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Theoretical expressions for widths

In some systems, when an anisotropic spectrum is detected at low temperatures, increasing the temperature leads to averaging of the principal components of the hyperfine and g tensors, and therefore to isotropic spectra. As an example, we show in Figure lb the ESR spectrum at 278 K of VO + in polyacrylamide networks swollen by a water/acetone mixture (80 20 v/v), which consists of eight equally spaced lines of equal intensity (22,23). The height of each line is different, because the dynamical process gives lines with different widths. The experimental spectrum is well reproduced (broken lines) using a theoretical expression for the... [Pg.2451]

Figure 6.29c shows that the half-peak width, WV2, changes in the extreme negative and positive values of AE between 90 mV (E c ) and 45 mV (Ei e-) for an EE process, but a sharp jump in the half-peak width, WV2, is observed at AEf + —135 mV, which corresponds to a y/ — E curve with two peaks, whose central trough is situated just at the half-peak height. As in the case of the peak current, a theoretical expression has been reported for the half-peak width when only one peak appears [66, 67] ... [Pg.442]

The (1 -f- c2)2 term arises from the assumption that specimens deform isotropically in width and thickness. Volume strain vs. longitudinal strain curves are shown for three specimens of ABS 1 in Figure 7. For comparison, theoretical curves for total cavitation, i.e., c2 = 0, and pure shear, i.e., AV = 0, are also shown. Volume strain vs. longitudinal strain curves, together with nominal stress vs. nominal strain curves, for ABS 1, ABS 2, and ABS 3 are shown in Figure 8. Because of the size of the strains involved, it is not possible to approximate Equation 3 with an expression which contains only first-order powers of strain when calculating volume strains. [Pg.256]

Viscometric measurements suggest that an aqueous carbopol solution behaves as a Bingham plastic fluid with yield stress of 1.96 Pa and plastic viscosity 3.80 Pa s. The liquid flows down a plate inclined at an angle 6 to the horizontal. Derive an expression for the volumetric flow rate per unit width of the plate as a function of the system variables. Then, show that the following experimental results for 0 = 5° are consistent with the theoretical predictions. [Pg.411]

The complex distribution system that results from the frontal analysis of a multicomponent solvent mixture on a thin layer plate makes the theoretical treatment of the TLC process exceedingly difficult. Although specific expressions for the important parameters can be obtained for a simple, particular, application, a general set of expressions that can help with all types of TLC analyses has not yet been developed. One advantage of the frontal analysis of the solvent, however, is to produce a concentration effect that improves the overall sensitivity of the technique. The primary parameter used in TLC is the (Rf) factor which is a simple ratio of the distance traveled by the solute to the distance traveled by the solvent front. The (Rf) factor will always be less than unity. If a standard is added to the mixture, then the ratio of the (Rf) factors of the solute to that of the standard is termed the (Rx) factor and is thermodynamically equivalent to the separation ratio (a) in GC or LC. In a similar manner, the capacity ratio (k ) of a solute can be calculated for TLC from its (Rf) factor. Resolution is measured as the distance between the centers of two spots to the mean spot width. Alternative expressions for the resolution can be given in terms of the (Rf) factor and the plate efficiency. The plate efficiency is taken (by analogy to GC and LC) as sixteen times the square of the ratio of the retention distance of the spot to the spot width, but the analogy between TLC and the techniques of GC and LC can only be used with extreme caution. The so called... [Pg.457]

A theoretical description of the depletion interaction between two plates caused by ideal polymer chains with a finite width of a Schulz-Zimm distribution was published by Tuinier and Petukhov. They derived an exaa expression for the potential... [Pg.318]

The shortening of is not directly visible in the ESR spectrum, but can be detected by saturation measurements with better sensitivity and higher precision than the shortening of T2. In such CW ESR saturation measurements, the spectra are recorded as a function of mw power both in the presence and in the absence of the quencher. For nitroxides, a fit of the power dependence of the amplitude of the central line by a theoretical expression yields the parameter Py2, which is the power where the amplitude is reduced to one-half its value in the absence of saturation. The difference of AP1/2 values in the presence and absence of quencher is a measure for the accessibility of the spin label by the quencher. Normalization to the width of the central line and to the half... [Pg.14]

Cathodic polarization obtained with Alclad compared with the Al-Co-Ce metallic coating expressed as the potential difference, AE, between and the galvanic couple potential at the center of the scratch (x=1 cm at C-line of Fig. 9.6(a)) attained for different scratch widths at a fixed half sample length of 1 cm. The theoretical AE for Alclad and the other coatings are shown on the ordinate at S=0. The potential difference between the E., of AA 2024-T3 and the galvanic couple potential at x=1 cm are shown in the plot for each half-scratch width. Boundary conditions for the Alclad used ... [Pg.281]


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See also in sourсe #XX -- [ Pg.505 ]




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