A Kinetic Approach to Homogeneous Nucleation Theory

Katz, Joseph; Donohue, Marc D.

doi:10.1002/9780470142592.ch3

Cited by 87 publications

(12 citation statements)

References 49 publications

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“…4 The rates of evaporation are evaluated based on the condensation rates and the equilibrium concentrations of the corresponding clusters in saturated vapor. This kinetic model is thermodynamically consistent.…”

Section: Impact Of the Thermodynamic Inconsistency Of The Partially Rmentioning

confidence: 99%

See 1 more Smart Citation

Complete thermodynamically consistent kinetic model of particle nucleation and growth: Numerical study of the applicability of the classical theory of homogeneous nucleation

Чесноков

Krasnoperov

2007

The Journal of Chemical Physics

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A complete thermodynamically consistent elementary reaction kinetic model of particle nucleation and growth from supersaturated vapor was developed and numerically evaluated to determine the conditions for the steady-state regime. The model treats all processes recognized in the aerosol science (such as nucleation, condensation, evaporation, agglomerationcoagulation, etc.) as reversible elementary reactions. It includes all possible forward reactions (i.e., of monomers, dimers, trimers, etc.) together with the thermodynamically consistent reverse processes. The model is built based on the Kelvin approximation, and has two dimensionless parameters: S0-the initial supersaturation and Theta-the dimensionless surface tension. The time evolution of the size distribution function was obtained over the ranges of parameters S0 and Theta. At low initial supersaturations, S0, the steady state is established after a delay, and the steady-state distribution function corresponds to the predictions of the classical nucleation theory. At high initial supersaturations, the depletion of monomers due to condensation on large clusters starts before the establishing of the steady state. The steady state is never reached, and the classical nucleation theory is not applicable. The boundary that separates these two regimes in the two dimensionless parameter space, S0 and Theta, was determined. The model was applied to several experiments on water nucleation in an expansion chamber [J. Wolk and R. Strey, J. Phys. Chem. B 105, 11683 (2001)] and in Laval nozzle [Y. J. Kim et al., J. Phys. Chem. A 108, 4365 (2004)]. The conditions of the experiments performed using Laval nozzle (S0=40-120) were found to be close to the boundary of the non-steady-state regime. Additional calculations have shown that in the non-steady-state regime the nucleation rate is sensitive to the rate constants of the initial steps of the nucleation process, such as the monomer-monomer, monomer-dimer, etc., reactions. This conclusion is particularly important for nucleation from supersaturated water vapor, since these processes for water molecules at and below the atmospheric pressure are in the low pressure limit, and the rate constants can be several orders of magnitude lower than the gas kinetic. In addition, the impact of the thermodynamic inconsistency of the previously developed partially reversible kinetic numerical models was assessed. At typical experimental conditions for water nucleation, S0=10 and Theta=10 (T=250 K), the error in the particle nucleation rate introduced by the thermodynamic inconsistency exceeds one order of magnitude.

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Section: Impact Of the Thermodynamic Inconsistency Of The Partially Rmentioning

confidence: 99%

“…For a period of time, an analytical approach known as the classical nucleation theory was used to describe the nucleation dynamics. [1][2][3][4] Later, numerical models of the kinetics of particle nucleation and growth have been developed. [5][6][7][8] Courtney applied a kinetic model to a non-steady-state nucleation of water vapor.…”

Section: Introductionmentioning

confidence: 99%

Complete thermodynamically consistent kinetic model of particle nucleation and growth: Numerical study of the applicability of the classical theory of homogeneous nucleation

Чесноков

Krasnoperov

2007

The Journal of Chemical Physics

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“…In both cases, the time dependence at constant temperature comes through the solute concentration, that is,

c = c (t)

, where t is time. Beginning with a kinetic model, Katz and Donohue derived a result similar to Equation with the concentrations being replaced by forward and backward attachment rate coefficients so that the time dependence for the nucleation rate depends upon behavior of these coefficients …”

Section: Introductionmentioning

confidence: 99%

“…Beginning with a kinetic model, Katz and Donohue derived a result similar to Equation (1) with the concentrations being replaced by forward and backward attachment rate coefficients so that the time dependence for the nucleation rate depends upon behavior of these coefficients. 3 A rigorous treatment of the time dependence of the nucleation phenomenon comes from the kinetic model of Szilard and Farkas. 4,5 This complete, subsequent monomer addition mechanism has been studied theoretically by many workers.…”

Section: Introductionmentioning

confidence: 99%

The kinetics of homogeneous and two‐step nucleation during protein crystal growth from solution

Barlow¹,

Gregus

2019

Int J of Chemical Kinetics

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Many experimental reports for the kinetics of crystal nucleation and growth, from an isothermal solution, point to a sigmoidal‐like behavior for the process. Here we consider three different nucleation models from the literature and show that all lead to sigmoidal or sigmoidal‐like behavior for the kinetics of nucleation. A two‐step nucleation process is known to occur within certain supersaturated protein solutions, and it is demonstrated in this report how the sigmoidal law yields kinetic information for the two‐step and homogeneous nucleation modes. We propose here that two‐step solute‐rich associates form in the solution around seed nuclei that are already present at or near the point in time when the solution is prepared. Using this hypothesis, we are able to model the time‐dependent volume of the two‐step phase per unit volume of solution and show that this compares well with reported experimental data. A kinetic model is given for the proposed process, which leads to a sigmoidal rate law. Additionally, a relation between the initial and final nuclei densities and the induction time is derived. As a result of this study, the conclusion is that two‐step activity increases with increasing initial supersaturation or increasing salt concentration.

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“…The same type of conclusions were obtained with more complex models of similar systems (Proulx & Bilodeau, 1991;Chiu, 1992;Girshick et al, 1993). Another important contribution from the research work reported above is the development of a selfconsistent nucleation theory which is derived from the classical nucleation theory (Katz & Donohue, 1979) by using the Boltzmann expression for the equilibrium cluster distribution self-consistently (Girshick, 1991). When using the MOM, the self-consistent nucleation rate is preferred over the classical expression, because the self-consistent gives similar results compared to other more refined techniques (i.e.…”

Section: Introductionmentioning

confidence: 99%

Modeling of the production of ultra fine Aluminium particles in rapid quenching turbulent flow

Aristizabal

Munz

Berk

2006

Journal of Aerosol Science

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A Kinetic Approach to Homogeneous Nucleation Theory

Cited by 87 publications

References 49 publications

Complete thermodynamically consistent kinetic model of particle nucleation and growth: Numerical study of the applicability of the classical theory of homogeneous nucleation

Complete thermodynamically consistent kinetic model of particle nucleation and growth: Numerical study of the applicability of the classical theory of homogeneous nucleation

The kinetics of homogeneous and two‐step nucleation during protein crystal growth from solution

Modeling of the production of ultra fine Aluminium particles in rapid quenching turbulent flow

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