{"product_id":"the-poisson-boltzmann-equation-von-ralf-blossey","title":"The Poisson-Boltzmann Equation","description":"\n                                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. \n                \n                \u003cbr\u003e\n                                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. \n                \n                \u003cp\u003e\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e\u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031247811\"\u003e\u003ch3\u003eAn Introduction\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783031247811","offer_id":40940376293469,"sku":"9783031247811","price":58.84,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/2aba158b-7caa-4893-8698-81ff2bbda7d6.jpg?v=1775795971","url":"https:\/\/shop.autorenwelt.de\/en\/products\/the-poisson-boltzmann-equation-von-ralf-blossey","provider":"Autorenwelt Shop","version":"1.0","type":"link"}