Nielsen tortuous path model

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 order to explain the permeability of tin-filled polymer systems, the tortuous path model was developed by Nielsen. Particulates are impermeable and are responsible for tortuous diffusion path for gas or water molecules. The efficiency of the fiUer in reducing permeation depends on its concentration, orientation and aspect ratio. If the filler platelets are aligned perpendicularly to the diffusion direction, the Nielsen model can be adequately represented by Equation (12.4) ... 

If the filler particles are substantially impenetrable to a diffusing gas or liquid molecule, then the diffusing molecules must go around the filler particles. This can lead to a very tortuous path for such molecules. Nielsen (89) defined a tor-tuousity factor, t, as the distance a molecule must travel through the film divided by the thickness of the film. This is modeled in Figure 13.33 (89), where L represents the length of the plates, and W the width. 

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