TY - BOOK ID - 118328590 TI - The Poisson-Boltzmann Equation AU - Blossey, Ralf AU - SpringerLink (Online service) PY - 2023 SN - 9783031247828 PB - Cham Springer International Publishing :Imprint: Springer DB - UniCat KW - Statistical Physics. KW - Electrochemistry. KW - Differential equations. KW - Surfaces (Technology). KW - Thin films. KW - Differential Equations. KW - Surfaces, Interfaces and Thin Film. KW - Films, Thin KW - Solid film KW - Solid state electronics KW - Solids KW - Surfaces (Technology) KW - Coatings KW - Thick films KW - Materials KW - Surface phenomena KW - Friction KW - Surfaces (Physics) KW - Tribology KW - 517.91 Differential equations KW - Differential equations KW - Chemistry, Physical and theoretical KW - Physics KW - Mathematical statistics KW - Surfaces KW - Statistical methods KW - Equations. KW - Poisson's equation. KW - Differential equations, Elliptic KW - Algebra KW - Mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:118328590 AB - 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. . ER -