The Use of Multivariate Analysis for Accurate Control of the Oscillation Frequency of Homogeneous and Heterogeneous Systems
Authors: Kitagaki Bianca Tieme , Pinto Maria Rodrigues , Queiroz Adriana , Breitkreitz Marcia Cristina , Rossi Federico , Nagao Raphael 
Published: July 2021

The control of the frequency of oscillation from experimental parameters is extremely important for a better understanding of how oscillatory systems work. Knowing this, much effort has been made to understand the effect of experimental parameters on it. Two-dimensional diagrams are constructed by varying each parameter individually, while the others are kept constant. However, as these oscillators have many control parameters, the use of multivariate statistical analysis is necessary for the accurate selection of the oscillation frequency. In addition, through this analysis it is possible to measure the possible synergistic combinations between the experimental parameters. Knowing this, in this work we performed a multivariate statistical analysis of homogeneous and heterogeneous oscillators. The homogeneous oscillator used is the Belousov-Zhabotinsky reaction while the heterogeneous system is an electrochemical deposition of Cu/Cu2O
The experiments of the homogeneous system (BZ reaction) were performed by a CSTR to keep the frequency of oscillation constant. For the experiments, two solutions were used, one of NaBrO3 and H2SO4 and the other of malonic acid (MA) and ferroin. These solutions were pumped by a peristaltic pump in a cuvette. The oscillations were monitored with a UV-visible spectrophotometer (λ=520nm). The experiments were conducted by a factorial design 23 with a central point in which the parameters analyzed were [NaBrO3], [MA] and temperature.
The experiments of the heterogeneous system (Cu/Cu2O oscillatory deposition) were carried out in an electrochemical cell with three electrodes. These are a platinized-platinum foil as a counter electrode, a saturated calomel electrode as a reference electrode and a polycrystalline platinum sheet as a working electrode. The solution used was Cu(II) lactate (0.5mol L-1 + 2.50 mol L-1 of lactate) was prepared and was left under stirring for 4 days at 2000 RPM. The experiments were conducted according to Central Composite Design (CCD), with the axial distance set at α = 1. The factors were defined as pH, current density, and temperature.
The factorial design 23 with the central point for the BZ reaction observed in Figure-1a shows that the dependence of the experimental parameters on the frequency is linear. We also see in Figure-1c that the parameter that most affected the oscillation frequency was [NaBrO3] followed by the temperature. Another important information that we observed in this graph is that there is a synergistic effect between [NaBrO3] and temperature, which is information that is not obtained through univariate analysis.
The CDD used for the electrochemical system demonstrated a dependence on a wide combination of parameters, resulting in quadratic terms. This quadratic dependency can be seen in Figure-1b, d. We note that the parameter that most affects the frequency of oscillation is the current density followed by the pH. It is evident that the interaction effects demonstrated by this type of analysis contribute to the non-linearity of the system.
The differences observed between the oscillators in which the most evident is the linearity of the oscillation frequency with the experimental parameters for the BZ reaction and the quadratic dependence on the oscillatory deposition of Cu/Cu2O can be attributed to the intrinsic nature of the oscillators. For the BZ reaction, the reaction rate constants are kept unchanged during oscillations. The oscillatory system, however, the rate constants are described by the Butler-Volmer kinetics and, therefore, exhibit a potential dependency. In addition, it is necessary to consider the mass transport processes present in the electrochemical system that is absent in the BZ reaction. It is also important to note that the electrochemical oscillators show a transient time series, even though we used the most stable region of the time series. All these characteristics justify the differences observed between the chemical and electrochemical oscillatory systems.
The observed results can contribute, for example, in the synthesis of self-organized materials, in which an accurate selection of frequencies is necessary and, depending on their value, different physicochemical properties are obtained. In addition, the results demonstrate the importance of using multivariate statistical analysis due to the possibility of measuring the interactions between experimental parameters.

Figure 1