Debye parameters

Figure 18 Variation of the ground state energy of helium-like ions agai nst the Debye parameter. The lowermost curve is for He and the uppermost curve is for Ar16+ Reprinted with permission from [192] 2002, Springer Science + Business Media...

Figure 19 Plot of the lowest four S energies (au) of helium-like ions against different Debye parameters (au). The ionization limit is set to zero. Reprinted with permission from [193] 2002, Elsevier...

Using the double Debye parameters given in Pickwell et al. [58], the reflection coefficient expected from human skin has been calculated by the authors and monotonically decreases from 0.75 at low frequencies to 0.35 at 1 THz. These results show a general trend of decreasing reflectivity as the frequency is increased due to increased absorption and decreased refractive index. 

Fig. 14.4. Theoretical critical velocity as a function of separation distance for different values of solute radius/pore radius ratio (A). Solute radius (a) = 5 nm ko= 1.0 (k is the Debye parameter) membrane and solute surface potential = 50 mV. Values of A (a) 0.8 ...

As we see, the parameter 1 results from Langevin reorientation of the polarizability ellipsoid and is always positive. The second of the above parameters, 2, corresponds to Bom s term in the Kerr effect and can be positive or negative, depending on the electric structure of the molecule. The third, the Debye parameter 3, has no counterpart in other phenomena of molecular orientation, and is specific to the non-linear dielectric behaviour of dipolar substances. 

The Debye parameter, k (compare equation iii in Figure 9.19), is defined... 

Two systems discussed in the present study are determined by two different volume fraction r] = (it/(])(> I )A occupied by the micellar macroions in a bulk suspension, namely, r] = 0.01 and 0.05. According to Table 1, these two volume fractions are associated with the SDS micellar solutions characterized by two different surfactant concentrations of 0.03 and 0.10 mol/L and two different values of the Debye radius h 1. To be close to the real macroion suspensions, the value of the Debye parameter, used in computer modelling, was fixed at kD = 1.5 when macroion volume fraction is rj = 0.01, and kD = 2 in the case of rj = 0.05. Afterwards, two simulated macroion system that are characterized by these two sets of parameters are referred to as the macroion suspension of low surfactant concentration and high surfactant concentrations, respectively. 

In those cool alcohols studied, methanol to butanol, the final e absorption spectra are marginally blue shifted but the solvation times become longer and extend into nanoseconds. In order to reexamine these data from this hydrodynamic perspective we calculated the Debye parameters, which should remain constant for a given hquid. The... 

Here a is the radium of the tracer particle, and K is the Debye parameter defined as... 

This approach is satisfactory for mixtures of nonelectrolytes. The situation is a little more complex for mixtures of electrolytes because of the long range of the Coulomb potential. However, each ion in the mixture tends to be surrounded by ions of opposite charge, which causes the potential to decay exponentially with a decay factor, k, the Debye parameter, which is proportional to the square root of the product of the density and T. As a result, an appropriate expansion parameter for electrolytes is k, or which is different from nonelectrolytes, where T is the expansion parameter. These ideas become quantitative in the Debye-Htickel theory. 

Figure 4- The orbital energies e of the Is orbital (A), the transition energies A E to P(ls2p) (B), and the electric dipole polarizability a (C), scaled by appropriate powers of the nuclear charge Z, plotted versus the Debye parameter //.

R is the distance parameter, defining the upper limit of ion association. For spherical ions forming contact ion pairs it is simply the sum of the crystallographic radii of the ions, a = a+ + a, for solvent shared and solvent separated ion pairs it equals a+xora + 2x respectively, where x is the length of an oriented solvent molecule. For molecular ions the determination of the distance parameters a and R is more complicated the distances must be taken from experimental determinations or semiempirical quantum-mechanical calculations as shown in Ref [194]. For 1 1 salts the Debye parameter kd and Bjermm parameter qs are given by the... 

An interesting case is that the interatomic forces act only between nearest neighbors, in cubic stmctures, and at high temperatures (i.e., T > 0 ). Then the two displacements are equal and hence independent of the mass ratio MJM2 (1,14). This counterintuitive result, with equal thermal displacements of the light nonmetal and heavy metal atoms in NaCl crystal-type refractory carbides and nitrides, seems to hold approximately even though the condition on the interatomic forces is not strictly obeyed. This is illustrated in Table 3, which gives the Debye parameter B... 

Table 3 Displacements of Metal and Nonmetal Atoms at Room Temperature, as Given by the Debye Parameter B, Based on Experiments and from an Unpublished Compilation...

---