Dielectric constant measurement procedure

It has been mentioned that microwave intensities are determined by the size of the electric dipole moment, so one might suppose that accurate measurements of intensities might provide values of /. This turns out not to be practical for various reasons. However, another very accurate procedure can be used. If an electric field is applied to a rotating molecule, a well-understood phenomenon known as the Stark effect splits the rotational transitions into a number of components. Precise measurements of these small splittings (typically several MHz) lead to very precise values of the electric dipole moment. Values of jj, determined by this method refer to particular quantum states and are thus much more meaningful theoretically than those determined by classical bulk-gas relative permittivity (dielectric constant) measurements. 

Dielectric constants of metals, semiconductors and insulators can be detennined from ellipsometry measurements [38, 39]. Since the dielectric constant can vary depending on the way in which a fihn is grown, the measurement of accurate film thicknesses relies on having accurate values of the dielectric constant. One connnon procedure for detennining dielectric constants is by using a Kramers-Kronig analysis of spectroscopic reflectance data [39]. This method suffers from the series-tennination error as well as the difficulty of making corrections for the presence of overlayer contaminants. The ellipsometry method is for the most part free of both these sources of error and thus yields the most accurate values to date [39]. 

Until one develops a feel for recrystallization, the best procedure for known compounds is to duplicate a selection in the literature. For new compounds, a literature citation of a solvent for an analogous structure is often a good beginning point. To assist in the search, Table A3.4 lists several of the common recrystallizing solvents with useful data. The dielectric constant can be taken to be a rough measure of solvent polarity. 

Dielectric constant and dissipation factor measurements were conducted according to the procedures of ASTM D-150-87. Tensile strength and modulus and percent elongation were measured on an Instron model 1125 according to the procedures of ASTM-D-882-83. 

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... 

Procedure. Equation 1 indicates that it is necessary to determine the concentration, resistance, dielectric constant, viscosity, and temperature of the system. These data were acquired for five different solvent systems. A series of measurements, in which the concentration of lithium bromide was varied from about 10 5N to 10 3N, was made on each system. The solvents used were acetone (I), 0.02063m bromosuccinic acid in acetone (II), 0.05009m bromosuccinic acid in acetone (III), 0.09958m bromosuccinic acid in acetone (IV), and 0.05047m dimethyl bromosuccinate in acetone(V). Each solvent was used to prepare stock solutions of 10-2 and 10 3m lithium bromide. All mixed solvents and solutions were prepared in the dry box. 

As we pointed out in previous chapters, the quality and purity of the solvent and supporting electrolyte used is important in electrochemical measurements. For most measurements in aprotic solvents it is necessary to keep water levels as low as possible. Earlier in this chapter procedures were described for purifying solvents and supporting electrolytes. However, it is tedious work, which requires time and energy. Moreover, it is not possible to obtain as low water levels as those available from specialized companies. From our own experience the solvents purified by Burdich Jackson ( distilled in glass grade ), a division of Baxter, can be used in electrochemical measurements without further purification (most attempts to improve their materials result in higher H20 levels). Table 7.12 lists maximum water contents and dielectric constants for several Burdick Jackson solvents that are frequently used by electrochemists. However, the actual water level in most cases is much lower. 

An elegant way to avoid this non-ideality correction, especially when operating at high pressures (up to 16.5 MPa), where it can become predominant, was proposed by Bose et al. (1987). In their method, for each equilibrium point the density of the adsorptive is determined experimentally from its dielectric constant, which is measured in a gas capacitance cell at the same temperature and pressure as the adsorption system studied. The rest of their adsorption procedure is comparable to the... 

If the dielectric constant is also to be measured at Dry lee temperature ( 78.5°C), the evacuated cell should be immersed in a large Dewar flask containing barely enough acetone to submerge the main body of the cell, and crushed Dry lee should be added slowly until further addition of Dry lee causes no increase in gas evolution enough more is added to allow for further vaporization over the time of the experiment. The procedure described for determining the oscillator frequencies should be repeated, with allowance for the additional time that may be required for the attainment of equilibrium at the lower temperature. It is possible also to make measurements above room temperature if means are available to obtain satisfactory temperature control for the duration of the measurements. 

The nature of the tracer dictates the detection system. For the liquid phase, quite often the tracers (e.g., NaCl, H2S04, etc.) are such that the detection probe is directly inserted into the reactor and continuous monitoring of the concentration at any fixed position is obtained by means of an electrical conductivity cell and a recorder. In this case, no external sampling of liquid is necessary. If the tracer concentration measurement requires an analytical procedure such as titration, etc., sampling of the liquid is required. For the solid phase, a magnetic tracer is sometimes used. The concentration of a solid-phase tracer can also be measured by a capacitance probe if the tracer material has a different dielectric constant than the solid phase. In general, however, for solid and sometimes gas phases, some suitable radioactive tracer is convenient to use. The detection systems for a radioactive tracer (which include scintillation counters, a recorder, etc.) can be expensive. Some of the tracers for the gas, liquid, and solid phases reported in the literature are summarized in Table 3-1. 

Accurate methods for evaluating Ka based on this equation, involving the use of conductance measurements, have been already described in Chap. V these require a lengthy experimental procedure, but if carried out carefully the results are of high precision. For solvents of high dielectric constant the calculation based on the Onsager equation may be employed (p. 165), but for low dielectric constant media the method of Fuoss and Kraus (p. 167) should be used. 

Electrical Data. The electrical properties of cured specimens of the epoxy resin, containing various quaternary phosphonium compounds, were obtained on 2 in. diameter discs (0.125 in. to 0.25 in. thick) using standard procedures (ASTM D150-65T). In these tests, the power factor (100 x tan 6) and dielectric constant (e ) data were usually measured at 150 C (and a frequency of 60 Hz) on resin samples which had been cured for 16 h at 135 C + 5 h at 150 C. 

If the dielectric constant of the aqueous phase enclosed inside the heme binding site of apomyoglobin can be measured and the dielectric constant of the protein is deduced from that data (26), there is no reason why the same procedure cannot be applied to membrane proteins. If the geminate recombination of proton-excited pyranine anion can be monitored in the anion channel of the Pho-E protein (27), the interior of other channels can also be investigated. 

The experimental setups for measuring powder resistivity in Figures 3-1 can also be used to measure the effective dielectric constant of the bulk powder. The procedure is to measure the capacitance with 0 and without the powder. Using the definition of capacitance c= eA/x for parallel plates of area A and separation distance x gives... 

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