The Experimental Plan

In the first publication [16], the experimental strategy was applied to just ten different stationary phases, in part different modifications of the same silica-based material. Phases with incorporated polar fimctions were not included. The eluent conditions were kept constant. The chromatographic experiments with all of the neutral substances were carried out with a H2O/CH3CN (1 1, vjv) eluent with buffer additives, while basic and acidic solutes were eluted with a 31.2 mM phosphate buffer at pH 2.8. The selected pH value does not imply very critical conditions, as it suppresses dissociation of most residual silanol groups and of weakly acidic solutes. A variation of the eluent conditions wiU be discussed in a later section. 

3 Determination of the Five LFER Parameters - A Procedure in Eight Steps 

The mathematical plan for determining the parameters from the chromatographic data is divided into eight steps, as discussed in the following. In a first step, the retention of all i selected test solutes is related to that of ethylbenzene (ideally hydrophobic substance by definition) according to Eq. (7). This results in a data point log oq p for each column P. 

In the second step, a reference phase (RP) is selected, which, in the given case, is HP Zorbax SB Cjg (SB 100) with a maximum degree of alkyl derivatization. The correlation of all of the log oq p values with the log tt pp values of the reference column has been checked for all of the substances (see Fig. 6). The correlation of the aU log oq jjp-values with the log oq jjp-values of the reference column was checked for aU substances. When the reference phase is compared to a very similar stationary phase (e.g., HP Zorbax SB Cjg with only 90% alkyl derivatization) the correlation of the data adopts high values (r = 0.9996) as expected. However, when a phase like Inertsil ODS-3 is compared, the standard error of the correlation Sy was more than 7 times higher (r=0.9822). Especially the strongly basic substances (amitriptyline, nortriptyline, diphenhydramine and propranolol) and N,N -dimethyl acetamide scatter markedly from the linear correlation. These first correlation experiments enable the identification of all ideally hydrophobic compounds within the pool of test solutes. The selection criterion is a maximum deviation from the linear fit of 0.01 log a units. This can be fulfilled for 24 solutes from the complete set of 67 test substances. For these 24 compoimds, a pure hydrophobic retention mechanism is assumed. Hence, the relative retention of these compounds can be described by a phase parameter H (interpreted as hydrophobicity) and a related solute parameter, resulting in Eq. (8) for each solute i on a specific column P  

In the third step, the H parameter is calculated for each of the P stationary phases. Assuming an H value of 1.000 for the reference phase (Hpp), this can be done from the data of the 24 ideal substances by applying Eq. (9)  

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Practical considerations enter into the experimental plan in various other ways. In many programs, variables are introduced at different operational levels. For example, in evaluating the effect of alloy composition, oven temperature, and varnish coat on tensile strength, it may be convenient to make a number of master alloys with each composition, spHt the alloys into separate parts to be subjected to different heat treatments, and then cut the treated samples into subsamples to which different coatings are appHed. Tensile strength measurements are then obtained on all coated subsamples. 

The experimental plan will also specify approximate values for The reaction rate for a key component is calculated using Equation (7.10), and the results are regressed against measured values of bgut, , and... 

As far as the bench-chemist is concerned, the following nonexhaustive list of points should be incorporated into the experimental plan ... 

This approach can be used with other simple rate expressions in order to determine a representative value of the reaction rate constant. Moreover, the experimental plan on which this technique is based will provide data over such a range of fraction conversions that it is readily... 

Figure 11.4 Three illustrative examples why the density and choice of points are essential for the experimental planning stage. It can be seen in all three cases that the wrong choice of experimental points can result in missing the opportunity of finding the local optimum.

To ensure that the experimental plan is in compliance with standards for microarray information collection... 

The planning of good experiments for an in situ spectroscopic homogeneous catalytic study is a non-trivial matter. Indeed, the number and quality of the pure component spectra recovered are strongly dependent on the experimental planning. 

At this point, a model has to be postulated based on the significant factors the main types are linear, linear with interactions, and quadratic pol)momial models. The next step is the definition of the experimental plan, which is closely dependent on the model chosen and on the number of factors. 

These factors are introduced in the experimental plan at the bench-scale before the pilot--plant stage. On the bench-scale, glass or steel laboratory reactors of about 1 to 2 L will be used for MSSR and a 30 cm diameter and 2 m height for BSCR. 

A Taguchi experimental plan with two levels and four variables (temperature, exposure time, decompression rate, and reduced density) was adopted. The experimental plan, covering the variable ranges commonly usedfor transesterification reactions (1), is presented inTable 1. The experiments were accomplished randomly, and duplicate runs were carried out for all experimental conditions leading to an average reproducibility better than 5%. The activity loss was then modeled empirically in order to determine the influence of the process variables on main and cross-interaction parameters. 

With respect to this experimental effort, it is important to specify that it is sometimes difficult to measure the variables involved in a chemical process. They include concentrations, pressures, temperatures and masses or flow rates. In addition, during the measurement of each factor or dependent variable, we must determine the procedure, as well as the precision, corresponding to the requirements imposed by the experimental plan [5.4]. When the investigated process shows only a few independent variables. Fig. 5.3 can be simplified. The case of a process with one independent and one dependent variable has a didactic importance, especially when the regression function is not linear [5.15]. 

Here Zj, j = 1, k introduce the original values of the factors. The point with coordinates (ZjjZj,. ..z ) is recognized as the centre of the experimental plan or fundamental level. Azj introduces the unity or variation interval respect to the axis Zj, j = l,k. At this point, we have the possibility to transform the dimensional coordinates Zj,Z2,. ..z to the dimensionless ones, which are introduced here by relation (5.97). We also call these relations jbrmulas. 

It is not difficult to observe that, by using this system of dimensionless coordinates for each factor, the upper level corresponds to -i-l, the lower level is -1 and the fundamental level of each factor is 0. Consequently, the values of the coordinates of the experimental plan centre will be zero. Indeed, the centre of the experiments and the origin of the system of coordinates have the same position. In our current example, we can consider that the membrane remains unchanged during the experiments, i.e. the membrane porosity (e) and the zeolite concentration (Cj.) are not included in the process factors. 

Using the experimental plan from Table 5.20 it is possible to estimate the constant terms and the three coefScients related to the linear terms from the regression relationship. 

The example shown above, introduces the necessity for a statistical investigation of the response surface near its great curvature domain. We can establish the proximity of the great curvature domain of the response surface by means of more complementary experiments in the centre of the experimental plan (xj = 0,X2 = 0,...Xij = 0). In these conditions, we can compute y, which, together with Pq (computed by the expression recommended for a factorial experiment... 

An increase in the number of experiments in the centre of the experimental plan (ng). 

N gives the total number of experiments in the plan. When we use a complete second order plan, it is not necessary to have parallel trials to calculate the reproducibility variance, because it is estimated through the experiments carried out at the centre of the experimental plan. The model adequacy also has to be examined with the next procedure ... 

In the method of Latin squares, the experimental plan, given by the matrix of experiments, is a square table in which the first line contains the different levels of the first factor of the process whereas the levels for the second factor are given in the first column. The rest of the table contains capital letters from the Latin alphabet, which represent the order in which the experiments are carried out (example for pressure level Pj, four experiments for the temperature levels Tj, T2, T3, T4 occur in the following sequence A, B, C, A where A has been established as the first experiment, B as the second experiment, etc). The suffixes of these Latin capital letters introduce the different levels of the factors. Table 5.58 presents the schema of a plan of Latin squares. We can complete the description of this plan showing that the values of the process response can be written in each letter box once the experiment has been carried out. Indeed, we utilize three indexes for the theoretical utterance of a numerical value of the process response (v). For exam-... 

The simplest problem concerns only one pi term. The complexity of the analysis increases rapidly with increasing number of pi terms because then the choice of the experimental plan related to the proposed relationship for the dimensionless pi groups cannot be solved by an automatic procedure. 

Example 46 There seems to be a clear reduction in the residual standard deviation, and the F-test supports this notion F (6.6/4.5) = 2.15, with F(26, 26, 0.05) = 1.93. Point No. 8 (see Fig. 4.21) is now only 0.011 AU above the parabola, which means it is barely outside the 2 band all other residuals are smaller. From the practical point of view there is little incentive for further improvement the residual standard deviation +4.5 mAU is now only about twice the experimental standard deviation (repeatability), which is not all that bad when one considers that two dilutions and a derivatization step are involved. The scatter appears to increase towards higher concentrations Indeed, this may be so, but to underpin the case statistically one would have to run at least eight repeats at a low and another eight at a high concentration if Shigh = 2 low, because Fcrit(7, 7,0.05) = 3.8. Should 5high only be 1.5 - low, then the experimental plan would call for nhigh = niow 18. 

The data we observe are in contradiction with the data published by [7], They observe an increase of the pyrolytic carbon deposition up to 800 °C followed by a decrease up to 1000 °C. But the authors [7] publish result only for three temperatures (600, 800 and 1000 C) and give only one value for each test without any information on the experimental plan (number of replications for example). 

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