Diffusion-controlled Reaction Rate Research Articles

In Situ Ultrasound Irradiation for Regulating the Electrochemiluminescence Intensity and Layer.

Electrochemiluminescence (ECL) has manifested a surface-confined emitting character and a low light background occurring near the electrode surface. However, the luminescence intensity and emitting layer are limited by the slow mass diffusion rate and electrode fouling in a stationary electrolyte. To address this problem, we developed an in situ strategy to flexibly regulate the ECL intensity and layer thickness by introducing an ultrasound (US) probe to the ECL detector and microscope. Herein, we explored the ECL responses and the thickness of ECL layer (TEL) under US irradiation in different ECL routes and systems. ECL microscopy with an ultrasonic probe discovered that ultrasonic radiation enhanced the ECL intensity under the catalytic route, while an opposite trend was observed under the oxidative-reduction route. Simulation results demonstrated that US promoted the direct electrochemical oxidation of TPrA radicals by the electrode rather than oxidant Ru(bpy)33+, which made the TEL thinner than that in the catalytic route under the same US condition. In situ US boosted the ECL signal from 1.2 times to 4.7 times by improving the mass transport and weakening electrode fouling due to the cavitation role. It significantly enhanced the ECL intensity beyond the diffusion-controlled ECL reaction rate. In addition, a synergistic sonochemical luminescence is validated in the luminol system to enhance the whole luminescence because cavitation bubbles of US promoted the generation of reactive oxygen species. This in situ US strategy provides a new opportunity to understand ECL mechanisms and a new tool in regulating TEL to meet the needs of ECL imaging.

A reaction mechanism for plasma electrolysis of AgNO3 forming silver nanoclusters and nanoparticles

In plasma-driven solution electrolysis (PDSE), gas-phase plasma-produced species interact with an electrolytic solution to produce, for example, nanoparticles. An atmospheric pressure plasma jet (APPJ) directed onto a liquid solution containing a metallic salt will promote reduction of metallic ions in solution, generating metallic clusters that nucleate to form nanoparticles. In this article, results from a computational investigation are discussed of a PDSE process in which a radio-frequency APPJ sustained in helium impinges on a silver nitrate solution, resulting in growth of silver nanoparticles. A reaction mechanism was developed and implemented in a global plasma chemistry model to predict nanoparticle growth. To develop the reaction mechanism, density functional theory was used to generate probable silver growth pathways up to Ag9. Neutral clusters larger than Ag9 were classified as nanoparticles. Kinetic reaction rate coefficients for thermodynamically favorable growth pathways were estimated based on an existing, empirically determined base reaction mechanism for smaller Ag particle interactions. These rates were used in conjunction with diffusion-controlled reaction rate coefficients that were calculated for other Ag species. The role of anions in reduction of Agn ions in forming nanoparticles is also discussed. Oxygen containing impurities or admixtures to the helium, air entrainment into the APPJ, and dissociation of saturated water vapor above the solution can produce additional reactive oxygen species in solution, resulting in the production of anions and O2− in particular. For a given molarity, delivering a sufficient fluence of reducing species will produce similar nanoparticle densities and sizes for all applied power levels. Comparisons are made to alternate models for nanoparticle formation, including charged nanoparticles and use of direct current plasmas.

Synthesis of 1,2‐Propylene Glycol in a Continuous Down‐Flow Fixed‐Bed Reactor With Cu/Al2O3Catalyst

AbstractGlycerol hydrogenolysis to 1,2‐propylene glycol in a continuous down‐flow fixed‐bed reactor with 60 %Cu/Al2O3catalyst was investigated. The routes of main, intermediate and by‐products formation were proposed. It is shown that an increase in the catalyst particle size from 0.1–0.16 to 1.6–2.5 mm transfers the process from the kinetic mode to an intermediate mode between the kinetic and internal diffusion controlled reaction rate. In this case, the observed activation energy decreased by 30 %. The optimal conditions for the process have been determined.

Intensification of the rate of diffusion-controlled reactions involved in wastewater treatment by using a rotating array of vertical cylinders reactor

The mass transfer behavior of a circular rotating array of vertical cylinders was studied using an electrochemical technique which involves measuring the limiting current of the cathodic reduction of potassium ferricyanide. Variables studied were: array rotation speed, cylinder diameter, cylinder separation, and physical properties of the solution. It was found that the rate of mass transfer at the cylinder array increases with increasing rotation speed while increasing cylinder diameter decreased the rate of mass transfer, cylinder spacing within the array was found to have little effect. The data were correlated by a dimensionless equation including all affecting parameters. The reactor was tested in removing copper ions from dilute solutions and found to be promising. Possible applications of the rotating cylinder array in building electrochemical reactors and catalytic reactors e.g., photocatalytic and immobilized cell (or enzyme) biochemical reactions suitable for wastewater treatment were highlighted.

A Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation

The Poisson–Boltzmann equation (PBE) arises in various disciplines including biophysics, electrochemistry, and colloid chemistry, leading to the need for efficient and accurate simulations of PBE. However, most of the finite difference/element methods developed so far are rather complicated to implement. In this study, we develop a ResNet-based artificial neural network (ANN) to predict solutions of PBE. Our networks are robust with respect to the locations of charges and shapes of solvent–solute interfaces. To generate train and test sets, we have solved PBE using immersed finite element method (IFEM) proposed in (Kwon, I.; Kwak, D. Y. Discontinuous bubble immersed finite element method for Poisson–Boltzmann equation. Communications in Computational Physics 2019, 25, pp. 928–946). Once the proposed ANNs are trained, one can predict solutions of PBE in almost real time by a simple substitution of information of charges/interfaces into the networks. Thus, our algorithms can be used effectively in various biomolecular simulations including ion-channeling simulations and calculations of diffusion-controlled enzyme reaction rate. The performance of the ANN is reported in the result section. The comparison between IFEM-generated solutions and network-generated solutions shows that root mean squared error are below 5·10−7. Additionally, blow-ups of electrostatic potentials near the singular charge region and abrupt decreases near the interfaces are represented in a reasonable way.

A pH dependent sulfate formation mechanism caused by hypochlorous acid in the marine atmosphere

Secondary sulfate plays a crucial role in forming marine aerosol, which in turn is an important source of natural aerosol at a global level. Recent experimental studies suggest that oxidation of S(IV) compounds, in practice dissolved sulfur dioxide, to sulfate (S(VI)) by hypochloric acid could be one of the most significant pathways for sulfate formation in marine areas. However, the exact mechanism responsible for this process remains unknown. Using high-level quantum chemical calculations, we studied the reaction between dissolved sulfur dioxide and hypochloric acid. We account for the dominant protonation states of reactants in the pH range 3.0–9.0. We also consider possible catalytic effects of species such as H2O. Our results show that sulfate formation in HOCl+HOSO2− and HOCl+SO32− reactions relevant to acidic and nearly neutral conditions can occur either through previously proposed Cl+ transfer or through a novel HO+ transfer mechanism. In alkaline conditions, where the dominant reactants are OCl− and SO32−, an O atom transfer mechanism proposed in previous experimental studies may be more important than Cl+ transfer. Catalysis by common cloud-water species is found to lower barriers of Cl+ transfer mechanisms substantially. Nevertheless, we find that the dominant S(IV) + HOCl reaction mechanism for the full studied pH range is HO+ transfer from HOCl to SO32−, which leads directly to sulfate formation without ClSO3− intermediates. The rate-limiting barrier of this reaction is low, leading to an essentially diffusion-controlled reaction rate. S(IV) lifetimes due to this reaction decrease with increasing pH due to the increasing fractional population of SO32−. Especially in neutral and alkaline conditions, depletion of HOCl by the reaction is so rapid that S(IV) oxidation will be controlled mainly by mass transfer of gas-phase HOCl to the liquid phase. The mechanism proposed here may help to explain marine sulfate sources missing from current atmospheric models.

The Significant and Profound Impacts of the Studies on the Rate of Diffusion-Controlled Reactions of Enzyme

About 47 years ago a very important paper on the rate of diffusion-controlled reactions of enzyme [1] was published....

Transcription Factors and DNA Play Hide and Seek.

Transcription factors (TFs) bind to specific DNA motifs to regulate the expression of target genes. To reach their binding sites, TFs diffuse in 3D and perform local motions such as 1D sliding, hopping, or intersegmental transfer. TF-DNA interactions depend on multiple parameters, such as the chromatin environment, TF partitioning into distinct subcellular regions, and cooperativity with other DNA-binding proteins. In this review, how current understanding of the search process has initially been shaped by prokaryotic studies is discussed, as well as what is known about the parameters regulating TF search efficiency in the context of the complex eukaryotic chromatin landscape.

Viscoadaptation Controls Diffusion and Intracellular Reaction Rates in Response to Heat and Energy Availability

Cells must precisely orchestrate thousands of reactions in both time and space. Yet reaction kinetics are highly dependent on uncontrollable environmental conditions such as temperature and energy availability. Here, we uncover a mechanism by which budding yeast counteract these environmental fluctuations by modulating viscosity to control the rate of cellular processes. This “viscoadaptation” is achieved via two carbohydrates, trehalose and glycogen, whose regulated production varies the viscosity of the intracellular environment, slowing the motion of individual proteins while maintaining their solubility. Viscoadaptation functions as both an acute stress response and a homeostatic mechanism, allowing cells growing from 22°C to 40°C to maintain constant rates of intracellular diffusion and diffusion-controlled chemical reactions. Multiple conditions that lower ATP trigger viscoadaptation, linking energy availability to reaction rate control. Viscoadaptation reveals viscosity to be a tunable property by which cells regulate diffusion-controlled processes dynamically in response to a changing environment.

Viscoadaptation Controls Diffusion and Reaction Rates in Response to Heat and Energy Availability

Cells must precisely orchestrate thousands of reactions in both time and space. Yet reaction kinetics are highly dependent on uncontrollable environmental conditions such as temperature and energy availability. Here, we uncover a mechanism by which budding yeast counteract these environmental fluctuations by modulating viscosity to control the rate of cellular processes. This “viscoadaptation” is achieved via two carbohydrates, trehalose and glycogen, whose regulated production varies the viscosity of the intracellular environment, slowing the motion of individual proteins while maintaining their solubility. Viscoadaptation functions as both an acute stress response and a homeostatic mechanism, allowing cells growing from 22℃ to 40℃ to maintain constant rates of intracellular diffusion and diffusion-controlled chemical reactions. Multiple conditions that lower ATP trigger viscoadaptation, linking energy availability to reaction rate control. Viscoadaptation reveals viscosity to be a tunable property by which cells regulate diffusion-controlled processes dynamically in response to a changing environment.

Diffusion-influenced reactions on non-spherical partially absorbing axisymmetric surfaces.

The calculation of the diffusion-controlled reaction rate for partially absorbing, non-spherical boundaries presents a formidable problem of broad relevance. In this paper we take the reference case of a spherical boundary and work out a perturbative approach to get a simple analytical formula for the first-order correction to the diffusive flux onto a non-spherical partially absorbing surface of revolution. To assess the range of validity of this formula, we derive exact and approximate expressions for the reaction rate in the case of partially absorbing prolate and oblate spheroids. We also present numerical solutions by a finite-element method that extend the validity analysis beyond spheroidal shapes. Our perturbative solution provides a handy way to quantify the effect of non-sphericity on the rate of capture in the general case of partial surface reactivity.

Steady-state reaction rate of diffusion-controlled reactions in sheets.

In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional settings, the behavior of the macroscopic reaction rate and its dependence on geometric parameters are not yet understood. Modeling the geometric setup by a capped cylinder with a concentric disk-like reactive region on one of the lateral surfaces, we provide an exact semi-analytical solution of the steady-state diffusion equation and compute the diffusive flux onto the reactive region. We explore the dependence of the macroscopic reaction rate on the geometric parameters and derive asymptotic results in several limits. Using the self-consistent approximation, we also obtain a simple fully explicit formula for the reaction rate that exhibits a transition from two-dimensional to three-dimensional behavior as the separation distance between lateral surfaces increases. Biological implications of these results are discussed.

Product interactions and feedback in diffusion-controlled reactions.

Steric or attractive interactions among reactants or between reactants and inert crowders can substantially influence the total rate of a diffusion-influenced reaction in the liquid phase. However, the role of the product species, which has typically different physical properties than the reactant species, has been disregarded so far. Here we study the effects of reactant-product and product-product interactions as well as asymmetric diffusion properties on the rate of diffusion-controlled reactions in the classical Smoluchowski-setup for chemical transformations at a perfect catalytic sphere. For this, we solve the diffusion equation with appropriate boundary conditions coupled by a mean-field approach on the second virial level to account for the particle interactions. We find that all particle spatial distributions and the total rate can change significantly, depending on the diffusion and interaction properties of the accumulated products. Complex competing and self-regulating (homeostatic) or self-amplifying effects are observed for the system, leading to both decrease and increase in the rates, as the presence of interacting products feeds back to the reactant flux and thus the rate with which the products are generated.

Transport in active systems crowded by obstacles

The reactive and diffusive dynamics of a single chemically powered Janus motor in a crowded medium of moving but passive obstacles is investigated using molecular simulation. It is found that the reaction rate of the catalytic motor reaction decreases in a crowded medium as the volume fraction of obstacles increases as a result of a reduction in the Smoluchowski diffusion-controlled reaction rate coefficient that contributes to the overall reaction rate. A continuum model is constructed and analyzed to interpret the dependence of the steady-state reaction rate observed in simulations on the volume fraction of obstacles in the system. The steady-state concentration fields of reactant and product are shown to be sensitive to the local structure of obstacles around the Janus motor. It is demonstrated that the active motor exhibits enhanced diffusive motion at long times with a diffusion constant that decreases as the volume fraction of crowding species increases. In addition, the dynamical properties of a passive tracer particle in a system containing many active Janus motors is studied to investigate how an active environment influences the transport of non-active species. The diffusivity of a passive tracer particle in an active medium is found to be enhanced in systems with forward-moving Janus motors due to the cooperative dynamics of these motors.

Photoprotolytic Processes of Lumazine

Steady-state and time-resolved UV-vis spectroscopies were used to study the photoprotolytic properties of lumazine, which belongs to a class of biologically important compounds-the petridines. We found that in water an excited-state proton transfer occurs with a time constant of ∼70 ps and competes with a nonradiative rate of about the same value. The nonradiative rate of the protonated form of lumazine in polar and nonpolar solvents is large knr ≥ 1.5 × 1010s-1. The fluorescence properties indicate that in water, the ground-state neutral form of lumazine is already stable in two tautomeric forms. The fluorescence of the deprotonated form is quenched by protons in acidic solutions with a diffusion-controlled reaction rate. We conclude that the neutral form of lumazine is an irreversible mild photoacid.

Diffusion-controlled reaction rates for clusters of binding sites on a cell

The Berg-Purcell expression for the diffusion-controlled binding rate to N sites uniformly distributed on the surface of a sphere is generalized to clusters of receptors located at the poles of a cell. By replacing a partially reactive surface with one that is covered with N circular sites that act independently, one can derive analytic expressions for the diffusion-controlled rate constant for clusters of binding sites. This has application to systems where the reactive sites are located in a specific region or regions on the surface of the protein or cell. These include peptide hormones reacting with target receptors, protein-ligand reactions and bacterial chemotaxis. Multiple sensory receptors both at one and two poles of a sphere are studied.

A Molecular Dynamics simulation study on nitrobenzene and [rad]OH radical in supercritical water

With Molecular Dynamics simulation method, the diffusion of nitrobenzene and OH radical in supercritical water was studied at the temperature of 643.2K–843.2K and under the pressure of 23MPa–29MPa. The diffusion-controlled reaction rate constant was calculated. Thus, guidance for reaction kinetics study on the nitrobenzene oxidation in supercritical water process can be provided. Additionally, the microstructure of supercritical water-nitrobenzene system under different conditions was investigated. The deviation of the calculation results of infinite dilute diffusion coefficients obtained from the data processing method in this work is within 9%, compared with experimental values in the literatures. With MD simulation method, at the temperature of 643.2K–823.2K and under the pressure of 23MPa–29MPa, the infinite dilute diffusion coefficients of nitrobenzene and OH radical in supercritical water were obtained. Based on the infinite dilute diffusion coefficients of nitrobenzene and OH radical in supercritical water, the rate constant of the diffusion-controlled reaction was calculated.

Metabolic Channeling and Spatial Effects of Bifunctional Enzymes

Synthetic multi-enzymes complexes (MECs) hold promise to increase metabolic fluxes and reduce undesirable and hard-to-characterize contextual interactions with host systems. A major advantage of MECs in metabolism is referred as metabolic channeling [1] wherein a product is channeled to the subsequent active site in the MECs. Yet this mechanism is not very well characterized. We develop a compartmentalized minimal model of two sequential metabolic reactions. We assume that a “vicinity volume” surrounds each enzyme, where the corresponding binding reaction happens. Reactants are assumed to be well-mixed inside the vicinity and in the bulk solution. We explore the advantages of metabolic channeling by comparing bifunctional enzymes (BIFE) and its two corresponding monofunctional enzymes (MOFE) side-by-side using both theoretical analysis and simulations. The theoretical analyses are based on classic Michaelis-Menton Kinetics, the diffusion-controlled reaction rate and the diffusive reaction rate formulated in [2]. Smoldyn is used for simulations [3]. We find that the level of substrate channeling is determined by a governing dimensionless group α, which is the ratio between the diffusive timescale and the reactive timescale. The steady state level of the reactant in the bulk solution in BIFE system is always lower than the MOFE system and α determines the level of this reduction. The dynamical properties also show important differences. Reaction flux is increased in a short timescale in BIFE system compared to MOFE system, and the level of the increase is again determined by the dimensionless parameter α. This increase in flux vanishes after both systems reach the steady state.

Brownian aggregation rate of colloid particles with several active sites.

We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called "patchy particles") are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shown to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.

Diffusion-controlled reaction rates for two active sites on a sphere.

BackgroundThe diffusion-limited reaction rate of a uniform spherical reactant is generalized to anisotropic reactivity. Previous work has shown that the protein model of a uniform sphere is unsatisfactory in many cases. Competition of ligands binding to two active sites, on a spherical enzyme or cell is studied analytically.ResultsThe reaction rate constant is given for two sites at opposite ends of the species of interest. This is compared with twice the reaction rate for a single site. It is found that the competition between sites lowers the reaction rate over what is expected for two sites individually. Competition between sites does not show up, until the site half angle is greater than 30 degrees.ConclusionsCompetition between sites is negligible until the site size becomes large. The competitive effect grows as theta becomes large. The maximum effect is given for theta = pi/2.