Molar absorptivity, defined

The amount of UV light absorbed is expressed as the sample s molar absorptivity (e), defined by the equation... 

The basic principle of most colorimetric measurements consists in comparing under well-defined conditions the colour produced by the substance in unknown amount with the same colour produced by a known amount of the material being determined. The quantitative comparison of these two solutions may, in general, be carried out by one or more of six methods. It is not essential to prepare a series of standards with the spectrophotometer the molar absorption coefficient can be calculated from one measurement of the absorbance or... 

Brightness defined as the quantum yield multiplied by the molar absorption... 

LOD is defined as the lowest concentration of an analyte that produces a signal above the background signal. LOQ is defined as the minimum amount of analyte that can be reported through quantitation. For these evaluations, a 3 x signal-to-noise ratio (S/N) value was employed for the LOD and a 10 x S/N was used to evaluate LOQ. The %RSD for the LOD had to be less than 20% and for LOQ had to be less than 10%. Table 6.2 lists the parameters for the LOD and LOQ for methyl paraben and rhodamine 110 chloride under the conditions employed. It is important to note that the LOD and LOQ values were dependent upon the physicochemical properties of the analytes (molar absorptivity, quantum yield, etc.), methods employed (wavelengths employed for detection, mobile phases, etc.), and instrumental parameters. For example, the molar absorptivity of methyl paraben at 254 nm was determined to be approximately 9000 mol/L/cm and a similar result could be expected for analytes with similar molar absorptivity values when the exact methods and instrumental parameters were used. In the case of fluorescence detection, for most applications in which the analytes of interest have been tagged with tetramethylrhodamine (TAMRA), the LOD is usually about 1 nM. 

Absorptivity is defined as A = ebC where A = absorbance, 8 = molar absorptivity (L/mol/cm), b = path length of radiation through sample (cm), and C = molar concentration. 

Modern terminology defines A as the absorbance, a as the absorptivity, b as the optical path length and c as the concentration. In the second equation s represents the molar absorptivity. Table 5.4 compares these terms. 

Symmetry-forbidden transitions. A transition can be forbidden for symmetry reasons. Detailed considerations of symmetry using group theory, and its consequences on transition probabilities, are beyond the scope of this book. It is important to note that a symmetry-forbidden transition can nevertheless be observed because the molecular vibrations cause some departure from perfect symmetry (vibronic coupling). The molar absorption coefficients of these transitions are very small and the corresponding absorption bands exhibit well-defined vibronic bands. This is the case with most n —> n transitions in solvents that cannot form hydrogen bonds (e 100-1000 L mol-1 cm-1). 

Although oscillator strength is proportional to the integrated intensity of absorption J rfv, there is often a fairly good correlation between / and emax, the molar absorption coefficient at the band maximum. This correlation is valid if we assume a Lorenzian shape for the absorption band and replace the integral by max A v, where Av is the half-band-width of the absorption band (Figure 3.5b). The half-band-width is defined as the width of the absorption band (in cm-1) where the value of Hence... 

Figure 22 Absorption spectrum and MCD of Ni(CN) in HzO. 1

Since the absorbance, A, is derived from a ratio (-log /// ), it is unitless. The term E, which is a proportionality constant, defines the efficiency or extent of absorption. If this is defined for a particular chromophore at a specific wavelength, the term absorption coefficient or absorptivity is used. However, students should be aware that in the older biochemical literature, the term extinction coefficient is often used. The units of E depend on the units of l (usually cm) and c (usually molar) in Equation 5.4. For biomolecules, E is often used in the form molar absorption coefficient, e, which is defined as the absorbance of a 1 M solution of pure absorbing material in a 1-cm cell under specified conditions of wavelength and solvent. The units of e are M l cm-1. To illustrate the use of Equation 5.4, consider the following calculation. 

Notice that the units of e are defined by the concentration units of the tyrosine solution M) and the dimension units of the cuvette (cm). Although E is most often expressed as a molar absorption coefficient, you may encounter other units such as A°/0, which is the absorbance of a l°/o (w/v) solution of pure absorbing material in a 1-cm cuvette at a specified wavelength, A. 

Brightness is defined as product of molar absorptivity coefficient and... 

As mentioned previously, the task of model-based data fitting for a given matrix Y is to determine the best rate constants defining the matrix C, as well as the best molar absorptivities collected in the matrix A. The quality of the fit is represented by the matrix of residuals, R = Y - C x A. Assuming white noise, i.e., normally distributed noise of constant standard deviation, the sum of the squares, ssq, of all elements is statistically the best measure to be minimized. This is generally called a least-squares fit. 

In a second, more realistic thought experiment, we assume to know the molar absorptivity sAiX of species A only, and thus have to fit sB X and k. The equivalent ssq analysis as above leads to a surface in a three-dimensional space when we plot ssq vs. k and sBiX. This is illustrated in Figure 7.4. Again, the task is to find the minimum of the function defining ssq, or in other words, the bottom of the valley (at A s 0.05 s 1... 

The rate constants (together with the model and initial concentrations) define the matrix C of concentration profiles. Earlier, we have shown how C can be computed for simple reactions schemes. For any particular matrix C we can calculate the best set of molar absorptivities A. Note that, during the fitting, this will not be the correct, final version of A, as it is only based on an intermediate matrix C, which itself is based on an intermediate set of rate constants (k). Note also that the calculation of A is a linear least-squares estimate its calculation is explicit, i.e., noniterative. 

There are clear advantages and also clear disadvantages in this new approach for the analysis of nonisothermal measurements [33], Now there are two new parameters, AS and AH, for each rate constant, i.e., there are twice as many parameters to be fitted. Naturally, this can lead to difficulties if not all of them are well defined. Another problem lies in the fact that molar absorptivity spectra of the species can show significant temperature dependencies. Advantages include the fact that, in... 

Unless a sample is reasonably well defined, there is a chance that solutes will not be detected, and a combination of detectors may be necessary. Dual detection almost always provides more than double the information obtained with either detector. For research purposes, the most valuable information to aid in interpreting separations data can be obtained from both the UV and RI detectors in series. The RI response correlates more closely with concentration while the UV response is selective and reflects both concentration and the molar absorptivity of the detected solute. A very large UV peak, therefore, may indicate an exceptionally good UV absorber or a high concentration of low or intermediate molar absorptivity material or both. 

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