Curvature induced

Fig. 4.4 Molecular model of (a) surface containing positive and negative curvature induced by a pentagon (red) and a heptagon (blue), respectively (b) molecular model of 5-7 defects (yellow) and a Thrower-Stone-Wales defect (green) [82] (c) high-resolution transmission electron microscopy (HRTEM) images of bond rotations V2 (555-777) divacancy, and (d) V2(5555-6-7777) divacancy within graphene scale bar is 1 nm [75].

Emulsilication through phase inversion is based on a change in the surfactant spontaneous curvature induced by temperature. This concept can be generalized considering any parameter influencing the spontaneous curvature of a surfactant, for example, salinity, pH, presence of a cosurfactant, and nature of the oil. The concept of inversion has often been reported in the literature by means of a formulation-composition map. In the following, we shall sum up this empirical approach which can be useful for formulators. 

Sasaki K, Saito R, Dresselhaus G, Dresselhaus MS, Farhat H, Kong J (2008) Curvature-induced optical phonon frequency shift In metallic carbon nanotubes. Phys Rev B 77(24) 245441... 

Due to their larger diameters, MWCNTs experience smaller curvature-induced strain on the C=C bonds. Thus, the resistance to oxidation increases, leading to higher activation energies and oxidation temperatures compared to SWCNTs and DWCNTs. In order to determine the temperature range for the oxidation of the... 

Figure 9.30 In (a), gas diffuses from small bubbles to large ones because of a curvature-induced difference in chemical potential. For a similar reason, in (b), gas diffuses across a curved film. (From Durian, MRS Bulletin, April 1994, reprinted with permission.)...

This idea can be illustrated in schematic form through the example of the motion of a single curved interface in two dimensions under the action of curvature-induced forces. For convenience, we will represent the interface as a function (rather than via a discrete set of parameters as in the discussion of the variational principle above) of a parameter s as r(x). In this case, the rate of change of Gibbs free energy is given by... 

Not surprisingly, this equation of motion implies the curvature-induced shrinkage of the particle. 

Bicerano et al. (1999) provide a simplified scaling viscosity model for particle dispersions that states the importance of the shear conditions, the viscosity profile of the dispersing fluid, the particle volume fraction and the morphology of the filler in terms of its aspect ratio, the length of the longest axis and the minimum radius of curvature induced by flexibility. 

Higher fuUerenes are by far less abound than the archetypical compound 50. The formation of these cage-like compounds is kineticaUy controUed among the fuUerenes, is by no means the molecule with the least enthalpy per carbon atom. Normally the larger, thermodynamically more stable homologs (refer to Section 2.4) should be more abundant than 50 with its higher curvature-induced... 

An interesting question that arises in this connection is the relationship between the Bergman metric ds2B and the Poincare metric ds2p of constant negative curvature induced from the standard metric on H ... 

Atomistically, both mechanisms entail the diffusion of ions from the grain boundary region toward the neck area, for which the driving force is the curvature-induced vacancy concentration. Because there are more vacancies in the neck area than in the region between the grains, a vacancy flux develops away from the pore surface into the grain boundary area, where the vacancies are eventually annihilated. Needless to say, an equal atomic flux will diffuse in the opposite direction, filling the pores. 

Another point of view is to consider the space-time curvature induced by the rest mass mo of the electron outside a volume of radius rq. According to general relativity theory, the curvature radius Rg around the electron would be given by [18,19] ... 

Recently, a quantitative analysis of the Raman spectra of such samples, carried out by G. Samsonidze et al, revealed that the separation efficiency is complicated by variations in the tube diameter [127]. In particular, poor enrichment is observed for large-diameter tubes, becoming more efficient towards smaller tube diameters. The origin of this diameter dependence on the enrichment is not yet understood, but the authors point to electronic amine-SWNT interactions or curvature-induced stabilization. 

R.W. Curtis, Root curvatures induced by culture filtrates of Aspergillus niger, Science 128 661-662 (1958)... 

The simple picture afforded by the wormlike chain model is likely to break down under conditions of extreme deformation, as discussed in Section 9.13.2. The internal organization of dsDNA is likely to have instances where the chain is highly deformed, significantly beyond the range where linear elasticity theory is an adequate description. In addition, the potential for dsDNA to exhibit curvature-induced softening may promote... 

The thermodynamic driving force for sintering is the reduction in total interfacial energy. However, in terms of kinetics, the differences in bulk pressure, vapour pressure and vacancy concentration due to interface curvature induce material transport. Note that the three kinds of thermodynamic phenomena (differences in bulk pressure, vapour pressure and vacancy concentration) occur simultaneously and independently. 

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