Experimental design, mixture experiments

Experience with Experimental Design, Mixture theory and Optimisation routines. Conceptual models relating coating structure and morphology to target properties (e.g. pigment packing, composite material science, colloid science). 

In the optimization of tablet formulations, different approaches can be used. The one variable at a time method requires many experiments and there is no guarantee that an optimal formulation is achieved. Moreover the interaction between different factors, which may influence the tablet properties, will not be detected [10]. The use of an experimental design can be helpful in the optimization of tablet formulations. Mixture designs can be used to describe the response (tablet properties) as a function of the... 

A more efficient experimental design provides concentrations and standard deviations in fewer than nine experiments. One of many efficient designs is shown in Figure 7-12. Instead of titrating each acid by itself, we titrate mixtures of the acids. For example, in row 5 of the spreadsheet, a mixture containing 2 mL A, 2 mL B, and 2 mL C required 23.29 mL of 0.120 4 M NaOH, which amounts to 2.804 mmol of OH. In row 6, the acid mixture contained 2 mL A, 3 mL B, and 1 mL C. Other permutations are titrated in rows 7 and 8. Then row 5 is repeated independently in row 9. Column E gives mmol of base for each run. 

The most frequently used mixture-"composition-property designs of experiments belong to simplex-lattice designs suggested by Scheffe [5], The basis of this kind of designing experiments is a uniform scatter of experimental points on the so-called simplex lattice. Points, or design points form a [q,n] lattice in a (q-1) simplex, where q is the number of components in a composition and n is the degree of a polynomial. For each component there exist (n+1) similar levels Xp0,l/n,2/n.1 and all... 

Systematic work on experimental designs in the area of mixture experiments was originated by Henry Scheffe, [3, 4], Cornell provides an extensive reference on the subject [5],... 

Another standard mixture experiment strategy is the so-called simplex centroid design, where data are collected at the extremes of the experimental region and for every equal-parts two-component mixture, every equal-parts three-component mixture, and so on. Figure 5.22 identifies the blends included in a p = 3 simplex centroid design. 

We should point out that the ability to fit equations of the form (5-18) or like (5-19), or of an even more complicated form, is predicated on having data from enough different mixtures to allow unambiguous identification of the parameters b. This requires proper data collection strategy. Much of the existing statistical research on the topic of mixture experiment design has to do with the question of wise allocation of experimental resources under the assumption that a particular type of equation is to be fit. 

The mixture experiment counterpart to conventional screening/fractional factorial experimentation also is possible. So-called axial designs have been developed for the purpose of providing screening-type mixture data for use in rough evaluation of the relative effects of a large number of mixture components on a response variable. The same kind of sequential experimental strategy illustrated in the process improvement example is applicable in mixture contexts as well as contexts free of a constraint such as (5-15). 

Statistical experimental design, also called design of experiments (DoE), is a well-established concept for planning and execution of informative experiments. DoE can be used in many applications. An important type of DoE application refers to the preparation and modification of mixtures. It involves the use of mixture designs for changing mixture composition and exploring how such changes will affect the properties of the mixture [32],... 

In recent years there has been significant interest in thermally coupled systems and dividing wall columns for ternary mixtures. In this subsection we discuss such column arrangements, their energy requirements, design and optimization methods, controllability and operability, experimental and industrial experience, and extension to more than three components. 

DVB were valid in this system as well. These concern the dependence of surface area and pore volume on the amount of diluent and cross-linker. The surface area increases with the amount of EDMA and goes through a maximum with increasing amount of diluent. Using cyclohexanol-dodecanol as a solvent-non-solvent pair, the factors of importance for the structure and morphology of the polymers were studied by experimental design [34]. In these experiments the concentration of the diluent mixture was varied between 20 and 77% (volume/total volume), the concentration of EDMA between 25 and 100% (volume/monomer volume), the concentration of initiator (AIBN) between 0.2 and 4% (w/w), the concentration of non-solvent (dodecanol), between 0 and 15% (v/v) and the polymerisation temperature between 70° and 90°C. The surface area (determined by nitrogen sorption), pore volume (determined by mercury porosimetry) (see Section 2.11.6.) and the mechanical properties were chosen as responses. 

Thus, one can conclude that reliable verification and validation of kinetic models require a special arrangement of experiments. In the ideal it includes a thorough description of reaction conditions, complete analysis of the reaction mixture, and use of adequate criteria for the comparison of experimental and calculated data. We must confess, however, that a consistent execution of these requirements is very time and resource consuming. This is why a pragmatic (trade-off) approach can be elaborated for the design of experiments. The following elements of this approach can be also employed for the selection of already published experimental data for verification of kinetic models ... 

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