Polarizability dielectric properties

Ah initio calculations of polymer properties are either simulations of oligomers or band-structure calculations. Properties often computed with ah initio methods are conformational energies, polarizability, hyperpolarizability, optical properties, dielectric properties, and charge distributions. Ah initio calculations are also used as a spot check to verify the accuracy of molecular mechanics methods for the polymer of interest. Such calculations are used to parameterize molecular mechanics force fields when existing methods are insulficient, which does not happen too often. 

PollockEL, Alder BJ, Patey GN (1981) Static dielectric properties of polarizable Stockmayer fluids. Physica A Stat Theor Phys 108(1) 14—26... 

Harder E, Anisimov VM, Whitfield TW, MacKerell AD, Roux B (2008) Understanding the dielectric properties of liquid amides from a polarizable force field. J Phys Chem B 112(11 ) 3509—3521... 

In contrast with Eq. (5), Eq. (11) gives the frequency behavior in relation to the microscopic properties of the studied medium (polarizability, dipole moment, temperature, frequency of the field, etc). Thus for a given change of relaxation time with temperature we can determine the change with frequency and temperature of the dielectric properties - the real and imaginary parts of the dielectric permittivity. 

The nonlinear optical and dielectric properties of polymers find increasing use in devices, such as cladding and coatings for optical fibres, piezoelectric and optical fibre sensors, frequency doublers, and thin films for integrated optics applications. It is therefore important to understand the dielectric, optical and mechanical response of polymeric materials to optimize their usage. The parameters that are important to evaluate these properties of polymers are their dipole moment polarizability a, hyperpolarizabilities 0... 

We have shown in this paper the relationships between the fundamental electrical parameters, such as the dipole moment, polarizability and hyperpolarizability, and the conformations of flexible polymers which are manifested in a number of their electrooptic and dielectric properties. These include the Kerr effect, dielectric polarization and saturation, electric field induced light scattering and second harmonic generation. Our experimental and theoretical studies of the Kerr effect show that it is very useful for the characterization of polymer microstructure. Our theoretical studies of the NLDE, EFLS and EFSHG also show that these effects are potentially useful, but there are very few experimental results reported in the literature with which to test the calculations. More experimental studies are needed to further our understanding of the nonlinear electrooptic and dielectric properties of flexible polymers. 

Water absorption can also cause significant changes in the permittivity and must be considered when describing dielectric behavior. Water, with a dielectric constant of 78 at 25°C, can easily impact the dielectric properties at relatively low absorptions owing to the dipolar polarizability contribution. However, the electronic polarizability is actually lower than solid state polymers. The index of refraction at 25°C for pure water is 1.33, which, applying Maxwell s relationship, yields a dielectric constant of 1.76. Therefore, water absorption may actually act to decrease the dielectric constant at optical frequencies. This is an area that will be explored with future experiments involving water absorption and index measurements. 

The study of behavior of many-electron systems such as atoms, molecules, and solids under the action of time-dependent (TD) external fields, which includes interaction with radiation, has been an important area of research. In the linear response regime, where one considers the external held to cause a small perturbation to the initial ground state of the system, one can obtain many important physical quantities such as polarizabilities, dielectric functions, excitation energies, photoabsorption spectra, van der Waals coefficients, etc. In many situations, for example, in the case of interaction of many-electron systems with strong laser held, however, it is necessary to go beyond linear response for investigation of the properties. Since a full theoretical description based on accurate solution of TD Schrodinger equation is not yet within the reach of computational capabilities, new methods which can efficiently handle the TD many-electron correlations need to be explored, and time-dependent density functional theory (TDDFT) is one such valuable approach. 

The dipole, the oetupolar moment and the polarizability of protonated dpg molecules, and therefore the optieal and dielectric properties of dpg salts, depend on the orientation of the rings, whieh justifies the need to determine aecurate struetural data for these eompounds. At the present time sufficient structures have been reported so that eommon conformations or patterns can be identified. Table 7 eontains a brief identification of all the struetures analyzed in this review. 

Figure 6 Singly occupied molecular orbital (SOMO) of a propeller-like trimer radical anion of acetonitrile obtained using density functional theory. The structure was immersed in a polarizable dielectric continuum with the properties of liquid acetonitrile. Several surfaces (on the right) and midplane cuts (on the left) are shown. The SOMO has a diffuse halo that envelops the whole cluster within this halo, there is a more compact kernel that has nodes at the cavity center and on the molecules.

The induced dipole moment of a polymer in an electric field is proportional to the strength of the field, and the proportionality constant is related to the polarizability of the atoms in the polymer. The dielectric properties of polymers are affected adversely by the presence of moisture, and this effect is greater in hydrophilic than in hydrophobic polymers. 

Atomic polarizability is too small a contribution to affect the dielectric properties appreciably. It appears that fluorine substitution decreases the atomic polarizability slightly, but the small magnitude of the effect precludes precise determination.52... 

Argon, krypton, and xenon have polarizabilities of 16.5, 25.4, and 41.3 X 10 26 cm.3, respectively. McDonald found that these gases produce shifts of 8, 16, and 19 cm.-1. Nitrogen, oxygen, and methane, which have polarizabilities of 17.6, 16.0, and 26.0 X 10-26 cm.3, produce shifts of 24, 12, and 32 cm.-1, respectively. McDonald interpreted these results as showing that the polarizability is not the only factor involved and that the frequency shifts depend on an additional factor related to the chemical nature of the adsorbed molecules. He concluded that the frequency shifts cannot be completely explained in terms of macroscopic dielectric properties. 

The dielectric constant varies with coal rank (Chatterjee and Misra, 1989). The theorem that the dielectric constant is equal to the square of the refractive index (which is valid for nonconducting, nonpolar substances) holds only for coal at the minimum dielectric constant. The decreasing value of dielectric constant with rank may be due to the loss of polar functional groups (such as hydroxyl or carboxylic acid functions), but the role of the presence of polarizable electrons (associated with condensed aromatic systems) is not fully known. It also appears that the presence of intrinsic water in coal has a strong influence on the dielectric properties (Chatterjee and Misra, 1989). 

The structure of this contribution is as follows. After a brief summary of the theory of optical activity, with particular emphasis on the computational challenges induced by the presence of the magnetic dipole operator, we will focus on theoretical studies of solvent effects on these properties, which to a large extent has been done using various polarizable dielectric continuum models. Our purpose is not to give an exhaustive review of all theoretical studies of solvent effects on natural optical activity but rather to focus on a few representative studies in order to illustrate the importance of the solvent effects and the accuracy that can be expected from different theoretical methods. 

E. L. Pollock, B. J. Alder and G. N. Patey, Static dielectric properties of polarizable Stock-mayer fluids, Physica A, 108 (1981) 14—26. 

The most important dielectric properties are the dielectric constant, e, and the dielectric loss factor, tan 8. These properties are of interest for alternating currents indicates the polarizability in an electric field, and, therefore, it governs the magnitude of the alternating current transmitted through the material when used in a capacitor. For most polymers e is between 2 and 5, but it may reach values up to 10 for filled systems. 

Kirouac S, Bose TK (1976) Polarizability and dielectric properties of helium. J Chem Phys 64 1580-1582... 

Rigorous formulations of the problems associated with solvation necessitate approximations. From the computational point of view, we are forced to consider interactions between a solute and a large number of solvent molecules which requires approximate models [75]. The microscopic representation of solvent constitutes a discrete model consisting of the solute surrounded by individual solvent molecules, generally only those in close proximity. The continuous model considers all the molecules surrounding the solvent but not in a discrete representation. The solvent is represented by a polarizable dielectric continuous medium characterized by macroscopic properties. These approximations, and the use of potentials, which must be estimated with empirical or approximate computational techniques, allows for calculations of the interaction energy [75],... 

Casimir and Polder also showed that retardation effects weaken the dispersion force at separations of the order of the wavelength of the electronic absorption bands of the interacting molecules, which is typically 10 m. The retarded dispersion energy varies as R at large R and is determined by the static polarizabilities of the interacting molecules. At very large separations the forces between molecules are weak but for colloidal particles and macroscopic objects they may add and their effects are measurable. Fluctuations in particle position occur more slowly for nuclei than for electrons, so the intermolecular forces that are due to nuclear motion are effectively unretarded. A general theory of the interaction of macroscopic bodies in terms of the bulk static and dynamic dielectric properties... 

As discussed in the previous section, the dielectric properties of materials at microwave frequencies are strongly dependent on the ionic polarization. Theoretical dielectric constants of materials can be obtained from the dielectric polarizabilities of composing ions through the understanding of crystal structure. Let us consider the basic relationships between the dielectric polarizabilities and dielectric constants and how the control of dielectric properties and the search for new materials can be achieved by the additive rule. 

Most of the search for improved microwave materials has been mainly empirical, and it is necessary that the intrinsic properties of materials be known to control and design the dielectric properties of materials. Recently there have been reports on the intrinsic properties of materials by the IR reflectivity spectra and calculation of theoretical polarizability. However, there are discrepancies between the intrinsic properties obtained from these methods and the measured properties due to grain, grain boundary, and pores. Therefore the effects of porosity on the dielectric properties should be considered to evaluate the intrinsic dielectric properties and to predict the dielectric properties of ceramics with pores. 

Previous Reviews. A general survey of the effects of molecular interactions on the optical properties of matter was recently given by Buckingham [435]. The work concerning ab initio and approximate computations of pair polarizabilities has recently been reviewed by Hunt [80] a careful comparison of the data available from various measurements reveals a high degree of consistency with the fundamental theory. Hunt has also reviewed the utility of the DID model and its limitations [79]. The results of measurements of the polarizability invariants of rare-gas pairs have been reviewed by one of the authors [271]. Substantial discussions of induced polarizabilities can be found in a number of review articles on CILS and dielectric properties [11,27, 143, 274, 343, 376]. 

---