The tortuous path model for barrier in nanocomposites

The barrier properties of a number of polymer-clay nanocomposites can be predicted reasonably well by a simple tortuous path model first proposed by Nielsen [1]. In the simple two-dimensional model, the clay nanoparticles act as impermeable barriers to the migration of gas molecules. The equation for the model is  

In this model the interaction between the clay and polymer is assumed to be minimal and the plates are in a perfectly tiled arrangement parallel to the surface of the polymer film. The Lj2W term for aspect ratio is derived from the assumption that the morphology of the clay particle s cross-section is a rectangle. 

It is clear from much of the data presented in previous chapters that in the range of 5% clay loadings is the point of diminishing return in mechanical performance improvements for thermoplastics. Although the aspect ratio strongly affects the relative permeability, it is also important to look at the effect of clay loading. 

1000 aspect ratio composite reaches the point of diminishing return at low loadings of 2 to 3 wt.%. The 150 aspect ratio does not start leveling off until above 7 wt.%. It would appear that for most clays, the practical limit of loading will be determined by factors such as film clarity, or physical properties such as impact resistance. 

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