Electric polarization results

Electric polarization resulting from a splay or bend deformation of the director of a nematic liquid crystal. 

Coupling of mechanic stress and electrical polarization results in piezoelectricity. KDP type materials are piezoelectrics at room temperature and ADP was formerly used in submarine applications to emit and receive ultrasonic waves. Berlinite, AIPO4, is structurally related to the common piezoelectric a -Si02 (see Section 5.1.2) and has superior properties in some respects. 

The second component is called afield effect and is attributed to through-space interactions of the electric dipoles resulting from polar bonds. 

Vibration Diagram Method. In actuality the last cases above are not described accurately by this dipole array model because actual phases of the electric fields are significantly altered from those of linear waves. (A more realistic, but complex model is to consider amplitude and phase characteristics of the oscillating vertically polarized component of electric field resulting from rotation of a line of transverse dipoles of equal magnitude but rotated relative to each other along the line such that their vertical components at some reference time are depicted by Figure 2.) For this reason and to handle details of focused laser beams one must resort to a more mathematically based description. Fortunately, numerical... 

Method involves placing a specimen between parallel plate capacitors and applying a sinusoidal voltage (frequencies ranging from 1 mHz to 1 MHz) to one of the plates to establish an electric field in the specimen. In response to this field, a specimen becomes electrically polarized and can conduct a small charge from one plate to the other. Through measurement of the resultant current, the dielectric constant and dielectric loss constant for a specimen can be measured. The sharp increases in both the dielectric constant and the dielectric loss constant during a temperature scan are correlated with the occurrence of Tg... 

Chirality (or a lack of mirror symmetry) plays an important role in the LC field. Molecular chirality, due to one or more chiral carbon site(s), can lead to a reduction in the phase symmetry, and yield a large variety of novel mesophases that possess unique structures and optical properties. One important consequence of chirality is polar order when molecules contain lateral electric dipoles. Electric polarization is obtained in tilted smectic phases. The reduced symmetry in the phase yields an in-layer polarization and the tilt sense of each layer can change synclinically (chiral SmC ) or anticlinically (SmC)) to form a helical superstructure perpendicular to the layer planes. Hence helical distributions of the molecules in the superstructure can result in a ferro- (SmC ), antiferro- (SmC)), and ferri-electric phases. Other chiral subphases (e.g., Q) can also exist. In the SmC) phase, the directions of the tilt alternate from one layer to the next, and the in-plane spontaneous polarization reverses by 180° between two neighbouring layers. The structures of the C a and C phases are less certain. The ferrielectric C shows two interdigitated helices as in the SmC) phase, but here the molecules are rotated by an angle different from 180° w.r.t. the helix axis between two neighbouring layers. 

The return to equilibrium of a polarized region is quite different in the Debye and Lorentz models. Suppose that a material composed of Lorentz oscillators is electrically polarized and the static electric field is suddenly removed. The charges equilibrate by executing damped harmonic motion about their equilibrium positions. This can be seen by setting the right side of (9.3) equal to zero and solving the homogeneous differential equation with the initial conditions x = x0 and x = 0 at t = 0 the result is the damped harmonic oscillator equation ... 

The most useful piezoelectric constant is the tensor which relates electric polarization to the stress causing the polarisation. The d-constant is also identified to the derivative of the resulting strain with respect to the applied electric field [24] ... 

Most important is, however, the fact that Pr strongly depends on VF2 content. This is because the copolymers adopt the all-trans highly polar conformation (see Sect 3) and with increasing number of VF2 units the resulting dipole moment within each crystal increases. In fact, it has been shown that the electric polarization in these copolymers increases with the fraction of ferroelectric crystals in the material... 

Results for improved by introducing the surrounding 4 water molecules into the cavity, but still only leads to 45% of the gas-to-liquid shift for the 170 nucleus (97). Likewise, this method fails to account for all of the gas-to-liquid shift of 19F in fluoromethanes (99) and of 77Se in H2Se (100). Clearly, medium effects can not be treated accurately by using a reaction field model. The major problem with the above two approaches is that only the electric polarization effects are included in the model. 

When the change in the solute-solvent interactions results mainly from changes in the solute charge distribution, one can employ the theory of electric polarization to formulate the dynamic response of the system. This formulation involves the nonlocal dielectric susceptibility m(r, r, i) of the solution. While this first step might lead to either the molecular or the continuum theory of solvation, in the continuum approach (r, r, t) is related approximately to the pure solvent susceptibility (r, r, t) in the portions of... 

However the precise sequence of coordinate participation in the reaction path is solvent dependent. For the case just discussed, the water solvent is rapid, largely because of the small moment of inertia involved in the water molecule reorientations underlying the change of the electrical polarization. Dimethyl formamide (DMF) solvent is less rapid, and the resulting coordinate sequence on the way to the TS [3] is again in the order of decreasing slowness, but now the solvent coordinate is the slowest of the three, followed by the bend angle and finally the C - Cl bond stretch. The reaction path depends on the solvent time scale. 

The factors 2 and 4 in the denominators are due to the definition of the field amplitudes (Eq.(14) and Eq.(15)). In order to prevent these factors some authors drop the factor 1/2 in the definitions of the amplitudes. The disadvantage of this convention is the unusual convergence behaviour of the electric field as the frequency to approaches zero. This different field definition of course additionally complicates the comparison of different hyperpolarizability values. The factors in the numerator arise from the different possibilities to permute the input frequencies. As an example, in self-phase modulation the three input electric fields each provide a factor 1/2 which, with the factor 1/2 from the polarization, results in a denominator of 4. The negative frequency for SPM allows three permutations yielding finally a prefactor of 3/4. 

All materials undergo a small change in dimensions when subjected to an electric field. If the resultant strain is proportional to the square of the field it is known as the electrostrictive effect. Some materials show the reverse effect - the development of electric polarization when they are strained through an applied stress. These are said to be piezoelectric (pronounced pie-ease-oh ). To a first approximation the polarization is proportional to the stress and the effect is said to be direct . Piezoelectric materials also show a converse effect, i.e. the development of a strain x directly proportional to an applied field. 

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