Strain-Induced Stiffness

The PDF peak intensity of the first shell for the real particle is lower than that for the ideal case. 

PDF peak intensities of the real case at higher correlation distances diminish more rapidly than the ideal nanoparticle. 

PDF peak widths for the real case are broader than the ideal one. 

The PDF peak positions shift closer to the reference atom, which is more apparent at r = 1.0 and 1.4 nm (shortened by 0.008 and 0.02 nm, respectively), indicating a contraction of the mean bond length of the real nanoparticle. 

The frequency of lattice vibration shift from the bulk value of 7.1 to 11.6 THz, implying bond stiffening. 

---

The difference between a solid composed of nanoparticles and a solid in an amorphous state is the distribution of atoms with CN imperfection. Undercoordinated atoms are located only at the surface of a nanosolid but distribute randomly inside the amorphous solid. The distribution of CN imperfection is sensitive to processing conditions of amorphous states. In probing statistical information, the low-CN atoms contribute identically irrespective of their locations. It is anticipated that the PDF correlation length, or core size, increases with nanocrystal size. Further verification by measuring different sizes would afiinn the shell-strain-induced stiffness. 

Compared with rubber-based stretchable conductors, the mechanical weakness of the extended networks could pose a problem. We have observed that mechanical failure always occurs around the bases of the struts, which then causes electric disconnections when too much tension is apphed to the device. This observation indicates that the major part of the strain is induced at the base of the struts and is rather small in the stiff intersection areas. In the present design, each transistor is positioned at the center of the intersection areas furthermore, the area of the transistor is much smaller than that of the intersection areas to minimize strain induced in the transistors. 

While each material exhibits particular physical characteristics, they all follow a broad pattern of behaviour as shown in Figure 24.3. Where an item has a load applied to it, provided that the strain induced does not go beyond the elastic limit, then when the load is removed the item will return to its original size, i.e. there will have been no permanent deformation. However, if the elastic limit is exceeded permanent deformation occurs and the characteristic of the material will have changed. Typical stiff brittle materials are cast iron, glass and ceramics which have no ductility and will fracture at the elastic limit. Ductile materials include mild steel and copper, and elastic materials include plastics. 

If a piezoelectric transducer is simply being used as a displacement or strain indicator, then the relationships described above are sufficient to allow the calculation of the electrical signal which will be generated upon perturbation of a device. All that must be known are the stiffness constants (elastic properties), the piezoelectric strain coefficients (piezoelectric properties) of the transducer material, and the strain induced. If however, acoustic waves are being employed for mass sensing applications, then one must consider the dynamics of particle motion and how wave propagation is affected by the finite boundaries of a transducer. 

In this regard, crystallization is very important in the case of elastomers, since crystallites can act as reinforcing agents, particularly if they are strain induced. For this reason, it is of interest to make siloxane-type backbones with increased stiffness, in an attempt to increase the Tm of the polymer. Examples of ways to make a polymer more rigid is to combine two chains into a ladder structure, insert rigid units such as p-phenylene groups into the chain backbone, or add bulky side groups to the backbone. 

Physical crosslinks can be introduced into polymer segments by various means. For example, they can be crystalline fractions inherent to any of the blend components, or they may be formed after homogenization of the polymer blend, due to physical entanglements or strain-induced crystallization (i.e., orientation). The addition of fillers has also been widely used to increase the stiffness of polymer blends, while post-blending processes to induce covalent chemical crosslinking can also be effective in this respect. 

Figure 6.10. Sketch of force response of free random coil and adsorbed chain in dependence on the coil strain related to the maximum elongation, 100% 0.81 Nh. Whilst free coil exhibits Gaussian response under given low strain approximately up to 20%, adsorbed loops and bridges, represented by A = 10 and 100, are highly Langevineau with incremental stiffness considerably increased. Strain induced perturbation of interphase accompanied by desorption of trains causes significant local stress and strain relief and, consequently, a lower stiffness...

The procedure initially developed by Lee (1974) and later refined by Chaney (1979,1980) and Makdisi et al. (1978) involved the concept that permanent seismic deformations of a slope may be computed by evaluating dynamic-induced softened pseudo slope stiffness values for soil elements with the resultant settling of the slope to a new condition being compatible with pseudo or apparent stress-strain properties of the soils comprising the slope. Figure 11.17 shows an example of the use of the permanent deformation method for evaluating the deformation of the continental slope off Flaifa, Israel, under earthquake loading from a transform fault on the Jordan rift valley. 

---