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Chemical Thermodynamics Set

coordinated by

Michel Soustelle

Volume 7

Thermodynamics of Surfaces and Capillary Systems

Michel Soustelle

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Preface

This book – an in-depth examination of chemical thermodynamics – is written for an audience of engineering undergraduates and Masters students in the disciplines of chemistry, physical chemistry, process engineering, materials, etc., and doctoral candidates in those disciplines. It will also be useful for researchers at fundamental- or applied-research labs, dealing with issues in thermodynamics during the course of their work.

These audiences will, during their undergraduate degree, have received a grounding in general thermodynamics and chemical thermodynamics, which all science students are normally taught. This education will undoubtedly have provided them with the fundamental aspects of macroscopic study, but usually the phases discussed will have been fluids exhibiting perfect behavior. Surface effects, the presence of an electrical field, real phases, the microscopic aspect of modeling, and various other aspects, are hardly touched upon (if at all) during this early stage of an academic career in chemical thermodynamics.

This set of books, which is positioned somewhere between an introduction to the subject and a research thesis, offers a detailed examination of chemical thermodynamics that is necessary in the various disciplines relating to chemical or material sciences. It lays the groundwork necessary for students to go and read specialized publications in their different areas. It constitutes a series of reference books that touch on all of the concepts and methods. It discusses both scales of modeling: microscopic (by statistical thermodynamics) and macroscopic, and illustrates the link between them at every step. These models are then used in the study of solid, liquid and gaseous phases, either of pure substances or comprising several components.

The various volumes of the set will deal with the following topics:

  1. – phase modeling tools: application to gases;
  2. – modeling of liquid phases;
  3. – modeling of solid phases;
  4. – chemical equilibrium states;
  5. – phase transformations;
  6. – electrolytes and electrochemical thermodynamics;
  7. – thermodynamics of surfaces, capillary systems and phases of small dimensions.

Appendices in each volume give an introduction to the general methods used in the text, and offer additional mathematical tools and some data.

This series owes a great deal to the feedback, comments and questions from all my students at the Ecole Nationale Supérieure des Mines (engineering school) in Saint Etienne who have “endured” my lecturing in thermodynamics for many years. I am very grateful to them, and also thank them for their stimulating attitude. This work is also the fruit of numerous discussions with colleagues who teach thermodynamics in the largest establishments – particularly in the context of the “Thermodic” group, founded by Marc Onillion. My thanks go to all of them for their contributions and kindness.

This seventh instalment is devoted to the study of surface phenomena and to the properties of phases with small dimensions. Chapter 1 looks at the system composed of the interface between a pure liquid and its vapor. A thermodynamic approach is used to determine the influence of the temperature and pressure on the surface tension and its consequences for the specific heat capacities and the latent heats. Chapter 2 describes the modeling and properties of the interfaces between a liquid and a liquid solution or a gaseous mixture. An example of a model of the interface is studied with the model of the strictly-regular solution. Chapter 3 examines the surfaces of solids and solid–solid and solid–liquid interfaces. It closes with the study of electro-capillary phenomena. Chapter 4 deals with small-volume phases, droplets or solids of small dimensions. The thermodynamic values are determined on the basis of Reiss’ potential functions. The chapter concludes with a thermodynamic study of the phenomenon of nucleation of a condensed phase. In Chapter 5, we study firstly the thermodynamics of cylindrical capillary, and secondly the properties of thin liquid films. Chapters 6 and 7, respectively, discuss the phenomena of physical adsorption and chemical adsorption of gases by solid surfaces. Finally, in an appendix, we present the application of physical adsorption to the determination of the specific areas of solids and their porosity.

Michel SOUSTELLE

Saint-Vallier

April 2016

Notations and Symbols

A: area of a surface or an interface.
Image: Hamaker constant between two media 1 and 2.
Image affinity.
Image electrochemical affinity.
AM: molar area.
Am: molecular area.
a: pressure of cohesion of a gas or radius of the elementary cell of a liquid.
A, B, …: components of a mixture.
b: cosurface of an adsorbed gas.
image set of variables with p intensive variables chosen to define a system.
F: Helmholtz energy.
image heterogeneous wetting function.
image electrocapillary Gibbs energy.
ht: spreading coefficient.
h: Planck’s constant.
Hspr:Harkins spreading coefficient of one liquid over another.
imagethermodynamic coefficient associated with the set of variables image is its definition variable and Yi is its definition function.
image equilibrium constant of adsorption.
Kfe: equilibrium function of adsorption.
kB: Boltzmann’s constant.
lc: capillary length.
M: molar mass.
Na: Avogadro’s number.
NA: number of molecules of component A.
P: pressure of a gas.
p: spreading parameter.
qϕ: equilibrium heat of adsorption.
qd: differential heat of adsorption.
qisost: isosteric heat of adsorption.
R: perfect gas constant.
R: mean radius of curvature of a surface.
rc: radius of a cylindrical tube.
rK: Kelvin radius.
T: temperature.
vmono: volume of a monolayer of adsorbed gas.
image molar fraction of the component k in the α phase.
xi: molar fraction of the component i in a solution. Yi and Xi: conjugate intensive and extensive values.
yi,j: Mayer function.
image characteristic function with the set image as canonical variables.
image characteristic function.
imageexcess surface or surface concentration of component i.
image excess surface or surface concentration of component i in relation to j.
image activity coefficient of component i in the pure-substance reference.
image activity coefficient of component i in the infinitely dilute-solution reference.
image activity coefficient of component i in the molar-solution reference.
image spreading on a liquid.
image value of A associated with the transformation r.
θ: fraction of coverage.
θi: surface fraction of a component.
image surface energy.
image surface density of electrical charges.
image surface tension.