Descriptive dispersion measure

For this reason, a detailed description of the console in this paper is superfluous, except for a brief list of those features which, in our opinion, any research-grade FFC console should possess in order to guarantee maximum versatility of NMR dispersion measurements. 

The Onsager cavity description of solvation treats the solvent as a dielectric continuum. The dielectric dynamics of the solvent is typically characterized by the frequency-dependent complex dielectric constant s(co). The measurement of (co) for a neat solvent is conventionally called a dielectric dispersion measurement. 

The terms dispersion characteristic and respective or constituent amount need further explanation. The dispersion characteristic, also called particle size, grain size, fineness index, or dispersion parameter, is a physical property which can be measured and defines, in a suitable way, the dispersity or, in a narrower sense, the dimensions of the particles. In the case of spheres, diameter would be the most descriptive dispersion characteristic. If the particles are irregularly shaped, other linear dimensions must be chosen, e.g. the statistical chord lengths according to Martin or Feret (Figure 21), the mesh size of a screen through which the particle just passes, or so-called equivalent diameters. Equivalent diameters are calculated from other dispersion characteristics, which must not necessarily be linear dimensions, using mathematical relationships and/or physical laws. 

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

Descriptive statistics are used to summarize the general nature of a data set. As such, the parameters describing any single group of data have two components. One of these describes the location of the data, while the other gives a measure of the dispersion of the data in and about this location. Often overlooked is the fact that the choice of which parameters are used to give these pieces of information implies a particular type of distribution for the data. 

The use of the mean with either the SD or SEM implies, however, that we have reason to believe that the sample of data being summarized are from a population that is at least approximately normally distributed. If this is not the case, then we should rather use a set of statistical descriptions which do not require a normal distribution. These are the median, for location, and the semiquartile distance, for a measure of dispersion. These somewhat less familiar parameters are characterized as follows. 

The value in units of incident dose per unit area for either a positive or negative resist system is of little value unless accompanied by a detailed description of the conditions under which it was measured. This description should include, at the minimum, the initial film thickness, the characteristics of the substrate, the temperature and time of the post- and pre-bake, the characteristics of the exposing radiation, and the developer composition, time and temperature. The structure, copolymer ratio, sequence distribution, molecular weight, and dispersity of polymers included in the formulation should also be provided. 

Unfortunately, little direct information is available on the physicochemical properties of the interface, since real interfacial properties (dielectric constant, viscosity, density, charge distribution) are difficult to measure, and the interpretation of the limited results so far available on systems relevant to solvent extraction are open to discussion. Interfacial tension measurements are, in this respect, an exception and can be easily performed by several standard physicochemical techniques. Specialized treatises on surface chemistry provide an exhaustive description of the interfacial phenomena [10,11]. The interfacial tension, y, is defined as that force per unit length that is required to increase the contact surface of two immiscible liquids by 1 cm. Its units, in the CGS system, are dyne per centimeter (dyne cm" ). Adsorption of extractant molecules at the interface lowers the interfacial tension and makes it easier to disperse one phase into the other. 

In contrast to the large variety of averages and measures of dispersion prevalent in the literature, the number of basic distributions which have proved useful is relatively small. In droplet statistics, the best known distributions include the normal, log-normal, Rosin-Rammler, and Nukiyama-Tanasawa distributions. The normal distribution often gives a satisfactory representation where the droplets are produced by condensation, precipitation, or by chemical processes. The log-normal and Nukiyama-Tanasawa distributions often yield adequate descriptions of the drop-size distributions of sprays produced by atomization of liquids in air. The Rosin-Rammler distribution has been successfully applied to size distribution resulting from grinding, and may sometimes be fitted to data that are too skewed to be fitted with a log-normal distribution. 

Dayhoff [50] suggested that one might measure a rest mass of photon by designing a low-frequency oscillator from an inductor-capacitor (LC) network. The expected frequency can be calculated from Maxwell s equations, and this may be used to give an effective wavelength for photons of that frequency. He claimed that one would have a measure of the dispersion relationship at low frequencies. Williams [51] calculated the effective capacitance of a spherical capacitor using Proca equations. This calculation can then be generalized to any capacitor with the result that a capacitor has an additional term that is quadratic in the area of the plates of the capacitor. However, this term is not exactly the one that Dayhoff referred to. But it seems to be a very close description of it. One can add two identical capacitors C in parallel and obtain the result... 

Statistical mechanics was originally formulated to describe the properties of systems of identical particles such as atoms or small molecules. However, many materials of industrial and commercial importance do not fit neatly into this framework. For example, the particles in a colloidal suspension are never strictly identical to one another, but have a range of radii (and possibly surface charges, shapes, etc.). This dependence of the particle properties on one or more continuous parameters is known as polydispersity. One can regard a polydisperse fluid as a mixture of an infinite number of distinct particle species. If we label each species according to the value of its polydisperse attribute, a, the state of a polydisperse system entails specification of a density distribution p(a), rather than a finite number of density variables. It is usual to identify two distinct types of polydispersity variable and fixed. Variable polydispersity pertains to systems such as ionic micelles or oil-water emulsions, where the degree of polydispersity (as measured by the form of p(a)) can change under the influence of external factors. A more common situation is fixed polydispersity, appropriate for the description of systems such as colloidal dispersions, liquid crystals, and polymers. Here the form of p(cr) is determined by the synthesis of the fluid. 

Eq. (15) and 1.1 10- 7 m2/s according to Eq. (14). This significant difference may be explained by the fact, the Kang et al. used particles of uniform size whereas van der Meer et al. measured dispersion between two fractions of different particle size in a segregated fluidized bed. As adsorption in a frontal mode is performed using classified or otherwise stabilized fluidized beds, the lower Daxp resulting from van der Meer s correlation may be a better description of the solid phase dispersion in a fluidized bed for protein adsorption. 

For this description of PCS, it is evident that, for mono-disperse systems, the technique can provide an absolute measurement of hydrodynamic size knowledge of the density or refractive index of the particles is not required, and no calibration or correction is needed. With the advent of digital correlators and microprocessors, PCS has also become a very fast and precise technique. Recent studies of latex using PCS include adsorbed layers (8), particle sizes (16), surface characterization (17) and aggregation (181- ... 

Good descriptions of practical experimental techniques in conventional electrophoresis can be found in Refs. [81,253,259]. For the most part, these techniques are applied to suspensions and emulsions, rather than foams. Even for foams, an indirect way to obtain information about the potential at foam lamella interfaces is by bubble electrophoresis. In bubble microelectrophoresis the dispersed bubbles are viewed under a microscope and their electrophoretic velocity is measured taking the horizontal component of motion, since bubbles rapidly float upwards in the electrophoresis cells [260,261]. A variation on this technique is the spinning cylinder method, in which a bubble is held in a cylindrical cell that is spinning about its long axis (see [262] and p.163 in Ref. [44]). Other electrokinetic techniques, such as the measurement of sedimentation potential [263] have also been used. 

More detailed descriptions are given in Refs. [295,408,409]. Further details on the principles, measurement and applications to dispersion stability of interfacial viscosity are reviewed by Malhotra and Wasan [408], and Miller et al. [410]. 

Another common category of descriptive statistics is the measure of dispersion of a set of data about a central value. The range is the arithmetic difference between the greatest (maximum) and the least (minimum) value in a data set. While this characteristic is easily calculated and is useful in initial inspections of data sets,... 

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