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Surface Thermodynamics, Lecture notes of Thermodynamics

University of Illinois - Urbana-ChampaignThermodynamics

A primer for heat transfer physical scientists on surface thermodynamics. It discusses the thermodynamics of surfaces, statistical mechanics of surfaces, equilibrium shape, surface stress, and heat of adsorption. based on lecture notes by Prof. Gert Ehrlich and is authored by David Cahill from the Department of Materials Science and Engineering, Materials Research Laboratory, University of Illinois at Urbana-Champaign. relevant for students studying materials science, thermodynamics, and heat transfer.

Typology: Lecture notes

2021/2022

Uploaded on 05/11/2023

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Surface Thermodynamics
A primer for heat transfer physical scientists
David Cahill
Department of Materials Science and Engineering,
Materials Research Laboratory,
University of Illinois at Urbana-Champaign
Partially based on lecture notes by Prof. Gert Ehrlich
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Surface Thermodynamics

A primer for heat transfer physical scientists

David Cahill Department of Materials Science and Engineering, Materials Research Laboratory, University of Illinois at Urbana-Champaign

Partially based on lecture notes by Prof. Gert Ehrlich

Motivation for understanding thermodynamics of

surfaces

  • At the nanoscale, atoms and molecules near surfaces and interfaces become a significant fraction of the overall system.
  • In this lecture, I will use the term “surface” to describe the transition region between two phases.
  • Gibbs (1878) introduced the concept of a “dividing surface” to deal with the thermodynamics of this (often inhomogenous) transition region. - See Tolman, J. Chem. Phys. 16 , 758 (1948)

Part I: classical thermodynamics of surfaces

  • Surface excess contributions to the extensive variables - Gibbs adsorption equation
  • Thermodynamic potentials and surface excess free energy - Landau thermodynamic potential for multicomponent systems - Surface tension, surface energy, surface stress
  • Equilibrium shape; Laplace pressure; thermodynamic driving force for coarsening

Part II: statistical mechanics of surfaces

  • Landau thermodynamic potential and the grand partition function - Equilibrium between 2D and 3D ideal gases - Equilibrium between monolayer lattice gas and 3D ideal gas (Langmuir adsorption)
  • Comparison to kinetic models for evaporation and condensation
  • Connection back to thermodynamics: heat of adsorption

Surface excess of the extensive variables

Surface excess of the extensive variables

Gibbs adsorption equation

Surface excess free energy

Difficult to measure the surface tension of a solid

  • Need an experiment that can access the reversible mechanical work needed to create new surface
  • Zero creep experiment

Surface tension, surface energy, surface stress

  • I usually reserve the term “surface energy” for the surface tension at zero temperature.

Equilibrium shape

Equilibrium shape: Wulff construction

Equilibrium between a small crystal and its liquid or vapor

Equilibrium between a small crystal and its liquid or vapor