Thermodynamic properties and homogeneous nucleation rates for surface-melted physical clusters

McClurg, Richard B.; Flagan, Richard C.; Goddard, William A.

doi:10.1063/1.473002

Cited by 14 publications

(5 citation statements)

References 52 publications

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“…He assumed, provisionally, that δ can be taken as a constant in the region of interest and, solving eq 1 on this basis, arrived at his famous equation In a companion paper, Kirkwood and Buff developed a general statistical mechanical theory of interfacial phenomena and confirmed the essential validity of Tolman's approach. Since the publication of Tolman's paper, a considerable literature has ensued, − either demonstrating the consequences of this phenomenon in the kinetics of nucleation and other phenomena or attacking the problem via statistical thermodynamics. Quite a few papers have proposed methods to derive the value of δ , many assuming with Tolman that δ is independent of drop size.…”

Section: Introductionmentioning

confidence: 99%

Tolman's δ, Surface Curvature, Compressibility Effects, and the Free Energy of Drops

Bartell

2001

J. Phys. Chem. B

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An extension of a treatment by Laaksonen and McGraw leads to an analytical expression for the variation of Tolman's δ with drop size. According to this approach, the change in sign of δ as a drop becomes large is a consequence of compressibility. An expression for the reversible work to produce a small drop from bulk liquid is given that corrects conventional expressions for effects of compressibility and Tolman's δ. It is shown, however, that when this expression is applied to the formation of a drop from the supersaturated vapor, the reversible work, W rev‘, in excess of volume work no longer explicitly involves the Tolman δ or the compressibility, in agreement with treatments by Gibbs and by Debenedetti and Reiss. Nevertheless, if the expression for W rev‘ is to be related to directly measurable quantities, compressibility and δ still play a role.

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Section: Introductionmentioning

confidence: 99%

Tolman's δ, Surface Curvature, Compressibility Effects, and the Free Energy of Drops

Bartell

2001

J. Phys. Chem. B

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“…In equation ( 67 34,35 (see Supplementary Note 6 for more details). (dashed lines) Best fits of equation (7).…”

Section: T T Cmentioning

confidence: 99%

Thermodynamic Origin of Nuclei Seed Formation and Monomer Supply Rate-Dependent Crystallization Dynamics

Song,

Kim,

Kang

et al. 2024

Preprint

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Supersaturation and nucleus seed formation are universal processes that precede all phase transitions. Despite extensive research on nucleation, our understanding on supersaturation, nucleus seed formation and phase transition dynamics remains rudimentary. Here, we present exact statistical thermodynamic formula for the saturation degree, the most-probable size distribution of mesoscopic nuclei, and their phase transition, introducing the mesoscopic state defined by temperature, the total monomer concentration, and the largest cluster size (LCS). These results show that supersaturation emerges even at equilibrium for mesoscopic nuclei systems and decreases with the LCS. The size-distribution of nucleus seeds is either a unimodal or a monotonically decreasing function of size, depending on the system and temperature. There exists a critical supersaturation condition under which nucleus seeds undergo a phase transition, during which the most probable size exhibits an abrupt change. We also investigated nonequilibrium dynamics of supersaturation, nucleus seed formation, and phase transition, accounting for the monomer-supply-rate effects. Nucleus seeds attain either nonequilibrium-steady-state (NESS) or transient-oscillatory-state (TOS) depending on the monomer-supply-rate, before undergoing phase transition. In both NESS and TOS, nuclei assume a quasi-equilibrium size distribution; their population exhibits a universal power-law relaxation during the phase transition. This work can be extended to investigate diverse nucleation and phase transition phenomena prevalent across nature and industry.

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“…An example of such system is the Mackay icosahedral cluster made of noble gas atoms at low temperatures (Fig. 2) [35,36]. For this case, we have…”

Section: E Shape Of Nucleus-size-distributionmentioning

confidence: 99%

Thermodynamic Principles governing Supersaturation, Nucleus Seed Formation, and Crystallization

Song,

Kim,

Kang

et al. 2024

Preprint

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Supersaturation and nucleus seed formation are universal processes that precede all phase transitions. Despite extensive research on nucleation, thermodynamic equations governing supersaturation, formation of nucleus seeds and their crystallization have long remained missing. Here, we present exact statistical thermodynamic formula for the saturation degree, the most-probable size distribution of mesoscopic nuclei, and their crystallization, introducing mesoscopic state defined by temperature, the total monomer concentration, and the largest cluster size (LCS). Our results show how supersaturation emerges for mesoscopic nuclei systems and the supersaturation degree decreases with the LCS. The size-distribution of nucleus seeds is either a unimodal or a monotonically decreasing function of size, depending on the system and temperature. For nucleus seeds with a unimodal size distribution, their most probable size increases with temperature. We discover a critical supersaturation condition under which nucleus seeds undergo a phase transition, characterized by an abrupt increase in the most probable size. We also investigated nonequilibrium dynamics of supersaturation, nucleus seed formation, and phase transition, accounting for the monomer-supply-rate effects. Nucleus seeds attain either nonequilibrium-steady-state (NESS) or transient-oscillatory-state (TOS) depending on the monomer-supply-rate, before undergoing phase transition. In both NESS and TOS, nuclei assume a quasi-equilibrium size distribution. During crystallization, the survival probability of nuclei in solution phase exhibits a power-law relaxation regardless of the monomer-supply-rate. This work can be extended to investigate diverse nucleation and phase transition phenomena prevalent across nature and industry.

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Thermodynamic properties and homogeneous nucleation rates for surface-melted physical clusters

Cited by 14 publications

References 52 publications

Tolman's δ, Surface Curvature, Compressibility Effects, and the Free Energy of Drops

Tolman's δ, Surface Curvature, Compressibility Effects, and the Free Energy of Drops

Thermodynamic Origin of Nuclei Seed Formation and Monomer Supply Rate-Dependent Crystallization Dynamics

Thermodynamic Principles governing Supersaturation, Nucleus Seed Formation, and Crystallization

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