Broadening modeling

The effeets of sueh eollisionally indueed kieks are treated within the so-ealled pressure broadening (sometimes ealled eollisional broadening) model by modifying the free-rotation eorrelation funetion through the introduetion of an exponential damping faetor exp( - t /x) ... 

In order to obtain a model that indeed reproduces the experimental results, inhomogeneous broadening (modeled by a diagonal disorder of... 

Longitudinal diffusion term, Bin A term in chromatographic band-broadening models that accounts for longitudinal diffusion. Lower control limit, LCL The lower boundai7 that has been set for satisfactory performance of a process or measurement. Luminescence Radiation resulting from photoexcitation (photoluminescence), chemical excitation (chemiluminescence), or theiTnal excitation (thermoluminescence). 

Broadening models g, A and D strain, unresolved hyperfine splittings Non-equilibrium populations Perpendicular and parallel detection mode... 

Case studies that encompass real-life optimization scenarios in the refinery Applications that broaden model scope beyond engineering purposes (i.e. refinery production planning)... 

Figure C2.17.13. A model calculation of the optical absorjDtion of gold nanocrystals. The fonnalism outlined in the text is used to calculate the absorjDtion cross section of bulk gold (solid curve) and of gold nanoparticles of 3 mn (long dashes), 2 mn (short dashes) and 1 mn (dots) radius. The bulk dielectric properties are obtained from a cubic spline fit to the data of [237]. The small blue shift and substantial broadening which result from the mean free path limitation are...

In experimental measurements, sueh sharp 5-funetion peaks are, of eourse, not observed. Even when very narrow band width laser light sourees are used (i.e., for whieh g(co) is an extremely narrowly peaked funetion), speetral lines are found to possess finite widths. Let us now diseuss several sourees of line broadening, some of whieh will relate to deviations from the "unhindered" rotational motion model introdueed above. 

Statistical analysis can range from relatively simple regression analysis to complex input/output and mathematical models. The advent of the computer and its accessibiUty in most companies has broadened the tools a researcher has to manipulate data. However, the results are only as good as the inputs. Most veteran market researchers accept the statistical tools available to them but use the results to implement their judgment rather than uncritically accepting the machine output. 

In numerous applications of polymeric materials multilayers of films are used. This practice is found in microelectronic, aeronautical, and biomedical applications to name a few. Developing good adhesion between these layers requires interdiffusion of the molecules at the interfaces between the layers over size scales comparable to the molecular diameter (tens of nm). In addition, these interfaces are buried within the specimen. Aside from this practical aspect, interdififlision over short distances holds the key for critically evaluating current theories of polymer difllision. Theories of polymer interdiffusion predict specific shapes for the concentration profile of segments across the interface as a function of time. Interdiffiision studies on bilayered specimen comprised of a layer of polystyrene (PS) on a layer of perdeuterated (PS) d-PS, can be used as a model system that will capture the fundamental physics of the problem. Initially, the bilayer will have a sharp interface, which upon annealing will broaden with time. 

Fig. 3. (a) Diffraction pattern of a well formed rope (superlattice) of armchair-like tubes. Note the presence of superlattice spots in the inset (b). The broadening of the streaks of 1010 type reOexions is consistent with a model in which the SWCNTs have slightly different chiral angles. 

The main phenomenological difference in BM compared to MG is a broadening of the resonance peak at which, however, does not shift. The model calculations in Fig. 11 have been performed for spheres (N = 1/3) with filling factors of 0.5 and 0.9. The parameters, chosen to be equal for both models, are given in the figure caption. It immediately appears that we will not find any drastic difference in the interpretation of the data for the MG or the BM model. 

Fig. 11. The Bruggeman model (BM) lakes into account the modification of the effective medium by the adjunction of metal in the medium. The net effect is a broadening of the resonance peak. The parameters of the metallic spheres in these calculations are fuHp = I eV and fiV = 0.1 eV. The insulating host is defined by ftcOp i = 1 eV and ftf = 1 eV and fidiy = 20 eV. Note that the normal Drude curve is superimposed with the Bruggeman curve with/= 1.

The schematic model is depicted in Fig. 8. As the bias voltage increases, the number of the molecular orbitals available for conduction also increases (Fig. 8) and it results in the step-wise increase in the current. It was also found that the conductance peak plotted vs. the bias voltage decreases and broadens with increasing temperature to ca. 1 K. This fact supports the idea that transport of carriers from one electrode to another can take place through one molecular orbital delocalising over whole length of the CNT, or at least the distance between two electrodes (140 nm). In other words, individual CNTs work as coherent quantum wires. 

The role of disorder in the photophysics of conjugated polymers has been extensively described by the work carried out in Marburg by H. Bassler and coworkers. Based on ultrafast photoluminescence (PL) (15], field-induced luminescence quenching [16J and site-selective PL excitation [17], a model for excited state thermalizalion was proposed, which considers interchain exciton migration within the inhomogenously broadened density of states. We will base part of the interpretation of our results in m-LPPP on this model, which will be discussed in some detail in Sections 8.4 and 8.6. 

B) The model of De Wolff disorder gives no explanation for the line broadening of reflections which are not affected by this type of lattice disorder. Chabre and Pannetier ascribed this effect to a micro twinning of the ramsdel-lite/rutile lattice on the planes [0 2 1] and [0 6 1], These faces are believed to be growth planes of EMD [45, 46],... 

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

Fortunately most molecules, except H2 and D2, are non-adiabatically broadened. Only small corrections for rotational adiabaticity are required for such molecules as N2, but in the first approximation even these may be neglected. In this extreme, which is valid at A diffusion model. The non-adiabatic impact operator... 

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