ABSTRACT
Global organization of three-dimensional (3D) Lagrangian chaotic transport is difficult to infer without extensive computation. For 3D time-periodic flows with one invariant, we show how constraints on deformation that arise from volume-preservation and periodic lines result in resonant degenerate points that periodically have zero net deformation. These points organize all Lagrangian transport in such flows through coordination of lower-order and higher-order periodic lines and prefigure unique transport structures that arise after perturbation and breaking of the invariant. Degenerate points of periodic lines and the extended 3D structures associated with them are easily identified through the trace of the deformation tensor calculated along periodic lines. These results reveal the importance of degenerate points in understanding transport in one-invariant fluid flows.
ABSTRACT
The kinetics of liquid solvent sorption in polymeric systems and their nanocomposites often deviate from normal Fickian behaviour. This needs to be understood and interpreted, in terms of their underlying mechanistic origins. In the present study, the results of time dependent toluene sorption measurements in model segmented polyurethane-urea/clay nanocomposites have been analysed at room temperature. The studies revealed pronounced S-shaped sorption curves and unusually higher swelling of the nanocomposites compared to the neat polyurethane-urea matrix. Dynamic mechanical analysis (DMA) and small angle X-ray scattering (SAXS) measurements on the nanocomposites in the dry and liquid toluene saturated state have been carried out. The DMA studies revealed a significant decrease in the α relaxation temperature and storage modulus of the nanocomposites in the swollen state compared to the dry samples. The SAXS results showed that the nanoclay dispersion morphology transformed from intercalation in the dry state to exfoliation in the swollen state and the interdomain distance between hard segments increased upon swelling. Thermodynamic analysis of the Flory-Huggins interaction parameter (χ) of nanocomposite/toluene systems revealed increasingly negative χ values with increased clay loading. These results imply a significant plasticization effect of toluene on the nanocomposites. An interpretation of these data, which relates the abovementioned results, is presented in the framework of differential swelling stress (DSS) induced deviation from Fickian transport characteristics. We expect that these findings and methods may provide new insight into the analysis of the solvent diffusion process in heterogeneous polymers and their nanocomposites.
ABSTRACT
There has been an increasing recognition of the fact that purely geometric factors associated with clay platelet dispersion in a polymer matrix cannot adequately explain the barrier properties of polymer/clay nanocomposites. The objective of the present work is to understand the nanoclay induced structural changes in a polyurethane-urea matrix and clay dispersion at different length scales using segment-specific characterization techniques and implications of the same in gas barrier properties using He, N2 and CO2 as probe molecules. Wide angle X-ray diffraction (WAXD) and positron annihilation life time spectroscopy (PALS) studies revealed nanoclay induced alterations in the chain packing of the amorphous soft segments of the polyurethane matrix at a molecular scale of a few Angstroms. The hard segment organization and the phase morphology of the nanocomposites, spanning length scales of several nanometers, were investigated by small angle X-ray scattering (SAXS), scanning electron microscopy (SEM) and atomic force microscopy (AFM). Furthermore, the presence of a constrained amorphous region surrounding the nanoclay was confirmed from AFM, WAXD and PALS results. Several pertinent structural variables from the gas transport point of view were deduced from these characterization techniques to understand the effect of the barrier properties in tandem with the clay dispersion morphology.
