotactic polypropylene ( sPP) was observed by light attenuation measurements. The initial stages of temperature dependent sPP crystallization fall in the range of Rayleigh scattering and Rayleigh-Debye- Gans scattering. Initial time and growth time of crystallization were obtained, and the trend of crystallization temperature dependent linear attenuation coefficient on the radius and the index of the refraction of the spherulite were evaluated. of polymer crystallization are usually carried out by differential scanning calorimetry or X-ray scattering in the wide- and small-angle range, sometimes also by light scattering, dilatometry or time dependent vibrational spectroscopy. Although based on different properties there is not much difference in the sensitivity of all these methods. Reliable data are only obtained from values of the crystallinity in the range of some percent of the final values. This means that for growing spherulites, which usually reach end sizes in the order of several micrometers, measurements start only at sizes of several hundred nanometers. This, however, is already far away from the initial stages. Nuclei have sizes in the order of several to ten nanometers and these, together with the small hedrites and spherulites existing at the beginning, cannot be observed. To study the objects in these initial stages, one can now use atomic force microscopy (AFM), but this technique has also some shortcomings. Observations by AFM principally refer to the development and growth of spherulites at the free surface of a melt, and conditions here may differ from those in the bulk. In addition, deriving global properties from observations of the development of single objects is sometimes difficult, because a certain selectivity is usually involved. Presently, the work on polymer crystallization has given considerable attention to the possibility that the crystal phase in the final semicrystalline state could be preceded by a transient liquid phase with density different from that of the initial quenched bulk isotropic melt or annealed glassy state. A number of papers have explicitly criticized the spinodal hypothesis and associated experimental studies, favoring the traditional picture of nucleation and growth. Various studies have suggested that the denser transient phase involves chain orientation, and there are good reasons to assume a crystal nucleation and growth which include an intermediate phase in the form of a coverage of the whole volume by a prior mesomorphic phase developing by a mechanism which resembles a spinodal process (7) , or a nucleation into a mesomorphic phase (8) , or the existence of a

Atomistic Mechanisms of Phase Separation and Formation of Solid Solutions: Model Studies of NaCl, NaCl−NaF, and Na(Cl1-xBrx) Crystallization from the Melt

The crystallization of sodium chloride from its melt and mixtures with other sodium halides is investigated by means of transition path sampling molecular dynamics simulations. From this we explore the nucleation mechanisms of both the solidification and the melting process at the atomistic level of detail. By incorporation of impurities the nucleation picture of the eutectic mixtures changes considerably. Doping the NaCl crystal with fluoride ions, we observed the substitutional defects to act as favored nucleation centers for the melting transition. This phenomenon plays a critical role during the solidification process of NaCl-NaF melts of low NaF concentration and is demonstrated to account for the segregation of fluoride ions. While NaCl-NaF corresponds to a eutectic system, we also investigated NaCl-NaBr mixtures. The bromide ions were observed to behave very similarly to chloride ions. As a consequence, no phase separation occurs and Na(Cl1-xBrx) solid solutions are formed. At the example of these two prototypes we demonstrate the study of the atomistic mechanisms related to phase separation processes and solid solution formation during the nucleation and growth of crystals from multinary melts.

Temperature-controlled martensitic phase transformations in a model NiAl alloy

Reversible martensitic phase transformations in a partially disordered Ni–Al alloy within the composition range from 60to65at.% of Ni are investigated using molecular dynamics simulation. During a complete temperature cycle a wide hysteresis in enthalpy, volume, and shape of the simulated crystals is observed. The temperature T0 of the phase transformation is found from the calculated free energy evolution. To investigate the atomic-scale development during the phase transformation a local order parameter is defined which is based on a combined method of Voronoy tessellation [J. Reine Angew. Math. 134, 198 (1908)] with common-neighbor analysis. This local order parameter allows us to get a detailed localized picture of nucleation and growth of the new phases. Both homogeneous formation of the new phase and heterogeneous nucleation are observed. The velocity of new phase growth front is estimated.

Freezing of a Lennard-Jones Fluid: From Nucleation to Spinodal Regime

Using molecular dynamics, we investigate the crystal nucleation in a Lennard-Jones fluid as a function of the degree of supercooling. At moderate supercooling, a nucleation picture applies, while for deeper quenches, the phenomenon progressively acquires a spinodal character. We show that in the nucleation regime, the freezing is a two-step process. The formation of the critical nucleus is indeed preceded by the abrupt formation of a precritical crystallite from a density fluctuation in the fluid. In contrast, as the degree of supercooling is increased, crystallization proceeds in a more continuous and collective fashion and becomes more spatially diffuse, indicating that the liquid is unstable and crystallizes by a spinodal mechanism.

Superparamagnetic transitions in ultrathin film NiFe nanolines

We found that the coercivity of electron-beam patterned nanoscale NiFe and Co lines (width ranging from 55 nm to 1 μm) has a distinct inverse-width dependence when the film thickness is greater than 3.5 nm. This inverse-width dependence is consistent with a nucleation picture in which the magnetization reversal is controlled by a small nucleus, which spreads across the width of the nanoline but is independent of the length. However, the inverse-width dependence breaks down for the narrowest NiFe lines at room temperature in films below 3.5 nm in thickness. In this thickness regime the coercivity drops rapidly as a function of decreasing width as the controlling nucleus size approaches the superparamagnetic limit. The Arrhenius–Néel equation for this equivalent volume very effectively models the data. As the temperature is decreased, the coercivity of the narrowest lines rapidly increases and the inverse-width trend is recovered.

Systematic study of the magnetization reversal in patterned Co and NiFe Nanolines

We report a universal dependence of switching field of patterned magnetic nanolines as a function of the linewidth for Co and NiFe films of various thicknesses. This dependence is shown to be consistent with a nucleation picture in which the magnetization reversal is controlled only by a small nucleus equivalent to a particle with an aspect ratio of 1.25, which spreads across the width of the nanoline. Micromagnetic simulation, taking into account of the edge roughness, agrees well with the observed results.

Non-equilibrium interface of a two-dimensional low-temperature crystal

We study the interface in an Ising system with nearest-neighbor interaction on a square lattice at very low temperatures, when the Wulff shape of a nucleus is almost a perfect square. Spins are randomly flipped via Metropolis-type dynamics. At moderately strong undercoolings, the step nucleation rates can be evaluated from the first principles. This permits the description of the growth of an infinite interface using a step-on-step nucleation picture. The averaged shape of the interface is universal (i.e., it does not depend on any parameters as long as the interface remains stable), and its growth rate, in appropriate variables, also has no free parameters. For finite sizes of two-dimensional crystals their growth can be dominated by nucleation of single steps, and becomes size-dependent. For both infinite- and finite-size interfaces growth rates are in good agreement with large-scale Monte Carlo simulations. At high undercoolings the interface becomes very rough, in which case the crystals switch to circular shapes, in contrast to the equilibrium Wulff expectation.

The region of validity of homogeneous nucleation theory

We examine the region of validity of Langer's picture of homogeneous nucleation. Our approach is based on a coarse-grained free energy that incorporates the effect of fluctuations with momenta above a scale k. The nucleation rate I= A k exp(− S k ) is exponentially suppressed by the action S k of the saddle-point configuration that dominates tunnelling. The factor A k includes a fluctuation determinant around this saddle point. Both S k and A k depend on the choice of k, but, for 1/ k close to the characteristic length scale of the saddle point, this dependence cancels in the expression for the nucleation rate. For very weak first-order phase transitions or in the vicinity of the spinodal decomposition line, the pre-exponential factor A k compensates the exponential suppression exp(− S k ). In these regions the standard nucleation picture breaks down. We give an approximate expression for A k in terms of the saddle-point profile, which can be used for quantitative estimates and practical tests of the validity of homogeneous nucleation theory.

The concept of nucleation

The authors of the two commentaries that follow have done a service to the folding community by presenting their contrasting views of the concept of nucleation in protein folding. The realization that folding might resemble the process of crystallization is an old one that can be traced back to Pauling. The seductive term ‘nucleation’ is familiar to most scientists despite the complexity of defining that word precisely for many situations. Workers in physical chemistry are quite aware of the difficulties in even formulating a quantitative nucleation theory. Although the idea was introduced by Becker, Doering, and Frenkel earlier in this century, there have been quantitative arguments about the nature of nucleation in simple systems such as crystallizing liquids that rage up until the present day. This is why metallurgy is by no means a dead subject. Thus, it is no surprise that in the context of protein folding many different ideas about nucleation would be bandied about.Many of the qualitative notions of nucleation theory are still unconnected from precise quantifications of the kinetic process. The status of the issue is made clear by noting that neither commentary mentions how one could compute a folding rate de novo using either nucleation picture. A precise definition requires such an algorithmic recipe. In this situation, it seems clear that Thirumalai is using the term ‘nucleus’ in the sense of a critical nucleus that determines rates through an activation free energy in a Kramers-like description, whereas Shakhnovich introduces another specific term, ‘postcritical nucleus’, which has some additional criteria on the transmission factor involved in its formulation. The latter may prove to be an interesting concept for visualizing the folding process.We can see that the term ‘nucleus’ in protein folding has clearly evolved since the earliest times when it seemed to mean a pre-existing structure in the denatured ensemble. It is quite useful, therefore, that the authors of these commentaries quote directly the definitions that were used at the time the various papers were published. In fact, most readers will be able to see that real progress has been made over the years of discussion of this concept. The study of simple models has now prepared the way for quantitatively addressing the factors that determine the folding speeds of real proteins in the laboratory.

Evidence of two-species nucleation of InAs islands on (100) and (111)B GaAs substrates

The nucleation of InAs islands on (100) and (111)B GaAs substrates during metalorganic chemical vapor deposition has been investigated via scanning electron microscopy. The measured values of island density are 4–5 orders of magnitude smaller than those predicted using conventional one-species nucleation theory. In addition, the effect of an increase in arsine flow on island density is opposite in sense for the two substrate orientations. To explain these observations, we further develop a two-species picture of nucleation—originally proposed by Stoyanov [Appl. Phys. A 50, 349 (1990)]—in which the InAs island density is an explicit function of both the indium flux and the arsenic partial pressure at the growth interface. This more realistic physical model is in good agreement with the complete set of experimental data.