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.     

Effective concentration difference model to study the effect of various factors on the effective diffusion coefficient in the dialysis membrane

Cellulose acetate dialysis membrane (CDM) has been used in the diffusive gradients in thin films (DGT) technique, where accurate diffusion coefficients are essential for the assessment of the concentrations of labile metal in solution. Effective concentration difference model (ECDM), based on the assumption that the effective diffusion coefficient of metal ion in the dialysis membrane is determined by the effective concentration difference (ΔC(e)) across the dialysis membrane, is proposed and applied to study the effect of ionic strength, binding agent, ligands and Donnan potential on the effective diffusion coefficient. The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in receptor solutions with binding agent were almost the same as those in receptor solutions without binding agent at higher ionic strengths (0.01-1 M) but much higher than those at lower ionic strengths (0.001-0.0001 M). The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in deionized water receptor solutions with binding agent were not significantly different from those in synthetic receptor solutions (receptor solutions with various ionic strengths) with binding agent. The DGT-labile fractions were measured in synthetic solutions and natural waters, which indicated that the effective diffusion coefficients, through the dialysis membrane immersed in the deionized water solution with binding agent as receptor solution and in the spiked natural water as source solution, were more suitable for DGT application.     

A macrokinetic model of redox sorption on metal–ion exchanger nanocomposites at electrochemical polarization

A conceptual macrokinetic model of redox sorption on metal–ion exchanger nanocomposites upon electrochemical polarization is formulated and a corresponding mathematical model is constructed. The solution to a multi-point boundary value problem for the concentration of a sorbed substance (oxygen) is given. The concentration front of the sorbed substance is characterized by a concentration gradient in the near-surface layer of the solution, by layers of the products of metal oxidation in the composite forming due to both external and internal diffusion transfer, and by chemical and electrochemical reactions at the interphase boundaries. A considerable reduction in the concentration gradient of the sorbate in layers of the products of oxidation of metal and the growth of the diffusion layer of the solution with polarizing currents weaker than the limiting diffusion current are noted.     

Chemodynamics of metal complexation by natural soft colloids: Cu(II) binding by humic acid

The chemodynamics of Cu(II) complexation by humic acid is interpreted in terms of recently developed theory for permeable charged nanoparticles. Two opposing electric effects are operational with respect to the overall rate of association, namely, (i) the conductive enhancement of the diffusion of Cu(2+), expressed by a coefficient f(el), which accounts for the accelerating effect of the negative electrostatic field of the humic particle on the diffusive transport of metal ions toward it, and (ii) the ionic Boltzmann equilibration with the bulk solution, expressed by a factor f(B), which quantifies the extent to which Cu(2+) ions accumulate in the negatively charged particle body. These effects are combined in the probability of outer-sphere metal-site complex formation and the covalent binding of the metal ion by the complexing site (inner-sphere complex formation) as in the classical Eigen mechanism. Overall "experimental" rate constants for CuHA complex formation, k(a), are derived from measurements of the thermodynamic stability constant, K*, and the dissociation rate constant, k(d)*, as a function of the degree of metal ion complexation, θ. The resulting k(a) values are found to be practically independent of θ. They are also compared to theoretical values; at an ionic strength of 0.1 mol dm(-3), the rate of diffusive supply of metal ions toward the particles is comparable to the rate of inner-sphere complex formation, indicating that both processes are significant for the observed overall rate. As the ionic strength decreases, the rate of diffusive supply becomes the predominant rate-limiting process, in contrast with the general assumption made for complexes with small ligands that inner-sphere dehydration is the rate-limiting step. The results presented herein also resolve the discrepancy between experimentally observed and predicted dissociation rate constants based on the above assumption.     

Donnan effects in the steady-state diffusion of metal ions through charged thin films

The steady-state diffusion of metals ions through thin films with fixed charged groups was investigated using diffusive gradients in thin films (DGT) measurements. Copolymers of acrylamide and sodium acrylate cross-linked with N,N'-methylenebisacrylamide were used as diffusive gels. The rate of diffusion of cadmium ions through the gels was measured by determining the mass of cadmium bound to a backing chelex resin after a known deployment time. Variation of the ionic strength as well as the fixed charge density and the thickness of the gel layer allowed evaluation of the impact of the Donnan partitioning and the diffusion layer in solution on the observed steady-state flux of ions through the layer. The results underscore that, as the Donnan partitioning increases, the impact of the diffusion layer in solution becomes more significant. At modest Donnan potentials, Donnan partitioning controls the net flux of metal ions, whereas at conditions of increasing Donnan potential, i.e., at decreasing ionic strength, the flux is increasingly limited by diffusion in solution. An analytical expression is developed to describe the influence of Donnan partitioning on the observed steady-state flux of metal ions.     

Periodic precipitation of silver chromate/dichromate in gelatin

The spatial and temporal evolution of silver chromate/dichromate Liesegang Rings (LR) in gelatin is studied microdensitometrically and microscopically. The analysis of the distribution of various ionic species in dichromate solutions leads to a notion of the possibility of both silver chromate and silver dichromate precipitation. A simple mathematical model of diffusion in thin layers has been developed. The results of the turbidity front progression measurements are consistent with this model and, together with the secondary structure observations, support the postnucleation hypothesis of primary LR formation.     

Modeling isothermal free-radical frontal polymerization with gel effect using free volume theory, with and without inhibition

Frontal Polymerization is a process that converts monomers into polymers by means of a propagating spatially localized reaction front. Such fronts exist with free-radical polymerization, where in the simplest case, a mixture of monomers and initiator is placed into a test tube and upon initiation of the reaction at one end of the tube, a self-sustained wave develops and propagates through the tube. Isothermal Frontal Polymerization (IFP), often referred to as interfacial gel polymerization, occurs due to the coupling of mass diffusion of the species and the gel effect. Utilizing the free volume theory of Vrentas and Duda for describing the self-diffusive behavior of the gel effect, we mathematically model and study this IFP process. We determine, both numerically and analytically, characteristics of the process including the propagation velocity of the reaction zone, the structure of the wave, and the distance traveled by the front before it breaks down due to reactions ahead of the front     

A model for self-diffusion of guanidinium-based ionic liquids: a molecular simulation study

We propose a novel self-diffusion model for ionic liquids on an atomic level of detail. The model is derived from molecular dynamics simulations of guanidinium-based ionic liquids (GILs) as a model case. The simulations are based on an empirical molecular mechanical force field, which has been developed in our preceding work, and it relies on the charge distribution in the actual liquid. The simulated GILs consist of acyclic and cyclic cations that were paired with nitrate and perchlorate anions. Self-diffusion coefficients are calculated at different temperatures from which diffusive activation energies between 32-40 kJ/mol are derived. Vaporization enthalpies between 174-212 kJ/mol are calculated, and their strong connection with diffusive activation energies is demonstrated. An observed formation of cavities in GILs of up to 6.5% of the total volume does not facilitate self-diffusion. Instead, the diffusion of ions is found to be determined primarily by interactions with their immediate environment via electrostatic attraction between cation hydrogen and anion oxygen atoms. The calculated average time between single diffusive transitions varies between 58-107 ps and determines the speed of diffusion, in contrast to diffusive displacement distances, which were found to be similar in all simulated GILs. All simulations indicate that ions diffuse by using a brachiation type of movement: a diffusive transition is initiated by cleaving close contacts to a coordinated counterion, after which the ion diffuses only about 2 A until new close contacts are formed with another counterion in its vicinity. The proposed diffusion model links all calculated energetic and dynamic properties of GILs consistently and explains their molecular origin. The validity of the model is confirmed by providing an explanation for the variation of measured ratios of self-diffusion coefficients of cations and paired anions over a wide range of values, encompassing various ionic liquid classes as well as the simulated GILs. The proposed diffusion model facilitates the qualitative a priori prediction of the impact of ion modifications on the diffusive characteristics of new ionic liquids.     

An electrodynamics-based model for ion diffusion in microbial polysaccharides

An electrodynamics-based model was formulated for simulation of ion diffusion in microbial polysaccharides. The fixed charges and electrostatic double layers that may associate with microbial polysaccharides and their effects on ion diffusion were explicitly built into the model. The model extends a common multicomponent ion diffusion formulation that is based on irreversible thermodynamics under a zero ionic charge flux condition, which is only applicable to the regions without fixed charges and electrostatic double layers. An efficient numerical procedure was presented to solve the differential equations in the model. The model well described key features of experimental observations of ion diffusion in negatively charged microbial polysaccharides including accelerated diffusive transport of cations, exclusion of anions, and increased rate of cation transport with increasing negative charge density. The simulated diffusive fluxes of cations and anions were consistent with a cation exchange diffusion concept in negatively charged polysaccharides at the interface of plant roots and soils; and the developed model allows to mathematically study such diffusion phenomena. An illustrative example was also provided to simulate dynamic behavior of ionic current during ion diffusion within a charged bacterial cell wall polysaccharide and the effects of the ionic current on the compression or expansion of the bacterial electrostatic double layer at the interface of the cell wall and bulk solution.     

Steady Marangoni flow traveling with chemical fronts

When autocatalytic chemical fronts propagate in thin layers of solution in contact with air, they can induce capillary flows due to surface tension gradients across the front (Marangoni flows). We investigate here such an interplay between autocatalytic reactions, diffusion, and Marangoni effects with a theoretical model coupling the incompressible Navier-Stokes equations to a conservation equation for the autocatalytic product concentration in the absence of gravity and for isothermal conditions. The boundary condition at the open liquid/air interface takes the surface activity of this product into account and introduces the solutal Marangoni number M representing the intensity of the coupling between hydrodynamics and reaction-diffusion processes. Positive and negative Marangoni numbers correspond, respectively, to the cases where the product decreases or increases surface tension behind the front. We show that, in both cases, such coupled systems reach an asymptotic dynamics characterized by a steady fluid vortex traveling at a constant speed with the front and deforming it, with, however, an asymmetry between the results for positive and negative M. A parametric study shows that increased propagation speed, front deformation, and possible transient oscillating dynamics occur when the absolute value of M is increased.     

Electrochemical Behaviour Study of Mixed Ligand Complexes of Diaminopropane and Phthalate with Cd(II) Using Differential Pulse Polarography and Cyclic Voltammetry Techniques

Abstract

Differential pulse(d. p.)polarography has been used to study the simple and mixed ligand complexes of 1, 3 diaminopropane (DAMP) and phthalate(PHLT) with Cd(II) at constant ionic strength (u= 1.0 M NaNO₃) at 25°C The overall formation constants of simple and mixed complexes were calculated. The reduction of the simple and mixed species is reversible and diffusion controlled. The postive values of the mixing constants for the mixed-ligand complexes indicate that the mixed-ligand complexes are more stable than simple binary complexes. The equilibria between the various mixed-ligand species in the solution and their equilibrium are given.     

Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as square root Ra for Ra>5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)].     

Modeling growth of organized nanoporous structures by anodic oxidation

Nanostructured porous oxides are produced by anodic dissolution of several metals. A scaling approach is introduced to explain pattern nucleation in an oxide layer, and a related microscopic model shows oxide growth with long nanopores. The scaling approach matches the time of ion transport across the thin oxide layer, which is related to metal corrosion, and the time of diffusion along the oxide/solution (OS) interface, which represents the extension of oxide dissolution. The selected pattern size is of order (dD(S)/v(O))(1/2), where d is the oxide thickness, v(O) is the migration velocity of oxygen ions across the oxide, and D(s) is the diffusion coefficient of H(+) ions along the oxide/solution interface. This result is consistent with available experimental data for those quantities, predicts the increase of pore size with the external voltage, and suggests the independence of pore size with the solution pH. Subsequently, we propose a microscopic model that expresses the main physicochemical processes as a set of characteristic lengths for diffusion and surface relaxation. It shows a randomly perturbed OS interface at short times, its evolution to pore nucleation and to stable growth of very long pores, in agreement with the mechanistic scenario suggested by two experimental groups. The decrease of the size of the walls between the pores with the interface tension is consistent with arguments for formation of titania nanotube arrays instead of nanopores. These models show that pattern nucleation and growth depend on matching a small number of physicochemical parameters, which is probably the reason for the production of nanostructured porous oxides from various materials under suitable electrochemical conditions.     

Numerical simulation of coupled‐stress case II diffusion in one dimension

This article is concerned with the robust and efficient numerical simulation of case II diffusion, which constitutes an important regime of solvent diffusion into glassy polymers. Even in the one‐dimensional case considered here, the numerical simulation of case II diffusion is made difficult by the extreme nonlinearities and coupling in the governing model equations due to a nonlinear flux law needed to produce sharp solvent fronts, a concentration‐dependent relaxation time of the polymer used to model the glass‐rubber transition, and coupling between the diffusion and deformation phenomena. Having an efficient and accurate solution to such equations is central to advancing a clear understanding of the meaning of such models. The difficulties due to coupling and nonlinearities are highlighted by the consideration of a specific, normalized, one‐dimensional case II diffusion model laid out in a general framework of balance laws. Issues such as the stiffness of the spatially discrete differential algebraic equations obtained from the finite element discretization of the governing equations and their bearing on the choice of time‐stepping schemes are discussed. The key requirements of numerical schemes, namely, robustness and efficiency, are addressed by the use of an implicit, adaptive, second‐order backward differentiation formula with error control for time discretization. Error control is used to maximize the step size to satisfy a target error and the radius of convergence requirements while nonlinear algebraic equations are solved at each time step. An example of an initial boundary value problem is solved numerically to show that the chosen model reproduces case II behavior and to validate that the stated objectives for the numerical simulation are met. Finally, the features and numerical implementation of this model are compared with those of a closely related case II diffusion model due to Wu and Peppas. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2091–2108, 2003     

Modeling and simulation of chemo-electro-mechanical behavior of pH-electric-sensitive hydrogel

A chemo-electro-mechanical multi-field model, termed the multi-effect-coupling pH-electric-stimuli (MECpHe) model, has been developed to simulate the response behavior of smart hydrogels subject to pH and electric voltage coupled stimuli when the hydrogels are immersed in a pH buffer solution subject to an externally applied electric field. The MECpHe model developed considers multiphysics effects and formulates the fixed charge density with the coupled buffer solution pH and electric voltage effects, expressed by a set of nonlinear partial differential governing equations. The model can be used to predict the hydrogel displacement and the distributive profiles of the concentrations of diffusive ionic species and the electric potential and the fixed charge density in both the hydrogels and surrounding solution. After validation of the model by comparison of current numerical results with experiment data extracted from the literature, one-dimensional steady-state simulations were carried out for equilibrium of the smart hydrogels subject to pH and electric coupled stimuli. The effects of several important physical conditions, including the externally applied electric voltage, on the distributions of the concentrations of diffusive ionic species, the electric potential, the fixed charge density, and the displacement of the hydrogel strip were studied in detail. The effects of the ionic strength on the bending deformation of the hydrogels under the solution pH and electric voltage coupled stimuli are also discussed.     

Computing steady-state metal flux at microorganism and bioanalogical sensor interfaces in multiligand systems. A reaction layer approximation and its comparison with the rigorous solution

In complicated environmental or biological systems, the fluxes of chemical species at a consuming interface, like an organism or an analytical sensor, involve many coupled chemical and diffusion processes. Computation of such fluxes thus becomes difficult. The present paper describes an approximate approach, based on the so-called reaction layer concept, which enables one to obtain a simple analytical solution for the steady-state flux of a metal ion at a consuming interface, in the presence of many ligands, which are in excess with respect to the test metal ion. This model can be used for an unlimited number of ligands and complexes, without limit for the values of the association/dissociation rate constants or diffusion coefficients. This approximate solution is compared with a rigorous approach for the computation of the fluxes based on an extension of a previously published method (J. Galceran, J. Puy, J. Salvador, J. Cecília, F. Mas and J. L. Garcés, Phys. Chem. Chem. Phys., 2003, 5, 5091-5100). The comparison is performed for a very wide range of the key parameters: rate constants and diffusion coefficients, equilibrium constants and ligand concentrations. Their combined influence is studied in the whole domain of fully labile to non-labile complexes, via two combination parameters: the lability index, L, and the reaction layer thickness, mu. The results show that the approximate solution provides accurate results in most cases. However, for particular combinations of metal complexes with specific values of L or mu, significant differences between the approximate and rigorous solutions may occur. They are evaluated and discussed. These results are important for three reasons: (i) they enable the use of the approximate solution in a fully reliable manner, (ii) when present, the differences between approximate and rigorous solution are largely due to the coupling of chemical reactions, whose importance can thus be estimated, (iii) due to its simple mathematical expression, the individual contribution of each metal species to the overall flux can be computed.     

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.     

The effect of a trithiol and inorganic fillers on the photo‐induced thermal frontal polymerization of a triacrylate

Thermal frontal polymerization is a process in which a localized reaction propagates through an unstirred system by the coupling of the thermal diffusion and the Arrhenius kinetics of an exothermic polymerization. A trithiol was found to affect the front velocity and the time for inducing a front upon exposure to UV light for trimethylolpropane triacrylate polymerization fronts with either kaolin or calcium carbonate filler present. The addition of trithiol and filler both decreased the front velocity. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 8091–8096, 2008     

The role of Pd nanoparticles in ionic liquid in the Heck reaction

Pd(0) nanoparticles with approximately 2 nm diameter, immobilized in 1-n-butyl-3-methylimidazolium hexafluorophosphate ionic liquid, are efficient catalyst precursors for coupling of aryl halides with n-butylacrylate. In situ TEM analysis of the ionic liquid catalytic solution after the catalytic reaction shows the formation of larger nanoparticles ( approximately 6 nm). The palladium content in the organic phase during the arylation reaction was checked by ICP-AS and shows significant metal leaching (up 34%) from the ionic phase to the organic phase at low substrate conversions and drops to 5-8% leaching at higher conversions. These results strongly suggest that the Pd(0) nanoparticles serve as a reservoir of "homogeneous" catalytic active species.