Solids, macroscopic polarization

Fig. 7. Two-dimensional packing observed for the main-chain polymer with two odd numbered spacers of different length. Solid lines and arrows indicate the two-dimensional rectangular lattice and macroscopic polarization, respectively (Watanabe et al. [68])...

The macroscopic polarization (P) of a solid comprising many individual molecules may be expressed as... 

It should be noted, however, that the flexoelectric effect is not necessarily related to the ordering of molecular dipoles. Frost and Marcerou proposed another microscopic mechanism of the flexoelectric effect, which requires neither the asymmetry of the molecular shape nor the permanent molecular dipole. The macroscopic polarization may simply appear in the direction of the gradient of average density of the molecular quadrupole moments. The quadrupole mechanism of flexoelectricity is more general because, in principle, it should manifest itself in any anisotropic material with a non-zero quadrupole density including solid crystals d and elastomers. 

This behavior is also known in the solid state, e.g., in the chiral structure NaN02, and the order is called helicoidal antiferroelectric. A shorter useful name is helielec-tric. The helielectric smectic C has zero macroscopic polarization (like an antiferroelectric), no hysteresis, no threshold, and no bistability. However, by an artifice it can be turned into a structure with very different properties. This is illustrated in Fig. 16. If the smectic layers are made perpendicular to the confining glassplates, there is no boundary condition compatible with the... 

By extending some previous heuristic proposal [238,239], the phase in the polarized state of a ID solid of macroscopic length L was expressed in [240] as... 

Polarization in the point dipole model occurs not at the surface of the particle but within it. If dipoles form in particles, an interaction between dipoles occurs more or less even if they are in a solid-like matrix [48], The interaction becomes strong as the dipoles come close to each other. When the particles contact each other along the applied electric field, the interaction reaches a maximum. A balance between the particle interaction and the elastic modulus of the solid matrix is important for the ER effect to transpire. If the elastic modulus of the solid-like matrix is larger than the sum of the interactions of the particles, the ER effect may not be observed macroscopically. Therefore, the matrix should be a soft material such as gels or elastomers to produce the ER effect. 

The fact that the molecules are adsorbed on a solid surface giv rise to a number of new effects compared to the gas phase situation. The experimental situation consists of a monolayer of molecules adsorbed on a metal surface, on which we shine infrared radiation and then detect the reflected light. The macroscopic theory for the electromagnetic response of such a system is reproduce in the previous reviews. A more microscopic treatment has been given by Persson, showing that the integrated infrared absorptance for p-polarized light is given by ... 

An individual atom or ion in a dielectric is not subjected directly to an applied field but to a local field which has a very different value. Insight into this rather complex matter can be gained from the following analysis of an ellipsoidal solid located in an applied external field Ea, as shown in Fig. 2.28. The ellipsoid is chosen since it allows the depolarizing field Edp arising from the polarization charges on the external surfaces of the ellipsoid to be calculated exactly. The internal macroscopic field Em is the resultant of Ea and Edp, i.e. Ea — Edp. 

Physical parameters Molecular 0.1-1 nm Dipole-dipole interaction Second moment, fourth moment of lineshape Incoherent magnetization transfer characteristic times for cross-polarization and exchange Mesoscopic lnm-0.1 p,m Longitudinal relaxation time Ti Transverse relaxation time T2 Relaxation time Tip in the rotating frame Solid-echo decay time T2e Spin-diffusion constant Microscopic 0.1-lOp.m Molecular self-diffusion constant D Macroscopic 10 p,m and larger Spin density... 

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