Surface bending energy

The above representation for the shell energy contains three different terms describing the bending energy of the shell, the deformation energy of the middle surface, and the work done by the exterior force /, respectively. 

Mag., 25(1), 131 (1972)] conclude that these measurements are valid when 50 percent corrections are added for the bending energy of the crystal. Kuznetzov ranks other materials by a relative wear test. His results substantiate the efficiencies given earlier. Attempts to measure efficiency of the grinding process by calorimetiy involve errors that exceed the theoretical surface energy of the material being ground. 

It is independent of the radius It does not depend on the radius because the bending energy per unit area increases but the surface area decreases. Both effects just compensate each other. See also exercise 6. 

Davis summarized the concepts about HLB, PIT, and Windsor s ternary phase diagrams for the case of microemulsions and reported topologically ordered models connected with the Helfrich membrane bending energy. Because the curvature of surfactant lamellas plays a major role in determining the patterns of phase behavior in microemulsions, it is important to reveal how the optimal microemulsion state is affected by the surface forces determining the curvature... 

The mechanism for cantilever bending is assumed to be adsorption-induced stress. The adsorption decreases the surface free energy and surface free energy is density is surface stress. It is speculated that the hydrogen bonding between the nitro groups of the explosives molecules and the hydroxyl group of 4-MBA is responsible for the easily reversible adsorption of explosive vapours on the SAM-coated top surface of the cantilever. This... 

Under this assumption, the bending energy Eg can be represented in terms of the membrane s curvature. For this reason. Eg is also referred to as the curvature elastic energy. The curvature of smooth surfaces is characterized by two functions that depend on the local canonical curvatures, h t) and h lr), in a surface element dS centered at r. These functions are the mean curvature, H = ( 1 + hi) , and the Gaussian curvature, K = hih2- In general, H and K change with the point r. 

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