In this paper, two different approaches for modeling the behaviour of carbon nanotubes are presented. The first method models carbon nanotubes as an inhomogeneous cylindrical network shell using the asymptotic homogenization method. Explicit formulae are derived representing Young's and shear moduli of single-walled nanotubes in terms of pertinent material and geometric parameters. As an example, assuming certain values for these parameters, the Young's modulus was found to be 1.71 TPa, while the shear modulus was 0.32 TPa. The second method is based on finite element models. The inter-atomic interactions due to covalent and non-covalent bonds are replaced by beam and spring elements, respectively, in the structural model. Correlations between classical molecular mechanics and structural mechanics are used to effectively model the physics governing the nanotubes. Finite element models are developed for single-, double-and multi-walled carbon nanotubes. The deformations from the finite element simulations are subsequently used to predict the elastic and shear moduli of the nanotubes. The variation of mechanical properties with tube diameter is investigated for both zig-zag and armchair configurations. Furthermore, the dependence of mechanical properties on the number of nanotubules in multi-walled structures is also examined. Based on the finite element model, the value for the elastic modulus varied from 0.9 to 1.05 TPa for single and 1.32 to 1.58 TPa for double/multi-walled nanotubes. The shear modulus was found to vary from 0.14 to 0.47 TPa for single-walled nanotubes and 0.37 to 0.62 for double/multi-walled nanotubes.
Using molecular dynamics simulations with a reactive force field (ReaxFF), we generate models of amorphous carbon (a-C) at a wide range of densities (from 0.5 g/cc to 3.2 g/cc) via the "liquid-quench" method. A systematic study is undertaken to characterize the structural features of the resulting a-C models as a function of carbon density and liquid quench simulation conditions: quench rate, type of quench (linear or exponential), annealing time and size of simulation box. The structural features of the models are investigated in terms of pair correlation functions, bond-angles, pore-size distribution and carbon hybridization content. Further, the influence of quench conditions on hybridization/graphitization is investigated for different stages of the simulation. We observe that the structural features of generated a-carbon models agree well with similar models reported in literature. We find that in the low-density regime, 2 effects play an important role in determining the pore size distribution and the structures are predominantly anisotropic. Whereas, at densities larger than 1.0 g/cc, the structures are spacefilling and differences exist only in terms of carbon hybridization. The rate of structural evolution (pore size and hybridization) during the quench process is observed to be dependent on the quench type, rate and the annealing time. IntroductionCarbon shows remarkable versatility since it exists in various chemical and structural forms. On one hand, crystalline and ordered phases such as graphene, diamond, carbon nanotubes, etc., confer an extraordinary range of properties. On the other, equally important is the plethora of amorphous structures of carbon (denoted as a-C and alternately referred to as disordered carbon) existing in a wide range of densities ranging from low-density, char-like carbon to high-density diamond-like and tetrahedral amorphous carbon (denoted as ta-C [1]), with varied structural and chemical features. Correspondingly, this confers a-C with a wide variety of properties and applications, ranging from low-conductivity heat-shield ablators [2,3] in the low-density regime, to high-hardness, chemically inert and optically transparent coatings [4,5], magnetic storage applications [6] among others [5] for diamond-like amorphous carbon films.The term "amorphous carbon" can be attributed as an umbrella term to carbon at a large range of densities ranging from char-like carbon (~ 0.2 to 0.5 g/cc [3]) to high-density, diamond-3 like carbon (~3.2 g/cc [5]). Since there is no well-defined order for amorphous carbon, it has been a challenge to characterize and fully understand their structure [7]. It is in this regard that models of a-C structure generated by computer simulation techniques become very useful in understanding complex structure-property relations and optimize desired properties.
Motivated by the need to develop a spatially resolved theory of irradiation-induced microstructure evolution in metals, we present a phase field model for void formation in metals with vacancy concentrations exceeding the thermal equilibrium values. This model, which is phenomenological in nature, is cast in the form of coupled Cahn–Hilliard and Allen–Cahn type equations governing the dynamics of the vacancy concentration field and the void microstructure in the matrix, respectively. The model allows for a unified treatment of void nucleation and growth under the condition of random generation of vacancies, which is similar to vacancy generation by collision cascade in irradiated materials. The basic features of the model are illustrated using two-dimensional solutions for the cases of void growth and shrinkage in supersaturated and undersaturated vacancy fields, void–void interactions, as well as the spontaneous nucleation and growth of a large population of voids.
Mesoscale computer simulations are used to study the effective thermal conductivity of two-dimensional polycrystalline model microstructures containing finely dispersed stationary voids. The microstructural evolution is captured by phase-field modeling in which the competing mechanisms of curvature-driven grain-boundary (GB) migration and Zener pinning due to the void/grain-boundary interactions control the grain-growth kinetics. We investigate porosity fractions between 0% and 8% by systematically increasing the number of voids in the simulation cell. The temperature distribution throughout the microstructure at progressive instances in time is calculated by solving the solid-state heat-conduction equation. The thermal conductivity of each grid point is assigned a value according to the microstructural feature it represents (grain interiors, GBs, and voids) as determined by the phase-field order parameters. The effective conductivities of the microstructures are analyzed with respect to average grain size as well as porosity fraction, and good agreement with theoretical models is obtained.
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