Solid second-order effects

The different techniques which have been applied to determine transport in polymer electrolytes are listed in Table 6.1. For a fully dissociated salt all the techniques yield the same values of t (small differences may arise due to second order effects such as long range ion interactions or solvent movement which may influence the different techniques in different ways). In the case of associated electrolytes, any of the techniques within one of the three groups will respond similarly, but the values obtained from different groups will, in general, be different. Space does not permit a detailed discussion of each technique, this is available elsewhere (see Bruce and Vincent (1989) and the references cited therein). However, we will consider one technique from each group to illustrate the differences. A solid polymer electrolyte containing an associated uni-univalent salt is assumed. 

So far, most of the quantum-chemical computations of solid compounds have assumed a free molecular model that is the intermolecular effects are initially not considered. Although these second-order effects are minor in many cases and do not cause much disagreement with solid-state NMR measurements, they might become significant and should not be neglected. Recently a series of publications has addressed this problem, based on a supercell technique.38-41 The appealing feature of this new method is that it can deal not only with free molecules but also with crystals, amorphous materials or materials with defects. 

T = 50 K, alignment parallel to c-axis. Lower Central transition, alignment perpendicular to c-axis, showing similar second-order effects in the distribution of the EFGs as in the satellite transition spectrum. From Takigawa et al. (1991). B. Relationship between the O relaxation rate and the Cu relaxation rate for the planar sites of YBa2Cu30v with temperature as an implicit parameter. The solid line of unity slope indicates the relationship Cu V O T = 19.3. The data deviate from this relationship above 110 K. From Hammel et al. (1989). Both figures used by permission of the... 

Since 81 out of the approximately 110 NMR active nuclides have a quadrupole moment, these second-order effects are extremely important for the investigation of inorganic materials. Most spectra of quadrupole nuclides in solids are obtained by observing only the central (5, —5) transition. 

Spectroscopic studies of liquid interfaces provide important information about the composition and structure of the interfacial region. Early work was mainly carried out at the solid liquid interface and involved techniques such as neutron and X-ray diffraction, and reflection FTIR spectroscopy. More recently, powerful techniques have been developed to study the liquid liquid and liquid gas interfaces. These studies are especially important because of their relevance to biological systems such as cell membranes. The techniques described here are second-harmonic generation (SHG) and vibrational sum frequency spectroscopy (VSFS). They are both second-order non-linear optical techniques which are specific to the interfacial region. Since the second-order effects involve signals of low intensity, they rely on high-power lasers. 

Spin-Hamiltonian Second order effects in solids... 

Another spin-1 nucleus causing second-order effects is (Table 3). MAS NMR spectra of solid deuterated organic molecules show distorted triplets, as expected from Equation [6] when 0. In this case, the small value of x for is compensated by a large dipolar coupling constant D (Table 4). 

An elegant alternative which provides an intrinsic surface specificity is provided by non-linear optical reflection techniques based on a second-order effect (Fig. 1). Second-harmonic-generation (SHG) and sum-frequency-generation (SFG) spectroscopy contributed significantly to our current understanding of liquid-air, solid-liquid and liquid-liquid interfaces. Many fundamental insights on the structure of liquid-air interfaces are based on SHG and SFG experiments which are discussed in the next section. 

Unlike linear optical effects such as absorption, reflection, and scattering, second order non-linear optical effects are inherently specific for surfaces and interfaces. These effects, namely second harmonic generation (SHG) and sum frequency generation (SFG), are dipole-forbidden in the bulk of centrosymmetric media. In the investigation of isotropic phases such as liquids, gases, and amorphous solids, in particular, signals arise exclusively from the surface or interface region, where the symmetry is disrupted. Non-linear optics are applicable in-situ without the need for a vacuum, and the time response is rapid. 

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