Volume polarization

Fig. 5.19. Shock-induced volume polarizations have been observed in a wide range of solids due to a number of different physical phenomena, including piezoelectricity and ferroelectricity. The signals observed from polymers and ionic crystals are not due to established phenomena, and are described as due to shock-induced polarization effects.

The interaction between permanent or induced electric dipoles with an applied electric field is called polarization, which is the induced dipole moment per unit volume. Polarization causes positive charge to accumulate on the bottom surface next to the... 

Even for a simple reaction, involving just one reactant species and one product species, such as a keto-enol tautomerism or a cis-trans isomerization, the above equation for a given solvent is complicated. StUl, in specific cases it is possible to unravel the solvent effects of cavity formation, for the solute species have different volumes, polarity/polarizability if the solute species differ in their dipole moments or polarizabilities, and solvent Lewis acidity and basicity if the solutes differ in their electron-pair and hydrogen-bond acceptance abilities. 

Curie s equation applies to gases, solutions, and some crystals. For other crystals a more general equation, the Weiss equation, may be used (derived by P. Weiss in 1907). Weiss assumed that the local magnetic field orienting the dipoles is equal to the applied field plus an added field proportional to the magnetic volume polarization M ... 

Fig. 29. Temperature dependence of complex piezoelectric strain constant of composite film of polyester resin and powdered PZT (50% of the volume) polarized at room temperature under a d.c. field of 100 kV/cm. Reproduced from Fukada and Date [Polymer Journal, 1,410 (1970)] by permission of the Society of Polymer...

Although it is possible to correlate solute solubility to different physical properties, such as molar volume, polarity, polarizability, and chain length, the most frequently used property is the... 

There are two other main directions for the calculation of the electrostatic interaction between the solute and a surrounding dielectric continuum for molecular-shaped cavities. Both require intensive numerical calculations and are thus slower than GB methods. The first direction is the direct numerical solution of the Poisson equation for the volume polarization P(r) at a position r of the dielectric medium ... 

D. M. Chipman, Energy correction to simulation of volume polarization in reaction field theory, J. Chem. Phys., 116 (2002) 10129-10138. 

SVPE Surface and volume polarization for electrostatic interactions... 

This combination of Equations [5] and [16] is called the Generalized Born/Surface Area model (GB/SA), and it is currently available in the Macro-ModeP computer package. The speed of the molecular mechanics calculations is not significantly decreased by comparison to the gas phase situation, making this model well suited to large systems. Moreover, the model takes account of some first-hydration-shell effects through the positive surface tension as well as the volume polarization effects. A selection of data for aqueous solution is provided later (Table 2), and the model is compared to experiment and to other models. Nonaqueous solvents have been simulated by changing the dielectric constant in the appropriate equations, 8 but to take the surface tension to be independent of solvent does not seem well justified. 

To examine the role of the LDOS modification near a metal nanobody and to look for a rationale for single molecule detection by means of SERS, Raman scattering cross-sections have been calculated for a hypothetical molecule with polarizability 10 placed in a close vicinity near a silver prolate spheroid with the length of 80 nm and diameter of 50 nm and near a silver spherical particle with the same volume. Polarization of incident light has been chosen so as the electric field vector is parallel to the axis connecting a molecule and the center of the silver particle. Maximal enhancement has been found to occur for molecule dipole moment oriented along electric field vector of Incident light. The position of maximal values of Raman cross-section is approximately by the position of maximal absolute value of nanoparticle s polarizability. For selected silver nanoparticles it corresponds to 83.5 nm and 347.8 nm for spheroid, and 354.9 nm for sphere. To account for local incident field enhancement factor the approach described by M. Stockman in [4] has been applied. To account for the local density of states enhancement factor, the approach used for calculation of a radiative decay rate of an excited atom near a metal body [9] was used. We... 

Although many possible relationships between the amount solubilised and various physical properties of the solubilisate molecule (for example, molar volume, polarity,... 

Generalized Bom (GB) approach. The most common implicit models used for small molecules are the Conductor-Like Screening Model (COSMO) [77,78], the DPCM [79], the Conductor-Like Modification to the Polarized Continuum Model (CPCM) [80,81], the Integral Equation Formalism Implementation of PCM (IEF-PCM) [82] PB models, and the GB SMx models of Cramer and Truhlar [23,83-86]. The newest Minnesota solvation models are the SMD universal Solvation Model based on solute electron density [26] and the SMLVE method, which combines the surface and volume polarization for electrostatic interactions model (SVPE) [87-89] with semiempirical terms that account for local electrostatics [90]. Further details on these methods can be found in Chapter 11 of Reference [23]. 

Other descriptors included in the regression (volume, polar surface area, total contact area, and second principal moment) were found to be insignificant and not included in the final equation. Wifh fhe framing sef of 23 proteins, the model yielded an of 0.65 and a of 0.56. On an exfernal fesf set of 35 profeins, 94% of the known druggable pockets were correctly predicted as druggable. 

The problem of the errors in the computed apparent charges is different for the lEF method. In an article appeared on the Journal of Chemical Physics, Chipman proposed and examined a new tractable formulation to get an accurate approximation of volume polarization effects arising from... 

For solvation of small molecules, the polarizable continuum model (PCM) and its variants have been widely used for calculation of solvation energy. The conductor-like PCM (CPCM) model gives a concise formulation of solvent effect, in which the solvent s response to the solute polarization is represented by the presence of induced surface charges distributed on the solute-solvent interface. In this formulation, no volume polarization (extension of solute s electron distribution into the solvent region) is allowed. The induced surface charge counterbalances the electrostatic potential on the interface generated by the solute molecule. 

Methods based on an ASC have a long history in quantum-mechanical (QM) calculations with continuum solvent [60, 61, 77], where they are generally known as polarizable continuum models (PCMs). However, PCMs have seen little use in the area of biomolecular electrostatics, for reasons that are unclear to us. In the QM context, such methods are inherently approximate, even with respect to the model problem defined by Poisson s equation, owing to the volume polarization that results from the tail of the QM electron density that penetrates beyond the cavity and into the continuum [13, 14, 89], The effects of volume polarization can be treated only approximately within the ASC formalism [14, 15, 89], For a classical solute, however, there is no such tail and certain methods in the PCM family do afford a numerically exact solution of Poisson s equation, up to discretization errors that are systematically eliminable. Moreover, ASC methods have been generalized to... 

Equation (11.7) can be used to eliminate the exterior derivative of (p from Eq. (11.6). Then, given some initial approximation for rp (perhaps just tpf, which is known once the solute s wave function has been computed), one could compute the surface charge, and thus the reaction-field potential, without the need to perform any calculations outside of the solute cavity. For a QM solute, this procedure must then be iterated to self-consistency. The original PCM of Miertus, Scrocco, and Tomasi [60, 61] used precisely this approach this model is now known as D-PCM. It is less desirable than more modern PC Ms, owing to the need to compute the normal electric field, which may be subject to increased numerical noise relative to later formulations that involve only electrostatic potentials [77]. Perhaps more significantly, the formulation of this model has conflated the apparent and actual surface charge distributions, and corresponds to a neglect of volume polarization [13]. 

As such, an exact treatment of volume polarization [13, 18, 89], which is not considered here, requires discretization of three-dimensional space in order to solve Eq. (11.10). 

This is as far as one can go with an exact formulation, unless one is willing to solve Eq. (11.10) in three dimensions. However, the effect of volume polarization can be approximated by introducing an additional surface charge, a(s), that is defined such that its electrostatic potential at the cavity surface is identical to that generated by cp. Let us define an operator S that acts on functions /(s) defined on F, generating the corresponding electrostatic potential ... 

For QM solutes, volume polarization is treated approximately (but accurately [89]) by Eq. (11.17), and Chipman has called this approach surface and simulation of volume polarization for electrostatics [SS(V)PE] [15]. An equivalent form of Eq. (11.17) was actually derived prior to Chipman s work, where it was called the integral equation formalism (lEF) [10, 58]. The equivalence is not obvious, as the original lEF requires the solute s electric field as an input in addition to its electrostatic potential, but it was later shown that the former could be eliminated in order to obtain Eq. (11.17) [9]. The operator K can similarly be manipulated into different forms, by means of the identity [15]... 

Chipman, D. M. (2006). New formulation and implementation for volume polarization in dielectric continuum theory, /. Chem. Phys. 124, pp. 224111 1-10. 

Chipman DM. Vertical electronic excitation with a dielectric continuum model of solvation including volume polarization. I. Theory. J Chem Phys. 2009 131(1) 014103— 014111. http //dx.doi.org/10.1063/E3157464. 

Polyethylene (PE) is a member of the polyolefin family, which also includes PP and various plastics with different molecular linearily, densities, polymerization processes, and substitution types. PE densities are relatively low with values ranging from 0.940 to 0.970 g/cm for HOPE and from 0.916 to 0.940 g/cm for LLDPE. Typically, these PEs not only have good processability (e.g., can be converted into bags, films, and bottles) but also exhibit an excellent water vapor barrier property, which is required for many water-sensitive food products such as dried and liquid foods. However, this type of plastic is not appropriate for easily oxidized food products due to its low oxygen barrier property. The properties of polyolefins can be significantly affected by environmental conditions and physical factors, such as the density, crystallinity, presence of free volume, polarity, humidity, and temperature [44]. 

The surface and simulation of volume polarization for electrostatics [SS(V)PE] solvation model [6] was used to calculate the excited states of solvated zwitterionic amino acids in combination with the RI-CIS(D) method. 

As yet, the principles of electret formation are not fully understood. It is likely that both volume and surface polarizations can occur. A volume polarization is obtained with fields below 10 kV/cm. That is, if an electret is parted parallel to the charged surface, two new capacitors result. With fields of more than 10 kV/cm, an ionization, electronic failure, or break-... 

---