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The poisson-boltzmann equationan introduction /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The poisson-boltzmann equationby Ralf Blossey.
Reminder of title:	an introduction /
Author:	Blossey, Ralf.
Published:	Cham :Springer International Publishing :2023.
Description:	xiv, 101 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Poisson's equation.
Online resource:	https://doi.org/10.1007/978-3-031-24782-8
ISBN:	9783031247828$q(electronic bk.)

The poisson-boltzmann equationan introduction /
Blossey, Ralf.

The poisson-boltzmann equationan introduction /[electronic resource] :by Ralf Blossey. - Cham :Springer International Publishing :2023. - xiv, 101 p. :ill., digital ;24 cm. - SpringerBriefs in physics,2191-5431. - SpringerBriefs in physics..

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

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.

ISBN: 9783031247828$q(electronic bk.)

Standard No.: 10.1007/978-3-031-24782-8doiSubjects--Topical Terms:

947281
Poisson's equation.

LC Class. No.: QA377 / .B56 2023

Dewey Class. No.: 515.352

The poisson-boltzmann equationan introduction /
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245 1 4 $a The poisson-boltzmann equation $h [electronic resource] : $b an introduction / $c by Ralf Blossey.
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505 0 $a Derivation of the Poisson-Boltzmann equation -- Generalizations of the Poisson-Boltzmann equation -- Theory and its Confrontation with Experiment.
520 $a 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.
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