In the last years more and more interest has been devoted to the study of nanocomposite materials obtained through the addition of inorganic filler with at least one dimension in the scale of nanometer to a polymeric matrix. Continuum-based composite modeling reveals that the enhanced properties are strongly dependent on particular features of the second-phase ‘particles'; in particular, the particle volume fraction Φ and the particle aspect ratio α. A CFD algorithm was used to investigate the transport properties of a system with an impermeable phase dispersed in a polymer matrix; it is a pure diffusion phenomenon of small penetrant molecules in a composite media, simulated from a macroscopic point of view using a finite volume algorithm.

We invoke a simple model developed to describe the permeability in filled polymers; it strives to predict the observed permeability based strictly on tortuosity arguments. The reduction of permeability arises from the longer diffusive path that the pentrants must travel in the presence of the filler.

The simulations are performed on these random geometries at different loading fractions and different aspect ratios in order to have a fairly wide set of data: therefore it shows that the permeability decays as function of the filler volume concentration, all the trends appear similar, the same behavior for different lamella characteristic parameters. As one can see analyzing the data set, there is a clear and unique trend considering α times Φ as the ruling parameter. The permeability decay shows a power law dependence on α Φ scaled with the inverse of the polymeric volume fraction; the exponent seems to have a value in between 1.0, as in Nielsen's model, and 2.0, which is the one in the most famous Cussler's formulation.

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