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Record Nr. |
UNINA9910739477103321 |
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Autore |
Blossey Ralf |
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Titolo |
The Poisson-Boltzmann Equation : An Introduction / / Ralf Blossey |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer Nature Switzerland AG, , [2023] |
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©2023 |
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ISBN |
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9783031247828 |
9783031247811 |
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Edizione |
[First edition.] |
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Descrizione fisica |
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1 online resource (113 pages) |
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Collana |
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SpringerBriefs in Physics Series |
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Disciplina |
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Soggetti |
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Equations |
Poisson's equation |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Derivation of the Poisson-Boltzmann equation -- Generalizations of the Poisson-Boltzmann equation -- Theory and its Confrontation with Experiment. |
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Sommario/riassunto |
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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 |
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