Macroscopic methods

Interfacial Tension. The interfacial energy a between a crystal and an aqueous solution cannot (at least in general) be measured by macroscopic methods. But it may be deduced from homogeneous nuclea-tion data (20-24). For the purpose of determining the edge energy Y = a CT one may either take the individual value determined on the actual substance (if it is determined) or use the general correlation with the solubility cs, expressed for instance by (10,18)... 

We presented fully self-consistent separable random-phase-approximation (SRPA) method for description of linear dynamics of different finite Fermi-systems. The method is very general, physically transparent, convenient for the analysis and treatment of the results. SRPA drastically simplifies the calculations. It allows to get a high numerical accuracy with a minimal computational effort. The method is especially effective for systems with a number of particles 10 — 10, where quantum-shell effects in the spectra and responses are significant. In such systems, the familiar macroscopic methods are too rough while the full-scale microscopic methods are too expensive. SRPA seems to be here the best compromise between quality of the results and the computational effort. As the most involved methods, SRPA describes the Landau damping, one of the most important characteristics of the collective motion. SRPA results can be obtained in terms of both separate RPA states and the strength function (linear response to external fields). 

Satterfield (S2, S3) carried out a number of interesting macroscopic studies of simultaneous thermal and material transfer. This work was done in connection with the thermal decomposition of hydrogen peroxide and yielded results indicating that for the relatively low level of turbulence experienced the thermal transport did not markedly influence the material transport. However, the results obtained deviated by 10 to 20 from the commonly accepted macroscopic methods of correlating heat and material transfer data. The final expression proposed by Satterfield (S3), neglecting the thermal diffusion effect (S19) in the boundary layer, was written as... 

Villard (1896) proposed an indirect macroscopic method to determine hydration number, which uses the heat of formation, both above and below the ice point. In his review, Schroeder (1927) indicates that after 1900, researchers abandoned direct measurement of hydrate phase composition, preferring Villard s method (see Section 4.6.2) that relies on easier measurements of pressure and temperature. Miller and Strong (1946) provided another thermodynamic method to determine hydration number, discussed in Section 4.6.2.2. 

With the evolution of these new structures, the possibility of forming metastable hydrate phases (Section 3.2), and the fact that different structures form at different thermodynamic conditions (pressure, temperature, composition), it is clear that macroscopic methods cannot adequately predict the hydrate structure(s) present. 

Figure 8.12 shows the macroscopic method of AAs. In the top portion of the figure, hydrates are agglomerated into a plug, analogous to that in the far right of Figure 8.8. In the lower portion of the figure, the hydrate particles are dispersed in the hydrocarbon liquid, so that they will continue to flow.

The values of A calculated by microscopic and by macroscopic methods tend to be similar in the non-retarded range. The macroscopic approach predicts a smaller retardation effect (i.e. better applicability of equations 8.8-8.10 for relatively large values of H) than the microscopic approach104. 

Hamaker constants for single materials usually vary between about 10" 20 J and 10 19 J. Some examples are given in Table 8.3. Where a range of values is quoted for a given material, this reflects different methods of calculation within the basic microscopic or macroscopic method. 

Macroscopic methods for chemical analysis essentially take either all of the particulate matter sampled or a significant protion of it for bulk analysis. Traditionally, this has been approached by the application of standard microchemical techniques of wet chemistry. The unique analytical requirement for aerosol particle samples is the microgram quantities collected. The analytical methods adopted must be capable of detecting these quantities in... 

Many of the macroscopic methods incorporate some features from molecular theory and are then usually more useful for prediction and extrapo-... 

In the most simplistic means of defining particle shape, measurements may be classified as either macroscopic or microscopic methods. Macroscopic methods typically determine particle shape using shape coefficients or shape factors, which are often calculated from characteristic properties of the particle such as volume, surface area, and mean particle diameter. Microscopic methods define particle texture using fractals or Fourier transforms. Additionally electron microscopy and X-ray diffraction analysis have proved useful for shape analysis of fine particles. 

The use of tubes of rectangular cross section provides a maximum amount of wall area and so facilitates the removal of heat to the surroundings, and the maintenance of the apparatus at somewhat below 4 , where the variation of the density of the liquid with temperature is very small, greatly diminishes convection effects. With these improvements, and a device for obtaining initially sharp boundaries, the macroscopic method has proved a valuable means for the study of electrophoresis, and for its utilization to separate particles moving with different speeds. 

To show the influence of various microscopic and structural factors on linear and non-linear effects in dense dielectrics, it is convenient to apply first a semi-macroscopic treatment of the theory, and then to proceed to its molecular-statistical interpretation, assuming appropriate microscopic models. The semi-macroscopic method was initially applied by Kirkwood and modified by Frohlich in the theory of linear dielectrics, and has beat successfully used in theories of non-linear tUelectrics. "... 

Macroscopic Methods Sorption Rate (12) IR spectroscopy (16, 17) Frequency response (20) Chromatography (12) ZLC (13) Differential adsorption bed (21) TAP reactor (22) Imaging (23) Membrane permeation (14,15) Effectiveness factor (18, 19) Tracer methods (12)... 

The induced molecular dipole replaces the polarization and the local field, E, acting on the molecule is introduced in place of the macroscopic field. There are two conventions in use for defining the hyperpolarizability series one is the exact analogue of the macroscopic method (B convention), the other uses a Taylor series expansion (T convention) where a factor (l/ ) is introduced into wth order terms. The notation introduced by WRBS as been used. For a noncentros5unmetric molecule subjected to an internal field,... 

There are macroscopic (uptake measurements, liquid chromatography, isotopic-transient experiments, and frequency response techniques), and microscopic techniques (nuclear magnetic resonance, NMR and quasielastic neutron spectrometry, QENS) to measure the gas diffusivities through zeolites. The macroscopic methods are characterized by the fact that diffusion occurs as the result of an applied concentration gradient on the other hand, the microscopic methods render self-diffusion of gases in the absence of a concentration gradient [67]. 

Neutron Scattering (QENS) [13], and Temporal-Analysis of Products (TAP) [14] (Figure 6, solid symbols). The isobutane diffusivities determined by the macroscopic methods, such as MEMBRANE, TAP, and FR show reasonable agreement. The self-difiusivity coefficient derived from QENS is about one order of magnitude lower. The E, values of 34 kJ mof and 25 kJ mol obtained by the MEMBRANE and the TAP methods, respectively, are higher than those determined by methods where the conditions of the mesurements correspond to sorption equilibrium or quasi-equilibrium, such as QENS (17 kJ mol )orFR(21 kJ mol ). 

An advantage of the AFM approach over macroscopic methods is that distribution of local lEP can be determined for a heterogeneous surface. This can be done when the difference in lEP between different parts of the surface is sufficiently large, and specific example of such results have not been reported. Aral et al. [76] observed two zero points in plots of force between two different surfaces measured at separation of half of Debye length as a function of pH and they argue that these points correspond to lEP of the two materials of interest. Indeed, their estimated values are close to lEP reported in literature. Phosphate buffer was used to establish the pH, so the results are probably affected by strong specific adsorption of phosphates. 

Some general comments might be useful, however, before considering the individual methods. First, the techniques may be divided into (i) macroscopic methods, which are used to measure the effect of long-range motion of atoms and (ii) microscopic methods, which are used to measure the effect of jump frequencies of atoms [210, 212]. In principle, for a simple jump process via point defects in a solid, the two are interconnected by the classical Einstein-Smoluchowski equation [204] ... 

Two macroscopic methods to design adsorption columns are the scale-up and kinetic approaches. Both methods rely on breakthrough data obtained from pilot columns. The scale-up method is very simple, but the kinetic method takes into account the rate of adsorption (determined by the kinetics of surface diffusion to the inside of the adsorbent pore). The scale-up approach is useful for determining the breakthrough time and volume (time elapsed and volume treated before the maximum allowable effluent concentration is achieved) of an existing column, while the kinetic approach will determine the size requirements of a column based on a known breakthrough volume. 

In our 1981 review,1 we suggested that analyses using a microscopic description of dynamics would increasingly influence our interpretation of the properties of large systems that the merging of the microscopic and macroscopic methods of analysis would lead to an understanding of the gradual transition from the behavior characteristic of the intramolecular dynamics of... 

This has been attempted either by treating the problem as a diffusion problem, or by applying the superposition principle, that is by a macroscopical method. To understand the latter treatment, suppose that a static field is applied and suddenly cut off at t — 0. At a given moment t, the distribution function will be given by... 

There is a lot of information available about the rate of action of channel blocking antagonist because this is relatively easy to determine by single-channel methods and also can often be obtained by macroscopic methods like voltage jump relaxations [e.g., Colquhoun et al. (55)] or noise analysis (107). 

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