Simultaneous interpretive methods

Simultaneous interpretive methods (table 5.7d) provide a way to locate the global optimum from a relatively low number of experiments. The price that should be paid for this very important advantage of these methods is an increased effort from the chromatographer to provide knowledge (to model the retention surfaces), increased computational requirements and the necessity to recognize all the individual solutes in each chromatogram. The reliability of the final result will depend on the accuracy of the model. 

Table 5.7d suggests that simultaneous interpretive methods are highly promising for selectivity optimization, but that there is still much room for improvement if research effort is directed at... 

Iterative designs (table 5.7e) have two main advantages over the simultaneous interpretive methods described above. 

Simultaneous interpretive methods are a good way to locate the global optimum in a small number of experiments, but the requirements are shifted towards good models, computers, and peak recognition methods. 

A subset of simultaneous methods which overcomes the difficulty of mapping complex response surfaces by an exhaustive series of experiments are the interpretive methods, in which retention surfaces are modeled using a minimum number of experimental data points. Retention surfaces thus obtained for the individual solutes are then used to calculate (via computer) the total response surface according to some predetermined criterion. The total response surface is then searched for the optimum. 

In the following two sections we will describe two kinds of interpretive methods. In section 5.5.1 we will discuss simultaneous methods, which involve a fixed experimental design. In the iterative procedures of section 5.5.2, an initial design that consists of a minimum number of experiments is used and the location of the next data point is calculated during the optimization process. 

By definition, all interpretive methods of optimization require knowledge of the capacity factors of all individual solutes. This is the fundamental difference between the simultaneous and sequential methods of optimization (sections 5.2 and 5.3, respectively) and the interpretive methods of section 5.5. Moreover, in the specific cases in which only a limited number of components is of interest or in which weighting factors are assigned to the individual solutes (see section 4.6.1) it is also necessary to recognize the individual peaks (at least the relevant ones) in each chromatogram. In section 5.5 we have tacitly assumed that it would be possible to obtain the retention data (capacity factors) of all the individual solutes at each experimental location. 

Interpretive methods will generally arrive at the global optimum after a limited number of experiments. However, (by definition) the recognition of the individual solutes is required in each experimental chromatogram. Also, the computational requirements are relatively high, especially if the simultaneous optimization of several parameters is considered. For example, (linear) ternary gradients (one parameter) will be much easier to optimize than quaternary gradients (two parameters). 

The many interactions that the solutes experience in a micellar chromatographic system enhances the differences among them. The possibility of using, simultaneously, the three most significant variables that affect the retention (j. e., pH, and concentrations of surfactant and modifier), will improve the capability of resolution of complex mixtures of ionic and nonionic compounds. The high accuracy in the prediction of retention factors in MLC permits the reliable and relatively rapid optimization of the composition of the mobile phase for the separation of a mixture of compounds, by using an interpretive method and a reduced number of mobile phases (at least two for one variable, four or five for two variables, and nine for three variables). 

Procedure. Run one or more simultaneous equation programs to determine the C—C and C—H bond energies and interpret the results. The error veetor is the veetor of ealeulated values minus the veetor of bond enthalpies taken as tme from an aeeepted source. Caleulate the enor veetor using a standard souree of bond enthalpies (e.g., Laidler and Meiser, 1999 or Atkins, 1994). Expand the method for 2-butene (2-butene) = —11 kJ mol ] and so obtain the C—H, C—C,... 

The effects of adsorbed inhibitors on the individual electrode reactions of corrosion may be determined from the effects on the anodic and cathodic polarisation curves of the corroding metaP . A displacement of the polarisation curve without a change in the Tafel slope in the presence of the inhibitor indicates that the adsorbed inhibitor acts by blocking active sites so that reaction cannot occur, rather than by affecting the mechanism of the reaction. An increase in the Tafel slope of the polarisation curve due to the inhibitor indicates that the inhibitor acts by affecting the mechanism of the reaction. However, the determination of the Tafel slope will often require the metal to be polarised under conditions of current density and potential which are far removed from those of normal corrosion. This may result in differences in the adsorption and mechanistic effects of inhibitors at polarised metals compared to naturally corroding metals . Thus the interpretation of the effects of inhibitors at the corrosion potential from applied current-potential polarisation curves, as usually measured, may not be conclusive. This difficulty can be overcome in part by the use of rapid polarisation methods . A better procedure is the determination of true polarisation curves near the corrosion potential by simultaneous measurements of applied current, corrosion rate (equivalent to the true anodic current) and potential. However, this method is rather laborious and has been little used. 

As stated earlier, a commercially useful computational method must be fast, accurate, transferable, and interpretable. Logical steps one can take towards this goal are now presented. It is important to point out that under current resources, these four criteria cannot be simultaneously optimized. With current computational capabilities, the most complete theoretical description of protein-ligand interactions (which may involve many-body terms) cannot... 

Labels are distinguished based on whether they are context dependent or context-free. Context-dependent labels require simultaneous consideration of time records from more than one process variable context-free labels do not. Thus, generating context-free trend, landmark, and fault descriptions is considerably more simple than generating context-dependent descriptions. Context-free situations can take advantage of numerous methods for common, yet useful, interpretations. Context-dependent situations, however, require the application of considerable process knowledge to get a useful interpretation. In these situations, performance is dependent on the availability, coverage, and distribution of labeled process data from... 

Unless the coverage of adsorbate is monitored simultaneously using spectroscopic methods with the electrochemical kinetics, the results will always be subject to uncertainties of interpretation. A second difficulty is that oxidation of methanol generates not just C02 but small quantities of other products. The measured current will show contributions from all these reactions but they are likely to go by different pathways and the primary interest is that pathway that leads only to C02. These difficulties were addressed in a recent paper by Christensen and co-workers (1993) who used in situ FT1R both to monitor CO coverage and simultaneously to measure the rate of C02 formation. Within the reflection mode of the IR technique used in this paper this is not a straightforward undertaking and the effects of diffusion had to be taken into account in order to help quantify the data obtained. 

Mutlicorer. The MC-400 collects four simultaneous cores two of which were analyzed for total metals and 210-lead, respectively. Details of field methods, Hg analyses and 210-lead interpretation can be found elsewhere (Parsons, et al.,... 

The possibilities for combining thermoanalytical methods like TG with other techniques and to carry out such measurements in certain cases simultaneously are increasing. This is of great significance for the easier and sometimes unambiguous interpretation of results. 

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