Broadening contribution

Because the polydispersity of the polymer is reflected in the width of the chromatographic peak, we require that the column band broadening contribution to the peak width be minor compared to that from the polymer itself. This criterion cannot always be met. 

The general understanding of the electronic structure and the bonding properties of transition-metal silicides is in terms of low-lying Si(3.s) and metal-d silicon-p hybridization. There are two dominant contributions to the bonding in transition-metal compounds, the decrease of the d band width and the covalent hybridization of atomic states. The former is caused by the increase in the distance between the transition-metal atoms due to the insertion of the silicon atoms, which decreases the d band broadening contribution to the stability of the lattice. 

In flames, only Doppler and, to a lesser extent, collisional broadening contribute significantly to the overall linewidth. 

Dead volume N is decreased due to band-broadening contributions to peak width... 

Thus, data rates of 0.5 seconds/point are required to suppress band-broadening contributions from data acquisition. 

X-ray diffraction patterns from fibres generally contain a few closely overlapping peaks, each broadened by the contributions of crystallite size, crystallite-size distribution, and lattice distortion. In order to achieve complete characterisation of a fibre by X-ray methods, it is first necessary to separate the individual peaks, and then to separate the various profile-broadening contributions. Subsequently, we can obtain measures of crystallite size, lattice distortion and peak area crystallinity, to add to estimates of other characteristics obtained in complementary experiments. 

The half width of the luminescence line by the phonon interaction mechanism, from Eq. (8.11), is 2[(2 In 2) ji This is 0.25 eV for the maximum phonon energy of 0.05 eV from the silicon network vibrations, which is a little less than the observed line width. Thus the phonon model indicates that the luminescence spectrum is dominated by the phonon interaction and that the disorder broadening contributes less. 

The band-broadening contributions can be described in the form of a plate-height equation, where one usually assumes, as in chromatography, mutual independence of terms. 

Samples with higher polydispersity do not generally yield symmetrical elution profiles. Moreover, a detailed MWD [either m(M) or n(M)] is often desired. As mentioned earlier, band broadening does not significantly affect the elution profile when low flow rates are used. Therefore, the elution profile can be directly converted into a MWD by the procedures outlined. If, on the other hand, fast flow rates are used to shorten the analysis time, the observed elution profile must be adjusted to account for the effects of band broadening. A deconvolution algorithm that filters out the band-broadening contribution to the elution... 

In near-isothermal systems, it is assumed that the heat transfer between mobile and stationary phases is slow. This causes an additional band broadening contribution to appear [53]. Such a contribution can be especially important on the front of a sharp concentration profile. On the other hand, the heat transfer between the chromatographic column and the outside is fast enough to prevent the formation of a temperature front and of an associated secondary mass transfer zone. 

In order to obtain the characteristics of the column the values of and must be first corrected for the extra-column band broadening contributions that... 

The second moment contains line-broadening contributions only from pairwise interactions between spins. The effects of multi-spin correlations, if any, are contained in the higher moments. 

The individual band-broadening contributions to H can be described mathematically by... 

The natural linewidth of a molecular spectral line in the MMW region is related inversely to the spontaneous emission coefficient of the upper state (Equation 1.5) and consequently imparts a Lorenteian shape to the line profile (Equation 1.32). As the upper state can radiate to more than one lower state, the actual natural linewidth is related to the sum of the squared dipole moment matrix elements of the states involved. In any case its contribution to the overall linewidth is negligible in comparison with the other broadening contributions at 100 GHz it would be 10 Hz. 

Rcav is the effective cavity volume that is occupied by the electric field. The electric field in a Fabry-Perot cavity operating in TMqo mode is largely confined to a cylindrical element of radius (Al/2 r)i and length L equal to the mirror spacing (Section 2.1). The term cEqE equates to the power density term P in the Karplus and Schwinger equation. The power broadening contribution in that equation therefore becomes for a Fabry-Perot cavity... 

The total FWHM resolution on a peak at energy E is a combination of the preamplifier noise contribution Fnoise the ionization statistics Fjonization. and other line-broadening contributions Foiher such as incomplete charge collection. The total FWHM resolution is given by... 

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