The accuracy of the approximations in classical nucleation theory

The mathematical approximations involved in the theory of homogeneous nucleation are shown to produce negligible error in the predicted rates of nucleation.     

A monte carlo method for approximating critical cluster size in the nucleation of model systems

A formalism is presented for estimating critical cluster size as defined in classical models for nucleation phenomena. The method combines Bennett's Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism. A simple form for the free energy of formation of then cluster [including a termA (n)n ^2/3] is used to predict critical cluster size and critical supersaturation ratio, S^*. This approach is applied to Lennard-Jones vapor clusters at 60 K. Results for free-energy differences for the 13, 18, 24, and 43 clusters predict a critical cluster size of 70 ± 5 atoms at a critical supersaturation ratio given bylnS ^*=2,45 0.15. This method is intended to provide estimates of critical cluster size for more ambitious attempts to calculate cluster free energies or for initializing conditions in microscopic simulations of nucleating systems.This material is based upon work supported by the National Science Foundation under Grant No. ATM80 15790 and the National Aeronautics and Space Administration under Grant No. NAS8-31150.     

The translation-rotation paradox in the nucleation theory

The factor of 10¹⁷ proposed by Lothe and Pound in the theory of nucleation of droplets from the vapor phase is studied using classical statistical mechanics. The controversial factor is derived from partition functions for an isolatedn-mer and for ann-molecular cluster imbedded in the bulk liquid phase. The rotational degrees of freedom have no place in, in agreement with Reiss, Katz, and Cohen's treatment. It is proved that the surface free energy of a cluster is proportional to the surface area. The estimate of what Lothe and Pound called the replacement term is different from those of previous authors. It is concluded that is written as a ratio = _g/_l, where _g and _l , are the volumes per molecule in the gas phase and in the liquid phase, respectively. For water at 300K, is approximately equal to 10₄.     

The thermodynamics of cluster formation in nucleation theory

We have derived a precise thermodynamic definition of the standard free energy to form a cluster which is used in nucleation theory. The results [Eq. (9)] have a form differing slightly from the form usually used in nucleation theory and show that the Lothe-Pound correction factor is based on a misconception concerning the standard states involved.     

Adsorption and nucleation on smooth surfaces

The nucleation and growth of condensate nuclei on smooth surfaces, e.g., an immiscible liquid or a smooth solid, can occur both by the direct addition of molecules from the vapor and from those adsorbed on the substrate. We show how to generalize nucleation theory to allow for the simultaneous occurrence of both mechanisms. The vapor-condensate-substrate interfacial forces, the contact angle, the critical supersaturation, and the coefficient in the adsorption isotherm are different ways of expressing the affinity between vapor molecules and the substrate surface. The critical supersaturations for nucleation on the surface of an immiscible liquid and nucleation on the surface of a perfectly smooth solid are predicted in terms of these parameters and the relationships among them. For most values of these parameters we find that adsorbed molecules are usually far more important to the nucleation process than those in the vapor phase.     

A nucleation theory of cell surface capping

We propose a new theory of cell surface capping based on the principles of nucleation. When antibody interacts with cell surface molecules, the molecules initially form small aggregates called patches that later coalesce into a large aggregate called a cap. While a cap can form by patches being pulled together by action of the cell's cytoskeleton, in the case of some molecules, disruption of the cytoskeleton does not prevent cap formation. Diffusion of large aggregates on a cell surface is slow, and thus we propose that a cap can form solely through the diffusion of small aggregates containing just one or a few cell surface molecules. Here we consider the extreme case in which single molecules are mobile, but aggregates of all larger sizes are immobile. We show that a set of patches in equilibrium with a sea of free cell surface molecules can undergo a nucleation-type phase transition in which the largest patch will bind free cell surface molecules, deplete the concentration of such molecules in the sea, and thus cause the other patches to shrink in size. We therefore show that a cap can form without patches having to move, collide with each other, and aggregate.     

On a reconsideration of classical nucleation theory

A correct account of the collective motion of a cluster does not require the Lothe-Pound correction; furthermore, this correction is shown to contradict the laws of thermodynamics.     

On the dependence of the condensation coefficient on surface curvature

It is concluded that there is as yet no adequate theoretical solution for the size dependence of the condensation coefficient, the Okuyama-Zung approach to this problem being discounted.     

Treatment of droplike clusters by means of the classical phase integral in nucleation theory

The translation inconsistency in the theory of nucleation is discussed in historical perspective. A theory is then developed, beginning with the classical phase integral, which not only allows all approximations to be well defined, but also leads to the most natural droplike model for the cluster. The theory makes it possible to apply, in a consistent manner, the thermodynamics of curved surfaces or, alternatively, moleculardynamic numerical computation schemes to the evaluation of the partition function of the cluster. If the cluster is treated as a macroscopic drop (having the free energy of a macroscopic drop), the result for the distribution of clusters differs in only a minor way from that prescribed by the conventional theory of nucleation. It is concluded that for liquid nuclei the conventional theory is consistent, but that a replacement factor may be necessary for solid nuclei. In general, however, the major problems confronting the theory involve the precise evaluation of the work of cluster formation.     

Treatment of droplike clusters in nucleation theory using Reiss's method

The expression of the correction factor in nucleation theory is derived by extending the method Reiss used recently. is the factor appearing in the number of critical nuclei (formed as a vapor condenses into liquid drops) as a correction to the conventional theory. It is shown that=p _l / _g /kT, wherep _l is the pressure of the liquid phase inside the drop, _g , is the volume per molecule in the vapor phase,k is the Boltzmann constant, andT is the absolute temperature. The difference between this and Reiss's expression isp _l , which replaces hisp _g (the vapor pressure in equilibrium with the drop). The derived in this paper is compatible with the expression= _g / _l ( _l is the molecular volume in the liquid phase) previously proposed by the present author.     

Determination of the colloidal crystal nucleation rate density

Colloidal suspensions of charged latex microspheres in water exhibit liquid-like or crystalline ordering depending on particle interaction and concentration. By virtue of large particle spacing and slow dynamics, colloidal systems offer a unique opportunity to study interfacial structure and dynamics. This paper presents the first reported experimental study of the nucleation rate density, c, of an nonequilibrium (supercooled) colloidal liquid to colloidal crystal first order phase transition. Local and global observations of colloidal crystals growing from a metastable colloidal liquid were used to determine c. Microscopic local observations revealed homogeneous nucleation and constant interface velocity growth of quasispherical crystallites in the bulk and heterogeneous nucleation of a crystalline sheet with lower growth velocity at the cell wall. Complementary global observations of the recrystallization transition made by measuring the time dependence of the suspension transparency (the fraction of transmitted laser light) determined c by fitting this curve to a model based on an extension of Avrami's theory of crystallization.     

Modelling nucleation from solution with the string method in the osmotic ensemble

ABSTRACT

Direct molecular simulation of nucleation from solution is a challenging task, requiring a combination of ‘rare events’ techniques and methods to control the chemical potential. Rare event methods usually keep the total number of molecules fixed, resulting in artificial free energy profiles due to the depletion of solute from the solution phase. In order to address this issue, we present a new approach that uses the string method in collective variables in the osmotic ensemble to obtain minimum free energy pathways for nucleation at constant supersaturation. Our method does not require using an explicit reservoir of solute molecules, or making additional assumptions about the activity coefficients in the solution. We apply the new method to the crystallisation of sulfamerazine from acetonitrile and methanol solutions, and compare the resulting potential of mean force profiles to those obtained using analytical corrections previously employed in the literature.     

Characteristics of acoustic emissions during nucleation of superheated droplets

Superheated droplet nucleation and subsequent bubble oscillation produces an acoustic pressure pulse that contains valuable information about the nucleation process. Spectral analysis of the pressure pulse indicates excitation of different modes of bubble oscillations in the nucleation process. In the present study it is observed that gamma induced droplet nucleation excites higher modal oscillations and also emits higher intensity acoustic emission compared to that of spontaneous nucleations.     

The kinetics of homogeneous nucleation of silver nanoparticles stabilized by polymers

The formation of Ag nanoparticles synthesized by homogeneous nucleation, stabilized by polymers (PVA and PVP) was monitored by UV–Vis spectrophotometry and transmission electron microscopy. Our aim was to differentiate between the two main phases of particle formation, i.e. nucleation and growth and to characterize their rates with the help of appropriate kinetic equations. Time resolved spectrophotometric measurements revealed that particle formation is an autocatalytic process: a slow, continuous nucleation phase (3–5 min) is followed by a rapid, autocatalytic growth phase where the maximal particle size is 5–7 nm. By freezing the reaction mixture, the process of particle growth can be followed from 5 to 40 min on TEM pictures. The first order rate constants were calculated and they are strongly depend on the polymer concentration. If the growing particles are attached by PEI to the surface of a solid support, the formation of silver nanoparticles can also be followed by atomic force microscopy (AFM) and we can control the particle growth on mica surface. The cross section analysis of the pictures show, that the particle growing process can be also monitored at solid–liquid interface.     

State-dependent diffusion coefficients and free energies for nucleation processes from Bayesian trajectory analysis

ABSTRACT

The rate of nucleation processes such as the freezing of a supercooled liquid or the condensation of supersaturated vapour is mainly determined by the height of the nucleation barrier and the diffusion coefficient for the motion across it. Here, we use a Bayesian inference algorithm for Markovian dynamics to extract simultaneously the free energy profile and the diffusion coefficient in the nucleation barrier region from short molecular dynamics trajectories. The specific example we study is the nucleation of vapour bubbles in liquid water under strongly negative pressures, for which we use the volume of the largest bubble as a reaction coordinate. Particular attention is paid to the effects of discretisation, the implementation of appropriate boundary conditions and the optimal selection of parameters. We find that the diffusivity is a linear function of the bubble volume over wide ranges of volumes and pressures, and is mainly determined by the viscosity of the liquid, as expected from the Rayleigh–Plesset theory for macroscopic bubble dynamics. The method is generally applicable to nucleation processes and yields important quantities for the estimation of nucleation rates in classical nucleation theory.     

The nonlinear Cahn-Hilliard equation: Transition from spinodal decomposition to nucleation behavior

The behavior of the nonlinear Cahn-Hilliard equation for asymmetric systems,c _t =²(±c+Bc ²+c ³-² c) within the unstable subspinodal region is explored. Energy considerations and amplitude equation methods are employed. Evidence is given for a transition from periodically structuredspinodal behavior to nucleation behavior somewhere within the traditional spinodal. A mechanism for describing a time-dependent lengthening of the dominant wavelength is explored.     

Dimple‐assisted dewetting: heterogeneous nucleation in undercooled wetting films

Undercooled wetting films near a first‐order wetting transition exhibit an unusually long lifetime: the thermal nucleation barrier for formation of a critical hole in a film of thickness F diverges according to Γ ∼ exp (ℰ_c/k_BT) where the excess free energy ℰ_c ∼ F^ζ with ζ ≥ 2. Localized perturbations of the liquid‐vapor interface (‘dimples’) are shown to be a useful tool in reducing Γ in a controlled way: they act as heterogeneous nucleation centers for thermal critical nuclei. For ⁴He wetting films on weak‐binding alkali substrates (Cs, Rb) dimples can be generated either by vortices in a superfluid film or by surface electrons. The theory of the heterogeneous nucleation process initiated by the presence of surface dimples (‘dimple‐assisted dewetting’) is developed, accompanied by quantitative predictions for experiment.     

The role of collision cascades and helium atoms in cavity nucleation

Abstract

The simultaneous production of helium atoms and collision cascades during irradiation may enhance the nucleation of cavities. The influence of parameters such as helium generation rate and recoil energy on the possibility of cavity nucleation is investigated. The three most likely mechanisms by which cascade nucleation might occur are considered. Firstly, helium atoms that are present within the cascade may succeed in preventing the collapse of cascades into dislocation loops. Secondly, helium atoms in the cascades may be swept together during the cooling of the cascade to form cavity embryos. Thirdly, more distant helium atoms may be able to reach an uncollapsed vacancy aggregate in a cascade by diffusion before thermal annealing of the cascade.

Calculations indicate that it is unlikely that a sufficient number of helium atoms would be present in a cascade to prevent its collapse. The probability of several helium atoms being swept together within the volume of a cascade is also found to be rather small. Calculations suggest, however, that the cavity nucleation in cascades might become significant if helium atoms were to diffuse much faster than the substitutional diffusion rate during irradiation. The selfinterstitial replacement mechanism, for instance, would yield such a fast diffusion rate of helium.     

On the nucleation of hadronic domains in the quark-hadron transition

We present numerical results on bubble profiles, nucleation rates and time evolution for a weakly first-order quark-hadron phase transition in different expansion scenarios. We confirm the standard picture of a cosmological first-order phase transition, in which the phase transition is entirely dominated by nucleation. We also show that, even for expansion rates much lower than those expected in heavy-ion collisions nucleation is very unlikely, indicating that the main phase conversion mechanism is spinodal decomposition.     

Growth rate of critical nuclei near the critical point of a fluid

The growth rate of critical nuclei for a fluid near its critical point is discussed on the basis of the stochastic equation for the probability distribution function of the local order parameter, which was derived previously by the author. The growth rate was found to depend on , the range of correlation of the order parameter fluctuation, andR, the radius of critical nuclei, as ⁰ R ^–3, in conformity with dynamical scaling. The rate of nucleation at the liquid-gas transition near the critical point is also discussed on the basis of this result.