Line shapes, dynamical

Pump-probe absorption experiments on the femtosecond time scale generally fall into two effective types, depending on the duration and spectral width of the pump pulse. If tlie pump spectrum is significantly narrower in width than the electronic absorption line shape, transient hole-burning spectroscopy [101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112 and 113] can be perfomied. The second type of experiment, dynamic absorption spectroscopy [57, 114. 115. 116. 117. 118. 119. 120. 121 and 122], can be perfomied if the pump and probe pulses are short compared to tlie period of the vibrational modes that are coupled to the electronic transition. 

Loring R F, Van Y J and Mukamel S 1987 Time-resolved fluorescence and hole-burning line shapes of solvated molecules longitudinal dielectric relaxation and vibrational dynamics J. Chem. Phys. 87 5840-57... 

A completely different approach, in particular for fast imimolecular processes, extracts state-resolved kinetic infomiation from molecular spectra without using any fomi of time-dependent observation. This includes conventional line-shape methods, as well as the quantum-dynamical analysis of rovibrational overtone spectra [18, 33, 34 and 35]. 

Pulsed deuteron NMR is described, which has recently been developed to become a powerftd tool for studying molectdar order and dynamics in solid polymers. In drawn fibres the complete orientational distribution function for the polymer chains can be determined from the analysis of deuteron NMR line shapes. By analyzing the line shapes of 2H absorption spectra and spectra obtained via solid echo and spin alignment, respectively, both type and timescale of rotational motions can be determined over an extraordinary wide range of characteristic frequencies, approximately 10 MHz to 1 Hz. In addition, motional heterogeneities can be detected and the resulting distribution of correlation times can directly be determined. 

If phase-sensitive spectra are not required, then magnitude-mode Pico) (or absolute-mode ) spectra may be recorded by combining the real and imaginary data points. These produce only positive signals and do not require phase correction. Since this procedure gives the best signal-to-noise ratio, it has found wide use. In heteronuclear experiments, in which the dynamic range tends to be low, the power-mode spectrum maybe preferred, since the S/N ratio is squared and a better line shape is obtained so that wider window functions can be applied. 

Molecular mobility (dynamics) 0.5-500 nm Relaxation times and line-shapes multidimensional exchange experiments... 

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 the case of dynamic mechanical relaxation the Zimm model leads to a specific frequency ( ) dependence of the storage [G ( )] and loss [G"(cd)] part of the intrinsic shear modulus [G ( )] [1]. The smallest relaxation rate l/xz [see Eq. (80)], which determines the position of the log G (oi) and log G"(o>) curves on the logarithmic -scale relates to 2Z(Q), if R3/xz is compared with Q(Q)/Q3. The experimental results from dilute PDMS and PS solutions under -conditions [113,114] fit perfectly to the theoretically predicted line shape of the components of the modulus. In addition l/xz is in complete agreement with the theoretical prediction based on the pre-averaged Oseen tensor. 

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. 

The theoretical approach described before dealt with the short-time dynamic response of the star molecules. However, in the case of completely labelled stars [148] it was found that the line shape of the Zimm model provides a good description of the NSE spectra not only in the short-time regime (t < 5 ns), but also on longer time scales. 

Simulation programs for the ESR line shapes of peroxy radicals for specific models of dynamics have been developed for the study of oxidative degradation of polymers due to ionizing radiation [66]. The motional mechanism of the peroxy radicals, ROO, was deduced by simulation of the temperature dependence of the spectra, and a correlation between dynamics and reactivity has been established. In general, peroxy radicals at the chain ends are less stable and more reactive. This approach has been extended to protiated polymers, for instance polyethylene and polypropylene (PP) [67],... 

Dynamic parameters for heterogeneous systems have been explored in the liquid, liquid like, solid like, and solid states, based on analyses of the longitudinal or transverse relaxation times, chemical exchange based on line-shape analysis and separated local field (SLF), time domain 1H NMR, etc., as summarized in Figure 3. It is therefore possible to utilize these most appropriate dynamic parameters, to explore the dynamic features of our concern, depending upon the systems we study. 

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... 

The dynamic NMR (DNMR) spectroscopy has been used in studies of stereomutations of non-symmetrical di-Schiff bases [18].39 It was shown that the hindered Schiff bases exist in DMSO in two chiral conformations. The presence of a pair of conformers being in equilibrium was explained by the existence of two stereogenic axes a g (aligned to Cl—N8 bond) and a 7 (aligned to C6—N7 bond) due to restricted rotation around two Ar—N bonds. The trans to cis interconversion as well as enantio- or diastereoisomerisation barriers for the compounds studied have been established using line shape analysis. 

A great deal more could be said about models - to understand behavior like strong correlation, Coulomb blockade, and actual line shapes, it is necessary to use a number of empirical parameters, and a quite sophisticated form of density functional theory that deals with both static and dynamic correlation at a high level. Often this can be done only within a very simple representation of the electrons - something like the Hubbard model [51-53], which is very common in this situation. 

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. 

Lyotropic polymeric LC, formed by dissolving two aromatic polyamides in concentrated sulphuric acid, have been studied using variable-director 13C NMR experiments.324 The experimental line shapes at different angles w.r.t the external field were used to extract macromolecular order and dynamic in these ordered fluids. An interesting application of lyotropic LC is for the chiral discrimination of R- and S-enantiomers, and has recently been demonstrated by Courtieu and co-workers.325 The idea was to include a chiral compound 1-deutero-l-phenylethanol in a chiral cage (e.g., /1-cyclodextrin) which was dissolved and oriented by the nematic mean field in a cromolyn-water system. Proton-decoupled 2H NMR spectrum clearly showed the quad-rupolar splittings of the R- and S-enantiomers. The technique is applicable to water-soluble solutes. 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

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