Selectivity sensitivity plots

Notice that this equation has the form of a straight line Y= a + bX), where the y-intercept a) is TE and the slope (b) depends on the sensitivity of the QC procedure. The value for ASE ont is obtained from power curves for the control rules and ns of interest and for specified probabilities, such as 90% and 50%, A plot of bias eas versus s eas will describe the allowable limits of imprecision and inaccuracy for different control rules and different numbers of control measurements. A QC procedure can be selected by plotting the observed inaccuracy and imprecision as the method s operating point, then identifying the control rules and n s of the lines above the operating point... 

Fig. 3. Sensitivity obtainable in high-pressure borosilicate glass cells and sapphire eells. The sample contained 0.5 mM uniformly N-enriched Csp from Thermotoga maritima (TwCsp) in 50mM phosphate buffer (pH 6.5), 20mM NaCl, 0.2mM Na-EDTA, 0.1 pM NaNj, 10% D2O and 90% H20. Gradient selected sensitivity enhanced H- N-HSQC spectra were recorded under identical experimental conditions either in a sapphire cell (left) with an outer diameter of 3.18 mm, inner diameter of 1.72 mm or a borosilicate glass capillary (right) with an outer diameter of 5.0 mm and an inner diameter of 1.2 mm. Data were recorded with a 8 mm inverse triple-resonance probe at 600 MHz proton frequency. Total acquisition time, approximately 2.5 h resolution, 2048 points in the direct dimension and 256 points in the indirect dimension. The temperature was adjusted to 303 K. (Top) Only a small part of the spectra are shown and plotted at the same contour levels for the two experiments. (Bottom) 1-D trace through the maximum of the H -signal of K19. (After ref. 35.)...

The faradaic current at the WE is transduced to a potential output at a selected sensitivity, expressed in amperes per volt, and recorded in a digital or analog form. The CV response is plotted as current versus potential. Figure 2-3a shows the shap>e of a CV current response for a typical reduction process. During the forward sweep the oxidized form is reduced, while on the reverse sweep the reduced form near the electrode is reoxidized. Chemical reaction... 

The sensitivity plots of possible TPMs (e.g.. Figs 4 5) help us to select appropriate TPM at given design condition, at least qualitatively. For example, RR is a poor choice of TPM if the plant is designed at RR=10 (Fig. 4) and composition variation is a poor choice to handle production rate change if the plant is designed atyA/(VA+yB)=0.5 (Fig. 5). 

Figure 8.25 shows the open-loop sensitivity plots for both columns. The one on the left-hand side is for the heterogeneous azeotropic column with 1% changes in its reboiler duty, and the one on the right-hand side is for the preconcentrator/recovery column with 1% changes in its reboiler duty. Tray 7 of the heterogeneous azeotropic column and tray 9 of the preconcentrator/recovery column are selected as the temperature control points because of high sensitivity and nearly linear behavior. 

Instead of the definition in Eq. (7-82), the selectivity is often written as log k,). Another way to consider a selectivity-reactivity relationship is to compare the relative effects of a series of substituents on a pair of reactions. This is what is done when Hammett plots are made for a pair of reactions and their p values are compared. The slope of an LEER is a function of the sensitivity of the process being correlated to structural or solvent changes. Thus, in a family of closely related LFERs, the one with the steepest slope is the most selective, and the one with the smallest slope is the least selective.Moreover, the intercept (or some arbitrarily selected abscissa value, usually log fco for fhe reference substituent) should be a measure of reactivity in each reaction series. Thus, a correlation should exist between the slopes (selectivity) and intercepts (reactivity) of a family of related LFERs. It has been suggested that the slopes and intercepts should be linearly related, but the conditions required for linearity are seldom met, and it is instead common to find only a rough correlation, indicative of normal selectivity-reactivity behavior. The Br nsted slopes, p, for the halogenation of a series of carbonyl compounds catalyzed by carboxylate ions show a smooth but nonlinear correlation with log... 

The NO + CO reaction is only partially described by the reactions (2)-(7), as there should also be steps to account for the formation of N2O, particularly at lower reaction temperatures. Figure 10.9 shows the rates of CO2, N2O and N2 formation on the (111) surface of rhodium in the form of Arrhenius plots. Comparison with similar measurements on the more open Rh(llO) surface confirms again that the reaction is strongly structure sensitive. As N2O is undesirable, it is important to know under what conditions its formation is minimized. First, the selectivity to N2O, expressed as the ratio given in Eq. (7), decreases drastically at the higher temperatures where the catalyst operates. Secondly, real three-way catalysts contain rhodium particles in the presence of CeO promoters, and these appear to suppress N2O formation [S.H. Oh, J. Catal. 124 (1990) 477]. Finally, N2O undergoes further reaction with CO to give N2 and CO2, which is also catalyzed by rhodium. 

These high affinity sites determine most of the selectivity of the ion exchange. This is deduced from Fig. 6 in which the selectivity of the whole ion exchange (In Kn) is plotted as a function of g n, a magnetic parameter of cupric ions adsorbed on high affinity sites. This parameter is particularly sensitive to the degree of covalence of the bound between copper and its... 

Solid-Fluid Equilibria The solubility of the solid is very sensitive to pressure and temperature in compressible regions, where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature often exhibit fairly simple linear behavior (Fig. 20-19). To understand the role of solute-solvent interactions on sofubilities and selectivities, it is instructive to define an enhancement factor E as the actual solubihty divided by the solubility in an ideal gas, so that E = ysP/Pf, where P is the vapor pressure. The solubilities in CO2 are governed primarily by vapor pressures, a property of the solid... 

The procedure for the selection of the most appropriate time interval requires the integration of the state and sensitivity equations and the computation of lj(t), j=l,...,p at each grid point of the operability region. Next by plotting I/t), j=l,...,p versus time (preferably on a log scale) the time interval [t, tNp] where the information indices are excited and become large in magnitude is determined. This is the time period over which measurements of the output vector should be obtained. 

Fig. 4. Selectivity of detection of mechanical waves. The relative phase shift A4>/F (referred to as (4>(r, t, I/))/yG0M0cos F in Eq. (12)) is plotted versus the ratio a as v/vG for w= 1 (solid line), w = 4 (dashed line) and w=10 (dotted line) cycles of motion-sensitizing gradient. Note that the selectivity increases according to the number of periods of motion encoding. The open symbols are experimental relative intensities measured on wave images obtained with a SPAMM sequence with n = 1 (from Ref. 15, reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.).

Now, it is the forward rate constant that is almost invariant (because there is a common nucleophile H2O), whereas k is very sensitive to the nucleophilic character of X, i.e. it is an associative type reaction. Selectivity would be expected to lead to curved free energy plots but these have not yet been observed. 

Resolution versus Sensitivity. A quadrupole mass filter can be programmed to move through a series of RF and dc combinations. The Mathieu equation, which is used in higher mathematics, can be used to predict what parameters are necessary for ions to be stable in a quadrupole field. The Mathieu equations are solved for the acceleration of the ions in the X, Y, and Z planes. A selected mass is proportional to (dc x RF x inner radius)/(RF frequency). For a given internal quadrupole radius and radio frequency, a plot can be made of RF and dc values that predict when a given mass will be stable in a quadrupole field. This is called a stability diagram (Figure 13.3). RF and dc combinations follow the value shown... 

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