Critical cavities and the kinetic spinodal for superheated liquids

We present density-functional theory (DFT) calculations for critical cavities inside model superheated liquids with varying intermolecular potentials. Our calculations show that the radius of the critical cavity and the ratio of the work of formation of the critical cavity to the work of formation of the critical bubble as predicted by the classical nucleation theory exhibit universal scaling across similar intermolecular potentials. We then utilize this observed scaling behavior by proposing two new criteria for the kinetic spinodal of superheated liquids. These criteria are based on various properties of the critical cavity as obtained from our DFT studies of the superheated Lenanrd-Jones liquid. Our predictions of the kinetic spinodal compare favorably with experimental data of the limits of superheating for various organic liquids.     

Molecular dynamics simulation of cavitation in a lead melt at negative pressures

The molecular dynamics method was used to simulate cavitation in a metastable lead melt and determine the stability limits. States at temperatures below critical (T < 0.5T _c) and large negative pressures were considered. Interatomic interactions were described by the realistic embedded atom potential. The kinetic boundary of liquid phase stability was shown to be different from the spinodal. The kinetics and dynamics of cavitation were studied. The pressure dependences of cavitation frequencies were obtained over the temperature range 700–2700 K. The results of molecular dynamics calculations were compared with estimates based on classical nucleation theory.     

Crossover model for the work of critical cluster formation in nucleation theory

We propose a relation for the work of critical cluster formation in nucleation theory W for the systems with long-range interparticle interactions. The method of bridge functions is used to combine the system behavior at sufficiently small quenches, adequately predicted by the classical nucleation theory, with nonclassical effects at deep quenches in the vicinity of the thermodynamic spinodal, described within the framework of the field theoretical approach with an appropriate Ginzburg-Landau functional. The crossover between the two types of nucleation behavior takes place in the vicinity of the kinetic spinodal where the lifetime of a metastable state is of the order of the relaxation time to local equilibrium. We argue that the kinetic spinodal corresponds to the minimum of the excess number of molecules in the critical cluster. This conjecture leads to the form of W containing no adjustable parameters. The barrier scaling function Gamma = W/W(cl), where W(cl) is the classical nucleation barrier, depends parametrically on temperature through the dimensionless combination of material properties. The results for argon nucleation are presented.     

Nonequilibrium melting and crystallization of a model Lennard-Jones system

Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.     

Nucleation near the spinodal: limitations of mean field density functional theory

We investigate the diverging size of the critical nucleus near the spinodal using the gradient theory (GT) of van der Waals and Cahn and Hilliard and mean field density functional theory (MFDFT). As is well known, GT predicts that at the spinodal the free energy barrier to nucleation vanishes while the radius of the critical fluctuation diverges. We show numerically that the scaling behavior found by Cahn and Hilliard for these quantities holds quantitatively for both GT and MFDFT. We also show that the excess number of molecules Deltag satisfies Cahn-Hilliard scaling near the spinodal and is consistent with the nucleation theorem. From the latter result, it is clear that the divergence of Deltag is due to the divergence of the mean field isothermal compressibility of the fluid at the spinodal. Finally, we develop a Ginzburg criterion for the validity of the mean field scaling relations. For real fluids with short-range attractive interactions, the near-spinodal scaling behavior occurs in a fluctuation dominated regime for which the mean field theory is invalid. Based on the nucleation theorem and on Wang's treatment of fluctuations near the spinodal in polymer blends, we infer a finite size for the critical nucleus at the pseudospinodal identified by Wang.     

Homogeneous crystal nucleation triggered by spinodal decomposition in polymer solutions

We report dynamic Monte Carlo simulations of polymer crystal nucleation initiated by prior spinodal decomposition in polymer solutions. We observed that the kinetic phase diagrams of homogeneous crystal nucleation appear horizontal in the concentration region below their crossovers with the theoretical liquid-liquid spinodal. When the solution was quenched into the temperature beneath this horizontal boundary, the time evolution of structure factors demonstrated the spinodal decomposition at the early stage of crystal nucleation. In comparison with the case without a prior liquid-liquid demixing, we found that the prior spinodal decomposition can regulate the nanoscale small polymer crystallites toward a larger population, more uniform sizes, and a better spatial homogeneity, whereas chain folding in the crystallites seems little affected.     

Differences between solid superheating and liquid supercooling

The thermodynamic and kinetic behaviors for solid superheating and liquid supercooling were critically examined and compared via molecular-dynamics simulations. It is shown that the large elastic energy associated with internal melting and solid-liquid interface disorder play important roles in superheating. The growth rate is anisotropic for supercooling, but isotropic for superheating. Supercooling can be well described by the classical nucleation theory, whereas superheating shows many exceptions. The underlying mechanisms for these differences are discussed.     

A limit of stability in supercooled liquid clusters

We examine the metastable liquid phase of a supercooled gold nanocluster by studying the free energy landscape using the largest solidlike embryo as an order parameter. Just below freezing, the free energy exhibits a local minimum at small embryo sizes and a maximum at a larger critical embryo size. At T=660 K the free energy becomes a monotonically decreasing function of the order parameter as the liquid phase becomes unstable, indicating that we have reached a limit of stability. In contrast to the mean-field theory predictions for a spinodal, the size of the critical embryo remains finite as the limit of stability 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 on the order of kT. We suggest that this supports the idea that freezing becomes a barrierless process at low temperatures.     

Liquid Metastable Precursors of Ibuprofen as Aqueous Nucleation Intermediates

The nucleation mechanism of crystals of small organic molecules, postulated based on computer simulations, still lacks experimental evidence. In this study we designed an experimental approach to monitor the early stages of the crystallization of ibuprofen as a model system for small organic molecules. Ibuprofen undergoes liquid–liquid phase separation prior to nucleation. The binodal and spinodal limits of the corresponding liquid–liquid miscibility gap were analyzed and confirmed. An increase in viscosity sustains the kinetic stability of the dense liquid intermediate. Since the distances between ibuprofen molecules within the dense liquid phase are similar to those in the crystal forms, this dense liquid phase is identified as a precursor phase in the nucleation of ibuprofen, in which densification is followed by generation of structural order. This discovery may make it possible to enrich poorly soluble pharmaceuticals beyond classical solubility limitations in aqueous environments.     

Spinodal patterns indicating unstable regime of polymer crystallization

It has been considered that crystallization of polymer from melt proceeds via the coexistence of molten matrix and growing crystals that have once overcome a nucleation barrier to a critical size. The nucleation process has often been explained analogously with so-called nucleation and growth (NG) behavior of the phase separation of a binary mixture in metastable conditions, although the crystallization in one-component polymer is not a real component separation but a phase transition. Among the mechanisms of polymer crystallization, the topic is whether a liquid–liquid transition between states of different densities within one-component polymers takes place before the aforementioned nucleation process. The liquid–liquid transition between states, which is probably driven by chain orientation, is also categorized into NG and the controversial spinodal decomposition (SD) type processes depending on the quenching depth. This article provides the optical microscopic observations that favor the occurrence of the SD-like process when a one-component polymer melt is very rapidly quenched below a stability limit, including a drastic morphological change from a spherulitic to a spinodal pattern at the critical (or spinodal) temperature. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1817–1822, 2004     

Modeling of adsorption and nucleation in infinite cylindrical pores by two-dimensional density functional theory

In this paper, we present an analysis of argon adsorption in cylindrical pores having amorphous silica structure by means of a nonlocal density functional theory (NLDFT). In the modeling, we account for the radial and longitudinal density distributions, which allow us to consider the interface between the liquidlike and vaporlike fluids separated by a hemispherical meniscus in the canonical ensemble. The Helmholtz free energy of the meniscus was determined as a function of pore diameter. The canonical NLDFT simulations show the details of density rearrangement at the vaporlike and liquidlike spinodal points. The limits of stability of the smallest bridge and the smallest bubble were also determined with the canonical NLDFT. The energy of nucleation as a function of the bulk pressure and the pore diameter was determined with the grand canonical NLDFT using an additional external potential field. It was shown that the experimentally observed reversibility of argon adsorption isotherms at its boiling point up to the pore diameter of 4 nm is possible if the potential barrier of 22kT is overcome due to density fluctuations.     

Molecular dynamics analysis of the crystallization of an overcooled aluminum melt

The homogeneous nucleation of a crystal in an overcooled aluminum melt was modeled by the molecular dynamics (MD) method. The MD simulation used the embedded-atom potential. The crystallization delay times were determined from MD simulation data. In a set of systems at the same temperature and pressure, the lifetimes were distributed exponentially. Nucleation frequencies at different temperatures and pressures were determined. The resulting nucleation frequencies were compared with the ones predicted by classical nucleation theory.     

Conditions of nucleation in crystallizable polymers: reconnaissance of positions — a critical evaluation

 In view of the enormous difficulties in obtaining reliable experimental data for the purpose of structure simulation with the aid of computer programs (presently being so popular), every classifying endeavor must be considered of great importance. One of the goals of such an endeavor is the demarcation of characteristic temperature ranges. With the aid of thermodynamic considerations an estimate of the restricted temperature range of metastable undercooling, in which the classical theory of homogeneous nucleation, as developed for polymer solutions, is valid also for polymer melts (“thermal nucleation”) can be given. This consideration includes a discussion of the course of the relevant interface tensions along the co-existence lines of the P–T diagram. The so-called spinodal crystallization mode (see [1–3]) is found at lower temperatures and seems to be quite common in polymer crystallization. In this connection the so-called athermal nucleation can be identified with a specific process. However, the present author is not in favor of the term “spinodal mode”. This is explained by a comparison with the meaning of spinodal decomposition into two phases in the ordinary gas–liquid phase transition, which always occurs at the lower bound of the metastable undercooling. Remarkably, spinodal decomposition cannot be defined in the same way for the liquid–solid transition. Anyway, the author tries hard to induce unorthodox trains of thought in the hope to revive the discussion of a difficult matter, which has almost gone to sleep, before a satisfying settlement has been reached. Received: 3 June 1997 Accepted: 19 August 1997     

Liquid stability in a model for ortho-terphenyl

We report an extensive study of the phase diagram of a simple model for ortho-terphenyl, focusing on the limits of stability of the liquid state. Reported data extend previous studies of the same model to both lower and higher densities and to higher temperatures. We estimate the location of the homogeneous liquid-gas nucleation line and of the spinodal locus. Within the potential energy landscape formalism, we calculate the distributions of depth, number, and shape of the potential energy minima and show that the statistical properties of the landscape are consistent with a Gaussian distribution of minima over a wide range of volumes. We report the volume dependence of the parameters entering in the Gaussian distribution (amplitude, average energy, variance). We finally evaluate the locus where the configurational entropy vanishes, the so-called Kauzmann line, and discuss the relative location of the spinodal and Kauzmann loci.     

Does conventional nucleation occur during phase separation in polymer blends?

The kinetics of liquid–liquid phase separation in off-critical polymer blends was studied with time-resolved small-angle neutron scattering. Our objective was to study the nature of the nuclei that formed during the initial stages of the phase transition. The blends were composed of model polyolefins—deuterium-labeled poly(methyl butylene) (PMB) and poly(ethyl butylene) (PEB)—with molecular weights of about 200 kg/mol. A direct examination of the initial clustering of molecules before macroscopic phase separation was possible because of the large size of the polymer chains and concomitant entanglement effects. We discovered that the scattering profiles obtained during nucleation merged at a well-defined critical scattering vector. We propose that this is the signature of the critical nucleus and that the size of the critical nucleus is inversely proportional to the magnitude of the critical scattering vector. The kinetic studies were preceded by a thorough characterization of the equilibrium thermodynamic properties of our PMB/PEB blends. The locations of the binodal and spinodal curves of our system are consistent with predictions based on the Flory–Huggins theory. This combination of thermodynamic and kinetic experiments enabled the quantification of the dependence of the size and structure of the critical nuclei on the quench depth. Our results do not agree with any of the previous theories on nucleation. Some aspects of our results are addressed in recent theoretical work by Wang in which the effects of fluctuations on the classical binodal and spinodal curves in polymer blends are incorporated. Both theory and experiment support the notion that the traditional stability limit (spinodal) should be replaced by a metastability limit. Although Wang's theory provides an explanation for some of our observations, many fundamental issues regarding nucleation in polymer blends remain unresolved. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1793–1809, 2004     

Interplay between two phase transitions: crystallization and liquid-liquid phase separation in a polyolefin blend

The interplay between liquid-liquid phase separation (LLPS) and crystallization at several compositions in statistical copolymer blends of poly(ethyleneco-hexene) and poly(ethylene-cobutene) has been examined by optical microscopy (OM), atomic force microscopy (AFM), and differential scanning calorimetry (DSC). The phase contrast optical microscopy shows interconnected bicontinuous structures for deeply quenched LLPS, characteristic of spinodal decomposition. After a second quench to a temperature below the melting point, an overwhelming change in crystallization kinetics has been clearly observed, which is caused by the increase of the nucleation rate assisted by concentration fluctuations due to the spontaneous spinodal LLPS. We propose a new mechanism of "fluctuation assisted nucleation" in the crystallization process for such interactive process in a blend system. The experimental results from OM, AFM, and DSC measurements at various conditions are all consistent with the fluctuation assisted nucleation model.     

CaF2熔化温度的分子动力学模拟

The molecular dynamics method has been applied to simulate the melting temperatures of CaF 2 at elevated temperature and high pressure and to calculate the P～V equation of state of CaF 2 up to 100 GPa at 300 K. The interatomic potential was taken to be the sum of pairwise additive Coulomb, van der Waals attractions, and repulsive interactions. In addition, the shell model was used in molecular dynamics simulation. The pressure dependence of the melting temperature of CaF 2 was predicted up to 4 GPa. However, in order to account for the superheating melting of the molecular dynamic simulation, the simulated melting temperatures of CaF 2 were corrected by the modern theory of melting. Consequently, the melting temperatures of CaF 2 were accurately obtained at elevated temperature and high pressure. Therefore, it is shown that shell model molecular dynamics simulation at constant pressure indeed provides a useful tool for studying the melting temperatures of other materials under high pressures.     

Bubble nucleation in micellar solution: a density functional study

We explore the free energetics of bubble nucleation in the micellar solution subjected to a negative pressure using a density functional model of a non-ionic surfactant solution. In this two-component model, the solvent is represented by a single hard-core sphere and the surfactant is represented by two tangent hard-core spheres connected by a rigid bond. The attractive interactions between the particles are modeled by the simple 1/R(6) form. Under all conditions of pressure and interparticle interactions we studied, the free energy barrier of bubble nucleation is found to be lower in the binary surfactant solution than that in a pure solvent and to continue to decrease as the mole fraction of the surfactant in the solution increases. We analyze the free energy surface of the model system under the conditions where both the critical bubble nucleus and the stable micelle exist in equilibrium with the same metastable solution. Our study shows that at moderately low pressures, bubbles can nucleate from the stable micelle and that the resulting free energy barrier of bubble nucleation is expected to be lower than that in the absence of this mechanism. However, as the spinodal is approached at lower pressures, the mechanism of micelle-assisted bubble nucleation becomes less effective. The liquid-liquid miscibility of the model system correlates well with the mechanism of bubble nucleation from the stable micelle.