Effective reaction rates for diffusion-limited reaction cycles

2015 ◽  
Vol 143 (21) ◽  
pp. 215102 ◽  
Author(s):  
Paweł Nałęcz-Jawecki ◽  
Paulina Szymańska ◽  
Marek Kochańczyk ◽  
Jacek Miękisz ◽  
Tomasz Lipniacki
Keyword(s):  
Reaction Rates ◽  
Diffusion Limited ◽  
Reaction Cycles ◽  
Diffusion Limited Reaction ◽  
Effective Reaction

Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles

2015 ◽  
Vol 91 (2) ◽  
Author(s):  
Paulina Szymańska ◽  
Marek Kochańczyk ◽  
Jacek Miękisz ◽  
Tomasz Lipniacki
Keyword(s):  
Reaction Rates ◽  
Diffusion Limited ◽  
Effective Reaction

Local Reaction Probability Effects in Non-Classical Kinetics: Batch and Steady State

1992 ◽  
Vol 290 ◽  
Author(s):  
Zhong-You Shi ◽  
Raoul Kopelman
Keyword(s):  
Steady State ◽  
Nearest Neighbor ◽  
Local Reaction ◽  
Reaction Order ◽  
Reaction Probability ◽  
Neighbor Distance ◽  
Reaction Conditions ◽  
Diffusion Limited ◽  
Diffusion Limited Reaction ◽  
Effective Reaction

AbstractThe reaction A+A→0 is simulated in 1-D and 2-D square lattices with various local reaction probabilities, P. The effective reaction order, X, and the nearest neighbor distance distribution (NNDD), are evaluated in all these reactions. For batch reactions, sharp increases in X with increasing P occur at early times. Classical reaction limited kinetics is obtained at early times only when P→0. At long times, all reactions are in the non-classical, diffusion limited regime, regardless of P. For steady state reactions, our results demonstrate a similar behavior of X with P. The NNDD at steady state in 1-D media at P=1.0, i.e. diffusion limited reaction, follows the previously reported skewed exponential shape. This is no longer true for P<I. Finally, at P→0, as expected, an exponential (Poissonian) distribution is obtained for both reaction conditions.

The Effectiveness of Mass Fractal Catalysts

Fractals ◽  
1997 ◽  
Vol 05 (03) ◽  
pp. 493-505 ◽  
Author(s):  
Marc-Olivier Coppens ◽  
Gilbert F. Froment
Keyword(s):  
Active Sites ◽  
Reaction Rates ◽  
High Porosity ◽  
Fractal Surface ◽  
Porous Catalysts ◽  
Surface Areas ◽  
Diffusion Limited ◽  
Mass Fractal ◽  
Order Of Magnitude ◽  
Effective Reaction

Many porous catalysts have a fractal surface, but only rarely do they have a fractal volume, the main exceptions being extremely porous aerogels. It has been suggested that a fractal shape of their volume would be ideal, because it has an infinite area per unit mass that is easily accessible by the reactants. This paper investigates the efficiency of mass fractals by comparing them with nonfractal catalysts. It is found that the specific surface areas of comparable nonfractal catalysts are of the same order of magnitude, if not higher than those of mass fractals. Despite the high effectiveness factor of mass fractals due to the exceptionally easy accessibility of their active sites, production in a nonfractal catalyst is often higher than in a mass fractal, because of the high porosity of the latter. For some strongly diffusion limited reactions, especially in mesoporous catalysts, an added mass fractal macroporosity, with a finite scaling regime, would increase the yields beyond what is possible with a nonfractal catalyst. Nonetheless, when transport through viscous flow in macropores is very rapid the effective reaction rates in classical bimodal catalysts are higher than in fractal catalysts with their high macroporosity.

Solvent effects on the reactivity of solvated electrons with ammonium and nitrate ions in 1-butanol–water solvents

1993 ◽  
Vol 71 (9) ◽  
pp. 1303-1310 ◽  
Author(s):  
Ruzhong Chen ◽  
Gordon R. Freeman
Keyword(s):  
Solvent Effects ◽  
Pure Water ◽  
Reaction Rates ◽  
Dielectric Relaxation Time ◽  
Unusual Behavior ◽  
Solvated Electrons ◽  
Water Solvent ◽  
Electrical Conductances ◽  
Average Size ◽  
Effective Reaction

Values of the rate constants, k2 (106 m3 mol−1 s−1), of solvated electrons,[Formula: see text] with several related salts, in pure water and pure 1-butanol solvents at 298 K are, respectively, as follows: LiNO3, 9.2, 0.19; NH4NO3, 10, 8.3; NH4ClO4, 1.5 × 10−3, 12 in 20 mol% water; LiClO4, 1.0 × 10−4, < 1.0 × 10−4. The value of [Formula: see text] in water solvent is 48 times larger than that in 1-butanol solvent, whereas [Formula: see text] in water is 10−4 times smaller than the value in 1-butanol. This enormous reversal of solvent effects on [Formula: see text] reaction rates is the first observed for ionic reactants. The solvent participates chemically in the [Formula: see text] reaction, and the overall rate constant increases with increasing viscosity and dielectric relaxation time. This unusual behavior is attributed to a greatly increased probability of reaction of an encounter pair with increasing duration of the encounter. Effective reaction radii κRr for [Formula: see text] and [Formula: see text] were estimated with the aid of measured electrical conductances of the salt solutions in all the solvents. Values of κRr are (2–7) × 10−10 m, except for NH4,s+ in 100 and 99 mol% water, which are 2.6 and 2.7 × 10−14 m, respectively. The effective radii of the ions for mutual diffusion increase with increasing butanol content of the solvent, from ~50 pm in water to ~150 pm in 1-butanol, due to the increasing average size of the molecules that solvate the ions.

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