Comparison between the Torquato-Rintoul theory of the interface effect in composite media and elementary results

TL;DR

This paper critically examines the Torquato-Rintoul theory of interface effects in composite media, demonstrating that their critical values are elementary and related to dipolar polarizability limits, and finds their bounds often coincide with or are less accurate than classical relations.

Contribution

The paper reveals that the TR interface effect theory is elementary and clarifies the relation of TR bounds to classical models, challenging their claimed novelty and accuracy.

Findings

TR critical values correspond to vanishing dipolar polarizability

TR bounds often match the Clausius-Mossotti relation

TR bounds do not align well with experimental data

Abstract

We show that the interface effect on the properties of composite media recently proposed by Torquato and Rintoul (TR) [Phys. Rev. Lett. 75, 4067 (1995)] is in fact elementary, and follows directly from taking the limit in the dipolar polarizability of a coated sphere: the TR ``critical values'' are simply those that make the dipolar polarizability vanish. Furthermore, the new bounds developed by TR either coincide with the Clausius-Mossotti (CM) relation or provide poor estimates. Finally, we show that the new bounds of TR do not agree particularly well with the original experimental data that they quote.