Diffusion-controlled reaction. VI. Radiation graft polymerization of styrene to polyethylene

The radiation graft polymerization of styrene to polyethylene was studied under diffusion-controlled conditions of radiation intensity I, monomer concentration M₁, and polymer sample thickness L. The results of the present study together with previous work under diffusion-free conditions verify our theoretical model for the diffusion-controlled reaction. The grafting rate is inverse first order in L for diffusion-controlled reaction and independent of L for diffusion-free reaction. The order of dependence of grafting rate on radiation intensity for diffusion-controlled reaction is one-half that for diffusion-free reaction. Diffusion control leads to a decrease in the order of dependence of grafting rate on monomer concentration. The decrease is greater than theoretically predicted; possible reasons for this effect are described.     

On the reactions of methyl radicals with TiO2 nanoparticles and granular powders immersed in aqueous solutions

Methyl radicals react with TiO(2) nanoparticles (NPs) immersed in aqueous solutions to form transients in which the methyls are covalently bound to the particles. The rate constant for this reaction approaches the diffusion-controlled limit and increases somewhat with the number of methyls bound to the particle. The transients decompose to yield ethane. Thus, formally the particles "catalyse" the dimerization of the radicals, a reaction that is diffusion-controlled. Rutile powders behave similarly to the TiO(2) NPs whereas the mechanism for the decomposition of the transients formed in the analogous reaction of the radicals with anatase powders differs. These results are of importance as alkyl radicals are formed near the surface of TiO(2) in a variety of important photocatalytic processes. The results imply that the reactions of alkyl radicals with TiO(2) have to be considered in these processes.     

Structure and polymerization kinetics of condensed phases

It is supposed that polymerization in the diffusion-controlled region occurs with chemically identical reaction centers in ordered and disordered parts kinetically nonequivalent, on account of differences in diffusion. Two types of medium are possible: in one the structure of the ordered regions favors the process, while defects act as kinetic traps in other defects more favorable to reaction than the ordered regions. The occurrence of several types of chemically identical but kinetically nonequivalent centers gives a qualitative explanation of various features of diffusion-controlled processes: stepwise loss of macroradicals, post-polymerization, anomalous temperature dependence of the molecular weight and polymerization rate near the phase transition point.     

Reactions under mixing in viscous polymeric media

Mixing of viscous liquids is of common occurence in polymer technology. We consider the effects of mixing on the simplest bimolecular reaction A+B→O. Under mixing often lamellar arrays of striations of the A and B reactants are formed. The structure of these arrays and the thinning of the striations during mixing determine the kinetics of the reaction. We consider both a premixed situation (where the reaction is diffusion-controlled) and also a situation where mixing and reaction take place simultaneously.     

Diffusion-controlled reaction. VI. Radiation graft polymerization of 4-vinylpyridine to polyethylene

The radiation-initiated graft polymerization of 4-vinylpyridine to high-density polyethylene was studied over a wide range of reaction conditions of radiation intensity I, monomer concentration M₁, and polymer film thickness L. The conditions included both diffusion-free and diffusion-controlled graft polymerizations. The results corroborate our previous theoretical predictions on the effect of I, M₁, and L on the experimental grafting rate. The grafting rate is inverse first order in L for diffusion-controlled reaction and independent of L for diffusion-free reaction. The dependence of grafting rate on radiation intensity decreases from 1/2 to 1/4 order for diffusion-controlled reaction. Diffusion control results in a decrease in the dependence of rate on monomer concentration. The observed decrease is somewhat greater than theoretically predicted.     

Many-particle effects in kinetics of bimolecular diffusion-controlled reactions

Starting from the generalized theory of bimolecular diffusion-controlled reactions between reagents in solids and liquids, we have performed calculations of the A + B → AB (Frenkel defect annihilation) and A + A → B (exciton annihilation) reaction kinetics over a wide time interval and for high initial concentrations. The predicted lowering at long times of the reaction rate in the course of the A + B → AB reaction and acceleration at short times of the A + A → B reaction due to dynamical aggregation of similar non-interacting reagents are demonstrated. The possibility of experimental checks of these effects is discussed.     

Finite concentration effects on diffusion-controlled reactions

The algorithm by Northrup, Allison, and McCammon [J. Chem. Phys. 80, 1517 (1984)] has been used for two decades for calculating the diffusion-influenced rate-constants of enzymatic reactions. Although many interesting results have been obtained, the algorithm is based on the assumption that substrate-substrate interactions can be neglected. This approximation may not be valid when the concentration of the ligand is high. In this work, we constructed a simulation model that can take substrate-substrate interactions into account. We first validated the model by carrying out simulations in ways that could be compared to analytical theories. We then carried out simulations to examine the possible effects of substrate-substrate interactions on diffusion-controlled reaction rates. For a substrate concentration of 0.1 mM, we found that the diffusion-controlled reaction rates were not sensitive to whether substrate-substrate interactions were included. On the other hand, we observed significant influence of substrate-substrate interactions on calculated reaction rates at a substrate concentration of 0.1M. Therefore, a simulation model that takes substrate-substrate interactions into account is essential for reliably predicting diffusion-controlled reaction rates at high substrate concentrations, and one such simulation model is presented here.     

On the o-Ps quenching reaction promoted by K2CrO4 in aqueous sucrose solutions

The o-Ps quenching reaction promoted by K₂CrO₄ was investigated in different sucrose aqueous solutions to confirm the influence of the dielectric constant of the reaction medium on the rate constant of the o-Ps diffusion-controlled reaction. The results obtained support the existence of such an effect. Its implications for the procedure usually applied for ascertaining if a reaction is diffusion controlled are briefly discussed.     

Experimental verification of the Smoluchowski theory for a bimolecular diffusion-controlled reaction in liquid phase

We report experimental verification of the Smoluchowski theory for diffusion-controlled reactions in solution at the steady-state limit. We have determined both the diffusion coefficients and the self-termination reaction rates of the diphenylmethyl radical simultaneously. Smoluchowski theory is insufficient to discuss the reaction rate for the self-termination reaction of the diphenylmethyl radical, so the reaction rate of an encounter complex based on the Collins-Kimball treatment is estimated.     

Thermogravimetric studies of non-stoichiometric cerium oxides under isothermal and quasi-isothermal conditions

Quasi-isothermal thermogravimetry is a new technique in which the programmed heating of a furnace automatically ceases when the rate of a reaction taking place in a sample, which is indicated by the DTG-signal, exceeds a preset limit. In this way reactions can be studied under nearly isothermal conditions. In this paper the data obtained using this method during oxidation and reduction experiments on nonstoichiometric cerium oxides are compared with the data obtained by conventional isothermal thermogravimetry. The kinetics of the composition changes during isothermal reduction and oxidation of CeO_2?x are also analyzed. It appears that, with some reservations, the experimental data are best described by the rate equation for a diffusion-controlled reaction. Finally, both the isothermal and the quasi-isothermal data suggest that the CeO_2?x phase region in the phase diagram consists of several subphases, each with a characteristic activation energy for the diffusion-controlled reactions.     

Flow effects in the polymer cyclization reaction

We investigate the effect of shear and uniaxial extensional flows on the rate of the cyclization reaction in polymers. We find that for such an intramolecular diffusion-controlled reaction the flow always reduces the reaction rate, in contrast to the previously studied case of intermolecular reactions, where linear flows enhance the reaction rate.     

Exact solution for anisotropic diffusion-controlled reactions with partially reflecting conditions

We investigate a generalization of the model of Solc and Stockmayer to describe the diffusion-controlled reactions between chemically anisotropic reactants taking into account the partially reflecting conditions on two parts of the reaction surface. The exact solution of the relevant mixed boundary-value problem was found for different ratios of the intrinsic rate constants. The results obtained may be used to test numerical programs that describe diffusion-controlled reactions in real systems of particles with anisotropic reactivity.     

Fluctuating reaction rate and non-exponential blinking statistics in single-enzyme kinetics

Extending the Michaelis–Menten kinetic scheme, we consider a three-state diffusion-controlled reaction model to investigate the effects of fluctuating reaction rate on the blinking statistics of single-enzyme catalytic reactions. As a result of conformational changes, the barrier-height and the reaction rate for the bottleneck enzymatic reaction could fluctuate in time, leading to non-exponential blinking statistics. To illustrate model applications, some reported experimental data for single β-galactosidase molecules were reanalyzed here to extract useful kinetic parameters.     

Size effects in reactive circular site interactions

The complete series solution for the reactant diffusion and reaction at two diffusion-controlled chemically reactive surface sites of radii a(1) and a(2), located in an inert plane an arbitrary center-to-center distance d apart, is presented. Rigorous, analytical forms are developed to calculate the site reaction rates in terms of the dimensionless intersite distance σ[=d/(a(1) + a(2))] and the site radius ratio γ(=a(1)∕/a(2)). Numerical simulation and approximate theoretical results from the recent literature are compared to the exact site reaction rates. While general agreement was noted over the ranges of γ and σ, significant errors in the Wilemski-Fixman-Weiss site rates were found at small γ and σ < 3.     

Kinetics of phenol oxidation with ozone in a thin layer on a solid surface

Ozone has been reacted with phenol in thin supported layers, and the dynamics of this reaction has been investigated. The stoichiometry of this reaction coincides with the stoichiometry of the same reaction in solution. Specific reaction rate (β) has been determined for various phenol conversions. The effective rate constant of the reaction, estimated by extrapolating β to zero reaction time, is significantly higher than the rate constant of the reaction in solution. The reaction between ozone and phenol is diffusion-controlled. The reaction products form a barrier layer, which protects the deeper phenol layers against ozone. The barrier layer is as thick as 8–15 phenol monolayers.     

Theory of diffusion-controlled reaction between non-simple molecules. I

A new vibrational principle is presented for reaction rates of diffusion-controlled chemical reaction. The variational principle is obtained by a modification of the closure approximation of Wilemski and Fixman. The closure approximation is found to correspond to a special choice of the trial function in this formation and to yield a lower bound of the reaction rate. This formulation is found to be especially useful for the analysis of reaction between non-simple molecules, such as macromolecules.     

XPS and AES investigations of the reaction behaviour of iodine with Zircaloy-4 surfaces

Summary The reaction behaviour of gaseous iodine on Zircaloy-4 surfaces is of interest with regard to the corrosion of fuel cladding tubes in light water reactors. XPS and AES have been employed for its investigation as these methods are most suitable because of their small information depth and their sensitivity to chemical states. It has been shown that the formation of zirconium iodide overlayers reduces further iodine uptake indicating a diffusion-controlled reaction. Further results are discussed in detail.

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XPS- und AES-Untersuchungen zum Reaktionsverhalten von Iod an Zircaloy-4 Oberflächen

     

Kinetic effects of multiple charge modifications in enzyme-substrate reactions: Brownian dynamics simulations of Cu,Zn superoxide dismutase

We used Brownian dynamics simulations of substrate O encounters with the enzyme bovine erythrocyte Cu, Zn superoxide dismutase (SOD) to study the effects of multiple charge modifications in the enzyme on the kinetics of its diffusion-controlled reaction. When the charges of two or three residues were changed, the calculated rate consant relative to that for the unmodified enzyme was usually found to be the product of relative rate constants for the enzymes with the corresponding single-site changes. This “multiplicativity” rule may be useful in the design of enzymes that operate with diffusion-controlled kinetics. Residues that deviate from the general rule are found in the active site channel of SOD, and the origin of these deviations is considered.     

Studies on Thiol Etching of Gold by Using QCM-D Sensor as the Sacrificial Probe

There is still a lack of deep understanding on the reaction kinetics and mechanism of thiol etching of gold. Herein, by using the sensor of quartz crystal microbalance (QCM) as the sacrificial probe, the etching reaction of gold has been studied by employing cysteamine (CS) as a typical thiol etchant. The etching reaction is verified as diffusion-controlled and shows a half-order reaction kinetics. It is demonstrated that intact thiol and amino on CS are both crucial for its etching ability to gold. Applied potentials can affect the electron transfer and hence can be used to regulate the gold etching. Our results also reveal that only two carbon atoms of the spacer between thiol and amino on CS are very critical to the excellent etching ability. This work exhibits a new route to explore the thiol etching reaction of gold and elucidates the reaction kinetics and mechanism.     

Convection/diffusion- and diffusion-controlled rapid-scan voltammetry in liquid chromatographic systems with a large-volume wall-jet detector

On-line voltammetric measurements under liquid chromatographic (LC) conditions yield voltammograms which are either purely diffusion- or purely convection/diffusion-controlled, or a combination of both. The dependence of this behaviour on flow-rate, scan-rate and electrode diameter is investigated for a large-volume wall-jet detector. It is shown that for 4 V s^?1 scan-rates at 1 ml min^?1 flow-rates (conventional LC conditions), S-shaped (convection/diffusion-controlled) voltammograms can be obtained with macro-electrodes (? 1 mm diameter). Distortion of voltammogram shape by the cell time constant is discussed for macro-electrodes. The behaviour of the cell in microbore and micro-LC applications is demonstrated. The advantage of being able to change from convection/diffusion-controlled to diffusion-controlled behaviour is discussed.