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

Abstract

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.

Evolution of Micron-Spaced Patterns within Precipitating Patterns of In Situ Synthesized Silver Nanoparticles in a Nanodot-Embedded PVA/PVP Film

“…26 The reaction−diffusion equations of this system can be written as follows K 2 , that is, [Ag-NP]* in these systems plays a very important role, as evident from the previous experimental and simulation studies. 13,22,32 Surface ligands such as thiol groups dictate the nucleation energy. K 2 gets dramatically reduced in the presence of such ligands and results in a decrease in the spacing coefficient.…”

“…To overcome the above limitation present in ionic species, we wished to investigate a novel Liesegang mechanism involving the in situ formation of metallic nanoparticles in a thin polymer film. The precipitation behavior of presynthesized oppositely charged nanoparticles has been investigated in millimeter-thick agarose gel. , Very recently, the precipitation behavior of silver nanoparticles (Ag NPs) has been studied by enabling the contact of agarose gel doped with silver ions with the surface of gelatin containing a reducing agent . Moreover, periodic patterns of plasmonic nanoparticles are of greater importance due to their application in surface plasmon resonance (SERS)-based sensors, electrochemical energy storage, and others. , In this work, commonly used polymer films, polyvinyl alcohol (PVA) and polyvinyl pyrrolidone (PVP), are chosen to investigate the pattern formation.…”

“…20,21 Very recently, the precipitation behavior of silver nanoparticles (Ag NPs) has been studied by enabling the contact of agarose gel doped with silver ions with the surface of gelatin containing a reducing agent. 22 Moreover, periodic patterns of plasmonic nanoparticles are of greater importance due to their application in surface plasmon resonance (SERS)-based sensors, electrochemical energy storage, and others. 23,24 In this work, commonly used polymer films, polyvinyl alcohol (PVA) and polyvinyl pyrrolidone (PVP), are chosen to investigate the pattern formation.…”

Regular-Type Liesegang Pattern of AgCl in a One-Dimensional System

“…By changing the shape of the gel, it is possible to yield gel materials with periodic Co(OH) 2 precipitates with one [ 2 ], two [ 3 ] and three dimensions [ 4 ]. In addition to Co(OH) 2 , gels with various materials include hydroxide salts [ 5 , 6 ], chromate and dichromate salts [ 7 , 8 , 9 , 10 ], phosphate salts [ 11 , 12 ], metal nanoparticles [ 13 , 14 , 15 ] and polymers [ 16 , 17 ].…”

Fine tuning of pattern selection in the cadmium–hydroxide-system

“…In heterogeneous reactions, the growth of solid particles inherently contains the necessary feedback, therefore precipitate reactions may result in nontrivial spatial structures 7,8 . In case of Liesegang patterns the externally imposed concentration gradient of one of the components in an appropriately chosen hydrogel medium drives a reaction that leads to periodic zones of precipitates: orderly spaced bands in a one-dimensional configuration and rings in a twodimensional [9][10][11][12] . A series of mathematical formulae to describe this periodic and/or monotonic spatial distribution of the precipitate stripes-spacing law 13 , width law 14 , time law 15 , and the Matalon-Packter-law 16 -are associated with the stationary structures that originate from the temporal evolution of the governing concentration gradients 17 .…”