Inhomogeneous mechanical field

We have elaborated out several versions of the eqiripment for creation of preliminarily established inhomogeneous mechanical field, as a result of cohesion in a polymeric body an established gradient of relative lengthening is formed, and consequently, so is the prehminarily established gradient birefringence. 

Curve 1 (Figure 58) displays distribution of longitudinal elongation by PVS width deformed in an inhomogeneous mechanical field. Countdowns are made for the most deformed part of the film, marked by digits 1-1 in Figure 57, b. It is clear from the Figure that... 

This chapter is concerned with the influence of mechanical stress upon the chemical processes in solids. The most important properties to consider are elasticity and plasticity. We wish, for example, to understand how reaction kinetics and transport in crystalline systems respond to homogeneous or inhomogeneous elastic and plastic deformations [A.P. Chupakhin, et al. (1987)]. An example of such a process influenced by stress is the photoisomerization of a [Co(NH3)5N02]C12 crystal set under a (uniaxial) chemical load [E.V. Boldyreva, A. A. Sidelnikov (1987)]. The kinetics of the isomerization of the N02 group is noticeably different when the crystal is not stressed. An example of the influence of an inhomogeneous stress field on transport is the redistribution of solute atoms or point defects around dislocations created by plastic deformation. 

Second, consider an experiment in which molecules are deflected by inhomogeneous electric field. According to the conventional description, the deflection is caused by the interaction between the field and the molecules represented by material points with permanent dipole moments. On the other hand, a rigorous quantum-mechanical treatment of this phenomenon calls for the consideration of the coupling between the overall motion of the center-of-mass and the perturbed spectroscopic states [24]. This coupling arises as a consequence of the fact that the total momenta of molecules are not conserved in the course of such an experiment. 

Molecules for which a temperature-dependent dielectric susceptibility is observed in gas phase are commonly called polar. Polar molecules have microwave spectra with transitions corresponding to AJ= 1 and are deflected by inhomogeneous electric fields. In the conventional approach, these phenomena are attributed to the presence of permanent dipole moments in such molecules. In contrast, the notion of permanent dipole moments (which are zero for spectroscopic states) plays no role at all in the fully quantum-mechanical treatment outlined above. The temperature-dependent component of x arises from the existence of low-lying spectroscopic states for which... 

The conventional description of molecules, which is obviously much more intuitive and straightforward than its quantum-mechanical counterpart, is often adequate. Nevertheless, the manifestations of quantum effects are easily detectable experimentally. For example, species such as HfeCD, HD, or CH D, which are clearly nonpolar by the conventional definition, do possess temperature-dependent % and observable microwave spectra, and do deflect in inhomogeneous electric fields [11,16]. In fact, if one insists upon the conventional approach, these observations can be consistently accounted for by assuming the presence of small (of the order of 0.01 [D]) permanent dipole moments in these molecules. However, a rigorous quantum-mechanical treatment of such cases is clearly preferable. 

It can be concluded, that various approach exist which can be used to control the inhomogeneity of the mechanical field in various equipment (Fig. 9,a and Fig. 9,e) rotation of clamps between 0longitudinal elongation and cross-sectional compression (Fig. 9,b) can also be used. In the device shown in Fig. 9,d the deformation is one of longitudinal elongation. The additional variation of the mechanical field inhomogeneity is possible by the use of clamps with any configuration [12]. 

The elongation uses the complex connection between control of the inhomogeneity of the mechanical field and the topographical picture of the elongation deformation distribution. The region of usable deformation, which is localized in the eenter of the sample gradually expands and takes up the whole width of the sample. 

The deformation of a material is governed not oidy by a constitutive relation between deformation and stress, like the neo-Hookean equation discussed above, it also must obey the principles of conservation of mass and conservation of momentum. We have already used die mass conservation principle (conservation of volume for an incompressible material) in solving the uniaxial extension example, eq. 1.4.1. We have not yet needed the momentum balance because the balance was satisfied automatically for the simple deformations we chose that is, they involved no gravity, no flow, nor any inhomogeneous stress fields. However, these balances are needed to solve more complex deformations. They are presented for a flowing system because we will use these results in the following chapters. Here we see how they simplify for a solid. Detailed derivations of these equations are available in nearly every text on fluid or solid mechanics. 

For condensed species, additional broadening mechanisms from local field inhomogeneities come into play. Short-range intermolecular interactions, including solute-solvent effects in solutions, and matrix, lattice, and phonon effects in soHds, can broaden molecular transitions significantly. 

---