scholarly journals Effects of the Size, the Number, and the Spatial Arrangement of Reactive Patches on a Sphere on Diffusion-Limited Reaction Kinetics: A Comprehensive Study

2020 ◽  
Vol 21 (3) ◽  
pp. 997 ◽  
Author(s):  
Changsun Eun
Keyword(s):  
Reaction Kinetics ◽  
Rate Constant ◽  
Brownian Dynamics ◽  
Kinetic Studies ◽  
Spatial Arrangement ◽  
The Finite Element Method ◽  
Diffusion Limited ◽  
Diffusion Controlled ◽  
Kinetics Of ◽  
Good Agreement

We investigate how the size, the number, and the spatial arrangement of identical nonoverlapping reactive patches on a sphere influence the overall reaction kinetics of bimolecular diffusion-limited (or diffusion-controlled) reactions that occur between the patches and the reactants diffusing around the sphere. First, in the arrangement of two patches, it is known that the overall rate constant increases as the two patches become more separated from each other but decreases when they become closer to each other. In this work, we further study the dependence of the patch arrangement on the kinetics with three and four patches using the finite element method (FEM). In addition to the patch arrangement, the kinetics is also dependent on the number and size of the patches. Therefore, we study such dependences by calculating the overall rate constants using the FEM for various cases, especially for large-sized patches, and this study is complementary to the kinetic studies that were performed by Brownian dynamics (BD) simulation methods for small-sized patches. The numerical FEM and BD simulation results are compared with the results from various kinetic theories to evaluate the accuracies of the theories. Remarkably, this comparison indicates that our theory, which was recently developed based on the curvature-dependent kinetic theory, shows good agreement with the FEM and BD numerical results. From this validation, we use our theory to further study the variation of the overall rate constant when the patches are arbitrarily arranged on a sphere. Our theory also confirms that to maximize the overall rate constant, we need to break large-sized patches into smaller-sized patches and arrange them to be maximally separated to reduce their competition.

scholarly journals Diffusion-Limited Reaction Kinetics of a Reactant with Square Reactive Patches on a Plane

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1744
Author(s):  
Changsun Eun
Keyword(s):  
Reaction Kinetics ◽  
Rate Constant ◽  
Spatial Arrangement ◽  
Total Surface Area ◽  
Reaction Model ◽  
Discrete Models ◽  
Diffusion Limited ◽  
Size Number ◽  
Surface Reaction Kinetics ◽  
Kinetics Of

We present a simple reaction model to study the influence of the size, number, and spatial arrangement of reactive patches on a reactant placed on a plane. Specifically, we consider a reactant whose surface has an N × N square grid structure, with each square cell (or patch) being chemically reactive or inert for partner reactant molecules approaching the cell via diffusion. We calculate the rate constant for various cases with different reactive N × N square patterns using the finite element method. For N = 2, 3, we determine the reaction kinetics of all possible reactive patterns in the absence and presence of periodic boundary conditions, and from the analysis, we find that the dependences of the kinetics on the size, number, and spatial arrangement are similar to those observed in reactive patches on a sphere. Furthermore, using square reactant models, we present a method to significantly increase the rate constant by sequentially breaking the patches into smaller patches and arranging them symmetrically. Interestingly, we find that a reactant with a symmetric patch distribution has a power–law relation between the rate constant and the number of reactive patches and show that this works well when the total reactive area is much less than the total surface area of the reactant. Since our N × N discrete models enable us to examine all possible reactive cases completely, they provide a solid understanding of the surface reaction kinetics, which would be helpful for understanding the fundamental aspects of the competitions between reactive patches arising in real applications.

Glancing Angle X-Ray Study of Crystallization of Amorphous Ge at the Ge-A1 Interface

1990 ◽  
Vol 202 ◽  
Author(s):  
S. M. Heald ◽  
J. K. D. Jayanetti ◽  
R. C. Budhani
Keyword(s):  
Initial Period ◽  
Time Characteristic ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffusion Limited ◽  
Glancing Angle ◽  
Lower Temperature ◽  
Kinetics Of ◽  
Diffusion Limited Reaction ◽  
Good Agreement

ABSTRACTThe amorphous to crystalline transformation of Ge in Al/Ge thin film couples has been studied using glancing angle EXAFS, x-ray reflectivity and diffraction. It was found that crystallization occurs at a much lower temperature (118-150 °C) than for bulk Ge, and initiates at the Al/Ge interface. X-ray diffraction studies were made at 152 °C to study the kinetics of the reaction. After an initial period we find good agreement with a square root dependence of the time, characteristic of a diffusion limited reaction.

Modulation spectroscopy. Kinetics for the self-reactions of some α-aminoalkyl radicals in solution

1982 ◽  
Vol 60 (3) ◽  
pp. 274-278 ◽  
Author(s):  
Paul R. Marriott ◽  
Arlindo L. Castelhano ◽  
David Griller
Keyword(s):  
Absorption Spectrum ◽  
Reaction Kinetics ◽  
Unpaired Electron ◽  
Rate Constants ◽  
Lone Pair ◽  
The Self ◽  
Modulation Spectroscopy ◽  
Alkyl Radicals ◽  
Diffusion Controlled ◽  
Kinetics Of

The optical spectra and reaction kinetics of some a-aminoalkyl radicals, RĊHN(CH2R)2; R≡H, Me, Ph, were measured in solution using the technique of modulation spectroscopy. These radicals undergo diffusion controlled self-reaction with rate constants [Formula: see text]. When R≡Ph, the absorption spectrum has a well defined maximum at 346 nm; ε = 3390 M−1 cm−1, while the spectra when R≡H or Me were less intense [Formula: see text] and tailed into the visible. These spectra are substantially red-shifted when compared with those of simple alkyl radicals, an effect which is thought to be due to the interaction between the unpaired electron and the lone pair of electrons on nitrogen.

The Anomalous Diffusion-limited Reaction Kinetics of a Phototrapping Reaction

1996 ◽  
Vol 464 ◽  
Author(s):  
Eric Monson ◽  
Anna L. Lin ◽  
Raoul Kopelman
Keyword(s):  
Laser Beam ◽  
Two Dimensions ◽  
One Dimensional ◽  
Rate Laws ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Diffusion Controlled ◽  
Kinetics Of ◽  
Diffusion Limited Reaction ◽  
Classical Constant

AbstractA focused laser beam acts as both a “phototrap”, bleaching fluorophore molecules which diffuse into the beam path, and as a confocal probe, detecting the excited, unbleached fluorophore molecules still present in the trap. With this focused laser beam, we observe anomalous asymptotic rate laws similar to those predicted for a diffusion-controlled elementary trapping reaction, A + T → T, in one and two dimensions. One dimensional diffusion-limited trapping kinetics are approached in capillaries with 10 μm diameters while two dimensional diffusion limited trapping kinetics are observed with unstirred samples having a quasi 2-D geometry. In the presence of stirring, the 2-D samplesexhibit the classical, constant trapping rate over time.

scholarly journals Kinetic studies of oxidized nicotinamide–adenine dinucleotide-facilitated reactions of d-glyceraldehyde 3-phosphate dehydrogenase

1974 ◽  
Vol 143 (2) ◽  
pp. 353-363 ◽  
Author(s):  
Patricia J. Harrigan ◽  
David R. Trentham
Keyword(s):  
Nicotinamide Adenine Dinucleotide ◽  
Temperature Jump ◽  
Reaction Pathway ◽  
Kinetic Studies ◽  
Rate Equations ◽  
First Order ◽  
Diffusion Controlled ◽  
Relaxation Temperature ◽  
Pig Muscle ◽  
Kinetics Of

The kinetics of the acylation of d-glyceraldehyde 3-phosphate dehydrogenase from pig muscle by 1,3-diphosphoglycerate in the presence of NAD+ has been analysed by using the relaxation temperature-jump method. At pH7.2 and 8°C the rate of acylation of the NAD+-bound (or holo-) enzyme was 3.3×105m−1·s−1 and the rate of phosphorolysis, the reverse reaction, was 7.5×103m−1·s−1. After a temperature-jump perturbation the equilibrium of NAD+ binding to the acyl-enzyme was re-established more rapidly than that of the acylation. The rate of phosphorolysis of the apoacylenzyme from sturgeon muscle and of aldehyde release from the d-glyceraldehyde 3-phosphate–apoenzyme complex were ≤40m−1·s−1 and ≤12s−1 respectively at pH8.0 and 22°C, which means that both processes are too slow to contribute significantly to the reaction pathway of the reversible NAD+-linked oxidative phosphorylation of d-glyceraldehyde 3-phosphate. Phosphorolysis of both acyl-apoenzyme and acyl-holoenzyme was first-order in Pi up to 100mm-Pi and more. PO43− could be the reactive species of the phosphorolysis of the acyl-holoenzyme, in which case phosphorolysis is a diffusion-controlled reaction, although other kinetically indistinguishable rate equations for the reaction are possible.

Kinetics of Reactive Extraction of Pyruvic Acid Using Tributylamine Dissolved in n-Butyl Acetate

2015 ◽  
Vol 13 (1) ◽  
pp. 63-69 ◽  
Author(s):  
Dharm Pal ◽  
Amit Keshav
Keyword(s):  
Aqueous Solution ◽  
Rate Constant ◽  
Pyruvic Acid ◽  
Butyl Acetate ◽  
Volume Ratio ◽  
Kinetic Studies ◽  
Extraction Process ◽  
Reactive Extraction ◽  
Kinetic Measurements ◽  
Kinetics Of

Abstract Studies have been made on the kinetics accompanied with mass transfer for the pyruvic acid/tributylamine (TBA)/n-butyl acetate system to investigate the effectiveness of reactive extraction for the separation of pyruvic acid from the aqueous solution. In the present work, kinetic studies, needed for the design of a recovery unit, were carried out using aqueous solution of pyruvic acid. TBA (conc. range 0.420–2.099 kmol/m3) dissolved in n-butyl acetate (conc. range 50–90%) was used as an extractant. The effect of reactant concentration, the effect of stirring speed and the effect of phase volume ratio on the extraction process were investigated. The kinetic parameters such as reaction order and rate constant were calculated. Kinetic measurements showed that the reaction is of second order occurring in the diffusion film and was found to be independent of hydrodynamic conditions. Rate constant was evaluated to be $0.419\,{{\rm{m}}^3}{\rm{mo}}{{\rm{l}}^{- 1}}{{\rm{S}}^{- 1}}$ .

The silver(I)-copper reaction in acetonitrile-water mixtures

1984 ◽  
Vol 37 (5) ◽  
pp. 903 ◽  
Author(s):  
FJ Hughes ◽  
IM Ritchie ◽  
P Singh
Keyword(s):  
Reaction Rate ◽  
Rotation Speed ◽  
Kinetic Studies ◽  
Polarization Curves ◽  
Limiting Current ◽  
Slow Step ◽  
Surface Roughening ◽  
Kinetic Rate ◽  
Diffusion Controlled ◽  
Good Agreement

An electrochemical and kinetic study of the silver(I)-copper displacement (cementation) reaction in acidified acetonitrile-water mixtures is reported. The cathodic polarization curves for the reduction of silver(I) were found to be those of a fast electrochemical reaction. From the variation of limiting current with rotation speed, the diffusion coefficient of silver(I) as a function of acetonitrile concen- tration was determined. The anodic oxidation of copper gave a Tafel slope of 60 mV per decade of current and was rotation-speed-dependent. It is suggested that the slow step in the reaction mechanism is the diffusion of copper(I) from the electrode surface. At all acetonitrile concentrations investigated, the two polarization curves intersected at a point where the current is fixed by the diffusion of silver(I); this suggests that the displacement reaction will be diffusion-controlled, which was confirmed by kinetic studies. Provided the silver deposit was not too thick, there was good agreement between the measured kinetic rate and that calculated from the silver(I) limiting-current measurements. However, when the deposit became too thick, some increase in reaction rate due to surface roughening was observed.

scholarly journals Reaction Kinetics of Carbon Dioxide in Aqueous Diethanolamine Solutions Using the Stopped-Flow Technique

2012 ◽  
Vol 19 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Marta Siemieniec ◽  
Hanna Kierzkowska-Pawlak ◽  
Andrzej Chacuk
Keyword(s):  
Carbon Dioxide ◽  
Reaction Kinetics ◽  
Rate Constants ◽  
Reaction Rate ◽  
Reaction Rate Constant ◽  
Stopped Flow ◽  
First Order ◽  
Pseudo First Order ◽  
Kinetics Of ◽  
Good Agreement

Reaction Kinetics of Carbon Dioxide in Aqueous Diethanolamine Solutions Using the Stopped-Flow Technique The pseudo-first-order rate constants (kOV) for the reactions between CO2 and diethanolamine have been studied using the stopped-flow technique in an aqueous solution at 293, 298, 303 and 313 K. The amine concentrations ranged from 167 to 500 mol·m-3. The overall reaction rate constant was found to increase with amine concentration and temperature. Both the zwitterion and termolecular mechanisms were applied to correlate the experimentally obtained rate constants. The values of SSE quality index showed a good agreement between the experimental data and the corresponding fit by the use of both mechanisms.

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