Relaxations, dielectric

4 Dielectric Relaxation The so-called slow water epithet pertains to the cooperative reorientation time of water molecules, = 8.27 0.02 ps in pure water 

10 to make it commensurate with the other values shown there). Structure-breaking ions have 1 and structure-making ones have 1. Another set of 

The relaxation of the static dielectric constant is related to the transition dynamics of electrons from the valence band to the conduction band. The dielectric constant relaxation depends functionally on Eq expansion, electron-phonon coupling, and lattice relaxation, showing the trend of interaction-enhancement resulted depression [60]. The dielectric permittivity x — 1) of a semiconductor is approx- 

On the framework developed, one may suggest the possible mechanism for the pressure- and cooling-enhanced dielectrics. Both compressing and cooling shorten the 0 H bond and lengthen the H-O bond with density increase in water and ice. What is the factor among the following to dictate the dielectric enhancement or all the factors come into play  

Interactions between water molecules and cells, membranes, proteins, etc., are areas that are fruitful for further investigation [66]. For instances, solvation water around proteins is denser than the bulk water [67]. Ice can absorb and entrap albumin (proteins) in solutions [68]. The geometry of the H-bond network within solvation layer differs from the one in bulk water to interact with protein surface. Unoccupied gap exists between the hydrophobic surface and neighboring solvation layer. The thickness of this gap depends on the local geometry of the water-protein interface, and it is a result of maintaining a balance between water-interface interactions and water-water interactions. Existence of this gap is one of the main factors that differentiate the hydrophobic hydration from hydration of the native form of kinesin [67]. 

The orientation of molecular dipoles cannot take place instantaneously when an electric field is applied. This is the exact analogy of a fact discussed in chapter 7, namely that the strain in a polymer takes time to develop after the application of a stress. In fact the two phenomena are not simply analogous the relaxation of strain and the rotation of dipoles are due to the same types of molecular rearrangement. Both viscoelastic 

Calculate the refractive index of PVC using the bond refractions given in table 9.1. Assume that the density of PVC is 1.39 Mg 

In section 7.2.1 the idea of a relaxation time is made explicit through the assumption that, in the simplest relaxation, the material relaxes to its equilibrium strain or stress on application of a stress or strain in such a way that the rate of change of strain or stress is proportional to the difference between the fully relaxed value and the value at any instant. A similar assumption is made in the present section for the relaxation of polarisation on application of an electric field. 

In considering dielectric relaxation it is, however, necessary to remember that there are two dilferent types of contribution to the polarisation of the dielectric, the deformational polarisation and the orientational polarisation so that P = + P. For the sudden application of a 

Assuming that, in any applied field with instantaneous value E, P responds in such a way that its rate of change is proportional to its deviation from the value that it would have in a static field of the same value E, it follows that 

In this discussion of dielectric constant the calculation was an equilibrium one and no account was taken of the way in which the equilibrium configuration is achieved. It was only necessary that some mechanism exist for the reorientation of molecular dipoles. In the next section we shall consider the mechanism of dielectric relaxation in detail and from this consideration will come an alternative method for calculating Cg. 

The dielectric relaxation of an ice crystal, involving as it does the rotation of molecular dipoles as described by certain internal co- 

Considering for the present simply an isotropic material, the dielectric constant e is defined by 

We know that if E is static then e has the value e, while for very rapidly varying fields e = e. Suppose now that the field E is simply switched on to a steady unit value at t = o, so that it can be represented by the unit step function u t). The simplest reasonable assumption is that e relaxes exponentially from to with a characteristic time t so that 

Now what we really want is the behaviour of the dielectric under the influence of an alternating field of frequency (o so that 

We now analyze a case where we have an instantaneous increase or a reduction of the electric field, E. This will lead to a polarization or depolarization process, which will follow with some delay or retardation due to the increase or reduction of the electric field, respectively. Consequently, in relation with a time-dependent variation of the electric field, E = E(t), the dielectric properties of the materials become dynamic events. In this regard, the time dependency of P = P(t) will not be the same as that of E = E (t), since the different polarization processes have different time delays, with respect to the appearance of the electric field. This delay is obviously related to the time-dependent behavior of the susceptibility % = %(t). 

The whole polarization of an arbitrary dielectric material is given by 

That is, the polarization process represented by P,(t) will be established throughout a time evolution. To mathematically express this process, the following time convolution integral (normally named the Duhamel s integral) [32] is used  

FIGU RE 1.27 Step-like constant electric field of magnitude E=Ea l(f - f0) and the corresponding polarization process. 

The electric displacement for a time-varying external voltage is given by [31] 

Simulation studies of the SD of the polar amino acid residues in each of the three helical segments of the protein HP36 reveal the presence of a small-amplitude slow component in the SD, which is an order of magnitude slower than that of the bulk. The correlation between the exposure of polar probe residues and the SD of different secondary structures of a protein molecule was also established. The more exposed the probe, the faster the SD is [6]. 

Constrained MD simulations with either frozen protein or frozen water revealed the molecular mechanism of slow hydration processes and elucidated the role of protein fluctuations. Slow water dynamics in MD simulations requires protein flexibility. However, there still remains the controversy on the origin of the slow component whether the slow component results from the water or the protein contribution. The initial dynamics in a few picoseconds represents fast local motions such as reorientations and translations of hydrating water molecules, followed by slow relaxation involving strongly coupled water-protein motions [7]. 

The role of protein side-chain motion in the slow dynamics of water around the protein surface is investigated by calculating the HB lifetime correlation function, S t), for two different conditions (i) when the side-chain protein motion is not constrained and (ii) when it is constrained. S i) showed a long-time tail in its natural condition the function initially decays slowly in its constrained condition compared to its natural condition and then decays to zero over a long time. 

Dielectric relaxation results are proven to be the most definitive to infer the distinctly different dynamic behavior of the hydration layer compared to bulk water. However, it is also important to understand the contributions that give rise to such an anomalous spectrum in the protein hydration layer, and in this context MD simulation has proven to be useful. The calculated frequency-dependent dielectric properties of an ubiquitin solution showed a significant dielectric increment for the static dielectric constant at low frequencies but a decrement at high frequencies [8]. When the overall dielectric response was decomposed into protein-protein, water-water, and water-protein cross-terms, the most important contribution was found to arise from the self-term of water. The simulations beautifully captured the bimodal shape of the dielectric response function, as often observed in experiments. 

Charge transfer can be studied from a macroscopic point of view, but emphasis can also be given to local phenomena. 

In neutron scattering, the elastic part reflects the static correlations (Bragg peaks reveal the unit cell structure and the diffuse pattern shows the non-periodic, local disorder). The inelastic scattering is due to the periodic motions of atoms or ions (phonons) and the quasi-elastic scattering is caused by any kind of non-periodic motion (or magnetic disorder). The transition between low frequency periodic motions (translational and rotational oscillation) and diffusive motion (non-periodic) is not well understood. 

The molecular reorientation case and ferroelectricity additional effect are illustrated in 

All the above descriptions use the Debye model, characterized by an arc of a circle in the plot e vs. , and a unique relaxation time. In most cases (polymers, glasses, liquids ), however, the spectrum does not correspond to an arc of a circle and is frequently interpreted in terms of a relaxation time distribution. The latter broadens with increasing temperature. Such distributions can be either intrinsic (disordered compounds) or due to lack of accuracy in the measurements fixed frequency measurements with too-widely spaced intervals, or insensitive apparatus. As we shall see later, protonic conductors give rise to better defined but more complex spectra because of the existence of various protonic and polyatomic species corresponding to fixed or mobile charges strong dipoles lead frequently to ferroelectric phenomena. 

Under the action of an alternating electric field, the electrical response of a system having dipolar interaction may be characterized by the complex permittivity e = s ((o) — ie (ro) as discussed above. Methods to measure the frequency-dependent permittivity use coaxial lines. The cell of our 

We now calculate the average dipole moment under a given electric field E(t). The diffusion equation to be solved is 

To obtain (u), we multiply both sides of eqn (8.84) by and integrate overs. 

As before, 0t u gives -2b, and 9tu 9ltl) is calculated from eqn (8.81). Hence 

We shall consider the linear response, in which case we can neglect the third term and evaluate the average in the second term for the isotropic distribution function of b  

The buildup of the electric field-induced polarization requires finite times. In quasi-DC fields all polarization mechanisms will be present, but at increasing frequencies they eventually drop out. 

To show this, let us follow the time dependence of the induced polarization P after turning on a static electric field E across the material. Obviously, after a very long time P will reach the final value Pjr given by  

Here f(0) is the zero frequency susceptibility. It is reasonable to assume that its change rate will be proportional to the deviation from the equilibrium value. This is the basic assumption of the irreversible thermodynamics describing how a thermodynamic variable relaxes back toward equilibrium. Accordingly  

If we turn off the field from tiie value P, we get that the polarization decays to zero as  

It is important to note that the switching time and the relaxation time are the same for small fields. 

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Fig. XIV-2. Dielectric relaxation spectrum of a water-in-oil emulsion containing water in triglyceride with a salt concentration of 5 wt % at a temperamre of 25°C. The squares are experimental points and the lines are fits to Eq. XIV-4. (From Ref. 9.)...

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. 

Loring R F, Van Y J and Mukamel S 1987 Time-resolved fluorescence and hole-burning line shapes of solvated molecules longitudinal dielectric relaxation and vibrational dynamics J. Chem. Phys. 87 5840-57... 

Polytetrafluoroethylene transitions occur at specific combinations of temperature and mechanical or electrical vibrations. Transitions, sometimes called dielectric relaxations, can cause wide fluctuations in the dissipation factor. 

The relaxatioa temperature appears to iacrease with increa sing HFP coateat. Relaxatioa iavolves 5—13 of the chaia carboa atoms. Besides a and y relaxations, one other dielectric relaxation was observed below —150° C, which did not vary ia temperature or ia magnitude with comonomer content or copolymer density (55). The a relaxation (also called Glass 1) is a high temperature transition (157°C) andy relaxation (Glass 11) (internal friction maxima) occurs between —5 and 29°C. 

It appears that the observed breakdown must be explained in terms of the transient behavior of stress-induced defects even though the stresses are well within the nominal elastic range. In lithium niobate [77G06] and aluminum oxide [68G05] the extent of the breakdown appears to be strongly influenced by residual strains. In the vicinity of the threshold stress, dielectric relaxation associated with defects may have a significant effect on current observed in the short interval preceding breakdown. 

Characteristic responses are readily obtained at pressures higher than 10 GPa, but differences have been observed with different loading arrangements. Piezoelectric responses at higher pressures are currently under study [92B01]. Dielectric relaxation and shock-induced conductivity may be involved. 

Dielectric relaxation measurements of polyethylene grafted with acrylic acid(AA), 2-hydroxyethyl methacrylate (HEMA) and their binary mixture were carried out in a trial to explore the molecular dynamics of the grafted samples [125]. Such measurements provide information about their molecular packing and interaction. It was possible to predict that the binary mixture used yields a random copolymer PE—g—P(AA/HEMA), which is greatly enriched with HEMA. This method of characterization is very interesting and is going to be developed in different polymer/monomer systems. 

In the previous section was given the experimental demonstration of two sites. Here the steady state scheme and equations necessary to calculate the single channel currents are given. The elemental rate constants are thereby defined and related to experimentally determinable rate constants. Eyring rate theory is then used to introduce the voltage dependence to these rate constants. Having identified the experimentally required quantities, these are then derived from nuclear magnetic resonance and dielectric relaxation studies on channel incorporated into lipid bilayers. 

K = 63 M 1, Kb = 1.4M-1)47 lithium-7 (K = 14 M 1 K" = 0.5 M 1) 49) and for cesium-133 (K, st 50 M-1, K = 4M 1)S0). In the case of sodium-23, transverse relaxation times could also be utilized to determine off-rate constants k ff = 3 x 105/sec k"ff = 2x 107/sec47,51). Therefore for sodium ion four of the five rate constants have been independently determined. What has not been obtained for sodium ion is the rate constant for the central barrier, kcb. By means of dielectric relaxation studies a rate constant considered to be for passage over the central barrier, i.e. for jumping between sites, has been determined for Tl+ to be approximately 4 x 106/sec 52). If we make the assumption that the binding process functions as a normalization of free energies, recognize that the contribution of the lipid to the central barrier is independent of the ion and note that the channel is quite uniform, then it is reasonable to utilize the value of 4x 106/sec for the sodium ion. 

Chemical models of electrolytes take into account local structures of the solution due to the interactions of ions and solvent molecules. The underlying information stems from spectroscopic, kinetic, and electrochemical experiments, as well as from dielectric relaxation spectroscopy. The postulated structures include ion pairs, higher ion aggregates, and solvated and selectively solvated ions. 

Despite the results from various experiments such as transference number measurements, polarographic studies, spectroscopic measurements, and dielectric relaxation studies in addition to conductivity measurements, unilateral triple-ions remain a matter of debate. For experimental examples and other hypotheses for the interpretation of conductance minima the reader is referred to Ref. [15] and the literature cited there. 

Williams, G. Molecular Aspects of Multiple Dielectric Relaxation Processes in Solid Polymers. Vol. 33, pp. 59—92. 

Wilkes, G. L. The Measurement of Molecular Orientation in Polymeric Solids. Vol. 8, pp. 91-136. Williams, G. Molecular Aspects of Multiple Dielectric Relaxation Processes in Solid Polymers. Vol. 33, pp. 59-92. 

From the various autocorrelation times which characterized macromolecular fluctuations, those associated with the fluctuation of the electrostatic field from the protein on its reacting fragments are probably the most important (see Ref. 8). These autocorrelation times define the dielectric relaxation times for different protein sites and can be used to estimate dynamical effects on biological reactions (see Chapter 9 for more details). 

Dielectric relaxation times, 122, 216 Diffusion, in proteins, simulated by MD, 120-122... 

Proteins, 109,110, 116.Seealso Enzymes Macromolecules average thermal amplitudes, MD simulations, 119 binding of ligands to, 120 dielectric relaxation time of, 122 electrostatic energies in, 122, 123-125 flexibility of, 209,221,226-227, 227 folding, 109,227... 

When an electrode potential that is initially settled at the rest potential is shifted to the anodic direction, the electrode system begins to move to a new equilibrium state. The resultant reconstruction of the double layer induces dielectric relaxation, which yields a new potential difference, maintaining electrostatic equilibrium. 

The same information may be obtained from purely rotational far infrared spectroscopy (FIR) and depolarized Rayleigh spectra. Dielectric relaxation measurements are also used for the same goal, most successfully in combination with far-infrared data. The absorption coefficient of a periodic electric field... 

Gross E. P. Inertial effects and dielectric relaxation, J. Chem. Phys. 23, 1415-23 (1955). 

Optical and electro-optical behavior of side-chain liquid crystalline polymers are described 350-351>. The effect of flexible siloxane spacers on the phase properties and electric field effects were determined. Rheological properties of siloxane containing liquid crystalline side-chain polymers were studied as a function of shear rate and temperature 352). The effect of cooling rate on the alignment of a siloxane based side-chain liquid crystalline copolymer was investigated 353). It was shown that the dielectric relaxation behavior of the polymers varied in a systematic manner with the rate at which the material was cooled from its isotropic phase. 

The accessibility of chitin, mono-O-acetylchitin, and di-O-acetylchitin to lysozyme, as determined by the weight loss as a function of time, has been found to increase in the order chitin < mono-O-acetylchitin < di-O-acetylchitin [120]. The molecular motion and dielectric relaxation behavior of chitin and 0-acetyl-, 0-butyryl-, 0-hexanoyl and 0-decanoylchitin have been studied [121,122]. Chitin and 0-acetylchitin showed only one peak in the plot of the temperature dependence of the loss permittivity, whereas those derivatives having longer 0-acyl groups showed two peaks. 

Bohidar et al. 1998, realized studies of Sol and Gel state properties of aqueous gelatin solutions of concentrations 4%, 6%, 8% and 10% (w/v) were investigated through dielectric relaxation studies done at various temperatures in the range from 20 to 60°C carried out over a frequency range 20Hz-10MHz and no relaxation of any nature was observed. 

Since we are interested in this chapter in analyzing the T- and P-dependences of polymer viscoelasticity, our emphasis is on dielectric relaxation results. We focus on the means to extrapolate data measured at low strain rates and ambient pressures to higher rates and pressures. The usual practice is to invoke the time-temperature superposition principle with a similar approach for extrapolation to elevated pressures [22]. The limitations of conventional t-T superpositioning will be discussed. A newly developed thermodynamic scaling procedure, based on consideration of the intermolecular repulsive potential, is presented. Applications and limitations of this scaling procedure are described. 

FIGURE 24.10 Dielectric relaxation times from Figures 24.7 through 24.9 plotted versus 7V, with mode independent -y = 3.0 (1,4-polyisoprene), = 2.5 (polypropylene glycol), and = 2.65 (polyoxyhutylene). 

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

Dielectric relaxation studies of phosphorylated polyethers from — 180° to 200 °C have been used to study their structures. The magnitude of the dielectric constants of high-phosphonic-acid-content polymers is much larger than predicted, which suggests a microphase-separated structure. Conductance studies on some aryl- and alkyl-phosphonium salts showed a higher conductance for the halides than for the nitrate. ... 

The observation of slow, confined water motion in AOT reverse micelles is also supported by measured dielectric relaxation of the water pool. Using terahertz time-domain spectroscopy, the dielectric properties of water in the reverse micelles have been investigated by Mittleman et al. [36]. They found that both the time scale and amplitude of the relaxation was smaller than those of bulk water. They attributed these results to the reduction of long-range collective motion due to the confinement of the water in the nanometer-sized micelles. These results suggested that free water motion in the reverse micelles are not equivalent to bulk solvation dynamics. 

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