Rapid and enhanced functionalization of MWCNTs in a dielectric barrier discharge plasma in presence of diluted CO<Subscript>2</Subscript>

Multiwalled carbon nanotubes (MWCNTs) have been functionalized in dielectric barrier discharge (DBD) plasma in presence of a mixture of carbon dioxide and a diluent gas at room temperature and atmospheric pressure. He, Ar, and N₂ were examined as the diluent gases. Temperature-programmed desorption was used to investigate the influence of various plasma parameters and type of diluent gas as well as the amount of diluent in the plasma gas. It is found that the quantity of functional groups on the surface of MWCNTs is a maximum when He is used as diluent gas. It also passes through a maximum when He content is 60%. The presence of He improves the reactivity of the plasma, which leads to an increase in the quantity of functional groups. However, high percentages of He decrease the CO₂ content, which in turn decreases the number of functional groups. FTIR and Raman spectroscopy showed the presence of Oxygen-containing functional groups on MWCNTs surfaces.     

Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials

In this article we propose a numerical scheme to solve the pantograph equation. The method consists of expanding the required approximate solution as the elements of the shifted Chebyshev polynomials. The Chebyshev pantograph operational matrix is introduced. The operational matrices of pantograph, derivative and product are utilized to reduce the problem to a set of algebraic equations. An error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results.