Broadening factor

If Other fall-off broadening factors arising m unimolecular rate theory can be neglected, the overall dependence of the rate coefficient on pressure or, equivalently, solvent density may be represented by the expression [1, 2]... 

Giddings, JC Bowman, LM Myers, MN, Isolation of Peak Broadening Factors in Exclusion Chromatography, Macromolecules 10,442, 1977. 

The major requirement of the light source for atomic absorption is that it should emit the characteristic radiation (the spectrum) of the element to be determined at a half-width less than that of the absorption line. The natural absorption line width is about 10 4 (A), but due to broadening factors such as Doppler and collisional broadening, the real or total width for most elements at temperatures between 2000 ° and 3000 °K is typically 0.02 — 0.1 A. Hence, a high resolution monochromator is not required. 

CE is a technique with a very high power of resolution. This is attributed to low diffusion and high plate numbers obtained from the absence of band-broadening factors (e.g., eddy diffusion, equilibrium dynamics, etc.) other than diffusion, which is also minimized by short analysis time. 

Recently, Troe developed an empirical model to resolve the discrepancy between the L-H model and the actual fall-off, in which a fall-off broadening factor F X) was introduced (Gardiner and Troe, 1984) ... 

Fig. 10.6 Band broadening factors in open tubular columns. Liquid...

In equation (C), A() (or A 111 as used earlier) is the low-pressure limiting rate constant and Ay is the high-pressure limiting rate constant. Fc is known as the broadening factor of the falloff curve its actual value depends on the particular reaction and can be calculated theoretically. Troe (1979) suggests that for reactions under atmospheric conditions, the value of Aft will be 0.7-0.9, independent of temperature. However, values as low as 0.4 are often observed. The NASA evaluations of stratospheric reactions (DeMore et al., 1997) take Aft = 0.6 for all reactions. The IUPAC evaluation (Atkinson et al., 1997a,b) does not restrict Fc to 0.6. However, it is important to note that the values of A0 and Ay will depend on the value of Fc used to match the experimental data. For example, for reaction (11)... 

S. H. Robertson, N. Snider, and D. M. Wardlaw, J. Phys. Chem., 97, 7556 (1993). Strong Collision Broadening Factors from Theories of Unimolecular Rate Coefficients. 

The factors that are included when calculating the intensity of a powder diffraction peak in a Bragg-Brentano geometry for a pure sample, composed of three-dimensional crystallites with a parallelepiped form, are the structure factor Fhkl 2=l/ TS )l2, the multiplicity factor, mm, the Lorentz polarization factor, LP(0), the absorption factor, A, the temperature factor, D(0), and the particle-size broadening factor, Bp(0). Then, the line intensity of a powder x-ray diffraction pattern is given by [20-22,24-26]... 

Usually, the FID is Fourier transformed after the application of an exponential window function (25). The line-broadening factor is selected to provide a good S/N. As a rule, the line broadening is selected according to the width of a narrow singlet resonance - in H NMR normally to a value from 0.1 to 0.5 Hz (cf. Figures 2 and 3). The resolution of the spectrum may be enhanced, though with reduced sensitivity, if the FID is multiplied, for example, by... 

Quadrupole broadening factor the second-order quadrupolar broadening of the central transition which is proportional to... 

At low temperatures, the broadening factors F1/2 do not deviate too much from unity. The dependence of k°° on the temperature T is expressed by a power function (except for cases with an established potential energy barrier), viz. 

The temperature dependence of spectra can be very useful in electronic spectroscopy. First, spectra at low temperatures are often, though not necessarily, better resolved. Inhomogeneous broadening factors may not change... 

In summary, variances rather than standard deviations are additive, and therefore it is well to reduce the size of the factor contributing most to band broadening and to operate a column under conditions where the several broadening factors are about equal in magnitude. 

Troe has also suggested a simpler form of the broadening factor product (F) which is adequate for most purposes... 

Diffusion, adsorption, and surface reaction are closely interconnected in heterogeneous catalysis characterization studies. Chromatographic separation is a physicochemical process based also on diffusion, adsorption, as well as liquid dissolution. Based on the broadening factors embraced by the van Deemter equation, precise and accurate physicochemical measurements have been made by GC, using relatively low-cost instmmentation and a very simple experimental setup. 

Because of the described multi-step character of the mechanism, broadening factors F(kolkJ) have to be introduced, i.e.. 

It remains to be discussed, whether eq. (17) provides an adequate representation of the falloff curves interpolating between and k and how the parameter Fcenter can be predicted. This question applies as well to neutrals as to ionic systems. The question has a strong collision and a weak collision aspect. If one concludes that (A ) and Pc are similar for ionic and for neutral systems, then the weak collision broadening factor ire TT-irc i-sc can be estimated [1] by... 

The strong colhsion broadening factor F requires the knowledge of all details of... 

On this basis, strong collision broadening factors were caleulated for reaetion (31) in [16], Figure 3 shows the results. is close to 0.2 and does not show a particular... 

Figure. 3 Strong collision broadening factors F (x) for the reaction NH3 + NH4 + M —> N2H7 + M from [16] (numbers in the figure = T/K, x = ko/L,.).

Nucleus I Natural abundance (%) Vo (MHz) at 7.05 T Relative receptivity Quadrupole moment (mb) Quadrupole broadening factor Stemheimer antishielding factor (y)... 

Figure 2-8 The effect of multiplying a free-induction decay by a line-broadening factor of 3, 2, I, and 0 Hz. (Reprinted with permission from J. W. Cooper and R. D. Johnson, FT NMR Techniques for Organic Chemists, IBM Instruments, Inc., 1986.)...

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