Low frequency dispersion

The interesting question is whether in dilute polymer solutions there exists a low frequency dispersion region described by the RB theory, so that just as in the bulk polymer we have to contend with two dispersion regions. The existence of a RB dispersion region in polymer solutions may be associated with entanglement and hence a very sensitive function of polymer concentration and molecular weight. 

Summary. The semiclassical Boltzmann-Langevin method is extended to calculations of higher cumulants of current. Rs efficiency is demonstrated for mesoscopic diffusive contacts and chaotic cavities. We show that in addition to a dispersion at the inverse RC time characteristic of charge relaxation, higher cumulants of noise have a low-frequency dispersion at the inverse dwell time of electrons in the system. 

At the present time, the theory of electrochemical impedance of electrodes with distributed potentials is not yet completed, and algorithms of parametrical and structural identification procedures are not available. In addition, the interpretation of the results is very complicated. For this reason, in this work we analyzed only the frequency characteristics of impedance s components in the modified electrode system. As a result, we obtained a set of response peculiarities in the frequency range under investigation. Rather low frequency dispersion was observed in a solution containing a ferri-ferrocyanide system for both active (Fig.3, curve 2) and reactive (Fig.4, curve 3) components. In our opinion, this fact confirms that the independent on frequency resistance of charge transfer determines the main contribution to the impedance. 

Nonlinear Impedance and Low-Frequency Dispersion Effects of a Polyelectrolyte Under High Sinusoidal Fields... 

Since the two major results we obtained in our experiments are a nonlinear impedance and a low frequency dispersion effect of polyelectrolytes under high fields, it is logical for us to provide the readers with some background review in the field of nonlinear effects and high-field dispersion effects of electrolytic solutions. Most of the studies in these fields were devoted to Wien effects and DFW dispersion theory which are briefly discussed here. A detailed discussion of these two groups of studies with their recent developments is reported in a separate review chapter in Nonlinear Electromagnetics. 

This conclusion is supported by the existence of low frequency dispersion of EB in solutions ofthesepolymers (Fig. For all PCEMA fractions studied in the frequency range 0.5 to... 

The dielectric relaxation processes of matter can be analyzed with an empirical model of dielectric dispersion, for example, the one described by Havriliak-Negami s equation. " We analyzed dielectric data obtained for our samples using a model of complex permittivity k with two dispersions (the main and the low-frequency dispersion of a space charge effect) and conductivity ao (caused by electrode discharge), as follows ... 

Depending on the appearance of the spectrum when the angular frequency cu approaches zero, dielectric responses of materials are often classified as being either dipolar in nature or carrier dominated. In the first case, the polarization is attributed to the reorientation of permanent dipoles, and in the latter to the displacement of partially mobile charge carriers. These two behaviors may be interpreted as being manifestations of different values of the exponent a in a power law of the form oc at low frequencies when cu approaches zero, tends to zero whenever the exponent a > 1 but increases indefinitely when a < 1. Likewise, the real part / approaches a finite value when a > 1 but increases indefinitely in the same way as the imaginary part when a < 1. Since no finite value is approached when a < 1, this case usually is referred to as low-frequency dispersion (104,105). 

It is interesting to contrast low-frequency dispersion with direct currents. To elucidate the effect of a nonzero direct-current (dc) conductivity (Tq on the frequency-domain response, let us assume that a driving force T = is applied, as in... 

Jonscher AK. Low-frequency dispersion in carrier-dominated dielectrics. Philos Mag B 1978 38 587-601. 

Dissado LA, Hill RM. Anomalous low-frequency dispersion near direct current conductivity in disordered low-dimensional materials. J Chem Soc Faraday Trans 2, 1984 80 291-319. 

Figure 18, Frequency dependence of the a-c conductivity and of the dielectric constant after Steinemann (140), (1) Pure ice, (2) Slightly impure ice, (a) Conductivity, (b) Dielectric constant. Curves for pure ice closely follow Equations 12a and 14, except for an incipient low-frequency dispersion that may result from very slight impurity content or from electroae polarization. Debye dispersion between 10 and 10 cps. As the impurity content increases (curves 2), the low-frequency dispersion (Steinemann s F dispersion) becomes more prominent and tends to coalesce with the Debye dispersion. Interpretation then becomes difficult. At still higher concentrations, the two dispersions separate again (see Ref. 140). A slight anisotropy of the dielectric constant, observed by Decroly et al. (34) for measurements parallel and perpendicular to the c axis of single crystals, has not been considered...

In this case, the dispersive capacitance can be described by another interfacial element capable of dealing with such low-frequency dispersion. A blocking capacitive interface response that takes into account a frequency dependency can generally be modeled by an interfacial impedance element such as ... 

Bisquert, J, G. Garcia-Belmonte, E, Eabregat-Santiago, and P.R. Bueno, Theoretical models for ac impedance of diffu.sion layers exhibiting low frequency dispersion. Journal of Electro-analytical Chemistry, 1999. 475 p. 152... 

Many of the specific applications of ferrites depend on their behaviour at high frequencies. When subjected to an ac field, ferrite permeability shows several dispersions as the field frequency increases, the various magnetisation mechanisms become unable to follow the field. The dispersion frequency for each mechanism is different, since they have different time constants. Fig. 4.59. The low-frequency dispersions are associated with domain wall dynamics and the high-frequency dispersion, with spin resonance the latter, usually in the GHz range, is discussed in Section 4.6.2. 

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. 

Schwartz, G., 1962. A theory of the low frequency dispersion of colloidal particles in electrolyte solution. 

Nonequilibrium electro-optical properties of polymers with mesogenic side groups are also very distinctive. In alternating electric fields, low-frequency dispersion of the Kerr effect is observed. The range of dispersion depends on the molecular weight of the fraction, just as for lyotropic polymers. Fig. 9 shows the dependence of the relative value of the Kerr constant at the field frequency V and at v=0 on the field frequency for solutions of... 

Hughes MP (2002) Dielectrophoretic behavior of latex nanospheres low-frequency dispersion. J Colloid Interface Sci 250 291-294... 

A particularly interesting case occurs when the static value of exceeds that of . In this case, as a result of the low-frequency dispersion in at a certain frequency /o, a change in sign of the dielectric anisotropy of the nematic liquid crystals can occur. Sometimes this frequency is low. 

J. Bisquert, G. Garcia-Belmonte, F. Fabregat-Santiago, P. R. Bueno, Theoretical model ofac impedance of finite diffusion layers exhibiting low frequency dispersion, J. Electroanal. Chem., 1999,475, pp. 152-163. 

Dissado, L.A., Hill, R.M., 1984. Anomalous low-frequency dispersion. J. Chem. Soc. Earaday Trans. 80, 291-319. 

Below it will be shown that field-cycling NMR relaxometry studies unambiguously reveal a crossover between high-frequency and low-frequency dispersion regimes that can be identified with the high-mode-number and low-mode-number limits of the renormalized Rouse models. Moreover, the variation of the power law exponents closely corresponds to that predicted by the renormalized Rouse models. These dynamic regimes cannot be ex-... 

Surprisingly, this paper concluded that these materials are not flexible chain polymers. Thermodynamic equilibrium in these polymers is observed to a rigidity, characterized by a Kuhn segment, which increases from 47 A to 64 A as the chain length increased from 3 to 7 carbons. The kinetic rigidity in these polymers is also asserted with a low frequency dispersion of dielelectric permittivity. 

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