In The Name Of God
Box-Behnken Design
By: Neda Salek Gilani
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1- Introduction
1-1- Application of multivariate techniques in analytical
Chemistry
In recent years, chemometric tools have been frequently
applied to the optimization of analytical methods, considering their advantages such as a reduction in the number of experiments that need be executed resulting in lower reagent consumption and considerably less laboratory work.
Furthermore these methods allow the development of mathematical models that permit assessment of the relevance as well as statistical significance of the factor effects being studied as well as evaluate the interaction effects between the factors.
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The univariate procedure may fail since the effect of one variable can be dependent on the level of the others involved in the optimization. That is why multivariate optimization schemes involve designs for which the levels of all the variables are changed simultaneously.
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Among the most relevant multivariate techniques used,in analytical optimization is response surface methodology (RSM).
Response surface methodology is a collection of mathematical and statistical techniques based on the fit of a polynomial equation to the experimental data, which must describe the behavior of a data set with the objective of making statistical previsions.
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Before applying the RSM methodology, it is first necessary to choose an experimental design. There are some experimental matrices for this purpose. Experimental designs for first-order models (e.g., factorial designs) can be used when the data set does not present curvature. However, to approximate a response function to experimental data that cannot be described by linear functions, experimental designs for quadratic response surfaces should be used, such as three-level factorial, Box–Behnken, central composite, and Doehlert designs.
2-1- Variables in multivariate optimization techniques
During the multivariate optimization procedure, there are two types of variables:
1- Responses
2- Factors
The responses are the dependent variables. Their values depend on the levels of the factors, which can be classified as qualitative or quantitative.
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2- Box-Behnken design as a tool for multivariate optimization
Box-Behnken designs (BBD) are a class of rotatable or nearly rotatable second-order designs based on three-level incomplete factorial designs. For three factors its graphical representation can be seen in two forms:
1. A cube that consists of the central point and the middlepoints of the edges, as can be observed in Fig. 1a.
2. A figure of three interlocking 22 factorial designs and a central point, as shown in Fig. 1b.
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3- The number of experiments (N) required for the development of BBD :
N=2k(k−1) + Co
k = number of factors
Full three-level factorial designs: N=3k
Central composite design: N= k2 +2k+cp
Doehlert design: N= k2+ k + Cp
For comparison:
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N for BBD is defined as:
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Efficiency=P/N
P= number of parameteres
N = number of experiments
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BBD and Doehlertmatrix are slightly more efficient than the central composite design but much more efficient than the three-level full factorial designs.
Another advantage of the BBD is that it does not contain combinations for which all factors are simultaneously at their highest or lowest levels. So these designs are useful in avoiding experiments performed under extreme conditions, for which unsatisfactory results might occur.
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4- Advantages of BBD
5- Applications of BBD:
1-5- Investigation of Cr(VI) adsorption onto chemically treated Helianthus aunnus: Optimization using Response Surface Methodology:
The percent chromium removal (R%) was calculated for each run by following expression:
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2-5- Optimization of oxidative desulfurization of thiophene using Cu/titanium silicate-1 by box-behnken design
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3-5- Determination of vitaminC in drug susing of an optimized novel TCPO–Amplex red–gold/silveralloynanoparticles–H2O2 chemiluminescence method by the Box–Behnken design
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Optimum Values
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[1] S.L.C. Ferreira et al. Analytica Chimica Acta 597 (2007) 179–186.
[2] G. Derringer et al. Talanta 76 (2008) 965–977
[3] Monika Jain, V.K. Garg , K. Kadirvelu Bioresource Technology 102 (2011) 600–605
[4] N. Jose, S. Sengupta, J.K. Basu Fuel 90 (2011) 626-632
[5] M.J. Chaichi, S.O. Alijanpour Journal of Luminscence 134 (2013) 195-200
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Refrences:
Thanks For Your Attention
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