A facile, efficient and environment friendly method is established to prepare poly(vinyl alcohol)(PVA) based graphene oxide-montmorillonite(GO-MMT) nanocomposites in aqueous media. GO-MMT nanohybrid is obtained by the combination of GO and MMT in water without any reducing or stabilizing agents. The formation of GO-MMT nanohybrid is due to the hydrogen bonding and crosslinking effects. The sodium ions within MMT sheets act as crosslinkers between GO sheets and MMT platelets. The resultant nanocomposites are characterized by means of X-ray diffraction(XRD), scanning electron microscopy(SEM), differential scanning calorimetry(DSC), thermogravimetric analysis(TGA) and mechanical testing. Compared to that of pure PVA, PVA nanocomposites show enhanced thermal stabilities and mechanical properties, which results from strong interfacial adhesion of the nanoadditives in PVA matrix. The further increase in the tensile strength and modulus results from strong interaction between PVA chains and layered GO-MMT as well as good mechanical properties of GO-MMT hybrid, compared to PVA/GO and PVA/MMT nanocompsoites. 相似文献
In 1962, Wunderlich published the article “On a developable Möbius band,” in which he attempted to determine the equilibrium shape of a free standing Möbius band. In line with Sadowsky’s pioneering works on Möbius bands of infinitesimal width, Wunderlich used an energy minimization principle, which asserts that the equilibrium shape of the Möbius band has the lowest bending energy among all possible shapes of the band. By using the developability of the band, Wunderlich reduced the bending energy from a surface integral to a line integral without assuming that the width of the band is small. Although Wunderlich did not completely succeed in determining the equilibrium shape of the Möbius band, his dimensionally reduced energy integral is arguably one of the most important developments in the field. In this work, we provide a rigorous justification of the validity of the Wunderlich integral and fully formulate the energy minimization problem associated with finding the equilibrium shapes of closed bands, including both orientable and nonorientable bands with arbitrary number of twists. This includes characterizing the function space of the energy functional, dealing with the isometry and local injectivity constraints, and deriving the Euler–Lagrange equations. Special attention is given to connecting edge conditions, regularity properties of the deformed bands, determination of the parameter space needed to ensure that the deformation is surjective, reduction in isometry constraints, and deriving matching conditions and jump conditions associated with the Euler–Lagrange equations.