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Title: On the determination of the crystal-vapor surface free energy, and why a Gaussian expression can be accurate for a system far from Gaussian

Abstract

The crystal-vapor surface free energy γ is an important physical parameter governing physical processes, such as wetting and adhesion. We explore exact and approximate routes to calculate γ based on cleaving an intact crystal into non-interacting sub-systems with crystal-vapor interfaces. We do this by turning off the interactions, ΔV, between the sub-systems. Using the soft-core scheme for turning off ΔV, we find that the free energy varies smoothly with the coupling parameter λ, and a single thermodynamic integration yields the exact γ. We generate another exact method, and a cumulant expansion for γ by expressing the surface free energy in terms of an average of e{sup −βΔV} in the intact crystal. The second cumulant, or Gaussian approximation for γ is surprisingly accurate in most situations, even though we find that the underlying probability distribution for ΔV is clearly not Gaussian. We account for this fact by developing a non-Gaussian theory for γ and find that the difference between the non-Gaussian and Gaussian expressions for γ consist of terms that are negligible in many situations. Exact and approximate methods are applied to the (111) surface of a Lennard-Jones crystal and are also tested for more complex molecular solids, the surface ofmore » octane and nonadecane. Alkane surfaces were chosen for study because their crystal-vapor surface free energy has been of particular interest for understanding surface freezing in these systems.« less

Authors:
 [1];  [1];  [2];  [3]
  1. Department of Chemical and Biomolecular Engineering, Ohio State University, Columbus, Ohio 43210 (United States)
  2. (United States)
  3. Department of Chemistry and Biochemistry, Ohio State University, Columbus, Ohio 43210 (United States)
Publication Date:
OSTI Identifier:
22678973
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 145; Journal Issue: 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ADHESION; APPROXIMATIONS; COUPLING; CRYSTALS; DISTRIBUTION; ELECTRONS; EXPANSION; FREE ENERGY; FREEZING; INTERACTIONS; OCTANE; PROBABILITY; SOLIDS; SURFACES; THERMODYNAMICS

Citation Formats

Modak, Viraj P., E-mail: virajmodak@gmail.com, Wyslouzil, Barbara E., E-mail: wyslouzil.1@osu.edu, Department of Chemistry and Biochemistry, Ohio State University, Columbus, Ohio 43210, and Singer, Sherwin J., E-mail: singer@chemistry.ohio-state.edu. On the determination of the crystal-vapor surface free energy, and why a Gaussian expression can be accurate for a system far from Gaussian. United States: N. p., 2016. Web. doi:10.1063/1.4959167.
Modak, Viraj P., E-mail: virajmodak@gmail.com, Wyslouzil, Barbara E., E-mail: wyslouzil.1@osu.edu, Department of Chemistry and Biochemistry, Ohio State University, Columbus, Ohio 43210, & Singer, Sherwin J., E-mail: singer@chemistry.ohio-state.edu. On the determination of the crystal-vapor surface free energy, and why a Gaussian expression can be accurate for a system far from Gaussian. United States. doi:10.1063/1.4959167.
Modak, Viraj P., E-mail: virajmodak@gmail.com, Wyslouzil, Barbara E., E-mail: wyslouzil.1@osu.edu, Department of Chemistry and Biochemistry, Ohio State University, Columbus, Ohio 43210, and Singer, Sherwin J., E-mail: singer@chemistry.ohio-state.edu. Sun . "On the determination of the crystal-vapor surface free energy, and why a Gaussian expression can be accurate for a system far from Gaussian". United States. doi:10.1063/1.4959167.
@article{osti_22678973,
title = {On the determination of the crystal-vapor surface free energy, and why a Gaussian expression can be accurate for a system far from Gaussian},
author = {Modak, Viraj P., E-mail: virajmodak@gmail.com and Wyslouzil, Barbara E., E-mail: wyslouzil.1@osu.edu and Department of Chemistry and Biochemistry, Ohio State University, Columbus, Ohio 43210 and Singer, Sherwin J., E-mail: singer@chemistry.ohio-state.edu},
abstractNote = {The crystal-vapor surface free energy γ is an important physical parameter governing physical processes, such as wetting and adhesion. We explore exact and approximate routes to calculate γ based on cleaving an intact crystal into non-interacting sub-systems with crystal-vapor interfaces. We do this by turning off the interactions, ΔV, between the sub-systems. Using the soft-core scheme for turning off ΔV, we find that the free energy varies smoothly with the coupling parameter λ, and a single thermodynamic integration yields the exact γ. We generate another exact method, and a cumulant expansion for γ by expressing the surface free energy in terms of an average of e{sup −βΔV} in the intact crystal. The second cumulant, or Gaussian approximation for γ is surprisingly accurate in most situations, even though we find that the underlying probability distribution for ΔV is clearly not Gaussian. We account for this fact by developing a non-Gaussian theory for γ and find that the difference between the non-Gaussian and Gaussian expressions for γ consist of terms that are negligible in many situations. Exact and approximate methods are applied to the (111) surface of a Lennard-Jones crystal and are also tested for more complex molecular solids, the surface of octane and nonadecane. Alkane surfaces were chosen for study because their crystal-vapor surface free energy has been of particular interest for understanding surface freezing in these systems.},
doi = {10.1063/1.4959167},
journal = {Journal of Chemical Physics},
number = 5,
volume = 145,
place = {United States},
year = {Sun Aug 07 00:00:00 EDT 2016},
month = {Sun Aug 07 00:00:00 EDT 2016}
}