Curve-fitting techniques errors

Using modern computer curve-fitting techniques,102 equations (17) and (27) can be fitted simultaneously with variables X, log CH+ and D, obtaining pATBH+. m, DB and DA as coefficients, which is a more precise technique than calculating log/ values first and using equation (17) and the error function61 discussed above. 

Experimental data may be treated according to Scott s modification [207] of the Benesi-Hildebrand equation [221], Technically easier and more exact may appear other methods described especially for the treatment of NMR data [222]. The known stoichiometry of the complex is a prerequisite for obtaining correct binding data. Almost all techniques described in the literature are suitable for 1 1 complexes. The formation of complexes of other stoichiometry may significantly complicate the treatment of the data or introduce a significant source of error in the calculations. Nonlinear curve-fitting techniques may avoid the problems of this kind. 

The error for the curve-fitting technique are is shown in Fig. 8 for 6 /6 = 0.25 to 1.5. These results were obtained using numerical... 

Figure 8. Absolute value of the error in corrosion current density due to the neglect of mass transport for curve-fitting technique. (61 points between -30 and -l-30mV). ...

The error of the curve-fitting technique is qualitatively the same as that of the idealized polarization-resistance technique. The absolute value of the error follows a similar type of bellshaped curve. Quantitatively, there are some discrepancies, which, in the extreme case, can approach an order of magnitude. The reason for these discrepancies is the same as discussed in Section IV.2(iii). 

In contrast, the errors of the polarization-resistance technique have been very thoroughly and quantitatively evaluated, and the reported errors are the smallest among the four techniques for all error categories. On the other hand, this technique has two more error possibilities (in linearization and Tafel-slope estimate) than the other techniques. Consequently, the overall error may be comparable to those of the three-point and curve-fitting techniques, and it has to be evaluated for each experimental situation. The systematic errors can be avoided by using the appropriately corrected polarization equations in the data evaluation however, that requires numerical values for the appropriate parameters, such as mass transport, double layer, solution resistance, equi-... 

To use this method, the sample is dissolved in a system containing two phases (e.g., water and octanol) such that the solution is at least about 5 x 10-4 M. The solution is acidified (or basified) and titrated with base (or acid) under controlled conditions. The shape of the ensuing titration curve is compared with the shape of a simulated curve, which is created in silico. The estimated p0Ka values (together with other variables used to construct the simulated curve such as substance concentration factor, CO2 content of the solution and acidity error) are allowed to vary systematically until the simulated curve fits as closely as possible to the experimental curve. The p0Ka values required to achieve the best fit are assumed to be the correct measured p0Ka values. This computerized calculation technique is called refinement , and is described elsewhere [14, 15]. 

Effective chloride diffusion coefficients can be back calculated from the fitting of chloride profiles to diffusion curves using the error function equation. An alternative technique is to plot the square root of the effective concentration (total minus background) vs. depth, and extrapolating a straight Une fit to the Y axis. This method is discussed in Chapters 3 and 9. 

The choice of suitable solvent suppression pulse sequences is not trivial. A variety of solvent suppression techniques yield excellent solvent-reduced spectra under qualitative considerations, but some of these techniques may lead to substantial quantification errors. Generally, cautious reduction of the solvent signal in combination with data analysis (e.g., Lorentzian-Gaussian curve fitting) should always be preferred to its complete suppression. Commonly used techniques such as presaturation are not recommended for quantitative studies because they are not sufficiently... 

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