Abstract. We study a frequency-dependent continuum model equation for electrostatics at the nano scale. It is motivated by the need to incorporate accurately the influence of dielectric correlations which are of the same length scale as the electrostatic fluctuations in protein–water systems. The model is based on a single parameter, a length scale for changes in the dielectric response, that is physically relevant. This parameter reflects the changes in the dielectric medium caused by local structuring of the molecules. We present three independent quantitative assessments of the model, including one in which the dielectric field is changing in time. The assessments involve modeling the local structuring of dielectrics around individual ions, explaining solvation of carbon nano-tube interiors and predicting accurately the electrostatic energy of ions in a carbon nano-tube. The latter involves comparing the frequency-dependent model equation directly with molecular dynamics simulations with explicit solvent. The model equation cannot be written as a differential equation but rather takes the form of a more general Fourier integral operator. It involves a non-local relationship between the polarization field and the electric field.

PACS numbers: 87.15.Aa, 41.20.Cv, 83.10.−y

Print publication: Issue 41 (15 October 2004)
Received 12 May 2004, in final form 22 July 2004
Published 29 September 2004