DYNAMIC ANALYSIS OF SINGLE WALLED CARBON NANOTUBE BASED MASS SENSOR

Abstract

The first reported observation about carbon nanotubes was made by Iijima (1991) for multi-wall carbon nanotubes. It took, however, less than two years before single walled carbon nanotubes were discovered experimentally by Iijima (1993) at the NEC Research Laboratory in Japan and by Bethune at the IBM Almaden Laboratory in California. These experimental discoveries and the theoretical work, which predicted many remarkable properties for carbon nanotubes, launched this field and propelled it forward. The field has been advancing at a breath taking pace ever since with many unexpected discoveries. The real progress in the last decade in nanotechnology has been due to a series of advances in a variety of complementary areas, such as the discoveries of atomically precise materials as nanotubes, fullerenes and the ability of the scanning probe; the development of manipulation techniques to image and manipulate atomic and molecular configurations in real materials; the conceptualization and demonstration of individual electronic and logic devices with atomic or molecular level materials; the advances in the self-assembly of materials to be able to put together larger functional or integrated systems; and above all, the advances in computational nanotechnology, i.e., physics- and chemistry- based modeling and simulation of possible nanomaterials, devices and applications. It turns out that at the nanoscale, devices and systems sizes have shrunk sufficiently small, so that, it is possible to describe their behavior quite accurately. The simulation technologies have become also predictive in nature, and many novel concepts and designs have been first proposed based on modeling and simulations and then were followed by their realization or verification through experiments. The primary objective of this work is to study the dynamic behaviour of single walled carbon nanotubes and focus on their applications as mass sensors. The computational methods employed in this work include: Continuum Mechanics, Finite Element Method and Molecular Structural Mechanics methods. Extended Finite Element Method has also been used to simulate the fracture in single walled carbon nanotube. The analytical formulation comprises of the use of Energy approach along with 4th order Runga Kutta method and Galerkin approach for the solution of equations. First of all, Continuum mechanics approach has been employed to study the effect of mass variations on the single walled carbon nanotube. The effects of different boundary conditions of the CNT on the computed frequencies and mode shapes have been investigated for possible applications of vibrating mass sensors or electromechanical resonators. Cantilever and bridged boundary conditions have been explored for femtograms scale mass. Euler Bernoulli ii principle has been utilized for modeling of a straight and wavy CNT based mass sensor. The excitations are due to the change in mass or as parametric excitations and due to various nanotube defects. The analytical formulation accounts for the cubic nonlinearity induced in the system due to the stretching of the midplane pertaining to the bridged boundary condition and quadratic nonlinearity due to the curvature (waviness) of the nanotube. The combined effects of various parameters like change in length, waviness and mass, for straight and non defective CNTs have been considered and analyzed. To analyze the dynamic behavior of such system, the techniques such as time series, Phase space, Poincare maps and FFT are used. Regions of periodic, sub-harmonic, quasi-periodic and chaotic response of an existing CNT based mass sensing system is observed. It has been observed that the mass sensitivity of single walled carbon nanotubes can reach to 10-21 grams. The effect of length is found to be more considerable as compared to diameter. It is also observed that short carbon nanotubes show more sensitivity to mass variations as compared to longer ones. Super harmonic and sub harmonic responses in the vibration signature have been observed with different levels of mass. The results obtained are also validated with the experimental work available in the literature. The excitations induced in the CNT system due to the presence of defects have been analyzed. A Molecular Structural Mechanics based Atomic Finite Element model consisting of beam elements and point masses has been utilized for modeling of CNTs with chiralities, atomic vacancies and other defects. A continuum mechanics based finite element model has been utilized for modeling of waviness and pinholes in CNT. The vibration responses of wavy doubly clamped CNT subjected to different mass variations have been analyzed. The vibration frequencies resulting from the interaction of defects like waviness and pinholes existing in SWCNT have been explored. It is observed that with the increase in the chiral angle frequency of CNT based mass sensors reduces for lower values of masses and becomes negligible for a mass value greater than 10-5 femtograms. It is seen that the effect of atomic vacancy is maximum when it is nearer to the fixed end. Further, moving of the vacancy to free end results in the negative shift; this means the exciting frequency of defected nanotube is larger than that of perfect one. SWCNTs with pinhole defects are less sensitive to change in diameter as compared to change in length. Lower dimensions of CNT shows more frequency reduction this is due to the fact that for lower dimensions pinhole defect causes more material removal (%) then for higher dimensions CNT. X-FEM is used for crack (fracture) propagation in CNT and contour integral technique is used to calculate the stress intensity factors and J integrals. Crack propagation results shows iii that crack tends to propagate in the same direction as initial one. During the entire analysis half crack length to diameter ratio (c/D) is kept constant. For same length and the diameter more the crack is located towards the loading end higher is the SIF and J-integral. So, if CNT is having a crack near to the loading end the severity is more and more are the chances for crack propagation and CNT breakage. Change in the diameter of CNT affects SIF as well as J integral. Applications of SWCNT based mass sensors have been explored. It has been shown that this type of mass sensing systems can be utilized for monitoring of acetone level in breath for monitoring diabetes. Based on the stiffness variation found between normal and cancerous cell it is revealed that early detection of cancer can be made possible. Apart from the applications in the medicine field, it is shown that this system is also used for sensing mass of gold, silver and chromium atoms. A Molecular structural mechanics approach has been utilized to sense the Zeptogram scale mass of biological objects using chiral SWCNT. The use of carbon nanotube based mass sensors for sensing zeptogram scale mass has been investigated. The shift in the resonant frequency due to the change in the attached mass has been used as a parameter for exploring SWCNT as a bio nano mass sensor. As cantilever configurations are four times more sensitive than bridged configurations, the cantilever boundary conditions have been used in the present study. Three atomically configured chiral Carbon Nanotubes have been used in the analysis. A Molecular structural mechanics based approach and an atomic finite element method is implemented for modeling of SWCNT. A higher frequency shift is observed for (8, 1) type of nanotube with the increase in the attached molecules of both the biological objects. This suggests that the frequency shift is high for lesser values of chiral angle of the nanotube. A greater amount of shift is observed for the molecule of Alanine with Amino terminal residue which has a smaller mass as compared to the DeOxy Adenosine with free residue.