The Poisson-Boltzmann Equation: An Introduction

This book provides a systematic entry to advanced students and researchers into the Poisson-Boltzmann equation, covering the linearized version of Debye-Hückel theory, exact solutions, statistical physics approach, and extension to explicit solvent. It equips graduate students with a solid background to access the research literature on the equation.

Format: Paperback / softback
Length: 101 pages
Publication date: 24 February 2023
Publisher: Springer International Publishing AG

This comprehensive book delves into the Poisson-Boltzmann equation in three interconnected chapters, providing a systematic approach for advanced students and researchers. In Chapter 1, the equation is formulated, and the linearized version of Debye-Hückel theory is developed, along with exact solutions for the nonlinear equation in simple geometries and generalizations to higher-order equations. Chapter 2 introduces the statistical physics perspective, enabling the treatment of fluctuation effects through loop expansion and a variational approach. Detailed applications are explored, including the problem of surface tension in the presence of salt, a classic problem discussed by Onsager and Samaras in the 1930s, which is modernized within the loop expansion framework. Additionally, the adsorption of a charged polymer on a like-charged surface is examined using the variational approach. Chapter 3 concludes by extending Poisson-Boltzmann theory to explicit solvent. This is accomplished in two ways: firstly, through a phenomenological nonlocal electrostatics approach, and secondly, through a statistical physics model that treats solvent molecules as molecular dipoles. This model is then analyzed in the mean-field approximation and the variational method introduced in Chapter 2, rounding up the development of mathematical approaches in Poisson-Boltzmann theory. Upon completing this book, a graduate student will possess a solid foundation to delve into the research literature on the Poisson-Boltzmann equation, enabling them to contribute to the field with expertise.

Weight: 191g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031247811
Edition number: 1st ed. 2023