Sabrina G. Sobel

Microscopic fluctuations and pattern formation in a supercritical oscillatory chemical system

The spontaneous formation of ordered spatial concentration patterns in an unstirred chemical medium, supported by dissipation of chemical free energy, has been considered often since a pioneering suggestion by Turing and early work by Prigogine et al. and more recent work by Ross et al. involving nonequilibrium thermodynamics. The prototype experimental example is the oscillatory Belousov–Zhabotinsky reaction, in which target patterns of outward-moving concentric rings are readily observed. One widely-studied question is whether “microscopic” fluctuations can nucleate these target centers, or whether a catalytic, nucleating heterogeneous center is required. Vidal and Pagola observed spontaneous initiation with no nucleating particles visible at 6-micron resolution; however Zhang, Forster, and Ross argued theoretically that this is impossible in regimes far from Hopf bifurcations. We describe here an explicit mechanism in a “supercritical regime,” following and near to the low-f Hopf bifurcation in a gener...

Spatial Heterogeneity and Imperfect Mixing in Chemical Reactions: Visualization of Density-Driven Pattern Formation

Imperfect mixing is a concern in industrial processes, everyday processes (mixing paint, bread machines), and in understanding salt water-fresh water mixing in ecosystems. The effects of imperfect mixing become evident in the unstirred ferroin-catalyzed Belousov-Zhabotinsky reaction, the prototype for chemical pattern formation. Over time, waves of oxidation (high ferriin concentration, blue) propagate into a background of low ferriin concentration (red); their structure reflects in part the history of mixing in the reaction vessel. However, it may be difficult to separate mixing effects from reaction effects. We describe a simpler model system for visualizing density-driven pattern formation in an essentially unmixed chemical system: the reaction of pale yellow Fe3

Oregonator Scaling Motivated by the Showalter–Noyes Limit

The Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. We investigate here a new scaling of the Oregonator model of BZ chemical kinetics and use this scaling to elucidate fundamental properties of BZ dynamics. In particular, the Showalter-Noyes criterion for oscillation, that the product [BrO3-][H+] exceeds a critical value, arises naturally as a subcritical Hopf bifurcation in this setting, as does the reduction to a two-variable model. We thus provide chemical explanations of the role of time scales in the BZ reaction.

The complexation of aqueous metal ions relevant to biological applications. 1. Poorly soluble zinc salts and enhanced solubility with added amino acid

Abstract The effect of added amino acid (glycine, alanine and serine) on the solubility of zinc citrate, zinc succinate and zinc oxalate was investigated. Equilibrated solutions were prepared and titrated to endpoint at pH 5.5 with Na2EDTA using Xylenol Orange indicator. In every case, a significant enhancement in solubility was seen as the amino acid increased from 1 to 50 molar excess. The increase was non-linear, and, with zinc succinate, showed saturation effects. In these cases, solution composition may be more complicated than initially thought, including mixed-ligand complexes and increasing percent free metal ion as the proportion of amino acid increases.

The complexation of aqueous metal ions relevant to biological applications: 2. Evaluation of simultaneous equilibria of poorly soluble zinc salts with select amino acids

Abstract Simultaneous equilibria calculations were completed for seven aqueous zinc-ligand systems: zinc citrate plus either glycine, alanine, or serine, and zinc succinate plus either glycine, alanine, or serine, and zinc oxalate plus glycine. Mixed-ligand complexes were predicted for all but the zinc citrate-glycine system, and the proportion tends to peak around 5 molar equivalents of amino acid. Potential bioavailability of zinc appears to be increased by the inclusion of amino acids in solution, roughly in parallel with the increase in solubility of the zinc salt. Therefore, measurement of the change in solubility caused by addition of amino acids to aqueous solution gives qualitative insight to the potential increase in bioavailability of the metal ion, and mixed-ligand complexes are a significant proportion of the complexes present in solution.

The complexation of aqueous metal ions relevant to biological applications. 2. Reactions of copper(II) citrate and copper(II) succinate with selected amino acids

Abstract Addition of amino acids, glycine, alanine, and serine, to poorly soluble copper(II) salts [copper(II) citrate and copper(II) succinate] all increase solubility of the copper(II) salts. Relative increases in solubility follow the polarity trend in the selected amino acids, with serine creating the greatest increase in solubility. Simultaneous equilibria calculations indicate the formation of mixed-ligand complexes in the copper(II) succinate–amino acid systems, the first time such mixed-ligand complexes have been observed. In contrast, mixed-ligand complexes are not predicted in the copper(II) citrate–amino acid systems. Potential bioavailability of copper(II) appears to be increased by the inclusion of amino acids in solution, roughly in parallel with the increase in solubility of the copper(II) salt. Therefore, measurement of the change in solubility caused by addition of amino acids to aqueous solution gives qualitative insight to the potential increase in bioavailability of the metal ion.

The Onset Of Fluctuations In The Ferroin‐Catalyzed Belousov‐Zhabotinski Reaction

We report on an experimental study of the onset of target waves in the ferroin‐catalyzed Belousov‐Zhabotinski (BZ) reaction. In the cardiac electrical system, another excitable medium, spontaneous activity can initiate ventricular tachycardia by interacting with normal or other spontaneous electrical activity to generate spiral waves. In normal hearts, these spiral waves generally break down to cause ventricular fibrillation (VF), leading to sudden cardiac death. Our results for the BZ reaction: (1) centers of target waves are spatially correlated, with the correlation likely due to mixing effects and long range modes arising in the “clocking phase”, (2) activitations begin after concentrations track an equilibrium through a Hopf bifurcation into an unstable “supercritical” state, (3) allowing very small fluctuations can generate targets.