Broadening parameter

Smith MAH, Rinsland C P and Fridovich B 1985 Intensities and collision broadening parameters from infrared spectra Molecular Spectroscopy Modem Research Volume Hied K N Rao (New York Academic) pp 118-19... 

One of the great advantages of Modulation Spectroscopy is its ability to fit the line shapes of sharp, localized structures, as illustrated in the lower part of Figure 1. These fits yield important relevant parameters, such as the value of the energy gap and the broadening parameter. 

Traditionally, column efficiency or plate counts in column chromatography were used to quantify how well a column was performing. This does not tell the entire story for GPC, however, because the ability of a column set to separate peaks is dependent on the molecular weight of the molecules one is trying to separate. We, therefore, chose both column efficiency and a parameter that we simply refer to as D a, where Di is the slope of the relationship between the log of the molecular weight of the narrow molecular weight polystyrene standards and the elution volume, and tris simply the band-broadening parameter (4), i.e., the square root of the peak variance. 

Herein are reported improved methods of molecular weight calibration where simultaneously, peak broadening parameters (a) are obtained through the use of multiple polydisperse molecular weight standards. There are two basic methods covered. The first and most reliable method employs the universal molecular weight calibration curve obtained using narrow MWD polystyrene standards. 

Two Pieces of Molecular Weight Data Per Standard. This method uses the fact that when equations (la) and (2a) or (la) and (3a) with proper modification are multiplied the peak broadening parameter vanishes. The equations for two broad MWD standards where M and M are known follow ... 

One Piece of Molecular Weight Data Per Standard. With this amount of molecular weight information per standard, one should estimate the peak broadening parameters (a ) for each standard using narrow MWD polystyrene standards. With this method there are various possible combinations of molecular weight data, Mj, and [q]. follow ... 

The molecular weight calibration curves obtained for PVC are shown plotted in Figure 3. Table III shows an investigation of the effect of the peak broadening parameter (a) assumed when a single broad MWD PVC standard is used. The corrections for imperfect resolution for PV2 and PVC with a a = 0.5 are now reduced to about k% for both standards. It is of interest to note that with a reduced correction for imperfect resolution the Mark-Houwink exponent obtained is closer to published literature values for PVC in THF (13). The use of the associated molecular weight calibration curve for PVC would reproduce the M j and M of the PVC standards with errors of about 15. ... 

Table III. Universal Calibration with Single Broad MWD PVC Standard with Known M and M - Effect of Peak Broadening Parameter(a) ([nfpR = 7.06 X 10-5 ...

Figures The variation of the peak-broadening parameters, o and i, against Vr for eleven narrow-MWD PS standards.

Yau derived characteristical properties of the EMG skewed peak model and proposed a new method to extract band broadening parameters from a skewed and noisy peak. 

F surface excess molar concentration of any species in the interfacial region (Lorenlzian broadening parameter) y surface tension... 

The dipolar broadening parameter AG, independent of the type of solvent used, is related to the residual second moment (AM2b) ... 

Fig. 23. Plot of the dipolar broadening parameter AG (left scale) and its relation to the square root of rigid lattice second moment, AM2 = 15 kHz (right scale), for polystyrene networks crosslinked with DVB (solid symbols) and EDM (open symbols) swollen to equilibrium, vs l/n, the reciprocal nominal number of C—C bonds between crosslinks points. Solvents CC14 ( ), CDC13 (A),...

By evaluation of the phonon-mode frequencies, information about strain [29] or about the incorporation of doping or alloying atoms can be derived. Besides the phonon-mode frequency, the phonon-mode broadening parameter provides information about crystal quality [30], because scattering due to a lower crystal quality or due to alloying makes the phonon-mode broadening parameter larger. 

The polar lattice modes split into TO- (cuto,%j) and LO-modes (u>lo,ij), with broadening parameters 7to,ij and 7lo,ij, respectively [73]. The parameters oo,i denote the high-frequency limits in this model approach, which are related to the static dielectric constants to, by the Lydanne-Sachs-Teller relation [110] (Sect. 3.3)... 

E13, and r13 are amplitude, transition energy, and broadening parameter, respectively. Lorentzian-broadened harmonic oscillators may be used as a good approximation for the description of adjacent (spectrally unresolvable) broadened CP structures... 

Typical phonon mode broadening parameters for a set of ZnO thin films grown on silicon by PLD with varying oxygen partial pressure and/or substrate heater power are shown in Fig. 3.14. Heitsch et al. [30] observed that the... 

Accordingly, the broadening parameter 7 cannot be determined. For setting up the MDF parameters, it is then often assumed 7 71, which has no influence... 

Fig. 3.14. Phonon mode broadening parameters, as determined by IRSE, vs. oxygen partial pressure for a set of PLD-grown ZnO thin films on (111) silicon. Triangles and squares represent data of thin films grown with substrate heater power of P = 400 W and P = 600 W, respectively. Reprinted with permission from [30]...

Fig. 3.15. Phonon mode broadening parameters of PLD-grown rocksalt-structure MgzZni-zO thin films on sapphire. Reprinted with permission from [74]...

In addition to defects and impurity incorporation, alloy-induced disorder further increases the phonon mode broadening parameters, as discussed... 

Magnetron-sputtered films contain randomly oriented crystallites, and the optical response is isotropic with one lattice mode broadening parameter only. 

Table 3.9. Typical energy, amplitude, and broadening parameters of near-band-gap CP structures Eq (a = A, B, and C) and their exciton polarizabilities of ZnO obtained from SE analysis of multiple sample sets at RT...

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