Bulk dielectric value

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

Another variant that may mrn out to be the method of choice performs the alchemical free energy simulation with a spherical model surrounded by continuum solvent, neglecting portions of the macromolecule that lie outside the spherical region. The reaction field due to the outer continuum is easily included, because the model is spherical. Additional steps are used to change the dielectric constant of that portion of the macromolecule that lies in the outer region from its usual low value to the bulk solvent value (before the alchemical simulation) and back to its usual low value (after the alchemical simulation) the free energy for these steps can be obtained from continuum electrostatics [58]. 

Manning s theory does not take the local effective dielectric constant into consideration, but simply uses the a value of bulk water for the calculation of E,. However, since counterion condensation is supposed to take place on the surface of polyions. Manning s 2, should be modified to E, by replacing a with aeff. The modified parameters E, is compared with E, in Table 1, which leads to the conclusion that the linear charge density parameter calculated with the bulk dielectric constant considerably underestimates the correct one corresponding to the interfacial dielectric constant. 

However, the equilibrium of the indicator adsorbed at an interface may also be affected by a lower dielectric constant as compared to bulk water. Therefore, it is better to use instead pH, the interfacial and bulk pK values in Eq. (50). The concept of the use at pH indicators for the evaluation of Ajy is also basis of other methods, like spin-labeled EPR, optical and electrochemical probes [19,70]. The results of the determination of the Aj by means of these methods may be loaded with an error of up to 50mV [19]. For some the potentials determined by these methods, Ajy values are in a good agreement with the electrokinetic (zeta) potentials found using microelectrophoresis [73]. It is proof that, for small systems, there is lack of methods for finding the complete value of A>. 

With the addition of a pseudopotential interaction between electrons and metal ions, the density-functional approach has been used82 to calculate the effect of the solvent of the electrolyte phase on the potential difference across the surface of a liquid metal. The solvent is modeled as a repulsive barrier or as a region of dielectric constant greater than unity or both. Assuming no specific adsorption, the metal is supposed to be in contact with a monolayer of water, modeled as a region of 3-A thickness (diameter of a water molecule) in which the dielectric constant is 6 (high-frequency value, appropriate for nonorientable dipoles). Beyond this monolayer, the dielectric constant is assumed to take on the bulk liquid value of 78, although the calculations showed that the dielectric constant outside of the monolayer had only a small effect on the electronic profile. 

A great variety of aqueous—organic mixtures can be used. Most of them are listed in Table I with their respective freezing point and the temperature at which their bulk dielectric constant (D) equals that of pure water. These mixtures have physicochemical properties differing from those of an aqueous solution at normal temperature, but some of these differences can be compensated for. For example, the dielectric constant varies upon addition of cosolvent and cooling of the mixture in such a way that cooled mixed solvents can be prepared which keep D at is original value in water and are isodielectric with water at any selected temperature (Travers and Douzou, 1970, 1974). 

The effective bulk dielectric constant is determined by measuring the distance between a maximum and minimum value of amplitude. The bulk loss factor is determined by measuring the amplitude of the signal under the sample with the loop, as a function of plunger distance from the beginning of the sample. 

For bulk dielectrics, a dielectric resonator can be formed by a cylindrically shaped piece of dielectric material. Dielectric thin films are more difficult to investigate, in particular when the loss tangent is very small. Planar resonator techniques as well as specially designed dielectric resonators can be used to examine their properties. For high-temperature superconductors both dielectric resonators and planar resonators represent an ideal tool to examine their surface impedance values. 

From an absolute matching of pfm and pfs we find eSurface to measure 140, much smaller than the bulk e value determined from dielectric spectroscopy (eBuik 500). 

Since ea is determined by the counterfields from the second and further shells, increasing incoherence with rising number of shells will tend to compensate for the increasing value ofthe summation as the number increases, so its effective value will be close to unity. An experimental value of COS0 derived from the bulk dielectric constant is used here, which will give an effective value. 

Incidentally, such plots (Figure 4) may be used to compute approximate values of the bulk dielectric constants of water-organic mixed solvents from the emf measurements provided that the bulk dielectric constant is higher than 40. In fact, for auto-ionizing solvents this may be a convenient method, and our calculations have shown that such computed values are within 5-7% of the experimental values. 

Our primary objective was to develop a computational technique which would correlate the ionization constant of a weak electrolyte (e.g., weak acid, ionic complexes) in water and the ionization constant of the same electrolyte in a mixed-aqueous solvent. Consideration of Equations 8, 22, and 28 suggested that plots of experimental pKa vs. some linear combination of the reciprocals of bulk dielectric constants of the two solvents might yield the desirable functions. However, an acceptable plot should have the following properties it should be continuous without any maximum or minimum the plot should include the pKa values of an acid for as many systems as possible and the plot should be preferably linear. The empirical equation that fits this plot would be the function sought. Furthermore, the function should be analogous to some theoretical model so that a physical interpretation of the ionization process is still possible. 

Through a series of parametrization, the most suitable linear combination was (1/c — 1/c") where c = c + (c — corg), = 2c — c0rg, = bulk dielectric constant of the mixed solvent, corg = bulk dielectric constant of the pure organic component, and c = bulk dielectric constant of water. (The dielectric constant data were obtained from literature these references are not being cited in order to save space. Some of the c values were obtained by these authors by interpolation. For the convenience of the reader we have compiled the values of bulk... 

Notwithstanding the considerations of Section 2.12.1, the use of the bulk dielectric constant of water for dilute solutions of nonelectrolyte is not very inaccurate in the region outside the primary solvation sheath. The point is that in this region (i.e., at distances > 500 to 1000 pm from the ion s center), there is neghgible structure breaking and therefore a neghgible decrease in dielectric constant from the bulk value. 

Measurements of the dynamic properties of the surface water, particularly NMR measurements, have shown that the characteristic time of the water motion is slower than the bulk water value by a factor of less than 100. The motion is anisotropic. There is litde or no irrotadonally bound water. Study of a protein labeled covalently with a nitroxide spin probe (Polnaszek and Bryant, 1984a,b) has shown that the diffusion constant of the surface water is about 5-fold below the bulk water value. The NMR results are in agreement with measurements of dielectric relaxation of water in protein powders (Harvey and Hoekstra, 1972). 

Tlie numerical value obtained from Eq. 3G above, using e = 78 for the bulk dielectric constant of water at room temperature and a typical value of 2x10 cm for d, is 0.34 mF/cm, more than 20 times the experimentally observed value of 16 iiF/cm. ... 

In the examples presented here, the extension to the Lindhard RPA [23] suggested by Mermin [24] is used for the bulk dielectric function. This allows one to use non-zero values of the electron gas damping, keeping the number of electrons in the system constant. We want to emphasize that this description incorporates both single-particle excitations (creation of electron-hole pairs) and collective excitations (bulk and surface plasmons). 

By using the bulk dielectric permittivity, the value of A,s includes consideration not only of the dipole moment of the solvent but also its polarizability and other features which are necessary to describe ion iipole and dipole lipole interac-... 

---