EAN: 9783031247811

SPRINGERBRIEFS IN PHYSICS THE POISSON-BOLTZMA...

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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