Surface Tension of an Ideal Dielectric - Electrolyte Boundary: Exactly Solvable Model

Details Surface Tension of an Ideal Dielectric - Electrolyte Boundary: Exactly Solvable Model Surface Tension of an Ideal Dielectric - Electrolyte Boundary: Exactly Solvable Model

2001-01-04

arxiv.org/abs/cond-mat/0101044v1

J.Statist.Phys. 103 (2001) 737-752

Physics

Condensed Matter

Statistical Mechanics

17 pages, Latex

Scientific paper

The model under consideration is a semi-infinite two-dimensional two-component plasma (Coulomb gas), stable against bulk collapse for the dimensionless coupling constant $\beta<2$, in contact with a dielectric wall of dielectric constant $=0$. The model is mapped onto an integrable sine-Gordon theory with a ``free'' Neumann boundary condition. Using recent results on a reflection relationship between the boundary Liouville and sine-Gordon theories, an explicit expression is derived for the surface tension at a rectilinear dielectric -- Coulomb gas interface. This expression reproduces the Debye-H\"uckel $\beta \to 0$ limit and the exact result at the bulk collapse border, the free-fermion point $\beta =2$, where the surface tension keeps a finite value. The surface collapse, identified with the divergence of the surface tension, occurs at $\beta =3$.

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