Abstract
We report analytical and numerical studies of surface correlations in finite, homogeneously polarizable, classical Coulomb systems placed in an insulating or conducting environment. Their purpose is to understand the phenomenological, shape-dependent laws of electrostatics, from the point of view of statistical mechanics; we focus on the knowledge of the dielectric susceptibility of the system, a quantity proportional to the equilibrium fluctuation of the system's instantaneous polarization per unit volume. This goal has been achieved for a system in a conducting state. The picture is that the shape-dependent part of the susceptibilities results from the action of unbounded observables (the second moments of the instantaneous polarization of the system) on long-range surface correlations and that the relations of electrostatics are verified by means of shape-dependent thermodynamic limits. This picture is supported (i) by exact solutions and asymptotic analysis of the Debye-Hückel approximation of multicomponent plasmas in disks and spheres with insulating and conducting environment and also in ellipses in a vacuum, and (ii) by computer simulations of a one-component plasma in a disk with different environments, notably a conducting environment with permeable and impermeable wall. These observations have revealed for the first time the reason why the susceptibility of a conducting disk in a conductor with impermeable walls diverges linearly with the radius of the disk: this is due to the occurrence of long-range radial correlations in the conductor. These findings are quantitatively interpreted in terms of a novel “canonical” Debye-Huckel approximation as contrasted to the ordinary “grand canonical” version. Lastly a fresh look at the problem of the surface correlations of a conductor in a vacuum, which places the observer close to the surface of the conductor but in the vacuum, is presented and applied to the disk, the ellipse, the cylinder, the sphere, and the wedge.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ph. Choquard, B. Piller, and R. Rentsch,J. Stat. Phys. 43(1/2):197–205 (1985).
Ph. Choquard, B. Piller, and R. Rentsch,J. Stat. Phys. 46(3/4):599–633 (1986).
Ph. A. Martin,Sum rules in charged fluids, Rev. Mod. Phys. 60(4) (1988).
B. Jancovici,J. Stat. Phys. 28(1):43–65 (1982).
P. Kennedy and T. Federbush,Commun. Math. Phys. 102:361–423 (1985).
B. Jancovici, J. L. Lebowitz, and Ph. A. Martin,J. Stat. Phys. 41(5/6):941–974 (1985).
C. J. F. Böttcher,Theory of Electric Polarization, Vol. 1 (Elsevier, 1973).
J. A. Stratton,Théorie de l'Électromagnétisme (Dunod, Paris, 1961).
B. Jancovici and X. Artru,Mol. Phys. 49(2):487–497 (1983).
N. N. Lebedev,Special Functions and Their Applications (Prentice-Hall, 1965).
B. Jancovici,J. Stat. Phys. 29(2):263–280 (1982).
E. R. Smith,J. Phys. A: Math. Gen. 15:1271–1281 (1982).
D. J. Adams,Mol. Phys. 28:1241–1252 (1974).
D. J. Adams,Mol. Phys. 29:307–311 (1975).
D. Frenkel, inMolecular Dynamics, Simulations of Statistical Mechanical Systems, Proceedings of the International School of Physics “Enrico Fermi” (North-Holland, 1986).
J. P. Valleau and L. K. Cohen,J. Chem. Phys. 72:5935–5941 (1980).
J. P. Valleau, L. K. Cohen, and D. N. Card,J. Chem. Phys. 72:5942–5954 (1980).
W. von Megen and I. Snook,J. Chem. Phys. 73:4656–4662 (1980).
P. J. Forrester,J. Phys. A: Math. Gen. 18:1419–1434 (1985).
P. J. Forrester and E. R. Smith,J. Phys. A: Math. Gen. 15:3861–3868 (1982).
P. M. Morse and H. Feshbach,Methods of Theoretical Physics I and II (McGraw-Hill, 1953).
J. D. Jackson,Classical Electrodynamics (Wiley, 1975).
I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series and Products (Academic Press, 1980).
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Choquard, P., Piller, B., Rentsch, R. et al. Surface properties of finite classical Coulomb systems: Debye-Hückel approximation and computer simulations. J Stat Phys 55, 1185–1262 (1989). https://doi.org/10.1007/BF01041085
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01041085