Optimal Staging Design

With the analysis above, we can answer some important practical questions related to MFEP calculations. Should an MFEP calculation be used at all How many stages are needed How should the intermediates be formulated What is the necessary sample size for each stage  

we consider a multistage calculation consisting of a total of n intermediates 

The overall bias of the calculation is the sum of those for each stage (absolute value) and the overall variance is given as 

Now consider the optimal placement of intermediates leading to the least overall variance. The criterion of minimal variance is obtained by inserting (6.45) into the right-hand side of (6.47) for each stage, and minimizing the overall error subject to 

This means that, to obtain the least variance in a multistage calculation, the intermediates should be constructed to have equal entropy difference for all stages. This criterion differs from the often used but unjustified rule of thumb that free energy differences should be equal in all stages [22,42], Simulation tests show that the entropy criterion leads to a great improvement in calculation precision compared to its free energy counterpart [26]. The same optimization criterion holds for calculation of entropy and enthalpy differences [44], 

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This approach attempts to permit the designer to evaluate and optimize alternatives quickly, using shortcut hand calculations. However, if it is to be adopted by practicing design engineers it must be complemented by software for at least the analysis, evaluation, and optimization stages. 

In the Development stage, detailed product design is carried out. This is the key step for the chemical vapor deposition of thin silicon films. As described in the next section, to obtain uniform thin films rapidly, it is desirable to optimize the design of the plasma-enhanced, chemical-vapor-deposition (PECVD) reactor. 

It should be noted that the same designs as those applied here are sometimes used in the optimization stage of the method [18,24-27], i.e. before the validation. In that case it makes sense to apply levels that are further apart than in ruggedness testing. 

As HTS still remains the method of choice to discover novel hit compounds, researchers focused their attention to the design and development of appropriate tools to reduce the size of the chemical libraries to be tested while increasing the quality of the compounds, what could maximize the chances of identifying hit compounds amenable to the subsequent lead optimization stages... 

It is essential to characterize formulation flow properties—and the factors which impact on it (Table 7.8)—at the beginning of the formulation design and optimization stages. Several different methods are available for determining the flow properties of powder mixtures that can serve as tools for prototype formulation screening 55... 

Few simulations were needed to achieve a quasi-optimal column design with 38 equilibrium stages, a column diameter of 0.9 m, a section pressure drop of 34.7 kPa and a steam flow rate of 3600 kg/h. The values obtained for the number of equilibrium stages and steam demand, together with the composition of ethanol in the outlet stream (51.52 % w/w) agree well with results presented in Kwiatkowski et al. (2006). 

Question A discovery program designed to produce an agonist is in the lead optimization stage the chemists are actively... 

A preparative high-performance column packed with 5, 7 or 10 pm material and available from various manufactures is used after the analytical separation optimization stage (columns with coarser particles of around 40 pm are more suitable for easy separations requiring less than 100 theoretical plates). A 10 mm i.d. column is designed for 10-100 mg samples, rising to 21.5 mm (o.d. 1 in) for samples between 100 mg and 1 g. The transfer from analytical to preparative conditions works best if both columns are packed with the same stationary phase. 

To show how the stage design may be optimized for various criteria... 

The appropriate criterion to optimize the design of a gaseous diffusion stage is that the... 

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