Análise de experimentos fatoriais de dois fatores com tratamentos adicionais

Experiments using factorial arrangement of treatments are rather common and useful in agricultural research. The main advantage is the possibility of testing many hypotheses, allowing broader conclusions over different factors, studied simultaneously. Factorial arrangements are used to compare levels of each factor (main effects), and also to verify if the differences among levels of a given factor are dependent on the levels of the other factors (interacions). In the analysis of data from factorial experiments, difficulty is increased when additional treatments are included. Inclusion of one or more additional treatments is a quite common practice, since such treatments are usually taken as reference or standard for evaluation and comparasion of the remaimng treatments, or aiming complementary information. This increase of difficulty is however low, compared to the advantages. As in literature there are few references about the statistical analysis of factorial experiments with additonal treatments, and given straightforward use in experimentation, the objective of this work was the presentation of approach for the use of factorial experiments with additonal treatments trough the analysis of some examples using the SAS® software, with the corresponding theoretical development, obtaining the system of normal equations, estimators of the parameters and variance of contrasts among two treatment means. It is suggested that additional treatments should be used with caution. The analysis of variance of such kind of experiment was presented using matrix notation.

Ativação da ligação c-h no metano por espécies MOm n+ (M = Nb, Fe; m = 0, 1; n = 0, 1, 2): estrutura eletrônica, mecanismo de reação e reatividade

The need for renewal and a more efficient use of energy resources has provided an increased interest in studies of methane activation processes in the gas phase by transition metal oxides. In this respect, the present work is an effort to assess , by means of a computational standpoint, the reactivity of NbOm n+ and FeOm n+ (m = 1, 2, n = 0, 1, 2) oxides in the activation process of the methane C-H bond, which corresponds to the first rate limiting step in the process of converting methane to methanol. These oxides are chosen, primarily, because the iron oxides are the most experimentally studied, and iron ions are more abundant in biological mediums. The main motive for choosing niobium oxides is the abundance of natural reserves of this mineral in Brazil (98%), especially in Minas Gerais. Initially, a thorough investigation was conducted, using different theoretical methods, to analyze the structural and electronic properties of the investigated oxides. Based on these results, the most reliable methodology was selected to investigate the activation process of the methane C-H bond by the series of iron and niobium oxides, considering all possible reaction mechanisms known to activate the C-H bond of alkanes. It is worth noting that, up to this moment and to our knowledge, there are no papers, in literature , investigating and comparing all the mechanisms considered in this work. I n general, the main results obtained show different catalytic tendencies and behaviors throughout the series of monoxides and dioxides of iron and niobium. An important and common result found in the two studies is that the increase in the load on the metal center and the addition of oxygen atoms to the metal, clearly favor the initial thermodynamics of the reaction, i.e., favor the approach of the metal center to methane, distorting its electron cloud and, thereby, decreasing its inertia. Comparing the two sets of oxides, we conclude that the iron oxides are the most efficient in activating the methane C-H bond. Among the iron oxides investigated, FeO + showed better kinetic and thermodynamic performance in the reaction with methane, while from the niobium oxides and ions NbO 2+ and NbO2 2+, showed better catalytic efficiency in the activation of the methane C-H bond.