DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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 = -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.

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)
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. https://doi.org/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. https://doi.org/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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Dynamics of Barrier Crossing in Classical Nucleation Theory
journal, November 2001

  • McGraw, Robert
  • The Journal of Physical Chemistry B, Vol. 105, Issue 47
  • DOI: 10.1021/jp011914q

Active sites in heterogeneous ice nucleation—the example of K-rich feldspars
journal, December 2016


Quantitative Characterization of Critical Nanoclusters Nucleated on Large Single Molecules
journal, February 2012


Direct Observations of Atmospheric Aerosol Nucleation
journal, February 2013


Heterogeneous multicomponent nucleation theorems for the analysis of nanoclusters
journal, May 2007

  • Vehkamäki, Hanna; Määttänen, Anni; Lauri, Antti
  • The Journal of Chemical Physics, Vol. 126, Issue 17
  • DOI: 10.1063/1.2723073

Temperature Dependence in Heterogeneous Nucleation with Application to the Direct Determination of Cluster Energy on Nearly Molecular Scale
journal, December 2017


A new phenomenological approach to gas–liquid nucleation based on the scaling properties of the critical nucleus
journal, June 1997

  • Talanquer, V.
  • The Journal of Chemical Physics, Vol. 106, Issue 23
  • DOI: 10.1063/1.473884

Formation of nanoparticles of blue haze enhanced by anthropogenic pollution
journal, October 2009

  • Zhang, R.; Wang, L.; Khalizov, A. F.
  • Proceedings of the National Academy of Sciences, Vol. 106, Issue 42
  • DOI: 10.1073/pnas.0910125106

The Problem of Measuring Homogeneous Nucleation Rates and the Molecular Contents of Nuclei: Progress in the Form of Nucleation Pulse Measurements
journal, August 1994

  • Strey, R.; Wagner, P. E.; Viisanen, Y.
  • The Journal of Physical Chemistry, Vol. 98, Issue 32
  • DOI: 10.1021/j100083a003

An adsorption theory of heterogeneous nucleation of water vapour on nanoparticles
journal, January 2016


A molecular based derivation of the nucleation theorem
journal, September 2000

  • Bowles, R. K.; McGraw, R.; Schaaf, P.
  • The Journal of Chemical Physics, Vol. 113, Issue 11
  • DOI: 10.1063/1.1288802

Scaling Properties of the Critical Nucleus in Classical and Molecular-Based Theories of Vapor-Liquid Nucleation
journal, April 1996


A general relation between the nucleation work and the size of the nucleus in multicomponent nucleation
journal, May 1994

  • Oxtoby, David W.; Kashchiev, Dimo
  • The Journal of Chemical Physics, Vol. 100, Issue 10
  • DOI: 10.1063/1.466859

Size Effect in Heterogeneous Nucleation
journal, September 1958

  • Fletcher, N. H.
  • The Journal of Chemical Physics, Vol. 29, Issue 3
  • DOI: 10.1063/1.1744540

Determination of cloud condensation nuclei production from measured new particle formation events
journal, January 2009

  • Kuang, C.; McMurry, P. H.; McCormick, A. V.
  • Geophysical Research Letters, Vol. 36, Issue 9
  • DOI: 10.1029/2009gl037584

Microphysics of Clouds and Precipitation
journal, March 1980

  • Pruppacher, Hans R.; Klett, James D.
  • Nature, Vol. 284, Issue 5751
  • DOI: 10.1038/284088b0

Microphysics of Clouds and Precipitation
journal, July 1979


Works referencing / citing this record:

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