Orientation gradient with respect

The purpose of this chapter is to continue the unification that was begun in Chapter 8. There, first and second derivatives of normal stress with respect to orientation were used we now examine the idea that the chemical potential of a component at a point can be a multivalued direction-dependent scalar like the normal-stress magnitude, and that it too can have a gradient with respect to orientation. 

The peak separation is then dependent on the orientation, expressed by the 0 angle, of the electric field gradient with respect to the magnetic field (Fig. 3.2.2). 

In solid samples, the magnitude of x depends on the orientation of the electric field gradient with respect to Bq. As a consequence, deuterium NMR has been developed as a sensitive probe of molecular motion in materials over the 0-125 kFIz range. A novel probe capable of rotating a sample about two different axes simultaneously has been developed to obtain narrow peaks for quadrupolar nuclei in solids. Quadrupolar nuclei give narrower signals at higher fields, and pulse sequences have been developed to further narrow lines. 

The measured viscosity rj depends on the director orientation L with respect to the shear flow Vz z) and its gradient dvzfdx, Fig. 2.21((b)-(e)). In order to provide reliable experimental results only very low fiow rates must be used, which, together with the orienting influence of the... 

The movement of the plate is coupled with a three-dimensional balancing flow. For isotropic liquids the influence of this flow can be taken into account by calibration with an isotropic liquid of known viscosity. For liquid crystals the influence is more complicated due to the fixed director orientation. The orientations of the velocity and the velocity gradient with respect to the director are different around the plate, and the effective viscosity also varies. Therefore, all viscosity coefficients contribute to the measured apparent viscosity. With a proper geometry the contribution of the unwanted viscosity coefficients can be minimized and the viscosity that is effective at the plate surface can be determined. 

Figure 15 A lamellar block copolymer phase is reoriented through external shear. The initial phase has the direction of the lamellae parallel to the shear gradient direction. The most stable state would be to orient the director parallel to the shear and shear gradient direction. However, the reorientation process gets stuck before true equilibrium is reached. The stuck orientation is relatively stable, because the lamellae have to be broken up before they can further align with respect to the shear flow. Reprinted with permission from Ref. 56.

Almost all of these examples involve diffusion of a chemical species measuring diffusion rates has long been a specialty of NMR spectroscopy. The studies of KBr and drawn polyethylene produced unique information in the latter case, the known orientation of the deuterium electric field gradient in C-D bonds is used to determine the orientation, with respect to the magnetic field, of a polymer chain of a uniaxially ordered polyethylene fiber. The real time imaging of the polymerization of methyl methacrylate is very interesting and may represent a major direction for NMR imaging applications to polymer science. 

Experimental knowledge of the directional cosines of the electric field gradient tensor at one lattice site with respect to the crystal axes, together with a knowledge of the crystal structure, is sufficient to calculate the orientation of all other electric field gradient tensors belonging to the same crystallographic point position. 

The NMR lineshape of solids is determined by the quadrupolar interaction, which can be described by two parameters the quadrupole frequency, o Q, and the asymmetry parameter, t/ (19,20). The parameter q)q is determined by the electric quadrupole moment of the deuteron and the zz component of the electric field gradient at the deuteron site. For deuterons bonded to carbon atoms, the asymmetry parameter is approximately zero and the z axis is along the C—D bond. In this case, the dependence of the resonance frequency, m, from the orientation of the molecule with respect to the magnetic field applied is given by a relation similar to Eq. (18) (19). 

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