Generalizing the Debye-Huckel equation in terms of density functional integral

Details Generalizing the Debye-Huckel equation in terms of density functional integral Generalizing the Debye-Huckel equation in terms of density functional integral

2000-04-12

arxiv.org/abs/cond-mat/0004193v2

Physics

Condensed Matter

Soft Condensed Matter

5 pages, RevTex, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.61.R6079

We discuss the validity of generalized Debye-H\"uckel (GDH) equation proposed by Fisher {\itshape et al.} from the functional integral point of view. The GDH theory considers fluctuations around prescribed densities of positive and negative charges. Hence we first formulate a density functional integral expression for the canonical system of Coulomb gas, and also demonstrate that this is a dual form to the Sine-Gordon theory. Our formalism reveals the following: (i) The induced charge distribution around supposed density favors not only the cancellation of additional electrostatic potential like the original DH theory, but also the countervailing of chemical potential difference between imposed and equilibrium value. (ii) As a consequence apparent charge, absent in the GDH equation, comes out in our generalized equation. (iii) That is, the GDH equation holds only in special cases.

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