Comparison between the Torquato-Rintoul bounds for the interface effect in composite media and elementary results

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Abstract
We show that the interface effect on the properties of composite media recently proposed by Torquato and Rintoul equally follows from taking the limit in the dipolar polarizability of a coated sphere: the critical values are simply those that make the dipolar polarizability vanish. We also show that the Torquato-Rintoul bounds are either close to the Clausius-Mossotti relation or provide poor estimates. Finally, we notice that their bounds do not agree particularly well with experimental data.
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