Inverse sensitivity

Figure 3.6 illustrates that using an input gas price of S4/GJ, there is a marked inverse sensitivity to rising oil price as the by-product credits from the natural gasoline rise. 

In atomic absorption spectrometry, the use of inverse sensitivity is commonly defined by the mass or concentration per 1% absorption (0.00436 absorbance units). The sensitivity can be given as a constant value for the whole concentration range only in the case of a straight-line calibration curve. In the case of curved calibration graphs, the sensitivity varies with concentration. 

L. Rodriguez-Lorenzo, R. de la Rica, R.A. Alvarez-Puebla, E.M. Eiz-Marzan, M.M. Stevens, Plasmonic nanosensors with inverse sensitivity by means of enzyme-guided crystal growth. Nature Mat. 11, 604 (2012)... 

Surfactants have also been of interest for their ability to support reactions in normally inhospitable environments. Reactions such as hydrolysis, aminolysis, solvolysis, and, in inorganic chemistry, of aquation of complex ions, may be retarded, accelerated, or differently sensitive to catalysts relative to the behavior in ordinary solutions (see Refs. 205 and 206 for reviews). The acid-base chemistry in micellar solutions has been investigated by Drummond and co-workers [207]. A useful model has been the pseudophase model [206-209] in which reactants are either in solution or solubilized in micelles and partition between the two as though two distinct phases were involved. In inverse micelles in nonpolar media, water is concentrated in the micellar core and reactions in the micelle may be greatly accelerated [206, 210]. The confining environment of a solubilized reactant may lead to stereochemical consequences as in photodimerization reactions in micelles [211] or vesicles [212] or in the generation of radical pairs [213]. 

NMR spectroscopy is always struggling for increased sensitivity and resolution, as well as more efficient use of the instrument time. To this end, numerous improvements of the simple inversion-recovery method have been proposed over the years. An early and unportant modification is the so-called fast mversion recovery... 

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

A number of surface-sensitive spectroscopies rely only in part on photons. On the one hand, there are teclmiques where the sample is excited by electromagnetic radiation but where other particles ejected from the sample are used for the characterization of the surface (photons in electrons, ions or neutral atoms or moieties out). These include photoelectron spectroscopies (both x-ray- and UV-based) [89, 9Q and 91], photon stimulated desorption [92], and others. At the other end, a number of methods are based on a particles-in/photons-out set-up. These include inverse photoemission and ion- and electron-stimulated fluorescence [93, M]- All tirese teclmiques are discussed elsewhere in tliis encyclopaedia. 

There are two ways in which the sensitivity can be increased. The first, and most obvious, is to decrease the concentration of the titrant, since it is inversely proportional to the sensitivity, k. The second method, which only applies if the analyte is multiprotic, is to titrate to a later equivalence point. When H2SO3 is titrated to the second equivalence point, for instance, equation 9.10 becomes... 

For example, when the activity is determined by counting 10,000 radioactive particles, the relative standard deviation is 1%. The analytical sensitivity of a radiochemical method is inversely proportional to the standard deviation of the measured ac-... 

An alternative way of acquiring the data is to observe the signal. These experiments are referred to as reverse- or inverse-detected experiments, in particular the inverse HETCOR experiment is referred to as a heteronuclear multiple quantum coherence (HMQC) spectmm. The ampHtude of the H nuclei is modulated by the coupled frequencies of the C nuclei in the evolution time. The principal difficulty with this experiment is that the C nuclei must be decoupled from the H spectmm. Techniques used to do this are called GARP and WALTZ sequences. The information is the same as that of the standard HETCOR except that the F and F axes have been switched. The obvious advantage to this experiment is the significant increase in sensitivity that occurs by observing H rather than C. 

The devitrification rate is extremely sensitive to both surface and bulk impurities, especially alkah. Increased alkah levels tend to increase the devitrification rate and lower the temperature at which the maximum rate occurs. For example, a bulk level of 0.32 wt % soda increases the maximum devitrification rate 20—30 times and lowers the temperature of maximum devitrification to approximately 1400°C (101). The impurity effect is present even at trace levels (<50 ppm) and can be enhanced with the addition of alumina. The devitrification rate varies inversely with the ratio of alumina-to-alkah metal oxide. The effect is a consequence of the fact that these impurities lower glass viscosity (102). 

In order for a solution for the systems of equations expressed in equation 11 to exist, the number of sensors must be at least equal to the number of analytes. To proceed, the analyst must first determine the sensitivity factors using external standards, ie, solve equation 11 for Kusing known C and R. Because concentration C is generally not a square data matrix, equation 11 is solved by the generalized inverse method. K is given by... 

Because and AAi are known, iC can be found using the generalized inverse method. The sensitivity coefficients matrix iCis given by... 

More recent research provides reversible oxidation-reduction potential data (17). These allow the derivation of better stmcture-activity relationships in both photographic sensitization and other systems where electron-transfer sensitizers are important (see Dyes, sensitizing). Data for an extensive series of cyanine dyes are pubflshed, as obtained by second harmonic a-c voltammetry (17). A recent "quantitative stmcture-activity relationship" (QSAR) (34) shows that Brooker deviations for the heterocycHc nuclei (discussed above) can provide estimates of the oxidation potentials within 0.05 V. An oxidation potential plus a dye s absorption energy provide reduction potential estimates. Different regression equations were used for dyes with one-, three-, five-methine carbons in the chromophore. Also noted in Ref. 34 are previous correlations relating Brooker deviations for many heterocycHc nuclei to the piC (for protonation/decolorization) for carbocyanine dyes the piC is thus inversely related to oxidation potential values. 

HC HMQC (heteronuclear multiple quantum coherence) and HC HSQC (heteronuclear single quantum coherence) are the acronyms of the pulse sequences used for inverse carbon-proton shift correlations. These sensitive inverse experiments detect one-bond carbon-proton connectivities within some minutes instead of some hours as required for CH COSY as demonstrated by an HC HSQC experiment with a-pinene in Fig. 2.15. 

HMBC Heteronuclear multiple bond correlation, inverse CH correlation via long-range CH coupling, same format and information as described for ( C detected) CH COLOC but much more sensitive (therefore less time-consuming) because of H detection... 

Zames, G. (1981) Feedback and Optimal Sensitivity Model Reference Transformations, Multiplicative Seminonus and Approximate Inverses, IEEE Trans, on Automat. Contr., AC-26, pp. 301-320. 

Equation (33) shows that the maximum capacity ratio of the last eluted solute is inversely proportional to the detector sensitivity or minimum detectable concentration. Consequently, it is the detector sensitivity that determines the maximum peak capacity attainable from the column. Using equation (33), the peak capacity was calculated for three different detector sensitivities for a column having an efficiency of 10,000 theoretical plates, a dead volume of 6.7 ml and a sample concentration of l%v/v. The results are shown in Table 1, and it is seen that the limiting peak capacity is fairly large. 

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