Modelling of surface exchange reactions and diffusion in composites and polycrystalline materials

Abstract  Surface exchange reactions and chemical diffusion in composites, consisting of a dilute distribution of inclusions in a matrix, and polycrystalline materials have been modelled by application of both a square grain and a spherical grain model. The diffusion equations have been solved numerically by employing a finite element approach in the case of the square grain model and the Laplace transform method involving numerical Laplace inversion with respect to the spherical grain model. The boundary conditions refer to oxygen exchange reactions between a gas phase and a mixed ionically–electronically conducting ceramic sample within the linear response regime, i.e. small variations of the oxygen partial pressure. Diffusion profiles as well as the time dependence of the total amount of exchanged oxygen (relaxation curves) have been calculated. A necessary requirement for effective medium diffusion is proposed, and appropriate relations for the effective chemical surface exchange coefficient and the effective chemical diffusion coefficient are derived. On the contrary, when the time constant for diffusion from the matrix into the inclusions of a composite exceeds considerably the relaxation time for effective medium diffusion, relaxation curves with two separate time constants are observed. Analogously, in the case of polycrystalline materials the overall transport process is determined by slow (rate-limiting) bulk diffusion from the grain boundaries into the grains. Adequate formulae for the relaxation times are given based on analytical approximations of the solution functions to the diffusion equations. In addition, the spherical grain model is applied to interpret the re-oxidation kinetics of the positive temperature coefficient of resistivity (PTC) ceramics based on conductivity relaxation experiments. Graphical abstract        

Modeling of oxygen transport and cell killing in type-II photodynamic therapy

Photodynamic therapy (PDT) provides an effective option for treatment of tumors and other diseases in superficial tissues and attracts attention for in vitro study with cells. In this study, we present a significantly improved model of in vitro cell killing through Type-II PDT for simulation of the molecular interactions and cell killing in time domain in the presence of oxygen transport within a spherical cell. The self-consistency of the approach is examined by determination of conditions for obtaining positive definitive solutions of molecular concentrations. Decay constants of photosensitizers and unoxidized receptors are extracted as the key indices of molecular kinetics with different oxygen diffusion constants and permeability at the cell membrane. By coupling the molecular kinetics to cell killing, we develop a modeling method of PDT cytotoxicity caused by singlet oxygen and obtain the cell survival ratio as a function of light fluence or initial photosensitizer concentration with different photon density or irradiance of incident light and other parameters of oxygen transport. The results show that the present model of Type-II PDT yields a powerful tool to quantitate various events underlying PDT at the molecular and cellular levels and to interpret experimental results of in vitro cell studies.     

Preparation of prolonged-release spherical micro-matrix of ibuprofen with acrylic polymer by the emulsion-solvent diffusion method for improving bioavailability

Prolonged-release spherical micro-matrices of ibuprofen with acrylic polymer (Eudragit RS) were prepared using a novel emulsion-solvent diffusion method. It was found by examining cross sections of the spherical matrix before and after dissolution tests with a scanning electron microscope and a porosimeter that the resultant micro-matrix had a sponge-like internal structure. The spherical matrices were successfully recovered with a relatively high concentration of the drug in ethanol (0.4-0.6 g/ml) and over a wide range of temperatures (5-35 degrees C). The size of the spherical matrix could be easily controlled by varying the agitation speed of the system and the concentration of emulsifier added to the aqueous medium. The drug release rate from the spherical matrix decreased with increasing concentration of polymer formulated due to the reduced diffusion path and increased tortuosity in the matrix. Spherical matrices with ibuprofen:Eudragit RS = 3:1 improved the bioavailability of the drug and prolonged the drug action in beagle dogs.     

Molecular dynamics investigation of oxygen vacancy diffusion in rutile

Oxygen vacancy diffusion in rutile was studied by Born-Oppenheimer molecular dynamics techniques in the framework of the semiempirical molecular orbital method MSINDO. Migration of an oxygen vacancy from the rutile (110) surface towards the bulk was simulated. The metadynamics technique was employed to accelerate the diffusion processes. In this way, transition state structures and activation energies for the diffusion processes were obtained. Rate constants and the time scale of diffusion processes were estimated for different temperatures using the calculated activation energy. It was found that the vacancies in the bulk are less stable than on the surface. The feasibility of oxygen vacancy diffusion under experimental conditions is discussed.     

Transport des CaO im Lichtbogenplasma

Transport of the excited CaO molecules, formed in the reaction between a small quantity of Ca atoms and oxygen in DC arc plasma, was followed by a high-speed camera. Axial transport velocities of substances were measured. The diffusion coefficient was determined from the distributions of the intensity of light and their time dependence (found by photometric measurements). The calculation of the diffusion coefficient was performed by using the equation corresponding to the spherical diffusion.     

Theoretical investigation of diffusion along columns packed with fully and superficially porous particles

Chromatographic columns packed with shell particles are now nearly twice more efficient than columns packed with conventional, fully porous particles. Shell particles are made of a solid core surrounded by a porous shell of constant thickness. Diffusion through the bed of packed columns is complex due to their heterogeneity. It involves diffusion through the external and the internal fluid, and surface diffusion. Six diffusion models are compared that combine these diffusion mechanisms. They involve the external porosity of the bed (?(e)), the ratio of the core to the particle diameters (ρ), and the ratio of the shell diffusivity to the bulk diffusion coefficient (Ω). Four different theoretical approaches were considered. They are based on (1) the additivity of the mass flux densities modulated by the obstruction factors caused by non-porous spherical inclusions; (2) the effective medium theory of Landauer; (3) the effective medium theory of Garnett for spherical inclusions; and (4) the probabilistic theory of Torquato (for binary composite materials only). The two Landauer models fail because they cannot account for the obstruction factor imposed by the presence of non-porous spherical inclusions. The ternary Garnett model (3) provides an excellent approximation of the actual diffusion mechanism but the most physically relevant model seems to be the one derived from a combination of the Garnett model for a binary core-shell particle and of the Torquato model for random dispersion of contacting spheres in a matrix. Accurate measurements of axial dispersion coefficients are needed to validate or reject the semi-empirical parallel diffusion models and to select the most appropriate one. The results of such measurements made with the peak parking method for various compounds are reported in the companion paper.     

Comparison between experimental and theoretical values of effectiveness factor in cephalosporin C production process with immobilized cells

Cells ofCephalosporium acretnonium ATCC 48272 immobilized in calcium alginate beads were utilized for cephalosporin C production and the results were compared with those obtained with free cells. The experiments were performed with synthetic medium containing glucose and sucrose as carbon and energy sources. Experimental effectiveness factor values were obtained at various cell and dissolved-oxygen concentrations, considering Monod kinetics for the respiration rate, and were compared with the values calculated with zero-order kinetics in spherical bioparticle. The results showed that the assumption of oxygen limitation by diffusion in the bioparticle was correct, and that cephalosporin C production with immobilized cells is perfectly viable, although a slightly lower rate than that obtained in the free cell process was observed.     

Modeling of surface exchange reactions and diffusion in composites including transport processes at grain and interphase boundaries

Surface exchange reactions and diffusion of oxygen in ceramic composites consisting of a dilute and random distribution of inclusions in a polycrystalline matrix (host phase) are modeled phenomenologically by employing the finite element method. The microstructure of the mixed conducting composite is described by means of a square grain model, including grain boundaries of the matrix and interphase boundaries between the inclusions and grains of the host phase. An instantaneous change of the oxygen partial pressure in the surrounding atmosphere may give rise to an oxygen exchange process, i.e., oxidation or reduction of the ceramic composite. Relaxation curves for the total amount of exchanged oxygen are calculated, emphasizing the role played by fast diffusion along the interfaces. The relaxation curves are interpreted in terms of effective medium diffusion, introducing appropriate equations for the effective diffusion coefficient and the effective surface exchange coefficient. When extremely fast diffusion along the grain and interphase boundaries is assumed, the re-equilibration process shows two different time constants. Analytical approximations for the relaxation process and relations for the separate relaxation times are provided for this limiting case as well as for blocking interphase boundaries. Furthermore, conductivity relaxation curves are calculated by coupling diffusion and dc conduction. In the case of effective medium diffusion, the conductivity relaxation curves do not deviate from those for the total amount of exchanged oxygen. On the contrary, the conductivity relaxation curves differ remarkably from the time dependence of the total amount of exchanged oxygen, when the different phases of the composite re-equilibrate with separate time constants.     

Kinetics of oxygen reduction by nanocomposite silver-ion exchanger

It was experimentally determined that the rate of reduction of molecular oxygen from water by the nanocomposite silver-ion exchanger KU-23 is substantially lower than by copper-containing composite and takes place with substantial kinetic inhibition. The kinetic parameters of the process were determined by solving the reverse kinetic problem; it was found that this was due to a reduction in the rate constant of the reaction of silver with oxygen at virtually constant internal diffusion coefficient of molecular oxygen. The transition from kinetic to diffusion control was determined to depend on the silver particle size.     

A diffusion quantum Monte Carlo study of geometries and harmonic frequencies of molecules

This article describes an approach in determination of equilibrium geometries and harmonic frequencies of molecules by the Ornstein-Uhlenbeck diffusion quantum Monte Carlo method based on the floating spherical Gaussians. In conjunction with a projected and renormalized Hellmann-Feynman gradient and an electronic energy at variational Monte Carlo and diffusion quantum Monte Carlo, respectively, the quasi-Newton algorithm implemented with the Broyden-Fletcher-Goldfarb-Shanno updated Hessian was used to find the optimized molecular geometry. We applied this approach to N2 and H2O molecules. The geometry and harmonic frequencies calculated were consistent with some sophisticated ab initio calculated values within reasonable statistical uncertainty.     

Determination of silver fission product in high-temperature nuclear reactor fuels by ion-exchange separation and γ-counting

The content of silver fission product and its radial distribution in spherical coated fuel particles can be measured by stepwise chemical removal of pyrolytic carbon layers coupled with an anion-exchange separation procedure and subsequent γ-counting. An adsorption efficiency better than 98% ranging over five orders of magnitude in silver concentration was found for a bromide-containing medium. Silver to carbon ratios down to 10^-12 are measurable so that this method is useful for studying the diffusion of silver in pyrolytic carbon.     

The sol-gel transition in gelatin viewed by diffusing colloidal probes

This paper reports a dynamic light scattering investigation of the sol-gel transition of gelatin solutions in the presence of latex spheres, which act as local probes for the viscoelasticity of the medium. The experimental procedure allows us to define a local gel time related to the size of the probes. In the sol state and in the gelling solutions, below the gel point, the dependence of the apparent diffusion coefficients of the spheres on correlation times, shows the existence of a fast local diffusion coefficient and of a slow long-term diffusion coefficient, related to viscosity. The behaviour of the fast diffusion coefficient during the course of gelation was quite unexpected, as it remained constant until the moment when the network was formed, when it suddenly started to increase. We propose a model for the diffusion of spherical particles in a viscoelastic medium (Voigt model) by using the Langevin equation. The experimental results are compared to the model. This investigation shows evidence for the coupling between the cooperative movements of the gel network and the local diffusion of the spheres. It illustrates the diffusion of particles through a disordered medium which leads to non-brownian, hypodiffusive regimes.     

掺Ag对氧化锰八面体分子筛催化CO氧化性能的影响

采用回流法在酸性介质中合成了掺杂贵金属Ag的氧化锰八面体分子筛(OMS-2).利用X射线衍射、低温N2吸附、透射电子显微镜及程序升温脱附(TPD)等技术对固体材料的结构进行了表征,考察了材料对CO氧化反应的催化性能,以及Ag的掺杂对该反应的影响.结果表明,合成的OMS-2材料属于cryptomelane一维隧道结构,适量Ag的掺杂使分子筛的有序性得到改善,孔径更均一.Ag的加入还能明显提高催化剂的反应活性.O2-TPD和CO-TPD实验表明,Ag的引入使材料对CO的吸附性能及晶格氧的扩散能力得到显著增强,这是提高催化剂对CO氧化催化能力的主要原因.     

The effect of water on the transport of oxygen through nylon-6 films

The effect of presence of water on the transport of oxygen through films of Nylon-6 was evaluated at 5, 23, and 40°C by permeation experiments. Through the oxygen permeability experiments it was found that the diffusion of oxygen through Nylon-6 is not a simple Fickian process and the total diffusion process can be expressed by a bimodal diffusion mechanism. Permeability, solubility, and diffusion coefficients were determined as a function of water activity for both mechanisms. The effect of sorbed water on the oxygen diffusion and solubility in the polymer is presented as a function of the state of water in the polymer and as a result of the molecular competition between water and oxygen. © 1994 John Wiley & Sons, Inc.     

Electroreduction of molecular oxygen on dispersed copper in an ion-exchange matrix

Electrochemical reduction of molecular oxygen was studied on a [dispersed copper]-[macroporous KU-23 15/100S sulfocation exchanger with various metal concentrations] composite electrode. It was found that a high proton concentration in the ion-exchange matrix causes a decrease in the oxygen reaction overvoltage. The nanostructured state of copper particles causes stabilization of the intermediate product, i.e., hydrogen peroxide. Using the rotating disk electrode method, it was detected that the process is limited by external diffusion of oxygen to composite grains. The oxygen reaction is mostly concentrated on the grain surface and surface layers; oxygen is reduced in the bulk due to dispersed copper oxidation.     

LYSIS OF EGG PHOSPHATIDYLCHOLINE LIPOSOMES BY SINGLET OXYGEN GENERATED IN THE GAS PHASE

Abstract Singlet molecular oxygen was generated in the gas phase by heterogeneous energy transfer from a film of dry Rose Bengal and bubbled into suspensions of egg phosphatidylcholine liposomes, leading to membrane lysis and lipid peroxidation. The analysis based on large target diffusion kinetics indicates that approximately 3000 interactions were required for lysis of 1.5 μm liposomes. This experimental method makes it possible to measure the reactivity of gas phase singlet oxygen with aqueous biological systems.     

Diffusion in hierarchical mesoporous materials: applicability and generalization of the fast-exchange diffusion model

Transport properties of cyclohexane confined to a silica material with an ordered, bimodal pore structure have been studied by means of pulsed field gradient nuclear magnetic resonance. A particular organization of the well-defined pore structure, composed of a collection of spatially ordered, spherical mesopores interconnected via narrow worm-like pores, allowed for a quantitative analysis of the diffusion process in a medium with spatially ordered distribution of the fluid density for a broad range of the gas-liquid equilibria. The measured diffusion data were interpreted in terms of effective diffusivities, which were determined within a microscopic model considering long-range molecular trajectories constructed by assembling the alternating pieces of displacement in the two constituting pore spaces. It has further been found that for the system under study, in particular, and for mesoporous materials with multiple porosities, in general, this generalized model simplifies to the conventional fast-exchange model used in the literature. Thus, not only was justification of the applicability of the fast-exchange model to a diversity of mesoporous materials provided, but the diffusion parameters entering the fast-exchange model were also exactly defined. The equation resulting in this way was found to nicely reproduce the experimentally determined diffusivities, establishing a methodology for targeted fine-tuning of transport properties of fluids in hierarchical materials with multiple porosities.     

Adsorption, diffusion, and dissociation of molecular oxygen at defected TiO2(110): a density functional theory study

The properties of reduced rutile TiO2(110) surfaces, as well as the adsorption, diffusion, and dissociation of molecular oxygen are investigated by means of density functional theory. The O2 molecule is found to bind strongly to bridging oxygen vacancies, attaining a molecular state with an expanded O-O bond of 1.44 A. The molecular oxygen also binds (with somewhat shortened bond lengths) to the fivefold coordinated Ti atoms in the troughs between the bridging oxygen rows, but only when vacancies are present somewhere in the surface. In all cases, the magnetic moment of O2 is lost upon adsorption. The expanded bond lengths reveal together with inspection of electron density and electronic density of state plots that charging of the adsorbed molecular oxygen is of key importance in forming the adsorption bond. The processes of O2 diffusion from a vacancy to a trough and O2 dissociation at a vacancy are both hindered by relative large barriers. However, we find that the presence of neighboring vacancies can strongly affect the ability of O2 to dissociate. The implications of this in connection with diffusion of the bridging oxygen vacancies are discussed.     

Transport behavior of oxygen and nitrogen through organasilicon-containing polystyrenes by molecular simulation

Molecular dynamics (MD) simulations have been used to study the transport properties of oxygen and nitrogen in the para-substituted polystyrenes which possess one to four Si atoms in each substituent. The Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force field was used to construct the polymers. Diffusion coefficients were obtained from molecular dynamics (NVT ensemble) with up to 3 ns simulation times. After molecular dynamic simulation, the trajectories of the small molecules in the polymer matrix were obtained. Then diffusion coefficients have been calculated from the Einstein relationship revealing a considerable agreement between the simulated and the experimental data. And solubility coefficients have been calculated by the Grand Canonical Monte Carlo (GCMC) method. The solubility of oxygen increased with increasing Si content in the polymer membrane. The para-substituted polystyrenes with a branched substituent at the alpha-position showed higher permeability than those of the nonbranched ones. The higher the glass transition temperature (T(g)) of the membrane, the larger the diffusion coefficients of oxygen and nitrogen obtained.     

Voltammetric determination of catalytic reaction parameters of laccase based on electrooxidation of hydroquinone and ABTS

A convenient method for the measurement of the catalytic activity of laccase is proposed based on the voltammetric determination of catalytic reaction substrates: 2,2'-azinobis-(3-ethylbenzothiazoline-6-sulfonate) diammonium salt (ABTS) and 1,4-benzenediol (hydroquinone). The measurement performed using microelectrodes working under spherical diffusion conditions is both accurate and simple, and allows to monitor parallely the consumption of substrate and formation of product of the catalytic reaction. The method proposed in this paper was compared with the two generally employed procedures based on oxygen measurement by Clark electrode and on spectrophotometry. The procedure described in the present paper was found to be simpler and more reproducible results were obtained than using Clark electrode. Compared to spectrophotometry a larger range of catalytic reaction substrates can be studied including colorless compounds.