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In the present paper, some further results of application of the generalized Gibbs’ approach [J. W. P. Schmelzer et al., J. Chem. Phys. 112, 3820 (2000); 114, 5180 (2001); 119, 6166 (2003)] to describing new-phase formation processes are outlined. The path of cluster evolution in size and composition space is determined taking into account both thermodynamic and kinetic factors. The basic features of these paths of evolution are discussed in detail for a simple model of a binary mixture. According to this analysis, size and composition of the clusters of the newly evolving phase change in an unexpected way which is qualitatively different as compared to the classical picture of nucleation-growth processes. As shown, nucleation (i.e., the first stage of cluster formation starting from metastable initial states) exhibits properties resembling spinodal decomposition (the size remains nearly constant while the composition changes) although the presence of an activation barrier distinguishes the nucleation process from true spinodal decomposition. In addition, it is shown that phase formation both in metastable and unstable initial states near the classical spinodal may proceed via a passage of a ridge of the thermodynamic potential with a finite work of the activation barrier even though (for unstable initial states) the value of the work of critical cluster formation (corresponding to the saddle point of the thermodynamic potential) is zero. This way, it turns out that nucleation concepts—in a modified form as compared with the classical picture—may govern also phase formation processes starting from unstable initial states. In contrast to the classical Gibbs’ approach, the generalized Gibbs’ method provides a description of phase changes both in binodal and spinodal regions of the phase diagram and confirms the point of view assuming a continuity of the basic features of the phase transformation kinetics in the vicinity of the classical spinodal curve. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In a recent paper [J. Chem. Phys. 118, 1837 (2003)], Kashchiev claimed to have developed a general thermodynamically consistent formula allowing one to describe correctly the work of critical cluster formation in one-component systems for a variety of cases of formation of gaseous, liquid, and solid phases. It is shown that most of the consequences drawn lack any substantiation. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Small atomic or molecular clusters provide the bridge between vapor and liquid phases. Nucleation is a rare event process by which clusters of a new phase are produced. This process is inherently dynamic and as such the new phase cannot exist until an activation barrier is surmounted. Dynamical nucleation theory (DNT) utilizes variational transition state theory to provide a framework in which cluster evaporation and condensation rate constants can be determined directly. To date, the fundamental nature regarding the intrinsic instability of the kinetics of the nucleation process has eluded theoretical efforts. In this paper we present a sensitivity analysis of the homogeneous nucleation rate on kinetic parameters used in DNT. Moreover, several classical interaction potentials for water exist, most of which have been parametrized to reproduce some bulk properties of water at ambient conditions. Thus, an analysis was undertaken to explore what effects different water potentials have on the dynamical quantities relevant to nucleation. The implication of these results on future work will be discussed. [ABSTRACT FROM AUTHOR]

We have employed density functional theory to study gas–liquid nucleation in binary fluids. Effects of surface enrichment and curvature are naturally included in this novel statistical mechanical approach, allowing the classical capillarity approximation to be tested. In this paper we apply the theory to mixtures of Lennard-Jones fluids (modeled on argon and krypton). For these nearly ideal mixtures, the magnitude of nonclassical effects tend to be small, but systematic deviations do appear, with the ratio of the classical to nonclassical rate showing a maximum at intermediate compositions. [ABSTRACT FROM AUTHOR]

We study low-salt, binary aqueous suspensions of charged colloidal spheres of size ratio Γ = 0.57, number densities below the eutectic number density nE, and number fractions of p = 1.00–0.40. The typical phase obtained by solidification from a homogeneous shear-melt is a substitutional alloy with a body centered cubic structure. In strictly gas-tight vials, the polycrystalline solid is stable against melting and further phase transformation for extended times. For comparison, we also prepare the same samples by slow, mechanically undisturbed deionization in commercial slit cells. These cells feature a complex but well reproducible sequence of global and local gradients in salt concentration, number density, and composition as induced by successive deionization, phoretic transport, and differential settling of the components, respectively. Moreover, they provide an extended bottom surface suitable for heterogeneous nucleation of the β-phase. We give a detailed qualitative characterization of the crystallization processes using imaging and optical microscopy. By contrast to the bulk samples, the initial alloy formation is not volume-filling, and we now observe also α- and β-phases with low solubility of the odd component. In addition to the initial homogeneous nucleation route, the interplay of gradients opens various further crystallization and transformation pathways leading to a great diversity of microstructures. Upon a subsequent increase in salt concentration, the crystals melt again. Wall-based, pebble-shaped β-phase crystals and facetted α-crystals melt last. Our observations suggest that the substitutional alloys formed in bulk experiments by homogeneous nucleation and subsequent growth are mechanically stable in the absence of solid–fluid interfaces but thermodynamically metastable. [ABSTRACT FROM AUTHOR]

The interaction of water with different substances in the earth's atmosphere lies at the heart of many processes that influence our climate. However, it is still unclear how different species interact with water on the molecular level and in which ways this interaction contributes to the water vapor phase transition. Here, we report the first measurements of water–nonane binary nucleation in the 50–110 K temperature range, along with unary nucleation data of both. The time-dependent cluster size distribution in a uniform post-nozzle flow was measured by time-of-flight mass spectrometry coupled with single-photon ionization. From these data, we extract experimental rates and rate constants for both nucleation and cluster growth. The observed mass spectra of water/nonane clusters are not or only slightly affected by the introduction of the other vapor, and the formation of mixed clusters was not observed during nucleation of the mixed vapor. Additionally, the nucleation rate of either substance is not much affected by the presence (or absence) of the other species, i.e., the nucleation of water and nonane proceeds independently, indicating that hetero-molecular clusters do not play a role during nucleation. Only at the lowest temperature of our experiment (i.e., 51 K) do the measurements suggest that interspecies interaction slows water cluster growth. The findings here are in contrast to our earlier work in which we showed that vapor components in other mixtures, e.g., CO2 and toluene/H2O, can interact to promote nucleation and cluster growth in a similar temperature range. [ABSTRACT FROM AUTHOR]

Freezing of water is the most common liquid-to-crystal phase transition on Earth; however, despite its critical implications on climate change and cryopreservation among other disciplines, its characterization through experimental and computational techniques remains elusive. In this work, we make use of computer simulations to measure the nucleation rate (J) of water at normal pressure under different supercooling conditions, ranging from 215 to 240 K. We employ two different water models: mW, a coarse-grained potential for water, and TIP4P/ICE, an atomistic nonpolarizable water model that provides one of the most accurate representations of the different ice phases. To evaluate J, we apply the Lattice Mold technique, a computational method based on the use of molds to induce the nucleus formation from the metastable liquid under conditions at which observing spontaneous nucleation would be unfeasible. With this method, we obtain estimates of the nucleation rate for ice Ih and Ic and a stacking mixture of ice Ih/Ic, reaching consensus with most of the previously reported rates, although differing with some others. Furthermore, we confirm that the predicted nucleation rates obtained by the TIP4P/ICE model are in better agreement with experimental data than those obtained through the mW potential. Taken together, our study provides a reliable methodology to measure nucleation rates in a simple and computationally efficient manner that contributes to benchmarking the freezing behavior of two popular water models. [ABSTRACT FROM AUTHOR]

A deep understanding for collective behavior in an active matter system with complex interactions has far-reaching impact in biology. In the present work, we adopt Langevin dynamics simulations to investigate diffusion dynamics and phase separation in an anisotropic active particle system with a tunable biased angle α defined as the deviation between the active force direction and anisotropic orientation. Our results demonstrate that the biased angle can induce super-rotational diffusion dynamics characterized by a power-law relationship between the mean square angle displacement (MSAD) and the time interval Δt in the form of MSAD ∼ Δtβ with β > 1 and also result in non-trivial phase separation kinetics. As activity is dominant, nucleation time shows a non-monotonic dependence on the biased angle. Moreover, there arises a distinct transition of phase separation, from spinodal decomposition without apparent nucleation time to binodal decomposition with prominent nucleation delay. A significant inhibition effect occurs at right and obtuse angles, where the remarkable super-rotational diffusion prevents particle aggregation, leading to a slow nucleation process. As active force is competitive to anisotropic interactions, the system is almost homogeneous, while, intriguingly, we observe a re-entrant phase separation as a small acute angle is introduced. The prominent super-rotational diffusion under small angles provides an optimum condition for particle adsorption and cluster growth and, thus, accounts for the re-entrance of phase separation. A consistent scenario for the physical mechanism of our observations is achieved by properly considering the modulation of the biased angle on the interplay between activity and anisotropic interactions. [ABSTRACT FROM AUTHOR]

In the theoretical interpretation of the kinetics of first-order phase transitions, thermodynamic concepts developed long ago by Gibbs are widely employed giving some basic qualitative insights into these processes. However, from a quantitative point of view, the results of such analysis, based on the classical Gibbs approach and involving in addition the capillarity approximation, are often not satisfactory. Some progress can be reached here by the van der Waals and more advanced density functional methods of description of thermodynamically heterogeneous systems having, however, its limitations in application to the interpretation of experimental data as well. Moreover, both mentioned theories—Gibbs’ and density functional approaches—lead to partly contradicting each other’s results. As shown in preceding papers, by generalizing Gibbs’ approach, existing deficiencies and internal contradictions of these two well-established theories can be removed and a new generally applicable tool for the interpretation of phase formation processes can be developed. In the present analysis, a comparative analysis of the basic assumptions and predictions of the classical and the generalized Gibbs approaches is given. It is shown, in particular, that—interpreted in terms of the generalized Gibbs approach—the critical cluster as determined via the classical Gibbs approach corresponds not to a saddle but to a ridge point of the appropriate thermodynamic potential hypersurface. By this reason, the classical Gibbs approach (involving the classical capillarity approximation) overestimates as a rule the work of critical cluster formation in nucleation theory and, in general, considerably. [ABSTRACT FROM AUTHOR]

Macroscopic models of nucleation provide powerful tools for understanding activated phase transition processes. These models do not provide atomistic insights and can thus sometimes lack material-specific descriptions. Here, we provide a comprehensive framework for constructing a continuum picture from an atomistic simulation of homogeneous nucleation. We use this framework to determine the equilibrium shape of the solid nucleus that forms inside bulk liquid for a Lennard-Jones potential. From this shape, we then extract the anisotropy of the solid-liquid interfacial free energy, by performing a reverse Wulff construction in the space of spherical harmonic expansions. We find that the shape of the nucleus is nearly spherical and that its anisotropy can be perfectly described using classical models. [ABSTRACT FROM AUTHOR]

Classical nucleation theory (CNT) is a promising way to predictively model the submicrosecond kinetics of phase transitions that occur under dynamic compression, such as the suite of experiments performed over the past two decades on the solidification of liquid water to the high-pressure ice VII phase. Myint et al. [Phys. Rev. Lett. 121, 155701 (2018)] presented the first CNT-based model for these types of rapid phase transitions, but relied on an empirical scaling parameter in their transient induction model to simulate the lag time that occurs prior to the onset of significant formation of ice VII clusters in the system. To build on that study, we model the liquid water–ice VII phase transformation using a numerical discretization scheme to solve the Zel'dovich–Frenkel partial differential equation, which is a fundamental CNT-based kinetic equation that describes the statistical time-dependent behavior of solid cluster formation. The Zel'dovich–Frenkel equation inherently accounts for transience in the nucleation kinetics and eliminates the need for the empirical scaling factor used by Myint et al. One major result of this research is that transience is found to play a relatively small role in the nucleation process for the dynamic-compression time scales of the liquid water–ice VII experiments being simulated. Instead, we show that it is possible to properly model the lag time using steady-state CNT by making small refinements to the interfacial free energy value. We have also developed a new dimensionless parameter that may be applied a priori to predict whether or not transient nucleation will be important in a given dynamic-compression experiment. [ABSTRACT FROM AUTHOR]

Effects of acoustic waves on a phase transformation in a metastable phase were investigated in our previous work [S. R. Haqshenas, I. J. Ford, and N. Saffari, "Modelling the effect of acoustic waves on nucleation," J. Chem. Phys. 145, 024315 (2016)]. We developed a non-equimolar dividing surface cluster model and employed it to determine the thermodynamics and kinetics of crystallisation induced by an acoustic field in a mass-conserved system. In the present work, we developed a master equation based on a hybrid Szilard-Fokker-Planck model, which accounts for mass transportation due to acoustic waves. This model can determine the kinetics of nucleation and the early stage of growth of clusters including the Ostwald ripening phenomenon. It was solved numerically to calculate the kinetics of an isothermal sonocrystallisation process in a system with mass transportation. The simulation results show that the effect of mass transportation for different excitations depends on the waveform as well as the imposed boundary conditions and tends to be noticeable in the case of shock waves. The derivations are generic and can be used with any acoustic source and waveform. [ABSTRACT FROM AUTHOR]

Nearly 20 years ago, transition path sampling (TPS) emerged as an alternative method to free energy based approaches for the study of rare events such as nucleation, protein folding, chemical reactions, and phase transitions. TPS effectively performs Monte Carlo simulations with relatively short molecular dynamics trajectories, with the advantage of not having to alter the actual potential energy surface nor the underlying physical dynamics. Although the TPS approach also introduced a methodology to compute reaction rates, this approach was for a long time considered theoretically attractive, providing the exact same results as extensively long molecular dynamics simulations, but still expensive for most relevant applications. With the increase of computer power and improvements in the algorithmic methodology, quantitative path sampling is finding applications in more and more areas of research. In particular, the transition interface sampling (TIS) and the replica exchange TIS (RETIS) algorithms have, in turn, improved the efficiency of quantitative path sampling significantly, while maintaining the exact nature of the approach. Also, open-source software packages are making these methods, for which implementation is not straightforward, now available for a wider group of users. In addition, a blooming development takes place regarding both applications and algorithmic refinements. Therefore, it is timely to explore the wide panorama of the new developments in this field. This is the aim of this article, which focuses on the most efficient exact path sampling approach, RETIS, as well as its recent applications, extensions, and variations. [ABSTRACT FROM AUTHOR]

I examined the polyamorphic behavior of glassy dilute aqueous solutions of polyols (ethylene glycol, glycerol, meso-erythritol, xylitol, and D-sorbitol) under pressure at low temperatures. Although the volume change of the glassy aqueous solution varied continuously against pressure, the rate of the volume change appeared to vary discontinuously at the onset pressure of the gradual polyamorphic transition. It is thought that low-density liquid-like solvent water and high-density liquid-like solvent water coexist during the transition. Moreover, the existence of a solute induces the shift of polyamorphic transition to the lower-pressure side. The effect of a solute on the polyamorphic transition becomes larger in the order ethylene glycol, glycerol, meso-erythritol, xylitol, and D-sorbitol. Therefore, the solute can become a variable controlling the polyamorphic state of liquid water. This experimental result suggests that the metastable-equilibrium phase boundary between the low-density and the high-density amorphs for pure water is likely to be located at 0.22-0.23 GPa at about 150 K, which is slightly larger than the previously estimated pressure. Moreover, the solute-nature dependence on the polyamorphic transition seems to connect to that on the homogeneous nucleation temperature of polyol aqueous solution at ambient pressure. The region in which a low-density liquid appears coincides with the region in which the nucleus of ice Ih appears, suggesting that the formation of a lowdensity liquid is a precursory phenomenon of the nucleation of ice Ih. [ABSTRACT FROM AUTHOR]

We have studied the limits of stability in the first order liquid-solid phase transition in a Lennard- Jones system by means of the short-time relaxation method and using the bond-orientational order parameter Q6. These limits are compared with the melting line. We have paid special attention to the supercooled liquid, comparing our results with the point where the free energy cost of forming a nucleating droplet goes to zero. We also indirectly estimate the dimension associated to the critical nucleus at the spinodal, expected to be fractal according to mean field theories of nucleation. [ABSTRACT FROM AUTHOR]

We examine nucleation of the stable body-centred-cubic (BCC) phase from the metastable uniform disordered phase in an asymmetric diblock copolymer melt. Our comprehensive, large-scale simulations of the time-dependent, mean-field Landau-Brazovskii model find that spherical droplets of the BCC phase nucleate directly from disorder. Near the order-disorder transition, the critical nucleus is large and has a classical profile, attaining the bulk BCC phase in an interior that is separated from disorder by a sharp interface. At greater undercooling, the amplitude of BCC order in the interior decreases and the nucleus interface broadens, leading to a diffuse critical nucleus. This diffuse nucleus becomes large as the simulation approaches the disordered phase spinodal. We show that our simulation follows the same nucleation pathway that Cahn and Hilliard found for an incompressible two-component fluid, across the entire metastable region. In contrast, a classical nucleation theory calculation based on the free energy of a planar interface between coexisting BCC and disordered phases agrees with simulation only in the limit of very small undercooling; we can expand this region of validity somewhat by accounting for the curvature of the droplet interface. A nucleation pathway involving a classical droplet persists, however, to deep undercooling in our simulation, but this pathway is energetically unfavourable. As a droplet grows in the simulation, its interface moves with a constant speed, and this speed is approximately proportional to the undercooling. [ABSTRACT FROM AUTHOR]

A phase transformation in a metastable phase can be affected when it is subjected to a high intensity ultrasound wave. In this study we determined the effect of oscillation in pressure and temperature on a phase transformation using the Gibbs droplet model in a generic format. The developed model is valid for both equilibrium and non-equilibrium clusters formed through a stationary or non-stationary process. We validated the underlying model by comparing the predicted kinetics of water droplet formation from the gas phase against experimental data in the absence of ultrasound. Our results demonstrated better agreement with experimental data in comparison with classical nucleation theory. Then, we determined the thermodynamics and kinetics of nucleation and the early stage of growth of clusters in an isothermal sonocrystallisation process. This new contribution shows that the effect of pressure on the kinetics of nucleation is cluster size-dependent in contrast to classical nucleation theory. [ABSTRACT FROM AUTHOR]

We discuss the microscopic mechanisms by which low-temperature amorphous states, such as ultrastable glasses, transform into equilibrium fluids, after a sudden temperature increase. Experiments suggest that this process is similar to the melting of crystals, thus differing from the behaviour found in ordinary glasses. We rationalize these observations using the physical idea that the transformation process takes place close to a "hidden" equilibrium first-order phase transition, which is observed in systems of coupled replicas. We illustrate our views using simulation results for a simple two-dimensional plaquette spin model, which is known to exhibit a range of glassy behaviour. Our results suggest that nucleation-and-growth dynamics, as found near ordinary first-order transitions, is also the correct theoretical framework to analyse the melting of ultrastable glasses. Our approach provides a unified understanding of multiple experimental observations, such as propagating melting fronts, large kinetic stability ratios, and "giant" dynamic length scales. We also provide a comprehensive discussion of available theoretical pictures proposed in the context of ultrastable glass melting. [ABSTRACT FROM AUTHOR]

Crystallization is one of the fundamental phase transition processes, and it is also important practically, for example, in the chemical, food, and pharmaceutical industries. Despite its importance, however, our basic understanding of crystallization, and especially crystal nucleation, at the molecular level is still incomplete. In this work, we present a general molecular simulation approach that can be used to investigate the nucleation of crystals from a subcooled liquid. Our method combines a previously proposed general method to construct structure-based order parameters [E. E. Santiso and B. L. Trout, J. Chem. Phys. 134, 064109 (2011)] with the string method in collective variables [L. Maragliano et al., J. Chem. Phys. 125, 024106 (2006)] to obtain a minimum free energy path connecting the liquid and solid basins. We then use Markovian milestoning with Voronoi tessellations [E. Vanden-Eijnden and M. Venturoli, J. Chem. Phys. 130, 194101 (2009); L. Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] to obtain the free energy profile along the path and the nucleation kinetics. We illustrate the application of this method to the nucleation of Benzene-I crystals from the melt, and compare the results to those previously found using transition path sampling [M. Shah et al., J. Phys. Chem. B 115, 10400-10412 (2011)]. [ABSTRACT FROM AUTHOR]

The method of molecular dynamics simulation has been used to investigate the phase decay of a metastable Lennard-Jones face-centered cubic crystal at positive and negative pressures. It is shown that at high degrees of metastability, crystal decay proceeds through the spontaneous formation and growth of new-phase nuclei. It has been found that there exists a certain boundary temperature. Below this temperature, the crystal phase disintegrates as the result of formation of voids, and above, as a result of formation of liquid droplets. The boundary temperature corresponds to the temperature of cessation of a crystal-liquid phase equilibrium when the melting line comes in contact with the spinodal of the stretched liquid. The results of the simulations are interpreted in the framework of classical nucleation theory. The thermodynamics of phase transitions in solids has been examined with allowance for the elastic energy of stresses arising owing to the difference in the densities of the initial and the forming phases. As a result of the action of elastic forces, at negative pressures, the boundary of the limiting superheating (stretching) of a crystal approaches the spinodal, on which the isothermal bulk modulus of dilatation becomes equal to zero. At the boundary of the limiting superheating (stretching), the shape of liquid droplets and voids is close to the spherical one. [ABSTRACT FROM AUTHOR]

A popular hypothesis that explains the anomalies of supercooled water is the existence of a metastable liquid-liquid transition hidden below the line of homogeneous nucleation. If this transition exists and if it is terminated by a critical point, the addition of a solute should generate a line of liquid-liquid critical points emanating from the critical point of pure metastable water. We have analyzed thermodynamic consequences of this scenario. In particular, we consider the behavior of two systems, H2O-NaCl and H2O-glycerol. We find the behavior of the heat capacity in supercooled aqueous solutions of NaCl, as reported by Archer and Carter [J. Phys. Chem. B 104, 8563 (2000)], to be consistent with the presence of the metastable liquid-liquid transition. We elucidate the nonconserved nature of the order parameter (extent of "reaction" between two alternative structures of water) and the consequences of its coupling with conserved properties (density and concentration). We also show how the shape of the critical line in a solution controls the difference in concentration of the coexisting liquid phases. [ABSTRACT FROM AUTHOR]

Nucleation is often accompanied by heat transfer between the surroundings and a nucleus of a new phase. The interface between two phases gives an additional resistance to this transfer. For small nuclei the interfacial curvature is high, which affects not only equilibrium quantities such as surface tension, but also the transport properties. In particular, high curvature affects the interfacial resistance to heat and mass transfer. We develop a framework for determining the curvature dependence of the interfacial heat and mass transfer resistances. We determine the interfacial resistances as a function of a curvature. The analysis is performed for a bubble of a one-component fluid and may be extended to various nuclei of multicomponent systems. The curvature dependence of the interfacial resistances is important in modeling transport processes in multiphase systems. [ABSTRACT FROM AUTHOR]

In standard nucleation theory, the nucleation process is characterized by computing ΔΩ(V ), the reversible work required to form a cluster of volume V of the stable phase inside the metastable mother phase. However, other quantities besides the volume could play a role in the free energy of cluster formation, and this will in turn affect the nucleation barrier and the shape of the nucleus. Here we exploit our recently introduced mesoscopic theory of nucleation to compute the free energy cost of a nearly spherical cluster of volume V and a fluctuating surface area A, whereby the maximum of ΔΩ(V ) is replaced by a saddle point in ΔΩ(V,A). Compared to the simpler theory based on volume only, the barrier height of ΔΩ(V,A) at the transition state is systematically larger by a few kBT. More importantly, we show that, depending on the physical situation, the most probable shape of the nucleus may be highly non-spherical, even when the surface tension and stiffness of the model are isotropic. Interestingly, these shape fluctuations do not influence or modify the standard Classical Nucleation Theory manner of extracting the interface tension from the logarithm of the nucleation rate near coexistence. [ABSTRACT FROM AUTHOR]

We study numerically the crystallization process in a supersaturated suspension of repulsive colloidal particles driven by simple shear flow. The effect of the shear flow on crystallization is two-fold: while it suppresses the initial nucleation, once a large enough critical nucleus has formed its growth is enhanced by the shear flow. Combining both effects implies an optimal strain rate at which the overall crystallization rate has a maximum. To gain insight into the underlying mechanisms, we employ a discrete state model describing the transitions between the local structural configurations around single particles. We observe a time-scale separation between these transitions and the overall progress of the crystallization allowing for an effective Markovian description. By using this model, we demonstrate that the suppression of nucleation is due to the inhibition of a pre-structured liquid. [ABSTRACT FROM AUTHOR]

Thermodynamic and kinetic peculiarities of nucleation, deliquescence and efflorescence transitions in the ensemble of droplets formed on soluble condensation nuclei from a solvent vapor have been considered. The interplay of the effects of solubility and the size of condensation nuclei has been analyzed. Activation barriers for the deliquescence and phase transitions and for the reverse efflorescence transition have been determined as functions of the relative humidity of the vapor-gas atmosphere, initial size, and solubility of condensation nuclei. It has been demonstrated that, upon variations in the relative humidity of the atmosphere, the crossover in thermodynamically stable and unstable variables of the droplet state takes place. The physical meaning of stable and unstable variables has been clarified. The kinetic equations for establishing equilibrium and steady distributions of binary droplets have been solved. The specific times for relaxation, deliquescence and efflorescence transitions have been calculated. [ABSTRACT FROM AUTHOR]

In this work, we study the nucleation mechanism of vapor-to-liquid phase transition from rough substrates, which are modeled as flat substrates decorated with square nanopores with one open end. Our calculations in a constrained lattice density functional theory shows that the presence of nanopores results in an intermediate state, either metastable or unstable, which divides the whole nucleation process into two sequential sub-processes, i.e., pore filling and phase transition outside the pores. Therefore, the nucleation mechanism was found to be one-step (with unstable intermediate states) or two-step (with metastable intermediate states), depending on the fluid-solid interaction, chemical potential, and pore size. The constructed phase diagram of nucleation mechanism shows that there exist six different nucleation mechanisms. In addition, our calculations show that the presence of nanopores on a rough substrate may change the morphology of critical nuclei from their counterpart on a smooth substrate. [ABSTRACT FROM AUTHOR]

Based on classical density functional theory (DFT), we investigate the demixing phase transition of a two-dimensional, binary Heisenberg fluid mixture. The particles in the mixture are modeled as Gaussian soft spheres, where one component is characterized by an additional classical spin-spin interaction of Heisenberg type. Within the DFT we treat the particle interactions using a mean-field approximation. For certain magnetic coupling strengths, we calculate phase diagrams in the density-concentration plane. For sufficiently large coupling strengths and densities, we find a demixing phase transition driven by the ferromagnetic interactions of the magnetic species. We also provide a microscopic description (i.e., density profiles) of the resulting non-magnetic/magnetic fluid-fluid interface. Finally, we investigate the phase separation using dynamical density functional theory, considering both nucleation processes and spinodal demixing. [ABSTRACT FROM AUTHOR]

We follow the vapor-liquid phase transition of N2 in a cryogenic supersonic nozzle apparatus using static pressure measurements. Under our operating conditions, condensation always occurs well below the triple point. Mean field kinetic nucleation theory (MKNT) does a better job of predicting the conditions corresponding to the estimated maximum nucleation rates, Jmax = 1017±1 cm-3 s-1, than two variants of classical nucleation theory. Combining the current results with the nucleation pulse chamber measurements of Iland et al. [J. Chem. Phys. 130, 114508-1 (2009)], we use nucleation theorems to estimate the critical cluster properties. Both the theories overestimate the size of the critical cluster, but MKNT does a good job of estimating the excess internal energy of the clusters. [ABSTRACT FROM AUTHOR]

We consider experimental data on the dynamics of water (1) in glass-forming aqueous mixtures with glass transition temperature Tg approaching the putative Tg = 136 K of water from above and below, (2) in confined spaces of nanometer in size, and (3) in the bulk at temperatures above the homogeneous nucleation temperature. Altogether, the considered relaxation times from the data range nearly over 15 decades from 10-12 to 103 s. Assisted by the various features in the isothermal spectra and theoretical interpretation, these considerations enable us to conclude that relaxation of un-crystallized water is highly non-cooperative. The exponent βK of its Kohlrausch stretched exponential correlation function is not far from having the value of one, and hence the deviation from exponential time decay is slight. Albeit the temperature dependence of its α-relaxation time being non-Arrhenius, the corresponding Tg-scaled temperature dependence has small steepness index m, likely less than 44 at Tg, and hence water is not ''fragile' as a glassformer. The separation in time scale of the α- and the β-relaxations is small at Tg, becomes smaller at higher temperatures, and they merge together shortly above Tg. From all these properties and by inference, water is highly non-cooperative as a glass-former, it has short cooperative length-scale, and possibly smaller configurational entropy and change of heat capacity at Tg compared with other organic glass-formers. This conclusion is perhaps unsurprising because water is the smallest molecule. Our deductions from the data rule out that the Tg of water is higher than 160 K, and suggest that it is close to the traditional value of 136 K. [ABSTRACT FROM AUTHOR]

We numerically study crystal nucleation and glassy slow dynamics of the one-component Gaussian core model (GCM) at high densities. The nucleation rate at a fixed supercooling is found to decrease as the density increases. At very high densities, the nucleation is not observed at all in the time window accessed by long molecular dynamics (MD) simulation. Concomitantly, the system exhibits typical slow dynamics of the supercooled fluids near the glass transition point. We compare the simulation results of the supercooled GCM with the predictions of mode-coupling theory (MCT) and find that the agreement between them is better than any other model glassformers studied numerically in the past. Furthermore, we find that a violation of the Stokes-Einstein relation is weaker and the non-Gaussian parameter is smaller than canonical glassformers. Analysis of the probability distribution of the particle displacement clearly reveals that the hopping effect is strongly suppressed in the high density GCM. We conclude from these observations that the GCM is more amenable to the mean-field picture of the glass transition than other models. This is attributed to the long-ranged nature of the interaction potential of the GCM in the high density regime. Finally, the intermediate scattering function at small wavevectors is found to decay much faster than its self part, indicating that dynamics of the large-scale density fluctuations decouples with the shorter-ranged caging motion. [ABSTRACT FROM AUTHOR]

Heterogeneous nucleation of a new bulk phase on a flat substrate can be associated with the surface phase transition called wetting transition. When this bulk heterogeneous nucleation occurs on a completely wettable flat substrate with a zero contact angle, the classical nucleation theory predicts that the free-energy barrier of nucleation vanishes. In fact, there always exists a critical nucleus and a free-energy barrier as the first-order prewetting transition will occur even when the contact angle is zero. Furthermore, the critical nucleus changes its character from the critical nucleus of surface phase transition below bulk coexistence (undersaturation) to the critical nucleus of bulk heterogeneous nucleation above the coexistence (oversaturation) when it crosses the coexistence. Recently, Sear [J. Chem. Phys. 129, 164510 (2008)] has shown, by a direct numerical calculation of nucleation rate, that the nucleus does not notice this change when it crosses the coexistence. In our work, the morphology and the work of formation of critical nucleus on a completely wettable substrate are re-examined across the coexistence using the interface-displacement model. Indeed, the morphology and the work of formation changes continuously at the coexistence. Our results support the prediction of Sear and will rekindle the interest on heterogeneous nucleation on a completely wettable substrate. [ABSTRACT FROM AUTHOR]

Heat and mass transfers are coupled processes, also in nucleation. In principle, a nucleating cluster would have a different temperature compared to the surrounding supersaturated old phase because of the heat release involved with attaching molecules to the cluster. In turn a difference in temperature across the cluster surface is a driving force for the mass transfer to and from the cluster. This coupling of forces in nonisothermal nucleation is described using mesoscopic nonequilibrium thermodynamics, emphasizing measurable heat effects. An expression was obtained for the nonisothermal nucleation rate in a one-component system, in the case where a temperature difference exists between a cluster distribution and the condensed phase. The temperature is chosen as a function of the cluster size only, while the temperature of the condensed phase is held constant by a bath. The generally accepted expression for isothermal stationary nucleation is contained as a limiting case of the nonisothermal stationary nucleation rate. The equations for heat and mass transport were solved for stationary nucleation with the given cluster distribution and with the temperature controlled at the boundaries. A factor was defined for these conditions, determined by the heat conductivity of the surrounding phase and the phase transition enthalpy, to predict the deviation between isothermal and nonisothermal nucleation. For the stationary state described, the factor appears to give small deviations, even for primary nucleation of droplets in vapor, making the nonisothermal rate smaller than the isothermal one. The set of equations may lead to larger and different thermal effects under different boundary conditions, however. [ABSTRACT FROM AUTHOR]

A general thermodynamic analysis of nucleation-growth processes in confined space in initially metastable states of the ambient phase is performed based on the generalized Gibbs approach to the description of heterogeneous systems. In particular, it is shown analytically how the parameters of critical clusters and clusters in stable equilibrium with the ambient phase depend on the volume of the system for initially fixed intensive state parameters of the ambient phase. Qualitatively, the results are shown to be similar independent on the boundary conditions employed. It is demonstrated further that the behavior of systems in confined space is directly related to the kinetics of phase transformation processes in spatially extended systems, when ensembles of clusters are formed. The results of the thermodynamic analysis of cluster formation and growth in a confined space are employed then, in particular, to the derivation of kinetic equations for the description of the process of coarsening or Ostwald ripening. In the analysis of both the nucleation in confined space and the description of Ostwald ripening, no specific assumptions concerning the equations of state of the system under consideration and the number of components both in the ambient and newly evolving phases are made. Consequently, the results are of very general nature and hold always as far as the necessary condition for the possibility of a phase transformation is fulfilled. [ABSTRACT FROM AUTHOR]

The late stage growth mechanism for a first order phase transition, either through nucleation growth or spinodal decomposition, is well understood to be an Ostwald ripening or coarsening process, in which larger domains grow at the expense of smaller ones. The growth kinetics in this regime was shown by Lifshitz and Slyozov to follow at1/3 law. However, the kinetics is altered if there exists a barrier ahead of the growth front, irrespective of the physical origin of the boundary layer. We present an analytic calculation for the growth kinetics in the presence of a boundary layer, showing that in the limit of barrier-dominated growth, the domains grow with at1/2 law. This result holds true in the dilute regime independent of whether the growing nuclei are spherical or cylindrical. [ABSTRACT FROM AUTHOR]

Density functional theory (DFT) with square gradient approximation for the free energy functional and a model density profile are used to obtain an analytical expression for the size-dependent free energy of formation of a liquid drop from the vapor through the process of homogeneous nucleation, without invoking the approximations used in classical nucleation theory (CNT). The density of the liquid drop in this work is not the same as the bulk liquid density but it corresponds to minimum free energy of formation of the liquid drop. The theory is applied to study the nucleation phenomena from supersaturated vapor of Lennard-Jones fluid. The barrier height predicted by this theory is significantly lower than the same in CNT which is rather high. The density at the center of the small liquid drop as obtained through optimization is less than the bulk density which is in agreement with other earlier works. Also proposed is a sharp interface limit of the proposed DFT of nucleation, which is as simple as CNT but with a modified barrier height and this modified classical nucleation theory, as we call it, is shown to lead to improved results. [ABSTRACT FROM AUTHOR]

The element distribution in the Cu3Au(001) surface region has been determined on the basis of directional Auger electron spectroscopy polar profiles measurements and interpreted in the frame of thermodynamic approach formulated for the inhomogeneous systems by using the Néel sublattices concept. Both approaches, experimental and theoretical, allowed us to present the temperature dependence of element concentration in a layer resolved mode. The wide temperature range explored in the experiment ensured the large data base for the theoretical analysis which enabled us to propose the distribution of intra-layer and inter-layer pairwise interactions leading to proper temperature dependence of segregation profiles in the surface region. This kind of interaction distribution can be understood as strain induced. [ABSTRACT FROM AUTHOR]

We introduce a new forward flux sampling in time algorithm to efficiently measure transition times in rare-event processes in nonequilibrium systems and apply it to study the first-order (discontinuous) kinetic transition in the Ziff-Gulari-Barshad model of catalytic surface reaction. The average time for the transition to take place, as well as both the spinodal and transition points, is efficiently found by this method. [ABSTRACT FROM AUTHOR]

We have studied the crystalline-amorphous coexistence for systems of polydisperse soft spheres that interact via a purely repulsive power law potential. Potential softness quantified by the exponent of the potential was a primary input in our simulations. Simulations were performed in the isobaric semigrand statistical ensemble, i.e., the composition of the parent distribution was not fixed in our systems. Gibbs–Duhem integration was used to trace the coexistence pressure as a function of potential softness for monodisperse systems. A second Gibbs–Duhem integration, initiated from the monodisperse coexistence curve, was employed to determine coexistence pressure versus imposed variance of the activity distribution. Amorphous-crystalline coexistence densities and volume fractions were determined to be monotonically increasing functions of the breadth of particle size dispersity. Semigrand ensemble simulations testified to the existence of a terminal diameter dispersity, i.e., a dispersity above which no amorphous-crystalline phase coexistence was observed. At the terminus size dispersity increases from 5.8% to 6.1% to 6.4% and to 6.7% and 6.5% for the crystalline phase as the steepness parameter n, takes on smaller values: from 100 to 50 to 12 to 10 and 8, respectively. In sharp contrast to the crystalline phases’ enhanced, by potential softness, allowable size dispersity the amorphous phase exhibits an opposite trend, as potential interactions soften. Furthermore, amorphous phases accommodate, on average, smaller particles than those of the ordered (fcc) phase. Contrary to widely accepted intuition crystalline phases composed of size-disperse particulates exhibit a higher degree of local order than their monodisperse counterparts, admittedly at differing thermodynamic conditions. [ABSTRACT FROM AUTHOR]

We present the results of Monte Carlo simulations of crystal nucleation from the vapor phase. We studied the Lennard–Jones system at conditions close to, but below, the triple point. This system is expected to show surface melting. The nucleation pathway that we observe consists of two distinct steps. In the first step, a liquid droplet nucleates from the vapor. Its nucleation rate depends strongly on the vapor supersaturation. In the second step, the final crystal phase nucleates in the liquid droplet, provided that this liquid droplet exceeds a minimum size. Our simulations show that within a liquid droplet the crystal nucleation rate does not depend on the vapor supersaturation. In a recent independent study Chen et al. [J. Phys. Chem. B 112, 4069 (2008)] investigated the same phenomenon using umbrella sampling to compute free energy barriers and hence nucleation rates. We use a different numerical approach where we focus on computing the nucleation rates directly using forward-flux sampling. Our results agree with the findings of Chen et al. and both methods observe two-step nucleation. This finding indicates that this nucleation process can be described with a quasiequilibrium theory. Due to different cutoffs for the interaction potential the results cannot be compared quantitatively. [ABSTRACT FROM AUTHOR]

The phase transition between liquid and solid phases in body-centered cubic (bcc) metal nanoparticles of iron, chromium, molybdenum, and tungsten with size ranging from 2000 to 31250 atoms was investigated using a molecular dynamics simulation. The nucleation from an undercooled liquid droplet was observed during cooling in all nanoparticles considered. It was found that a nucleus was generated near one side of the particle and solidification spread toward the other side the during nucleation process. On the other hand, the surface melting and subsequent inward melting of the solid core of the nanoparticles were observed during heating. The depression of the melting point was proportional to the inverse of the particle radius due to the Gibbs–Thomson effect. On the other hand, the depression of the nucleation temperature during cooling was not monotonic with respect to the particle radius since the nucleation from an undercooled liquid depends on the event probability of an embryo or a nucleus. [ABSTRACT FROM AUTHOR]

The homogeneous nucleation and growth in a simplest two-dimensional phase field model is numerically studied using the cell dynamics method. The whole process from nucleation to growth is simulated and is shown to follow closely the Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation. Specifically the time evolution of the volume fraction of new stable phase is found to follow closely the KJMA formula. By fitting the KJMA formula directly to the simulation data, not only the Avrami exponent but the magnitude of nucleation rate and, in particular, of incubation time are quantitatively studied. The modified Avrami plot is also used to verify the derived KJMA parameters. It is found that the Avrami exponent is close to the ideal theoretical value m=3. The temperature dependence of nucleation rate follows the activation-type behavior expected from the classical nucleation theory. On the other hand, the temperature dependence of incubation time does not follow the exponential activation-type behavior. Rather the incubation time is inversely proportional to the temperature predicted from the theory of Shneidman and Weinberg [J. Non-Cryst. Solids 160, 89 (1993)]. A need to restrict thermal noise in simulation to deduce correct Avrami exponent is also discussed. [ABSTRACT FROM AUTHOR]

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e., at coexistence, where the critical nucleus becomes infinitely large. [ABSTRACT FROM AUTHOR]

The shear-induced isotropic-to-lamellar phase transition in the amphiphilic systems in the vicinity of the quiescent order-to-disorder transition point is investigated by the large-scale parallel nonequilibrium molecular dynamics simulations of simple amphiphilic model systems. There is a shear-induced upward shift of the ordering temperature. The initial isotropic phase orders into a lamellar phase perpendicular to the shear vorticity. The phase diagram as a function of temperature and shear rate is established. The dependency of the ordering transition on interaction strength and shear rate is rationalized by the competition between shear rate and chain relaxation. The time evolution of morphology reveals that the shear-induced ordering proceeds via nucleation and growth, a signature of a first-order phase transition. At low shear rate, a single ordered domain grows after an incubation period. With increasing shear rate ordering speeds up, but eventually develops in a lamellar system with disordered shear bands. The time dependence of the order parameter follows that of the mean-squared end-to-end distance, shear viscosity, and bulk pressure, and follows an Avrami scheme with an Avrami exponent between 2 and 4. [ABSTRACT FROM AUTHOR]

The dynamics of phase transformation due to homogeneous nucleation has long been analyzed using the classic Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory. However, the dynamics of phase transformation due to heterogeneous nucleation has not been studied systematically even though it is vitally important technologically. In this report, the author studies the dynamics of heterogeneous nucleation theoretically and systematically using the phenomenological time-dependent Ginzburg-Landau (TDGL)-type model combined with the cell dynamics method. In this study the author focuses on the dynamics of phase transformation when the material is sandwiched by two supporting substrates. This model is supposed to simulate phase change storage media. Since both homogeneous and heterogeneous nucleations can occur simultaneously, the author predicts a few scenarios of phase transformation including homogeneous nucleation regime, heterogeneous nucleation regime, and the homogeneous-heterogeneous coexistence regime. These predictions are directly confirmed by numerical simulation using the TDGL model. The outcome of the study was that the KJMA formula has limited use when heterogeneous nucleation exists, but it could still give some information about the microscopic mechanism of phase transformation at various stages during phase transformation. [ABSTRACT FROM AUTHOR]

Molecular dynamics methods have been used to investigate the kinetics of the liquid-gas phase transition in a two-component Lennard-Jones system at negative pressures and elastic stretches of the liquid to values close to spinodal ones. The molecular dynamics system consists of 2048 interacting particles with parameters of the Lennard-Jones potential for argon and neon. Density dependences of pressure and internal energy have been calculated for stable and metastable states of the mixture at a temperature T*≈0.7±0.01 and three values of the concentration. The location of mechanical and the diffusion spinodals has been determined. It has been established that a gas-saturated mixture retains its stability against finite variations of state variables up to stretches close to the values near the diffusion spinodal. The statistic laws of the process of destruction of the metastable state have been investigated. The lifetimes of the metastable phase have been determined. It is shown that owing to the small height of the potential barrier that separates the microheterogeneous from the homogeneous state a system of finite size has a possibility to make the reverse transition from the microheterogeneous into the homogeneous state. The lifetimes of the system in the microheterogeneous state, as well as the expectation times of the occurrence of a critical nucleus, are described by Poissonian distributions. [ABSTRACT FROM AUTHOR]

Classical expressions for the critical cluster work of formation approximate the nonclassical expressions based in the density functional theory of capillarity for the limit of low supersaturation degrees. However, the ratio between classical and nonclassical expressions for nucleation rates grows as the supersaturation degree decreases. Here, with the aim to obtain simple and more accurate expressions that approximate the modern nucleation rate formulas, an asymptotic expansion of the Cahn-Hilliard expression of the critical work of formation is developed within the limit of low supersaturation. In such asymptotic expansion, terms up to third order are retained. The ratios between the corrected classical expressions and the nonclassical ones are now decreasing for supersaturation degrees tending to zero. However, the corrected approximate formulas are as difficult to handle as the exact Cahn-Hilliard expressions. When only the two first low-order terms of the asymptotic expansion are retained, a simpler corrected classical expression is obtained but it can only approximate nonclassical expressions up to order unity. Finally, using a Becker-Doring model of nucleation, the kinetic prefactor of the critical nuclei rate of formation is modeled consistently with the Cahn-Hilliard approach to the critical work of formation. [ABSTRACT FROM AUTHOR]

Formation of the new disperse phase via homogeneous nucleation plays a fundamental role wherever the first-order phase transitions occur. Inconsistent temperature dependence of the nucleation rates and poor agreement of theoretical critical supersaturations with experimental data for a number of substances are fundamental problems of the classical nucleation theory (CNT). Here we show that these problems can be solved with a simple empirical correction to CNT. Despite its simplicity, the corrected CNT (CCNT) accurately predicts temperature dependences and absolute values of the critical supersaturations for both organic and inorganic substances with widely varying properties at different ambient conditions and it works surprisingly well in a wide size range down to few molecules. The difference in predictions of CCNT and other versions of the classical nucleation theory commonly used in analyzing experimental data is discussed. It has been found that CCNT consistently gives better agreement with experimental data than other versions of classical nucleation theory. [ABSTRACT FROM AUTHOR]

For a nearest-neighbor Ising model on a square lattice all cluster configurations with 17 or fewer spins are identified. In neglect of cluster-cluster interactions, critical sizes and barriers to nucleation are obtained as functions of temperature and magnetic field for two alternative definitions of a “critical cluster.” © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This work presents a self-consistent description of phase transition dynamics of disperse liquid phase precipitating from a supersaturated gas mixture. The unified approach integrates the macroscale transport phenomena of cloud dynamics with the essential microphysical kinetic processes of droplet condensation, evaporation, and droplet collisions simultaneously taking place in stochastic population of liquid droplets. A complete set of governing equations with well-defined dissipative fluxes and kinetic rates is derived for phase transition dynamics from nucleation to postnucleation to coarsening stages. The local thermodynamics of precipitating system, which is considered as ternary mixture of disperse liquid phase and water vapor with dry air, is redefined to explicitly include on equal basis both the vapor content and liquid content into the fundamental thermodynamic relations and equation of state. The molecular kinetic flux regularization method for growth of submicron droplets is reexamined to include, among others, significant contribution of vapor molecular energy flux into total heat flux, resulting in new expressions for the droplet temperature, growth rate, and effective diffusion coefficients. The local kinetic rates are determined on the basis of microscale kinetic equation for the droplet distribution function. This is in contrast to commonly used semiempirical parametrization schemes for kinetic rates with adjustable parameters, wherein the probabilistic aspects of microphysical processes are not rigorously addressed. Stochastic diffusion interactions among droplets competing for the available water vapor and modifications in the kinetic equation for droplets growing in stochastic population with direct long-range diffusion interactions amongst them are discussed and formulated as well. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The initial stages of nucleation during liquid-liquid phase separation in polymer mixtures were studied by time-resolved small angle neutron scattering. The time required for nucleation vanishes exponentially as the stability limit (spinodal) is approached. The critical nucleus size decreases monotonically with increasing quench depth and remains finite at the spinodal. Our data differ qualitatively from theoretical predictions. [ABSTRACT FROM AUTHOR]