03268nam 2200505 450 991073947710332120230522180700.09783031247828(electronic bk.)978303124781110.1007/978-3-031-24782-8(MiAaPQ)EBC7207216(Au-PeEL)EBL7207216(CKB)26183421900041(DE-He213)978-3-031-24782-8(PPN)268206074(EXLCZ)992618342190004120230522d2023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe Poisson-Boltzmann Equation An Introduction /Ralf BlosseyFirst edition.Cham, Switzerland :Springer Nature Switzerland AG,[2023]©20231 online resource (113 pages)SpringerBriefs in Physics SeriesPrint version: Blossey, Ralf The Poisson-Boltzmann Equation Cham : Springer International Publishing AG,c2023 9783031247811 Includes bibliographical references and index.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. .SpringerBriefs in physics.EquationsPoisson's equationEquations.Poisson's equation.512.9Blossey Ralf1424195MiAaPQMiAaPQMiAaPQ9910739477103321The Poisson-Boltzmann Equation3553239UNINA