Dipole phase

Anti-Stokes broadening, 101 Atomic dipole phases, 68... 

S. Fukao et al., A Numerical Consideration on Edge Effect of Planar Dipole Phased Arrays, Radio ScL, Vol. 21, January-February 1986, pp. 1-12. 

We consider a very general two-phase system with a dipole phase D and a matrix phase M. The dipole phase may consist of any type of nanoseopie, mieroscopic, or macroscopic dipoles such as ionic charges of opposite polarity in the lattice of an inorganic solid, polar molecules or polar molecular units, ionic crystalline particles, polymer crystallites in a semicrystalline polymer, partieles with eharges of opposite polarity on their opposing faces, cavities with internal surfaee eharges of one or both polarities, etc. The matrix phase may be the material between or around ionic charges, the polymer matrix of a composite, the amorphous phase of... 

The elastic moduli Y of the matrix phase and Yd of the dipole phase can also be calculated from the spring constants k ainx and k ipoie in Figs. 2, 3, and 4, respectively, if the particular geometrical arrangement of the springs is taken into account. 

According to Eq. 6, direct piezoelectricity can be separated into a matrix (or dipole-density) effect ( secondary piezoelectricity ) and a dipole-moment effect ( primary piezoelectricity ). The two alternative situations are illustrated in Figs. 3 and 4, respectively. However, if the matrix and dipole phases have the same elastic modulus (i.e., spring constant), no piezoelectricity is observed (affine deformation). This situation has been illustrated in the spring model of Fig. 2 above where the electrode eharges do not change upon deformation. 

In real piezoeleetric materials, one phase will be stiffer and the other softer so that a nonzero response is observed. Equation 6 tells us how to design piezoelectric materials with two or more phases such as ferroelectrets from cellular foams (the dipole phase typically consists of air-filled foam cells or cavities) or Maxwell-Wagner piezoelectrets from particle-polymer composites (in which the dipole phase may consist, e.g., of hard particles that cannot be compressed very much). 

Equation 7 includes the prediction that the ratio of the piezoelectric coefficient and the remanent polarization P3 = Pr should be approximately equal to the elastic compliance /Ym of the matrix phase for the dipole-density effect or to the elastic compliance HYd of the dipole phase for the dipole-moment effect, respectively (or inversely proportional to the respective elastic modulus). First results assembled from the literature and from our own experimental data on PVDF and on cellular-foam PP and tubular-channel FEP ferroelectrets (Altafim et al. 2009) are shown in Fig. 5 (Qiu et al. 2013, 2014). They provide experimental evidence that the direct piezoelectric thickness coefficient of polymer materials can indeed be roughly approximated by the product of the remanent polarization in the poled material and of its overall elastic compliance. Additional data from the literature on other... 

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

McConnell et al. [196] and Andelman and co-workers have predicted [197,198] an ordered array of liquid domains in the gas-liquid coexistence regime caused by the dipole moment difference between the phases. These superstructures were observed in monolayers of dipalmitoyl phosphatidylcholine monolayers [170]. 

Stigter and Dill [98] studied phospholipid monolayers at the n-heptane-water interface and were able to treat the second and third virial coefficients (see Eq. XV-1) in terms of electrostatic, including dipole, interactions. At higher film pressures, Pethica and co-workers [99] observed quasi-first-order phase transitions, that is, a much flatter plateau region than shown in Fig. XV-6. 

Because of the charged nature of many Langmuir films, fairly marked effects of changing the pH of the substrate phase are often observed. An obvious case is that of the fatty-acid monolayers these will be ionized on alkaline substrates, and as a result of the repulsion between the charged polar groups, the film reverts to a gaseous or liquid expanded state at a much lower temperature than does the acid form [121]. Also, the surface potential drops since, as illustrated in Fig. XV-13, the presence of nearby counterions introduces a dipole opposite in orientation to that previously present. A similar situation is found with long-chain amines on acid substrates [122]. 

The surface potential of the phase, due to the presence of surface dipoles. At the metal-vacuum... 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

In writing equation (Cl. 4.3) we have made use of tire fact tliat tire time-average dipole has in-phase and inquadrature components. 

Figure C2.2.5. Fmstrated smectic phases. Here tire arrows denote longitudinal molecular dipoles.

TIk experimentally determined dipole moment of a water molecule in the gas phase is 1.85 D. The dipole moment of an individual water molecule calculated with any of thv se simple models is significantly higher for example, the SPC dipole moment is 2.27 D and that for TIP4P is 2.18 D. These values are much closer to the effective dipole moment of liquid water, which is approximately 2.6 D. These models are thus all effective pairwise models. The simple water models are usually parametrised by calculating various pmperties using molecular dynamics or Monte Carlo simulations and then modifying the... 

The range of systems that have been studied by force field methods is extremely varied. Some force fields liave been developed to study just one atomic or molecular sp>ecies under a wider range of conditions. For example, the chlorine model of Rodger, Stone and TUdesley [Rodger et al 1988] can be used to study the solid, liquid and gaseous phases. This is an anisotropic site model, in which the interaction between a pair of sites on two molecules dep>ends not only upon the separation between the sites (as in an isotropic model such as the Lennard-Jones model) but also upon the orientation of the site-site vector with resp>ect to the bond vectors of the two molecules. The model includes an electrostatic component which contciins dipwle-dipole, dipole-quadrupole and quadrupole-quadrupole terms, and the van der Waals contribution is modelled using a Buckingham-like function. 

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