Areal elasticity

Film Elasticity The differential change in surface tension of a surface film with relative change in area. Also termed surface elasticity, dilata-tional elasticity, areal elasticity, compressional modulus, surface dilata-tional modulus, or modulus of surface elasticity. For fluid films, the surface tension of one surface is used. The Gibbs film (surface) elasticity is the equilibrium value. If the surface tension is dynamic (time-dependent) in character, then for nonequilibrium values, the term Marangoni film... 

To illustrate, consider a simplified surface geometry, a soap film that is stretched on a wire frame (see Figure 3.2). For small areal changes, the dynamic tension difference A /d between the starting and ending positions can be approximated by using the surface elasticity, EM,... 

In Section 3.2.4 we considered the effects of an ideal mass layer on SAW response. In the model used to derive the mass-loading response, the layer was assumed to be (1) infinitesimally thick, and (2) subject only to translational motion by the SAW. Translational motion was found to induce a change in SAW velocity proportional to the areal mass density (pfc) contributed by the film — the mass loading response. Since no power dissipation arises in film translation, no attenuation response was predicted. With an actual film having finite thickness and elastic properties, it is important to also consider the effects of SAW-induced film deformation. Energy storage and power dissipation due to film deformation cause additional contributions to SAW velocity and attenuation that were neglected in the earlier treatment. 

The scaling law in Eq. (10-33) was predicted by Marrucci (1984) by assuming that the disclination density at steady state is set by a balance between the viscous energy density r]Y and the Frank elastic energy density K ja. Since the areal density pa is proportional to Pvh a h/a, this balance is... 

Elastic modulus mismatch Interface failure mechanism Interface porosity, flaws and damage Areal variation and batch-to-batch variation Exposure condition effects on microstructure and properties... 

Substrate composition and phases Surface hardness and roughness at interface Grain size/microstructure Anisotropy in structure and properties Areal variation and batch-to-batch variation Elastic/plastic mechanical properties Fracture mechanics Flaw population and distribution Strain rate effects... 

If the areal change remains small, then the difference in thermodynamic tension can be approximated by using the surface dilational elasticity m. 

In this article, we will focus in particular on the so-called coupled monolayer models [18,20-26,28,29], where membranes are described as stacks of two sheets (monolayers), each with their own elastic parameters. Mraiolayers are bound to each other by a local harmonic potential that accounts for the areal compressibility of lipids within the membrane and their constant volume [22, 28]. Li et al. have recently compared the elastic properties of amphiphilic bilayers with those of the corresponding monolayers within a numerical self-consistent field study of... 

The chance that one particle from the beam ejects a recoil of element Z2, M2) in such a way that it starts moving in the direction of the detector is proportional to the areal density (atom cm ) of this element and the detector solid angle of the detector. Treating the interaction as purely Rutherford scattering (since the energy available in the center of mass is at least five times below the Coulomb barrier) the elastic scattering cross-section is given by Rutherford differential cross-section for ERD i.e.,... 

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