Strain energy concentration

At present direct experimental determination of ui is not possible due to CNTs extremely small size. Alternatively, the strain energy can be estimated through molecular mechanics calculations. Owing to the discrete atomic structures of CNTs, we propose strain energy concentration for CNT fracture analysis. The strain energies, Ei, for the nanotube and m, for the crack front C-C bond can be approximately fitted into quadratic functions at small strains, e, such that... 

The total area under the curve A—D, shown as shaded in Figure 1, is the strain energy stored in a body. This energy is not uniformly distributed throughout the material, and it is this inequaUty that gives rise to particle failure. Stress is concentrated around the tips of existing cracks or flaws, and crack propagation is initiated therefrom (Fig. 2) (1). 

The structure of CNTs can be understood as sheets of graphene (i.e. monolayers of sp2 hybridized carbon, see Chapter 2) rolled-up into concentric cylinders. This results in the saturation of part of the dangling bonds of graphene and thus in a decrease of potential energy, which counterbalances strain energy induced by curvature and thus stabilizes the CNTs. Further stabilization can be achieved by saturating the dangling bonds at the tips of the tubes so that in most cases CNTs are terminated by fullerene caps. Consequently, the smallest stable fullerene, i.e. C60, which is - 0.7 nm in diameter, thus determines the diameter of the smallest CNT. The fullerene caps can be opened by chemical and heat treatment, as described in Section 1.5. 

There is related evidence from the studies by Rust (13) on the oxidations of neat 2,3- and 2,4-dimethylpentanes that the strain energy in the five-membered ring is higher than 6.3 kcal. Rust found mainly diperoxy compound from the oxidation of the 2,4-isomer, showing that the internal hydrogen atom abstraction from the y-carbon atom competes favorably (/— 19-fold faster) with external abstraction of a similar hydrogen atom. With estimated A-factors of 1010-8 sec."1 and 108 3 liter/mole-sec., respectively for the internal and external abstractions and an effective liquid phase concentration of tertiary C—H bonds of lOAf, we predict a ratio... 

From this descriptive introduction, it follows that the coherent spinodal decomposition is a continuous transport process occurring in a supersaturated matrix. It is driven by chemical potential gradients. Strain energy and concentration gradient energy have to be adequately included in the component chemical potentials. We expect that the initial stages of decomposition are easier to treat quantitatively than the later ones. The basic result will be the (directional) build-up of periodic variations in concentration [J.W. Cahn (1959), (1961), (1968)]. 

Abstract When subjected to a mechanical loading, the solid phase of a saturated porous medium undergoes a dissolution due to strain-stress concentration effects along the fluid-solid interface. Through a micromechanical analysis, the mechanical affinity is shown to be the driving force of the local dissolution. For cracked porous media, the elastic free energy is a dominant component of this driving force. This allows to predict dissolution-induced creep in such materials. 

Linear and non-linear correlations of structural parameters and strain energies with various molecular properties have been used for the design of new compounds with specific properties and for the interpretation of structures, spectra and stabilities 661. Quantitative structure-activity relationships (QSAR) have been used in drug design for over 30 years 2881 and extensions that include information on electronic features as a third dimension (the electron topological approach, ET) have been developed and tested 481 (see Section 2.3.5). Correlations that are used in the areas of electron transfer, ligand field properties, IR, NMR and EPR spectroscopy are discussed in various other Chapters. Here, we will concentrate on quantitative structure-property relationships (QSPR) that involve complex stabilities 124 289-2911. 

Nonequilibrium conditions may occur with respect to disturbances in the interior of a system, or between a system and its surroundings. As a result, the local stress, strain, temperature, concentration, and energy density may vary at each instance in time. This may lead to instability in space and time. Constantly changing properties cannot be described properly by referring to the system as a whole. Some averaging of the properties in space and time is necessary. Such averages need to be clearly stated in the utilization and correlation of experimental data, especially when their interpretations are associated with theories that are valid at equilibrium. Components of the generalized flows and the thermodynamic forces can be used to define the trajectories of the behavior of systems in time. A trajectory specifies the curve represented by the flow and force components as functions of time in the flow-force space. 

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