Ti-News n. 14 // July 2015 - page 4

Ti news
4
Fig. 1, Source: J. Tronto, A. Cláudia Bordonal, Z. Naal and J. Barros Valim (2013). Conducting Polymers / Layered Double Hydroxides
Intercalated Nanocomposites, Materials Science - Advanced Topics, Prof. Yitzhak Mastai (Ed.), ISBN: 978-953-51-1140-5, InTech,
DOI: 10.5772/54803 - Source: R. K. Bharadwaj, Modeling the Barrier Properties of Polymer-Layered Silicate Nanocomposites, Macro-
molecules 2001, 34, 9189-9192.
A simple model used to describe the permeability of filled polymers is based exactly on this kind
of argument describing the increase in length of the diffusion pathway in terms of a tortuosity
factor (
τ
): the reduction of permeability arises from the longer diffusive path that the penetrant
must travel in the presence of the filler.
A sheet-like morphology as that of clay particles is particularly efficient at maximizing the path
length due to the large length-to-width ratio compared to other shapes of fillers such as spheres
or cubes. The tortuosity factor (
τ
) is defined as the ratio of the actual distance (
d’
) that a penetrant
must travel to the shortest distance (
d
) that it would have traveled in the absence of the filler.
According to equ. (1), the tortuosity factor strongly depends on the length (
L
), width (
W
) of the filler
particles in the direction of the diffusion pathway and, of course, on its volume fraction (
s
) as
Barrier properties of
Clay-Polymer Nanocomposite
Scientific Corner
The effect of tortuosity on the permeability is expressed as
where Ps and Pp represent the permeabilities of the polymer composite and pure polymer,
respectively. From equ. (1) it is obvious that the greatest effect can be achieved if filler particles
of platelet shape of a high aspect ratio such as clay platelets are properly aligned perpendicular
to the direction of diffusion. Oriented in this way, clay platelets increase the barrier properties of
polymers effectively by simply increasing the length of the diffusion path of penetratingmolecules
as illustrated in the figure below.
Although eq. 2 was developed
to model the diffusion in filled
polymers (conventional composites),
it does extremely well in tracking
the
experimental
results
for
relative permeability in polymer-
clay nanocomposites. Treating the
problem as outlined above, the
composite is approximated by a
continuum model which does not require the introduction of a specific ‘‘nano-effect’’. Nevertheless,
nanoscale dimensions of suchfillers are strongly preferred tomaintain high transparency and a smooth
surface. These are properties critical for food packaging applications.
Permeation path imposed by nanoplatelet modification of polymer films.
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