Homogeneous nucleation in vapor-liquid phase transition of Lennard-Jones fluids: a density functional theory approach

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.     

Gas-vapor bubble nucleation--a unified approach

In a solution which is saturated with gas near the superheat limit, one might expect a bubble formed from both dissolved gas and vapor molecules to appear. The integration of the surface-energy concepts, that are postulated on completely different physical bases for gas and vapor bubble formation is a major issue. In this paper, we reformulate gas and vapor bubble nucleation by a scaling transformation, which turns the surface energy for the bubble formation from both dissolved gases and vapor molecules to the translational energy of a molecule, (3/2)kBT. With this unified approach, one could estimate the dissolved gas effect on the superheat limit of the liquid. The driving force and the molecular volume are important quantities for determining the number of gas and vapor molecules composed of a critical cluster. This approach, of course, can predict pure gas bubble formation, as well as pure vapor bubble formation, as limiting cases. Also, this approach makes it possible to find that the possible occurrence of gas bubble nucleation by dissolved gases prevents measuring the theoretical superheat limit of water at atmospheric pressure, 300 degrees C.     

Free energy landscapes for homogeneous nucleation of ice for a monatomic water model

We simulate the homogeneous nucleation of ice from supercooled liquid water at 220 K in the isobaric-isothermal ensemble using the MW monatomic water potential. Monte Carlo simulations using umbrella sampling are performed in order to determine the nucleation free energy barrier. We find the Gibbs energy profile to be relatively consistent with that predicted by classical nucleation theory; the free energy barrier to nucleation was determined to be ~18 k(B)T and the critical nucleus comprised ~85 ice particles. Growth from the supercooled liquid gives clusters that are predominantly cubic, whilst starting with a pre-formed subcritical nucleus of cubic or hexagonal ice results in the growth of predominantly that phase of ice only.     

Nucleation in hydrophobic cylindrical pores: a lattice model

We consider the nucleation process associated with capillary condensation of a vapor in a hydrophobic cylindrical pore (capillary evaporation). The liquid-vapor transition is described within the framework of a simple lattice model. The phase properties are characterized both at the mean-field level and with Monte Carlo simulations. The nucleation process for the liquid to vapor transition is then specifically considered. Using umbrella sampling techniques, we show that nucleation occurs through the condensation of an asymmetric vapor bubble at the pore surface. Even for highly confined systems, good agreement is found with macroscopic considerations based on classical nucleation theory. The results are discussed in the context of recent experimental work on the extrusion of water in hydrophobic pores.     

Crystal nucleation of colloidal hard dumbbells

Using computer simulations, we investigate the homogeneous crystal nucleation in suspensions of colloidal hard dumbbells. The free energy barriers are determined by Monte Carlo simulations using the umbrella sampling technique. We calculate the nucleation rates for the plastic crystal and the aperiodic crystal phase using the kinetic prefactor as determined from event driven molecular dynamics simulations. We find good agreement with the nucleation rates determined from spontaneous nucleation events observed in event driven molecular dynamics simulations within error bars of one order of magnitude. We study the effect of aspect ratio of the dumbbells on the nucleation of plastic and aperiodic crystal phases, and we also determine the structure of the critical nuclei. Moreover, we find that the nucleation of the aligned close-packed crystal structure is strongly suppressed by a high free energy barrier at low supersaturations and slow dynamics at high supersaturations.     

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.     

Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: a comparison of simulation techniques

Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Sch?tzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.     

Bubble nucleation in polymeric liquids. II. theoretical considerations

A theory based on classical nucleation theory is developed for bubble nucleation in polymer solutions. The theory requires information on solubility, diffusivity, concentration, surface tension, temperature, and degree of supersaturation. The effects of supersaturation and of the presence of large molecules in a liquid mixture on the free energy of bubble formation are included in the theoretical development. A semiempirical equation for the determination of bubble nucleation rate is developed, with the aid of experimental results reported in part I of this series. Using the experimental data, computer simulations of bubble nucleation in polymer solutions are performed. The consumptions of the volatile component in a liquid mixture, due to bubble nucleation and subsequent growth, and the variation of bubble nucleation rate during the expansion process are included in the simulation of the bubble nucleation process.     

Rate of homogeneous crystal nucleation in molten NaCl

We report a numerical simulation of the rate of crystal nucleation of sodium chloride from its melt at moderate supercooling. In this regime nucleation is too slow to be studied with "brute force" molecular-dynamics simulations. The melting temperature of ("Tosi Fumi") NaCl is approximately 1060 K. We studied crystal nucleation at T = 800 and 825 K. We observe that the critical nucleus formed during the nucleation process has the crystal structure of bulk NaCl. Interestingly, the critical nucleus is clearly faceted, the nuclei have a cubical shape. We have computed the crystal-nucleation rate using two completely different approaches, one based on an estimate of the rate of diffusive crossing of the nucleation barrier, the other based on the forward flux sampling and transition interface sampling methods. We find that the two methods yield the same result within an order of magnitude. However, when we compare the extrapolated simulation data with the only available experimental results for NaCl nucleation, we observe a discrepancy of nearly five orders of magnitude. We discuss the possible causes for this discrepancy.     

Ion-induced nucleation in polar one-component fluids

We present a Ginzburg-Landau theory of ion-induced nucleation in a gas phase of polar one-component fluids, where a liquid droplet grows with an ion at its center. By calculating the density profile around an ion, we show that the solvation free energy is larger in gas than in liquid at the same temperature on the coexistence curve. This difference much reduces the nucleation barrier in a metastable gas.     

Volumes of critical bubbles from the nucleation theorem

A corollary of the nucleation theorem due to Kashchiev [Nucleation: Basic Theory with Applications (Butterworth-Heinemann, Oxford, 2000)] allows the volume V(*) of a critical bubble to be determined from nucleation rate measurements. The original derivation was limited to one-component, ideal gas bubbles with a vapor density much smaller than that of the ambient liquid. Here, an exact result is found for multicomponent, nonideal gas bubbles. Provided a weak density inequality holds, this result reduces to Kashchiev's simple form which thus has a much broader range of applicability than originally expected. Limited applications to droplets are also mentioned, and the utility of the p(T,x) form of the nucleation theorem as a sum rule is noted.     

Multicomponent dynamical nucleation theory and sensitivity analysis

Vapor to liquid multicomponent nucleation is a dynamical process governed by a delicate interplay between condensation and evaporation. Since the population of the vapor phase is dominated by monomers at reasonable supersaturations, the formation of clusters is governed by monomer association and dissociation reactions. Although there is no intrinsic barrier in the interaction potential along the minimum energy path for the association process, the formation of a cluster is impeded by a free energy barrier. Dynamical nucleation theory provides a framework in which equilibrium evaporation rate constants can be calculated and the corresponding condensation rate constants determined from detailed balance. The nucleation rate can then be obtained by solving the kinetic equations. The rate constants governing the multistep kinetics of multicomponent nucleation including sensitivity analysis and the potential influence of contaminants will be presented and discussed.     

Phase behavior of self-associating fluids with weaker dispersion interactions between bonded particles

In this study, we explore the global phase behavior of a simple model for self-associating fluids where association reduces the strength of the dispersion interactions between bonded particles. Recent research shows that this type of behavior likely explains the thermodynamic properties of strongly polar fluids and certain micellar solutions. Based on Wertheim's theory of associating liquids [M. S. Wertheim, J. Stat. Phys. 42, 459 (1986); 42, 477 (1986)], our model takes into account the effect that dissimilar particle interactions have on the equilibrium constant for self-association in the system. We find that weaker interactions between bonded molecules tend to favor the dissociation of chains at any temperature and density. This effect stabilizes a monomeric liquid phase at high densities, enriching the global phase behavior of the system. In particular, for systems in which the energy of mixing between bonded and unbonded species is positive, we find a triple point involving a vapor, a dense phase of chain aggregates, and a monomeric liquid. Phase coexistence between the vapor and the monomeric fluid is always more stable at temperatures above the triple point, but a highly associated fluid may exist as a metastable phase under these conditions. The presence of this metastable phase may explain the characteristic nucleation behavior of the liquid phase in strongly dipolar fluids.     

Atomistic simulation of the homogeneous nucleation and of the growth of N2 crystallites

We report on a computer simulation study of the early stages of the crystallization of molecular nitrogen. First, we study how homogeneous nucleation takes place in supercooled liquid N(2) for a moderate degree of supercooling. Using the umbrella sampling technique, we determine the free energy barrier of formation for a critical nucleus of N(2). We show that, in accord with Ostwald's rule of stages, the structure of the critical nucleus is predominantly that of a metastable polymorph (alpha-N(2) for the state point investigated). We then monitor the evolution of several critical nuclei through a series of unbiased molecular dynamics trajectories. The growth of N(2) crystallites is accompanied by a structural evolution toward the stable polymorph beta-N(2). The microscopic mechanism underlying this evolution qualitatively differs from that reported previously. We do not observe any dissolution or reorganization of the alpha-like core of the nucleus. On the contrary, we show that alpha-like and beta-like blocks coexist in postcritical nuclei. We relate the structural evolution to a greater adsorption rate of beta-like molecules on the surface and show that this transition actually starts well within the precritical regime. We also carefully investigate the effect of the system size on the height of the free energy barrier of nucleation and on the structure and size of the critical nucleus.     

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.     

Nucleation in the presence of slow microscopic dynamics

Nucleation of a new thermodynamic phase is often a slow process due to the need to overcome a high free-energy barrier. However, there are other sources of slow dynamics; for example, at high densities/low temperatures, the movement of individual molecules or spins may be slow. Here, we study nucleation in a simple phenomenological model that has this type of slow microscopic dynamics. We do this to better understand how the two sources of slow dynamics interact. We find that as nucleation is intrinsically slow, only very slow microscopic dynamics strongly affect how nucleation occurs. The composition of the nucleus at the top of the nucleation barrier is much less sensitive to slow microscopic dynamics than is the composition of the nucleus once it is postcritical. However, slow dynamics affects not only the rate but also the pathway, which no longer goes over the saddle point in the free energy. We also find that the slow microscopic dynamics can cause sampling problems in an algorithm developed to calculate nucleation rates, and so cause it to predict the rate incorrectly.     

Cluster free energies and nucleation: a density functional approach

Density functional methods of statistical mechanics are applied to calculate the average density profiles and free energies of small (50–500 particles) liquid clusters in unstable or metastable equilibrium with respect to the vapor. The results are compared with those obtained from experiments on homogeneous nucleation of liquids from the vapor.