Travelling waves in an open cubic autocatalytic system

A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter D _A /D _B (D _A ,D _B being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that 4, a result confirmed by numerical integrations of an initial-value problem. For values of larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration.     

Travelling waves in an open quadratic autocatalytic chemical system

The travelling waves that are initiated in an autocatalytic reaction–diffusion system with quadratic rate law are considered. The system is modelled on the basis of a continuous-flow, unstirred reactor. The model is used to determine whether any of the complex structures reported for cubic autocatalytic reaction–diffusion systems can also be observed in the quadratic model. This is found not to be the case. The range of behaviour of the quadratic model is much less complex, with only front waves being initiated under the necessary conditions, which are established. There are, however, some unusual transient features to be found after the initial passage of the wave front. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Mechanism of revert spacing in a PbCrO4 Liesegang system

Periodic precipitation of sparingly soluble salts yields parallel Liesegang bands in 1D whose spacings obey either one of two known trends. The overwhelming trend is an increase in spacing as we move away from the junction, while some systems display a decrease in spacing as the bands get further away from the interface. The latter trend is much less common and is known as the revert spacing law. Whereas the direct (normal) spacing law is generally well-understood, the revert spacing trend has not been explicitly and distinctly elucidated. In this paper, we propose a mechanism of revert spacing governed by the adsorption of the diffusing CrO4(2?) ions on the formed PbCrO4 Liesegang bands and carry out a set of experiments that support the suggested scenario. It is shown that this adsorption increases as the band number (n) increases in revert spacing systems, while it decreases as n increases in direct spacing systems. It is concluded that this correlation in opposite directions decisively reveals the role of adsorption in the mechanism. The attraction between the CrO4(2?) and Pb(2+) in the gel causes the bands to form gradually closer and closer. Secondary structure (thinner bands formed within the main ones) obtained under some conditions is discussed in view of the light sensitivity of the chromate ion and the stability of the lead chromate sol.     

Density and energy relaxation in an open one-dimensional system

A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically. In this model, the random walkers interact through excluded volume interaction (single-file system); and the total number of walkers in the lattice can fluctuate because of exchange with a bath. In addition, the movement of the random walkers is biased by an external perturbation. Two models for the latter are considered: (1) an inverse potential (V proportional, variant 1/r), where r is the distance between the center of the perturbation and the random walker and (2) an inverse of sixth power potential (V proportional, 1/r6). The calculated density of the walkers and the total energy show interesting dynamics. When the size of the system is comparable to the range of the perturbing field, the energy relaxation is found to be highly nonexponential. In this range, the system can show stretched exponential (e-(t/taus)beta) and even logarithmic time dependence of energy relaxation over a limited range of time. Introduction of density exchange in the lattice markedly weakens this nonexponentiality of the relaxation function, irrespective of the nature of perturbation.     

Liesegang patterns: Estimation of diffusion coefficient and a plausible justification for colloid explanation

The Liesegang phenomenon is interpreted as a moving boundary problem. The existing time law, spacing law, and width law are revisited and reformulated on the basis of the new scenario. A better understanding of the basic facts associated with pattern formation is made possible with the new concept. The phenomenon is explained on the basis of colloidal kinetics. Diffusion coefficients of the outer electrolyte in the gel for various experiments in the literature are calculated. The diffusion coefficients so calculated range from 1.792-5.996᎒^-10 m² s^-1. It is suggested that such values confirm the fast colloidal dynamics during the process of periodic precipitation pattern formation.     

Secondary structure of periodic precipitation patterns in gelatin

The primary and secondary Liesegang rings in the silver dichromate-gelatin system were studied microscopically and microdensitometrically. The close mutual connection of both structures is evident from these measurements. Examination of the temporal sequence of ring development showed that the formation of fine secondary rings precedes the growth of primary precipitation patterns. The experimental results confirm the view that the formation of both primary and secondary rings has a common basis and pattern.     

Water between plates in the presence of an electric field in an open system

Molecular dynamics simulations of water at 298 K and 1 atm of pressure are used to investigate the electric-field dependence of the density and polarization density of water between two graphite-like plates of different sizes (9.8 x 9.2 and 17.7 x 17.2 A) in an open system for plate separations of 8.0, 9.5, and 16.4 A. The interactions with water were tuned to "hard-wall-like" and "normal" C-O hydrophobic potentials. Water between the larger plates at 16.4 A separation is layered but is metastable with respect to capillary evaporation at zero field (Bratko, D.; Curtis, R. A.; Blanch, H. W.; Prausnitz, J. M. J. Chem. Phys. 2001, 115, 3873). Applying a field decreases the density of the water between the plates, in apparent contradiction to thermodynamic and integral equation theories of bulk fluid electrostriction that ignore surface effects, rendering them inapplicable to finite-sized films of water between hydrophobic plates. This suggests that the free energy barrier for evaporation is lowered by the applied field. Water, between "hard-wall-like" plates at narrower separations of 9.5 A and less, shows a spontaneous but incomplete evaporation at zero field within the time scale of our simulation. Evaporation is further enhanced by an electric field. No such evaporation occurs, on these time scales, for the smaller plates with the "hard-wall-like" potential at a separation of 8.0 A at zero field, signaling a crossover in behavior as the plate dimension decreases, but the water density still diminishes with increasing field strength. These observations could have implications for the behavior of thin films of water between surfaces in real physical and biological systems.     

Design of equidistant and revert type precipitation patterns in reaction-diffusion systems

In the past years considerable attention has been devoted to designing and controlling patterns at the microscale using bottom-up self-assembling techniques. The precipitation process proved itself to be a good candidate for building complex structures. Therefore, the techniques and ideas to control the precipitation processes in space and in time play an important role. We present here a simple and technologically applicable technique to produce arbitrarily shaped precipitation (Liesegang) patterns. The precipitation process is modelled using a sol coagulation model, in which the precipitation occurs if the concentration of the intermediate species (sol) produced from the initially separated reactants (inner and outer electrolytes) reaches the coagulation threshold. Spatial and/or temporal variation of this threshold can result in equidistant and revert (inverse) type patterns in contrast to regular precipitation patterns, where during the pattern formation a constant coagulation threshold is supposed and applied in the simulations. In real systems, this threshold value may be controlled by parameters which directly affect it (e.g. temperature, light intensity or ionic strength).     

Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability

We describe a new type of solitary waves, which propagate in such a manner that the pulse periodically disappears from its original position and reemerges at a fixed distance. We find such jumping waves as solutions to a reaction-diffusion system with a subcritical short-wavelength instability. We demonstrate closely related solitary wave solutions in the quintic complex Ginzburg-Landau equation. We study the characteristics of and interactions between these solitary waves and the dynamics of related wave trains and standing waves.     

Pattern formation and self-organization in a simple precipitation system

Various types of pattern formation and self-organization phenomena can be observed in biological, chemical, and geochemical systems due to the interaction of reaction with diffusion. The appearance of static precipitation patterns was reported first by Liesegang in 1896. Traveling waves and dynamically changing patterns can also exist in reaction-diffusion systems: the Belousov-Zhabotinsky reaction provides a classical example for these phenomena. Until now, no experimental evidence had been found for the presence of such dynamical patterns in precipitation systems. Pattern formation phenomena, as a result of precipitation front coupling with traveling waves, are investigated in a new simple reaction-diffusion system that is based on the precipitation and complex formation of aluminum hydroxide. A unique kind of self-organization, the spontaneous appearance of traveling waves, and spiral formation inside a precipitation front is reported. The newly designed system is a simple one (we need just two inorganic reactants, and the experimental setup is simple), in which dynamically changing pattern formation can be observed. This work could show a new perspective in precipitation pattern formation and geochemical self-organization.     

Fabrication of magnetically separable mesostructured silica with an open pore system

Magnetically separable mesostructured silica with an unobstructed pore system was fabricated through the deposition of cobalt nanoparticles on the outer surface of the submicron-sized silica particles. These cobalt nanoparticles were further protected by a nanometer-thick carbon shell against acid erosion. Due to the fact that the magnetic particles are grafted on the outer surface of the porous silica, the pores are still accessible for further modification, which could widen the application range of porous silica.     

Indirect atomic absorption spectrometric determination of mixtures of chloride and iodide by precipitation in an unsegmented flow system

Chloride and iodide are injected into a carrier silver nitrate and the precipitates formed are retained on a stainless-steel filter, so that total chloride and iodide can be determined by the decrease in the atomic absorption signal for silver. The silver chloride precipitate is subsequently dissolved with ammonia and chloride only is determined. Iodide is determined by difference. Mixtures of these anions at μg ml^?1 levels can be determined for chloride/iodide ratios from 7.5:1 to 1:60, with a sampling frequency of ca. 10 h^?1. Applications to the determination of chloride in foodstuffs and wines are described. Up to 10 samples per hour can be handled and 50–100 samples can be run before the filter must be cleaned.     

Adsorption and precipitation of an aminoalkylphosphonate onto calcite

The mechanism of nitrilotris(methylenephosphonic acid) (H6NTMP)/calcite reaction was studied with a large number of batch experiments where phosphonic acid was neutralized with 0 to 5 equivalents of NaOH per phosphonic acid and the concentration ranged from about 10 nmol/L to 1 mol/L. It is proposed that the phosphonate/calcite reactions are characterized in three steps. At low phosphonate concentration (<1 micromol/L NTMP concentration), the phosphonate/calcite reaction can be characterized as a Langmuir isotherm. At saturation, only approximately 7% of the calcite surface is covered with phosphonate; presumably these are the kinks, step edges, or other imperfect sites. At higher phosphonate concentrations, the attachment is characterized by calcium phosphonate crystal growth to a maximum of four to five surface layer thick, with solid phase stoichiometry of Ca(2.5)HNTMP and a constant solubility product of 10(-24.11). After multiple layers of phosphonate are formed on the calcite surface, the solution is no longer at equilibrium with calcite. Further phosphonate retention is probably due to mixed calcium phosphonate solid phase formation at lower pH and depleted solution phase Ca conditions. The proposed mechanism is consistent with phosphate/calcite reaction and can be used to explain the fate of phosphonate in brines from oil producing wells and the results are compared with two oil wells.     

Catalytic pyrolysis of propane-butane hydrocarbon mixture on the composite ceramic materials in an open system

Catalytic pyrolysis of propane-butane hydrocarbon mixture on the composite ceramic materials with the surface modified with zinc-, cadmium- phosphorus- and silicon-containing compounds in an open system was studied in the temperature range 500–850°C, at the rate of the gas mixture flow 20–200 ml min⁻¹, contact duration 0.75–155 s, and the values of the heterogeneity factor 2.0 to 2.9×10⁵ cm⁻¹. The catalytic activity of the systems under similar conditions was compared, the influence of various factors on the yield of ethylene and propylene was investigated and the sooting was estimated.     

Systematic front distortion and presence of consecutive fronts in a precipitation system

A new simple reaction-diffusion system is presented focusing on pattern formation phenomena as consecutive precipitation fronts and distortion of the precipitation front. The chemical system investigated here is based on the amphoteric property of aluminum hydroxide and exhibits two unique phenomena. Both the existence of consecutive precipitation fronts and distortion are reported for the first time. The precipitation patterns could be controlled by the pH field, and the distortion of the precipitation front can be practical for microtechnological applications of reaction-diffusion systems.     

Moving waves and spatiotemporal patterns due to weak thermal effects in models of catalytic oxidation

We analyze the behavior of a microkinetic model of a catalytic reaction coupled with weak enthalpy effects to show that under fixed gas-phase concentrations it can produce moving waves with an intrinsic length scale, when the underlying kinetics is oscillatory. The kinetic model incorporates dissociative oxygen adsorption, reactant adsorption and desorption, and surface reaction. Three typical patterns may emerge in a one-dimensional system (a long wire or a ring): homogeneous oscillations, a family of moving waves propagating with constant velocities, and patterns with multiple source/sink points. Pattern selection depends on the ratio of the system length to the intrinsic wave length and the governing parameters. We complement these analysis with simulations that revealed a plethora of patterned states on one- and two-dimensional systems (a disk or a cylinder). This work shows that weak long-range coupling due to high feed rates maintains such patterns, while low feed rates or strong long-range interaction can gradually suppress the emerging patterns.