The fractal model of mechanical stress transfer in nanocomposites polyure-thane/carbon nanotubes

G.V. Kozlov, I.V. Dolbin


The transfer of applied mechanical stress from polymer matrix to nanofiller and? Hence, a properties of nanocomposites polymer/carbon nanotubes are defined by structure of aggregates (ring-like formations) of nanofiller, treated within the frameworks of fractal analysis.In this communication effect of structure of nanofiller (carbon nanotubes) on transfer of applied to sample mechanical stress from polymer matrix to nanofiller was considered on exam-ple of nanocomposites polyurethane/carbon nanotubes. It was postulated that carbon nanotubes are formed in polymer matrix of nanocomposite ring-like formations, which are structural ana-logue of macromolecular coils of branched polymer chains and specific type of aggregation for carbon nanotubes in virtue of their low transverse stiffness and high anisotropy degree. Indicated formations structure can be characterized most precisely and physically strictly by its fractal di-mension. It has been found, that transfer of mechanical stress in nanocomposite deteriorates at enhancement of indicated fractal dimension and at reaching of this dimension of value of pa-rameter for surrounding Euclidean space nanofiller losses ability to reinfore matrix polymer ow-ing to absence of mechanical stress transfer between its components. Thickness of interfacial layer in polymer nanocomposite is structural characteristic, defining efficiency of applied me-chanical stress transfer. The using of alternative methodics for determination of radius of ring-like formations of carbon nanotubes shows enhancement of their number per one indicated formation at increasing of nanofiller contents. This effect results also to enhancement of fractal dimension of ring-like formation of carbon nanotubes. By analogy with “permeable” macromolecular coils of polymer chains this type of aggregation of carbon nanotubes is realized at fractal dimension of their for-mations of 1.50 and more. Indicated analogue application allows to estimate the Flory-Huggins interaction parameter, which proves to be higher essentially in comparison with polymer macro-molecules.

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