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Polyimide nanocomposites were prepared with 0 and 1 wt% single wall-and double wall- CNTs (functionalized and non-functionalized) from BPADA and BAPP by refluxing in NMP. These nanocomposites were characterized using FT-IR, TGA, DSC, tensile strength, and Positron annihilation lifetime spectroscopy (PALS). The FT-IR spectra for all the samples showed the characteristic peaks of polyimide. TGA curves showed weight loss with temperature in two stages. The first stage 180-300 °C showed a weight loss of ~ 15% that may be associated with the release of trapped NMP. The second stage 500-750 °C with a drastic weight loss is associated with decomposition. The residual weight is ~ 40% at 750 °C for both pure polyimide and polyimide nano composites made with functionalized single or double wall CNTs. The non-functionalized CNT dispersed polyimide showed similar two-step behavior, but the weight loss is remarkably less and about 80% weight remained at 750 °C. DSC curves of all polyimide samples showed two distinguishable endothermic peaks at around 90 °C (the onset of NMP release) and 200 °C (structural change). PALS was used to study the nano-porosity. Positron lifetime has a correlation with tensile strength showing a decrease in tensile strength with increasing pore size in CNT-polyimide composites.

Positron Annihilation Lifetime Spectroscopy (PALS) is used to study the nanoporosity and fractional free volume in Ultra High Molecular Weight Polyethylene (UHMWPE) and composites with the addition of Martian Regolith (UHMWPE-MR) as-made and irradiated with 56Fe heavy ions at an energy of 600 MeV/u to three different doses (10, 32, 64 Gy). The positron lifetime spectra were obtained using 22Na positron source and the spectra were analyzed to two lifetime components using POSFIT program. First short lifetime component around 0.28 ns is related to positron annihilation in material including vacancy defects and the second long lived component around 1.7 ns is due to Positronium formation in free volume pores. UHMWPE-MR composites were shown to be less porous with much lower nanopores concentration compared to the UHMWPE polymer. The average size of the nanopores is around 0.5 nm (obtained from a simple model). Larger variations in positron lifetime parameters are observed with increasing irradiation dose for UHMWPE polymer compared to UHMWPE+MR composites. The 3-point bend test results also showed larger variations with increasing irradiation dose for the UHMWPE polymer. The variations in PALS parameters may indicate an increasing competition between two processes at higher irradiation doses: 1) vacancy defects aggregation and 2) escape of vacancy defects as the local temperature increases at higher doses resulting in increased vacancy defects mobility. Present results clearly indicate a qualitative inverse relationship between nanoscale porosity measured by positron life time and mechanical properties of UHMWPE and its composite with MR.

The method of upper and lower solutions guarantees the interval of existence of nonlinear differential equations with initial conditions. To compute the solution on this interval, we need coupled lower and upper solutions on the interval of existence. We provide both theoretical as well as numerical methods to compute coupled lower and upper solutions by using a superlinear convergence method. Further, we develop monotone sequences which converge uniformly and monotonically, and with superlinear convergence, to the unique solution of the nonlinear problem on this interval. We accelerate the superlinear convergence by means of the Gauss–Seidel method. Numerical examples are developed for the logistic equation. Our method is applicable to more general nonlinear differential equations, including Riccati type differential equations.