V. I. Kalikmanov

Argon nucleation: bringing together theory, simulations, and experiment.

We present an overview of the current status of experimental, theoretical, molecular dynamics (MD), and density functional theory (DFT) studies of argon vapor-to-liquid nucleation. Since the experimental temperature-supersaturation domain does not overlap with the corresponding MD and DFT domains, separate comparisons have been made: theory versus experiment and theory versus MD and DFT. Three general theoretical models are discussed: Classical nucleation theory (CNT), mean-field kinetic nucleation theory (MKNT), and extended modified liquid drop model-dynamical nucleation theory (EMLD-DNT). The comparisons are carried out for the area below the MKNT pseudospinodal line. The agreement for the nucleation rate between the nonclassical models and the MD simulations is very good--within 1-2 orders of magnitude--while the CNT deviates from simulations by about 3-5 orders of magnitude. Perfect agreement is demonstrated between DFT results and predictions of MKNT (within one order of magnitude), whereas CNT and EMLD-DNT show approximately the same deviation of about 3-5 orders of magnitude. At the same time the agreement between all theoretical models and experiment remains poor--4-8 orders of magnitude for MKNT, 12-14 orders for EMLD-DNT, and up to 26 orders for CNT. We discuss possible reasons for this discrepancy and the ways to carry out experiment and simulations within the common temperature-supersaturation domain in order to produce a unified picture of argon nucleation.

Classical Nucleation Theory

Nucleation refers to the situation when a system (parent phase) is put into a nonequilibrium metastable state. Experimentally it can be achieved by a number of ways (for definiteness we refer to the vapor-liquid transition): e.g. by isothermally compressing vapor up to a pressure \(p^\mathrm v \) exceeding the saturation vapor pressure at the given temperature \(p_{\mathrm{{sat}}}(T)\).

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.

Role of elasticity forces in thermodynamics of intercalation compounds: Self-consistent mean-field theory and Monte Carlo simulations

We propose a self-consistent mean-field lattice-gas theory of intercalation compounds based on effective interactions between interstitials in the presence of the host atoms. In addition to short-range screened Coulomb repulsions, usually discussed in the lattice gas models, the present theory takes into account long-range effective attractions between intercalants due to elasticity of the host matrix. The mean-field phase diagram in the space of interaction parameters contains the domains of first- and second-order transitions of the order-disorder type, separated by a tricritical line, and the domain of the first-order transition of the gas–liquid-type separated from the homogeneous state by a critical line. Theoretical predictions are shown to be in qualitative agreement with the grand canonical Monte Carlo simulations. The peculiarities of the phase diagram give an insight into different types of behavior of the open circuit voltage observed in rechargeable batteries, in which an intercalation compound is used as an electrode material.

Efficient approach to nucleation and growth dynamics: Stationary diffusion flux model

A new model describing the evolution of clusters in the processes of nucleation and growth is proposed. The diffusion flux in the nonstationary Fokker-Planck equation with an unknown distribution function is approximated by the closed form expression containing the steady-state solution of the Zeldovich-Frenkel equation. This is justified due to the smallness of induction time of cluster formation compared to the time scale observed in experiments. The resulting stationary diffusion flux model is valid for all cluster sizes, computationally efficient and applicable to various types of cluster formation processes. Its application to a nucleation pulse experiment shows an excellent agreement with the solution of the set of formally exact Becker-Doring equations.

Molecular dynamics simulation of nucleation in the binary mixture n-nonane/methane

Vapor-liquid nucleation in the binary system n-nonane/methane is investigated by molecular dynamics simulation. The supersaturation is achieved by cooling down the system during the expansion in order to closely mimic the real process. Binary clusters formed by nucleation are frequently inhomogeneous objects in which components are not well mixed. By studying high-pressure nucleation and cluster growth in the n-nonane/methane mixture, we demonstrate the role of structuring effects in these processes. At typical simulation conditions-pressure 60 bar, temperature 240 K, and nucleation rate ∼10(26) cm(-3)s(-1)-the mole fraction of methane in the critical cluster reaches 80 percent, which is much higher than its equilibrium value in the bulk liquid at the same pressure and temperature. These observations are supported by the recently formulated coarse-grained theory for binary nucleation as well as by the experimental observations.

Multi-Component Nucleation

Understanding multi-component nucleation is of great importance for atmospheric and environmental sciences. Vivid examples are: polar stratospheric clouds, acid rains and air pollution. All these phenomena occur because Earth’s atmosphere is a multi-component gaseous system in which nucleation leads to formation of droplets of complex composition. A rich field of applications of multi-component nucleation is associated with the natural gas industry since nucleation is the primary mechanism responsible for formation of mist during the expansion of natural gas [1]. This is the key process of the non-equilibrium gas-liquid separation technology[2].

Some Thermodynamic Aspects of Two-Phase Systems

In this chapter we briefly recall the basic features of equilibrium thermodynamics of a two-phase system, i.e. a system consisting of two coexisting bulk phases, which will serve as ingredients for the nucleation models discussed in this book.

Binary Nucleation: Density Functional Theory

Classical theory of binary nucleation can be drastically in error and even lead to unphysical behavior when applied to strongly non-ideal systems with substantial surface enrichment—a vivid example is the water/alcohol system, for which BCNT predicts the decrease of nucleation rate with increasing partial pressures.

Density Functional Theory

Classical phenomenological description of nucleation is based on the capillarity approximation treating all droplets (clusters) as if they were macroscopic objects characterized by a well defined rigid boundary of radius \(R\) with a bulk liquid density inside \(R\) and bulk vapor density outside \(R\). Moreover, the surface free energy of the cluster is the same as for the planar interface at the same temperature, and therefore is characterized by the planar surface tension.