{"product_id":"the-poissonboltzmann-equation-an-introduction-9783031247811","title":"The Poisson-Boltzmann Equation: An Introduction","description":"\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003e\n\u003cbr\u003eThis book provides a systematic entry to advanced students and researchers into the Poisson-Boltzmann equation, covering the linearized version of Debye-Hückel theory, exact solutions, statistical physics approach, and extension to explicit solvent. It equips graduate students with a solid background to access the research literature on the equation. \u003c\/blockquote\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Paperback \/ softback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 101 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 24 February 2023\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Springer International Publishing AG\u003cbr\u003e\u003c\/p\u003e \u003cp\u003e\u003cbr\u003eThis comprehensive book delves into the Poisson-Boltzmann equation in three interconnected chapters, providing a systematic approach for advanced students and researchers. In Chapter 1, the equation is formulated, and the linearized version of Debye-Hückel theory is developed, along with exact solutions for the nonlinear equation in simple geometries and generalizations to higher-order equations. Chapter 2 introduces the statistical physics perspective, enabling the treatment of fluctuation effects through loop expansion and a variational approach. Detailed applications are explored, including the problem of surface tension in the presence of salt, a classic problem discussed by Onsager and Samaras in the 1930s, which is modernized within the loop expansion framework. Additionally, the adsorption of a charged polymer on a like-charged surface is examined using the variational approach. Chapter 3 concludes by extending Poisson-Boltzmann theory to explicit solvent. This is accomplished in two ways: firstly, through a phenomenological nonlocal electrostatics approach, and secondly, through a statistical physics model that treats solvent molecules as molecular dipoles. This model is then analyzed in the mean-field approximation and the variational method introduced in Chapter 2, rounding up the development of mathematical approaches in Poisson-Boltzmann theory. Upon completing this book, a graduate student will possess a solid foundation to delve into the research literature on the Poisson-Boltzmann equation, enabling them to contribute to the field with expertise.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 191g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 235 x 155 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9783031247811\u003cbr\u003e \u003cstrong\u003eEdition number\u003c\/strong\u003e: 1st ed. 2023\u003c\/p\u003e","brand":"Ralf Blossey","offers":[{"title":"Paperback \/ softback","offer_id":44280911724794,"sku":"9783031247811","price":45.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/noImage_1_ce7f53f6-1e2a-487b-9b9e-0b75f98660d2.jpg?v=1686818121","url":"https:\/\/shulphink.com\/products\/the-poissonboltzmann-equation-an-introduction-9783031247811","provider":"Shulph Ink","version":"1.0","type":"link"}