A comprehensive treatment of classical nucleation in a supercooled or superheated fluid (original) (raw)
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A limit of stability in supercooled liquid clusters
The Journal of chemical …, 2007
We examine the metastable liquid phase of a supercooled gold nanocluster by studying the free energy landscape using the largest solid-like embryo as an order parameter. Just below freezing, the free energy exhibits a local minimum at small embryo sizes and a maximum at larger embryo sizes which denotes the critical embryo size. At T = 660K the free energy becomes a monotonically decreasing function of the order parameter as the liquid phase becomes unstable, indicating we have reached a spinodal. In contrast to the usual mean-field theory predictions, the size of the critical embryo remains finite as the spinodal is approached. We also calculate the rate of nucleation, independently from our free energy calculations, and observe a rapid increase in its temperature dependence when the free energy barrier is in the order of kT . This supports the idea that freezing becomes a barrierless process around the spinodal temperature. PACS numbers: 61.46.Df, 64.60.Qb, 64.60.My
Interplay between the range of attractive potential and metastability in gas-liquid nucleation
2010
We find an interesting interplay between the range of the attractive part of the interaction potential and the extent of metastability (as measured by supersaturation) in gas-liquid nucleation. We explore and exploit this interplay to obtain new insight into nucleation phenomena. Just like its dependence on supersaturation (S), the free energy barrier of nucleation is found to depend strongly on
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">mml:mrowmml:msupmml:mrowmml:mn10mml:mrowmml:mn6-particle molecular-dynamics study of homogeneous nucleation of crystals in a supercooled a...
Physical review, 1990
Molecular-dynamics simulations of 15000 and 10 particles have been performed to study the onset of crystallization in supercooled Lennard-Jones liquids. The calculations were performed by suddenly cooling an equilibrated liquid and calculating the subsequent time evolution of the system (at constant energy and volume with periodic boundary conditions). The configurations at evenly spaced times along the trajectory were subjected to an analysis that consisted of a short steepestdescents energy minimization toward an inherent structure followed by a Voronoi analysis to identify crystalline regions. The sequence of these quenched configurations was analyzed to study the time evolution of the solidlike regions. Several observations are consistent with the existence of a free-energy barrier to crystallization, as described by classical nucleation theory, including an identification of a critical nucleus size. Critical nuclei by our analysis and under the conditions of this simulation consist of 10 to 20 particles in face-centered cubic and hexagonal close-packed environments. A steady-state distribution of sizes of precritical clusters is observed at intermediate times, but the first critical and postcritical nuclei form and there is a significant amount of crystallization before this steady-state distribution is achieved.
Critical nucleus size for crystallization of supercooled liquids in two dimensions
Physical Review E
Using molecular dynamics simulations, we study the crystallization of supercooled liquids in two dimensions in which particles interact with other particles via the Lennard-Jones-Gauss potential. We first prepare supercooled liquids at various temperatures by rapid quenching from the melt. The simulations are performed with a crystalline seed inserted at the center of the initial system. We investigate the time evolution of the inserted nucleus and its surroundings and determine the critical nucleus size n c defined as the smallest nucleus which survives. The results show that n c scales as ∼(T m − T) −2 with the melting temperature T m , as expected in the classical nucleation theory. We also obtain the crystallization time at various temperatures as a function of nucleus size and show that the presence of a crystalline seed significantly affects the crystallization time when the temperature is higher than the characteristic temperature T * at which the crystallization time becomes the shortest. This indicates that the crystallization is controlled by thermodynamics in this temperature range. When the temperature is lower than T * , the effect of the inserted nucleus on crystallization is less significant, which indicates that crystallization is controlled by emergence and merging of small crystalline nuclei.
Stability and instability of a hot and dilute nuclear droplet
The European Physical Journal A, 2000
The diabatic approach to collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for infinite nuclear matter. For small densities below 30% of normal nuclear matter density and for temperatures below 5 MeV all relevant bulk modes become unstable with the same growth rates. The surface modes have a larger spinodal region, reaching out to densities and temperatures way beyond the spinodal line for bulk instabilities. Essential experimental features of multifragmentation, like fragmentation temperatures and fragmentmass distributions (in particular the power-law behavior) are consistent with the instability properties of an expanding nuclear droplet, and hence with a dynamical fragmentation process within the spinodal regime of bulk and surface modes (spinodal decomposition).
Elucidating the Mechanism of Nucleation near the Gas-Liquid Spinodal
Physical Review Letters, 2007
We have constructed, using a variant of umbrella sampling technique, a multidimensional free energy surface of nucleation of the liquid phase from the parent vapor phase near the gas-liquid spinodal as a function of relevant nucleation coordinates. Extensive simulation studies have been performed for the supercooled Lennard-Jones gas and the 3-dimensional Ising model. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. Close to the spinodal, the free energy, as a function of the size of the largest cluster, develops surprisingly a minimum at a sub-critical cluster size. It is this minimum at intermediate size that is found to be responsible for the barrier towards further growth of the nucleus at large supersaturation. An alternative free energy pathway involving the participation of many sub-critical clusters is found near the spinodal where the growth of the nucleus is promoted by a coalescence mechanism. Temperature quench trajectory analyses reveal that the growth of the stable phase becomes more collective and spatially diffuse, and the significance of a 'critical nucleus' is lost for deeper quenches.
Nucleation as a local subsystem fluctuation
Physica A-statistical Mechanics and Its Applications, 2002
A nucleation theory has been advanced, in which a metastable system is considered as the sum of statistically independent subsystems. This theory provides a flexible scheme taking into account actually all initiating factors, including even a separate “weak” point in a system. In the case of a homogeneous nucleation, the difference between the classical and alternative approaches consists in the expression for the preexponential. Depending on the diameter of the critical nucleus, numerical estimates of this preexponential by the two theories differ by 0–4 orders of magnitude for a supersaturated steam and 1–5 orders of magnitude for a superheated liquid.
The Journal of Chemical Physics, 2010
The free energy of forming a droplet and a bubble with a given particle number n and volume v within the pure-component Lennard-Jones supercooled vapor and superheated liquid, respectively, are further explored using density-functional theory. Similar to what was found previously ͓M. J. Uline and D. S. Corti, Phys. Rev. Lett. 99, 076102 ͑2007͒; M. J. Uline and D. S. Corti, J. Chem. Phys. 129, 234507 ͑2008͔͒, the limits of stability again appear within both free energy surfaces evaluated at two other metastability conditions, one closer to the binodal and one closer to the spinodal. Furthermore, an ad hoc bond connectivity criterion is also applied in an attempt, however approximately, to eliminate certain configurational redundancies that arise from the chosen droplet and bubble definitions. What results are free energy surfaces describing the formation of equilibrium embryos that should be an improved representation of the fluctuations that are relevant to those nonequilibrium embryos seen in an actual nucleation event. Finally, we discuss in some detail the use of the ͑n , v͒ reaction coordinate within the framework of an equilibrium-based theory and its relation to other descriptions of nucleation.
Supercooled water escaping from metastability
Scientific reports, 2014
The return of supercooled water to a stable equilibrium condition is an irreversible process which, in large enough samples, takes place adiabatically. We investigated this phenomenon in water by fast imaging techniques. As water freezes, large energy and density fluctuations promote the spatial coexistence of solid and liquid phases at different temperatures. Upon synchronously monitoring the time evolution of the local temperature, we observed a sharp dynamic transition between a fast and a slow decay regime at about 266.6 K. We construe the observed phenomenon in terms of the temperature dependence of heat transfers from solid and liquid volumes already at their bulk coexistence temperature towards adjacent still supercooled liquid regions. These findings can be justified by observing that convective motions induced by thermal gradients in a supercooled liquid near coexistence are rapidly suppressed as the nucleated solid fraction overcomes, at low enough temperatures, a characteristic percolation threshold. W ater exhibits several pronounced thermodynamic, structural and dynamic anomalies 1-7. In the last few decades, much attention has been devoted to explaining the apparent divergence of several transport properties of supercooled water below the homogeneous nucleation temperature 8. This behavior has often been taken as an indirect evidence of a liquid-liquid phase transition hidden in the deeply supercooled regime 9-11. Indeed, a first-order phase transition between a low-density liquid (LDL) and a high-density liquid (HDL) phase has been observed in the ST2 model of water 9. A few indirect experimental indications on a liquidliquid transition have been reported in water 12,13 as well as in other molecular liquids 14-16. However, a conventional (i.e., non transient) HDL-LDL phase coexistence would be likely inaccessible to any experimental investigation performed on bulk water because of fast ice nucleation at temperatures higher than those expected for the transition to occur. The origin of water anomalies in the supercooled regime remains rather controversial 17-21. In this respect, it is somewhat surprising that relatively few efforts have been made to clarify the process of water crystallization in the bulk and the kinetic pathways leading to ice nucleation (in this respect, notable exceptions are Refs. 22, 23). Liquid water is a strongly correlated molecular system whose microscopic and macroscopic behavior is dominated by intermolecular hydrogen bonds, which produce an unusually slow relaxation and a very rich phase diagram at low temperatures. This makes the description of ice nucleation so complicated that the size and structure of critical nuclei have not been safely ascertained yet. Certainly, a satisfactory description of ice nucleation goes well beyond the scope of the classical nucleation theory 8,24,25. It has also been proposed that the polymorphism of supercooled water is relevant to ice nucleation since it may offer several alternative routes to the escape of the liquid from metastability 26,27. Recently, it has been argued that the widely adopted scheme describing the nucleation of a solid phase from a supercooled liquid as an isothermal process can be fundamentally wrong since it disregards any enthalpy contribution 28-30. In fact, solid nucleation always occurs exothermically on a local scale, which implies that the liquid warms up while (partially) solidifying 31. Generally speaking, any metastable system will eventually move in an irreversible way towards a stable thermodynamic condition, which means that the phase transformation does not require an energy exchange with the environment. In a globally isolated system some spontaneous fluctuations sooner or later will drive the system to the boundary between the metastable and the stable equilibrium basins in phase space and, if the amplitude of the fluctuation is large enough, the system will overcome the freeenergy barrier between the two basins. Crossing the nucleation barrier is an irreversible process which takes place adiabatically in an isolated system (see, e.g., Ref. 32). A comparison between the enthalpy content of homogeneous supercooled water and that of its corresponding heterogeneous stable state at the melting temperature shows
Dynamics of highly supercooled liquids
AIP Conference Proceedings, 1999
The diffusivity of tagged particles is demonstrated to be heterogeneous on time scales comparable to or less than the structural relaxation time in a highly supercooled liquid via 3D molecular dynamics simulation. The particle motions in the relatively active regions dominantly contribute to the mean square displacement, giving rise to a diffusion constant systematically larger than the Stokes-Einstein value. The van Hove self-correlation function G s (r, t) is shown to have a large r tail which can be scaled in terms of r/t 1/2 for t < ∼ 3τ α , where τ α ∼ = the stress relaxation time. Its presence indicates heterogeneous diffusion in the active regions. However, the diffusion process eventually becomes homogeneous on time scales longer than the life time of the heterogeneity structure (∼ 3τ α).