Front motion in an A+B-->C type reaction-diffusion process: effects of an electric field

We study the effects of an external electric field on both the motion of the reaction zone and the spatial distribution of the reaction product, C, in an irreversible A- + B+ -->C reaction-diffusion process. The electrolytes A identical with (A+,A-) and B identical with (B+,B-) are initially separated in space and the ion-dynamics is described by reaction-diffusion equations obeying local electroneutrality. Without an electric field, the reaction zone moves diffusively leaving behind a constant concentration of C's. In the presence of an electric field which drives the reagents towards the reaction zone, we find that the reaction zone still moves diffusively but with a diffusion coefficient which slightly decreases with increasing field. The important electric field effect is that the concentration of C's is no longer constant but increases linearly in the direction of the motion of the front. The case of an electric field of reversed polarity is also discussed and it is found that the motion of the front has a diffusive as well as a drift component. The concentration of C's decreases in the direction of the motion of the front, up to the complete extinction of the reaction. Possible application of the above results to the understanding of the formation of Liesegang patterns in an electric field is briefly outlined.     

Simulation of a crossover from the precipitation wave to moving Liesegang pattern formation

Model simulations to investigate the precipitation wave phenomenon and a crossover from the precipitation wave to moving Liesegang patterns were performed. The chemical scheme contains four chemical species via the interaction of precipitation and redissolution (complex formation), in which the precipitation reaction term was based on Ostwald's supersaturation theory. In this article, for the first time, all the features and behaviors of the heterogeneous traveling waves are reproduced, which were observed experimentally in the work of Zrínyi et al. (Zrínyi, et al. J. Phys. Chem. 1991, 95, 1618.). The detailed investigation of the pattern formation showed three possible states of the system, which depend on the initial concentration of the inner and outer electrolytes, respectively. These are the precipitation wave (single moving precipitation band), the moving Liesegang pattern (moving precipitation bands), and the state where these two patterns coexist.     

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.     

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.     

Phase-separation transition in liquid mixtures near curved charged objects

We study the thermodynamic behavior of nonpolar liquid mixtures in the vicinity of curved charged objects, such as electrodes or charged colloids. There is a critical value of charge (or potential), above which a phase-separation transition occurs, and the interface between high- and low-dielectric constant components becomes sharp. Analytical and numerical composition profiles are given, and the equilibrium front location as a function of charge or voltage is found. We further employ a simple Cahn-Hilliard type equation to study the dynamics of phase separation in spatially nonuniform electric fields. We find an exponential temporal relaxation of the demixing front location. We give the dependence of the steady-state location and characteristic time on the charge, mixture composition and ambient temperature.     

Kinetics of the formation of Liesegang rings

The kinetics of the formation of Liesegang rings is considered and they are classified. The relationship between the position of the propagating diffusion front and the moments of the formation of Liesegang rings is shown. In order to describe the formation processes of the Liesegang rings a generalized model based on the diffusion equation hierarchy is proposed. The kinetics of changes in the dispersed phase sizes at the initial stage of the formation of Liesegang rings is studied.     

Sweeping of alprenolol enantiomers with an organic solvent and sulfated β‐cyclodextrin in capillary electrophoresis

Sweeping, an on‐line sample concentration technique in CE, is the picking and accumulation of analytes by the pseudostationary phase or complexing additive. In the presence of an electric field, the analytes concentrated at the additive front that initially penetrated the sample zone. Here, we describe the sweeping of cationic alprenolol enantiomers using sulfated β‐CD and organic solvent. The separation solution contained the anionic additive while ACN was in the sample solution. With fused silica capillaries, positive polarity, and solutions buffered at pH 3, the direction of the enantiomers' effective electrophoretic mobility was the same as the electrophoretic mobility (or electrophoretic mobility without additive). When the amount of ACN in the sample was increased (i.e. 60%), the interaction between the analytes and additive became negligible. This caused the sweeping boundary to shift from the electrophoretically moving β‐CD front to the zone between the sample and separation solution. The equation that described the narrowing of injected sample zone was derived. The performance of sweeping with 60% ACN in the sample was then studied under different operating conditions (e.g. type of injection, injection time, and CD concentration). The low interaction between enantiomers and additive gave only moderate increases in sensitivity (approximately tenfold), but was improved when field enhancement was used during electrokinetic injection. With a conductivity difference (separation/sample solution) of 70 and a short injection time of 30 s at 20 kV, peak improvements of >100‐fold was easily achieved.     

Patterns with high rhythmicity levels in multicomponent Liesegang systems.

Liesegang banding is the display of rhythmic strata of precipitate as co-precipitate ions interdiffuse in a gel medium. Complex periodic patterns as well as aperiodic structures could emerge, notably in systems where more than one salt is precipitated. The use of three cations (Co2+) Ni2+, and Mg2+) in the banded precipitation of their hydroxides resulted in an unusual pattern with a consistently increasing rhythmicity. A periodic structure marked by the succession of band multiplets with increasing number of bands (from singlets to doublets to triplets to quadruplets, consistently) was observed. Such rhythmic patterns are obtained as the initial Mg2+ concentration ([Mg2+]0), chosen as a control parameter, increases through a critical value. At high [Mg2+]0, the trend breaks after a long time elapses. Two types of bifurcation are therefore experienced by such a system: concentration bifurcation and diffusive (time/space) bifurcation. The dynamics is elucidated on the basis of an analysis of the bands in certain groups, and gel regions between these groups, as well as between group blocs (here, a bloc denotes a succession of multiplet groups, with repetitively the same number of bands). Finally, similarities between our system and naturally occurring rhythmic patterns are emphasized and discussed.     

Nonlinear relaxation patterns in the Cahn-Hilliard equation: an exact solution

We consider the 1-D Cahn-Hilliard equation with the order parameter v and derive an equation for a modified order parameter g such that g'=v'. The new equation allows for separation of variables. This yields exact solutions for v expressed in terms of generalized hypergeometric functions. These solutions have an infinite gradient at their zeros and the first three derivatives of zero at their extrema. The amplitude of these patterns decreases as the inverse square root of time. It is suggested that the phenomenon of compartmentalization of evolving structures typically observed in evolutionary models of the Cahn-Hilliard type is a manifestation of relaxation patterns similar to those derived in this paper.     

Band propagation, scaling laws and phase transition in a precipitate system. I: Experimental study

In the first part of this work, we present an experimental study of the precipitation/redissolution reaction-diffusion system of initially separated components in two distinct organic gels: agar and gelatin. The system is prepared by diffusing a concentrated ammonia solution into a gel matrix that contains nickel sulfate. In agar, the system exhibits a pulse propagation due to the concomitant precipitation reaction between Ni(II) and hydroxide ions and redissolution due to ammonia. At a later stage of propagation, a transition to Liesegang banding is shown to take place. The dynamics of the distance traveled by the precipitation pulse, its width, and mass are shown to exhibit power laws. Moreover, the mass of the bands is shown to oscillate in time, indicating the emergence of a complex mass enrichment mechanism of the formed Liesegang bands. At the microscopic level, we show evidence that the system undergoes a continuous polymorphic transition concomitant with a morphological change whereby the solid in the pulse, which consists of nanospheres of α-nickel hydroxide transforms to form the bands, which consists of larger platelets of β-nickel hydroxide. This clearly indicates the existence of a dynamic Ostwald ripening mechanism that underlies the dynamics on both scales. On the other hand, in gelatin, although we can still obtain similar power laws as in the case of agar, no transition to bands was observed. It is shown that in this case, the propagating pulse is made of nanoparticles of α-nickel hydroxide with an average diameter ~50 nm.     

Pattern forming precipitation in gels due to coupling of chemical reactions with diffusion

Precipitate-forming chemical reactions have been studied in chemically cross-linked poly(vinyl alcohol) gel medium. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into it. Depending on the experimental conditions the reaction-diffusion process often results in patterns of different type. Experiments performed in tubes and in thin layers were carried out in order to investigate the effects of various factors (cross-linking density, swelling degree as well as the concentrations of the outer and inner electrolytes) on the morphologies of the precipitate patterns. It was found that precipitation occurs not only in the Liesegang bands, but also between bands. Beside Liesegang-type structures, tree-like patterns have been observed, showing a characteristic periodicity in the density profile obtained by digitalized image analyses.     

Effects of a constant electric field on the diffusional instability of cubic autocatalytic reaction fronts

An electric field applied in the direction of propagation of a chemical reaction-diffusion front can affect the stability of this front with regard to diffusive instabilities. The influence of an applied constant electric field is investigated by a linear stability analysis and by nonlinear simulations of a simple chemical system based on the cubic autocatalytic reaction A-+2B--->3B-. The diffusional stability of the front is seen to depend on the intensity E and sign of the applied field, and D, the ratio diffusion coefficients of the reactant species. Depending on E, the front can become more or less diffusively unstable for a given value of D. Above a critical value of E, which depends on D, electrophoretic separation of the two fronts is observed.     

Liesegang图案

介绍了Liesegang图案的生长规律、实验研究方法、形成影响因素、理论进展、应用及存在的问题,同时对当前两个活跃的研究方向即复杂Liesegang环和Liesegang图案的微观形成机制进行了讨论.该领域研究的新突破有助于理解自然界中一些复杂图案的形成和控制材料制备中的自组装结构及动物代谢中的结石生长.     

The morphology and dynamics of polymerization-induced phase separation

The morphology and dynamics of polymerization-induced phase separation in the initially homogeneous solution of a non-reactive component in reactive monomers are investigated by incorporating the reaction kinetics into the Cahn-Hilliard equation. Analytical results show that there is a reduction of the initial length scale in the early stage of phase separation. The reason is the increase of the molecule weight of emerging polymer, independent of the fact whether the system goes through the metastable region or not. The numerical results are in good agreement with theoretical prediction quite well.     

Numerical simulation of bubble dynamics in a micro-channel under a nonuniform electric field

A numerical method is used to simulate the motion and coalescence of air bubbles in a micro-channel under a nonuniform electric field. The channel is equipped with arrays of electrodes embedded in its wall and voltages are applied on the electrodes to generate a specified electric field gradient in the longitudinal direction. In the study, the Navier-Stokes equations are solved by using the level set method handling the deformable/moving interfaces between the bubbles and the ambient liquid. Both the polarization Coulomb force and the dielectrophoresis force are considered as the force source of the Navier-Stokes equations by solving the Maxwell's equations. The flow field equations and the electric field equations are coupled and solved by using the finite element method. The electric field characteristics and the dynamic behavior of a bubble are analyzed by studying the distributions of the electric field and the force, the deformation and the moving velocity of the air bubble. The result suggests that the model of dispersed drops suspended in the immiscible dielectric liquid and driven by a nonuniform electric field is an effective method for the transportation and coalescence of micro-drops.     

Transient electrophoretic processes in capillaries of non-uniform cross-section

The previous model of electrofocusing in a tapered capillary was extended to cover both focusing and non-focusing modes of capillary electrophoresis. The more general equation derived can be used either for tapered or for funnel-like segments of capillary for which the product of the local cross-section and the length-based separation coordinate is constant. The particular forms of the equation are used to discuss the changes in the vaRiance of a moving Gaussian zone in practically interesting cases of electrophoresis in a capillary of non-uniform cross-section.     

Selective extraction of size-fractioned DNA samples in microfabricated electrophoresis devices

We have designed and constructed a microfabricated device for separation of double-stranded DNA fragments using a crosslinked sieving medium and spatially selective extraction of the desired fraction. Based on measuring the width and spacing of migrating bands, a narrow side channel is constructed perpendicular to the separation channel to collect the DNA fragments of interest. This selective collection technique was tested using a 100 base pair double-stranded DNA ladder. We successfully demonstrate selective extraction of the desired fragment with minimal interference from the adjacent bands in an electric field of 31 V/cm. We also achieve extraction of multiple DNA fragments using an array of microelectrodes in this side channel. The device uses cross-linked polyacrylamide gel matrix, allowing the separation to be performed in a distance of 1 cm or less and at a low electric field strength. Together with on-chip electrode, this design is amenable to integration with reaction chambers into a single device for portable genetic-based analysis.     

存在外加浓度梯度时的沉淀斑图形成

本文主要讨论了内电解质非均匀分布情况下的沉淀图案形成。通过施加反应物的不同浓度梯度,可以观察到几类新的沉淀斑图结构,如分叉状,苞芽状斑图,以及有断环间隔的Liesegang环。分析表明,尽管外加了浓度梯度,但第n个环形成的位置与形成的时间还是满足普通Liesegang环的简单定律。所不同的是,反应体系中一旦有断环形成,相邻沉淀条纹间距比值X_n+1/X_n就会偏离原来的线性关系。     

Continuous voltage gradients and their application to true moving bed electrophoresis

Gradient elution has been practiced in chromatographic separations for many years. The application of discontinuous "step" gradients in simulated moving bed (SMB) chromatography has been very successful in increasing both processing rates and column productivity, resulting in a reduction in the number of SMB columns required. With the advent of the field gradient focusing techniques, electrophoresis has gained the ability to apply a continuous electric field gradient to a true moving bed (TMB) electrophoretic separation. Application of a spatial gradient allows a large degree of control of the product concentrations inside the separation unit as well as a large increase in product throughput. A model of moving bed electrophoretic separations has been developed that demonstrates the potential advantages of applying a continuous gradient to the moving bed process. These advantages include the reduction of detrimental peak tailing and the ability to decrease the concentrations of the compounds being separated in comparison with commonly used step gradient elution.     

Experimental study of the dynamics of front propagation in the Co(OH)2/NH4OH Liesegang system using spectrophotometry

In this paper we study the temporal dynamics of the Co(OH) 2/NH 4OH Liesegang system with redissolution by complex formation with ammonia using UV-vis spectrophotometry with a special setup. The formation of precipitate bands is accompanied with band redissolution at the top, and because of such precipitation-redissoultion dynamics, the bands appear as a propagating wave. The spectrophotometric technique developed in this study allows us to study at the kinetics of formation of the bands and their redissolution in great details. The formation, growth, and dissolution of multiple bands are monitored by the time evolution of the absorbance. It was found that the individual band formation is sudden and takes between 15 min to half an hour to form before the next band appears. The speed of formation of bands was different for different bands and the maxima of these speeds fit a Gaussian curve. The content of cobalt hydroxide in these bands was calculated and is shown to increase to a maximum away from the interface and then decreases. The bands later grow by further precipitation. This growth was demonstrated to be nonlinear in time. On the other hand, the dissolution of bands was shown to take place simultaneously and collectively among the multiple bands under study. The effect of the concentration of Co (+2) ions on the dynamics of band formation and dissolution was studied. A time law for this Liesegang system was also determined. The system was also found to be very sensitive to temperature fluctuations.