Difference dielectric spectra

It is now well understood that the static dielectric constant of liquid water is highly correlated with the mean dipole moment in the liquid, and that a dipole moment near 2.6 D is necessary to reproduce water s dielectric constant of s = 78 T5,i85,i96 holds for both polarizable and nonpolarizable models. Polarizable models, however, do a better job of modeling the frequency-dependent dielectric constant than do nonpolarizable models. Certain features of the dielectric spectrum are inaccessible to nonpolarizable models, including a peak that depends on translation-induced polarization response, and an optical dielectric constant that differs from unity. The dipole moment of 2.6 D should be considered as an optimal value for typical (i.e.. 

Let us first discuss estimates fi om DR measurements that provide several important pieces of information. These experiments measure the frequency-dependent dielectric constant and provide a measure of a liquid s polarization response at different frequencies. In bulk water, we have two dominant regions. The low-frequency dispersion gives us the well-known Debye relaxation time, Tq, which is equal to 8.3 ps. There is a second prominent dispersion in the high-frequency side with relaxation time constant less than Ips which contains combined contributions from low-frequency intermolecular vibrations and libra-tion. Aqueous protein solutions exhibit at least two more dispersions, (i) A new dispersion at intermediate frequencies, called, d dispersion, which appears at a timescale of about 50 ps in the dielectric spectrum, seems to be present in most protein solutions. This additional dispersion is attributed to water in the hydration layer, (ii) Another dispersion is present at very low frequencies and is attributed to the rotation of the protein. 

A few hyperbranched poly(ester amide)s have been prepared using a similar A2 + BBV approach, in which phthalic anhydride or maleic anhydride as an A2 monomer and diethanol amine as a BB 2 monomer were used. The polycondensation polymerisation technique is used to prepare the polymers. These poly(ester amide)s are modified by long alkyl chain (fatty acids) end groups. The dielectric properties of the modified polymers were investigated over a range of frequencies and temperatures. No relaxation peak was noticed in the dielectric spectrum at different temperatures. Castor oil and Mesua ferrea L. seed oil-based hyperbranched poly(ester amide)s are prepared using diethanol fatty amide of the oils with different types of anhydrides and dibasic acids with or without diethanolamine. 

Very often a rotation of a complex molecule includes a motion of different molecular dipoles and the dielectric spectrum "((d) is not as simple as shown in the picture. It becomes somewhat blurred and the correspondent time Td cannot be found with sufficient accuracy. In order to improve the analysis, a simple procedure is used based on the Debye Eq. 7.32. 

Lou K, Zhang X, Xia Z (2012) Piezoelectric performance of floor polymer sandwiches with different void structures. Appl Phys A 107 613-620 Meltmger A (2002) Piezoelectric resonances in the dielectric spectrum of polymer films. Dielectr Newsl Novoconttol 16, Issue April ... 

The question arises why cis-polyisoprene, different from poly(vinyl-acetate), shows in its dielectric spectrum the chain reorientation. The reason becomes clear when we look at the chemical constitution of polyisoprene, and focus in particular on the associated dipole moments. Figure 5.22 displays the chemical structure. The main point is that isoprene monomers are polar units which possess a longitudinal component p of the dipole moment, which always points in the same direction along the chain. As a consequence, the longitudinal components of the dipoles of all monomers become added up along the contour, giving a sum which is proportional to the end-to-end distance vector R. In the dielectric spectrum the kinetics of this total dipole of the chain is observable, hence also the chain reorientation as described by the time dependence R t). 

The time t is the relaxation time for dipole reorientation in an electric field of frequency (0 (radians s ). For real systems there may be a number of contributions to the electric permittivity, each relaxing at a different frequency, for example due to internal dipole motion in flexible molecules or collective dipole motion. If these contributions to the electric permittivity are at sufficiently different frequencies, they can be separated in the dielectric spectrum, and it is possible to apply Eq. (9) to each relaxation process. At low frequencies (g)->0), the orientation polarization contribution to... 

The question arises as to why cis-polyisoprene, different from poly (vinylacetate), shows the chain reorientation in its dielectric spectrum. The reason becomes clear when we look at the chemical constitution of polyisoprene, and... 

The mobility in the disordered regions of polyethylene shows great variations. The / -process, as observed in dielectric measurements, is unusually broad and changes its shape with temperature. Figure 6.30 presents results obtained for a sample of polyethylene that included vinylacetate groups as co-units in the chains. These co-units are rejected from the crystallites and accumulate in the amorphous regions. Because the groups carry a dipole moment, their dynamics shows up in the dielectric spectrum. The difference in... 

The microwave spectrum of isothiazole shows that the molecule is planar, and enables rotational constants and NQR hyperfine coupling constants to be determined (67MI41700>. The total dipole moment was estimated to be 2.4 0.2D, which agrees with dielectric measurements. Asymmetry parameters and NQR coupling constants show small differences between the solid and gaseous states (79ZN(A)220>, and the principal dipole moment axis approximately bisects the S—N and C(4)—C(5) bonds. 

In quadrupole-based SIMS instruments, mass separation is achieved by passing the secondary ions down a path surrounded by four rods excited with various AC and DC voltages. Different sets of AC and DC conditions are used to direct the flight path of the selected secondary ions into the detector. The primary advantage of this kind of spectrometer is the high speed at which they can switch from peak to peak and their ability to perform analysis of dielectric thin films and bulk insulators. The ability of the quadrupole to switch rapidly between mass peaks enables acquisition of depth profiles with more data points per depth, which improves depth resolution. Additionally, most quadrupole-based SIMS instruments are equipped with enhanced vacuum systems, reducing the detrimental contribution of residual atmospheric species to the mass spectrum. 

Many other measures of solvent polarity have been developed. One of the most useful is based on shifts in the absorption spectrum of a reference dye. The positions of absorption bands are, in general, sensitive to solvent polarity because the electronic distribution, and therefore the polarity, of the excited state is different from that of the ground state. The shift in the absorption maximum reflects the effect of solvent on the energy gap between the ground-state and excited-state molecules. An empirical solvent polarity measure called y(30) is based on this concept. Some values of this measure for common solvents are given in Table 4.12 along with the dielectric constants for the solvents. It can be seen that there is a rather different order of polarity given by these two quantities. 

We have seen in Chapter 2 that the frequency of an EPR spectrum is not a choice for the operator (once the spectrometer has been built or bought) as it is determined by the combined fixed dimensions of the resonator, the dewar cooling system, and the sample. Even if standardized sample tubes are used and all the samples have the same dielectric constant (e.g., frozen dilute aqueous solutions of metalloproteins), the frequency will still slightly vary over time over a series of consecutive measurements, due to thermal instabilities of the setup. By consequence, two spectra generally do not have the same frequency value, which means that we have to renormalize before we can compare them. This also applies to difference spectra and to spectra... 

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