Series of polymer nanocomposites films consisting of pretreated multiwalled carbon nanotubes (PT-MWCNTs) and poly (vinyl alcohol) (PVA) were prepared at room temperature. The MWCNTs were initially pretreated with 1.0 M sulfuric acid (PT-MWCNTs) and then allowed to disperse in aqueous solutions at different pH values (2–14). It was found that the dispersion of the PT-MWCNTs is a pH dependent. The best PT-MWCNTs dispersion was obtained at pH = 10. Films of PT-MWCNTs/PVA, at this optimum pH-value, were then prepared by casting technique at different PT-MWCNTs weight fractions. The resulted PT-MWCNTs/PVA films were characterized through the direct visualization, Fourier transform infrared, and morphology test. Besides, current–voltage and direct current electrical conductivity for PT-MWCNTs/PVA nanocomposites at 60°C showed that the conductivity mechanism was ohmic and the percolation threshold was around 0.8 wt% PT-MWCNTs. Optical results showed that PT-MWCNTs are homogeneously distributed in the neat PVA and optical gap is significantly decreased from 4.40 to 2.96 eV.

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The solution of the complex neutron diffusion equations system of equations in a spherical nuclear reactor is presented using the homotopy perturbation method (HPM); the HPM is a remarkable approximation method that successfully solves different systems of diffusion equations, and in this work, the system is solved for the first time using the approximation method. The considered system of neutron diffusion equations consists of two consistent subsystems, where the first studies the reactor and the multi-group subsystem of equations in the reactor core, and the other studies the multi-group subsystem of equations in the reactor reflector; each subsystem can deal with any finite number of neutron energy groups. The system is simplified numerically to a one-group bare and reflected reactor, which is compared with the modified differential transform method; a two-group bare reactor, which is compared with the residual power series method; a two-group reflected reactor, which is compared with the classical method; and a four-group bare reactor compared with the residual power series.

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