Film bending, schematic

Figure 2.15 Electrothermal bending of a MWNT-PDMS composite film, (a) Schematic structure of a U-shaped actuator consisting of a thin layer of super-aligned MWNT-PDMS composite and a thick layer of pristine PDMS. The dashed lines represent the direction of CNT alignment, (b) Photographs of the actuator without (left) and with (right) an applied DC voltage of 40 V. Reprinted by permission from the American Chemical Society.

As a result of the difference in tensions, the film will bend until reo = ny,. If re > re, the area at the oil side has to expand (resulting in reduction of re ) until reo = rew - in this case a W/O microemulsion is produced. If re(, > re, the area at the water side expands until re = reo. In this case an O/W microemulsion is produced. Figure 10.3 gives a schematic representation of film bending for production of 3 0 or 0 microemulsions. 

The above concept of duplex film can be used to explain both the stability of microemulsions and the bending of the interface. Considering that initially the flat duplex film has different tensions (i.e., different values) on either side of it, then the deriving force for film curvature is the stress of the tension gradient which tends to make the pressure or tension in both sides of the curved film the same. This is schematically shown in Figure 1. For example if ir > ir on the flat... 

Fig. 6.4. (a) Schematic diagram of an n-type organic thin film transistor, (b) Energy level scheme of an accumulation layer for an n-type semiconductor with a single trap level of energy E . qVs is the band bending at the surface [158]. 

Figure 5.2 Schematic illustration of two defect reduction mechanisms for a strained film (dark gray) grown on a porous substrate (light gray), (a) Dislocations bending toward the open surface at the tube walls, (b) Formation of relatively dislocation-free regions in the GaN film where the film has laterally grown over the pores. Reproduced from C. K. Inoki etal., Pbys. Stat. Soli, (a) 200, 44. Copyright (2003), with permission from John Wiley Sons, Ltd...

In summary, the different pressures are shown schematically in Fig. 2. The attractive van der Waals forces act across the film and favor thinner film thicknesses, the bending elastic forces depend on the fourth-order derivatives of the height variations and essentially penalizes curvature in the height, the contact pressure is included for numerical stability and ensures that the solid capping layers do not overlap, and finally the stretching elastic forces describe the pressure on the fluid due to in-plane displacements in the solid capping layers. The behavior of the model depends upon the interactions of all these pressures, as well as the kinetics of fluid transport, in response to these pressures. 

Figure 2. Schematic of various pressures accounted for in the model. We include the pressures due to the bending and stretching of the solid capping layers, the van der Waals forces across the film, and a pressure term that accounts for contact mechanics between the top and bottom solid layers.

Schematic representation of an apparatus for the determination of mechanical film stresses using the bending beam technique with optical detection [150].

FIGURE 39.3 Schematic illustration of three types of film response (a)elastic half-space behavior, dominated by bulk compression of the film, (b) plate behavior, dominated by bending deformation of the film, and (c) membrane behavior, dominated by axial stretching of the film. 

FIGURE 39.15 Schematic of the peel test, and associated mode-mixity phase angle for the case of a flexible film on a rigid substrate mode II arises from bending near the debond edge. 

Figure 3.26. (a) Experimental setup and (b) photographs of the homeotropic film that exhibits photoinduced bending and unbending behavior. The white dash lines show the edges of the films, and the inset of each photograph is a schematic illustration of the film state, (c) Schematic illustration of the bending mechanism in the homeotropic film. Source Kondo et al., 2006. 

Fig. 5.13 Photomechanical effects. Schematic illustration of UV-light-induced bending of a cross-linked liquid-crystalline polymer film containing azobenzene groups. Light is absorbed at the upper surface layer of the film and causes anisotropic contraction. Adapted from Ikeda et al. [51] with permission from Wiley-VCH.

Figure 8.83 shows the schematic construction of a chemomechanical rotor, where anisotropic expansion causes rapid bending of the film due to the sorption of water vapor from one side of the film [140]. The rotation continued until the adsorbates were completely vaporized. This moving device may become a clean and silent power source for use as a molecular engine where the chemical free adsorption energy is transduced into the mechanical work. 

A schematic diagram presenting the comparative effects of spontaneous curvature and elasticity of the interfacial film in W/O microemulsions is shown in Fig. 3.8. In a W/O microemulsion, therefore, a maximum water solubilization can be achieved when the interfacial bending stress of rigid interfaces, as also the attractive interdroplet interaction of fluid interfaces is minimized, keeping the interfacial curvature and elasticity at an optimum level. 

The simplest physical idealization of the film that incorporates bending resistance is that of an elastic plate which admits extensional and bending deformation but no shear deformation this model is known commonly as a Kirchhoff plate. The boundary value problem is illustrated schematically in Figure 4.4, where the film and the substrate have been separated to show the shear stress distribution q x) and the normal stress distribution p x) together which represent interaction between the film and substrate. Also shown acting on a section of the film at distance x from the edge is an internal extensional force t x), an internal shear force s x) and an internal bending moment m x), all measured per unit thickness in the j/—direction. 

Fig. 5.5. Schematic showing the combination of pure bending and extension at a distance behind the delamination front which is on the order of the film thickness.

Fig. 5.9. Schematic representation of the edge force and bending moment for an axisymmetric buckle which forms on a circular region along the film-substrate interface.

Fig. 5.29. Schematic diagram of a section of a straight-sided pressurized bulge for large deflections, with the main part of the film exhibiting membrane behavior as illustrated on the left. The diagram on the right represents a boundary layer region near the edge of the bulge in which bending effects must be taken into account to enforce the boundary conditions.

FIG U RE 3.53 Schematic of in situ diazonium generation and electroreduction onto an ITO-coated flexible PEN substrate. The digital photograph shows the flexible TTO substrate grafted with silver-polymer nanocomposite film under bending stress. (Adapted from Samanta, S. et al. Langmuir 30, 2014 9397-9406.)... 

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