A unifying identity for the work of cluster formation in heterogeneous and homogeneous nucleation theory

Journal Article · 24 August 2018 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/1.5040459 · OSTI ID:1466606

McGraw, Robert L.  ^[1]; Winkler, Paul M. ^[2]; Wagner, Paul E. ^[2]

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1. Brookhaven National Lab. (BNL), Upton, NY (United States)
2. Univ. of Vienna (Austria)

A unifying identity is derived relating the reversible work of cluster formation (W), and its molecular number content (n) and surface work (Φ) components, each ratioed to the corresponding values for a spherical capillary drop of critical size in classical nucleation theory. The result is a relationship that connects these ratios: fW = -2f_N + 3f_S where f_W=W/W*_CNT , f_N =n/ n* _CNT, and f_S =Φ/Φ* _CNT . Shown to generalize two early thermodynamic relationships of Gibbs, the new result is demonstrated here for Fletcher’s model of heterogeneous nucleation, resulting in a unified treatment of condensation on flat and curved substrates and smooth passage to the homogeneous limit. Additional applications are made to clusters of non-critical as well as critical size, and to a molecular-based extension of classical nucleation theory based on the Kelvin relation. The new identity serves as a consistency check on complicated theoretical expressions and numerical calculations and can be used to guide construction of theory and interpretation of measurements.

• Research Organization: Brookhaven National Lab. (BNL), Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
• Grant/Contract Number: SC0012704
• OSTI ID: 1466606
• Report Number(s): BNL--207941-2018-JAAM
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 8 Vol. 149; ISSN 0021-9606
• Publisher: American Institute of Physics (AIP)Copyright Statement
• Country of Publication: United States
• Language: English