{"product_id":"9783031247828","title":"The Poisson-Boltzmann Equation: An Introduction","description":"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. \u003cbr\u003eChapter 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. \u003cp\u003e\u003c\/p\u003e  \u003cp\u003e\u003c\/p\u003e","brand":"Springer-Verlag New York, LLC","offers":[{"title":"Default Title","offer_id":46554155286769,"sku":"9783031247828","price":49.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0674\/5433\/7265\/files\/9783031247828_p0.jpg?v=1765561140","url":"https:\/\/shop.barnesandnoble.com\/products\/9783031247828","provider":"Barnes \u0026 Noble","version":"1.0","type":"link"}