Abstract. The Van der Waals and Casimir interactions between graphene and a material plate are studied by using the Lifshitz theory and approximate expressions for the free energy and force. The reflection properties of electromagnetic oscillations on graphene are governed by specific boundary conditions imposed on the infinitely thin positively charged plasma sheet, carrying a continuous fluid with some mass and charge density. The obtained formulas are applied to the cases of a graphene interacting with Au plate. We calculated also the Casimir interaction between carbon nanotube single wall and Au plate. The comparision with other recently obtained theoretical results are made and the generalizations to more complicated carbon nanostructures are discussed.
In 2006, Daniel A. Heller et al. [1] demonstrated that carbon nanotubes (CNNTs) wrapped with DNA can be placed inside living cells and detect trace amounts of harmful contaminants using near infrared light. This discovery could lead to new types of optical sensors and biomarkers at the sub cellular level. The working principle of this optical bio-sensor from DNA and CNNTs can be explained by a simple theoretical model which was introduced in [3]. In this paper, the pH-dependence of DNA and the pH-dependence of solution around CNNTs are shown by using data analysis method. By substituting them into the same model, the pH-dependence of DNA-wrapped CNNTs was elicited in this paper. The range of parameters for workable conditions of this bio-sensor was indicated that the solution should have pH from 6 to 9 and the concentration of ions should be more than a critical value. These results are according to the experimental data and the deduction about pH and salt concentration in solution. They are very useful as using such a new bio-sensor like this in living environment.
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