Oscillations of the Bray−Liebhafsky Reaction at Low Flow Rates in a Continuous Flow Stirred Tank Reactor

Immobilization and Characterization of RuCl2(PPh3)3 Mesoporous Silica SBA-3

The five-fold coordinated ruthenium (II) catalyst RuCl2(PPh3)3 is heterogenized on the surface of amine functionalized mesoporous silica material SBA-3 and studied by BET, XRD and 31P CP-MAS solid-state NMR. The spectra indicate the replacement of one or two of the triphenyl-phosphine groups in the course of the grafting. To distinguish between both possibilities two-dimensional J-resolved 31P MAS solid-state NMR combined with quantum chemical calculations is employed. The changes of the scalar coupling pattern between the neat catalyst and the immobilized catalyst suggest the replacement of two of the PPh3-groups by coordinative bonds to the amine-functions of the linker. DFT calculations reveal the absence of two chemically and magnetically equivalent phosphines and confirm the replacement of two PPh3-groups. This finding is similar to the results observed for the binding of the rhodium in the Wilkinson's catalyst, despite the different coordination of the metals (four-fold versus five-fold), the presence of two chlorine ligands and the different transition metal.

Structures of chaos in open reaction systems

By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions.

Complex and chaotic oscillations in a model for the catalytic hydrogen peroxide decomposition under open reactor conditions

Numerous periodic and aperiodic dynamic states obtained in a model for hydrogen peroxide decomposition in the presence of iodate and hydrogen ions (the Bray-Liebhafsky reaction) realized in an open reactor (CSTR), where the flow rate was the control parameter, have been investigated numerically. Between two Hopf bifurcation points, different simple and complex oscillations and different routes to chaos were observed. In the region of the mixed-mode evolution of the system, the transitions between two successive mixed-mode simple states are realized by period-doubling of the initial state leading to a chaotic window in which the next dynamic state emerges mixed with the initial one. It appears in increasing proportions in concatenated patterns until total domination. Thus, with increasing flow rate the period-doubling route to chaos was obtained, whereas with decreasing flow rate the peak-adding route to chaos was obtained. Moreover, in very narrow regions of flow rates, chaotic mixtures of mixed-mode patterns were observed. This evolution of patterns repeats until the end of the mixed-mode region at high flow rates that corresponds to chaotic mixtures of one large and many small amplitude oscillations. Starting from the reverse Hopf bifurcation point and decreasing the flow rate, simple small amplitude sinusoidal oscillations were encountered and then the period-doubling route to chaos. With a further decreasing flow rate, the mixed-mode oscillations emerge inside the chaotic window.