title: When is a conductor not perfect? Sum rules fail under critical fluctuations.
abstract: Perfect screening of all charges characterizes a conductor, a fact embodied in the Stillinger-Lovett sum rule: namely, the charge-charge correlation or structure factor, S(ZZ)(k), varies with momentum transfer k→0 as ξ(D)(2)k(2) where the Debye length ξ(D) is a universal function, √k(B)T/ρq(D)(2), of T and the ion density ρ, with a scaled charge q(D). For a charge-symmetric hard-sphere electrolyte our grand canonical simulations, with a new finite-size scaling device, confirm the Stillinger-Lovett rule except, contrary to current theory, for its failure at criticality. Furthermore, the k(4) term in the S(ZZ)(k) expansion is found to diverge like the compressibility when T→T(c) at ρ(c).
authors.affiliation: Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India.
authors.forename: Subir K
authors.initials: SK
authors.lastname: Das
authors.forename: Young C
authors.initials: YC
authors.lastname: Kim
authors.forename: Michael E
authors.initials: ME
authors.lastname: Fisher