Pulse-Front Propagation and Interaction During the Growth of CdS Nanoparticles in a Gel

Probing the mystery of Liesegang band formation: revealing the origin of self-organized dual-frequency micro and nanoparticle arrays

Periodic precipitation processes in gels can result in impressive micro- and nanostructured patterns known as periodic precipitation (or Liesegang bands). Under certain conditions, the silver nitrate-chromium(vi) system exhibits the coexistence of two kinds of Liesegang bands with different frequencies. We now present that the two kinds of bands form independently on different time scales and the pH-dependent chromate(vi)-dichromate(vi) equilibrium controls the formation of the precipitates. We determined the spatial distribution and constitution of the particles in the bands using focused ion beam-scanning electron microscopy (FIB-SEM) and scanning transmission X-ray spectromicroscopy (STXM) measurements. This provided the necessary empirical input data to formulate a model for the pattern formation; a model that quantitatively reproduces the experimental observations. Understanding the pattern-forming process at the molecular level enables us to tailor the size and the shape of the bands, which, in turn, can lead to new functional architectures for a range of applications.

Understanding the formation of aligned, linear arrays of Ag nanoparticles

A self-assembly process, the Liesegang phenomenon, was applied to align silver nanoparticles in highly periodic linear arrays and two alternative mechanisms were proposed to explain the process.

Growth of nanoparticles and microparticles by controlled reaction-diffusion processes

The synthesis of different sizes of nanoparticles and microparticles is important in designing nanostructured materials with various properties. Wet synthesis methods lack the flexibility to create various sizes of particles (particle libraries) using fixed conditions without the repetition of the steps in the method with a new set of parameters. Here, we report a synthesis method based on nucleation and particle growth in the wake of a moving chemical front in a gel matrix. The process yields well-separated regions (bands) filled with nearly monodisperse nanoparticles and microparticles, with the size of the particles varying from band to band in a predictable way. The origin of the effect is due to an interplay of a precipitation reaction of the reagents and their diffusion that is controlled in space and time by the moving chemical front. The method represents a new approach and a promising tool for the fast and competitive synthesis of various sizes of colloidal particles.

Liesegang patterns engineered by a chemical reaction assisted by complex formation

Liesegang rings based on a chemical reaction, not a conventional precipitation reaction, have been developed by appropriate design of the nucleation dynamics in a system involving complex formation in a matrix. The periodic and concentric rings consisted of well-dispersed Ag nanoparticles with diameters of a few nanometers. The approach modeled here could be applied to form novel micropatterns out of inorganic salts, metal nanoparticles, organic nanocrystals, or polymeric fibers, and it could also offer a scaffold for novel models of a wide variety of reaction-diffusion phenomena in nature.

Transition from rings to spots in a precipitation reaction–diffusion system

We report for the first time the transition from rings to spots with squared/hexagonal symmetry in a periodic precipitation system, which consists of sulfide/hydroxide ions diffusing into a gel matrix containing dissolved cadmium(ii) ions.

Controlling and engineering precipitation patterns

Controlling and engineering chemical structures are the most important scientific challenges in material science. Precipitation patterns from ions or nanoparticles are promising candidates for designing bulk structure for catalysis, energy production, storage, and electronics. There are only a few procedures and techniques to control precipitation (Liesegang) patterns in gel media (e.g., using an electric field, varying the initial concentration of the electrolytes). However, those methods provide just a limited degree of freedom. Here, we provide a robust and transparent way to control and engineer Liesegang patterns by varying gel concentration and inducing impurity by addition of gelatin to agarose gel. Using this experimental method, different precipitation structures can be obtained with different width and spatial distribution of the formed bands. A new variant of a sol-coagulation model was developed to describe and understand the effect of the gel concentration and impurities on Liesegang pattern formation.

Scaling and crossover dynamics in the hyperbolic reaction-diffusion equations of initially separated components

In this paper we investigate the dynamics of front propagation in the family of reactions (nA + mB (k)→ C) with initially segregated reactants in one dimension using hyperbolic reaction-diffusion equations with the mean-field approximation for the reaction rate. This leads to different dynamics than those predicted by their parabolic counterpart. Using perturbation techniques, we focus on the initial and intermediate temporal behavior of the center and width of the front and derive the different time scaling exponents. While the solution of the parabolic system yields a short time scaling as t(1/2) for the front center, width, and global reaction rate, the hyperbolic system exhibits linear scaling for those quantities. Moreover, those scaling laws are shown to be independent of the stoichiometric coefficients n and m. The perturbation results are compared with the full numerical solutions of the hyperbolic equations. The crossover time at which the hyperbolic regime crosses over to the parabolic regime is also studied. Conditions for static and moving fronts are also derived and numerically validated.