Debye-type mechanisms

Figure 6.2. Schematic representation of the signal ascribed to a single-relaxation-time (Debye-type) mechanism (Su = 2, e, = 12, and x = ls) (a) e and e" versus log(cor) (b) M, M" and tan 5 versus log(cor).

This result was first published by Peter Debye in 1927, and is called a Debye-type relaxation mechanism. 

Small proteins and biopolymers of 1 pm sizes also possess the Debye-type orientation relaxation in MHz (for small molecules of several angstroms this relaxation would be in the GHz range) that can overlap with the P-relaxation. Small dipoles and molecules exhibiting rotational orientation, the relaxation mechanism can be approximated as spherical particles of radius a in solvent of viscosity i), where their charge z can often be assumed to be unity [6]. The high-frequency relaxation times corresponding to this phenomenon can be described in a simplified expression ... 

The hole correction of the electrostatic energy is a nonlocal mechanism just like the excluded volume effect in the GvdW theory of simple fluids. We shall now consider the charge density around a hard sphere ion in an electrolyte solution still represented in the symmetrical primitive model. In order to account for this fact in the simplest way we shall assume that the charge density p,(r) around an ion of type i maintains its simple exponential form as obtained in the usual Debye-Hiickel theory, i.e.,... 

In seeking to re-establish faith in Debye s intuitive concept, we tend to view that these difficulties derive from the present limitations of statistical mechanics in dealing with what is essentially an electrostatic problem. Because of the failure to recognize the differences in the two types of averaging process, Debye s critics have illogically attributed the limitations of DH theory to an inadequacy of the LPBE, whereas all the evidence suggests that it is the unlinearized equation which is suspect (19). 

At very high pressures, above 12 GPa, and temperatures above 1000 K, a transparent,yellowish, ultra-hard material, believed to consist of the remnants of collapsed molecules, is formed. In several cases ultrasonic, scratch, and indentation studies have shown this material to have a bulk modulus and hardness far exceeding that of diamond [123,131,147], although these reports are by no means uncontested [124,148,149]. The material is extremely disordered and probably has a high fraction of sp2 coordinated bonds, but the structure is unknown. There are some similarities with amorphous carbon (ta-C),but differences in Raman spectra and mechanical properties show that the structures differ. The question of bond types is interesting, since sp2 bonds are known to be stronger than sp3 ones. The materials are semiconducting and have Debye temperatures near 1450 K, somewhat lower than that of diamond [150]. 

In our previous papers , we have shown that collective jump motions of atoms take place in highly supercooled fluid states, mainly contributing to the a relaxation, and therefore represents the molecular-level mechanisms. The main purpose of this paper is to study both a and / relaxations from S q,u>) and x (9,w) in a supercooled fluid by a super-long-time molecular dynamics (MD) simulation for a model fluid of binary soft-sphere mixtures. In particular, we focus on studying the type of each relaxation (Debye or non-Debye ) and the molecular-level processes for the / relaxation. 

The calculated moment thus considerably exceeds the experimental value and furthermore represents the dipole as acting in the opposite direction the chlorine is represented as positive and the hydrogen negative. This result is clearly incorrect and Debye has shown that the error is due to the fact that the Lorentz-Lorenz equation is not valid at the small distances considered owing to the non-uniform character of the field. If the internuclear distances were of the order of 5 A, this type of calculation would be permissible. Attempts have been made to calculate the polarizability in a non-uniform electric field by the methods of wave mechanics , but have not yet been successful in producing a theory of the intermediate type of bond. 

Most water-soluble metal complexes, unlike typical organic reactants, are cations or anions and are therefore subject to Coulombic ion-ion interactions in solution. In essence, these are of two kinds the Debye-Hiickel or ionic atmosphere type, which affects the activity coefficients of the complex ion and hence the kinetics of its reactions, and ion association—usually considered simply as anion-cation pair formation.29 For cationic substrates in particular, pairing with an anionic incoming ligand may give an illusion of bimolecularity (an SN2 mechanism) when in fact the reaction may be dissociatively activated within the ion pair or encounter complex . 

ERF dielectric response can be appropriately described by the classical Debye circuit model (Section 4-4). The model contains 1 pF/cm bulk base oil capacitance in parallel with Tohm range base oil resistance This combination results in a circuit with a time constant on the order of 10 seconds, typical of the impedance behavior of dielectric materials with very low ionic content. The presence of 10 to 50 percent polarizable particles results in the development of a parallel bulk-solution conduction mechanism through the particles. When compared to the ions that transport current by electrophoretic mobility, the ERF particles have larger sizes and lower mobility and are capable of becoming polarized and reoriented in the external electric field. This percolation type of conduction mechanism can be represented by a series of the particle resistance and the contact impedance between the particles (Figure 12-8). As the ionic content is essentially absent in the... 

In the so-called Debye absorption region, dipole vibrations occur at a frequency lower than kT/li = 10 s , i.e. the solvent behaves as a classical system. But not all types of solvent polarization behave classically. For example, the atomic polarization of water has frequencies above 4 kT/ti, i.e. it behaves in a quantum-mechanical way. Moreover, even a small fraction of the Debye polarization has high natural frequencies, > kT/ti. Naturally, only the classical part of the Debye polarization determines the activation energy. And it is these coordinates that should be used when plotting potential energy diagrams for ion + solvent systems. 

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