Electric field induced polarization force

Since the dielectric constants of particle and the dispersing medium are different, the excess amount of charge appears on the particle surfaces under an electric field. The induced dipole moment p can be expressed as [34]  

When those two particles are far away from each other, they can be regarded as point-dipole, and the interaction energy between tw o point dipoles Upd [34] 

Various dimensionless groups have been used to describe the relative importance of the forces described above. According to Gast and Zukoski [34], those forces can be simply scaled as shown in Table 2 and thus the dimensionless groups can be obtained by simply taking the ratio between them. 

Here / is the shear rate, fhe relative importance between the viscous and thermal forces is described by the Peclect number, Pe. The relative importance of the polarization to the thermal energy is described by the 

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The van der Waals radius determines the shortest distance over which intermolecu-iar forces operate it is aiways larger than the covalent radius. Intermolecular forces are much weaker than bonding (intramolecular) forces. Ion-dipole forces occur between ions and poiar molecules. Dipole-dipole forces occur between oppositely charged poles on polar molecules. Hydrogen bonding, a special type of dipole-dipole force, occurs when H bonded to N, O, or F is attracted to the lone pair of N, O, or F in another molecule. Electron clouds can be distorted (polarized) in an electric field. Dispersion (London) forces are instantaneous dipole-induced dipole forces that occur among all particles and increase with number of electrons (molar mass). Molecular shape determines the extent of contact between molecules and can be a factor in the strength of dispersion forces. 

Kumar and coworkers proposed a mechanism on the basis of the observation that an electric field component in the direction of mass flow was required (Yang et ah, 2006 Bian et al., 2000 Viswanathan et ah, 1999a Kumar et ah, 1998). This force is essentially an optical gradient force (Chaumet and Nieto-Vesperinas, 2000 Ashkin, 1997, 1970). Spatial variation of light (electric field intensity and orientation) leads to a variation of the material susceptibility, %, at the sample surface. The electric field then polarizes the material. The induced polarization is related to the light intensity and local susceptibility ... 

Dielectric FFF Dielectrophoretic forces result from the interaction of field-induced polarized particles and a nonuniform AC electrical field. The magnitude of the force depends on the frequency of the applied field and the polarizability of the particles, which in turn is affected by the chemical composition. Gascoyne and coworkers in Texas have performed a separation of human leukocytes in focusing mode FFF, where the gravitational force on the cells toward the accumulation wall was balanced by the upward dielectrophoretic force. Thus the separation illustrated the combined use of two different fields (Dl-Gr/ FoFFF). This is smely an exciting new development in FFF. 

A reorientation or depolarization of the domain is also effected by mechanical stress (e.g. 20... 50 N/mm for PZT). Influencing factors besides the stress magnitude are its direction and frequency as well as the kind of electrical circuit (e.g. open circuit, load or short circuit). If the electrical field induced by a force is in the polarization direction, the nonlinearities are essentially smaller than those of a generated field in the opposite direction or in the case of short circuit. 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

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. 

The total electric field, E, is composed of the external electric field from the permanent charges E° and the contribution from other induced dipoles. This is the basis of most polarizable force fields currently being developed for biomolecular simulations. In the present chapter an overview of the formalisms most commonly used for MM force fields will be presented. It should be emphasized that this chapter is not meant to provide a broad overview of the field but rather focuses on the formalisms of the induced dipole, classical Drude oscillator and fluctuating charge models and their development in the context of providing a practical polarization model for molecular simulations of biological macromolecules [12-21], While references to works in which the different methods have been developed and applied are included throughout the text, the major discussion of the implementation of these models focuses... 

Usually we call neutral molecule as polar one if it has considerable permanent electric dipole moment /i°. The total dipole moment should include also an induced one, aR (a is a polarizability of the molecule, R is the intensity of electric field interacting with molecule), and may be presen ted as /i = /<° + a . Permanent part of dipole moment for nonsymmetrical organic molecules usually accepted to be essentially larger than induced one that is why orientational forces or interactions of permanent electric dipoles are the most important in polar solutions [1,2,4,12, 39]. 

London dispersion or induced dipoie forces Any atom or molecule can become polarized when placed in an electrical field E, and the induced dipole moment is proportional to its polarizability factor a by... 

Closely related to ferroelectricity is piezoelectricity in which polarization is induced and an electric field is established across a specimen by the application of external force (see Figure 6.28a,b). Reversing the direction of the external force, as from tension to compression, reverses the direction of the field. Alternatively, the application of an external electric field alters the net dipole length and causes a dimensional change, as in Figure 6.28c. Piezoelectric materials can be used as transducers—devices that... 

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