Kinetics of the formation of Liesegang rings

Кузьмин, В. С.; Gadzaov, A. F.; Tytik, D. L.; Busev, S. A.; Ревина, А. А.; Высоцкий, В. В.

doi:10.1134/s0022476613080167

Cited by 7 publications

(20 citation statements)

References 2 publications

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“…Literature data on all observed types of Liesegang rings [2,4] were analyzed [3], and a classification was proposed for the structures' ring type precipitates, with this classification being based on the hierarchy of functions e x , x λ , lnx, and lnlnx that are space argu ments of the solution of the one dimensional diffusion equation for different sequences of ring positions.…”

Section: This Article Is Presented In Commemoration Of Re Liesegangmentioning

confidence: 99%

“…Long term (6 months) monitoring of the process in test tubes with Liesegang rings [3] demonstrated a nontrivial dynamics of the system. For example, after the formation of all rings in the test tubes (in more than 12 days), a transparent solution in the gaps between the rings became turbid, thereby indicating the formation of nanoparticles.…”

Section: This Article Is Presented In Commemoration Of Re Liesegangmentioning

confidence: 99%

“…Preliminary dynamic light scattering (DLS) stud ies [3] showed the presence of nanoparticles in the vicinity of the zones in which Liesegang rings were formed. The measurement of time variations in the intensity of light scattered by nanoparticles with dif ferent sizes during the formation of Liesegang rings indicated periodic physicochemical processes occur ring at the microscopic level.…”

Section: This Article Is Presented In Commemoration Of Re Liesegangmentioning

confidence: 99%

“…In [3], a kinetic study was performed for the forma tion of Liesegang rings as a macroscopic process, which was continuously registered for 12 days. The deep experimental data confirmed, in particular, that variations in the distances between neighboring rings are described by a geometric series with a certain geo metric ratio.…”

Section: Introductionmentioning

confidence: 99%

“…As a first approximation, a hierarchy of diffusion equations comprising nonlinear functions as time and space arguments was proposed for simulating the effect [3]. This approach resulted in determining effective parameters for describing the formation mechanisms of Liesegang rings via nonlinear (hetero geneous) properties of a medium in which the process is realized.…”

Section: Introductionmentioning

confidence: 99%

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Formation kinetics of nanoparticles as the basis for simulating the generation mechanism of Liesegang rings in gels

et al. 2014

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An approach has been proposed for determining the space-time parameters of the formation pro cess of Liesegang rings. This approach relates the processes of the formation of nanoparticles and dense peri odic precipitates from them. Dynamic light scattering is employed to reveal periodic variations in the inten sity of light scattered by nanoparticles with different sizes, from which Liesegang rings are formed. A relation ship between the periods of the variations in the intensity of light scattered by nanoparticles (microscopic process) and the times of the formation of Liesegang rings as a whole (macroscopic process) has been found.

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Section: This Article Is Presented In Commemoration Of Re Liesegangmentioning

confidence: 99%

Section: This Article Is Presented In Commemoration Of Re Liesegangmentioning

confidence: 99%

Section: This Article Is Presented In Commemoration Of Re Liesegangmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Formation kinetics of nanoparticles as the basis for simulating the generation mechanism of Liesegang rings in gels

et al. 2014

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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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Role of Nuclei in Liesegang Pattern Formation: Insights from Experiment and Reaction-Diffusion Simulation

et al. 2018

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Many types of periodic patterns can spontaneously form in nature across wide spatiotemporal scales. Construction of a chemical model that mimics these periodic patterns are of considerable interest from both scientific and technological viewpoints. The Liesegang phenomenon is one of the chemical models to form periodic patterns with well-defined periodicity. However, the parameters that influence the mechanism and resultant pattern geometry are not completely known. In this study, we use surface chemistry methods to evaluate the influence of nucleation threshold on the geometry of Liesegang patterns. Cysteine was used as an additional ligand for the precursors (Agn nuclei and/or Ag nanoparticles in the present system) to reduce their surface free energy and thus the nucleation free energy. As a result, the formed Liesegang patterns had smaller spacing coefficient (i.e., finer periodic patterns), a phenomenon that was also reproduced using reaction-diffusion simulation with lowered nucleation threshold. The small spacing coefficient at lowered nucleation threshold was discussed in terms of a slower rate of Ostwald ripening. Similar control of the nucleation threshold through surface chemistry can be applied to various precipitation systems, as well as gaining insight into the comprehensive mechanism underlying various animate and inanimate patterns formed in nature.

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Kinetics of the formation of Liesegang rings

Cited by 7 publications

References 2 publications

Formation kinetics of nanoparticles as the basis for simulating the generation mechanism of Liesegang rings in gels

Formation kinetics of nanoparticles as the basis for simulating the generation mechanism of Liesegang rings in gels

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

Role of Nuclei in Liesegang Pattern Formation: Insights from Experiment and Reaction-Diffusion Simulation

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