Linewidth analysis

3 Linewidth Analysis From the power spectrum, we can obtain the linewidth F = Acoi/2 = q D (Chu and Nose, 1980). If the measurement is carried out for a polymer in a semidilute solution, we can relate asymptotically F to D and c (concentration) following the scaling law 

It is the determination of an accurate volue of (F) from experimental data that matters. One method to achieve this is first to define a normalized distribution function G(F)  

The evaluation of G(r) can be performed with the cumulant analysis as follows (Koppel, 1972). We take the logarithm of the normalized correlation function  

Pecora, Dynamic Light Scattering. New York Wiley, 1976. 

Laser Light Scattering Basic Principles and Practice, 2nd ed. New York Academic, 1991. 

---

As in the case of the concentration dependence of the chemical shift, the H and 13C band shapes of the surfactant resonance peaks are also concentration dependent. Analysis of H NMR band shapes for large aggregates of a cetyl trimethyl ammonium bromide-water system results in a CMC of 1.0 mM this is consistent with the value measured by other methods.57 The H NMR bands of alkyl trimethyl ammonium salicylate and hexadecyl pyridinium salicylate aqueous systems start to broaden at concentrations just above the CMC. The broadening continues up to a concentration above which the band shape is almost constant, as the concentration is further increased.-58 I3C NMR linewidth analysis of sodium octanoate in aqueous solution gives reasonable estimated CMC values.59... 

A.2.3 Importance of Linewidth Analysis in ESCA Studies of Silicates. In some aluminates the structure of the Al 2p ESCA peak is rather symmetric (Gaussian— Lorentzian). This often occurs because only one type of Al is present (as in glaucophane), and sometimes because the amounts of f Al and ( JaI are... 

Result of hypotheses made during the linewidth analysis. Not definitively assigned. 

EPR Linewidth analysis of spectrum of complex with Ci6H33N+(CH3)3Br- Sllssl... 

Structure-activity relationships have been probed by the use of EPR. Thus rate constants, determined by EPR linewidth analysis, were in good agreement with those obtained by optical spectroscopy. This method not only provides rate data but also provides structural features which may allow the determination of structure-activity relationships combining kinetic, structural, and steric factors. The rearrangement rates of a range of 2-aryl-3,3-dimethylmethylenecyclopropanes have been measured in order to calculate and determine s values for a range of substituents. A range of substituents named super stabilizers were identified (43). ... 

Fe Q-band ENDOR study of the isotopically enriched Ni-C state of D. gigas and D. desulfuricans hydrogenases and Ni-B state of D. desulfuricans revealed a weak coupling between the Fe and the nickel atoms when the enzyme was in the Ni-A forms while no coupling was observed for the Ni-B form (186). A careful analysis of linewidth of Ni-A and Ni-B EPR signals detected in Fe enriched and nonenriched hydrogenase samples indicated that hyperfine interactions are lost in the spectral linewidth and, hence, nonde-tectable. 

One of the most commonly studied systems involves the adsorption of polynuclear aromatic compounds on amorphous or certain crystalline silica-alumina catalysts. The aromatic compounds such as anthracene, perylene, and naphthalene are characterized by low ionization potentials, and upon adsorption they form paramagnetic species which are generally attributed to the appropriate cation radical (69, 70). An analysis of the well-resolved spectrum of perylene on silica-alumina shows that the proton hyperfine coupling constants are shifted by about four percent from the corresponding values obtained when the radical cation is prepared in H2SO4 (71). The linewidth and symmetry require that the motion is appreciable and that the correlation times are comparable to those found in solution. 

Our finding that linewidth anisotropy in biomolecular EPR spectra can be described by a statistical theory in which the random variables that cause the broadening are fully correlated, does not only make analysis by simulation practical it also holds a message on the nature of the ultimate source of the broadening if the three principal elements of the p-tensor are fully correlated, then they should find their cause in a single, scalar quantity. 

---