EAN: 9783031247811

Bilder-Quelle: discount24.de - Sport-Freizeit

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 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.

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