Dipolar particles, polarizable

Vapors dilute and not-so-dilute In a dilute vapor, the external electric field polarizing any one particle—atom or molecule—is unchanged by electric fields emanating from dipoles induced on the other particles. (These dipolar fields drop off as the inverse cube of the distance from the particle.) The total polarization per unit volume of the dilute gas is the sum of individual particle dipoles. If a(a>) denotes the single-particle polarizability and N is the number of particles per unit volume, then for a vapor... 

Almost all the formalism and the approximation schemes of Sections II and III have a natural extension to systems of polarizable dipolar particles, but the precise details of the extension depend on the way polarizability is introduced into the Hamiltonian. We refer to the two quite distinct Hamiltonian models that have been most thoroughly developed in this context as the constant-polarizability model and the fluctuating-polarizability model. The dielectric behavior of the former was first systematically investigated from a statistical mechanical viewpoint by Kirkwood and by Yvon, who considered the model almost exclusively in the absence of permanent dipole moments. (Kirkwood S subsequently pioneered an exact formulation of the statistical mechanics of polar molecules, but largely as a separate enterprise that did not attempt to treat the polarizability exactly.) The general case of polar-polarizable particles remained only very partially developed ... 

In numerical simulations of systems of N polarizable dipolar particles the induced dipoles must be computed by solving a set of N linear equations depending on the positions and orientations of the N dipoles of the system. The solution of this set of equations requires of the order of operations and deteriorates considerably the efficiency of MC simulations since, in principle, for each MC elementary move involving, for instance, the displacement of one particle, the N linear equations have to be solved. The vaUdity of numerical procedures allowing us to overcome this problem is discussed in [94]. The procedures are based on the choice of an adequate cut-off of the interparticle distances such that the computation of the induced dipole of a displaced particle depends only on the positions and orientations of dipoles located at a distance of the trial particle position smaller than the cut-off. 

The electrostatic polarization theory is commonly employed to describe ER response. The model assumes that ER fluids are dispersions of nonionic polarizable particles in a low dielectric medium and that free charges and charge-transfer electrochemical processes can be neglected. This model is based on the fact that, due to the permittivity mismatch between the particles 6p and the continuous phase e, the dipolar particles are polarized and aligned with the neighboring particles. When an electric field is superimposed on the point dipole interaction, the orientation of the dipoles in relation to the exter-... 

A particle is subdivided into a small number of identical elements, perhaps 100 or more, each of which contains many atoms but is still sufficiently small to be represented as a dipole oscillator. These elements are arranged on a cubic lattice and their polarizability is such that when inserted into the Clausius-Mossotti relation the bulk dielectric function of the particle material is obtained. The vector amplitude of the field scattered by each dipole oscillator, driven by the incident field and that of all the other oscillators, is determined iteratively. The total scattered field, from which cross sections and scattering diagrams can be calculated, is the sum of all these dipolar fields. 

The polarizability, a, is a measure of the extent to which the electronic distribution over a molecule can be distorted by the electric field of charged particles, or dipolar molecules. 

An increase of T is also observed if a polarizability is added to Stock-mayer particles, since the main effect of polarizability is to increase, on average, the magnitude of the permanent dipole moment [128]. Similar sensitivity of the 1-g transition to the relative strength of the dispersion potential and dipolar interaction occurs in the Q2D Stockmayer fluid [45]. Compared to the 3D Stockmayer fluid the critical temperature is reduced by confinement of the centres of mass in a plane and the coexistence curve is much flatter. In [45] no estimate has been given for the dipole strength at which the 1-g transition is expected to be superseded by the chain formation. 

Mie theory gives the rigorous solutions of wave equations only for spherical nanoparticles. For particles with other shapes like ellipsoids, Mie theory cannot be applied, and treatment with the dipolar approximation is useful to discuss the optical properties of the particle qualitatively. By taking the shape-dependent depolarization factor into account, the polarizability of the ellipsoid can be obtained as a form similar to that of the sphere [42]. 

While all the spectra are still dominated by the dipolar plasmon mode, the contribution from the quadrupolar mode increases as nanoparticle size increases the quadrupolar polarizability in fact increases with the fifth power of the particles size, against the third power for the dipolar one. 

Assembly of NPs in electric and magnetic fields occurs due to induced polarization between magnetically and electrically polarizable colloids, respectively. The induced field surrounding a polarized particle transforms into a dipole and results in an anisotropic dipole-dipole interaction between NPs. One of the key factors governing the assembly of NPs via field-induced interactions is the relationship between dipolar interactions and thermal forces. The dipole strength relative to thermal energy is... 

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