NONLINEAR BEHAVIOR IN BRAY-LIBHAFSKY CHEMICAL REACTION

J. Chil. Chem. Soc., 53, Nº 3 (2008) NONLINEAR BEHAVIOR IN BRAY-LIBHAFSKY CHEMICAL REACTION JIE REN, JINZHANG GAO*, JIE QU, XIAOXIA WEI, XIAODONG CHEN, WU YANG (College of Chemistry and Chemical Engineering, Northwest Normal University, Lanzhou, 730070, P. R. China) (Received: January 16, 2008 - Accepted: June 17, 2008) ABSTRACT The Bray-Liebhafsky reaction exhibits different nonlinear behaviors during the iodate catalyzed decomposition of acidic hydrogen peroxide in the different conditions. Both the chaotic and regular oscillations were observed. The largest Lyapunov exponent (λL), the power spectrum and the log(P)-log(f) dependence for power spectrum were used to evaluate these nonlinear behaviors. The effect of initial concentration of reactants on the types of oscillations and the initial potential (E o) were discussed in detail. The possible mechanism of the Bray-Liebhafsky reaction was also approached in this work. Keywords: Bray-Liebhafsky reaction; largest Lyapunov exponent; power spectrum; mechanism INTRODUCTION The nonlinear chemical phenomena known as “oscillating chemical reaction” are complex dynamic systems that have so far been examined mainly in physico-chemical terms in order to elucidate the complex mechanism. Thus, various dynamics regimes including regular oscillations, periodic doubling, quasi-periodicity and deterministic chaos have been explored with a view to their characterization in recent years [1-4]. In general, a system exhibits different nonlinear phenomena because of the control parameters. Changing the control parameters may lead to the appearance of simple, single-peak periodic oscillations, complex multipeak periodic oscillations and chaotic dynamics. Transitions between these oscillations are caused by various bifurcations. So it is very important for experiments to identification of bifurcations, because it allows us to predict the value of control parameter at which appropriate type of oscillations or chaos occurs [5-6]. Several oscillating chemical systems, such as the Belousov-Zhabotinsky (B-Z) system, the Cu(II)-catalysed reaction between hydrogen peroxide and sodium thiocyanate in alkaline medium, the Bray-Libhafsky (B-L) [7] and Briggs-Rauscher (B-R) [8, 9] systems have been studied. The most widely known and studied oscillating chemical is based on the B-Z reaction, which involves the oxidation of an organic substrate by bromate ion in sulfuric acid medium. However, over 30 years before the discovery of B-Z oscillating reaction, Bray [7] observed oscillations during the B-L nonlinear system. The B-L oscillating chemical reaction involves the decomposition of hydrogen peroxide in the presence of iodate ion in acidic medium. The overall chemical reaction can be described simply by the following process: 2H2O2(aq)→2H2O(aq) +O2(g) Although the B-L reaction seems to be simpler than the B-Z system, it is not easy to describe the mechanism. Just due to the simple system having fewer variables and the detection of product (oxygen) being difficult, there have been few papers of the analysis of mechanism of such reaction [10, 11]. Matsuzaki [12] proposed a mechanism involving I3-; the question is how to verify it by experiment. Schmitz and Rooze [13] assumed that the HOI should be oxidized at fictitious equilibrium state, meanwhile, Sharma and Noyes [11] considered further that free radical may be formed in the redox process. Up to now there is an open question. For studying nonlinear chemical system, the following methods were often used to describe them: the largest Lyapunov exponent (λL), the time series curve, power spectrum and the signal calculated from power spectrum, phase diagram, Poincare mapping and so on [14, 15]. The objective of the present paper is to describe the nonlinear phenomena of B-L oscillating system and discuss the effect concentration of reactants in detail. EXPERIMENTAL Chemicals All chemicals were of analytical-reagent grade and used as received. The solution of hydrogen peroxide was made daily and standardized with the KMnO4 solution; and then kept in a black polyethylene bottle to avoid decomposition. Solution of KIO3 was freshly made just before the use and kept in refrigerator. Doubly distilled and deionized water was used throughout. 1620 e-mail: Apparatus The oscillating assembly comprised a 50 ml glass reaction vessel fitted with a Model CS-501 thermostat (Shanghai Pujiang Analytical Instrumental Factory, China) and a Model ML-902 magnetic stirrer (Shanghai Pujiang Analytical Instrumental Factory, China) for homogenization. A CHI 832 electrochemical analytical instrumental (Shanghai Chenhua Instrumental Company, China) was used to record the potential change. A Type 213 platinum electrode was used as working electrode, a Type 213 platinum electrode as the counter electrode and a Type 217 saturated calomel electrode as the reference electrode against which all potentials were reported. Procedure Potentiometric measurements: Potentiometric measurements were performed in a closed thermostatregulated glass container equipped with a magnetic stirrer. The stirring rate was kept at 800 rpm. All of the experiments were performed at 303±0.05K. The reagents were respectively maintained as the following concentrations: KIO3, 0.05-0.3 M, 5 mL; H2O2, 0.1-0.6 M, 5 mL; H2SO4, 0.2-1.0 M, 5 mL. RESULTS AND DISCUSSION 3.1 Results: The largest Lyapunov exponent (λL) gives a quantitative measure for the chaotic regime. The value is defined as [16,17] Where ΔL oi is the distance between nearby trajectories in the phase space of a system at time t oi and ΔLi is the value at time ti. Due to the value of λL characterizing the divergence of nearby trajectories in the phase space, a plenty of nonlinear behaviors (regular oscillation or chaos) in the system could be expressed. In general, when the value of λL is larger than 0.01, the behaviors of oscillating system approach to chaos. Figure 1 shows the nonlinear behaviors observed in the B-L chemical system, in which the values of λL are -0.000475 in Figure 1a and 0.038893 in Figure 1b, respectively. That is to say, the oscillating behavior of system is changing from regular oscillation to chaos. When the above results in Figure 1 were reexpressed by using power spectrum, the clear time series for chaos or periodic oscillations were obtained. That is to say, for a periodic oscillation, there are only limited frequencies in the power spectrum, whereas for chaos, there are incalculable frequencies. Over the main frequency fo the power spectrum is characterized by log(P)-log(f). When using this relationship to characterize the results in Figure 2, the new profiles are showing in Figure 3, here the value of tg(α) indicates the type of nonlinear behaviors (regular oscillation or chaos). Usually, when the value of tg(α) approaches 1, the oscillating behavior of system could be considered as the regular oscillation and when it less than 1 far away the behavior of system should (...truncated)