Generalized diffusion equation of interacting brownian particles

Macroscopic behavior of a system of brownian particles interacting with each other through potential forces is described by a generalized diffusion equation (GDE) for the density of particles. The diffusion coefficient in the GDE is given by the generalized Stokes—Einstein relation and generally depends on the density. In the presence of long-range interactions, the GDE becomes non-local in space. When a Coulomb interaction exists, the GDE corresponds to an improvement of the Poisson—Boltzmann equation.     

Effect of reactant size on discrete stochastic chemical kinetics

This paper is aimed at understanding what happens to the propensity functions (rates) of bimolecular chemical reactions when the volume occupied by the reactant molecules is not negligible compared to the containing volume of the system. For simplicity our analysis focuses on a one-dimensional gas of N hard-rod molecules, each of length l. Assuming these molecules are distributed randomly and uniformly inside the real interval [0,L] in a nonoverlapping way, and that they have Maxwellian distributed velocities, the authors derive an expression for the probability that two rods will collide in the next infinitesimal time dt. This probability controls the rate of any chemical reaction whose occurrence is initiated by such a collision. The result turns out to be a simple generalization of the well-known result for the point molecule case l=0: the system volume L in the formula for the propensity function in the point molecule case gets replaced by the "free volume" L-Nl. They confirm the result in a series of one-dimensional molecular dynamics simulations. Some possible wider implications of this result are discussed.     

Stability of solutions to a reaction diffusion system based upon chemical reaction kinetics

In this paper, we deal with the stability problem to some mathematical models that describe chemical reaction kinetics. One is a set of ordinary differential equations induced by one reversible chemical reaction mechanism containing three chemical species. The other is a set of reaction diffusion equations based on the same chemical reaction. We show that all solutions of the model are asymptotically stable by applying the Liapunov method. We thus find that the concentration of each species has certain limits as time proceeds.      

Effect of chemical structure and crystallinity on sorption,diffusion and chemical stability of polyurethaneacetals

The diffusion of water in non-isocyanate polyurethaneacetals (PUA) of various kinds and compositions has been studied. The direct relationship between the composition of polymers, their degree of crystallinity, morphology and diffusional characteristics has been demonstrated. It has been shown that by changing the polymer composition one can obtain hydrated polymer systems of every type, hydrophobic, hydrophilic and moderately hydrophilic. The kinetics of hydrolytic degradation of PUA in HCl solutions (pH = 0·1) between 20 and 75°C has been investigated. Hydrolysis of acetal bonds has been found to occur in the amorphous phase of a polymer sample, which is mostly formed by the fragments of urethane glycol.The influence of morphology on PUA diffusional characteristics and their stability to hydrolysis has been determined.It has been shown that the physico-chemical properties of PUA can be regulated without the introduction of new compounds.     

Effect of the segmental mobility restriction on the thermoset chemical kinetics

The cure kinetics of an epoxy–amine commercial thermoset system have been investigated with the isothermal differential scanning calorimetry technique. In particular, a kinetic study has been performed in the glass–transition zone, in which diffusion phenomena compete with the chemical transformations and the overall reaction rate is partially slowed by the reduced segmental chain mobility. A generalized form of the Vogel equation has been formulated to account for the effect of the increasing glass–transition temperature on the chain mobility and, therefore, on the overall reaction rate. The kinetic model has been expressed with two factors representing the chemical reaction rate and the segmental mobility reduction. As the main result, the activation energy relative to the diffusion phenomena has been found to be very low, having a value of 42.5 K ≈ 0.356 kJ/mol, which is compatible only with the small‐angle rotation of the reactive unit. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3757–3770, 2002     

Effect of defect structure of lanthanum manganite on oxygen exchange kinetics and diffusion

The method of oxygen isotopic exchange was used to study the oxygen exchange kinetics and diffusion in the LaMnO_{3 + δ} oxide at the temperatures of 600–850°C and in the range of oxygen pressures of 133.3–9332.4 Pa. The rate of interface exchange and diffusion coefficient of oxygen are much lower in the case of LaMnO_{3 + δ} as compared to LaCoO_{3 − δ}, which may be due to the different defect structure of these oxides. It is shown that the first exchange type prevails in LaMnO_{3 + δ} occurring without participation of oxygen from the oxide surface. At the same time, in the case of LaCoO_{3 - δ}, an increase in the temperature results in a significant contribution of both the second and third exchange types with participation of one and two oxygen atoms of the oxide surface, accordingly. The rate determining exchange stage is the process of dissociative oxygen adsorption/desorption on the oxide surface.     

Defect chemistry, redox kinetics, and chemical diffusion of lithium deficient lithium niobate

High-temperature optical in situ spectroscopy was used to investigate the defect absorption, redox kinetics, and chemical diffusion of a lithium deficient (48.4 mol% Li(2)O) congruent melting lithium niobate single crystal (c-LN). Under reducing atmospheres of various oxygen activities, a(O(2)), UV-Vis-NIR spectra measured at 1000 °C are dominated by an absorption band due to free small polarons centered at about 0.93 eV. The polaron band intensity was found to follow a power law of the form a(O(2))(m) with m = -1/4. A chemical reduction model involving electrons localized on niobium ions on regular lattice sites can explain the observed defect absorption and its dependence on oxygen activity. The kinetics of reduction and oxidation processes upon oxygen activity jumps and the associated chemical diffusion coefficients are found in close agreement over a range from -0.70 to -14.70 in log a(O(2)), indicating a reversible redox process. Assuming coupled fluxes of lithium vacancies and free small polarons for the attainment of stoichiometry, the diffusion coefficients of lithium vacancies as well as of lithium ions in the lithium deficient c-LN have been determined at 1000 °C.     

Effect of oxygen nonstoichiometry on kinetics of oxygen exchange and diffusion in lanthanum-strontium manganites

Porous _963-1 (x = 0, 0.4, 0.6) materials are synthesized using a ceramic technique. The method of isotopic oxygen exchange with gas-phase analysis was used to study the kinetics of oxygen exchange in La_1-x Sr _x MnO_3±δ at 600–850°C and at oxygen pressure of 0.13–9.33 kPa. The values of oxygen interphase exchange rate, diffusion coefficient, and contributions of three exchange types are calculated. It is found that the rate of oxygen interphase exchange rate and diffusion coefficient grow at an increase in the concentration of strontium. The values of effective activation energies of oxygen exchange and diffusion decrease at an increase in the strontium content. Oxygen diffusion and its exchange mechanism are considered as related to the defect structure of oxides in the La_1-x Sr _x MnO_3±δ system.     

Effect of oxygen nonstoichiometry on kinetics of oxygen exchange and diffusion in lanthanum-strontium cobaltites

The method of isotopic exchange was used to study the kinetics of oxygen exchange and diffusion in complex oxides of La_{1 − x} Sr _x Co_{1 − y} Fe _y O_{3 − δ} (x = 0.0, y = 0.0; x = 0.6, y = 0.2, 0.4). The rates of oxygen interfacial exchange and its diffusion coefficient were determined for LaCoO_{3 − δ} at the pressure of 5 torr in the temperature range of 600–850°C and at the temperature of 700°C in the pressure range of 1–70 torr. The contributions of the three exchange types were calculated. The order of the dependence of the interfacial exchange rate on the oxygen pressure was 0.51 ± 0.01. In the case of La_0.4Sr_0.6Co_{1 − y} Fe _y O_{3 − δ} (y = 0.2, 0.4) in the temperature range of 600–900°C at the oxygen pressure of 10 torr, the oxygen exchange rates and diffusion coefficients were determined in the material bulk and in the subsurface region; contributions of the three types of exchange were calculated. The paper considers the mechanism of oxygen exchange and diffusion as compared to nonstoichiometry in the oxygen sublattice of the La_{1 − x} Sr _x Co_{1 − y} Fe _y O_{3 − δ} oxides.     

Non-hydrodynamic contribution to the concentration dependence of the self diffusion of interacting brownian macroparticles

One-dimensional single-channel scattering calculations on an effective potential are used to discuss resonances in collinear reactions and to predict their energetic location almost quantitatively. The effective potential includes the vibrationally adiabatic potential and the adiabatic diagonal correction in Delves' mass-weighted polar coordinates (hyperspherical coordinates). This $\text{di}$agonal corrected $\text{v}$ibrational $\text{a}$diabatic $\text{h}$yperspherical (DIVAH) model is tested for a variety of reactions (H + H₂, H + MuH, I + HI, F + H₂) and a detailed discussion of the effective potential and its physical implications is given.     

Comments on current aspects of chemical kinetics

An aged kineticist was awakened in 1989 from a 50-year slumber. After arduous study he sized-up the present situation, with occasional reflections on the state of knowledge in 1939.     

Capillary diffusion and interfacial kinetics

Mathematical expressions have been derived to show how the rate constant for the interfacial transfer of a solute between two immiscible phases may be found using a capillary diffusion technique. Laplace transform theory has been used to develop the equations, and theoretical concentration profiles illustrating the dependence upon the interfacial kinetics are presented.     

Mechanism and kinetics of hydrated electron diffusion

Molecular dynamics simulations are used to study the mechanism and kinetics of hydrated electron diffusion. The electron center of mass is found to exhibit Brownian-type behavior with a diffusion coefficient considerably greater than that of the solvent. As previously postulated by both experimental and theoretical works, the instantaneous response of the electron to the librational motions of surrounding water molecules constitutes the principal mode of motion. The diffusive mechanism can be understood within the traditional framework of transfer diffusion processes, where the diffusive step is akin to the exchange of an extramolecular electron between neighboring water molecules. This is a second-order process with a computed rate constant of 5.0 ps(-1) at 298 K. In agreement with experiment the electron diffusion exhibits Arrhenius behavior over the temperature range of 298-400 K. We compute an activation energy of 8.9 kJ mol(-1). Through analysis of Arrhenius plots and the application of a simple random walk model it is demonstrated that the computed rate constant for exchange of an excess electron is indeed the phenomenological rate constant associated with the diffusive process.     

Electrical properties and defect chemistry of TiO2 single crystal. III. Equilibration kinetics and chemical diffusion

The equilibration kinetics of high-purity single-crystal TiO(2) were monitored using measurements of electrical conductivity in the temperature range 1073-1323 K and oxygen activity, p(O(2)), range 10(-13) to 75 kPa. The kinetics data were used to determine the chemical diffusion coefficient (D(chem)) within narrow ranges of p(O(2)). There was observed a complex effect of the p(O(2)) on the D(chem), which exhibits a maximum at the n-p transition. The effect of the p(O(2)) on the D(chem) was discussed in terms of the defect disorder and the related semiconducting properties. The activation energy of the D(chem), which also varies with the p(O(2)), exhibits a maximum at p(O(2)) = approximately 10(4) Pa (143 kJ/mol).     

Kinetics of partly diffusion controlled reactions. II. Competition between physical and chemical kinetics. Theoretical treatment

We propose a quantitative method for computing the time-dependent value of the apparent rate constant of a bimolecular reaction in the liquid phase in The model proposed permits one to determine the time-dependence of the apparent rate constant of a bimolecular process in the case where a competition The results are necessary for the understanding of the deactivation of excited electronic states by various quenchers. As a matter of fact, it appears that in numerous experimental cases, such a competition is physically significant.     

Kinetics of partly diffusion controlled reactions. III. Competition between physical and chemical kinetics. Experimental results

In a previous paper (II in this series), we showed that the kinetic parameters of a partly diffusion controlled reaction could be calculated when the p Three examples of fluorescence quenching of electronically excited states were studied: pyrene by biacetyl; sulforhodamine G by I^?; and POPOP by fluorescence and fluorescence polarization measurements. They illustrate the kinetic models derived in papers I and II of this series.     

Integral invariants in chemical kinetics

Integral invariants of classical mechanical systems are used for the mathematical treatment of equilibrium systems of chemical reaction kinetics. Some conserved quantities and Hamilton equations in chemistry are shown.

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Mean-field cooperativity in chemical kinetics

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on statistical mechanics models and it is developed analytically via mean-field techniques. First of all, we show that, when the coupling strength is set positive, a cooperative behavior naturally emerges from the model; in particular, by means of various cooperative measures previously introduced, we highlight how the degree of cooperativity depends on the interaction strength among components. Furthermore, we introduce a criterion to discriminate between weak and strong cooperativity, based on a measure of “susceptibility.” We also properly extend the model in order to account for multiple attachments phenomena: this is realized by incorporating within the model p-body interactions, whose non-trivial cooperative capability is investigated too.     

Rheologic studies on chemical cross-linking kinetics for LDPE

Crosslinking reaction of LDPE resin in the presence of dicumyl peroxide(DCP) was studied by isothermal rheological measurements at different temperatures and non-isothermal differential scanning calorimetry(DSC) technique with different heating rates.The kinetic parameters of crosslinking reaction were calculated by both rheological and DSC measurements.The results reveal that with the increase of DCP contents,the apparent activation energy,E_a,ranges from about 140 kj/mol to 170 kj/mol and the order of crosslinking reaction,n,approaches unity.The influence of measurement frequency,ω,on crosslinking reaction was also investigated.It can be found that n does not change with the increase ofω, and E_a decreases slightly with the increase ofω.