Book contents
- Frontmatter
- Contents
- List of tables
- Preface
- PRELUDE
- LEVEL 1 INTRODUCTION
- LEVEL 2 PRACTICE
- LEVEL 3 FOUNDATIONS
- L3.1 Story, stance, strategy
- L3.2 Notation used in level 3 derivations
- L3.3 A heuristic derivation of Lifshitz' general result for the interaction between two semi-infinite media across a planar gap
- L3.4 Derivation of van der Waals interactions in layered planar systems
- L3.5 Inhomogeneous media
- L3.6 Ionic-charge fluctuations
- L3.7 Anisotropic media
- Problem sets
- Notes
- Index
L3.6 - Ionic-charge fluctuations
from LEVEL 3 - FOUNDATIONS
Published online by Cambridge University Press: 08 January 2010
- Frontmatter
- Contents
- List of tables
- Preface
- PRELUDE
- LEVEL 1 INTRODUCTION
- LEVEL 2 PRACTICE
- LEVEL 3 FOUNDATIONS
- L3.1 Story, stance, strategy
- L3.2 Notation used in level 3 derivations
- L3.3 A heuristic derivation of Lifshitz' general result for the interaction between two semi-infinite media across a planar gap
- L3.4 Derivation of van der Waals interactions in layered planar systems
- L3.5 Inhomogeneous media
- L3.6 Ionic-charge fluctuations
- L3.7 Anisotropic media
- Problem sets
- Notes
- Index
Summary
Because they have so many unexpected features and because they are kind of a hybrid with electrostatic double-layer forces, ionic-charge-fluctuation forces deserve separate consideration.
In the language of dielectric response, how is one to regard the movement of mobile ions?
First, through conductivity. An applied electric field creates an electric current in a salt solution. Formally, a conductivity σ appears in the form that varies with frequency as ∼ {iσ /[ω (1 − iωτ)]} in the dielectric permittivity ɛ(ω). In the limit of low frequency, ωτ → 0, this diverges as ∼ (iσ/ω). In that limit, a conducting material begins to appear as an infinitely polarizable medium, its mobile charges able to move indefinitely long distances.
In real life, we know this is not necessarily so. An electric field applied to a conducting medium can be maintained only as long as reactions or transfers of charges occur at the walls. The electrical outlet delivers and removes electrons; the electrodes react to remove or to produce ions. In real life we must recognize what goes on at the walls bounding a conducting medium. In the ideal “bad-electrode” limit there is no removing or producing a reaction at the walls. In that limit, under the action of a constant applied electric field, the charges pile up to create electrostatic double layers. When oscillating fields settle down at ω → 0 there is a spatially varying electric field across the space between the bounding walls.
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- Van der Waals ForcesA Handbook for Biologists, Chemists, Engineers, and Physicists, pp. 313 - 317Publisher: Cambridge University PressPrint publication year: 2005