Influence of Aspect Ratio on Barrier Properties of Polymer-Clay Nanocomposites

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.

Figure 1

Schematic of exfoliated clay morphologies of PCNs, where inset (a) shows the state of intercalation and inset (b) is a simple tortuosity-based model to describe the gas/liquid permeability in filled polymers. Note the concentration of clay is much lower than that shown in the sketch.

Figure 2

An $n$-order cell is shown as a simple cube with its corners representing eight constitutive ($n-1$)-order elements. Each corner is marked by a solid dot when the corresponding ($n-1$)-order element acts as a barrier. There are 22 different topological configurations labeled 0, 1, 2a,…, 8, with their multiplicities given in parentheses. Of all $2^8=256$ combinations, there are 81 cases in which the silicate platelets act as barriers (and these are highlighted in bold letters below the relevant configurations).

Figure 3

Illustration of two typical topologies referenced to Fig. 2: (a) represents case 4c in which the gas/liquid molecules can easily pass through the matrix; and (b) is for case 4d, where the silicate platelets (marked in gray color) act as barriers.

Figure 4

Critical volume fraction ${\varphi }_c$ versus aspect ratio $L/W$ of silicate platelets with $S=0$. Thresholds for several typical clay fillers are obtained directly from Eq. (4) based on their aspect ratios [3] (open symbols). Two solid symbols indicate the test data of ${\mathrm{O}}_2$ gas permeability in ${\mathrm{C}}_{18}$-montmorillonite ($L/W=150$ and ${\varphi }_c=1.25\%$ [5]) and polyester-clay ($L/W\approx 200$, ${\varphi }_c=1.4\%$ [6]) nanocomposites. There is good agreement with the theoretical curve.

Figure 5

Critical volume fraction ${\varphi }_c$ versus orientation $S$ of silicate platelets with $L/W=100$. The insets are three typical patterns of silicate platelets in a polymer matrix for cases of $S=-1/2$, 0, and 1, respectively.