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The Emergence of Order in Space
Published in Pier Luigi Gentili, Untangling Complex Systems, 2018
The earth has provided and still provides chemical environments that mimic those employed by Liesegang to obtain periodic precipitations. The Liesegang rings are obtained in closed systems, in the presence of a gel that prevents convective motions of the fluid and allows only the diffusion of the reactants, one of which is placed on the gel.22 Therefore, the optimal geological environment for observing Liesegang rings should be a homogeneous gelatinous substrate with pronounced boundaries and in physical contact with a chemical reagent. Many patterns resembling Liesegang rings are found in quartz in its many natural forms. Beautiful examples are the agates (an agate is shown in Figure 9.28). Some geologists justify the presence of distinct layers in agates, by assuming that all quartz on earth was at one time a silica hydrogel. This hypothesis was reinforced over one hundred years ago when a vein of gelatinous silica was found in the course of deep excavations through the Alps for the Simplon Tunnel, which is a railway tunnel that connects Italy and Switzerland (Henisch 1988). However, there are some geologists who believe that the formation of rings, like those in agates, derive from the deposition of layers of silica filling voids in volcanic vesicles or other cavities. Each agate forms its own pattern based on the original cavity shape. The layers form in distinct stages and may fill a cavity completely or partially. When the filling is not complete, a hollow void can host crystalline quartz growth, and the agate becomes the outer lining of a geode (in the agate shown in Figure 9.28, there is a small geode indicated by the black arrow).
Micro and Nanopatterning
Published in Allen J. Bard, Michael V. Mirkin, Scanning Electrochemical Microscopy, 2022
Bard et al. described a novel SECM-based surface patterning of fluorescent molecules onto a solid substrate by forming covalent bonds through a click chemistry reaction.132 Patterned images could be observed by their fluorescence, and the formation of Liesegang rings in the diffusion-reaction system were also detected. Click chemistry was used also by others as described in the next section.
Modelling non-equilibrium self-assembly from dissipation
Published in Molecular Physics, 2020
A. Arango-Restrepo, Daniel Barragán, J. Miguel Rubi
Gelation and Liesegang banding can take place simultaneously as has been shown for example in the case in which the gel is deformed by the action of mechanical stresses while Liesegang patterns form in the gel [47]. Currently, there is a great deal of interest in the control of micro-architecture and porosity of hydrogel structures for medical applications [7–12], and to the synthesis of self-assembled particles for technological purposes [16–18]. In Liesegang ring formation, the BB and intermediate structures diffuse, react and agglomerate in a gel medium wherein the nature and the architecture play a key role in formation kinetics. Gelation thus determines the formation of Liesegang rings and their shape. How to model the movement of the constituents, intermediate structures, and other components through the gel under the action of a driven force such as a chemical potential difference, a temperature gradient or an electric field still remains an open problem. The model has to integrate the architecture of the gel with that of the formed structures to describe the motion of the components through the gel medium.