Concentration dependence of the diffusion controlled steady-state rate constant

2002 ◽  
Vol 117 (6) ◽  
pp. 2987-2988 ◽  
Author(s):  
I. V. Gopich ◽  
A. M. Berezhkovskii ◽  
Attila Szabo
Keyword(s):  
Steady State ◽  
Concentration Dependence ◽  
Rate Constant ◽  
Diffusion Controlled ◽  
Steady State Rate ◽  
State Rate

Effect of the potential-energy surface on the diatom dissociation rate constant for F 2 in Ar at 3000 K

1987 ◽  
Vol 414 (1847) ◽  
pp. 297-314
Keyword(s):  
Steady State ◽  
Rate Constant ◽  
Rate Constants ◽  
Reaction Rate ◽  
Energy Surface ◽  
Rate Coefficient ◽  
Classical Mechanics ◽  
Rate Coefficients ◽  
Steady State Rate ◽  
State Rate

Gas-phase dissociation of fluorine ( 1 Ʃ + g ) molecules in an agron bath at 3000 K was studied by using the 3D Monte Carlo classical trajectory (3DMCCT) method. To assess the importance of the potential energy surface (PES) in such calculations, three surfaces, with a fixed, experimentally determined F 2 dissociation energy, were constructed. These surfaces span the existing experimental uncertainties in the shape of the F 2 potential. The first potential was the widest and softest; in the second potential the anharmonicity was minimized. The intermediate potential was constructed to ‘localize’ anharmonicity in the energy range in which the collisions are most reactive. The remaining parameters for each PES were estimated from the best available data on interatomic potentials. By using the single uniform ensemble (SUE) method (Kutz, H. D. & Burns, G. J. chem. Phys . 72, 3652-3657 (1980)), large ensembles of trajectories (LET) were generated for the PES. Two such ensembles consisted of 30000 trajectories each and the third of 26200. It was found that the computed one-way-flux equilibrium rate coefficients (Widom, B. Science 148, 1555-1560 (1965)) depend in a systematic way upon the anharmonicity of the potential, with the most anharmonic potential yielding the largest rate coefficient. Steady-state reaction-rate constants, which correspond to experimentally observable rate constants, were calculated by the SUE method. It was determined that this method yields (for a given trajectory ensemble, PES and translational temperature) a unique steady-state rate constant, independent of the initial, arbitrarily chosen, state (Tolman, R. C. The principles of statistical mechanics , p. 17. Oxford University Press (1938)) of the LET, and consequently independent of the corresponding initial value of the reaction rate coefficient. For each initial state of the LET, the development of the steady-state rate constant from the equilibrium rate coefficient was smooth, monotonic, and consistent with the detailed properties of the PES. It was found that, although the increased anharmonicity of the F 2 potential enhanced the equilibrium rate coefficients, it also enhanced the non-equilibrium effects. As a result, the steady-state rate constants were found to be insensitive to the variation of the PES. Thus, the differences among the steady-state rate constants for the three potentials were of the order of their standard errors, which was about 15% or less. On the other hand, the calculated rate constants exceeded the experimental rate constant by a factor of five to six. Because within the limitations of classical mechanics the calculations were ab initio , it was tentatively concluded that the discrepancy of five to six is due to the use of classical mechanics rather than details of the PES structure.

scholarly journals The kinetics of ox kidney biliverdin reductase in the pre-steady state. Evidence that the dissociation of bilirubin is the rate-determining step

1989 ◽  
Vol 259 (3) ◽  
pp. 709-713 ◽  
Author(s):  
E Rigney ◽  
T J Mantle ◽  
F M Dickinson
Keyword(s):  
Steady State ◽  
Rate Constant ◽  
Ph Dependence ◽  
Order Rate Constant ◽  
Protein Fluorescence ◽  
Biliverdin Reductase ◽  
Rate Determining Step ◽  
Steady State Rate ◽  
State Rate ◽  
Kinetics Of

When the production of bilirubin by biliverdin reductase was monitored at 460 nm by stopped-flow spectrophotometry a ‘burst’ was observed with a first-order rate constant at pH 8 of 20 s-1. The steady-state rate was established on completion of the ‘burst’. When the reaction was monitored at 401 nm there was no observed steady-state rate, but a diminished pre-steady-state ‘burst’ reaction was still seen with a rate constant of 22 s-1. We argue that the rate-limiting reaction is the dissociation of bilirubin from an enzyme.NADP+.bilirubin complex. With NADPH as the cofactor the hydride-transfer step was shown to exhibit pH-dependence associated with an ionizing group with a pK of 7.2. The kinetics of NADPH binding to the enzyme at pH 7.0 were measured by monitoring the quenching of protein fluorescence on binding the coenzyme.

Corticosterone secretion in rats as a function of ACTH input and adrenal blood flow

1965 ◽  
Vol 209 (4) ◽  
pp. 811-814 ◽  
Author(s):  
John C. Porter ◽  
M. S. Klaiber
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Steady Increase ◽  
Constant Input ◽  
Corticosterone Secretion ◽  
Steady State Rate ◽  
State Rate

The rate of secretion of corticosterone from the left adrenal of rats receiving a constant input of ACTH was determined for different flows of blood through the adrenal during the 2- to 3-hr interval following hypophysectomy. Two hours after hypophysectomy the secretion of corticosterone was low in all groups regardless of flow. An input of 0.26 mU ACTH/min caused a steady increase in secretion for 30–40 min before a steady-state rate was attained. The average steady-state rate of secretion was 1.1, 2.4, 3.5, 6.2, 7.2, 6.2, and 6.2 µg/5 min for flows of 0.005, 0.012, 0.023, 0.034, 0.039, 0.051, and 0.058 ml/min, respectively. Under the conditions of these experiments where the input of ACTH was 0.26 mU/min the secretion of corticosterone increased significantly with time of input of ACTH and with flow of blood through the adrenal.

scholarly journals The Natural Rate of Interest and the Optimal Rate of Interest in the Steady State

2021 ◽  
pp. 17-41
Author(s):  
Carl Christian von Weizsäcker ◽  
Hagen M. Krämer
Keyword(s):  
Steady State ◽  
Public Debt ◽  
Fundamental Equation ◽  
Optimal Rate ◽  
Natural Rate ◽  
Real Rate ◽  
Capital Theory ◽  
Steady State Rate ◽  
Natural Rate Of Interest ◽  
State Rate

AbstractThe “natural rate of interest” is the hypothetical, risk-free real rate of interest that would obtain in a closed economy, if net public debt were zero. It is considerably less than the optimal steady-state rate of interest, which is equal to the system’s growth rate. This holds for a very general “meta-model.” The fundamental equation of capital theory holds on the optimal steady-state path: T = Z − D, where T is the overall economic period of production, Z is the representative private “waiting period” of consumers and D is the public debt ratio. Prosperity is at least 30% lower at the natural rate of interest than at the optimal rate.

Kinetic Study Of Crystallisation In Amorphous Thin Lpcvd Si Films

1993 ◽  
Vol 321 ◽  
Author(s):  
B. Pieraggi ◽  
J. P. Guillemet ◽  
B. de Mauduit
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Isothermal Annealing ◽  
Nucleation Kinetics ◽  
Crystallisation Kinetics ◽  
Crystallisation Behaviour ◽  
Steady State Rate ◽  
State Rate ◽  
Si Films

ABSTRACTThe crystallisation behaviour of LPCVD silicon films has been investigated by TEM from in situ isothermal annealing of undoped a-Si films deposited from disilane (Si2H6) at temperatures 450,465 and 480 °C and at gas pressure of 200 MTorr. Nucleation kinetics, grain growth rates and crystallisation kinetics were determined for temperatures ranging from 600 to 675 °C. Nucleation kinetics have been experimentally determined in the early first stages of annealing : they do not show any steady-state rate and are fitted according to a power law. Experimental data for crystallisation kinetics are fitted by an Avrami law without introducing any incubation time.

scholarly journals Calcium-induced dissociation of human plasma factor XIII and the appearance of catalytic activity

1974 ◽  
Vol 141 (3) ◽  
pp. 683-691 ◽  
Author(s):  
Rodney D. Cooke
Keyword(s):  
Steady State ◽  
Protein Concentration ◽  
Factor Xiiia ◽  
Lag Phase ◽  
Conformation Change ◽  
Platelet Factor ◽  
Plasma Enzyme ◽  
Plasma Factor ◽  
Steady State Rate ◽  
State Rate

1. The Ca2+dependence of the activity of plasma Factor XIIIa was studied by using the continuous assay based on the incorporation of dansylcadaverine into dephosphorylated acetylated β-casein (β-substrate). The Km for Ca2+is about 0.170mm. 2. At low concentrations of Ca2+there was a lag in attaining the steady-state rate. The size of the lag was decreased and eventually abolished if the enzyme was preincubated with a high concentration of Ca2+before assay. The concentration of Ca2+required to decrease the lag phase by 50% in 10min depended on the protein concentration: at 0.87mg of protein/ml it required 17mm-Ca2+and at 0.44mg/ml it needed 10mm-Ca2+. 3. The concentrations of Ca2+required either to abolish the lag phase in the appearance of enzyme activity or to activate the essential thiol for reaction with 5,5′-dithiobis-(2-nitrobenzoate) in 10min incubation were similar at the same protein concentration. This indicated that Ca2+induces a conformation change that is responsible for both phenomena. A model is proposed that links this conformation change to the dissociation of the tetrameric enzyme. 4. This was supported by the observation that the addition of excess of b chains to the Factor XIIIa (a′2b2) increased the concentration of Ca2+required to expose the reactive thiol, and inhibited the Ca2+-dependent aggregation of a′ chains. 5. Platelet Factor XIIIa (a′2) was inhibited by 5,5′-dithiobis-(2-nitrobenzoate) in the absence of Ca2+, and no lag phases were observed in attaining the steady-state rate at low Ca2+concentrations, thus confirming the model for the activation of the plasma enzyme. 6. The Ca2+dependence of platelet Factor XIIIa indicated that Ca2+has an additional role in the enzyme mechanism of the plasma enzyme, perhaps being involved in substrate binding. 7. The dependence of the stability of plasma Factor XIIIa on Ca2+and protein concentration indicates that the decay in activity is related to the tetramer dissociation. 8. β-Substrate decreased the Ca2+concentration required for (1) abolition of the lag phase and (2) enzyme inhibition by thiol reagents. The effect on the former is greater than on the latter. 9. The role of the b chains of the plasma Factor and the evolutionary significance of the plasma and platelet Factors are considered.

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