The Importance of Factorial Design of Experiments in Functional Nanomaterials Preparation and Performance

The experimental planning and design are important parts for successful performance and result analysis in a project. Both for industry and academic settings, there is the constant need to analyze the influence of many variables in the different types of responses. Traditionally, the influence of different variables in the experimental outcome has been analyzed by changing “one factor at a time”, which is usually described as univariate or OFAT approach. However, unless all variables are close to their optimum value, there is no guarantee that this approach will lead to the best optimized outcome. Additionally, the OFAT approach can lead to the implementation of an excessive number of experiments, which usually increases the expenses related to the project. Pursuing to analyze how the synergy between different variables can influence the experimental outcomes, there is the multivariate approach, where two or more variables are changed simultaneously enabling the experimentalist to analyze the beneficial or antagonistic effect of this combination of variables in the experimental outcome. Moreover, the multivariate approach may improve the chances to find the best outcome possible with the conduction of a fewer number of experiments. In this sense, this chapter introduces the concept of factorial design of experiments, a multivariate approach based on choosing two or more levels for multiple variables, calculating the effects of each variable individually and of each possible combination of variables, obtaining a model from these results, applying this model to predict untested conditions and judge the statistic significance of the model. The examples presented in the chapter will all be focused on the preparation and performance of nanomaterials. For instance, how the concentrations of different precursors can influence the particle size of colloidal silica nanoparticles. Or how different variables, such as, time, temperature and reagents concentration can influence the thickness of manganese sulfide (MnS) thin films. The chapter begins providing the definition of the basic terms underlying the factorial design, then, it presents examples from literature applying factorial designs starting with the simpler ones, such as 2³. Then, the chapter evolves presenting optimization and response surface methodologies factorial designs, for instance, central composite, Box-Behken, and Doehlert designs. Finally, the chapter presents tables with references from papers published in the period from 2015 to 2020. In each one of them, the factorial design of experiments was used for the development of functional materials applied in nanoparticles preparation, drug delivery and encapsulation, wastewater remediation, and solar cells development. With this chapter, the author hopes to introduce a powerful and underexplored statistical tool to scientists, engineers, and all practitioners of nanomaterials science. Focus will be placed on how they can benefit from the concepts and examples presented, and possibly adapt them for their own projects, instead of relying on heavy mathematical notations and calculations.