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.     

Investigation of vapour--liquid nucleation properties for spherical and chain-like fluids by density functional theory

The excess Helmholtz free energy functional for nonpolar chain-like molecules is formulated in terms of a weighted density approximation （WDA） for short-range interactions and a Weaks Chandler Andersen （WCA） approximation and a Barker Henderson （BH） theory for long-range attraction. Within the framework of density functional theory （DFT）, vapour liquid interracial properties including density profile and surface tension, and vapour-liquid nucleation properties including density profile, work of formation and number of particles are investigated for spherical and chain- like molecules. The obtained vapour liquid surface tension and the number of particles in critical nucleus for Lennard- Jones （L J） fluids are consistent with the simulation results. The influences of supersaturation, temperature and chain length on vapour liquid nucleation properties are discussed.[第一段]     

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 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.     

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.     

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.     

Generalized surface thermodynamics with application to nucleation

Gibbs formulated a complete and general thermodynamics for surfaces in multicomponent fluid systems. When considering solid–fluid surfaces, he restricted attention to single-component solids in contact with fluids that could contain multiple components. Attempts that have been offered to generalize Gibbs’ results for surfaces between multicomponent solids and fluid are problematic owing to the difficulty that the surface chemical potentials for components that also reside on substitutional lattice sites in the solids are not well defined. Therefore any expressions involving these surface chemical potentials, such as the conventional definition of the surface energy, will also not be well defined. In order to formulate a general thermodynamics of equilibrium that takes into account capillary effects in systems containing surfaces between a multicomponent solids and fluids, it is shown that the concept of thermodynamic availability (exergy) can be employed that, when applied to surfaces, depends on the extensive but not the intensive variables (such as the chemical potentials) of the surfaces. Using this approach, Gibbs–Thomson–Freundlich effects for finite-size solids, an adsorption equation for solid–fluid surfaces and the thermodynamics of nucleation during solidification can be treated in a straightforward manner without referring to the ill-defined surface chemical potentials. A derivation is given that appears to be the first one that properly generalizes Gibbs’ analysis for the reversible work to form a critical nucleus to the case of solidification.     

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.     

调幅分解及形核对相分离作用机理研究

以SCN-30wt%H₂O, SCN-50 wt%H₂O和SCN-80 wt%H₂O三组透明体系, 在恒温场下实现了形核和调幅分解两种过程; 在此基础上, 施加温度梯度, 研究了第二相液滴的迁移运动规律. 结果表明, 相分离在临界成分体系以调幅分解方式进行, 在另外两种体系中以形核长大方式进行; 调幅分解与形核过程相比, 反应进行得更快, 液滴长大到同一尺寸所需时间仅为形核所需时间的1/3—1/2. 且临界成分体系有更大的不混溶间隙, 所以第二相液滴具有更多迁移时间, 揭示了偏晶体系相分离过程中在临界成分处易获得壳-核组织的内在机理. 在单向温度场中, 测量了不同半径的液滴迁移速率, 并且与理论Marangoni迁移速率值作比较, 发现液滴迁移速率和Marangoni理论迁移速率符合较好. 说明了在较好地抑制自然对流条件下Marangoni迁移对于相分离过程起主要作用.     

掺金玻璃在电场热处理中的形核过程

利用电场热处理工艺,成功制备出含纳米尺寸金颗粒掺杂的硼硅酸盐玻璃，采用x射线衍射、扫描电子显微镜和吸收光谱分析了在不同工艺条件下制备得到的玻璃样品的相成分、微观形貌和光学性能.然后在理论上分析了外电场对掺杂玻璃热处理过程的影响，提出了适合掺金玻璃的电场热处理热力学模型.模型中的关键因素是电场能量变化量，对此采用两种方法计算，一种是在一定简化后的理论计算；另一种是利用计算机有限元方法计算.两种方法的结果比较相近，并且都能解释前面的实验现象. 关键词： 掺金玻璃 形核 电场     

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.     

氘氚冰籽晶的形核行为

为了实现激光约束核聚变(ICF)的自持聚变目标,对靶壳内氘氚冰的质量提出了极其苛刻的要求,冰层内表面和靶壳的同心度要求大于99.9%,冰层内表面均方根粗糙度(RMS)优于1μm.高质量的冷冻氘氚靶建立在靶壳内高质量氘氚冰层的前提之上.单晶是冰层的最好形态,在靶壳内获得氘氚冰籽晶是基础条件.本文通过采用逐渐降低升温速率的台阶控温方法,开展了充气微管内保留籽晶的研究,揭示了充气微管内保留籽晶的形核机理,实验结果表明,利用充气管口可保留稳定、单一的籽晶,在相同的过冷度下,当氘氚籽晶c轴方向与充气管轴向平行时,生长速度较c轴垂直于充气管轴向时的速度慢约1—2个量级,为获得高质量的籽晶从而形成高质量的氘氚冰提供了参考和支撑.     

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.