Diffusion-limited Reaction Research Articles

A diffusion-limited reaction model for self-propagating Al/Pt multilayers with quench limits

A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quench limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. This higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.

A role of solvent polarity on bimolecular quenching reactions of 3-acetyl-7-(diethylamino)-2H-chromen-2-one in binary solvent mixtures

The study on preferential salvation was carried out for the 3-acetyl-7-(diethylamino)-2H-chromen-2-one (3ADHC) molecule in different binary solvent mixtures of acetonitrile (ACN) and 1,4-dioxane (DXN) at room temperature. Further, the fluorescence quenching of 3ADHC molecule with aniline was characterized by Stern-Volmer plots which shows upward curvature from linearity in all acetonitrile/1,4-dioxane mixtures. By the make use of different quenching models, Stern-Volmer constant and various other quenching rate parameters have been determined. Efficient quenching was observed for 3ADHC. Ground state complex formation does not hold in our proximity. Quenching reactions hold within the sphere of action for 3ADHC. Diffusion limited reactions are found to be more prominent in high polarity solvent mixtures namely 100% ACN+0% DXN, 80% ACN+20% DXN and 60% ACN+40% DXN. The relation between quenching constant and dielectric constant of the binary solvent mixtures have been studied.

Hollow polycrystalline Y zeolite shells obtained from selective desilication of Beta-Y core-shell composites

Hollow polycrystalline Y zeolite spheres have been obtained by combining zeolite crystallization and selective dissolution steps. Beta-Y core shell composites were first obtained by hydrothermal recrystallization of a synthesis mixture containing as-made Beta crystals in the presence of Y zeolite seeds. Under such conditions, Beta zeolite crystals served not only as cores but they also progressively dissolved and provided the necessary Si species for the formation of the shell. The proportion of Beta zeolite remaining in the composite strongly depended on the composition of the solution, in particular the amount of Al and the alkalinity. It could not be decreased below 45–50 wt. % without formation of contaminating phases, mainly zeolites with GME, GIS and LTA topologies. Successive additions of Al could significantly reduce the amount of Beta zeolite in the composite but to the detriment of faujasite crystal size. Hollow shells with less than 10 wt. % Beta have been obtained by selective removal of Beta zeolite from a composite containing 20 wt. % Beta and obtained after two successive recrystallizations in the presence of aluminum. These shells are built up from faujasite nanocrystals with a high silicon content, making them potentially interesting in diffusion-limited catalytic reactions.

Manganese Oxide/Hemin-Functionalized Graphene as a Platform for Peroxynitrite Sensing

Peroxynitrite (ONOO−, PON) is a powerful oxidizing agent generated in vivo by the diffusion-limited reaction of nitric oxide (NO) and superoxide (O2˙−) radicals. Under oxidative stress, cumulated peroxynitrite levels are associated with chronic inflammatory disorders and other pathophysiological conditions. The accurate detection of peroxynitrite in biological systems is important, not only to understand the genesis and development of diseases, but also to explore and design potential therapeutics. Herein, a manganese oxide/hemin-modified graphene interface is explored as a platform for peroxynitrite amperometric detection. Hemin-functionalized reduced graphene oxide was further modified with manganese oxide nanoparticles to provide a composite material with catalytic activity toward the electrochemical oxidation of peroxynitrite. The morphology of the composite material was characterized using scanning electron microscopy, energy dispersive X-ray analysis, X-ray photoelectron spectroscopy, and UV-Vis absorption measurements. We investigated the electrocatalytic oxidation of peroxynitrite on graphite electrodes modified with the composite material using cyclic voltammetry and amperometry. The results showed that the incorporation of manganese oxide nanoparticles into graphene/hemin material enhances the catalytic detection of peroxynitrite compared to graphene/hemin alone.

Asymptotics of diffusion-limited fast reactions

We are concerned with the fast-reaction asymptotics λ → ∞ \lambda \to \infty for a semi-linear coupled diffusion-limited reaction system in contact with infinite reservoirs of reactants. We derive the system of limit equations and prove the uniqueness of its solutions for equal diffusion coefficients. Additionally, we emphasize the structure of the limit free boundary problem. The key tools of our analysis include (uniform with respect to λ \lambda ) L 1 L^1 -estimates for both fluxes and products of reaction and a balanced formulation, where combinations of the original components which balance the fast reaction are used.

Effect of surface curvature on diffusion-limited reactions on a curved surface

To investigate how the curvature of a reactive surface can affect reaction kinetics, we use a simple model in which a diffusion-limited bimolecular reaction occurs on a curved surface that is hollowed inward, flat, or extended outward while keeping the reactive area on the surface constant. By numerically solving the diffusion equation for this model using the finite element method, we find that the rate constant is a non-linear function of the surface curvature and that there is an optimal curvature providing the maximum value of the rate constant, which indicates that a spherical reactant whose entire surface is reactive (a uniformly reactive sphere) is not the most reactive species for a given reactive surface area. We discuss how this result arises from the interplay between two opposing effects: the exposedness of the reactive area to its partner reactants, which causes the rate constant to increase as the curvature increases, and the competition occurring on the reactive surface, which decreases the rate constant. This study helps us to understand the role of curvature in surface reactions and allows us to rationally design reactants that provide a high reaction rate.

The magnitude of the intrinsic rate constant: How deep can association reactions be in the diffusion limited regime?

Intrinsic and effective rate constants have an important role in the theory of diffusion-limited reactions. In a previous paper, we provide detailed microscopic expressions for these intrinsic rates [A. Vijaykumar, P. G. Bolhuis, and P. R. ten Wolde, Faraday Discuss. 195, 421 (2016)], which are usually considered as abstract quantities and assumed to be implicitly known. Using these microscopic expressions, we investigate how the rate of association depends on the strength and the range of the isotropic potential and the strength of the non-specific attraction in case of the anisotropic potential. In addition, we determine the location of the interface where these expressions become valid for anisotropic potentials. In particular, by investigating the particles' orientational distributions, we verify whether the interface at which these distributions become isotropic agrees with the interface predicted by the effective association rate constant. Finally, we discuss how large the intrinsic association rate can become, and what are the consequences for the existence of the diffusion limited regime.

Magnesium homeostasis protects Salmonella against nitrooxidative stress

The PhoPQ two-component regulatory system coordinates the response of Salmonella enterica serovar Typhimurium to diverse environmental challenges encountered during infection of hosts, including changes in Mg2+ concentrations, pH, and antimicrobial peptides. Moreover, PhoPQ-dependent regulation of gene expression promotes intracellular survival of Salmonella in macrophages, and contributes to the resistance of this pathogen to reactive nitrogen species (RNS) generated from the nitric oxide produced by the inducible nitric oxide (NO) synthase of macrophages. We report here that Salmonella strains with mutations of phoPQ are hypersensitive to killing by RNS generated in vitro. The increased susceptibility of ∆phoQ Salmonella to RNS requires molecular O2 and coincides with the nitrotyrosine formation, the oxidation of [4Fe-4S] clusters of dehydratases, and DNA damage. Mutations of respiratory NADH dehydrogenases prevent nitrotyrosine formation and abrogate the cytotoxicity of RNS against ∆phoQ Salmonella, presumably by limiting the formation of peroxynitrite (ONOO−) arising from the diffusion-limited reaction of exogenous NO and endogenous superoxide (O2•−) produced in the electron transport chain. The mechanism underlying PhoPQ-mediated resistance to RNS is linked to the coordination of Mg2+ homeostasis through the PhoPQ-regulated MgtA transporter. Collectively, our investigations are consistent with a model in which PhoPQ-dependent Mg2+ homeostasis protects Salmonella against nitrooxidative stress.

Effect of germanium doping on the formation kinetics of vacancy-dioxygen complexes in high dose neutron irradiated crystalline silicon

The effect of germanium (Ge) doping on the formation kinetics of vacancy-dioxygen (VO2) complexes in high dose neutron irradiated crystalline silicon (c-Si) has been quantitatively investigated using infrared spectroscopy at 10 K. It is observed that Ge doping of 1019 cm−3 enhances the formation of vacancy-oxygen (VO) complexes by ∼15% during neutron irradiation and slightly suppresses the conversion of VO into VO2 complexes. By studying the generation kinetics of VO2 complexes in the temperature range of 300–345 °C, it is found that the activation energies of VO2 generation are determined to be 1.52 and 1.71 eV in the reference and Ge-doped c-Si, respectively. According to the theory for diffusion limited reactions, it is suggested that Ge doping can retard the VO diffusion in c-Si and therefore reduce the capture probability of Oi for VO complexes. This may be attributed to the temporary trapping of vacancies by Ge atoms. Hence, the formation of VO2 complexes in c-Si is slightly suppressed by Ge doping.

Force-activated DNA substrates for probing individual proteins interacting with single-stranded DNA.

Single-molecule force spectroscopy provides insight into how proteins bind to and move along DNA. Such studies often embed a single-stranded (ss) DNA region within a longer double-stranded (ds) DNA molecule. Yet, producing these substrates remains laborious and inefficient, particularly when using the traditional three-way hybridization. Here, we developed a force-activated substrate that yields an internal 1000 nucleotide (nt) ssDNA region when pulled partially into the overstretching transition (∼65 pN) by engineering a 50%-GC segment to have no adjacent GC base pairs. Once the template was made, these substrates were efficiently prepared by polymerase chain reaction amplification followed by site-specific nicking. We also generated a more complex structure used in high-resolution helicase studies, a DNA hairpin adjacent to 33 nt of ssDNA. The temporally defined generation of individual hairpin substrates in the presence of RecQ helicase and saturating adenine triphosphate let us deduce that RecQ binds to ssDNA via a near diffusion-limited reaction. More broadly, these substrates enable the precise initiation of an important class of protein–DNA interactions.

Effect of Hydrodynamic Interactions on Reaction Rates in Membranes

The Brownian motion of two particles in three dimensions serves as a model for predicting the diffusion-limited reaction rate, as first discussed by von Smoluchowski. Deutch and Felderhof extended the calculation to account for hydrodynamic interactions between the particles and the target, which results in a reduction of the rate coefficient by about half. Many chemical reactions take place in quasi-two-dimensional systems, such as on the membrane or surface of a cell. We perform a Smoluchowski-like calculation in a quasi-two-dimensional geometry, i.e., a membrane surrounded by fluid, and account for hydrodynamic interactions between the particles. We show that rate coefficients are reduced relative to the case of no interactions. The reduction is more pronounced than the three-dimensional case due to the long-range nature of two-dimensional flows.

Cellular mechanisms of peroxynitrite-induced neuronal death.

Peroxynitrite (ONOO-) is a strong biological oxidant formed by the diffusion-limited reaction of nitric oxide (NO-) and superoxide anion (O2-). It has long been theorized that peroxynitrite generation could be the cause in a number of pathological conditions ranging from atherosclerosis to inflammatory, autoimmune, heart and neurodegenerative diseases. Its relatively long biological half-life and high reactivity allows peroxynitrite to oxidize a number of different targets in the cell. In physiologically relevant conditions peroxynitrite can directly react with thiols, or the radical products of peroxynitrite decomposition may indirectly oxidize other cellular components such as lipids, proteins and DNA. Downstream, oxidative modifications caused by peroxynitrite trigger cell death by a variety of mechanisms depending on the concentration of the oxidant. Peroxynitrite stimulates necrosis, apoptosis, autophagy, parthanatos and necroptosis. Here we review the mechanisms activated by peroxynitrite to cause neuronal death.

P 009 - Oxygen levels and free-radical processes in biosystems

Free-radical processes play an important role in functioning of living organisms. The probability of occurrence of the free-radical reactions is significantly affected by oxygen. Depending on the organ type and the nature of tissues and cells, the oxygen levels vary within the range of about 1 to 15%. The diffusion-limited reaction of O 2 with the carbon-centered radicals of biomolecules leads to their oxidation and oxidative destruction, accompanied with formation of cytotoxic products, which is deemed to be the main cause of the damage to the lipids, nucleic acids and proteins. In our studies, we have shown that the radicals formed from hydroxyl-containing molecules under conditions of low oxygen levels undergo various fragmentation reactions before interaction with O 2 takes place. These reactions result in causing damage to the initial substances and formation of bioactive products. Such reactions prevail when the reactive oxygen species interact with hydrocarbons, hydroxyl-containing glycerophospholipids, amino acids, peptides and sphingolipids. In the report, the issues will be discussed associated with the influence of oxygen and the structure of biologically relevant substances on the probability of various free-radical transformations to occur, the possible consequences of such processes and the ways of controlling them.

Facile synthesis of nano-sized hollow ZSM-5 zeolites with rich mesopores in shell

A hollow nano-ZSM-5 zeolites with mesoporous shell was successfully synthesized by a two-step alkaline treatment method. Firstly, nano-ZSM-5 zeolite was alkali treated with NaOH solution to dissolve internal silica of crystals and then the hollow structure was formed. After that, obvious mesopores were introduced in the shell of the hollow zeolites by a NaOH&TPAOH leaching based on the protective desilication. As a result, the external surface area was increased from 98 to 203 m2g-1, more than twice that of the untreated nano-ZSM-5. The thin shell and rich mesopores would improve its catalytic performance in many diffusion-limited reactions.

Reactive nanolaminate pulsed-laser ignition mechanism: Modeling and experimental evidence of diffusion limited reactions

Al/Pt nanolaminates with a bilayer thickness (tb, width of an Al/Pt pair-layer) of 164 nm were irradiated with single laser pulses with durations of 10 ms and 0.5 ms at 189 W/cm2 and 1189 W/cm2, respectively. The time to ignition was measured for each pulse, and shorter ignition times were observed for the higher power/shorter pulse width. Videographic images of the irradiated area shortly after ignition show a non-uniform radial brightness for the longer pulse, while the shorter pulse shows uniform brightness. A diffusion-limited single step reaction mechanism was implemented in a finite element package to model the progress from reactants to products at both pulse widths. The model captures well both the observed ignition delay and qualitative observations regarding the non-uniform radial temperature.

Growth and Aggregation Regulate Clusters Structural Properties and Gel Time.

When particles undergo aggregation, very often they form structures that can be described with fractal geometry concepts. The spatial organization of the particles embedded in these aggregates, quantified by means of their fractal dimension, plays a key role in the clusters' diffusion and aggregation process. Fractal dimensions are typically known for some specific, ideal aggregation scenarios, such as for diluted diffusion limited cluster aggregation (DLCA) or reaction limited cluster aggregation (RLCA). The situation becomes significantly more complicated as soon as the initial particle concentration increases and fractal-dimension changing phenomena, such as particle growth, occur. In this frame, the aim of the present work is twofold: (i) to investigate the clusters' spatial organization in a scenario where growth and aggregation occur simultaneously and (ii) to assess the corresponding aggregation kinetics. To this end, an ad hoc Monte Carlo model has been developed. Both DLCA and RLCA regimes have been explored at several initial primary particle concentrations and for different growth rates. The results were discussed in terms of the characteristic times of growth (τG) and aggregation (τA), as well as the rate at which the structural properties change, vR. It was then possible to propose empirical correlations in the form dm = dm (vR) and tgel = tgel (τA, τG) to relate the evolution of the mass mobility exponent dm and the gel times to the simultaneously occurring processes of growth and aggregation.

Acetophenone hydrogenation on Rh/Al2O3 catalyst: Flow regime effect and trickle bed reactor modeling

Flow regime effect and reactor modeling studies in a gas-liquid downward flow fixed bed reactor were conducted for acetophenone hydrogenation on 1% Rh/Al2O3 catalyst, a relatively complex reaction scheme typical of pharmaceutical applications, using a 7.1mm ID stainless steel reactor with 0.5mm catalyst spheres at elevated pressures. A flow regime transition map for trickle and bubbly flows was determined visually in a transparent reactor surrogate and confirmed by monitoring pressure drop fluctuations for different gas/liquid systems, tube/particle materials, and operating pressure and temperature. The flow regime at each operating condition for the opaque stainless steel reactor was identified solely using pressure drop fluctuations. The beneficial effect of bubbly flow on reaction rate was confirmed experimentally at gas and liquid superficial velocity ranges of 0.02–0.19m/s and 2.5–12mm/s, respectively, under 80–100°C, 11–26bar and 0.04–0.6M initial substrate concentration. Gas flow rate, temperature, and pressure variations were used to study the effects on reaction performance of partial wetting of the catalyst and of liquid-solid diffusion limited reaction. A reactor model including external/internal mass transfer and flow regime effects was developed using an adjustable parameter to account for partial wetting and flow regime effects. The parameter was fitted using a subset of the experiments, and the model provided good prediction (R2>95%) of all remaining experiments.

Nonequilibrium Self-Assembly of π-Conjugated Oligopeptides in Solution.

Supramolecular assembly is a powerful method that can be used to generate materials with well-defined structures across multiple length scales. Supramolecular assemblies consisting of biopolymer-synthetic polymer subunits are specifically known to exhibit exceptional structural and functional diversity as well as programmable control of noncovalent interactions through hydrogen bonding in biopolymer subunits. Despite recent progress, there is a need to control and quantitatively understand assembly under nonequilibrium conditions. In this work, we study the nonequilibrium self-assembly of π-conjugated synthetic oligopeptides using a combination of experiments and analytical modeling. By isolating an aqueous peptide solution droplet within an immiscible organic layer, the rate of peptide assembly in the aqueous solution can be controlled by tuning the transport rate of acid that is used to trigger assembly. Using this approach, peptides are guided to assemble under reaction-dominated and diffusion-dominated conditions, with results showing a transition from a diffusion-limited reaction front to spatially homogeneous assembly as the transport rate of acid decreases. Interestingly, our results show that the morphology of self-assembled peptide fibers is controlled by the assembly kinetics such that increasingly homogeneous structures of self-assembled synthetic oligopeptides were generally obtained using slower rates of assembly. We further developed an analytical reaction-diffusion model to describe oligopeptide assembly, and experimental results are compared to the reaction-diffusion model across a range of parameters. Overall, this work highlights the importance of molecular self-assembly under nonequilibrium conditions, specifically showing that oligopeptide assembly is governed by a delicate balance between reaction kinetics and transport processes.

Boundary homogenization for a sphere with an absorbing cap of arbitrary size.

This paper focuses on trapping of diffusing particles by a sphere with an absorbing cap of arbitrary size on the otherwise reflecting surface. We approach the problem using boundary homogenization which is an approximate replacement of non-uniform boundary conditions on the surface of the sphere by an effective uniform boundary condition with appropriately chosen effective trapping rate. One of the main results of our analysis is an expression for the effective trapping rate as a function of the surface fraction occupied by the absorbing cap. As the cap surface fraction increases from zero to unity, the effective trapping rate increases from that for a small absorbing disk on the otherwise reflecting sphere to infinity which corresponds to a perfectly absorbing sphere. The obtained expression for the effective trapping rate is applied to find the rate constant describing trapping of diffusing particles by an absorbing cap on the surface of the sphere. Finally, we find the capacitance of a metal cap of arbitrary size on a dielectric sphere using the relation between the capacitance and the rate constant of the corresponding diffusion-limited reaction. The relative error of our approximate expressions for the rate constant and the capacitance is less than 5% over the entire range of the cap surface fraction from zero to unity.

Theoretical and Experimental Study on Optimal Injection Rates in Carbonate Acidizing

Summary Optimal acid-injection rate is critical information for carbonate-matrix-acidizing design. This rate is currently obtained through fitting acidizing-coreflood experimental results. A model is needed to predict optimal acid-injection rates for various reservoir conditions. A wormhole forms when larger pores grow in the cross-sectional area at a rate that greatly exceeds the growth rate of smaller pores caused by surface reaction. This happens when the pore growth follows a particular mechanism, which is discussed in this paper. We have developed a model to predict wormhole-growth behavior. The model uses the mode size in a pore-size distribution—the pore size that appears most frequently in the distribution—to predict the growth of the pore. By controlling the acid velocity inside of it, we can make this particular pore grow much faster than other smaller pores, thus reaching the most-favorable condition for wormholing. This also results in a balance between overall acid/rock reaction and acid flow. With the introduction of a porous-medium model, the acid velocity in the mode-size pore is scaled up to the interstitial velocity at the wormhole tip. This interstitial velocity at the wormhole tip controls the wormhole propagation. The optimal acid-injection rates are then calculated by use of semiempirical flow correlations for different flow geometries. The optimal injection rate depends on the rock lithology, acid concentration, temperature, and rock-pore-size distribution. All these factors are accounted for in this model. The model can predict the optimal rates of acidizing-coreflood experiments correctly, compared with our acidizing-coreflood experimental results. In addition, on the basis of our model, it is also found that at optimal conditions, the wormhole-propagation velocity is linearly proportional to the acid-diffusion coefficient for a diffusion-limited reaction. This is proved both experimentally and theoretically in this study. Because there is no flow-geometry constraint while developing this model, it can be applied to field scales. Applications are presented in this paper.