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

Abstract

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.

Authors:
ORCiD logo [1];  [2];  [2]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. Univ. of Vienna (Austria)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
OSTI Identifier:
1466606
Report Number(s):
BNL-207941-2018-JAAM
Journal ID: ISSN 0021-9606
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 8; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES

Citation Formats

McGraw, Robert L., Winkler, Paul M., and Wagner, Paul E. A unifying identity for the work of cluster formation in heterogeneous and homogeneous nucleation theory. United States: N. p., 2018. Web. doi:10.1063/1.5040459.
McGraw, Robert L., Winkler, Paul M., & Wagner, Paul E. A unifying identity for the work of cluster formation in heterogeneous and homogeneous nucleation theory. United States. doi:10.1063/1.5040459.
McGraw, Robert L., Winkler, Paul M., and Wagner, Paul E. Fri . "A unifying identity for the work of cluster formation in heterogeneous and homogeneous nucleation theory". United States. doi:10.1063/1.5040459. https://www.osti.gov/servlets/purl/1466606.
@article{osti_1466606,
title = {A unifying identity for the work of cluster formation in heterogeneous and homogeneous nucleation theory},
author = {McGraw, Robert L. and Winkler, Paul M. and Wagner, Paul E.},
abstractNote = {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 = -2fN + 3fS where fW=W/W*CNT , fN =n/ n* CNT, and fS =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.},
doi = {10.1063/1.5040459},
journal = {Journal of Chemical Physics},
number = 8,
volume = 149,
place = {United States},
year = {2018},
month = {8}
}

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    New Particle Formation in the Atmosphere: From Molecular Clusters to Global Climate
    journal, July 2019

    • Lee, Shan-Hu; Gordon, Hamish; Yu, Huan
    • Journal of Geophysical Research: Atmospheres, Vol. 124, Issue 13
    • DOI: 10.1029/2018jd029356