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Carbon nanotubes (CNTs) are tubular structure of a layer or layers of carbon atoms. CNTs serve as a prototypical nanomaterial holding great promises for various basic and applied research applications in the fields of electrical, thermal, and structural materials owing to their superlative mechanical, thermal, electrical, optical, and chemical properties. Since the discovery of CNTs by Iijima in 1991, numerous researches have been conducted to quantify and understand the atomic origin of their high strength, exceptional thermal conductivity, and unique electrical properties. CNTs are also widely used as nanofillers in composite materials to enhance their mechanical properties such as fracture toughness and to serve as sensing agents. There is thus an imperative need to deeply understand the physical properties of CNTs and their responses to various models of deformations such as stretching, bending, twisting, and combinations thereof. In this thesis, we apply all-atom molecular dynamics simulations to study in detail the behavior of several single-walled, armchair CNTs under stretching and bending deformations, realized by imposing appropriate boundary conditions on the CNTs. The simulation results reveal unique scaling properties of the stretching and bending stiffness with respect to the CNT radius and length, which indicate that a single-walled CNT is best modeled as a thin cylindrical shell with a cross-sectional radius equal to the CNT radius and a constant wall thickness much smaller than the CNT radius. By studying the thermal fluctuations of carbon atoms on the CNT wall, the wall thickness is determined to be about 0.45~AA~for all the single-walled CNTs studied in this thesis and correspondingly, Young's modulus is estimated to be about 8.78 TPa for these CNTs. / Master of Science / Carbon atoms are magic building blocks of our world and the basis of life on the earth, and likely in the universe too. They can also form amazing materials with dimensionalities ranging from 0 to 3. For example, carbon atoms can form soccer-ball like spherical structures called fullerenes, with 0 dimensionality. They can also form 1-dimensional tubular structures with only one wall (i.e., one layer of carbon atoms) or multiple walls, called carbon nanotubes (CNTs) that have diameters typically in the nanometer range and lengths as long as 0.5 meter. Carbon atoms also form graphene sheets, which can be regarded as 2-dimensional structures, and 3-dimensional materials including graphite and diamond. In this work, we model CNTs using the molecular dynamics simulation method, where the motion of each atom is resolved and controlled if needed. Specifically, we study CNTs under stretching by fixing one end while pulling the other end in the axial direction, or bending by pulling the middle of a CNT along the radial direction in its cross-section while fixing its two ends. By fitting the simulation results to the continuum mechanics models, we show that a CNT is best described as a thin cylindrical shell with a radius equal to the CNT radius and a wall thickness much smaller than the radius. At the end, the wall thickness of all the CNTs studied here is determined to be about $0.45times 10^{-10}$ meter and their Young's modulus is estimated to be about $8.78times 10^{12}$ Pa, confirming that CNTs are one of the strongest and stiffest materials.

In this dissertation molecular dynamics simulations of behavior of polymer liquid crystals (PLC's) under tensile deformation have been performed. PLC's composed of random or block copolymers of rigid and flexible segments have been studies. Systems of fully flexible chains have been simulated for comparison. Stress-strain relations and fracture mechanics have been investigated.