1.

Record Nr.

UNINA9910739477103321

Autore

Blossey Ralf

Titolo

The Poisson-Boltzmann Equation : An Introduction / / Ralf Blossey

Pubbl/distr/stampa

Cham, Switzerland : , : Springer Nature Switzerland AG, , [2023]

©2023

ISBN

9783031247828

9783031247811

Edizione

[First edition.]

Descrizione fisica

1 online resource (113 pages)

Collana

SpringerBriefs in Physics Series

Disciplina

512.9

Soggetti

Equations

Poisson's equation

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Derivation of the Poisson-Boltzmann equation -- Generalizations of the Poisson-Boltzmann equation -- Theory and its Confrontation with Experiment.

Sommario/riassunto

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. .