Relaxation, Debye mechanisms

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. 

As an example in Figure 14 we show the real and imaginary parts of the complex permittivity for 6CB as a function of temperature at ambient pressure and as a function of pressure at constant temperature. A similarity of the pictures is evident. In both cases the observed relaxation process can be described by a single Debye mechanism, which is easily... 

When Wqi / Wq2 the magnetization recovery may appear close to singleexponential, but the time constant thereby obtained is misleading [50]. The measurement of 7) of quadrupolar nuclei under MAS conditions presents additional complications that have been discussed by comparison to static results in GaN [50]. The quadrupolar (two phonon Raman) relaxation mechanism is strongly temperature dependent, varying as T1 well below and T2 well above the Debye temperature [ 119]. It is also effective even in cases where the static NQCC is zero, as in an ideal ZB lattice, since displacements from equilibrium positions produce finite EFGs. 

Similar expressions can be generated for holes simply by letting coc - — relaxation time xB needs justification, which will not be attempted here. Suffice it to say that this assumption is not bad for elastic scattering processes, which include most of the important mechanisms. A well-known exception is polar optical-phonon scattering, at temperatures below the Debye temperature (Putley, 1968, p. 138). We have further assumed here that t is independent of energy, although this condition will be relaxed later. 

An alternative approach that was used in the past was to treat the photoelectrochemical cell as a single RC element and to interpret the frequency dispersion of the "capacitance" as indicative of a frequency dispersion of the dielectric constant. (5) In its simplest form the frequency dispersion obeys the Debye equation. (6) It can be shown that in this simple form the two approaches are formally equivalent (7) and the difference resides in the physical interpretation of modes of charge accumulation, their relaxation time, and the mechanism for dielectric relaxations. This ambiguity is not unique to liquid junction cells but extends to solid junctions where microscopic mechanisms for the dielectric relaxation such as the presence of deep traps were assumed. 

Here /jn(f) is the intensity of the incident radiation and 0 is the phase of the interferometer in the dark. The functions N(< >) and M(< >) relate the intensities of the transmitted and intracavity fields to that of the incident light. The function 7ref (0 corresponds to the intensity of radiation from an additional source, which is very likely to be present in a real device to control the operating point. This description is valid in a plane-wave approximation, provided that we neglect transverse effects and the intracavity buildup time in comparison with the characteristic relaxation time of nonlinear response in the system. It has been shown that the Debye approximation holds for many OB systems with different mechanisms of nonlinearity. 

Agmon N. 1996. Tetrahedral displacement The molecular mechanism behind the Debye relaxation in water. JPhys Chem 100 1072-1080. 

In Section V the reorientation mechanism (A) was investigated in terms of the only (hat curved) potential well. Correspondingly, the only stochastic process characterized by the Debye relaxation time rD was discussed there. This restriction has led to a poor description of the submillimeter (10-100 cm-1) spectrum of water, since it is the second stochastic process which determines the frequency dependence (v) in this frequency range. The specific vibration mechanism (B) is applied for investigation of the submillimetre and the far-infrared spectrum in water. Here we shall demonstrate that if the harmonic oscillator model is applied, the small isotope shift of the R-band could be interpreted as a result of a small difference of the masses of the water isotopes. 

In such a case, no conclusion about the mechanisms can be reached from the form of 4(t) and the observed rate will be determined primarily by the fastest process. By extension of the argument, one easily sees that marked deviation of any of the parallel processes from exponential decay will be reflected in the overall rate with possible change in the functional form. Thus, if the rotation is described by exp(-2D t) as in Debye-Perrin theory, and the ion displacements by a non-exponential V(t), one finds from eq 5 that 4(t) = exp(-2D t)V(t) and the frequency response function c(iw) = L4(t) = (iai + 2D ) where iKiw) = LV(t). This kind of argument can be developed further, but suffices to show the difficulties in unambiguous interpretation of observed relaxation processes. Unfortunately, our present knowledge of counterion mobilities and our ability to assess cooperative aspects of their motion are both too meagre to permit any very definitive conclusions for DNA and polypeptides. 

Non-Debye dielectric relaxation was also observed in porous silicon (PS) [25,160,161], PS has attracted much attention recently, mainly due to its interesting optical and electro-optical properties that can be utilized for device applications [164,165], So far, most of the activity in this field has focused on the intense visible photoluminescence (PL) from nano-PS and the underlying physical mechanism that is responsible for the generation of light. In addition, transport and dielectric relaxation phenomena in PS have also attracted... 

The high-frequency (3, 7,. .. subsidiary peaks in amorphous polymers are characteristically very broad with a half-height width of several decades (compared with 1.14 decades for a single Debye relaxation process), although a good, linear Arrhenius plot is usually obtained, suggesting a non-co-operative mechanism. Figure 3.8 shows the Arrhenius plot for the /3-relaxation of poly(epichlorhydrin),... 

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