Electric-dipole interaction susceptibility

G2, to G3, and to G4, the effective enhancement was 10%, 36%, and 35% larger than the value estimated by the simple addition of monomeric values. The enhancement included the local field effect due to the screening electric field generated by neighboring molecules. Assuming the chromophore-solvent effect on the second-order susceptibility is independent of the number of chro-mophore units in the dendrimers, p enhancement can be attributed to the inter-molecular dipole-dipole interaction of the chromophore units. Hence, such an intermolecular coupling for the p enhancement should be more effective with the dendrimers composed of the NLO chromophore, whose dipole moment and the charge transfer are unidirectional parallel to the molecular axis. 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

The nonlinear interaction of light with matter is useful both as an optical method for generating new radiation fields and as a spectroscopic means for probing the quantum-mechanical structure of molecules [1-5]. Light-matter interactions can be formally classified [5,6] as either active or passive processes and for electric field based interactions with ordinary molecules (electric dipole approximation), both may be described in terms of the familiar nonlinear electrical susceptibilities. The nonlinear electrical susceptibility represents the material response to incident CW radiation and its microscopic quantum-mechanical formalism can be found directly by diagrammatic techniques based on the perturbative density matrix approach including dephasing effects in their fast-modulation limit [7]. Since time-independent (DC) fields can only induce a... 

What has been presented above is based on the interaction of electrons or atoms with the electric field through a quadratic harmonic potential. When potentials including higher-order terms are used, the polarization, electric dipole moment, and optical susceptibility include, in turn, higher order terms whose contributions are the basis of non-linear optics and anharmonic effects. 

We see, that the phase transitimi temperature increases, because the dipole-dipole interactions (f -term) stabilise the smectic C phase. Note that the held induced tilt angle (or electroclinic coefficient Cc) diverges at a temperature T. This means, that at even inhnitesimally low held would create a finite tilt. This is the soft mode of the director motion any small force (not necessary electric) would cause the tilt of the director, because, at the transition, the medium becomes soft with respect to the tilt. The corresponding dielectric susceptibility shows the Curie-Weiss law ... 

The coefficients in the various terms in Eqs. (2a) and (2b) are termed the nth-order susceptibilities. The first-order susceptibilities describe the linear optical effects, while the remaining terms describe the nth order nonlinear optical effects. The coefficients are the nth-order electric dipole susceptibilities, the coefficients G " are the nth-order quadrupole susceptibilities, and so on. Similar terminology is used for the various magnetic susceptibilities. For most nonlinear optical interactions, the electric dipole susceptibilities are the dominant terms because the wavelength of the radiation is usually much longer than the scattering centers. These will be the ones considered primarily from now on. 

The study of amphiphile ordering at interfaces is necessary to understand many phenomena, like microemulsions, foams or interfacial reactivity. It is expected that the preferential orientation taken by these compounds at interfaces is entirely determined by their interactions with the two solvants forming the interface and the intermolecular repulsion or attraction within the monolayer. As mentioned above, the SH response at liquid/liquid interfaces is dominated by electric dipole contributions and is therefore surface specific. Neglecting the contribution from the sol-vant molecules, which usually only have a weak nonlinear optical activity, the passage from the macroscopic susceptibility tensor xP to the microscopic molecular hyperpolarizability p of the adsorbate is obtained by merely taking the SHG response of the amphiphile monolayer as the superposition of the contribution from each single moiety. Hence, it yields... 

The susceptibility formula (2.20) can readily be used for calculating the attraction between atoms or molecules, if these particles are replaced by electric dipole oscillators. Let us consider two electric dipole oscillators i and j with elongations u,- and Uj at positions and rj. The electrostatic force exerted on dipole j by a unit moment of dipole i is given by the respective component of the dipole interaction tensor... 

The semiclassical substitution of electric dipole oscillators for molecules requires that one three-dimensional dipole is attached to each allowed electron transition. Each molecule has to be replaced by an ensemble k of independent three-dimensional dipole oscillators whose eigen-frequencies correspond to the allowed one-electron excitation energies. The energy of interaction of molecules i and j is derived by summing Eq. (2.22) over all dipoles k representing molecule i and over all dipoles / representing molecule j. These summations do not affect the dipole interaction tensors T. Tyj, which depend exclusively on the separation and mutual orientation of molecules i and J. We are left with the summation over the susceptibilities x (c(J) of dipoles k at molecule i... 

In the meantime Debye, who the year before had been appointed professor of theoretical physics at the University of Zurich, in 1912 introduced the idea of polar molecules , i.e., molecules with a permanent electric dipole moment (at that time a hypothesis) and worked out a theory for the macroscopic polarization in analogy with Langevin s theory of paramagnetic substances. He found, however, that the interactions in condensed matter could lead to a permanent dielectric polarization, corresponding to a susceptibility tending to infinity for a certain temperature, which he... 

At the surface, however, the inversion symmetry of the bulk is broken. Electric dipole contributions to the nonlinear polarization become possible due to the spatial structure of the surface and due to the discontinuity of the normal component of the electric field at the surface. In the case of a nonlocal interaction, the polarization at a given position r depends on the external field of the surroundings (i.e, "spatial dispersion"). In most cases, however, one assumes for the sake of simplicity a local interaction, in which case the susceptibility is independent of the polarization in the surroimdings. If one assumes that the main reason for this nonlinear polarization is the generation of a strong (static) dipole field at the surface, then it becomes clear that it should be localized in the uppermost atomic layers down to a depth of 0.5-1.5 nm (Sipe et al. 1987). 

We can divide commodity plastics into two classes excellent and moderate insulators. Polymers that have negligible polar character, typically those containing only carbon-carbon and carbon-hydrogen bonds, fall into the first class. This group includes polyethylene, polypropylene, and polystyrene. Polymers made from polar monomers are typically modest insulators, due to the interaction of their dipoles with electrical fields. We can further divide moderate insulators into those that have dipoles that involve backbone atoms, such as polyvinyl chloride and polyamides, and those with polar bonds remote from the backbone, such as poly(methyl methacrylate) and poly(vinyl acetate). Dipoles involving backbone atoms are less susceptible to alignment with an electrical field than those remote from the backbone. 

The interactions between the molecule and the environment can lead to distortions in the electrical properties due to the susceptibility of the molecules and the properties of the host matrix. The refractive index of the matrix acts as a screening factor, modifying the optical spectra and interaction between charges or dipoles embedded within it. Local field effects change the interaction with an electromagnetic field and should be considered along with orientation factors in the dipolar interaction. 

We have calculated the second- and fourth-order dipole susceptibilities of an excited helium atom. Numerical results have been obtained for the ls2p Pq-and ls2p f2-states of helium. For the accurate calculations of these quantities we have used the model potential method. The interaction of the helium atoms with the external electric held F is treated as a perturbation to the second- and to the fourth orders. The simple analytical expressions have been derived which can be used to estimate of the second- and higher-order matrix elements. The present set of numerical data, which is based on the Green function method, has smaller estimated uncertainties in ones than previous works. This method is developed to high-order of the perturbation theory and it is shown specihcally that the continuum contribution is surprisingly large and corresponds about 23% for the scalar part of polarizability. 

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