Determination of absorption coefficients

As described in Section 4.2.6.3 the absorption coefficients can be determined, if concentrations and absorbance at a distinct wavelength A are known at a sufficient number of states m. From now on the decadic absorption coefficients are used, since they are experimentally obtained. Transposition of the matrices in eq. (4.4) for some reaction times results 

The index A makes it obvious that the column vectors have to be formed at one wavelength for m different states (e.g. times). If 

However, if m the system is overdetermined. Therefore one finds accordingly using eq. (5.42) after multiplication by a a system of normal equations 

The matrix N describes the coefficient matrix of the normal equations. For further information see Section 4.2.6. 

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G. Gauglitz and E. Scheerer, Method for the determination of absorption coefficients, reaction rate constants and thermodynamic data in the system A-B, J. Photochem. Photobiol. A 71, 205-212... 

Since the determination of absorption coefficients is in only 10-23 fxm thick layers, only relative concentrations can be determined, given in Fig. 5.72. Accordingly the partial photochemical quantum yields can only be approximated. Their values in Table 5.9 demonstrate that the absorption coefficients are determined to be too small. However, their values relatively fit to the data obtained in stirred solutions. These results prove the ability of the formalism presented in this book to treat photokinetic data even under extreme conditions. 

As seen in Table 111.3, a 1% solution (10 g/1) of (3-carotene in hexane has an absorbance of 2,592 AU and a molecular weight of 537 g/mol (i.e., 1 mM = 0.537 g/1) therefore, the absorbance expected for a 1 mM solution is (0.537 gA)/(10 g/1) X (2,592 AU) = 139 AU/1 mM (3-carotene. Using this ratio, if a p-carotene solution has an absorbance of 5, then the concentration is given as (5 AU)/(139 AU/mM) = 0.036 mM. It is important to note that due to the inherent difficulties in procedures for accurate determination of absorption coefficients, there may be a significant level of uncertainty in some published values. Small variations (e.g., 2-3 nm) may also occur in published data of absorption maxima. Whenever possible, the spectrum of a compound tmder investigation should be compared directly with an authentic pure standard. The spectra of the unknown and the standard should be identical for both the X iax and the fine structure (%III/II). 

All IR methods for measuring copolym compositions are relative and need calibration with suitable standards. Three calibration m hods are usually used radiochemical standards, calibration with the homopolymer mixtures, and calibration with model compounds (33-36). Calibration with radiochemical standards is very precise and accurate but is limited by the availability of labelled olefins. Calibration with homopolymer mixtures is also very popular (33,37-41,43). It is a very simple method but has many drawbacks, the main one being the constitutional difference between such mixtures and real copolymers (32). Nevertheless, its use is justified if the chosen analytical bands are highly localized and if the copolymers examined have a block structure (rj rj > 1) similar to that of the polymer mixtures. The third calibration method consists in using model compounds for the determination of absorption coefficients. These model compounds are either homopolymers (42,44-47), in which case the method is in priiKiple the same as calibration with polymer mixtures, or special compoimds with structures resembling those of characteristic groups in copolymers (13,49,51). 

The reaction of the trapped holes with Br ions adsorbed at the colloidal particles was used to determine the absorption coefficient of the holes. In the presence of Br less absorption of the holes is observed after the flash, as the Br ions react with some of the holes during the laser flash. On the other hand, the absorption of Br, i.e. the oxidation product of Br , can be seen. By comparing the decrease in h absorption after the flash with the absorption of Br, , and knowing the absorption coefficient of Br, the absorption coefficient of the hole, = 9.2 x 10 cm , was cal-... 

A simple rocking device was tested for routine determination of distribution coefficients [9], Sample cells were constructed for two-phase [9] and three-phase [10] systems. The investigators claim that the rocking action causes the shape of each phase to vary slowly and constantly and that the precision associated with the distribution coefficient is similar to that for shake-out methods. The three-phase cell was tested as an in vitro model to simulate factors involved in the absorption process. Rates of drug transfer and equilibrium drug distribution were evaluated under conditions in which one aqueous phase was maintained at pH 7.4 and the other phase was maintained at another pH. 

It is important to stress that for this to work, the independently known matrix A of absorptivity coefficients needs to be square, i.e. it has previously been determined at as many wavelengths as there are chemical species. Often complete spectra are available with information at many more wavelengths. It would, of course, not be reasonable to simply ignore this additional information. However, if the number of wavelengths exceeds the number of chemical species, the corresponding system of equations will be over determined, i.e. there are more equations than unknowns. Consequently, A will no longer be a square matrix and equation (2.22) does not apply since the inverse is only defined for square matrices. In Chapter 4.2, we introduce a technique called linear regression that copes exactly with these cases in order to find the best possible solution. 

A spectrophotometer which allows spectroscopic and kinetic measurements to be made on a light irradiated sample has been developed by Ranalder et al. 5). The instrument is completely controlled by a small PDP-8/I computer. Great flexibility is introduced through software control. Several data collection routines have been written, and methods for determining molar absorption coefficients of metastable states have been discussed. 

GaudetM, CamartJ-C, BuchaUlot L, Arscott S (2005) Variation of absorption coefficient and determination of critical dose of su-8 at 365 nm. Appl Phys Lett 88 24107... 

Perturbation of a chemical equilibrium by ultrasound results in absorption of the sound. Ultrasonic methods determine the absorption coefficient, a (neper cm-1), as a function of frequency. In the absence of chemical relaxation the background absorption, B, increases with the square of the frequency f (hertz) that is, a/f2 is constant. For a single relaxation process the absorption increases with decreasing frequency, passing through an inflection point at the frequency at (radians sec-1 = 2nf) which is the inverse of the relaxation time, t (seconds), of the chemical equilibrium [Eq. (6) and Fig. 3]. 

The coupled spectrophone-dilution tube was first used to determine the absorption coefficient of airborne exhaust soot from a 2.4 liter Mercedes Diesel vs. NO2 as a standard (8). The value was found to be (5.5 1.0)m2g 1 at 514.5nm. (The automobile was run on a vehicle dynamometer at a cruise speed of 55 mph, with an average particulate concentration of 0.050 g m 3.)... 

Vodacek, A., Hoge, F., Swift, R.N., Yungei, J.K., Peltzer, E.T., and Blough, N.V. (1995) The use of in situ and airborne fluorescence measurements to determine UV absorption coefficients and DOC concentrations in surface waters. Limnol. Oceanogr. 40, 411-415. 

A standard sample of exactly known concentration of the analyte is used to determine the absorption coefficient a of the analyte according to Eq.5.1-4. Its value can be used afterwards to calculate the concentration of the analyte in unknown samples. 

B.G. Mitchell (1990). Algorithms for determining the absorption coefficient of aquatic particulates using the quantitative filter technique (QFT). Ocean Optics X, SPIE, 1302,137-148. 

For very deep inner shells, an interesting situation arises, where pure atomic physics experiments can actually be better performed on the solid very deep shells have a very small excitation cross section, because their effective radius is so small. This difficulty can be overcome by an enormous increase in the density of absorbers, i.e. by using thin metallic films. Another advantage of this approach is that absolute cross sections are then easily measured, merely by determining the absorption coefficients and weighing the sample, from which its density can be determined much more accurately than for atomic vapours. 

Since the absorption of X-rays generates an electron vacancy, it is possible to use all subsequent decay processes to determine the absorption coefficient (Figure 10.3). An electron from an outer shell can iiil the vacancy, accompanied... 

The quality of these approaches depends on the number of reaction components, the condition of the calibration matrix, the errors in determination, the absorption coefficients, and the measurement of the absorbances during kinetics. In any case the use of any of these algorithms can cause problems depending on the chosen algorithm and the specific behaviour of the reaction... 

This procedure was first applied to the model photoreaction of stilbene [191] to check the algorithms and the considerations. Figs. S.60 and 5.61 show the results. The photochemical quantum yields determined are in good agreement with those calculated using all the absorption coefficients, taking synthesised pure c/s-stilbene and undergoing a tedious procedure to determine its absorption coefficient. 

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