More rigorous approach

Two methods are commonly used to correct for the residual current. One method is to extrapolate the total measured current when the analyte s faradaic current is zero. This is the method shown in the voltammograms included in this chapter. The advantage of this method is that it does not require any additional data. On the other hand, extrapolation assumes that changes in the residual current with potential are predictable, which often is not the case. A second, and more rigorous, approach is to obtain a voltammogram for an appropriate blank. The blank s residual current is then subtracted from the total current obtained with the sample. 

Approximate design equations apphcable only to the case of pure physical desorption are developed later in this sec tion for both packed and plate stripping towers. A more rigorous approach using distiUation concepts may oe found in Sec. 13. A brief discussion of desorption with chemical reac tion is given in the subsec tion Absorption with Chemical Reaction. ... 

For preliminai y-screeniug worh the simpler methods may be adequate, but for final designs one shoiild seriously consider using a more rigorous approach. 

This example illustrates the simplified approach to film blowing. Unfortunately in practice the situation is more complex in that the film thickness is influenced by draw-down, relaxation of induced stresses/strains and melt flow phenomena such as die swell. In fact the situation is similar to that described for blow moulding (see below) and the type of analysis outlined in that section could be used to allow for the effects of die swell. However, since the most practical problems in film blowing require iterative type solutions involving melt flow characteristics, volume flow rates, swell ratios, etc the study of these is delayed until Chapter 5 where a more rigorous approach to polymer flow has been adopted. 

In this chapter we will develop more rigorous approaches to the analysis of gas turbine plants using both the first and second laws of thermodynamics. 

Young and Wilcock [7] provided a much more rigorous approach which includes an illuminating discussion of how the los.ses arise in the cooling process. They prefer to address the problem by breaking the overall flow into flows through the component ... 

Complete Example 11.4 for the case where Vg/Qg = 20s. Solve the governing ODEs analytically or numerically as you prefer. How does this more rigorous approach change the 95% response time calculated in Example 11.3 ... 

In this section a phenomenalogical approach to the description of solvent gradients will be adopted based largely on the linear solvent strength model prt osed by Snyder [552-555]. This is the least complicated of the models available and provides a reasonable approximation for typical experimental conditions. Mathematically more rigorous approaches have been developed by Jandera and Churacek [551,556], schoenmakers et al. [520,534,557] and Tomellini et al. [558]. 

The approaches described above give approximate values for the LoD and LoQ. This is sufficient if the analyte levels in test samples are well above the LoD and LoQ. If the detection limits are critical, they should be evaluated by using a more rigorous approach [1, 2, 14]. In addition, the LoD and LoQ sometimes vary with the type of sample and minor variations in measurement conditions. When these parameters are of importance, it is necessary to assess the expected level of change during method validation and build a protocol for checking the parameters, at appropriate intervals, when the method is in routine use. 

These rules are not foolproof but should serve as a first approximation. A more rigorous approach must be used for more quantitative assessments. One possibility is to compute defect formation energies for the compound in question using atomistic simulations or quantum mechanical theory. These formation energies can be inserted into formulas similar to those described for simple defect populations (Chapter 2) ... 

Worked Example 3.12 is somewhat artificial, because most reactions proceed with differing numbers of bonds breaking and forming. A more rigorous approach quantifies the energy per bond - the bond enthalpy AHEE (also called the bond dissociation energy ). 

One possible solution of this problem is to differentiate a radical first as electrophilic or nucleophilic with respect to its partner, depending upon its tendency to gain or lose electron. Then the relevant atomic Fukui function (/+ or / ) or softness f.v+ or s ) should be used. Using this approach, regiochemistry of radical addition to heteratom C=X double bond (aldehydes, nitrones, imines, etc.) and heteronuclear ring compounds (such as uracil, thymine, furan, pyridine, etc.) could be explained [34], A more rigorous approach will be to define the Fukui function for radical attack in such a way that it takes care of the inherent nature of a radical and thus differentiates one radical from the other. 

A more rigorous approach consists of considering that electron hopping between fixed redox sites is fundamentally a percolation problem, each redox center being able to undergo a bounded diffusion motion.16 If these are fast enough, a mean-field behavior is reached in which (4.24) applies replacing d2 by d2 + 3 Ad2, where Adr is the mean displacement of a redox molecule out of its equilibrium position. 

Bauschlicher [48] compared a number of approximate approaches for scalar relativistic effects to Douglas-Kroll quasirelativistic CCSD(T) calculations. He found that the ACPF/MTsmall level of theory faithfully reproduces his more rigorous calculations, while the use of non-size extensive approaches like CISD leads to serious errors. For third-row main group systems, studies by the same author [49] indicate that more rigorous approaches may be in order. 

Multiple Parallel Synthesis (MPS) is typically carried out in a plate containing a matrix of 8 x 12 wells. It is typical for each well to contain a different combination of reactants (say an acid and an amine). Since the number of outcomes is then restricted (to say 96 amides) it could reasonably be argued that a full analysis of individual spectra need not take place in order to validate the plate for further work. Indeed, it may well be that the plate is destined for high throughput (biological activity) screening, and only hits from that process would then warrant a more rigorous approach. 

The more rigorous approach to liquid water transport is a true two-phase model in which the two phases travel at different velocities. At the same time, the interfacial tension effect and GDL wettability, essential for successful PEEC operation, are fully accounted for. The work of Wang et al., Nguyen et ai 69 71 You and Liu, Mazumder and Cole, Bern-ing and Djilali, and Pasaogullari and Wang falls into this category. These two-phase models are reviewed in section 3.7. 

A SLIGHTLY MORE RIGOROUS APPROACH. In the above description, the system was treated as though the reactants were ideal gases. A better approach is to account for the free energy of the system as a function of added reactants, and for solutions, the most technically correct action is to use partial molal quantities. Because free energy, G(T, P, ni, H2,. ..), is a state function depending on temperature, pressure, and the moles of... 

Again, this is an epistemic approach and a more rigorous approach in the philosophy of science would consider this too simplistic, as it is based on the assumption that objects and levels of structures can be considered as separated. 

Certainly the effort of following a checklist cannot be avoided. A less rigorous alternative is to call several manufacturers, have their representatives stop by, visit their plants or customer locations and witness demonstrations of their equipment, and then decide which seems to best meet one s needs. Both this approach, which seems to be the standard in industry, and the more rigorous approach to overall planning suggested here, will yield a system. But the rigorous approach is most likely to yield a successful system and it is often an approach that is easier to sell to supervision and management. 

A more rigorous approach includes a transmission coefficient, k, which is a multiplication factor equal to the fraction of the transition state that proceeds to products. The transmission coefficient is generally close to 1.0 for simple reactions. There can be a large attenuation factor for complex reactions because of... 

Since these five-membered rings, however, differ markedly from benzene in their geometry a more rigorous approach, as for substituent effects in polycyclic systems, would appear to be calculation of appropriate a values by approaches of the Dewar-Grisdale equation [Eq. (2)] or multiparameter form [Eq. (3)] in the former case, the p values are taken as equivalent to that in benzenoid compounds. 

Using a pressure drop model based only on centrifugal acceleration and frictional drag, the HOC1 scale-up overpredicted the pressure drop of the commercial RPB by a factor of 2 (9). A more rigorous approach to pressure drop calculation that takes into account the conservation of angular momentum and the inlet and outlet zones of the rotor and housing (40) should provide more predictable scale-up performance. 

A more rigorous approach, however, is to directly compute the interaction between the transition densities. This was first done numerically by discretizing the transition densities into finite volume elements of a 3D grid in the transition density cube (TDC) method [84]... 

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