Polarization induced

Poiar stationary phases which have a polar moment. These phases interact with the dipoiar moments of poiar components themselves and those components capable of induced polarization such as aromatics. 

Nomially the amplitude of the total incident field (or intensity of the incident light) is such that the light/matter coupling energies are sufficiently weak not to compete seriously with the dark matter Hamiltonian. As already noted, when this is tire case, tlie induced polarization, P is treated perturbatively in orders of the total electric field. Thus one writes... 

This solution is appropriate for the regime of a weak driving field E(t). If we now treat the material as a collection of non-hiteracting oscillators, we may write the induced polarization as a sum of the individual... 

An electric dipole consists of two equal and opposite charges separated by a distance. AH molecules contain atoms composed of positively charged nuclei and negatively charged electrons. When a molecule is placed in an electric field between two charged plates, the field attracts the positive nuclei toward the negative plate and the electrons toward the positive plate. This electrical distortion, or polarization of the molecule, creates an electric dipole. When the field is removed, the distortion disappears, and the molecule reverts to its original condition. This electrical distortion of the molecule is caHed induced polarization the dipole formed is an induced dipole. 

The interactions between solute and the pha.ses are exactly the same as those present in LC separations, namely, dispersive, polar and ionic interactions. At one extreme, the plate coating might be silica gel, which would offer predominately polar and induced polar interactions with the solute and, con.sequently, the separation order would follow that of the solute polarity. To confine the polar selectivity to the stationai y phase, the mobile phase might be -hexane which would offer only dispersive interactions to the solute. The separation of aromatic hydrocarbons by induced polar selectivity could be achieved, for example, with such a system. 

LW) interactions refer to the purely physical London s (dispersion), the Keesom s (polar) and Debye s (induced polar) interactions and correspond to magnitudes ranging from approximately 0.1 to 10 kJ/mol (but in rare cases may be higher). The polar forces in the bulk of condensed phases are believed to be small due to the self-cancellation occurring in the Boltzmann-averaging of the multi-body... 

For many problems it is convenient to separate the piezoelectric (i.e., strain induced) polarization P from electric-field-induced polarizations by defining D = P + fi , where s is the permittivity tensor. For uniaxial strain and electric field along the 1 axis, when the material is described by Eq. (4.1) with the E term omitted. 

Fig. 5.19. Shock-induced volume polarizations have been observed in a wide range of solids due to a number of different physical phenomena, including piezoelectricity and ferroelectricity. The signals observed from polymers and ionic crystals are not due to established phenomena, and are described as due to shock-induced polarization effects.

Fig. 5.20. The shock-induced polarization of a range of ionic crystals is shown at a compression of about 30%. This maximum value is well correlated with cation radius, dielectric constant, and a factor thought to represent dielectric strength. A mechanically induced point defect generation and migration model is preferred for the effect (after Davison and Graham [79D01]).

Fig. 5.21. The shock-induced polarization of polymers as studied under impact loading is shown. For the current pulse shown, time increases from left to right. The increase of current in time is due to finite strain and dielectric constant change. (See Graham [79G01]).

Fig. 5JS2. Shock-induced polarization of polymers has been studied by many investigators, with data as summarized. The typical behavior indicates a threshold compression of about 10%-15% followed by a rapid increase in value. The polarizations shown vary over three orders of magnitude. The author has proposed a mechanically induced bond-scission model to describe the effects. (See Graham [79G01].)...

Several overall features of the shock-induced polarization are apparent. First, there appears to be a threshold compression below which the signals are not observed. The compression for this threshold is considerable, about 15%, such that it is not difficult to believe that the material must be considerably altered in structure before polarizations appear (shown in Fig. 5.22). Following the threshold compression, the polarizations increase extraordinarily rapidly with increasing compression, finally reaching a saturation value at compressions of perhaps 30%. 

Fig. 5.23. The shock-induced polarization of the indicated polymers containing benzene rings in their structure is shown to be strongly dependent on the number of rings (after Graham [82G02]).

These observations were the basis for the proposal that polymers, like ionic crystals, exhibit shock-induced polarization due to mechanically induced defects which are forced into polar configurations with the large acceleration forces within the loading portion of the shock pulse. Such a process was termed a mechanically induced, bond-scission model [79G01] and is somewhat supported by independent observations of the propensity of polymers to be damaged by more conventional mechanical deformation processes. As in the ionic crystals, the mechanically induced, bond-scission model is an example of a catastrophic shock compression model. 

In this chapter studies of physical effects within the elastic deformation range were extended into stress regions where there are substantial contributions to physical processes from both elastic and inelastic deformation. Those studies include the piezoelectric responses of the piezoelectric crystals, quartz and lithium niobate, similar work on the piezoelectric polymer PVDF, ferroelectric solids, and ferromagnetic alloys which exhibit second- and first-order phase transformations. The resistance of metals has been investigated along with the distinctive shock phenomenon, shock-induced polarization. 

Finally, the phenomenon of shock-induced polarization represents perhaps the most distinctive phenomenon exhibited by shock-compressed matter. The phenomenon has no counterpart under other environments. The delineation of the details of the phenomenon provides an unusual insight into shock-deformation processes in shock-loading fronts. Description of the phenomenon appears to require overt attention to a catastrophic description of shock-compressed matter. In the author s opinion, a study of shock-induced polarization represents perhaps the most intriguing phenomenon observed in the field. In polymers, the author has characterized the effect as an electrical-to-chemical investigation [82G02]. 

Shock phenomena, such as shock-induced polarization, have no known counterpart in other environments. In that regard, the distinctive behaviors present the greatest opportunity to determine details of shock-compression processes. Unexplored phenomena, such as electrochemistry [88G02], offer considerable potential for developing improved descriptions of shock-compressed matter. 

Continuum models of solvation treat the solute microscopically, and the surrounding solvent macroscopically, according to the above principles. The simplest treatment is the Onsager (1936) model, where aspirin in solution would be modelled according to Figure 15.4. The solute is embedded in a spherical cavity, whose radius can be estimated by calculating the molecular volume. A dipole in the solute molecule induces polarization in the solvent continuum, which in turn interacts with the solute dipole, leading to stabilization. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

For larger 6 values, tbe results for toluene can be read ofif at once from those for pyridine (Table I) reversing the sign of the 3 s in a given secular equation of the present type merely reverses the direction of the induced polarization, and leaves its magnitude unchanged. 

Here e is the dielectric constant of the gas, F the strength of the applied field, N the number of molecules in unit volumes, n the permanent electric moment of a molecule, and a the coefficient of induced polarization of a molecule cos 9 is the average value of cos 9 for all molecules in the gas, and cos 9 is the time-average of cos 9 for one molecule in a given state of motion, 6 being the angle between the dipole axis and the lines of force of the applied field. 

To be eligible to living anionic polymerization a vinylic monomer should carry an electron attracting substituent to induce polarization of the unsaturation. But it should contain neither acidic hydrogen, nor strongly electrophilic function which could induce deactivation or side reactions. Typical examples of such monomers are p-aminostyrene, acrylic esters, chloroprene, hydroxyethyl methacrylate (HEMA), phenylacetylene, and many others. 

The second part of this paper concerns the choice of the atomic basis set and especially the polarization functions for the calculation of the polarizability, o , and the hyperpo-larizabiliy, 7. We propose field-induced polarization functions (6) constructed from the first- and second-order perturbed hydrogenic wavefunctions respectively for a and 7. In these polarization functions the exponent ( is determined by optimization with the maximum polarizability criterion. These functions have been successfully applied to the calculation of the polarizabilities, a and 7, for the He, Be and Ne atoms and the molecule. 

This calculation has shown the importance of the basis set and in particular the polarization functions necessary in such computations. We have studied this problem through the calculation of the static polarizability and even hyperpolarizability. The very good results of the hyperpolarizabilities obtained for various systems give proof of the ability of our approach based on suitable polarization functions derived from an hydrogenic model. Field—induced polarization functions have been constructed from the first- and second-order perturbed hydrogenic wavefunctions in which the exponent is determined by optimization with the maximum polarizability criterion. We have demonstrated the necessity of describing the wavefunction the best we can, so that the polarization functions participate solely in the calculation of polarizabilities or hyperpolarizabilities. 

Dickson and Becke, 1996, use a basis set free numerical approach for obtaining their LDA dipole moments, which defines the complete basis set limit. In all other investigations basis sets of at least polarized triple-zeta quality were employed. Some of these basis sets have been designed explicitly for electric field response properties, albeit in the wave function domain. In this category belong the POL basis sets designed by Sadlej and used by many authors as well as basis sets augmented by field-induced polarization (FTP) func-... 

Lamoureux G, Roux B (2003) Modeling induced polarization with classical Drude oscillators theory and molecular dynamics simulation algorithm. J Chem Phys 119(6) 3025-3039... 

Sprik M (1991) Computer-simulation of the dynamics of induced polarization fluctuations in water. 

In dielectric materials there can be both permanent and induced polarization domains. The walls between these domains may also act as barriers to dislocation motion. They tend to have larger energies than magnetic domain walls so they may have more effect on hardness (McColm, 1990). 

This induces polarization and is resisted by a restoring force. The restoring force is essentially the same as the force that resists electric polarization and is determined by the polarizability (Gilman, 1997). 

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