Interfacial frequency dependence

The temperature and frequency dependence of the complex dielectric permittivity a for both 2-chlorocydohexyi isobutyrate (CCHI) and poly(2-chlorocyclohexyl acrylate) (PCCHA) is reported. The analysis of the dielectric results in terms of the electric modulus suggests that whereas the conductive processes in CCHI are produced only by free charges, the conductivity observed in PCCHA involves both free charges and interfacial phenomena. The 4x4 RIS scheme presented which accounts for two rotational states about the CH-CO bonds of the side group reproduces the intramolecular correlation coefficient of the polymer. 

In this section, the interpretation of interfacial admittance data in the case of an a.c. reversible reaction with adsorption of O is briefly described. The relationships expressing the frequency dependence were derived some time ago [15, 17], but the essential meaning of the parameters involved was fully explained only recently [143], The brief description here is derived from the latter reference. 

The frequency dependent derivation of Jq and p is somewhat lengthy and is therefore discussed here only qualitatively (see [36] for a full discussion). Essentially, one has to write the heat flux and the pressure at the polymer-air interface in terms of reflectivities and transmittances of all three interfaces (all of which are a function of the phonon frequency). The total heat-flux and interfacial pressure are then obtained in a self-consistent way by an integration over the Debye density of states [36],... 

FIGURE 15. Panel a shows the strain amplitude sweep experiment on the 2D film of Ag nanopartides. The storage modulus, C p), is higher than the loss modulus, C" (O) at low strain amplitudes. Panel b shows the frequency dependence of interfacial storage, C ( ), and loss, C" (o), moduli of the film. Reproduced from ref 33. Copyright 2007 American Chemical Society. 

First, a typical power spectrum of capillary waves excited at the W/NB interface is shown in Figure 3.4a. The errors on the values of the capillary wave frequency were 0.1 kHz, obtained as the standard deviation of 10 repeated measurements. Capillary wave frequency dependence on CeHsONa is shown in Figure 3.4b. The frequency decreased significantly with increasing CeHsONa concentration. This indicated that interfacial tension was decreased by the interfacial adsorption of CeHsONa. 

In summary, the results of our thin film drainage study as well as our investigation of oil spreading mechanisms and frequency dependence of dynamic interfacial tension all suggest that the C 2 0S system, which displays the m.ost unstable foam behavior in the presence of oil, should not perform as effectively as the Ci6A0S system in oil displacement experiments in porous media. 

The general expression (10.3) guides development of impedance models from proposed reaction sequences. The reaction mechanisms considered here include reactions dependent only on potential, reactions dependent on both potential and mass transfer, coupled reactions dependent on both potential and surface coverage, and coupled reactions dependent on potential, surface coverage, and mass transfer. The proposed reaction sequence has a major influence on the frequency dependence of the interfacial Faradaic impedance described in Qiapter 9. 

The interfaces in multiphase segmented copolymers are diffuse. Furthermore, in the case of the purified polymer systems being studied, there is no evidence for a differentiable trapping mechanism in the interfacial regions. The frequency-dependent complex permittivity e is calculated from (26) ... 

Figure 12.33 illustrates the set-up for LMMRS. The frequency response analyser replaces the single frequency lock-in amplifier used in the potential and light modulated microwave measurements described in Section 12.3. LMMRS detects the frequency-dependent modulation of the microwave reflectivity AR associated with the photogenerated minority carriers. This concentration decays by interfacial charge fransfer k d and recombination kKc)- The LMMRS response is therefore a semicircle with a characteristic frequency otam = + rec)- The low-frequency intercept of the... 

The interfacial capacitance may also be measured at solid polarizable electrodes in an impedance experiment using phase-sensitive detection. Most experiments are carried out with single crystal electrodes at which the structure of the solid electrode remains constant from experiment to experiment. Nevertheless, capacity experiments with solid electrodes suffer from the problem of frequency dispersion. This means that the experimentally observed interfacial capacity depends to some extent on the frequency used in the a.c. impedance experiment. This observation is attributed to the fact that even a single crystal electrode is not smooth on the atomic scale but has on its surface atomic level steps and other imperfections. Using the theory of fractals, one can rationalize the frequency dependence of the interfacial properties [9]. The capacitance that one would observe at a perfect single crystal without imperfections is that obtained at infinite frequency. Details regarding the analysis of impedance data obtained at solid electrodes are given in [10]. 

The dielectric constant of a material is a measnre of its polarizability in response to an electric field. This polarizability is the resnlt of reorganization of charge, which can be in the form of interfacial or space charge motion, ionic motion, dipolar motion, and electronic motion (see Figure 3.2.3) [14]. The timescale of the charge redistributions determines the frequency dependence of this contribution to the dielectric constant for a given material. In the case of ionic motion, the frequency range is up to 10 Hz. 

Te and Cu monolayers on gold, as well as Ag and Bi monolayers on platinum were obtained by cathodic underpotential deposition and investigated in situ by the potentiodynamic electrochemical impedance spectroseopy (PDEIS). PDEIS gives the graphical representation of the real and imaginary interfacial impedance dependencies on ac frequency and electrode potential in real-time in the potential scan. The built-in analyzer of the virtual spectrometer decomposes the total electrochemical response into the responses of the constituents of the equivalent electric circuits (EEC). Dependencies of EEC parameters on potential, especially the variation of capacitance and pseudocapacitance of the double layer, appeared to be very sensitive indicators of the interfacial dynamics. 

In recent years, several theoretical and experimental attempts have been performed to develop methods based on oscillations of supported drops or bubbles. For example, Tian et al. used quadrupole shape oscillations in order to estimate the equilibrium surface tension, Gibbs elasticity, and surface dilational viscosity [203]. Pratt and Thoraval [204] used a pulsed drop rheometer for measurements of the interfacial tension relaxation process of some oil soluble surfactants. The pulsed drop rheometer is based on an instantaneous expansion of a pendant water drop formed at the tip of a capillary in oil. After perturbation an interfacial relaxation sets in. The interfacial pressure decay is followed as a function of time. The oscillating bubble system uses oscillations of a bubble formed at the tip of a capillary. The amplitudes of the bubble area and pressure oscillations are measured to determine the dilational elasticity while the frequency dependence of the phase shift yields the exchange of matter mechanism at the bubble surface [205,206]. 

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 ... 

Electrochemical Stark effect As described already in Section 2.10.2, the Stark effect is based on the interaction of the interfacial static electric field with the transition electric dipole or molecular polarizability. The Stark effect may give rise to the first (or sometimes second) derivative of the absorption spectmm, depending on the type of interaction with the electric field. It is important to note that the ER signal due to the Stark effect should have the same frequency dependence as the ac change of the static electric field insofar as orientation change does not take place simultaneously, because the Stark effect is a field effect. In fact, this has been experimentally confirmed by frequency domain analysis [82]. 

Figure 13.7b shows the imaginary part of the dielectric modulus, M", versus/of a PA-11/BT 700-nm nanocomposite at 72°C for volume fractions / = 0.03,0.1, and 0.2. The maximum of M" decreases when the filler content increases, due to the increase in permittivity e. The filler content does not affect the frequency dependence of the three relaxations. However, the ratio between the maximum value of the a -mode versus the maximum value of the a-mode increases with increasing filler content, indicating the interphase effects between the polymer and the nanoparticles. The low-frequency relaxation associated with the MWS phenomena become more pronounced with increasing volume filler fraction compared to the other relaxations. This evolution is attributed to the increase in interfacial effects around the particles. 

It was discussed quite extensively, that interfacial dynamics and rheology are key properties of liquid disperse systems, such as foams and emulsions. The stability of such systems depends for example on the dilational elasticity and viscosity, however, surely not on the elasticity modulus (Borwankar et al. 1992). Here, the interfacial rheology with its frequency dependence comes into play, and data at respective frequencies will possibly correlate with the stability behaviour. 

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