When three variables are considered in the optimization process
using the Doehlert design, a spatial figure called cuboctahedron is
generated as result of the distribution of the variables over the
experimental region. The cuboctahedron is a solid with eight vertices
symmetrically truncated producing eight equilateral triangles whose
edges are equal to those of the remaining squares [26]. Fig. 1 shows
the plane projection of the design employed in this work with the real
levels of the variables. As mentioned previously, the experimental
variables selected for the optimization were: the concentrations of
surfactant (Triton X-100 or Triton X-114, depending on the design)
and HNO3 in such solution; and the volume of aqueous solution
employed in the emulsification process. The levels of the variables
were set according to the geometry of the design and the possible
range of application of each variable, resulting in a design with three
levels for the volume of aqueous solution (0.5 to 1.5 mL), five levels
for the surfactant concentration (1 to 9% w/v) and seven levels for the
HNO3 concentration (1 to 19% v/v). Each model was constructed after
performing a total of 15 experiments, which is the sum of the 13 regular
experiments drawn in the Doehlert design with 2 more experiments in
the central point of the design, employed to estimate the experimental
variance. Tables 3 and 4 show the experiments performed when Triton
X-100 and Triton X-114 were employed for emulsification, respectively,
and the global responses obtained in each experiment. The experiments
were executed randomly to avoid any tendency in the measurements.
A preliminary analysis of the results showed that the absorbance
signals of Cu and Pb had a different behavior when compared to the
absorbance signals of Fe. While the maximum absorbance signal for Fe
was verified in the experiments 2 and 4, using Triton X-100 as
emulsifier agent, the maximum absorbance for Cu and Pb, in the same
set of experiments, was registered in the central region of the
experimental domain, indicating the need of optimizing the system
through the use of a global response. The same phenomenon was not
observed when Triton X-114 was employed in the emulsification. This
probably occurred due to the lower variation of the absorbance
signals, for the three analytes, in the set of experiments performed
when the Triton X-114 was employed