Self-absorption probabilities

Steady-State Spectral Convolution. The steady state absorption and emission spectra of dilute dye samples can be measured using standard spectroscopic techniques. Once the extinction coefficient, e( ), and the normalized luminescence spectrum, f(v), are known for a particular dye, the self—absorption probability r over a pathlength L in the sample containing the dye at a concentration C is given by... 

Figure 7 Self-atsorption probabilities for rhodamine-575 This shows a juxtaposition of predicted self-absorption probabilities for three measurement methods spectral overlap convolution (solid), emission depolarization (boxes), and time-resolved spectra (bars). The second two techniques are plotted assuming the quantum efficiency of luminescence is one.

Due to the high accuracy possible with photon counting measurements of the lifetime, this technique yields the most accurate measurement of any technique we have studied of the product nr, the quantum efficiency of luminescence and the self—absorption probability, for low rates of self-absorption. 

Self-absorption occurs when the path-length is too large [35] and the X-rays emitted have a significant probability of being absorbed by the remainder of the sample before being detected. This has the consequence of reducing the amplitude of the EXAFS oscillations and producing erroneous results. As the sample becomes more dilute this probability decreases. All the atoms in the sample determine the amount of self-absorption hence the need for thin samples. 

The adsorption of ATP-14C to surface films of stearic acid and brain lipid was examined over an extended period of time under various conditions (Table I and Figure 6B). Table I shows the short-term results, where adsorption was studied during the first 30 minutes, and evaporation was not a factor. Upon adding stearic acid or brain lipid the measurable radioactivity decreased, probably as a result of displacement of ATP-14C from the surface layer and self-absorption of the beta particles by the lipid film. When PMCG was present, there was a slight but significant increase in the surface adsorption of ATP. The amount of ATP adsorbed was 4 X 10 10 moles/sq. cm. for stearic acid and 2.5 X 10"10 moles/sq. cm. for brain lipid. If the lipid concentration in the surface is assumed to be about 8 X 10 10M (as phospholipid in the case of brain lipid), the molar ratio of ATP to lipid would be about 0.5 for stearic acid and 0.3 for brain lipid. 

The photon hvx emitted in a radiating transition is reabsorbed with a certain probability by another molecule X or Y. By absorbing the photon the molecule makes a transition into the excited states X and Y, respectively. Thus the Y molecules are excited only by the radiating and nonradiating transfer of the excitation energy. The photons hvY emitted in a radiating transition which do not undergo self-absorption leave the scintillator. 

A crucial step in both emission and absorption studies is the conversion of intensities of bands or lines to concentrations of molecules. This is not easy. The transition probabilities for bands connecting excited states are not often known to any reasonable precision. Also, one further difficulty plagues the emission studies. In contrast to absorption studies the population of molecules in the lowest state, v = 0, is not measurable. Relative populations are usually reported. Self absorption measurements can be used to overcome this difficulty43. ... 

It has been noted by Wellegehausen (28,29) that one can obtain good laser emission in the A eJ-X eT and B IIy-X Eg systems of Li2 and Na2, only weak laser action in these systems of K2 but, so far, no laser emission has been observed in Rb2 and Cs2. The results presented here, together with unpublished calculations on excited states of LI2 (21) suggest that self absorption of any laser emission should become a more probable event the heavier the alkali dimer. Thus, it appears that Wellegehausen s observations might be explained by such self absorptions. 

Dalby and Bennett " which has given accurate probabilities for a series of transitions. The technique is described briefly onpp. 291-2. Accurate determination of concentrations may still be hindered by self-absorption of the radiation, particularly in the case of the hydroxyl radical. Penner and co-workers have overcome the difficulty by the use of a double path technique, and are able to determine the rotational temperature and concentration of hydroxyl radicals in both flame and shock-tube studies. The single and double path emissivities are compared simultaneously, the double path beam being chopped to give modulation at about 5 sec intervals. The method of correction for line widths and Doppler broadening is discussed . 

In an article which is critical of many generally accepted molecular fluorescence parameters of aromatic molecules (and by inference the parameters for other systems), Birks emphasizes the precautions necessary to eliminate errors due to self-absorption secondary fluorescence and/or self-quenching.1 The points are made that reliable data for rf and Of are available for only a few compounds, e.g. diphenylanthracene (DPA), perylene, quinine bisulphate, and acridone, and that these provide suitable standards. The value of Of (DPA) is now set at 0.83. The importance of solvent effects on Of and t( of DPA is stressed in a publication which reports Tf for DPA in cyclohexane and benzene.2 The value of 6.95 0.04 ns for benzene solution is in good agreement with the earlier work of Birks and Dyson3 and Ware and Baldwin 4 7 (7.35 0.05 ns). The value obtained for cyclohexane solution, 7.58 0.04 ns, although in poor agreement with earlier results, is probably the most acceptable. The absolute fluorescence quantum yield of quinine bisulphate has also been redetermined (Of = 0.56).8... 

This technique suggests what is probably the simplest way to determine the probability of self-absorption empirically for a particular plate. The peak position of the luminescence spectrum can be calculated for a variety of self—absorption rates using the above formalism. Thereafter, the self-absorption rate for a particular device can be found (crudely) by a moderate resolution measurement of the peak position of the luminescence spectrum. 

Dye stability is one important problem. We and others (17) have observed that many of the dye molecules tested have approximately a 50% probability of photodegrading over a number of excitations on the order of 10 . This rate should be increased by about two orders of magnitude or more to obtain acceptable stability levels if an LSC is to have a 20 year lifetime. This can be seen in the following way. In order to minimize self-absorption, we can require that a typical plate have a peak optical density of one. If we also make the reasonable assumption that a typical peak extinction coefficient for the dye is 50,000 liters/mole cm, then there will be about 10 molecules per square meter. (This argument will also pertain to the final dye in a multiple dye plate.) If the dye absorbs 30% of the usable visible solar spectrum, in 20 years the plate will have absorbed 10 photons per square meter. Acceptable performance, therefore, requires that the quantum efficiency of photodegradation be at most 10 molecules per photon instead of the typical 10 . 

The counting efficiencies obtained with in situ methods depend on various concurrent factors. The metabolites separated on the gel column must be fixed in a spaced way to minimize self-absorption. The spaced fixation must not be disturbed during dehydration and the following procedures. However, the counting efficiencies of the in situ method depends on the concentration of the gel. This is even more obvious when compared with those obtained with the in situ method described earlier (Gezelius, 1977) for a mixed gel of 2% polyacrylamide and 0.5% (Table 2 ). The reduction of the counting efficiencies in more concentrated gels is probably due to increased selfabsorption. 

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