Frequency-dependent behavior

The observed frequency dependent behavior of biopolymer solutions often resembles that of polar liquids and their solutions in nonpolar solvents, the most conspicuous differences being the very large effects of small concentrations of solute and the much lower frequencies. The classic theory of Debye (6) for polar liquids and solutions assumes N independent permanent dipoles of moment p reorienting in an applied field E(t) =... 

This paper is primarily concerned with the techniques usually described as time domain spectroscopy (TDS) or time domain reflectom-etry (TDR). These have been most commonly applied to studies of time or frequency dependent behavior of dielectrics with negligible ohmic or d.c. conductance, but can be used for substances with appreciable conductance and indeed for studies of any electrical properties which can be characterized by an effective admittance or impedance. 

The frequency-dependent behavior of electrode impedance is of more concern in intracellular microelectrode recording aqyplications, where electrode resistances are very high. In conjunction with the electrode capacitance and that of the recording circuit, a low-pass filter is formed at the microelectrode interface that tends to distort high-frequency portions of action events. 

The frequency-dependent behavior of the transfer function (i.e., the Bode diagram) takes on a characteristic shape that is largely determined by the damping faetor, as... 

The impedance Z(tu) for above models are given in Eq. 33 including Rp and in Eq. 34 neglecting Rp. Complex variables in the frequency domain are used to examine the frequency-dependent behavior. 

On the other hand, the Maxwell fluid model explains the response of complex fluids to an oscillatory shear rate. The frequency-dependent behavior of this model, displayed into linear responses to applied shear rates has been found to be applicable to a variety of complex fluid systems. Although the linear viscoelasticity is useful for understanding the relationship between the microstructure and the rheological properties of complex fluids, it is important to bear in mind that the linear viscoelasticity theory is only valid when the total deformation is quite small. Therefore, its ability to distinguish complex fluids with similar micro- and nanostructure or molecular structures (e.g. linear or branched polymer topology) is limited. However, complex fluids with similar linear viscoelastic properties may show different non-linear viscoelastic properties [31]. 

The frequency-dependent coefficients in this equation are given separate names and symbols to facilitate discussion. Remember it is these coefficients that determine the behavior of the system the trigonometric functions merely describe the oscillations. The following can be said of the coefficient of the cosine term ... 

Because of very high dielectric constants k > 20, 000), lead-based relaxor ferroelectrics, Pb(B, B2)02, where B is typically a low valence cation and B2 is a high valence cation, have been iavestigated for multilayer capacitor appHcations. Relaxor ferroelectrics are dielectric materials that display frequency dependent dielectric constant versus temperature behavior near the Curie transition. Dielectric properties result from the compositional disorder ia the B and B2 cation distribution and the associated dipolar and ferroelectric polarization mechanisms. Close control of the processiag conditions is requited for property optimization. Capacitor compositions are often based on lead magnesium niobate (PMN), Pb(Mg2 3Nb2 3)02, and lead ziac niobate (PZN), Pb(Zn 3Nb2 3)03. 

Moreover, if for pure polymer melts the correlation of the behavior of the functions ri (co) andrify) under the condition of comparing as y takes place, as a general rule, but for filled polymers such correlation vanishes. Therefore the results of measuring frequency dependences of a dynamic modulus or dynamic viscosity should not be compared with the behavior of the material during steady flow. 

Behavioral records should be written at periodic intervals (frequency depends on hospital or unit guidelines). An accurate description of die patient s behavior and cognitive ability aids the primary health care provider in planning tiierapy and thus becomes an... 

Although the conductivity change Aa [relation (8)] of microwave conductivity measurements and the Ac of electrochemical measurements [relation (1)] are typically not identical (owing to the theoretically accessible frequency dependence of the quantities involved), the analogy between relations (1) and (8) shows that similar parameters are addressed by (photo)electrochemical and photoinduced microwave conductivity measurements. This includes the dynamics of charge carriers and dipoles, photoeffects, flat band and capacitive behavior, and the effect of surface states. 

Some information concerning the intramolecular relaxation of the hyperbranched polymers can be obtained from an analysis of the viscoelastic characteristics within the range between the segmental and the terminal relaxation times. In contrast to the behavior of melts with linear chains, in the case of hyperbranched polymers, the range between the distinguished local and terminal relaxations can be characterized by the values of G and G" changing nearly in parallel and by the viscosity variation having a frequency with a considerably different exponent 0. This can be considered as an indication of the extremely broad spectrum of internal relaxations in these macromolecules. To illustrate this effect, the frequency dependences of the complex viscosities for both linear... 

Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simplified equivalent circuit for the liquid-liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clarified later, the photoinduced ET... 

Choi and Funayama [19] also measured sodium atom emission from sodium dodecylsulfate (SDS) solutions in the concentration range of 0.1-100 mM at frequencies of 108 kHz and 1.0 MHz. The sodium line intensity observed at 1 MHz was nearly constant in the concentration range from 3 to 100 mM and was considerably higher than that at 108 kHz. This frequency dependence of the intensity is opposite that for NaCl aqueous solution. The dynamical behavior of the absorption and desorption of surfactant molecules onto the bubble surface may affect the reduction and excitation processes of sodium atom emission. This point should be clarified in the future. 

Figure 5 presents the capacitance-frequency dependence from impedance spectroscopy measurements for CS48 and CS15 in acidic and organic medium. In the low frequency region (from ImHz to lOOmHz) nearly a complete penetration of the ions into the pores is allowed and the quite stable values indicate the domination of the capacitive behavior at the electro 1 ytc/carbon interface. All the curves show a typical drop of... 

The effect of forced concentration cycling was investigated on the oxidation of CO over industrial V2O5 catalyst. The resulting rate, when time-averaged, exhibited frequency-dependent harmonic behavior, with multiple extrema. Some preliminary interpretation is provided by analogy to an electrical network containing resistance and inductance. 

A constant phase element (CPE) rather than the ideal capacitance is normally observed in the impedance of electrodes. In the absence of Faradaic reactions, the impedance spectrum deviates from the purely capacitive behavior of the blocking electrode, whereas in the presence of Faradaic reactions, the shape of the impedance spectrum is a depressed arc. The CPE shows power law frequency dependence as follows129 130... 

A particular question of interest is whether the DNA torsional motions observed on the nanosecond time scale are overdamped, as predicted by simple Langevin theory, and as observed for Brownian motions on longer time scales, or instead are underdamped, so that damped oscillations appear in the observed correlation functions. A related question is whether the solvent water around the DNA exhibits a normal constant viscosity on the nanosecond time scale, or instead begins to exhibit viscoelastic behavior with a time-, or frequency-, dependent complex viscosity. In brief, are the predictions for... 

The voltammetric features of a reversible reaction are mainly controlled by the thickness parameter A = The dimensionless net peak current depends sigmoidally on log(A), within the interval —0.2 < log(A) <0.1 the dimensionless net peak current increases linearly with A. For log(A )< —0.5 the diSusion exhibits no effect to the response, and the behavior of the system is similar to the surface electrode reaction (Sect. 2.5.1), whereas for log(A) > 0.2, the thickness of the layer is larger than the diffusion layer and the reaction occurs under semi-infinite diffusion conditions. In Fig. 2.93 is shown the typical voltammetric response of a reversible reaction in a film having a thickness parameter A = 0.632, which corresponds to L = 2 pm, / = 100 Hz, and Z) = 1 x 10 cm s . Both the forward and backward components of the response are bell-shaped curves. On the contrary, for a reversible reaction imder semi-infinite diffusion condition, the current components have the common non-zero hmiting current (see Figs. 2.1 and 2.5). Furthermore, the peak potentials as well as the absolute values of peak currents of both the forward and backward components are virtually identical. The relationship between the real net peak current and the frequency depends on the thickness of the film. For Z, > 10 pm and D= x 10 cm s tlie real net peak current depends linearly on the square-root of the frequency, over the frequency interval from 10 to 1000 Hz, whereas for L <2 pm the dependence deviates from linearity. The peak current ratio of the forward and backward components is sensitive to the frequency. For instance, it varies from 1.19 to 1.45 over the frequency interval 10 < //Hz < 1000, which is valid for Z < 10 pm and Z) = 1 x 10 cm s It is important to emphasize that the frequency has no influence upon the peak potential of all components of the response and their values are virtually identical with the formal potential of the redox system. 

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