Specific polarizability

R. Improta, V. Barone, G. Scalmani, M.J. Frisch, A state-specific polarizable continuum model time dependent density functional theory method for excited state calculations in solution. J. Chem. Phys. 125, 054103 (2006)... 

The rates of the 5 2 reaction between phenacyl bromide and 2-mercaptobenzothia-zole in 17 protic and aprotic solvents have been measured. The effect on the rates is assessed in terms of the electrophilicity, the hydrogen-bond donor ability, the specific polarizability, and a non-specific polarity of the solvent. The relative infiuence of each factor is given and a linear solvation energy equation is proposed. 

Here (a ) is the specific polarizability of the sorbate within the sorbent/sorbate system considered. 

Measurements of the (static) dielectric permittivity (ers) of a sorbent/sorbate system allow the determination of the product of the specific polarizability of the molecules adsorbed (a ) and the Gibbs excess mass of the adsorbate (mQ ) Indeed we have from Sect. 2.2, Eq. (6.47)... 

In many chemical applications, however, it would be more interesting to know how polarizability can stabilize a charge introduced into a molecule. Thus, rather than the global molecular property, mean molecular polarizability, a local, site-specific value for polarizability is needed. 

There were two schools of thought concerning attempts to extend Hammett s treatment of substituent effects to electrophilic substitutions. It was felt by some that the effects of substituents in electrophilic aromatic substitutions were particularly susceptible to the specific demands of the reagent, and that the variability of the polarizibility effects, or direct resonance interactions, would render impossible any attempted correlation using a two-parameter equation. - o This view was not universally accepted, for Pearson, Baxter and Martin suggested that, by choosing a different model reaction, in which the direct resonance effects of substituents participated, an equation, formally similar to Hammett s equation, might be devised to correlate the rates of electrophilic aromatic and electrophilic side chain reactions. We shall now consider attempts which have been made to do this. 

Even in the absence of Faradaic current, ie, in the case of an ideally polarizable electrode, changing the potential of the electrode causes a transient current to flow, charging the double layer. The metal may have an excess charge near its surface to balance the charge of the specifically adsorbed ions. These two planes of charge separated by a small distance are analogous to a capacitor. Thus the electrode is analogous to a double-layer capacitance in parallel with a kinetic resistance. 

The basic premise of Kamlet and Taft is that attractive solute—solvent interactions can be represented as a linear combination of a nonspecific dipolarity/polarizability effect and a specific H-bond formation effect, this latter being divisible into solute H-bond donor (HBD)-solvent H-bond acceptor (HB A) interactions and the converse possibility. To establish the dipolarity/polarizability scale, a solvent set was chosen with neither HBD nor HBA properties, and the spectral shifts of numerous solvatochromic dyes in these solvents were measured. These shifts, Av, were related to a dipolarity/polarizability parameter ir by Av = stt. The quantity ir was... 

Attempts have also been made to separate non-specific effects of the local electrical field from hydrogen-bonding effects for a small group of ionic liquids through the use of the k scale of dipolarity/polarizability, the a scale of hydrogen bond donor acidity, and the (i scale of hydrogen bond basicity (see Table 3.5-1) [13, 16]. 

While it is not beyond the realm of possibility to evaluate the g s, h s, and Q for appropriate wave functions, some further simplification is necessary for our present arguments. We assume that the s are orthogonal to all y s. This is not necessarily true although the //s can be selected to make it true. Even without specific selection of /A s it is probably a good approximation for those s which contribute substantially to the polarizability. Then... 

Equation (17) expresses the cell potential difference in a general way, irrespective of the nature of the electrodes. Therefore, it is in particular valid also for nonpolarizable electrodes. However, since

interfacial structure, only polarizable electrodes at their potential of zero charge will be discussed here. It was shown earlier that the structural details are not different for nonpolarizable electrodes, provided no specifically adsorbed species are present. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

Atom dynamics Group contribution and rigid bonds/angels Specific adsorption Dipolar hard sphere SPC, ST2, TIPS Polarizable H Bonds... 

In recent years, many types of double-layer capacitors have been built with porous or extremely rough carbon electrodes. Activated carbon or materials produced by carbonization and partial activation of textile cloth can be used for these purposes. At carbon materials, the specific capacity is on the order of 10 J,F/cm of trae surface area in the region of ideal polarizability. Activated carbons have specific surface areas attaining thousands of mVg. The double-layer capacity can thus attain several tens of farads per gram of electrode material at the surfaces of such carbons. 

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