Dielectric constant experimental measurement

At the solvent density, p =0.6, we see that decreases continuously with increasing pj. This behavior is qualitatively consistent with experimental results for aqueous solutions, but the present model is much too simple to permit meaningful quantitative comparison. Also it is important to recall the is but one of the contributions to the apparent dielectric constant ejoL- measured experimentally. The behavior of at p =0.8 is somewhat different. Initially, decreases as before, but it now passes through a minimum and increases again at the higher concentrations. This is not observed experimentally, for a very simple reason.In the theoretical calculations the ions are added at constant volume rather than at constant pressure. Thus as ions are added, p remains constant but the total... 

Experimentally, the dielectric constant and density of the substance are measured. Either the dielectric constant is measured at several temperatures or the refractive index must be measured the dipole moment is then calculated. The dielectric constant is measured in a conductance cell on the vapor or, more often, in dilute solution in a nonpolar solvent such as benzene.J For accurate work, the dielectric constant is measured at several concentrations to allow extrapolation to infinite dilution. ... 

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

The validity of the above conclusions rests on the reliability of theoretical predictions on excited state barriers as low as 1-2 kcal mol . Of course, this required as accurate an experimental check as possible with reference to both the solvent viscosity effects, completely disregarded by theory, and the dielectric solvent effects. As for the photoisomerization dynamics, the needed information was derived from measurements of fluorescence lifetimes (x) and quantum yields (dielectric constant, where extensive formation of ion pairs may occur [60], the observed photophysical properties are confidently referable to the unperturbed BMPC cation. Figure 6 shows the temperature dependence of the... 

The liquid-liquid interface is not only a boundary plane dividing two immiscible liquid phases, but also a nanoscaled, very thin liquid layer where properties such as cohesive energy, density, electrical potential, dielectric constant, and viscosity are drastically changed along with the axis from one phase to another. The interfacial region was anticipated to cause various specific chemical phenomena not found in bulk liquid phases. The chemical reactions at liquid-liquid interfaces have traditionally been less understood than those at liquid-solid or gas-liquid interfaces, much less than the bulk phases. These circumstances were mainly due to the lack of experimental methods which could measure the amount of adsorbed chemical species and the rate of chemical reaction at the interface [1,2]. Several experimental methods have recently been invented in the field of solvent extraction [3], which have made a significant breakthrough in the study of interfacial reactions. 

There are several electrical measurements that may be used for analysis of solutions under in situ conditions. Among the properties that may be measured are dielectric constants, electrical conductivity or resistivity, and the redox potential of solutions. These properties are easily measured with instrumentation that is readily adapted to automatic recording operation. However, most of these techniques should be used only after careful calibration and do not give better than 1% accuracy without unusual care in the experimental work. 

Experimentally, one measures an incremental dielectric constant K. Thus... 

Dielectric constants of these materials can be further lowered by known means such as by incorporating air bubbles into the materials or by inhibiting crystallization. A difference of a couple of hundredths in the DE value may be important when one is at the low extremes. Recently Singh et al. calculated the DEs ofpolyimide films from the measured free volume fraction and found that the calculated values, are close to the experimental result.1415 ... 

This is possible if the equivalent conductivity is proportional to the square root of the concentration Cq, i.e. if the Debye-Hiickel-Onsager law is obeyed. It is known that this square-root law is also obeyed for non-aqueous solvents as a good approximation, as long as the dielectric constant of the solvent is not less than e = 30. Figure 19 shows the equivalent conductivities as a function of Vm for three examples. If one bears in mind that, because of experimental difficulties, the accuracy of measurements in aqueous solutions is not attained, then the square root law is obeyed to a good approximation. 

Confinement of water into regions with dimensions of only a few nanometers, such as typically those found in PEMs, accompanied by a strong electrostatic field due to the anions, will result in a significantly lower dielectric constant for the water than that observed in bulk water. Measurement of this structural ordering of the water has not been accomplished experimentally to date, and this was the motivation to the recent calculation of the dielectric saturation of the water in PEMs with an equilibrium thermodynamical formulation. " In addition to information concerning the state of the water this modeling has provided information concerning the distribution of the dissociation protons in sulfonic acid-based PEMs. 

The dielectric constant of the pure cyanurate network under dry nitrogen atmosphere at 20 °C is 3.0 (at 1 MHz). For the macroporous cyanurate networks, the dielectric constant decreases with the porosity as shown in Fig. 57, where the solid and dotted lines represent experimental dielectric results together with the prediction of the dielectric constant from Maxwell-Garnett theory (MGT) [189]. The small discrepancies between experimental results and MGT might be due to the error in estimated porosities, which are calculated from the density of the matrix material and cyclohexane assuming that the entire amount of cyclohexane is involved in the phase separation. It is supposed that a small level of miscibility after phase separation would result in closer agreement of dielectric constants measured and predicted. Dielectric constant values as low as 2.5 are measured for macroporous cyanurates prepared with 20 wt % cyclohexane. 

One of the drawbacks of ellipsometry is that the raw data cannot be directly converted from the reciprocal space into the direct space. Rather, in order to obtain an accurate ellipsometric thickness measurement, one needs to guess a reasonable dielectric constant profile inside the sample, calculate A and and compare them to the experimentally measured A and values (note that the dielectric profile is related to the index of refraction profile, which in turn bears information about the concentration of the present species). This procedure is repeated until satisfactory agreement between the modeled and the experimental values is found. However, this trial-and-error process is complicated by an ambiguity in determining the true dielectric constant profiles that mimic the experimentally measured values. In what follows we will analyze the data qualitatively and point out trends that can be observed from the experimental measurements. We will demonstrate that this... 

For our purpose, it is convenient to classify the measurements according to the format of the data produced. Sensors provide scalar valued quantities of the bulk fluid i. e. density p(t), refractive index n(t), viscosity dielectric constant e(t) and speed of sound Vj(t). Spectrometers provide vector valued quantities of the bulk fluid. Good examples include absorption spectra A t) associated with (1) far-, mid- and near-infrared FIR, MIR, NIR, (2) ultraviolet and visible UV-VIS, (3) nuclear magnetic resonance NMR, (4) electron paramagnetic resonance EPR, (5) vibrational circular dichroism VCD and (6) electronic circular dichroism ECD. Vector valued quantities are also obtained from fluorescence I t) and the Raman effect /(t). Some spectrometers produce matrix valued quantities M(t) of the bulk fluid. Here 2D-NMR spectra, 2D-EPR and 2D-flourescence spectra are noteworthy. A schematic representation of a very general experimental configuration is shown in Figure 4.1 where r is the recycle time for the system. 

We have no measurements of micellar size, since the translation of micelle size into the number of monomers in the micelle is not a simple task and requires assumptions not easily experimentally tested. We are hopeful of extending experimentation in this direction in future research. Table II lists dielectric constants, dipole moments and effective polarities for methanol, 1- and 2-octanol, and water at 25°C. 

In this expression e(/ ) is the dielectric constant —it is a function of frequency —along the imaginary frequency axis / it is measurable as the dissipative part of the spectrum of dielectric constant for any material. The latter is an experimentally determined function of frequency for each of the three components, and the complicated expression in Equation (64) is integrated over all frequencies. 

The Stern theory is difficult to apply quantitatively because several of the parameters it introduces into the picture of the double layer cannot be evaluated experimentally. For example, the dielectric constant of the water is probably considerably less in the Stern layer than it would be in bulk because the electric field is exceptionally high in this region. This effect is called dielectric saturation and has been measured for macroscopic systems, but it is difficult to know what value of e6 applies in the Stern layer. The constant K is also difficult to estimate quantitatively, principally because of the specific chemical interaction energy . Some calculations have been carried out, however, in which the various parameters in Equation (97) were systematically varied to examine the effect of these variations on the double layer. The following generalizations are based on these calculations ... 

It is interesting to note that the fluorine-containing BMIs are lower melting than the fluorine-free BMI. Furthermore, the expected reduction of the dielectric constants for the cured BMIs measured at 1 MHz was achieved. The values calculated by using the Clausisus-Mosotti equation are in reasonable agreement with the experimental results. 

Table 12.4 reports results on the comparison between predicted values of the dielectric constant and experimental values on wet samples measured at 1 kHz. Currently the method does not include the effect of moisture (or a frequency dependence of the dielectric constant). It is, however, interesting to see that there is a relatively better correlation between theory and experimental values for the wet samples. 

Figure 12.1. Comparison of predicted dielectric constants to experimental dielectric constants for a series of dry polyimide samples measured at a frequency of 10 MHz.

The dipole moment of naphthazarin has been deduced from the measurements of the dielectric constants of its solutions in benzene and dioxan, respectively. A heterodyne beat apparatus has been used at 4 4 Mhz, the temperature of the solution was 20°C. The molecular refraction has been computed [8] from standard bond refractions, the experimental determination being impossible because of the strong... 

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