### Abstract

This study is intended to give the reader a brief overview of the mathematical background to the thermodynamic theory of surfaces and interfaces. Some general aspects of the thermodynamics of systems with interfaces are discussed, and a concise treatment of interfaces within the framework of classical thermodynamics is provided. First, to introduce the reader to the topic, a reasonably simple thermodynamic treatment of interfaces, together with a brief description of the models widely used in the literature, is presented, the characteristics of the Gibbs “dividing plane” model and the Guggenheim “interphase” model are outlined, and a derivation of the Gibbs adsorption equation is given. In the subsequent sections, several important mathematical concepts (e.g., theory of homogeneous functions and partly homogeneous functions, Euler’s theorem and the Gibbs–Duhem equation, Legendre transformation) and various functional relationships of the thermodynamics of surfaces and interfaces are summarized, with particular attention to some alternative formulations. Some of the mathematical principles and methods are explained using illustrative examples.

Original language | English |
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Article number | 16 |

Journal | ChemTexts |

Volume | 1 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1 2015 |

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### Keywords

- Euler’s theorem
- Gibbs model
- Gibbs–Duhem equation
- Guggenheim model
- Homogeneous functions
- Interfacial thermodynamics
- Legendre transformation
- Partly homogeneous functions

### ASJC Scopus subject areas

- Chemistry(all)
- Biochemistry