Morphological Characteristics of Liesegang Rings and Their Simulations

Krug, Hans-Jürgen; Brandtstädter, Hermann

doi:10.1021/jp991092l

Cited by 64 publications

(59 citation statements)

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“…Liesegang rings are produced when diffusion is coupled with chemical reaction, unlike the process that we examine here. 17,18 It is also worth emphasizing that the size scale of Liesegang rings is typically on the order of millimeters, † Current address: Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011. First (a), a droplet containing solute in volatile solvent is placed in a confined geometry, in this example between crossed cylinders of freshly cleaved single crystals of mica.…”

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Patterns Formed by Droplet Evaporation from a Restricted Geometry

2005

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The spontaneous emergence of patterns at surfaces is a recurring theme in modern chemistry. Here we are concerned with patterns formed from solvent evaporation, leaving nonvolatile solute left behind. Work in this field has been dominated by the quest for definitive theoretical physical interpretation. [1][2][3][4][5][6][7] Too little attention has been given to the synthesis of patterns of high fidelity and regularity. Here we report a new method to achieve hundreds of concentric rings with definite spacing; each ring is approximately nanometers high and micrometers wide. This simple yet novel approach enables one to produce and organize surface patterns in a well-ordered gradient fashion. The key improvement over past procedures is that droplet evaporation is guided through use of a restricted geometry (Figure 1a), rather than allowing solvent evaporation from a drop sitting on a single solid surface, as in copious past work. 1-14 Tentatively, we attribute the reason for improvement to the fact that evaporation is constrained to occur at the droplet edges ( Figure 1b) rather than allowed over the entire droplet area as in the traditional approach, in which droplets evaporate from a single surface. The main point is that patterns of remarkably high fidelity and regularity result.A polymer was selected as the nonvolatile component. The selection of this polymer was motivated by the relevance of conjugated polymers to potential optoelectronic devices 15 but is not believed to be essential to the results presented below. The linear conjugated polymer, poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene], end-capped with dimethyl phenyl (MEH-PPV), was dissolved in toluene at concentration 0.5 mg/mL. The MEH-PPV employed here had the molecular mass of 50-300 kg/mol. To maximize homogeneity of surface chemistry and topography, single crystals of muscovite mica (ASTM V-2 grade) were cleaved, coated with a reflective film of silver on the backside for subsequent visualization of the contact spot by optical interferometry, and glued onto a cylindrical quartz mount having a diameter of ∼1 cm. These methods are adapted from the surface forces apparatus. 16 The two mica sheets were then placed about 500 µm apart with the cylinders at right angles to one another, and a drop of MEH-PPV solution was inserted (Figure 1a). Subsequently, the two curved mica sheets were brought into contact so that they touched; at the apex the geometry was equivalent to that of a sphere-on-flat. As shown in Figure 1b, this produced a capillary-held polymer solution (capillary bridge) with a diameter of ca. 6-7 mm, depending on the amount of liquid loaded. Experiments were performed at room temperature inside a sealed chamber containing the hygroscopic chemical, phosphorus pentoxide (P 2 O 5 ). Due to the wetting characteristics of toluene, a concave capillary bridge resulted.The evaporation generally took hours to complete. Afterward, the two surfaces were separated and examined by optical microscopy in the transmission mode (OM, Olympus, B...

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Patterns Formed by Droplet Evaporation from a Restricted Geometry

2005

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“…This characteristic pattern is due to the high flux of dissolved inter-band material that favours growth on both margins of the band, followed by intra-band ripening. Models that combine both pre-nucleation and post-nucleation mechanisms are also available [15,16,18].…”

Section: Liesegang Patterns: General Considerationsmentioning

confidence: 99%

Self-organized rhythmic patterns in geochemical systems

L’Heureux

2013

Phil. Trans. R. Soc. A.

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Chemical oscillating patterns are ubiquitous in geochemical systems. Although many such patterns result from systematic variations in the external environmental conditions, it is recognized that some patterns are due to intrinsic self-organized processes in a non-equilibrium nonlinear system with positive feedback. In rocks and minerals, periodic precipitation (Liesegang bands) and oscillatory zoning constitute good examples of patterns that can be explained using concepts from nonlinear dynamics. Generally, as the system parameters exceed some threshold values, the steady (time-independent) state characterizing the system loses its stability. The system then evolves towards other time-dependent solutions (‘attractors’) that may have an oscillatory behaviour or a complex chaotic one. In this review, we describe many of these pattern types taken from a variety of geological environments: eruptive, sedimentary, hydrothermal or metamorphic. One particular example (periodic precipitation of pyrite bands in an evolving sapropel sediment) is presented here for the first time. This will help in convincing the reader that the tools of nonlinear dynamics may be useful to understand the history of our planet.

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“…The rings also show a departure from circular symmetry, with deformations accompanied by ring breaking. Ring defects generally include ring breaking and segmentation [21], branch points, blank alleys and anastomoses [22]. Such imperfections were attributed to inhomogeneities in the gel texture [23], re-dissolution of precipitate [24], competitive particle growth [21], and other possible mechanical disturbances.…”

Section: Experiments I (Only Experiments In Set I)mentioning

confidence: 99%

“…Note however that spirals (in 2D) [25][26][27] and helicoidal structures (in 3D) [28,29] have been reported. Ring dislocations and spiral structures have been modeled theoretically [29,30,22].…”

Section: Experiments I (Only Experiments In Set I)mentioning

confidence: 99%