Modification of the classical nucleation theory based on molecular simulation data for surface tension, critical nucleus size, and nucleation rate

Clathrate hydrates are solid crystalline structures most commonly formed from solutions that have nucleated to form a mixed solid composed of water and gas. Understanding the mechanism of clathrate hydrate nucleation is essential to grasp the fundamental chemistry of these complex structures and their applications. Molecular dynamics (MD) simulation is an ideal method to study nucleation at the molecular level because the size of the critical nucleus and formation rate occur on the nano scale. Various analysis methods for nucleation have been developed through MD to analyze nucleation. In particular, the mean first-passage time (MFPT) and survival probability (SP) methods have proven to be effective in procuring the nucleation rate and critical nucleus size for monatomic systems. This study assesses the MFPT and SP methods, previously used for monatomic systems, when applied to analyzing clathrate hydrate nucleation. Because clathrate hydrate nucleation is relatively difficult to observe in MD simulations (due to its high free energy barrier), these methods have yet to be applied to clathrate hydrate systems. In this study, we have analyzed the nucleation rate and critical nucleus size of methane hydrate using MFPT and SP methods from data generated by MD simulations at 255 K and 50 MPa. MFPT was modified for clathrate hydrate from the original version by adding the maximum likelihood estimate and growth effect term. The nucleation rates calculated by MFPT and SP methods are within 5%, and the critical nucleus size estimated by the MFPT method was 50% higher, than values obtained through other more rigorous but computationally expensive estimates. These methods can also be extended to the analysis of other clathrate hydrates.

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Eliminating the Pre-exponential Factor in Classical Nucleation Theory

Chemical Science International Journal ◽

10.9734/csji/2019/v28i330140 ◽

2019 ◽

pp. 1-6

Author(s):

John H. Jennings

Keyword(s):

Molecular Weight ◽

Surface Tension ◽

Nucleation Rate ◽

Homogeneous Nucleation ◽

Polymer Concentration ◽

Nucleation Theory ◽

Classical Nucleation Theory ◽

Low Molecular Weight ◽

Exponential Factor ◽

New Equation

Blander and Katz give a formula in classical nucleation theory, J = A exp K, for homogeneous nucleation (liquid-->gas). Jennings proved that dlnA/dK = 1/6K for all pure liquids by combining two theories, taking the limit as polymer concentration-->0. This gives lnA = (1/12)ln(K2) + C, where C is the integration constant. The conjecture is that C is a constant for fluids of low molecular weight. We used data for 7 sample solvents, and solved for C. The surface tension drops out in C, which makes C more accurate, as the surface tension is difficult to get at 0.89Tc, the limit of superheat. Tc = critical point in Kelvin. All quantities are evaluated at the limit of superheat, which is approximately 0.89Tc for solvents. C = 74.77 ± 0.33 for the 7 solvents (not all alkanes). This eliminates the prefactor A, streamlining J: ln J = (1/12)ln(K2) + 74.77 + K is the exact new equation. A computer can more easily be used to calculate J, the nucleation rate.

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Classical Nucleation and Lattice Model Unite

Chemical Science International Journal ◽

10.9734/csji/2020/v29i430174 ◽

2020 ◽

pp. 32-36

Author(s):

John H. Jennings

Keyword(s):

Molecular Weight ◽

Surface Tension ◽

Nucleation Rate ◽

Lattice Model ◽

Polymer Solutions ◽

Bubble Nucleation ◽

Nucleation Theory ◽

Classical Nucleation Theory ◽

Molecular Weight Polymer ◽

To Come

Classical nucleation theory predicts the limit of superheat of liquids quite well. To come up with an equation for the limit of superheat of polymer solutions, the lattice model for polymer solutions was used to give the surface tension of polymer solutions. A formula for bubble nucleation in polymer solutions was derived by Jennings with the precursor equation dlnA/dK=1/(6K) where J=AexpK gives the nucleation rate for liquids. The aim of this paper was to show that the precursor equation holds for monomer in the polystyrene-cyclohexane system. Thus, the precursor equation is true for all molecular weight polymer. This happens because the surface tension of polystyrene is significantly more than cyclohexane and the influence of the surface tension dominates.

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Low-temperature nucleation anomaly in silicate glasses shown to be artifact in a 5BaO·8SiO2 glass

Nature Communications ◽

10.1038/s41467-021-22161-9 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Xinsheng Xia ◽

D. C. Van Hoesen ◽

Matthew E. McKenzie ◽

Randall E. Youngman ◽

K. F. Kelton

Keyword(s):

Nucleation Rate ◽

Experimental Approach ◽

Cluster Formation ◽

Heating Time ◽

Silicate Glasses ◽

Nucleation Theory ◽

Classical Nucleation Theory ◽

Real Phenomenon ◽

Satisfactory Answer ◽

Over 40 Years

AbstractFor over 40 years, measurements of the nucleation rates in a large number of silicate glasses have indicated a breakdown in the Classical Nucleation Theory at temperatures below that of the peak nucleation rate. The data show that instead of steadily decreasing with decreasing temperature, the work of critical cluster formation enters a plateau and even starts to increase. Many explanations have been offered to explain this anomaly, but none have provided a satisfactory answer. We present an experimental approach to demonstrate explicitly for the example of a 5BaO ∙ 8SiO2 glass that the anomaly is not a real phenomenon, but instead an artifact arising from an insufficient heating time at low temperatures. Heating times much longer than previously used at a temperature 50 K below the peak nucleation rate temperature give results that are consistent with the predictions of the Classical Nucleation Theory. These results raise the question of whether the claimed anomaly is also an artifact in other glasses.

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Homogeneous nucleation in a Poiseuille flow

Physical Chemistry Chemical Physics ◽

10.1039/d0cp06132h ◽

2021 ◽

Vol 23 (6) ◽

pp. 3974-3982

Author(s):

Fuqian Yang

Keyword(s):

Poiseuille Flow ◽

Homogeneous Nucleation ◽

Critical Nucleus ◽

Flow Speed ◽

Nucleus Size ◽

Average Flow ◽

Critical Nucleus Size

Variation of the critical nucleus size and the corresponding work of formation with average flow speed at axisymmetric axis.

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Trapping Effect on the Kinetic Critical Radius in Nucleation and Growth Processes

Materials Science Forum ◽

10.4028/www.scientific.net/msf.790-791.97 ◽

2014 ◽

Vol 790-791 ◽

pp. 97-102

Author(s):

Zoltán Erdélyi ◽

Zoltán Balogh ◽

Gabor L. Katona ◽

Dezső L. Beke

Keyword(s):

Critical Nucleus ◽

Solid Phase ◽

Kinetic Monte Carlo ◽

Mean Field ◽

Transformation Process ◽

Nucleus Size ◽

Critical Nucleus Size ◽

Acta Mater ◽

Order Of Magnitude ◽

The Difference

The critical nucleus size—above which nuclei grow, below dissolve—during diffusion controlled nucleation in binary solid-solid phase transformation process is calculated using kinetic Monte Carlo (KMC). If atomic jumps are slower in an A-rich nucleus than in the embedding B-rich matrix, the nucleus traps the A atoms approaching its surface. It doesn’t have enough time to eject A atoms before new ones arrive, even if it would be favourable thermodynamically. In this case the critical nucleus size can be even by an order of magnitude smaller than expected from equilibrium thermodynamics or without trapping. These results were published in [Z. Erdélyi et al., Acta Mater. 58 (2010) 5639]. In a recent paper M. Leitner [M. Leitner, Acta Mater. 60 (2012) 6709] has questioned our results based on the arguments that his simulations led to different results, but he could not point out the reason for the difference. In this paper we summarize our original results and on the basis of recent KMC and kinetic mean field (KMF) simulations we show that Leitner’s conclusions are not valid and we confirm again our original results.

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A semi-analytical method for calculating rates of new sulfate aerosol formation from the gas phase

Atmospheric Chemistry and Physics Discussions ◽

10.5194/acpd-7-2169-2007 ◽

2007 ◽

Vol 7 (1) ◽

pp. 2169-2196 ◽

Cited By ~ 1

Author(s):

J. Kazil ◽

E. R. Lovejoy

Keyword(s):

Steady State ◽

Gas Phase ◽

Nucleation Rate ◽

Atmospheric Modeling ◽

Sulfate Aerosol ◽

Nucleation Theory ◽

Rate Coefficients ◽

Classical Nucleation Theory ◽

Aerosol Formation ◽

Aerosol Model

Abstract. The formation of new sulfate aerosol from the gas phase is commonly represented in atmospheric modeling with parameterizations of the steady state nucleation rate. Such parameterizations are based on classical nucleation theory or on aerosol nucleation rate tables, calculated with a numerical aerosol model. These parameterizations reproduce aerosol nucleation rates calculated with a numerical aerosol model only imprecisely. Additional errors can arise when the nucleation rate is used as a surrogate for the production rate of particles of a given size. We discuss these errors and present a method which allows a more precise calculation of steady state sulfate aerosol formation rates. The method is based on the semi-analytical solution of an aerosol system in steady state and on parameterized rate coefficients for H2SO4 uptake and loss by sulfate aerosol particles, calculated from laboratory and theoretical thermodynamic data.

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