Fluorescence calculation

The solid line A in Fig. 5.4 represents the relative variation versus 1 IT of the quantum yield of the B fluorescence calculated for the DM ABN/ propanol solution by numerical integration of the exact expression of p t) with the corresponding best fit values of the parameters t° and t". This variation is compared to that of the viscosity (curve B). The apparent activation energy that can be deduced for the quantum yield ( obs 3.5kcalM 1) is significantly less than that of the viscosity in the considered temperature range (En 5 kcal M 1). 

A theoretical investigation by Malikov and Trifonov (1984) for YAG Nd at lOOK showed that if superradiance was possible, superfluotescence could not be observed in such a system, because it would be three orders of magnitude less intense than ordinary fluorescence. Calculations were based on a Ta = 17 ps and aL=5 for an inversion density of 10 cm . Superradiance could be obtained by the propagation of a short coherent pulse which could provide pulses with Tsr = 3 ps. 

Figure 2 A simulation of the autocorrelation function, AC(x), of the donor fluorescence calculated for different diffusion coefficients of one molecular end relative to the other end. The calculations were performed for a model oligopeptide whose end-to-end distance distribution function is given in Fig. 5, Ref. 15 (curve 8). R was assumed to be 25A. The time scale is given in units of 10 sec and each curve is marked by the value assumed for the intramolecular diffusion coefficients in units of 10 1( cm /sec. AC() is given in arbitrary units. (Reprinted with permission from Ref. 17).

CN] —> I + CN. Wavepacket moves and spreads in time, with its centre evolving about 5 A in 200 fs. Wavepacket dynamics refers to motion on the intennediate potential energy surface B. Reprinted from Williams S O and lime D G 1988 J. Phys. Chem.. 92 6648. (c) Calculated FTS signal (total fluorescence from state C) as a fiinction of the time delay between the first excitation pulse (A B) and the second excitation pulse (B -> C). Reprinted from Williams S O and Imre D G, as above. 

Figure Cl.5.14. Fluorescence images of tliree different single molecules observed under the imaging conditions of figure Cl.5.13. The observed dipole emission patterns (left column) are indicative of the 3D orientation of each molecule. The right-hand column shows the calculated fit to each observed intensity pattern. Molecules 1, 2 and 3 are found to have polar angles of (0,( ))=(4.5°,-24.6°), (-5.3°,51.6°) and (85.4°,-3.9°), respectively. Reprinted with pennission from Bartko and Dickson [148]. Copyright 1999 American Chemical Society.

Here t. is the intrinsic lifetime of tire excitation residing on molecule (i.e. tire fluorescence lifetime one would observe for tire isolated molecule), is tire pairwise energy transfer rate and F. is tire rate of excitation of tire molecule by the external source (tire photon flux multiplied by tire absorjDtion cross section). The master equation system (C3.4.4) allows one to calculate tire complete dynamics of energy migration between all molecules in an ensemble, but tire computation can become quite complicated if tire number of molecules is large. Moreover, it is commonly tire case that tire ensemble contains molecules of two, tliree or more spectral types, and experimentally it is practically impossible to distinguish tire contributions of individual molecules from each spectral pool. 

The measurement of fluorescence intensity from a compound containing cliromophores of two spectral types is an example of a system for which it is reasonable to operate witli tire average rates of energy transfer between spectral pools of molecules. Let us consider tire simple case of two spectral pools of donor and acceptor molecules, as illustrated in figure C3.4.2 [18]. The average rate of energy transfer can be calculated as... 

This behavior is consistent with experimental data. For high-frequency excitation, no fluorescence rise-time and a biexponential decay is seen. The lack of rise-time corresponds to a very fast internal conversion, which is seen in the trajectory calculation. The biexponential decay indicates two mechanisms, a fast component due to direct crossing (not seen in the trajectory calculation but would be the result for other starting conditions) and a slow component that samples the excited-state minima (as seen in the tiajectory). Long wavelength excitation, in contrast, leads to an observable rise time and monoexponential decay. This corresponds to the dominance of the slow component, and more time spent on the upper surface. 

Ema data can be quantitated to provide elemental concentrations, but several corrections are necessary to account for matrix effects adequately. One weU-known method for matrix correction is the 2af method (7,31). This approach is based on calculated corrections for major matrix-dependent effects which alter the intensity of x-rays observed at a particular energy after being emitted from the corresponding atoms. The 2af method corrects for differences between elements in electron stopping power and backscattering (the correction), self-absorption of x-rays by the matrix (the a correction), and the excitation of x-rays from one element by x-rays emitted from a different element, or in other words, secondary fluorescence (the f correction). 

Dioxetanones decompose near or below room temperature to aldehydes or ketones (56). The decomposition reactions are weakly chemiluminescent Qc ca 10 ein/mol) because the products are poorly fluorescent. However, addition of 10 M mbrene provides 2iQc ca 10 ein/mol, and 2iQc on the order of was calculated at mbrene concentrations above 10 M after correcting for yield loss factors (57). The decomposition rates are first order ia... 

A substantial effort has been appHed to iacreaskig i by stmctural modification (114), eg, the phthalaziQe-l,4-diones (33) and (34) which have chemiluminescence quantum yields substantially higher than luminol (115,116). The fluorescence quantum yield of the dicarboxylate product from (34) is 14%, and the yield of singlet excited state is calculated to be 50% (116). Substitution of the 3-amino group of lumiaol reduces the CL efficiency > 10 — fold, whereas the opposite effect occurs with the 4-amino isomer (117). A series of pyridopyridaziae derivatives (35) have been synthesized and shown to be more efficient than luminol (118). 

Compai ison with literature experimental and calculation data showed that the model proposed ensures the accurate behavior of the functional dependence of x-ray fluorescence intensity on the particle size. Its main advantage is the possibility to estimate the effect of particle size for polydispersive multicomponent substances. 

The methodical elaboration is included for estimation of random and systematic errors by using of single factor dispersion analysis. For this aim the set of reference samples is used. X-ray analyses of reference samples are performed with followed calculation of mass parts of components and comparison of results with real chemical compositions. Metrological characteristics of x-ray fluorescence silicate analysis are established both for a-correction method and simplified fundamental parameter method. It is established, that systematic error of simplified FPM is less than a-correction method, if the correction of zero approximation for simplified FPM is used by preliminary established correlation between theoretical and experimental set data. 

In another approach, which was previously mentioned, the mass thickness, or depth distribution of characteristic X-ray generation and the subsequent absorption are calculated using models developed from experimental data into a < )(p2) function. Secondary fluorescence is corrected using the same i flictors as in ZAP. The (pz) formulation is very flexible and allows for multiple boundary conditions to be included easily. It has been used successfully in the study of thin films on substrates and for multilayer thin films. 

A tabulation of the ECPSSR cross sections for proton and helium-ion ionization of Kand L levels in atoms can be used for calculations related to PIXE measurements. Some representative X-ray production cross sections, which are the product of the ionization cross sections and the fluorescence yields, are displayed in Figure 1. Although these A shell cross sections have been found to agree with available experimental values within 10%, which is adequate for standardless PKE, the accuracy of the i-shell cross sections is limited mainly by the uncertainties in the various Zrshell fluorescence yields. Knowledge of these yields is necessary to conven X-ray ionization cross sections to production cross sections. Of course, these same uncertainties apply to the EMPA, EDS, and XRF techniques. The Af-shell situation is even more complicated. 

Figura 1 Calculated K X-ray production cross sections for protons using the tabulated ECPSSR Ionization cross sections of Cohen end Harrigan, and the fluorescence yields calculated es In Johansson et al. (1 barn h IIT cm l.

Fig. 4.10. Fluorescence signal from small particles or thin films deposited on a silicon substrate used as sample carrier. The intensity was calculated for particles, thin films, or sections ofdiffe-rent thickness but equal mass of analyte, and plotted against the glancing angle f. A Mo-Ka beam was assumed for excitation. Particles or films more than 100 nm thick show double intensity below the critical angle of0.1° [4.21].

Fig. 4.14. Fluorescence intensity from layers buried in a thick substrate. The dependence of intensity on the glancing angle was calculated for layers of different thickness but with a constant analyte area density. Silicon was assumed as substrate and Mo-Ka X-rays as primary beam. Total reflection occurs in the region below 0.1°. Without total reflection, the dashed horizontal line would be valid throughout [4.21].

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