Ellipticity experimental

Evaluation of Elliptical Experimental Explosive Charges (Z-Test) , Rept No USAMERDC-2116(1974)... 

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. 

The effect of ellipticity also increases [77] above the 2.5 value obtained for spheres. Analytical functions as well as graphical representations like Fig. 9.3 are available to describe this effect in terms of the axial ratios of the particles. In principle, therefore, a/b values for nonsolvated, rigid particles can be estimated from experimental [77] values. 

We shall see in Sec. 9.10 that sedimentation and diffusion data yield experimental friction factors which may also be described-by the ratio of the experimental f to fQ, the friction factor of a sphere of the same mass-as contours in solvation-ellipticity plots. The two different kinds of contours differ in detailed shape, as illustrated in Fig. 9.4b, so the location at which they cross provides the desired characterization. For the hypothetical system shown in Fig. 9.4b, the axial ratio is about 2.5 and the protein is hydrated to the extent of about 1.0 g water (g polymer)". ... 

We have emphasized biopolymers in this discussion of the ultracentrifuge and in the discussion of diffusion in the preceding sections, because these two complementary experimental approaches have been most widely applied to this type of polymer. Remember that from the combination of the two phenomena, it is possible to evaluate M, f, and the ratio f/fo. From the latter, various possible combinations of ellipticity and solvation can be deduced. Although these methods can also be applied to synthetic polymers to determine M, they are less widely used, because the following complications are more severe with the synthetic polymers ... 

I should also mention Sommerfeld, who extended Bohr s theory to try and account for the extra quantum numbers observed experimentally. Sommerfeld allowed the electrons to have an elliptic orbit rather than a circular one. 

Unfortunately, in the VUV region no polarimetry data are available, but calculations indicate the degree of circular polarization achieved by the wiggler may be 80%, estimated to be no worse than 70% delivered at the experimental chamber [95, 96]. In PECD experiments, we have calibrated the polarization state by deduction from cross-comparison of results at a few fixed energies previously studied on the SU5 beamline where accurate polarimetry data was available [36]. Because the horizontal magnetic field array in the insertion device is electromagnetic, fast current reversal to switch left- and right-handed elliptical polarizations is possible, with the usual potential benefit for dichroism measurements. 

According to his deduction the common finding of ellipsoidal deformation of the reflections is indicative for affine deformation. Moreover, he arrives at an equation that permits to determine with high accuracy the microscopical draw ratio, Xd, of the structural entities from the ellipticity of the deformed Debye sphere. This value can be compared to the macroscopical draw ratio. Even the intensity distribution along the ellipsoidal ridge is predicted for a bcc-lattice of spheres, and deviations of experimental data are discussed. 

Figure 13.1 Near-field entrainment measurements in noncircular jets based on experimental and computational studies [16]. Subsonic regimes. Experiments 1 — elliptic [37] 2 — square [16] 3 — round [38]. Simulations 4 — square [16]. A ...

Protein concentrations were approximately 0.4%. Circular dichroism data were presented as mean residue ellipticity [0], in degrees X cm x decimole . The same mean residue weight 112.4 was employed for native lysozyme and its ozonized products, since the deviation caused by the ozonolysis of few amino acid residues of lysozyme is far less than the experimental error. 

In practice, it is the viscosity that is experimentally determined, and the correlations are used to determine axial ratios and shape factors. The viscosity can be determined by any number of techniques, the most common of which is light scattering. In addition to ellipticity, solvation (particle swelling due to water absorption) can have an effect on... 

Since the friction factor was measured experimentally, this value is correct regardless of the state of solvation or ellipticity of the hemoglobin molecules in solution. We see below how the combination of these two experimental approaches may be interpreted further to yield some information about solvation and ellipticity. 

We have already seen that the ratio f/f0 describes the effect on the friction factor of either solvation, ellipticity, or both. This ratio equals unity for an unhydrated sphere and increases with both the amount of bound solvent and the axial ratio of the particles. We are now in a position to see how this ratio may be evaluated experimentally. The steps of the procedure are the following ... 

Equations (40) and (41) allow the ratio /// to be evaluated for any axial ratio. The reverse problem, finding an axial ratio that is consistent with an experimental /// ratio, is best accomplished by interpolating from plots of Equations (40) and (41). These two equations, along with Equations (14) and (39), allow the states of solvation and ellipticity compatible... 

EXAMPLE 2.4 Solvation and Ellipticity of Human Hemoglobin from Sedimentation Data. The diffusion coefficient of the human hemoglobin molecule at 20°C is 6.9 10 11 m2 s "1. Use this value to determine f for this molecule. Evaluate f0 for hemoglobin using the particle mass calculated in Equation (35). Indicate the possible states of solvation and ellipticity that are compatible with the experimental flfQ ratio. 

Finally, we note that both solvation and ellipticity can occur together. The contours shown in Figure 4.13a illustrate how various combinations of solvation and ellipticity are compatible with an experimental intrinsic viscosity. The particle considered in Example 4.4 has an intrinsic viscosity of 4.50 and was calculated to be hydrated to the extent of 0.60 g HzO per gram of protein. The same value of [17] is also compatible with nonsolvated ellipsoids of... 

Experimentally, one can use degrees as the rotation unit and decimeters for the optical path length. Consequently, the experimentally obtained ellipticity [0 ], which is called specific ellipticity, is described as follows ... 

Example of Application Large-Scale Actinometry. Neural network modelling was applied to large-scale actinometry in a continuous elliptical photochemical reactor with a concentric annular reaction chamber [2, 3,108, 148], Uranyl oxalate was used as an actinometer, which is based on the photosensitized decomposition of oxalate ions (Eq. 89) [2, 3] the experimental data were taken from the literature [108],... 

Figure 23-8 Resolution of the visible circular dichroism (ellipticity) spectrum (A) and absorption spectrum (B) of the Pseudomonas blue protein into series of overlapping Gaussian hands (—). The numbers 1 to 6 refer to hands of identical position and width in both spectra. Absorption envelopes resulting from the sum of the set of overlapping Gaussian bands (—) correspond within the error of the measurement to the experimental spectra. The dashed part of the CD envelope above 700 nm was completed by a curve fitter with the use of a band in the position of hand 1 of the absorption spectrum. From Tang et al.68...

Atomic. From spectroscopic studies, it is known lliat when an electron is bound to a positively charged nucleus only certain fixed energy levels are accessible to the electron. Before 1926, the old quantum theory considered that the motion of the electrons could be described by classical Newtonian mechanics in which the electrons move in well defined circular or elliptical orbits around the nucleus. However, the theory encountered numerous difficulties and in many instances there arose serious discrepancies between its predictions and experimental fact. 

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