Revisited Chaos in a Diffusion–Precipitation–Redissolution Liesegang System

Hamad, Mostafa S.; Safieddine, Abbas; Sultan, Rabih

doi:10.1021/acs.jpca.8b03229

Cited by 14 publications

(8 citation statements)

References 23 publications

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“…(d) Effect of the chemical composition of the gel in the precipitation reaction of silver ions with dichromate ions in gelatin (5 m/v%) (the original Liesegang experiment) and agarose (0.5 m/v%, reproduced with permission from ref , copyright 2009 Elsevier). (e) Dissolution pattern in the cobalt hydroxide systems (reproduced from ref , copyright 2018 American Chemical Society).…”

Section: Liesegang Phenomenon (Periodic Precipitation)mentioning

confidence: 99%

“…A combination of this type of reaction with the diffusion of the reagents in a Liesegang-type experimental setup provides a seemingly moving precipitation zone or a set of bands traveling farther from the junction point (gel surface) of the electrolytes (Figure e). , These systems are the following: (i) cobalt hydroxide (Co 2+ (aq) + 2OH – (aq) → Co(OH) 2 (s), Co(OH) 2 (s) + 6NH 3 → [Co(NH 3 ) 6 ] 2+ (aq)); − (ii) aluminum hydroxide (Al 3+ (aq)+ 3OH – (aq) → Al(OH) 3 (s), Al(OH) 3 (s) + OH – (aq) → [Al(OH) 4 ] − (aq)); , and (iii) mercuric iodide (Hg 2+ (aq) + 2I – (aq) → HgI 2 (s), HgI 2 (s) + 2I – (aq) → [HgI 4 ] 2– (aq)) . In a precipitation–dissolution system, the deterministic chaotic variation of the number of the bands in time was reported …”

Section: Liesegang Phenomenon (Periodic Precipitation)mentioning

confidence: 99%

“…37 In a precipitation−dissolution system, the deterministic chaotic variation of the number of the bands in time was reported. 38 Empirical Rules. Intriguing characteristics of the Liesegang phenomenon include the spontaneous formation of intricate geometrical patterns, which have motivated researchers to derive a mathematical law underlying their geometrical regularity.…”

Section: ■ Introductionmentioning

confidence: 99%

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Pattern Formation in Precipitation Reactions: The Liesegang Phenomenon

2019

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Pattern formation is a frequent phenomenon in physics, chemistry, biology, and materials science. Bottom-up pattern formation usually occurs in the interaction of the transport phenomena of chemical species with their chemical reaction. The oldest pattern formation is the Liesegang phenomenon (or periodic precipitation), which was discovered and described in 1896 by Raphael Edward Liesegang, who was a German chemist and photographer who was born 150 years ago. The purpose of this feature article is to provide a comprehensive overview of this type of pattern formation. Liesegang banding occurs because of the coupling of the diffusion process of the reagents with their chemical reactions in solid hydrogels. We will discuss several phenomena observed and discovered in the past century, including reverse patterns, precipitation patterns with dissolution (due to complex formation), helicoidal patterns, and precipitation waves. Additionally, we will review all existing models of the Liesegang phenomenon including pre- and postnucleation scenarios. Finally, we will highlight several applications of periodic precipitation.

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Section: Liesegang Phenomenon (Periodic Precipitation)mentioning

confidence: 99%

Section: Liesegang Phenomenon (Periodic Precipitation)mentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

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Pattern Formation in Precipitation Reactions: The Liesegang Phenomenon

2019

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“…Many kinds of chemical LPs have been reported so far, and they typically consist of periodic spatial patterns of inorganic salt precipitates (e.g. copper chromate, − silver chromate, − and cobalt hydroxide − ). LP is usually formed when an aqueous solution (called the outer electrolyte) containing metal cations comes into contact with an anion-containing hydrogel (the inner electrolyte) .…”

Section: Introductionmentioning

confidence: 99%

Modification of the Matalon–Packter Law for Self-Organized Periodic Precipitation Patterns by Incorporating Time-Dependent Diffusion Flux

2021

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Spontaneous pattern formation is common in both inanimate and living systems. Although the Liesegang pattern (LP) is a well-studied chemical model for precipitation patterns, various recent LP systems based on artificial control could not be easily evaluated using classical tools. The Matalon–Packter (MP) law describes the effect of the initial electrolyte concentration, which governs the diffusion flux (F diff), on the spatial distribution of LP. Note that the classical MP law only considers F diff through the initial concentration of electrolytes, even though it should also depend on the volume of the reservoir used for the outer electrolyte because of the temporal change in the concentration therein due to diffusion. However, there has been no report on the relationship between the MP law, the reservoir volume, and F diff. Here, we experimentally demonstrated and evaluated the effect of the reservoir volume on LP periodicity according to the classical MP law. Numerical simulations revealed that the reservoir volume affects the temporal modulation of F diff. By expressing the MP law as a function of estimated F diff after a certain period of time, we provide a uniform description of the changes in periodicity for both small and large reservoir volumes. Such modification should make the MP law a more robust tool for studying LP systems.

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“…To date, periodic precipitation reactions have been studied for a wide range of chemical substances, a classification of their resulting periodic structures is given, and significant progress has been made in the theoretical understanding of this phenomenon; namely, main physicochemical mechanisms responsible for the formation of the structures observed are considered, theoretical approaches to their explanation are discussed, and phenomenological models are proposed to describe the formation of not only simple one-dimensional (1D) and two-dimensional Liesegang structures but also much more sophisticated, nontrivial ones (dislocations, helices, etc. ) − …”

Section: Introductionmentioning

confidence: 99%

Formation of Liesegang Structures under the Conditions of the Spatiotemporal Reaction of Polymer-Analogous Transformation (Salt → Base) of Chitosan

et al. 2020

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This paper presents the results of our study of the diffusion front progression of OH − ions in the bulk of a flat layer of the salt chitosan form during the course of the chemical reaction of the polymer-analogous salt → base transformation, accompanied by the formation of a water-insoluble polymeric phase as a gel film with its structure of concentric rings or tangential bands. Using scanning electron microscopy and polarization microscopy, structural and morphological features of these periodic formations were visualized. Physicochemical parameters and spatiotemporal mass transfer characteristics were obtained. The process under study is shown to obey the classical laws of ion-exchange reactions, and the formation kinetics and the ratio of the positions of periodic structures are described by the laws characteristic of the Liesegang phenomenon. The average diffusion coefficients of hydroxide ions in the periodic formations calculated, considering the protonation degree of amino groups, were found to be no more than a decimal order of magnitude lower than those in an aqueous solution. This confirms the fact of swelling of the formed chitosan base and the existence of a gel film, in whose liquid phase diffusion occurs.

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Revisited Chaos in a Diffusion–Precipitation–Redissolution Liesegang System

Cited by 14 publications

References 23 publications

Pattern Formation in Precipitation Reactions: The Liesegang Phenomenon

Pattern Formation in Precipitation Reactions: The Liesegang Phenomenon

Modification of the Matalon–Packter Law for Self-Organized Periodic Precipitation Patterns by Incorporating Time-Dependent Diffusion Flux

Formation of Liesegang Structures under the Conditions of the Spatiotemporal Reaction of Polymer-Analogous Transformation (Salt → Base) of Chitosan

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