Natural broadening

Tello, M., Kuzuyama, T., Heide, L., Noel, J.P. and Richard, S.B. (2008) The ABBA family of aromatic prenyltransferases broadening natural product diversity. Cell. Mol. Life Sci, 65,1459-63. 

The diffraction pattern of the physical mixture of silica-supported platinum clusters and iridium clusters in the lower field of Figure 4.23 consists of overlapping lines for the two individual types of clusters, and is clearly different from the pattern for the platinum-iridium bimetallic clusters. The overlapping is due to the broadened nature of the individual lines resulting from the small sizes of the individual clusters of platinum and iridium. 

If the probability Tik(co) of absorption or emission of radiation with frequency a> causing a transition Ek is equal for all the molecules of a sample that are in the same level i ,, we call the spectral line profile of this transition homogeneously broadened. Natural line broadening is an example that yields a homogeneous line profile. In this case, the probability for emission of light with frequency u> on a transition with the normalized Lorentzian profile L (o—u>o) and central frequency coq is given by... 

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

Spectral lines are fiirther broadened by collisions. To a first approximation, collisions can be drought of as just reducing the lifetime of the excited state. For example, collisions of molecules will connnonly change the rotational state. That will reduce the lifetime of a given state. Even if die state is not changed, the collision will cause a phase shift in the light wave being absorbed or emitted and that will have a similar effect. The line shapes of collisionally broadened lines are similar to the natural line shape of equation (B1.1.20) with a lifetime related to the mean time between collisions. The details will depend on the nature of the intemrolecular forces. We will not pursue the subject fiirther here. 

Fortunately, the worst broadening interactions are also removed naturally in most liquids and solutions, or at least greatly reduced in their effect, by the tumbling motions of the molecules, for many of the broadening... 

Apart from the natural lifetime due to spontaneous emission, both uni- and bimolecular processes can contribute to the observed value of T. One important contribution comes from coiiisionai broadening, which can be distmguished by its pressure dependence (or dependence upon concentration [M] of tlie collision partner) ... 

Wlrile tire Bms fonnula can be used to locate tire spectral position of tire excitonic state, tliere is no equivalent a priori description of the spectral widtli of tliis state. These bandwidtlis have been attributed to a combination of effects, including inlromogeneous broadening arising from size dispersion, optical dephasing from exciton-surface and exciton-phonon scattering, and fast lifetimes resulting from surface localization 1167, 168, 170, 1711. Due to tire complex nature of tliese line shapes, tliere have been few quantitative calculations of absorjDtion spectra. This situation is in contrast witli tliat of metal nanoparticles, where a more quantitative level of prediction is possible. 

Another feature of the spectrum shown in Figure 10.19 is the narrow width of the absorption lines, which is a consequence of the fixed difference in energy between the ground and excited states. Natural line widths for atomic absorption, which are governed by the uncertainty principle, are approximately 10 nm. Other contributions to broadening increase this line width to approximately 10 nm. 

Equation (2.27) illustrates what is called the natural line broadening. Since each atom or molecule behaves identically in this respect it is an example of homogeneous line broadening, which results in a characteristic lorentzian line shape. 

Natural line broadening is usually very small compared with other causes of broadening. However, not only is it of considerable theoretical importance but also, in the ingenious technique of Lamb dip spectroscopy (see Section 2.3.5.2), observations may be made of spectra in which all other sources of broadening are removed. 

Of the four types of broadening that have been discussed, that due to the natural line width is, under normal conditions, much the smallest and it is the removal, or the decrease, of the effects of only Doppler, pressure and power broadening that can be achieved. 

Consider the wave packet populating just one vibrational level. This occurs for only a short period of time (the length of the femtosecond pulse). Then we can think of vibration occurring in a classical fashion. The wave packet travels along the vibrational level until it reaches the other extremity when it may be reflected and continue to travel backwards and forwards along the level. Because of the strongly anharmonic nature of the vibration the wave packet is broadened, as shown, as r increases. 

In a skimmed supersonic jet, the parallel nature of the resulting beam opens up the possibility of observing spectra with sub-Doppler resolution in which the line width due to Doppler broadening (see Section 2.3.4) is reduced. This is achieved by observing the specttum in a direction perpendicular to that of the beam. The molecules in the beam have zero velocity in the direction of observation and the Doppler broadening is reduced substantially. Fluorescence excitation spectra can be obtained with sub-Doppler rotational line widths by directing the laser perpendicular to the beam. The Doppler broadening is not removed completely because both the laser beam and the supersonic beam are not quite parallel. 

The diverse nature of the cyanoacrylate adhesives appHcations illustrates vividly that there is no truly typical appHcation. The number of appHcations ia which these adhesives are used is being expanded daily as technological improvements continue to broaden their capabiUties. 

A reissue may be ordered to correct any minor or major mistake which occurred during prosecution of a patent, but the mistake must be one that makes the patent partially or whoUy inoperable. Inoperable essentially means that the patent caimot be enforced. For instance, a reissue proceeding can be used to correct inventorship or even broaden claims if the patent is less than two years old. However, such a request to broaden claims in the context of reissue may not be undertaken to recover subject matter canceled during examination. Further, a reissue proceeding may be undertaken to correct formal problems or address newly discovered prior art which affects the scope of the claims. The nature of a reissue proceeding directs that this mechanism should be used only when the vaUdity of the patent is in question owing to the error or problem in question. 

Natural linewidths are broadened by several mechanisms. Those effective in the gas phase include collisional and Doppler broadening. Collisional broadening results when an optically active system experiences perturbations by other species. Collisions effectively reduce the natural lifetime, so the broadening depends on a characteristic impact time, that is typically 1 ps at atmospheric pressure ... 

With improvements in Instrument sensitivity and the use of techniques such as enhancement by polarization transfer (INEPT), it can be expected that natural abundance N NMR spectra will become increasingly Important in heterocyclic chemistry. The chemical shifts given in Table 10 illustrate the large dispersion available in N NMR, without the line broadening associated with N NMR spectra. 

After 1930, when the true nature of polymers was at last generally, recognised, the study of polymers expanded from being the province of organic specialists physical chemists like Paul Flory and physicists like Charles Frank became involved. In this short chapter, I shall be especially concerned to map this broadening range of research on polymers. 

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