Relaxation time constants interface

C ((o) and C"((o) are the real and imaginary parts of the capacitance, respectively. Figure 4.13a shows a typical curve of C td) versus frequency [39]. With the increasing of frequency, the value of C (( ) sharply decreases and then seans to be less frequency dependent. This result relates to the electrode/electrolyte structures and their interfaces [39], As presented in Figure 4.13b, the imaginary of C"(< ) reaches a maximum value at frequency of/o (corresponding to a time constant of to = 1/fo). The to is called the relaxation time constant which has also been introduced iu Sectiou 1.4 [50],... 

Figure 5.25 The equivalent circuit models proposed for the interpretation of EIS results measured in corroding systems (a) simplest representation of an electrochemical interface, (b) one relaxation time constant with extended diffusion.

The Maxwell-Wagner dispersion effect due to conductance in parallel with capacitance for two ideal dielectric materials in series Rj Cj - Rj Cj can also be represented by Debye dispersion without postulating anything about dipole relaxation in dielectric. In the ideal case of zero conductivity for both dielectrics (R, — , R —> ), there is no charging of the interfaces from free charge carriers, and the relaxation can be modeled by a single capacitive relaxation-time constant. 

The addition of salts modifies the composition of the layer of charges at the micellar interface of ionic surfactants, reducing the static dielectric constant of the system [129,130]. Moreover, addition of an electrolyte (NaCl or CaCli) to water-containing AOT-reversed micelles leads to a marked decrease in the maximal solubihty of water, in the viscosity, and in the electrical birefringence relaxation time [131],... 

After addition of lipid DSPC into the organic phase a monolayer is formed at the interface, and the steady-state current increased at all potentials. On expansion, the time constant of the charging current is reduced to ca. 5 ms and a shift of ca. 100 mV is observed in the potential of zero charge. From the video image of the droplet a highly distorted and heterogeneous interface is seen which relaxes after the fast stage (a few... 

Time Constant Analysis, r is the relaxation time of the corrosion process and is dependent on the dielectric properties of the interface. r is given by r = R P, but can be measured independently r = wz"max Since and P vary with surface area in exactly opposite fashion, r (or wzBmax) should be independent of surface area. To verify that this is indeed the case, we examined the corrosion of N80 steel in uninhibited 15% HC1 at 65 C. With increasing exposure time, we observed a continuous decrease in R (hence an increase in corrosion rate) and a concomitant increase in P. And, as expected, wz"max did not vary at all (see Figure 8). 

The segmental mobility of the polymer in the monolayer is enhanced by the solvation of the hydrophobes with toluene (9) the relaxation rate constant at the toluene/aqueous interface was three times that at the air/aqueous interface, as shown by Experiments Numbers 1 and 2 in Table II. 

In several previous papers, the possible existence of thermal anomalies was suggested on the basis of such properties as the density of water, specific heat, viscosity, dielectric constant, transverse proton spin relaxation time, index of refraction, infrared absorption, and others. Furthermore, based on other published data, we have suggested the existence of kinks in the properties of many aqueous solutions of both electrolytes and nonelectrolytes. Thus, solubility anomalies have been demonstrated repeatedly as have anomalies in such diverse properties as partial molal volumes of the alkali halides, in specific optical rotation for a number of reducing sugars, and in some kinetic data. Anomalies have also been demonstrated in a surface and interfacial properties of aqueous systems ranging from the surface tension of pure water to interfacial tensions (such as between n-hexane or n-decane and water) and in the surface tension and surface potentials of aqueous solutions. Further, anomalies have been observed in solid-water interface properties, such as the zeta potential and other interfacial parameters. 

The relaxation time of the end-to-end vector correlation for the adsorbed chains depends on the number of contacts. Chains with one or two contacts have most of their segments free and thus due to their bulk like dynamics the end-to-end vector can rapidly relax. On the other hand, for the chains with most of their segments adsorbed this process becomes very slow as the segment dynamics are very sluggish inside the solid oligomer interface (Fig. 15). For strong wall attractions ( w=2 or 3) the chains with more than three contacts relax with almost the same time constant. This insensitivity shows that the slowdown of the dynamics is caused by the densification inside the first layer rather than the magnitude of the surface-fluid interactions [38a,d]. 

Thus, two types of surface charges occur in this case. The first one, Ei, corresponds to the situation in which some charge with density Eq is placed on the interface. In accord with eq. 1.168, such a charge decays exponentially with a time constant Tqs that is controlled by the conductivity and dielectric constant of the medium. Inasmuch as the relaxation time Tqs is usually very small with respect to measurement times, we will no further consider this type of charge and concentrate on the second type. 

Polymerizable film forming molecules were polymerized, at the air-water interface or after transfer to solid substrates, by exposure to ultraviolet light from a 254 nm wavelength lamp having an effective intensity of approximately 80 mW/cm. Polymerizations performed at the air-water interface were carried out after compressing a film to a given surface pressure, allowing time for any relaxation at constant... 

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