Application to absorption

To simplify notation we have removed the superscript (A) from the coefficients cj. Consider the rate at which such mode absorbs energy from the external field. It is convenient to assume the presence of a small damping term rjuj, taking 17 to zero at the end of the calculation. This makes it possible to treat the energy absorption as a steady-state process. The equation of motion is then 

At steady state uj oscillates with the same frequency of the driving field. Its motion is obtained from (7.83) by looking for a solution of the form My(z) = and solving for Uj. We get  

We have found that up to constant factors, the absorption lineshape is determined by the power spectriiin that characterizes the coordinate that couples to the external 

The result (7.88) is most easily obtained by solving variants of (7.83) with driving terms (1 /2)CyFe then combining the corresponding solutions 

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Araki, G., and Araki, H., Progr. Theoret. Phys. [Kyoto) 11, 20, Interaction between electrons in one-dimensional free-electron model with application to absorption spectra of cyanine dyes. ... 

Owing to aberrations, grating defects, and so on, it may not be adequate to approximate the response function by formulas based on idealized models. If a line source could be found having the spectrum that approximates a 8 function, then perhaps the measurement of such a line would adequately determine the response function. We have learned, however, that the spatial coherence of the source plays an important part in the shape of the response function. This precludes the use of a laser line source to measure the response function applicable to absorption spectroscopy. Furthermore, we... 

Only a few modifications of the algorithm were required to make it applicable to absorption and reboiled absorption. The changes were mainly in the handling of the enthalpy and total mass balance equations to accommodate different specification combinations involving the reflux, heat duties, and top and bottom product flow rates. The results of two example problems, one each for absorption and reboiled absorption, are shown in Table II. 

Multiple Linear Regression-Successive Projections Algorithm, Application to Absorption Data... 

The pioneering use of wavepackets for describing absorption, photodissociation and resonance Raman spectra is due to Heller [12, 13,14,15 and 16]- The application to pulsed excitation, coherent control and nonlinear spectroscopy was initiated by Taimor and Rice ([17] and references therein). 

Monson P R and McClain W M 1970 Polarization dependence of the two-photon absorption of tumbling molecules with application to liquid 1-chloronaphthalene and benzene J. Chem. Rhys. 53 29-37... 

Vibrational spectroscopy has been, and will continue to be, one of the most important teclmiques in physical chemistry. In fact, the vibrational absorption of a single acetylene molecule on a Cu(lOO) surface was recently reported [ ]. Its endurance is due to the fact that it provides detailed infonnation on structure, dynamics and enviromnent. It is employed in a wide variety of circumstances, from routine analytical applications, to identifying novel (often transient) species, to providing some of the most important data for advancing the understanding of intramolecular and intemiolecular interactions. 

Scherer J J, Paul J B, O Keefe A and Saykally R J 1997 Cavity ringdown laser absorption spectroscopy history, development, and application to pulsed molecular beams Chem. Rev. 97 25-51... 

Pollard W T, Dexhelmer S L, Wang Q, Peteanu L A, Shank C V and Mathles R A 1992 Theory of dynamic absorption spectroscopy of nonstatlonary states. 4. Application to 12 fs resonant Raman spectroscopy of bacterlorhodopsin J. Phys. Chem. 96 6147-58... 

Most of the qualitative relationships between color and structure of methine dyes based on the resonance theory were established independently during the 1940 s by Brooker and coworkers (16, 72-74) and by Kiprianov (75-78), and specific application to thiazolo dyes appeared later with the studies of Knott (79) and Rout (80-84). In this approach, the absorptions of dyes belonging to amidinium ionic system are conveyed by a group of contributing structures resulting from the different ways of localization of the 2n rr electrons on the 2n l atoms of the chromophoric cationic chain, rather than by a single formula ... 

As diverse as these techniques are all of them are based on the absorption of energy by a molecule and all measure how a molecule responds to that absorption In describing these techniques our emphasis will be on then application to structure determination We 11 start with a brief discussion of electromagnetic radiation which is the source of the energy that a molecule absorbs m NMR IR and UV VIS spectroscopy... 

RAIRS is a non-destructive infrared technique with special versatility - it does not require the vacuum conditions essential for electron spectroscopic methods and is, therefore, in principle, applicable to the study of growth processes [4.270]. By use of a polarization modulation technique surfaces in a gas phase can be investigated. Higher surface sensitivity is achieved by modulation of the polarization between s and p. This method can also be used to discriminate between anisotropic near-sur-face absorption and isotropic absorption in the gas phase [4.271]. 

The main advantage of absorption is its applicability to the control of pollutant gases present in large concentrations (several percent by volume). In these applications, removal efficiencies of 98°/ or greater can be achieved. The main disadvantage is inflexibility to achieve the best performance, the gas stream components are fixed once the column is designed, (see Table 13.1.3)... 

D. E. Martire and R. E. Boehm, Unified molecular theory of clrromatography and its application to supercritical fluid mobile phases. 1. Eluid-liquid (absorption) clrromatography , J. Phys. Chem. 91 2433-2446 (1987). 

Many operations in petrochemical plants require the absorption of components from gas streams into lean oils or solvents. The resultant rich oil is then stripped or denuded of the absorbed materials. The greatest use of this operation utilizes hydrocarbon materials, but the basic principles are applicable to other systems provided adequate equilibrium data are available. 

The height of the transfer unit has not been satisfactorily correlated for application to a wide variety of systems. If pilot plant or other acceptable data are available to represent the system, then the height of packing can be safely scaled-up to commercial units. If such data are not available, rough approximations may be made by determining Hg and Hl as for absorption and combining to obtain an Hqg (Ref. 74, pg. 330). This is only very approximate. In fact it is because of the lack of any volume of data on commercial units that many potential applications of packed towers are designed as tray towers. 

The electrical resistance of a coating on a pipeline will depend upon the effectiveness of its initial application to the metal and on its condition at the time of testing absorption of moisture may decrease the resistance by as little as 10% during a 2y-year period. The leakage resistance of a given section of pipeline can be determined by the following procedure ... 

The information given above should make it possible in general to predict the usefulness of x-ray methods in problems involving films. In principle, these methods should be useful occasionally when more than one film is present. The problems in such cases are complex rather than complicated. If these methods are applicable to a duplex film, for example, there will be three characteristic lines to be counted, and absorption effects in three regions to be considered. The three counts should, however, contain enough information in many cases to permit the drawing of valid conclusions. 

Excitation by Ao is the kind of excitation to which Equation 6-4 and its sequels apply this excitation leads to the absorption effects of the previous section. It can be treated successfully (as indicated above) by narrow, parallel beam geometry, which is certainly applicable to the well-collimated beam of a good spectrograph with a detector of small... 

The absorption of reactants (or desorption of products) in trickle-bed operation is a process step identical to that occurring in a packed-bed absorption process unaccompanied by chemical reaction in the liquid phase. The information on mass-transfer rates in such systems that is available in standard texts (N2, S6) is applicable to calculations regarding trickle beds. This information will not be reviewed in this paper, but it should be noted that it has been obtained almost exclusively for the more efficient types of packing material usually employed in absorption columns, such as rings, saddles, and spirals, and that there is an apparent lack of similar information for the particles of the shapes normally used in gas-liquid-particle operations, such as spheres and cylinders. 

X-ray absorption spectroscopy a new structural method and its applications to bioinorganic chemistry. S. P. Kramer and K, O. Hodgson, Prog, Inorg. Chem., 1979, 25,1-39 (71). 

Quantitative accuracy and precision (see Section 2.5 below) often depend upon the selectivity of the detector because of the presence of background and/or co-eluted materials. The most widely used detector for HPLC, the UV detector, does not have such selectivity as it normally gives rise to relatively broad signals, and if more than one component is present, these overlap and deconvolution is difficult. The related technique of fluorescence has more selectivity, since both absorption and emission wavelengths are utilized, but is only applicable to a limited number of analytes, even when derivatization procedures are used. 

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