Extinction deviations

Application of Fluorescence Correlation Spectroscopy 145 Table 8.1 Local temperature deviation, extinction coefficient, thermal conductivity. 

Here, eM, Ml, and / Ml2 are the respective extinction coefficients of all participants of Eq. (1) and [Mb is the total concentration of 1. The values of Kl and K2]j are summarized in Table II. The solid line in the inset was calculated using the best-fit values of mt / Ml2, A l, and K2h, while the broken line is the calculated prediction if K2l 0. The broken line deviates systematically from the experimental points confirming the binding of the second pyridine-type ligand. Imidazole behaves similarly (27). 

Fletsch and Richards [51] determined fluoride in seawater spectrophotometri-cally as the cerium alizarin complex. The cerium alizarin complex and chelate was formed in 20% aqueous acetone at pH 4.35 (sodium acetate buffer) and, after 20-60 min, the extinction measured at 625 nm (2.5 cm cell) against water. The calibration graph was rectilinear for 8-200 ig/l fluoride the mean standard deviation was 10 xg/l at a concentration of 1100 ig/l fluoride. 

The error in (a) is stated to compare favourably with calibration from benzene, since the absolute value of R90 is hardly known to this accuracy. In (b) the concentration of DNA was measured spectrophotometrically via the molar phosphorous extinction coefficient of 6415 (with a standard deviation of 2%). The low error in (c) arises from low levels of dust achieved as well as the integration over a period of 10 secs of the readings on a digital output. The specific refractive index increment used in (d) was an experimental one from the literature. In point of fact the assess-... 

Early studies of Mg isotope ratios in geological materials used the notation A Mg to mean per mil deviations from a standard as expressed in Equation (1) above, a convention that persists today (e.g., Elsu et al. 2000). The values assigned to A "Mg in those studies represent the level of mass-dependent isotopic fractionation relative to the standard. The same convention defined fi Mg as the per mil deviation from the standard after correction for the mass fractionation evidenced by A "Mg. In this system of nomenclature, A values refer to mass dependentfractionations while 5 values refer to deviations from mass-dependent fractionation (i.e., the S Mg defines excesses in Mg relative to mass fractionation attributable to decay of the extinct nuclide Al). In some cases A "Mg has been replaced by the symbol Fn,g (Kennedy et al. 1997) where the F refers to fractionation. ... 

This amount of thiocyanate is sufficient for both complete reduction and complex formation. Reduction is allowed to proceed for 30 to 45 s after the addition of the thiocyanate. A bright red color can readily be observed at a technetium (VII) concentration of 0.1 ng per ml. Acetone (6 ml) is then added and the volume of the solution mixed and adjusted to 10 ml with distilled water. At this point, the color has generally developed to less than 50% of its final intensity. Quartz 1-cm glass-stoppered cells are filled with the technetiiun solution and placed in a 20 °C water-cooled spectrophotometer. The extinction will approach a maximum intensity in 1 to 3 h. The maximiun extinction occurs at 510 nm with a molar extinction coefficient and standard deviation of 47,500 + 500 in 60 vol. % of the acetone-aqueous medium. An additional examination of the analysis may be carried out by extract-... 

Foster et al. have developed a method for determining technetium in dissolved nuclear fuel solutions. Tetrapropylammonium pertechnetate is doubly extracted from a basic medium into chloroform and the colored technetium (V) thiocyanate complex is formed in the chloroform phase by the addition of sulfuric acid, potassium thiocyanate and tetrapropylammonium hydroxide. The colored complex absorbs at 513 nm, has a molar extinction coefficient of 46,000 and is stable for several hours. Of more than 50 metals studied, none impairs measurements at ratios less than 100 to 1 mol with respect to technetium. Most anions do not disturb the determination of technetiiun. The standard deviation for a single determination is 0.09 fig over the range of 1 to 20 fig of technetium. 

Microgram amounts of pertechnetate can be determined by measuring the extinction of its colored complex with toluene-3,4-dithiol in 2.5 N hydrochloric acid after extraction into carbon tetrachloride . One hour must be allowed for the development of the color. The molar extinction coefficient at 450 nm is 15,000. Beer s law is followed over the range of 1.5 to 16.5 fig Tc per ml. The overall error does not exceed a standard deviation of 5%. Because many cations interfere, an initial separation of technetiiun is necessary. 

Miller and Zittef have used 1,5-diphenylcarbazide (0.25% solution in acetone) for the spectrophotometric determination of technetiiun. 1 to 15 /ig of technetium in 10 ml solution can be ascertained by measuring the extinction at 520 nm of the Tc (IV) complex in 1.5 M sulfuric acid. The development of the most intense color takes about 35 min the reduction of pertechnetate to Tc (IV) is effected by the reagent itself before complexation occurs. The molar extinction coefficient of the complex at 520 nm is 48,600. The relative standard deviation is 2%. Fe ", Ce ", and CrOj" clearly disturb measurements, VO , MoOj ,... 

At infrared wavelengths extinction by the MgO particles of Fig. 11.2, including those with radius 1 jam, which can be made by grinding, is dominated by absorption. This is why the KBr pellet technique is commonly used for infrared absorption spectroscopy of powders. A small amount of the sample dispersed in KBr powder is pressed into a pellet, the transmission spectrum of which is readily obtained. Because extinction is dominated by absorption, this transmission spectrum should follow the undulations of the intrinsic absorption spectrum—but not always. Comparison of Figs. 10.1 and 11.2 reveals an interesting discrepancy calculated peak extinction occurs at 0.075 eV, whereas absorption in bulk MgO peaks at the transverse optic mode frequency, which is about 0.05 eV. This is a large discrepancy in light of the precision of modern infrared spectroscopy and could cause serious error if the extinction peak were assumed to lie at the position of a bulk absorption band. This is the first instance we have encountered where the properties of small particles deviate appreciably from those of the bulk solid. It is the result of surface mode excitation, which is such a dominant effect in small particles of some solids that we have devoted Chapter 12 to its fuller discussion. 

The calculated extinction spectrum of a polydispersion of small aluminum spheres (mean radius 0.01 jam, fractional standard deviation 0.15) is shown in Fig. 11.4 both scales are logarithmic. In some ways spectral extinction by metallic particles is less interesting than that by insulating particles, such as those discussed in the preceding two sections. The free-electron contribution to absorption in metals, which dominates other absorption bands, extends from radio to far-ultraviolet frequencies. Hence, extinction features in the transparent region of insulating particles, such as ripple and interference structure, are suppressed in metallic particles because of their inherent opacity. But extinction by metallic particles is not without its interesting aspects. 

Figure 11.6 The effect of size dispersion on extinction of visible light by water droplets. Each curve is labeled with a, the standard deviation in the Gaussian size distribution.

To show the effect of increasing size dispersion on extinction,a series of calculations for water droplets is given in Fig. 11.6. The topmost curve reproduces the calculations of Fig. 11.5a for a single sphere the standard deviation a is increased in successively lower curves. 

When a low viscous solvent must be used in combination with a rather low molecular weight of the polymer, measurements are restricted to low /3-values, due to the discussed onset of turbulent flow. As in such a case the extinction angle % does not deviate very much from 45 degrees within the regime of laminar flow, it must be measured with a high absolute accuracy to furnish a reliable value for cos 2% or cot 2% [cf. eq. (3.42) or (3.44a)]. Measurements on a polydisperse sample become more reliable under such conditions due to the fact that cot 2 is increased by the polydispersity factor [eqs. (3.75a) and (3.83a)]. Examples for such a behaviour will be discussed in Section 3.8.3. 

For the calculation of the Maxwell-constant an assembly of frozen random conformations is considered. Brownian motion is taken into account only so far as rotary diffusion of the rigid conformations is concerned. In this way a first order approximation of the distribution function with respect to shear rate is obtained. This distribution function is used for the calculation of the Maxwell-constant, [cf. the calculation of the Maxwell-constant of an assembly of frozen dumb-bell models, as sketched in Section 5.I.3., eq. (5.22)]. Intrinsic viscosity is calculated for the same free-draining model, using average dimensions [cf. also Peter-lin (101)]. As for the initial deviation of the extinction angle curve from 45° a second order approximation of the distribution function is required, no extinction angles are given. 

It will now be clear that the accuracy that may be attained in crystal analysis depends on the number of observed reflections and on the precision with which their intensities can be measured. (We assume that the structure is not complicated by any randomness or disorder, and that the necessary absorption and extinction corrections can be made.) A very useful discussion of the requirements necessary for determining bond lengths to within a limit of error of 0-01 A has been given by Cruickshank (1960). This is, of course, a very ambitious limit, but if it could be achieved it would enable the predictions of the molecular-orbital and valence-bond theories in aromatic hydrocarbons to be distinguished. It is pointed out that at the 0-1% level of significance a bond length difference must be 3-3 times the standard deviation to be accepted as genuine, so the limit of error of 0-01 A would require an e.s.d. (estimated standard deviation) of 0-003 A or better in the bond difference, or a coordinate e.s.d. of 0-0015 A or better. 

Henrickson and Selmer-Olson [18] applied an autoanalyser to the determination of nitrate and nitrite in soil extracts. In an autoanalyser, the water sample, buffered to pH 8.6 with aqueous ammonia-ammonium chloride, is passed through a copperised cadmium reductor column. The nitrite formed is reacted with sulfuric acid and N-l-naphthylethylenediamine, and the extinction of the azo dye is measured at 520 nm. For soil extracts, the range and standard deviation are 0.5-1.0 and 0.007mg/1, respectively. 

Methods for calculating molar extinction coefficients of minerals are outlined in chapter 4 ( 4.3). The importance of the Beer-Lambert law, eq. (3.7), is that the molar extinction coefficient of an absorption band should be independent of the concentration of the absorbing species. Deviations from this law originating from cation ordering are discussed in chapter 4. 

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