Debye like dielectric relaxation

Such numerical simulations have played an important role in the development of our imderstanding of solvation dynamics. For example, they have provided the first indication that simple dielectric continuum models based on Debye and Debye-like dielectric relaxation theories are inadequate on the fast time scales that are experimentally accessible today. It is important to keep in mind that this failure of simple theories is not a failure of linear response theory. Once revised to describe reliably response on short time and length scales, e g., by using the Ml k and (o dependent dielectric response function e(k,( ), and... 

The first mention of the a(x) dependence was in experimental work [265], The dielectric relaxation data of water in mixtures of seven water-soluble polymers was presented there. It was found that in all these solutions, relaxation of water obeys the CC law, while the bulk water exhibits the well-known Debye-like pattern [270,271], Another observation was that a is dependent not only on the concentration of solute but also on the hydrophilic (or hydrophobic) properties of the polymer. The seven polymers were poly(vinylpyrrolidone) (PVP weight average molecular weight (MW) = 10,000), poly (ethylene glycol) (PEG MW = 8000), poly(ethylene imine) (PEI MW = 500,000), poly(acrylic acid) (PAA MW = 5000), poly(vinyl methyl ether) (PVME MW = 90,000), poly(allylamine) (PA1A MW = 10,000), and poly(vinyl alcohol) (PVA MW = 77,000). These polymers were mixed with different ratios (up to 50% of polymer in solution) to water and measured at a constant room temperature (25°C) [265]. 

In these equations the subscript 1 is used to identify the properties of the matrix, while 2 is used for the particles. These equations are for the special case of a highly insulating matrix of constant dielectric properties containing a small amount of well-dispersed spherical particles that are somewhat conductive. The important aspect of this result is that the particles produce a Debye-like dispersion centered at a frequency of roughly Oj/eq. With a conductivity of, say, 10 7 S/m (Siemens/meter) and 0 = 8.84 x 1CT12 F/m (Farads/meter) the frequency of the MWS dispersion will be around 10 kHz, where it can be easily confused with a dipolar relaxation process. As shown by equation (7-57), the magnitude of the MWS dispersion should increase linearly... 

Therefore to analyze the a- and the 6-relaxation of the polymers investigated another method has been employed. This is based on taking the derivative of e with respect to log f i.e. A= de/ Slog This way of analyzing dielectric data was introduced by van Turnhout and Wubbenhorst (van Turahout, J. Wiibbenhorst, M., personal coomunication). It can be shown for Debye-like relaxation processes that... 

For polymeric systems in the most cases, the measured dielectric loss is much broader and in addition the loss peak is asymmetric. This is called non-Debye or nonideal relaxation behavior. Formally such a non-Debye-like behavior can be described by a supposition of Debye functions... 

Figures 20.21c and d show that poly(VCN-a/f-MATRIF) copolymer exhibits a dynamic scenario with four relaxation processes two relaxations are above Tg, merging at low temperatures, while two others are below Tg. The addition of VCN unit increases the dielectric constant as well as the value of calorimetric glass transition Tgi (i) -relaxation (Debye-like and strong, i.e., low fragility index m = 44 [68]) (ii) a2-relaxation (broad and fragile, high fragility index m = 101 [68]), more separated from p-one effect of rigidity of VCN segment (iii) p-relaxation (faster), due to a less efficient packing similar effect for random copolymers based on butyl methacrylate (n-BMA) with styrene (ST) named poly( -BMA-5 fflf-ST) copolymer [123].

Even if we consider a single solvent, e g., water, at a single temperature, say 298K, depends on the solute and in fact on the coordinate of the solute which is under consideration, and we cannot take xF as a constant. Nevertheless, in the absence of a molecular dynamics simulation for the solute motion of interest, XF for polar solvents like water is often approximated by the Debye model. In this model, the dielectric polarization of the solvent relaxes as a single exponential with a relaxation time equal to the rotational (i.e., reorientational) relaxation time of a single molecule, which is called Tp) or the Debye time [32, 347], The Debye time may be associated with the relaxation of the transverse component of the polarization field. However the solvent fluctuations and frictional relaxation occur on a faster scale given by [348,349]... 

As an illustration of the observed behavior and types of functions to be transformed. Figure 2 shows the reflection R(t) from Equation 5 for a step-like voltage pulse and dielectric with "Debye" relaxation expressed by... 

According to EM theory, the dielectric loss may be contributed by the processes like natural resonance, Debye dipolar relaxation and electron polarization relaxation, etc. In the Debye dipolar relaxation regime, the relative complex permittivity can be expressed as ... 

A common approach to model the dielectric response, typically used for impedance spectroscopy, is based on equivalent circuits consisting of a number of resistors, capacitors, constant phase elements, and others. Alternatively, the dielectric response can be modeled by a set of model relaxation functions like the Debye function or more generalized (semiempirical) Cole-Cole, Cole-Davidson, or Dissado-Hill equation (Kremer and Schonhals 2002). 

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