Kinetics of Hill-Hermans diffusion of an unstable reagent

1955 ◽  
Vol 228 (1174) ◽  
pp. 397-410
Keyword(s):  
Continuous Method ◽  
Polymer Chemistry ◽  
Reactive Site ◽  
Transient Effect ◽  
Rubber Latex ◽  
Rate Law ◽  
First Order ◽  
Diffusion Controlled ◽  
Kinetics Of ◽  
Diffusion Controlled Reaction

This work deals with a generalization of the widely applicable theory of Hill's, later developed by Hermans. It concerns the diffusion-controlled reaction of a reagent with a polymer across an interface, in the course of which the reagent is captured by an infinitely reactive site ('sink') inside the polymer. For certain applications, it becomes necessary to introduce an alternative fate which the reagent may suffer during diffusion to the sink, namely, deactivation or decomposition. The present kinetic theory of this effect is based on the method of considering the elementary jumps responsible for diffusion, while Hill and Hermans used the complementary, continuous method based on Fick's law. The present derivation of a general rate law for the conversion of the polymer is based on a pseudo lattice model. The rate law takes the form of an infinite spectrum of first-order decay terms, and is little dependent on details of the model used or on curvature of the interface. It does depend critically on a stability constant s of the reagent, which is unity for a perfectly stable and zero for a completely unstable one. In the former case the rate law reduces substantially to that of Hill and Hermans, but covers the initial transient effect as well as the steady state. As s →0, the rate law converges uniformly to that of a first-order chemisorption of a monolayer over the appropriate range. Intermediate cases (0 < s < 1) are of interest in the chemistry of rubber latex, and probably in other fields of polymer chemistry.

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.

scholarly journals The Kinetics of Joined Action of Triplet-Triplet Annihilation and First-Order Decay of Molecules in T1State in the Case of Nondominant First-Order Process: The Kinetic Model in the Case of Spatially Periodic Excitation

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Paweł Borowicz ◽  
Bernhard Nickel
Keyword(s):  
Diffusion Coefficient ◽  
Kinetic Model ◽  
Periodic Pattern ◽  
Constructive Interference ◽  
First Order ◽  
Dependent Rate ◽  
Diffusion Controlled ◽  
Spatially Periodic ◽  
Kinetics Of ◽  
Triplet Triplet Annihilation

In this paper the model developed for estimation of the diffusion coefficient of the molecules in the triplet state is presented. The model is based on the intuitive modification of the Smoluchowski equation for the time-dependent rate parameter. Since the sample is irradiated with the spatially periodic pattern nonexponential effects can be expected in the areas of the constructive interference of the exciting laser beams. This nonexponential effects introduce changes in the observed kinetics of the diffusion-controlled triplet-triplet annihilation. Due to irradiation with so-called long excitation pulse these non-exponential effects are very weak, so they can be described with introducing very simple correction to the kinetic model described in the first paper of this series. The values of diffusion coefficient of anthracene are used to calculate the annihilation radius from the data for spatially homogeneous excitation.

Kinetics of strain-induced crystallization in natural rubber: A diffusion-controlled rate law

Polymer ◽  
2015 ◽  
Vol 72 ◽  
pp. 52-58 ◽  
Author(s):  
Karsten Brüning ◽  
Konrad Schneider ◽  
Stephan V. Roth ◽  
Gert Heinrich
Keyword(s):  
Natural Rubber ◽  
Rate Law ◽  
Diffusion Controlled ◽  
Strain Induced Crystallization ◽  
Kinetics Of ◽  
Induced Crystallization

Die Kinetik des Zerfalls von tert. Butylperoxypivalat bei hohen Drücken und Temperaturen / The Kinetics of the Decomposition of tert.Butylperoxypivalate up to High Pressures and Temperatures

1981 ◽  
Vol 36 (12) ◽  
pp. 1371-1377 ◽  
Author(s):  
M. Buback ◽  
H. Lendle
Keyword(s):  
Activation Energy ◽  
High Pressure ◽  
High Pressures ◽  
Activation Volume ◽  
Rate Law ◽  
First Order ◽  
Order Rate ◽  
High Pressures And Temperatures ◽  
Kinetics Of

AbstractThe decomposition of tert. butylperoxypivalate dissolved in n-heptane has been measured ir-spectroscopically in optical high-pressure cells up to 2000 bar at temperatures between 65 °C and 105 °C. The reaction follows a first order rate law with an activation energy Ea = 122.3 ±3.0 kJ · mol-1 and an activation volume ⊿V≠ = 1.6 ± 1.0 cm3 mol-1 .

Kinetics and mechanism of dehydrochlorination of N-aryl-C-ethoxycarbonylformohydrazidoyl chlorides

1986 ◽  
Vol 64 (5) ◽  
pp. 871-875 ◽  
Author(s):  
Ahmad S. Shawali ◽  
Hassan A. Albar
Keyword(s):  
Rate Constants ◽  
Water Solution ◽  
Chloride Ion ◽  
Order Conditions ◽  
Rate Law ◽  
First Order ◽  
Rate Determining Step ◽  
Pseudo First Order ◽  
Reaction Constants ◽  
Kinetics Of

The kinetics of triethylamine (TEA) catalyzed deydrochlorination of a series of N-aryl-C-ethoxycarbonylformohydrazidoyl chlorides 1a–m have been studied under pseudo-first-order conditions in 4:1 (v/v) dioxane–water solution at 30 °C. For all compounds studied, the kinetics followed the rate law: kobs = k2 (TEA). The values of the overall second-order rate constants for the studied compounds were correlated by the equation: log k2 = 0.533σ−-0.218. The results are compatible with a mechanism involving a fast reversible deprotonation step leading to the anion of 1, followed by rate-determining step involving the loss of the chloride ion from the anion. The reaction constants of these two steps were estimated to be 0.845 and −0.312, respectively.

Kinetics and mechanism of the oxidation of proline by periodate

1989 ◽  
Vol 67 (4) ◽  
pp. 634-638 ◽  
Author(s):  
Rosa Pascual ◽  
Miguel A. Herraez ◽  
Emilio Calle.
Keyword(s):  
Amino Acid ◽  
Rate Constants ◽  
Reaction Rate ◽  
Ph Dependence ◽  
Kinetics And Mechanism ◽  
Appreciable Amount ◽  
Kinetics Of Oxidation ◽  
Rate Law ◽  
First Order ◽  
Kinetics Of

The kinetics of oxidation of proline by periodate has been studied at pH 1.40–8.83 and 30.0 °C. The reaction rate is first order in both periodate and amino acid, and the overall reaction follows second-order kinetics. There was no evidence for the formation of an appreciable amount of intermediate. The reaction rate is highest at pH 4–7 and the oxidation is catalysed by [Formula: see text] ions. The pH dependence of the reaction rate can be explained in terms of reaction of periodate monoanion and the protonated and dipolar forms of the amino acid. The mechanism proposed and the derived rate law are consistent with the observed kinetics. The rate constants obtained from the derived rate law are in agreement with the observed rate constants, thus justifying the rate law and the proposed mechanistic scheme. Keywords: oxidation of proline, oxidation by periodate.

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