Line-shaped structures

In Figure 5, there exist several line-shaped structures. These lines run along the moving direction of receding front. One may notice that some lines look like they are going to split. This observation suggests a possible route of producing a dot pattern via instability of line-shaped structures. 

Figure B2.5.12 shows the energy-level scheme of the fine structure and hyperfme structure levels of iodine. The corresponding absorption spectrum shows six sharp hyperfme structure transitions. The experimental resolution is sufficient to detennine the Doppler line shape associated with the velocity distribution of the I atoms produced in the reaction. In this way, one can detennine either the temperature in an oven—as shown in Figure B2.5.12 —or the primary translational energy distribution of I atoms produced in photolysis, equation B2.5.35.

The coherent tunneling case is experimentally dealt with in spectroscopic studies. For example, the neutron-scattering structure factor determining the spectral line shape is... 

Parameters measured Surface topography (rms roughness, rms slope, and power spectrum of structure) scattered light line shape of periodic structure (width, side wall angle, height, and period)... 

There are at least four kinds of information available from an Auger spectrum. The simplest and by far most frequently used is qualitative information, indicating which elements are present within the sampling volume of the measurement. Next there is quantitative information, which requires a little more care during acquisition to make it extractable, and a little more effort to extract it, but which tells how much of each of the elements is present. Third, there is chemical information which shows the chemical state in which these elements are present. Last, but by far the least used, there is information on the electronic structure of the material, such as the valance-band density of states that is folded into the line shape of transitions involving valance-band electrons. There are considerations to keep in mind in extracting each of these kinds of information. 

In principle all the X-ray emission methods can give chemical state information from small shifts and line shape changes (cf, XPS and AES in Chapter 5). Though done for molecular studies to derive electronic structure information, this type of work is rarely done for materials analysis. The reasons are the instrumental resolution of commercial systems is not adequate and the emission lines routinely used for elemental analysis are often not those most useftil for chemical shift meas-ure-ments. The latter generally involve shallower levels (narrower natural line widths), meaning longer wavelength (softer) X-ray emission. 

These aspects of the optical spectra of solids are illustrated in the upper portion of Figure 1, which displays the reflectance curve (R) at room temperature for a typical semiconductor, GaAs. The fundamental absorption edge around 1.4 eV produces only a weak shoulder. Some structure is apparent in the two features around 3 eV and the large, broad peak near 5 eV. However, the dominant aspect of the line shape is the slowly varyii background. The derivative namre of Modulation Spectroscopy suppresses the uninteresting background effects in favor of sharp, deriva-... 

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. 

Structural and Chemical Information from Solid State NMR Line Shapes... 

RAIRS spectra contain absorption band structures related to electronic transitions and vibrations of the bulk, the surface, or adsorbed molecules. In reflectance spectroscopy the ahsorhance is usually determined hy calculating -log(Rs/Ro), where Rs represents the reflectance from the adsorhate-covered substrate and Rq is the reflectance from the bare substrate. For thin films with strong dipole oscillators, the Berre-man effect, which can lead to an additional feature in the reflectance spectrum, must also be considered (Sect. 4.9 Ellipsometry). The frequencies, intensities, full widths at half maximum, and band line-shapes in the absorption spectrum yield information about adsorption states, chemical environment, ordering effects, and vibrational coupling. 

Draw a line-bond structure for propane, CH3CH2CH3. Predict the value of each bond angle, and indicate the overall shape of the molecule. 

The two individual line-bond structures for acetate are called resonance forms, and their special resonance relationship is indicated by the doubleheaded arrow between them. The only difference between resonance forms is the placement of the r and nonbonding valence electrons. The atoms themselves occupy exactly the same place in both resonance forms, the connections between atoms are the same, and the three-dimensional shapes of the resonance forms are the same. 

However, a comparison of the line shape of the observed spectra with spectra of methyl radicals (Fig. lib) clearly proves that the species present here are not methyl radicals. The EPR spectrum of a methyl radical is a quartet of lines. However, the observed spectrum, though dominated by a quartet structure, shows a couple of additional lines pointing to additional interactions of the unpaired electron. By comparing the observed line shape to other alkyl radicals it turned out that the present spectrum can be attributed to ethyl radicals. Figure 11c shows the EPR spectrum of ethyl radicals created in an ethylchloride matrix generated by photolysis for comparison [121]. 

The analysis of XRPD patterns is an important tool studying the crystallographic structure and composition of powder compounds including the possibility to study deviation from ideal crystallinity, i.e. defects. Looking at an X-ray powder diffractogram the peak position reflects the crystallographic symmetry (unit cell size and shape) while the peak intensity is related to the unit cell composition (atomic positions). The shape of diffraction lines is related to defects , i.e. deviation from the ideal crystallinity finite crystallite size and strain lead to broadening of the XRPD lines so that the analysis of diffraction line shape may supply information about sample microstructure and defects distribution at the atomic level. 

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

It was mentioned above that the 1H N.M.R. spectrum of b% hydroxymethylated PBD sample (see Figure 10) shows a triplet at 3.62 ppm, which is due to the methylene protons adjacent to the hydroxyl group. From the observed line shape, splitting and ca. 3J (HH) of 6.b Hz, it can be concluded that the predominant structure of the hydroxymethyl ated PBD repeating unit is C. The presence of only structure C1 in the 5% hydroformyl ated PBD suggests the formation of structure C in the first i.e. hydroformylation step. 

Figure 31 compares the dynamic structure factors obtained from the crosslinks and the chain ends for two different Q-values. Without any analysis a strong reduction of the cross-link mobility compared to that of the chain end is obvious. A closer inspection also shows that the line-shape of both curves differs. While S(Q,t)/S(Q, 0) from the chain end decays continuously, S(Q,t) from the cross-links appears to decay faster at shorter than at longer times. This difference in line shape is quantified via the line shape parameter p. For the end-labelled chains, p is in close agreement with the p = 1/2 prediction of the... 

Comparing Eqs. (83), (84) and Eqs. (21), (22) it follows immediately that Rouse and Zimm relaxation result in completely different incoherent quasielastic scattering. These differences are revealed in the line shape of the dynamic structure factor or in the (3-parameter if Eq. (23) is applied, as well as in the structure and Q-dependence of the characteristic frequency. In the case of dominant hydrodynamic interaction, Q(Q) depends on the viscosity of the pure solvent, but on no molecular parameters and varies with the third power of Q, whereas with failing hydrodynamic interaction it is determined by the inverse of the friction per mean square segment length and varies with the fourth power of Q. 

Obviously, in the case of PS these discrepancies are more and more reduced if the probed dimensions, characterized by 2ti/Q, are enlarged from microscopic to macroscopic scales. Using extremely high molecular masses the internal modes can also be studied by photon correlation spectroscopy [111,112], Corresponding measurements show that - at two orders of magnitude smaller Q-values than those tested with NSE - the line shape of the spectra is also well described by the dynamic structure factor of the Zimm model (see Table 1). The characteristic frequencies QZ(Q) also vary with Q3. Flowever, their absolute values are only 10-15% below the prediction. 

In contrast to -conditions a large number of NSE results have been published for polymers in dilute good solvents [16,110,115-120]. For this case the theoretical coherent dynamic structure factor of the Zimm model is not available. However, the experimental spectra are quite well described by that derived for -conditions. For example, see Fig. 42a and 42b, where the spectra S(Q, t)/S(Q,0) for the system PS/d-toluene at 373 K are shown as a function of time t and of the scaling variable (Oz(Q)t)2/3. As in Fig. 40a, the solid lines in Fig. 42a result from a common fit with a single adjustable parameter. No contribution of Rouse dynamics, leading to a dynamic structure factor of combined Rouse-Zimm relaxation (see Table 1), can be detected in the spectra. Obviously, the line shape of the spectra is not influenced by the quality of the solvent. As before, the characteristic frequencies 2(Q) follow the Q3-power law, which is... 

The crossover from 0- to good solvent conditions in the internal relaxation of dilute solutions was investigated by NSE on PS/d-cyclohexane (0 = 311 K) [115] and on PDMS/d-bromobenzene(0 = 357K) [110]. In Fig. 45 the characteristic frequencies Qred(Q,x) (113) are shown as a function of t = (T — 0)/0. The QZ(Q, t) were determined by fitting the theoretical dynamic structure factor S(Q, t)/S(Q,0) of the Zimm model (see Table 1) to the experimental data. This procedure is justified since the line shape of the calculated coherent dynamic structure factor provides a good description of the measured NSE-spectra under 0- as well as under good solvent conditions. 

Whilst sample preparation may not be the most interesting aspect of NMR spectroscopy, it is nonetheless extremely important as it will have a huge bearing on the quality of the data obtained and therefore on your ability to make logical deductions about your compounds. This is particularly true when acquiring the most straightforward 1-D proton spectra. The most typical manifestation of sub-standard sample preparation is poor line shape. It is worth remembering that in terms of 1-D proton NMR, the devil can be very much in the detail . Detail , in this context, means fine structure and fine structure is always the first casualty of poor sample preparation. 

In the solid, dynamics occurring within the kHz frequency scale can be examined by line-shape analysis of 2H or 13C (or 15N) NMR spectra by respective quadrupolar and CSA interactions, isotropic peaks16,59-62 or dipolar couplings based on dipolar chemical shift correlation experiments.63-65 In the former, tyrosine or phenylalanine dynamics of Leu-enkephalin are examined at frequencies of 103-104 Hz by 2H NMR of deuterated samples and at 1.3 x 102 Hz by 13C CPMAS, respectively.60-62 In the latter, dipolar interactions between the 1H-1H and 1H-13C (or 3H-15N) pairs are determined by a 2D-MAS SLF technique such as wide-line separation (WISE)63 and dipolar chemical shift separation (DIP-SHIFT)64,65 or Lee-Goldburg CP (LGCP) NMR,66 respectively. In the WISE experiment, the XH wide-line spectrum of the blend polymers consists of a rather featureless superposition of components with different dipolar widths which can be separated in the second frequency dimension and related to structural units according to their 13C chemical shifts.63... 

In principle, valence band XPS spectra reveal all the electronic states involved in bonding, and are one of the few ways of extracting an experimental band structure. In practice, however, their analysis has been limited to a qualitative comparison with the calculated density of states. When appropriate correction factors are applied, it is possible to fit these valence band spectra to component peaks that represent the atomic orbital contributions, in analogy to the projected density of states. This type of fitting procedure requires an appreciation of the restraints that must be applied to limit the number of component peaks, their breadth and splitting, and their line-shapes. 

The main advantage of NMR spectroscopy is its use with proteins in solution. In consequence, rather than obtaining a single three-dimensional structure of the protein, the final result for an NMR structure is a set of more or less overlying structures which fulfill the criteria and constraints given particularly by the NOEs. Typically, flexibly oriented protein loops appear as largely diverging structures in this part of the protein. Likewise, two distinct local conformations of the protein are represented by two differentiated populations of NMR structures. Conformational dynamics are observable on different time scales. The rates of equilibration of two (or more) substructures can be calculated from analysis of the line shape of the resonances and from spin relaxation times Tj and T2, respectively. 

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