LEADER 03268nam 2200505 450 001 9910739477103321 005 20230522180700.0 010 $a9783031247828$b(electronic bk.) 010 $z9783031247811 024 7 $a10.1007/978-3-031-24782-8 035 $a(MiAaPQ)EBC7207216 035 $a(Au-PeEL)EBL7207216 035 $a(CKB)26183421900041 035 $a(DE-He213)978-3-031-24782-8 035 $a(PPN)268206074 035 $a(EXLCZ)9926183421900041 100 $a20230522d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Poisson-Boltzmann Equation $eAn Introduction /$fRalf Blossey 205 $aFirst edition. 210 1$aCham, Switzerland :$cSpringer Nature Switzerland AG,$d[2023] 210 4$dİ2023 215 $a1 online resource (113 pages) 225 1 $aSpringerBriefs in Physics Series 311 08$aPrint version: Blossey, Ralf The Poisson-Boltzmann Equation Cham : Springer International Publishing AG,c2023 9783031247811 320 $aIncludes bibliographical references and index. 327 $aDerivation of the Poisson-Boltzmann equation -- Generalizations of the Poisson-Boltzmann equation -- Theory and its Confrontation with Experiment. 330 $aThis brief book introduces the Poisson-Boltzmann equation in three chapters that build upon one another, offering a systematic entry to advanced students and researchers. Chapter one formulates the equation and develops the linearized version of Debye-Hückel theory as well as exact solutions to the nonlinear equation in simple geometries and generalizations to higher-order equations. Chapter two introduces the statistical physics approach to the Poisson-Boltzmann equation. It allows the treatment of fluctuation effects, treated in the loop expansion, and in a variational approach. First applications are treated in detail: the problem of the surface tension under the addition of salt, a classic problem discussed by Onsager and Samaras in the 1930s, which is developed in modern terms within the loop expansion, and the adsorption of a charged polymer on a like-charged surface within the variational approach. Chapter three finally discusses the extension of Poisson-Boltzmann theory to explicit solvent. This is done in two ways: on the phenomenological level of nonlocal electrostatics and with a statistical physics model that treats the solvent molecules as molecular dipoles. This model is then treated in the mean-field approximation and with the variational method introduced in Chapter two, rounding up the development of the mathematical approaches of Poisson-Boltzmann theory. After studying this book, a graduate student will be able to access the research literature on the Poisson-Boltzmann equation with a solid background. . 410 0$aSpringerBriefs in physics. 606 $aEquations 606 $aPoisson's equation 615 0$aEquations. 615 0$aPoisson's equation. 676 $a512.9 700 $aBlossey$b Ralf$01424195 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910739477103321 996 $aThe Poisson-Boltzmann Equation$93553239 997 $aUNINA