The Poisson-Boltzmann Equation (eBook)

An Introduction

Ralf Blossey (Autor)

eBook Download: PDF

2023 | 1st ed. 2023
101 Seiten
Springer International Publishing (Verlag)
9783031247828 (ISBN)

Infos

This brief book introduces the Poisson-Boltzmann equation in three chapters that build upon one another, offering a systematic entry to advanced students and researchers. Chapter one formulates the equation and develops the linearized version of Debye-Hückel theory as well as exact solutions to the nonlinear equation in simple geometries and generalizations to higher-order equations. 

   

Chapter two introduces the statistical physics approach to the Poisson-Boltzmann equation. It allows the treatment of fluctuation effects, treated in the loop expansion, and in a variational approach. First applications are treated in detail: the problem of the surface tension under the addition of salt, a classic problem discussed by Onsager and Samaras in the 1930s, which is developed in modern terms within the loop expansion, and the adsorption of a charged polymer on a like-charged surface within the variational approach. 

Chapter three finally discusses the extension of Poisson-Boltzmann theory to explicit solvent. This is done in two ways: on the phenomenological level of nonlocal electrostatics and with a statistical physics model that treats the solvent molecules as molecular dipoles. This model is then treated in the mean-field approximation and with the variational method introduced in Chapter two, rounding up the development of the mathematical approaches of Poisson-Boltzmann theory.

 

After studying this book, a graduate student will be able to access the research literature on the Poisson-Boltzmann equation with a solid background. 

Produkt-Details

• Erscheint lt. Verlag: 23.2.2023
• Reihe/Serie: SpringerBriefs in Physics
• Reihe/Serie: SpringerBriefs in Physics
• Zusatzinfo: XIV, 101 p. 20 illus., 16 illus. in color.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Debye-Hückel approach • Dipolar-Poisson-Boltzmann equation • Loop correction • Nonlinear Theory • Surface tension of electrolytes
• ISBN-13: 9783031247828 / 9783031247828