Elastic constants of single-walled carbon nanotubes (SWCNTs) and single-layer graphene sheets (SLGSs) are determined by studying their free vibration characteristics using molecular mechanics (MM) simulations with the MM3 potential and finding their equivalent continuum structures (ECSs). The computational framework has been validated by comparing the presently computed basal plane stiffness and frequencies of radial breathing modes (RBMs) with those available in the literature. We have considered armchair, zigzag and chiral SWCNTs of aspect ratios (length/ diameter in the unloaded relaxed configuration) ranging from 2 to 15. The wall thickness of ECSs of SWCNTs is determined by applying continuum theories, viz., beam, shell and 3D-linear elasticity to ECSs and equating their frequencies with those of SWCNTs obtained from the MM simulations. An expression for the wall thickness of an ECS of a SWCNT in terms of its chiral indices is deduced. The wall thickness of an ECS of a SWCNT is found to increase with an increase in its radius and to saturate at 1.37 Ã for the radius exceeding 15 Ã . Poisson's ratio for zigzag SWCNTs decreses with an increase in the tube radius, but that for armchair SWCNTs exhibits the opposite trend. For the same radius, Poisson's ratio of a chiral SWCNT is slightly more than that for an armchair tube but a little less than that for a zigzag tube. For zigzag SWCNTs, frequencies of inextensional modes of vibration saturate with an increase in the circumferential wave number but those of their ECSs do not. The MM simulations of uniaxial tensile deformations of SLGSs of aspect ratios (length/width) ~ 10 give the basal plane stiffness of ~ 340 N/m. The MM simulations of free vibrations of clamped SLGSs and the analysis of vibrations of their ECSs with a continuum theory gives a wall thickness of ~ 1 Ã for a SLGS. / Ph. D.

Pattern formation in buckled membranes was studied along with the morphology of flowers formed at the tip of silicon nanowires and ripples formed in suspended graphene sheets. Nash's perturbation method was tested for a simple case where initial and final metrics embed smoothly and there is a smooth path from one surface to another and was found to work successfully. The method was tested in more realistic conditions where a smooth path was not known and the method failed. Cylindrical flower-like membranes with a metric of negative Gaussian curvature were simulated in three and four dimensions. These four dimensional flowers had 2 orders of magnitude less energy than their three dimensional counterparts. Simulations were used to show that the addition of a fourth spatial dimension did not relieve all bending energy from the cylindrical membranes. Patterns formed at the tip of silicon nanowires were studied and found to be of the Dense Branching Morphology type. The rate of branching is dependent on the curvature of the gold bubble on which they are grown. Graphene was simulated using the modified embedded atom method potential and buckles were found to form if the carbon bonds were stretched. An energy functional was found for the energy of a sheet with a metric different from that of flat space. / text

The main objective of the research is to study the potential application of carbon nanotubes and graphene sheets as nano-resonator sensors in the detection of atoms/molecules with vibration and wave propagation analyses. It is also aimed to develop and examine new methods in the design of nano-resonator sensors for differentiating distinct gas atoms and different macromolecules, such as DNA molecules. The hypothesis in the detection techniques is that atoms or molecules attached on the surface of the nano-resonator sensors would induce a recognizable shift in the resonant frequency of or wave velocity in the sensors. With this regard, a sensitivity index based on the shift in resonant frequency of the sensors in the vibration analysis and/or a shift in wave velocity in the sensors in the wave propagation analysis is defined and examined. In order to achieve the objective, the vibration characteristics of carbon nanotubes and graphenes are studied using molecular dynamics simulations to first propose nano-resonator sensors, which are able to differentiate distinct gas atoms with high enough resolutions even at low concentration. It is also indicated that the nano-resonator sensors are effective devices to identify different genes even with the same number of nucleobases in the structure of single-strand DNA macromolecules. The effect of various parameters such as size and restrained boundary conditions of the sensors, the position of attached atoms/molecules being detected, and environment temperature on the sensitivity of the sensors is investigated in detail. Following the studies on vibration-based sensors, the wave propagation analysis in carbon nanotubes and graphene sheets is first investigated by using molecular dynamics simulations to design nano-resonator sensors. Moreover, a nonlocal finite element model is presented and calibrated for the first time to model propagation of mechanical waves in graphene sensors attached with atoms through a verification process with atomistic results. The simulation results reveal that the nano-resonator sensors are able to successfully detect distinct types of noble gases with the same mass density or at the same environmental condition of temperature and pressure.

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We developed a multiscale approach to explore the effective thermal conductivity of polycrystalline graphene sheets. By performing equilibrium molecular dynamics (EMD) simulations, the grain size effect on the thermal conductivity of ultra-fine grained polycrystalline graphene sheets is investigated. Our results reveal that the ultra-fine grained graphene structures have thermal conductivity one order of magnitude smaller than that of pristine graphene. Based on the information provided by the EMD simulations, we constructed finite element models of polycrystalline graphene sheets to probe the thermal conductivity of samples with larger grain sizes. Using the developed multiscale approach, we also investigated the effects of grain size distribution and thermal conductivity of grains on the effective thermal conductivity of polycrystalline graphene. The proposed multiscale approach on the basis of molecular dynamics and finite element methods could be used to evaluate the effective thermal conductivity of polycrystalline graphene and other 2D structures.

In recent years, increased use of electronic devices and wireless operations resulted in unavoidable electromagnetic (EM) pollution which has a significant impact on civil and military sectors. Considering the foremost requirement, huge efforts were invested in the development of electromagnetic interference (EMI) shielding materials. In this context, metals are usually preferred but design complexities like high density and susceptibility towards corrosion are limiting factors; additionally, the reflection of microwaves from the surface fails to serve as EM absorbers. The concern here is to minimize the reflection of the high frequency electromagnetic wave from the surface and to enhance the microwave absorption in GHz frequencies. In this thesis, we have made an attempt to design EMI shielding materials with exceptional absorption ability derived from Polycarbonate (PC)/ Poly styrene-co-acrylonitrile (SAN) based polymer blends. Herein, unique co-continuous micro-phase separated blend structures with selective localization of microwave active nanoparticles in one of the phases were realized to be most effective for microwave attenuation over just dispersing it in one polymer matrix (i.e. PC and SAN composites). The synergistic attenuation of electric and magnetic field associated with EM radiation was achieved through incorporation of various magnetic nanoparticles, however, dispersion of magnetic nanoparticles was a challenging task. Therefore, in order to localize magnetic nanoparticles in PC phase of the blends and to enhance the dispersion state, various modification strategies have been designed. In summary, we have developed a library of engineered nanoparticles to achieve synergistic attenuation of EM radiation mostly through absorption. For instance, the PC/SAN blends containing MWNTs and rGO-Fe3O4 nanoparticles manifested in exceptional EMI shielding, well above required shielding effectiveness value for most of the commercial applications, essentially through absorption. Taken together, the finding suggests that immiscible blends containing MWNTs and the decoration of magnetic nanoparticles (rGO-Fe3O4) on the surface of reduced graphene oxide sheets can be utilized to engineer high-performance EMI shielding materials with exceptional absorption ability.