The fit of fracture strength data of brittle materials $({\mathrm{Si}}_3{\mathrm{N}}_4,$ SiC, and ZnO) to the Weibull and normal distributions is compared in terms of the Akaike information criterion. For ${\mathrm{Si}}_3{\mathrm{N}}_4,$ the Weibull distribution fits the data better than the normal distribution, but for ZnO the result is just the opposite. In the case of SiC, the difference is not large enough to make a clear distinction between the two distributions. There is not sufficient evidence to show that the Weibull distribution is always preferred to other distributions, and the uncritical use of the Weibull distribution for strength data is questioned.

The barrier properties of polymer-clay nanocomposites, with far less inorganic contents of layered-silicate fillers, are remarkably superior to those of neat polymers or their conventional counterparts. A simple renormalization group model is proposed to assess the influence of geometric factors (such as aspect ratio, orientation, and extent of exfoliation) of layered-silicate fillers on the barrier properties of polymer-clay nanocomposites. The results show that the aspect ratio of exfoliated silicate platelets has a critical role in controlling the microstructure of polymer-clay nanocomposites and their barrier properties. The estimated percolation thresholds of clay content for minimum permeability are in good agreement with experimental data.