Mixtures designs

Alloys are solid metallic mixtures designed to meet specific needs (see Section 5.15). For example, the frames of racing bicycles can be made of a steel that contains manganese, molybdenum, and carbon to give them the stiffness needed to resist mechanical shock. Titanium frames are used, but not the pure metal. Titanium metal stretches easily, so much so that it becomes deformed under stress. However, when alloyed with metals such as tin and aluminum, titanium maintains its flexibility but keeps its shape. 

Analyses for the Saxitoxins. Early methods for analysis of the saxitoxins evolved from those used for toxin isolation and purification. The principal landmarks in the development of preparative separation techniques for the saxitoxins were 1) the employment of carboxylate cation exchange resins by Schantz et al. (82) 2) the use of the polyacrylamide gel Bio-Gel P2 by Buckley and by Shimizu (5,78) and 3) the development by Buckley of an effective TLC system, including a new solvent mixture and a new visualization technique (83). The solvent mixture, designated by Buckley as "E", remains the best for general resolution of the saxitoxins. The visualization method, oxidation of the saxitoxins on silica gel TLC plates to fluorescent degradation products with hydrogen peroxide and heat, is an adaptation of the Bates and Rapoport fluorescence assay for saxitoxin in solution. Curiously, while peroxide oxidation in solution provides little or no response for the N-l-hydroxy saxitoxins, peroxide spray on TLC plates is a sensitive test for all saxitoxin derivatives with the C-12 gemdiol intact. 

Keywords cosmetic, lipstick formulation, natural ingredient, mixture design, D-optimal 1.INTRODUCTION... 

A common problem in pre-formulation of the cosmetic product including lipstick is the optimisation of the mixture composition aimed to obtain a product with the required characteristic. Mixture design represents an efficient approach for solving such optimisation problem [10]. It has been proved to be an effective tool to select the best lipstick formulation [11]. 

In order to understand the relationship between the mixture component, physical properties and consumer acceptance of the lipstick, various lipstick formulations have to be produced. The physical properties of each formulation should be studied. The consumer acceptance towards the product also should be investigated. However, only a part of this work will be discussed in this paper. Here, natural waxes, oils and solvent have been used to produce natural ingredient based lipstick formulations based on the formulation suggested by the statistical mixture design. Contour plot and response surface graph were formed in order to understand the relationship between the mixture component and physical characteristic of the lipstick. 

Using experimental design such as Surface Response Method optimises the product formulation. This method is more satisfactory and effective than other methods such as classical one-at-a-time or mathematical methods because it can study many variables simultaneously with a low number of observations, saving time and costs [6]. Hence in this research, statistical experimental design or mixture design is used in this work in order to optimise the MUF resin formulation. 

The statistical mixture design for 5-components was carried out by using Design Expert, D-Optimal criterion (Version 6.10, Stat-Easy Inc., Minneapolis USA). In this study, there are restriction on the component proportions Xj that take the form of lower Lj and upper Uj constraint as Lj experimental results of the previous study [2,5]... 

The pectin/sucrose gels were characterized as follows (amounts per lOOg gel) 0.3 g AUA, 65% soluble solid substance, 0.01 mol sodium acetate / lactic acid buffer, pH 3.0 (20°C). The metal ions were added as combinations of chlorides according to a mixture design with constant amount of chloride ions (2.5 mmol / lOOg gel). Thus the total amount of metal ions... 

The experimental designs discussed in Chapters 24-26 for optimization can be used also for finding the product composition or processing condition that is optimal in terms of sensory properties. In particular, central composite designs and mixture designs are much used. The analysis of the sensory response is usually in the form of a fully quadratic function of the experimental factors. The sensory response itself may be the mean score of a panel of trained panellists. One may consider such a trained panel as a sensitive instrument to measure the perceived intensity useful in describing the sensory characteristics of a food product. 

Mixture-design, aobile phase optiaization (LC) 480 Mobile phase (GC) flow control 232 aodifiers 43 pressure control 232 purification 232 selection 4i velocity 44 viscosity 43 Mobile phase (LC) classification 460 degassing 553 gradient elution 485 ideal properties 458 aixed solvents 465 reservoirs 553... 

An important difference between the statistical mixture design techniques popular in HPLC and the PRISMA model is that the former yields a computed optimum solvent composition id>ile the latter relies on a structured trial and error approach, which is readily adaptable to TLC. Solvent changes and re-equilibration in HPLC can be quite time consuming, so that it becomes attractive to ainimize the number of experiments, while for TLC, experiments can be performed in parallel and time constraints are less significant. Changes in solvent strength are also more rapidly adjusted empirically within the PRISMA model when theoretical considerations are found inadequate or require modification due to differences in the experimental approach. 

Glajch, J. L., Kirkland, J. J., Squire, K. M., and Minor, J. M., Optimization of solvent strength and selectivity for reversed-phase liquid chromatography using an interactive mixture-design statistical technique, /. Chromatogr., 199, 57, 1980. 

Table V. Design II 3 Component Constrained Mixture Design...

For the regression analysis of a mixture design of this type, the NOCONSTANT regression command in MINITAB was used. Because of the constraint that the sum of all components must equal unity, the resultant models are in the form of Scheffe polynomials(13), in which the constant term is included in the other coefficients. However, the calculation of correlation coefficients and F values given by MINITAB are not correct for this situation. Therefore, these values had to be calculated in a separate program. Again, the computer made these repetitive and Involved calculations easily. The correct equations are shown below (13) ... 

Note that, again, three different types of variables were combined chain length, component ratio, and absolute component level. Thus, a "standard" constrained mixture design was not appropriate. In this case a full factorial, central composite design was used, with a total of 20 data points. The star points were... 

Figure 7. Constrained mixture design, showing relationship between real and pseudocomponents.

Techniques are presented for the analysis of mixture design responses and for the optimization of... 

Unlike conventional experimental designs which have independent variables, mixture designs possess variables which are interdependent in that the summation of the q component proportions must be unity. Typically, the individual component levels are restricted by lower (a ) and upper (bj) constraints imposed on the system by physical or chemical limitations of the formulation or by the selection of the level values by the formulator. These constraints are represented as ... 

The objectives of a formulator in performing a mixture design are to not only determine the component effects and blending relationships but also optimize the component levels to achieve a maximum or minimum response of a measured property. Unfortunately, the mixture design literature is sparse in references to mixture optimization. McLean and Anderson (9) in the classic flare example attempted to use Lagrange multipliers to maximize the equation describing the intensity of an ignited flare composition but obtained erroneous results. However, a secondary technique which was not discussed did produce the optimum. 

Example Optimization of an Eleven Component Glass Formulation. Piepel (6) discussed the generation and analysis of a mixture design consisting of eleven oxides used to prepare glasses for waste vitrification. Although many responses must be considered for the end use of this composition, the intent of Piepel s study was to minimize the response of leachability subject to the compositional constraints of ... 

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