Electrically quantitative description

Figure 9.2 Quantitative description of optical rotation. A vertically polarized electric field Em is incident on chiral system and induces vertically directed dipole moment i and magnetic moment m. Both act as sources of radiation, p, giving rise to vertically polarized field, m giving rise to horizontally polarized field. Sum of both fields is a new field E0ut with polarization rotated over angle 0.

Analysis of polyelectrolytes in the semi-dilute regime is even more complicated as a result of inter-molecular interactions. It has been established, via dynamic light-scattering and time-dependent electric birefringence measurements, that the behavior of polyelectrolytes is qualitatively different in dilute and semi-dilute regimes. The qualitative behavior of osmotic pressure has been described by a power-law relationship, but no theory approaching quantitative description is available. 

It has been pointed out that the high and variable electric field at the surface of a charged polymer makes the quantitative description of its equilibria very complecated (3). In this work the following assumptions were made in order to calculate the stability constants of the complexes of middle PO3 units with magnesium ion. 

The composition of this chapter is based on a well-known and well-understood model of the electrical double layer and therefore does not pretend to enhance overall understanding. It does, however, aim to answer the question of whether a useful mathematical technique exists that may allow for a numerical, if not analytical, description of the double layer for a surface of arbitrary shape and topography. It is fair to say that the colloid scientist ultimately seeks a quantitative description of the electrical double layer for whatever reason. The task then now faced is to uncover the most appropriate theoretical method of calculating the electrical double layer properties for a given nonideal situation. Here we suggest a few methods that may help in this respect. 

A quantitative description for the diffuse layer dates back to Gouy [40] and Chapman [41]. This model is fully described elsewhere [42], and we shall here only outline basic features of the theory. The first stage in this approach is to use the Poisson equation. Eq. (I), to describe the relationship between the electrical potential 4>(.v) and the charge density p of ions of charge at a distance v from a flat charged surface, with a regional permittivity f ... 

In their classic series of papers, Hodgkin and Huxley gave a quantitative description of the unique electrical behavior of the giant nerve fibers (axons) of squid. This behavior is described in terms of permeability of the surface membrane (measured as conductance per unit area of membrane) to different ion species, particularly Na+ and K+. The current carried by an ion species through the membrane is then calculated from the product of conductance and driving force on them (transmembrane voltage, V, minus ion equilibrium potential). The specific ionic conductances have several unique properties which challenge explanation at the molecular level ... 

Reversible electrical breakdown (REB) is particularly striking. (REB is actually a rapid discharge due to the high ionic conductivity caused by the gentle structural membrane rearrangement of multiple pore formation.) In our models, subcritical pores (i.e., nonrupture-causing pores) are responsible for this high conductance state (II). Our first quantitative description of REB (33, 34) correctly predicted many key features of U(t) and G(t) but had... 

Unless explicitly stated otherwise, the term pore hereafter refers to hydrophilic pores, because they are believed to provide pathways for ionic and molecular transport. A quantitative description of pore creation and destruction is essential, even if it cannot be made completely from first principles [e.g., by molecular dynamics (38)]. Generally a pore free energy , AE(r), is used in which the pore is approximated as a circular cylinder of radius r. Both mechanical (39, 40) and electrical (10-12) contributions are considered The contributions are emphasized by the form 4 (r, Up), where L7p is the local transmembrane voltage at the site of the pore. We use A E = A EM... 

If a certain potential, different from the equilibrium value, is applied to both sides of the interface, under potentiostatic conditions, electrical current through the interface can decrease to zero when equilibrium is established. The process is called electroextraction. The calculation as described in previous sections (see Figures 2-4, 8, and 19) can be used for a quantitative description of electroextraction. 

Althou, in principle, the general theory is superior to the band theory, the appropriate techniques for its application are not yet developed sufficiently well and a unified approach to a quantitative description of the structures and the physical properties of crystals is still lacking. The less generally valid band theory can at present give clearer and more convincing explanations of changes in the physical properties of crystals caused by variations in the temperature, pressure, magnetic and electric fields intensities, impurity concentrations, etc. However, many problems encoimtered in the study of chemical bonds in crystals cannot be considered within the framework of the standard band theory. They include, for example, determination of the elastic, thermal, and thermodynamic properties of solids, as well as the structure and properties of liquid and amorphous semiconductors. 

As chemical, mechanical and electrical properties attain their ultimate values during the last stages of cure, the diffusion-controlled regime appears to be a very important part of the curing process. An accurate quantitative description of the impact of mobility restrictions on cure is therefore essential. Diffusion control can be specific or non-specific (overall). 

This paper presents a quantitative description of a floating insulation for the surfaces of cryogenic fluids stored in open-topped dewar flasks. The technique makes use of polystyrene beads, which provide good thermal insulation, conform to a complex surface geometry—such as partially immersed equipment—and act as a good electrical insulator as well. Since the beads float on the liquid surface, they need not be removed when refilling the container and provide an easily visible liquid level indication. 

Energy source Here an easily understandable title, type of energy, quantitative description (e.g., voltage, current/power, etc. for electrical energy), and applicable phase, etc., shall be spelt out for proper identification of hazards. 

Chemical composition of surface Mechanical properties of filler particles Electric and thermal conductivity Quantitative description of interactions Composition of admixtures Optical properties... 

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