Kinetic Nucleation Model Research Articles

Development of a Kinetic Nucleation Modelfor a Free-Expanding Argon Condensation Flow

Using classical nucleation theory (CNT), a homogeneous condensation model has been developed in previous work to simulate condensation in a free-expanding plume using the direct simulation Monte Carlo (DSMC) method. However, the accuracy of the CNT nucleation theory is questionable due to unphysical assumptions such as the use of macroscopic cluster surface tension for small clusters and the lack of an incubation time for nucleation. Molecular dynamics (MD) simulations performed in previous work confirm that the fundamental mechanism for the initiation of condensation is through dimer formation in two-stage ternary collisions of monomers. We propose a kinetic nucleation model based on the mechanism whereby stable dimers are created from triple collisions. The new hybrid MD-DSMC kinetic nucleation model is implemented in a DSMC simulation of cluster growth processes, starting from dimers, in a condensation plume

Igneous microstructures from kinetic models of crystallization

During crystallization, a variety of competing kinetic processes determine the evolution of the igneous microstructure, yet, the relative contribution of each process remains elusive. To this end, a stochastic algorithm is developed to yield a detailed spatial representation of the igneous microstructure during progressive crystallization. This algorithm is used to test a variety of kinetic models for nucleation and crystal growth that yield realistic igneous microstructures. The algorithm itself relies on a theoretical model of crystallization (the Avrami method) and can therefore be internally validated in addition to being verified against natural microstructures using crystal size distributions (CSDs). The most realistic simulated igneous microstructure, in which the CSDs remain approximately log-linear throughout the crystallization interval, is produced using a kinetic model involving exponential nucleation rate and constant growth rate. An extension of the algorithm is used to simulate multiply saturated mineral growth, emulating basalt crystallization through simultaneous nucleation and growth of plagioclase and clinopyroxene. A fundamentally important feature of this procedure is the numerical production of detailed 3D representations of the microstructure that can be interrogated to study many physical and chemical processes. For example, the critical crystallinity necessary for the onset of a finite yield strength and the interstitial melt flow within the igneous microstructure depend on the percolation of the solid and melt phases, respectively. Bounds on the percolation thresholds, the critical crystallinity at which the phase of interest is connected or contiguous such that it extends across the full microstructure from one face to the opposite face, are determined for the simulated igneous microstructure and are comparable with previously published results for the percolation threshold of both the melt phase and solid network. The simulated igneous microstructure can also be used as input into other physical models to ascertain the physical properties of partially molten magmas that are otherwise difficult to estimate by experiment. In a real sense, these computed microstructures are equivalent to 3D microtomographic images of partially molten basalt within a solidification front.

Kinetic model for binary homogeneous nucleation in the H2O–H2SO4 system: Comparison with experiments and classical theory of nucleation

A kinetic model to predict nucleation rates in the sulfuric acid-water system is presented. It allows calculating steady-state nucleation rates and the corresponding time lag, using a direct solution of a system of kinetic equations that describe the populations of sub- and near-critical clusters. This kinetic model takes into account cluster-cluster collisions and decay of clusters into smaller clusters. The model results are compared with some predictions obtained with the classical nucleation theory (CNT) and also with available measurement data obtained in smog chambers or flow tubes. It is shown that in the case of slow nucleation processes, the kinetic model and the CNT as used by Shugard et al. [J. Chem. Phys. 75, 5298 (1974)] give the same results. However, in the case of intensive nucleation, a large part of the nucleation flux is due to cluster-cluster collisions and the CNT underestimates the nucleation rates.

A kinetic model of diamond nucleation and silicon carbide interlayer formation during chemical vapor deposition

The presence of thin silicon carbide intermediate layers on silicon substrates during nucleation and the early stages of diamond deposition have been frequently reported. It is generally accepted that the intermediate layer is formed by the bulk diffusion of carbon atoms into the silicon carbide layer and the morphology and orientation of the diamond film subsequently grown on the intermediate layer are strongly affected by that layer. While there have been considerable attempts to explain the mechanism for intermediate layer formation, limited quantitative data are available for the layer formation under the operating conditions conducive to diamond nucleation. This study employs a kinetic model to predict the time evolution of a β-SiC intermediate layer under the operating conditions typical of diamond nucleation in hot filament chemical vapor deposition reactors. The evolution of the layer is calculated by accounting for gas-phase and surface reactions, surface and bulk diffusions, the mechanism for intermediate layer formation, and heterogeneous diamond nucleation kinetics and of its dependence on the operating conditions such as substrate temperature and inlet gas composition. A comparison between the time scales for intermediate layer growth and diamond nuclei growth is also performed. Discrepancies in published adsorption energies of gaseous hydrocarbon precursors on the intermediate layer—ranging from 1.43 to 4.61 eV—are examined to determine the most reasonable value of the adsorption energy consistent with observed saturated thicknesses, 1–10 nm, of the intermediate layer reported in the literature. The operating conditions that lead to intermediate layer growth followed by diamond deposition vs. those that yield heteroepitaxial diamond nucleation without intermediate layer formation are discerned quantitatively. The calculations show that higher adsorption energies, 3.45 and 4.61 eV, lead to larger surface number densities of carbon atoms, lower saturated nucleation densities, and larger intermediate layer thicknesses. The observed saturated thicknesses of the intermediate layer may be reproduced if the true adsorption energy is in the range of 3.7–4.5 eV. The intermediate layer thickness increases by increasing substrate temperature and inlet hydrocarbon concentration and the dependence of the thickness on substrate temperature is especially significant. Heteroepitaxial diamond nucleation without intermediate layer formation reported in experimental results can be readily explained by the significant decrease of the intermediate layer thickness at lower substrate temperatures and at higher diamond nucleation densities. Further, the present model results indicate that the intermediate layer thickness becomes saturated when growing diamond nuclei cover a very small surface area of that layer.

Quasi-unary homogeneous nucleation of H2SO4-H2O

We show that the binary homogeneous nucleation (BHN) of H2SO4-H2O can be treated as quasi-unary nucleation of H2SO4 in equilibrium with H2O vapor. A scheme to calculate the evaporation coefficient of H2SO4 molecules from H2SO4-H2O clusters is presented and a kinetic model to simulate the quasi-unary nucleation of H2SO4-H2O is developed. In the kinetic model, the growth and evaporation of sulfuric acid clusters of various sizes are explicitly simulated. The kinetic quasi-unary nucleation model does not have two well-recognized problems associated with the classical BHN theory (violation of the mass action law and mismatch of the cluster distribution for monomers) and is appropriate for the situations where the assumption of equilibrium cluster distribution is invalid. The nucleation rates predicted with our quasi-unary kinetic model are consistent with recent experimental nucleation experiments in all the cases studied, while the most recent version of the classical BHN model systematically overpredicts the nucleation rates. The hydration of sulfuric acid clusters, which is not considered in the classical model but is accounted for implicitly in our kinetic quasi-unary model, is likely to be one of physical mechanisms that lead to lower nucleation rates. Further investigation is needed to understand exactly what cause the difference between the kinetic quasi-unary model and the classical BHN model.

Aerosol dynamics modeling of silicon nanoparticle formation during silane pyrolysis: a comparison of three solution methods

A numerical model has been developed to predict gas-phase nucleation, growth, and coagulation of silicon nanoparticles formed during thermal decomposition of silane. A detailed chemical kinetic model of particle nucleation was coupled to an aerosol dynamics model that includes particle growth by surface reactions, coagulation with instantaneous coalescence, and convective transport. Solution of the aerosol general dynamic equation was handled by three approaches: (1) the efficient and reasonably accurate method of moments; (2) the quadrature method of moments, which requires no prior assumption of the shape of the particle size distribution; and (3) a computationally more expensive sectional method (SM). The SM includes a conceptually simple and computationally efficient algorithm for treating coagulation that is found to be superior to widely used methods from the literature. All three approaches gave similar results for the evolution of the first few moments of the particle size distribution. The SM was able to capture the bimodal distribution that appears briefly at short residence times due to simultaneous nucleation and coagulation. At longer residence time, only coagulation remains important and both the sectional and moment methods give very similar results as they approach the self-preserving size distribution.

Pore formation by 6-ketocholestanol in phospholipid monolayers and its interpretation by a general nucleation-and-growth model accounting for the sigmoidal shape of voltage-clamp curves of ion channels.

6-Ketocholestanol (KC), a steroid that differs from cholesterol mainly by the presence of a carbonyl group, forms pores inside a dioleoylphosphatidylcholine monolayer self-assembled on mercury by a mechanism similar to that of channel-forming peptides and proteins. The potential steps responsible for pore formation by KC molecules give rise to potentiostatic charge vs time curves whose sigmoidal shape and potential dependence can be quantitatively interpreted on the basis of a mechanism of nucleation and growth of KC clusters. Pore formation by KC allows the penetration of thallous ions across the otherwise impermeable phosphatidylcholine monolayer, while pore disruption taking place at more negative potentials causes a drop in thallous ion permeation. Pore disruption is also accounted for by a mechanism of nucleation and growth of holes inside the KC clusters. The kinetic model of nucleation and growth is general, and accounts quantitatively for the sigmoidal shape and potential dependence of the classical Hodgkin-Huxley voltage-clamp curves of potassium channels in squid giant axon,(1) using a minimum number of free parameters.

Synthetic polycrystalline aragonite to calcite transformation kinetics: experiments at pressures close to the equilibrium boundary

¶This study experimentally investigated the transformation kinetics of synthetic polycrystalline aragonite to calcite at four temperature/pressure conditions (330 °C/200 MPa, 380 °C/325 MPa, 430 °C/580 MPa, and 480 °C/875 MPa), close to the calcite-aragonite equilibrium phase boundary. The extents of transformation measured as a function of time in a synthetic system, using in-situ annealed, high purity samples, are consistent with the kinetic model for grain-boundary nucleation and interface-controlled growth. The growth rates are slightly lower than those previously determined for a natural polycrystalline sample at 330 and 380 °C. The activation energy (158 kJ/mol) for calcite growth from synthetic samples is lower than that (247 kJ/mol) from natural samples, but is close to the previously reported value (163 kJ/mol) from a single crystal aragonite. The extrapolation of our experimental data to natural conditions reveals unusually fast transformation rates, in contrast to those of natural samples. The presence of deformational strain, fractures, defects or impurities in natural samples, and other factors may account for the discrepancy. This study suggests that the retrograde metamorphism of aragonite to calcite may proceed in a wide range of rates also depending on other geological factors than temperature and pressure.

Dynamical benchmarks of the nucleation kinetics of water

Recently a theory of vapor-to-liquid phase nucleation was developed based on the kinetics of cluster formation and decomposition. The new method used variational transition state theory (VTST) to obtain the evaporation and condensation rate constants needed in the kinetic model of nucleation. VTST provides a means to systematically improve estimates of rate constants involved in the nucleation process. In the current work, we perform dynamical simulations of the condensation process, estimating the effective reactive cross section using a definition of a cluster that is determined from VTST. These calculations allow us to characterize dynamical corrections to the VTST rate constants. We find that for water cluster sizes ranging from 10–40 waters, VTST estimates of the condensation and evaporation rate constants using a spherical dividing surface require dynamical corrections that are approximately a factor of two.

NEW UNDERSTANDINGS FOR TWO-DIMENSIONAL NUCLEATION (II)

Foreign particles adsorbed on flat crystal surfaces can serve as two-dimensional nucleation centers for the growth. In this paper, a kinetic model for heterogeneous two-dimensional nucleation is presented. The free energy barrier of two-dimensional nucleation in the presence of foreign particles and the kinetics for the nucleation and growth are examined theoretically. It follows that the contact angle, size and density of adsorbed foreign particles play a crucial role in controlling the 2D nucleation barrier and growth kinetics. The theory can be successfully applied to interpret experiments of dislocation-free growth.

Modeling of nucleation kinetics of ternary nitrides from vapour phase

Nucleation kinetics of ternary nitride layers on GaN substrate has been analysed using classical heterogeneous nucleation theory, incorporating the stress induced supercooling due to lattice mismatch between the substrate and grown layers. Using regular solution model the interfacial tension between the nucleus and substrate and hence interfacial tension between the substrate and mother phase of the compounds have been calculated. The amount of driving force available for the nucleation has been determined for different composition and the degree of supercooling. These values have been used to evaluate the nucleation parameters. It is shown that the nucleation barrier for the formation of ternary nucleus (AlGaN, InGaN and AlInN) on GaN substrate depends strongly on the composition of the alloy.

Thermodynamics and Kinetics of the Early Steps of Solid-State Nucleation in the Fluid Lipid Bilayer

Temperature-scanning (10−70 °C) calorimetric, densitometric, and acoustic measurements have been performed in aqueous dispersions of dipalmitoylphosphatidylcholine multilamellar vesicles. In the biologically relevant liquid-crystalline state close to the chain freezing point (within 42−50 °C, in our case), the measured quantities display anomalous deviations from the “ideal” shape of their temperature dependence curves. The deviations indicate the early steps of gel-state nucleation within the stable liquid-crystalline state (Frenkel's heterophase fluctuations). An earlier proposed kinetic model of nucleation (Kharakoz et al. J. Phys. Chem. 1993, 97, 9844−9851) has been refined to achieve more clear physical substantiation. When the deviations are analyzed through the refined model, both the thermodynamic and kinetic characteristics of nucleation are determined. The fluid−solid interface line tension energy is about 0.7 kT per boundary lipid molecule. The tension is strong enough for the phase transition to be first-order and, at the same time, weak enough to allow extensive heterophase fluctuations. The speed of new-phase-front propagation near the transition temperature is virtually proportional to the difference between the current temperature and transition temperature, the proportionality coefficient being 0.2 cm s-1 K-1 (estimated from ultrasonic relaxation data). The experimental data and the nucleation model are consistent with literature data on the anomalous “critical-like” behavior of lipid membranes near the main transition (bending rigidity drop, anomalous swelling, slowing relaxation processes, etc.). Thus, we show that most of the anomalies can be rationalized in terms of the weak first-order transition mechanism without a hypothesis on the proximity of bilayer to a critical state.

Kinetic model for nucleation in partitioning systems

The classical theory of nucleation is an interface-limited theory and cannot properly describe nucleation process when the concentrations of the initial and final phases are different. A new model for time-dependent homogeneous nucleation that takes account of the coupled fluxes of interfacial attachment and long-range diffusion is presented. Numerical solutions from this new model show that the time-dependent nucleation rates scale with the smaller mobility and that the steady-state rates, I s, and induction times, θ, frequently differ significantly from values predicted by the classical theory. Simple approximate analytical expressions for I s and θ are presented. The concentration of the region of the parent phase near sub-critical crystal clusters is shifted toward that of the new phase. This shift may explain the nanometer-sized microstructures frequently obtained on the devitrification of bulk and Al-rare-earth-transition metal glasses.

Kinetic model for diamond nucleation upon chemical vapor deposition

A kinetic model for diamond nucleation on an Si substrate upon chemical vapor deposition has been proposed, based on a surface reaction mechanism. Considering the atomic hydrogen etching effects on the Si substrate and the stable atomic cluster with diamond structure, a growth rate equation describing diamond nucleation was constructed, and from the time-dependent solutions of this equation, an important nucleation behavior was found that the atom amount, which the stable atomic cluster with diamond structure contains, exists the maximum value in the deposition process of the cluster. Accordingly, this means that the nucleation formation of diamond films could occur if the maximum value of the atom amount of the stable cluster with diamond structure arrive at the amount required by the diamond critical nucleus upon chemical vapor deposition. On the other hand, diamonds may not be nucleated permanently in the deposition process if the maximum value of the atom amount of the stable clusters do not reach the amount required by the diamond critical nucleus at the initial stage in the deposition. These theoretic results reasonably explained the relevant experimental observations of diamond nucleation on Si substrates and revealed some important kinetic mechanisms of diamond nucleation upon chemical vapor deposition.

Phase transformation of nanocrystalline anatase-to-rutile via combined interface and surface nucleation

The kinetics of phase transformation of nanocrystalline anatase samples was studied using x-ray diffraction at temperatures ranging from 600 to 1150 °C. Kinetic data were analyzed with an interface nucleation model and a newly proposed kinetic model for combined interface and surface nucleation. Results revealed that the activation energy of nucleation is size dependent. In anatase samples with denser particle packing, rutile nucleates primarily at interfaces between contacting anatase particles. In anatase samples with less dense particle packing, rutile nucleates at both interfaces and free surfaces of anatase particles. The predominant nucleation mode may change from interface nucleation at low temperatures to surface nucleation at intermediate temperatures and to bulk nucleation at very high temperatures. Alumina particles dispersed among the anatase particles can effectively reduce the probability of interface nucleation at all temperatures.

Graphite → diamond transition under high pressure: A kinetics approach

The graphite → diamond transition in the diamond stability field can be either direct or solvent-assisted. The direct transition may proceed by spreading a puckered basal plane of graphite in the direction perpendicular to it. The kinetics of such a transition may be approximated by the growth of a two-dimensional nucleus. The threshold temperature of the transition appears to depend on the degree of perfection of the original graphite. Hence, the more perfect the graphite is, the lower temperature it will transform into diamond. The solvent-assisted transition normally proceeds by rapid nucleation followed by growth of these nuclei. The kinetic model for continuous nucleation may be applied to the early stage of such transition. The activation energies for the transition can then be calculated. It is found that these activation energies seem to vary inversely with the solubility of carbon in these solvents at ambient pressure. Hence, the higher the amount of carbon a solvent dissolves at ambient pressure, the more effective it can be as a catalyst for the graphite → diamond transition under high pressure.

A kinetic model for nonisothermic homogeneous nucleation

A model for isothermal homogeneous nucleation is proposed that improves the classical model. A quasiequilibrium distribution of clusters was calculated on a basis of the Frenkel’-Lothe-Pound theory. The dependence of the free energy of clusters on their size was represented by an interpolation formula relating the free energy of dimers and large clusters to which a notion of macroscopic surface tension is applicable. The nucleation rate and the dependence of the cluster temperature on their size were calculated by balance equations describing the heating of from a cluster due to the condensation of monomers and its cooling due to collisions with an ambient gas. It is shown that the nucleation rate in excess buffer gas is higher than for the pure condensing gas by approximately two orders of magnitude. The model adequately describes the experimental data for the nucleation of methanol supersaturated vapor.

A new kinetic model for three-dimensional heterogeneous nucleation

Despite the relevance to most aspects of crystallization, a comprehensive understanding of the kinetics of heterogeneous nucleation has not been well established yet. In this paper, a new kinetic model based on the “steady-state” approach will be put forward to describe both heterogeneous and homogeneous nucleation. As a key point in this model, the effect of foreign particles on both the nucleation barrier, the “chain reaction” process and the transport of structural units is taken into account. Ranging from low to high supersaturations, heterogeneous nucleation plays a more comprehensive role in nucleation than we expected, depending on the size of foreign particles and the interaction and structural matching between foreign particles and the nucleating phase. It follows that genuine homogeneous nucleation may only be possible at very high supersaturations, and can become easier when convection is eliminated. The results have been verified by the CaCO3 nucleation experiments. This general model allows us to describe many unexpected nucleation phenomena for the first time, and will have significant impact on the control of nucleation, understanding of crystallization in microgravity, the measurement of the crystal–fluid interfacial tension, and crystallization in general.

Nucleation of strontium titanate films grown by PLD on silicon: a kinetic model

Nucleation and growth of strontium titanate (SrTiO 3) films, prepared by pulsed laser ablation deposition, has been investigated during on a (100) silicon substrate surface, using atomic force microscopy. A nucleation kinetic model has been derived from an analysis of the particle size distribution. The reconstructed nucleation trend was characterised by a systematic behaviour: the nucleation rate, negligible at the beginning, reaching a maximum after a certain time and tending to zero for longer deposition time. This behaviour prompted the design of a simple model which correlates these phenomena to two specific aspects: i) the nucleation occurs at certain limited number of sites on the substrate surface; ii) the nucleation process shows a temperature-dependent incubation time. In this model, the incubation time is related to the formation time of a ‘critical SrTiO 3 cluster’. The size of the critical cluster is determined both by thermodynamic quantities and by the amount of interface misfit strain energy of SrTiO 3 lattice with respect to substrate.

Pyrolysis Decomposition Kinetics of Cellulose-Based Materials by Constant Heating Rate Micropyrolysis

Fibrous, powdered fibrous, and acid-washed celluloses, newsprint, and paper dunnage were examined by Pyromat micropyrolysis to determine volatile organic compound evolution kinetic parameters. For the cellulose samples, the interpolated Tmax values (temperature of maximum evolution rate for a constant heating rate) indicate the fibrous cellulose is the least reactive. The fibrous cellulose samples have activation energies and frequency factors around 43 kcal/mol and 5 × 1012 s-1. A three-parameter nucleation kinetic model gave the best fits to the reaction profile, which is narrower than a first-order reaction. Newsprint and dunnage were also examined. The interpolated Tmax values indicate that dunnage is more reactive than the newsprint, and both are more reactive than the cellulose samples. Newsprint and paper dunnage have energy distributions that are similar but shifted from each other. Because of the diversity in chemical structure in the papers, the best fits were found using a discrete energy distr...