Diffusion-influenced reactions

We summarize three of our recent results on diffusion-influenced reactions in solutions. All deal with the concentration dependence of the reaction rate when the reactants must first diffuse together before reaction can occur. When one species (the sink species) is not dilute, the rate cannot be obtained by solution of a pair diffusion equation; the correlations among the sinks for the diffusing species must be accounted for. First, we consider fluorescence quenching when the quenchers are not dilute. For charged quenchers and fluorophores we discuss how the solution dielectric constant and ionic strength can strongly influence the deviations from the linear Stern-Volmer behavior (the dilute sink result) which arise due to the sink correlations. Second, we consider heterogeneous catalysis where a reactive species is adsorbed onto a surface and must surface diffuse to reactive sites (the sinks). We find that surface diffusion can be an important factor contributing to the rate of reaction; especially when surface diffusion is rapid relative to the adsorption/desorption rate. Third, we discuss diffusion influenced reactions with sinks which are long ellipsoids. Dilute long ellipsoids provide a large rate enhancement relative to a spherical sink; we show that this rate enhancement survives when nondilute ellipsoids are considered.     

Diffusion-controlled processes among partially absorbing stationary sinks

A general linear response theory is presented to calculate the zero-wavevector and zero-frequency reaction rate coefficient for particles diffusing into absorbing spheres. Allowance is made for possible incomplete particle absorption. A Faxén-like theorem for chemical reactions is derived. The problem is solved completely for a simple regular array of sinks. Exact analytic expressions for the rate coefficient as a function of sink volume fraction are obtained for the sc and fcc lattices. The case of a disordered array of sinks is also considered and the leading order nonanalytic density dependence of the rate coefficient is calculated. In both cases an increase in the rate coefficient with sink density in a local region of the system is found. The general formalism is extended to examine the modification to the particle diffusion coefficient due to the presence of the spheres. For regular arrays of spheres, the mean field result is reproduced.Research supported in part by a grant from the National Research Council of Canada.     

Scattering length and diffusion

An expression for an asymptotic property of the Green's function for the diffusion of a particle is obtained. It is shown that this provides (as a special case) a very simple derivation of a previous result of Kac and Luttinger relating the scattering length to a certain Wiener integral.Guggenheim Fellow, 1975–1976. This work was also supported in part by the National Science Foundation.     

Microscopic Chaos and Reaction-Diffusion Processes in the Periodic Lorentz Gas

We apply the hypothesis of microscopic chaos to diffusion-controlled reaction which we study in a reactive periodic Lorentz gas. The relaxation rate of the reactive eigenmodes is obtained as eigenvalue of the Frobenius–Perron operator, which determines the reaction rate. The cumulative functions of the eigenstates of the Frobenius–Perron operator are shown to be generalizations of Lebesgue's singular continuous functions. For small enough densities of catalysts, the reaction is controlled by the diffusion. A random-walk model of this diffusion-controlled reaction process is presented, which is used to study the dependence of the reaction rate on the density of catalysts.Aspirant FNRS     

Stationary Nonequilibrium Particle-Number Distribution Density Formed by Particle Sources and Sinks

We analyze an inhomogeneous diffusion equation with the given potential profile and the particle source and sink. The possibility of forming a nonequilibrium but stationary state of the system is discussed. For a time-constant point source, we obtain general formulas determining the nonequilibrium stationary density distributions of the particle number as a function of potential-profile shape. The influence of sources and sinks on the flow structure in a diffusion system is determined. Some examples are considered.     

Diffusion-controlled reactions among stationary sinks

We summarize results of some of our calculations in diffusion-controlled reaction theory. We derive the transport equation describing a diffusing species which can react with a set of randomly distributed spherical sinks. Both the form of the transport equation and the dependence on sink volume fraction of the reaction rate and the effective diffusion coefficient are discussed.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.Supported in part by the National Science Foundation under Grant No. CHE-78-07849.     

Solute reaction mediated precipitate patterns in cross gradient free systems

Recent studies on the spontaneous formation of undulatory patterns of precipitate concentration, such as Liesegang and related phenomena, have shown that these effects can be explained on the basis of a competitive particle growth mechanism as underlies Ostwald ripening. However these effects require an overall gradient or boundary perturbation to induce regular patterning on a scale greater than the interparticle spacing to override the single crystal-so called greedy giant instability. Here we show that by allowing for precipitate particle mediated reactions involving the solute species (from which the precipitate is constructed) a fastest growing mode of wave vectork _d , 0<k _d <, exists and thus pattern formation can occur completely autonomously at a well defined wave length without the need of cross gradients. These processes may be much more widely realized in physical and biological self organization processes than the familiar reaction diffusion (Turing) model due to the rather nonspecific nature of the present phenomenon.Research supported in part by grants from the National Science Foundation and the Petroleum Research FundA.P. Sloan Fellow, 1980–82NATO Fellow, 1982     

On the theory of void formation during irradiation

A simple theory of the swelling of materials subjected to high energy particle irradiation is developed. Chemical reaction rate equations are used as a basis. Point defects, interstitials and vacancies, are assumed to be produced randomly throughout the solid. They move by random walk through the material until they cease to exist either by recombination with the opposite type of defect or by incorporation into the crystal at sinks such as dislocations, grain boundaries and voids. The rate equations for interstitials and for vacancies, which are coupled via the recombination term, are solved for steady state conditions under irradiation. Defect concentrations, supersaturations, recombination and total sink annihilation rates are obtained in terms of the production rate, sink annihilation probabilities, jump frequencies and thermal equilibrium concentrations of defects. The swelling rate is derived using sink annihilation probabilities at three principally different types of sinks, i.e. voids, sinks which have a bias with regard to the annihilation of interstitials and vacancies (such as dislocations), and sinks with no bias. The defect annihilation probabilities at void, precipitate, dislocation and grain boundary sinks are estimated by using a cellular model and solving the diffusion equation for geometries approximating that of the cells, e.g. a concentric sphere around a void. The relative effects of different types of sinks, i.e. the microstructure, on the swelling rate is discussed. The swelling rate is integrated to give swelling-time or swelling-dose relations, making some simplifying assumptions about the changes in the sink structure as the irradiation proceeds. It is shown that the relation obtained is rather sensitive to the type of assumptions made.     

Carrier scattering mechanisms in manganese-doped gallium antimonide

The results are given of an investigation of the galvanomagnetic properties of manganese-doped gallium antimonide in the interval of temperatures 4.2–300°K and in magnetic fields up to 1.5 T. The manganese was introduced into the melt during zone melting in concentrations in the range 0.005–1 at.%. The samples possessed p-type conduction. It was shown that manganese forms in gallium antimonide a shallow acceptor level with ionization energy 16 ± 3 meV. The cluster mechanism makes a significant contribution to the carrier scattering in the considered temperature range. The parameters of this scattering mechanism were determined. It was shown that with increasing concentration of manganese in the sample the contribution to the mobility of the mechanism of carrier scattering by space-charge regions increases.Translated from Izvestiya Vysshikh Uchebnykh Zavedennii, Fizika, No. 1, pp. 53–57, January, 1992.We thank I. I. Burdinyan and D. D. Nedeoglo for constant interest in the work.     

Coulomb drag experiments in low density 2D hole bilayers

We performed experiments studying the Coulomb drag in low density 2D hole bilayers, with r_s ranging from roughly 10 to 20. As the carrier density is lowered into the dilute regime, we observe a significant enhancement of the drag resistivity, such that the interlayer carrier–carrier scattering rate constitutes a major component of the single layer resistivity. In addition, anomalies to the expected temperature and in-plane magnetic field dependences are observed, and are found to correlate with similar anomalies in the single layer resistivity. These results suggests that the origin of the 2D metal–insulator transition phenomena affects both transport properties in a very similar fashion.     

Change in the surface concentration during diffusion saturation at a constant rate

Solution of the inverse problem of one-dimensional diffusion with constant coefficient leads to kinetic dependences of the surface concentration which ensure constancy of the rate of diffusion saturation. Numerical calculations are made for saturation of the Ni-Al system with oxygen.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 39–41, March, 1981.     

Z → e+e− decay in a constant magnetic field

In the one-loop approximation we calculate the electronic contribution to the elastic scattering amplitude of a Z-boson in a constant homogeneous magnetic field. Using this amplitude we obtain the probability of the decay of a Z-boson into an e⁺e^– pair, and we investigate its dependence on the boson energy and the external field strength.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 44–49, May, 1987.In conclusion, the authors wish to express their gratitude to Professor I. M. Ternov for a number of valuable remarks.     

Resonances of nanocylinders with gap defects

We have investigated the plasmonic resonance characteristics of canonical circular and square cylinders, with gap defects, that are illuminated by a plane wave. The circular and square cylinders have vee shaped gaps and constant width gaps, respectively. The electric and magnetic fields are obtained by solving the Lippmann–Schwinger equation from which we compute the far-field scattering cross-section and near-field local electromagnetic energy density.Numerical results are given for numerous wavelength and gap dimensions to qualitatively present the effects of gap defects on the scattering cross-section and local electromagnetic energy density.     

The Nosé–Hoover Thermostated Lorentz Gas

We apply the Nosé–Hoover thermostat and three variations of it, which control different combinations of velocity moments, to the periodic Lorentz gas. Switching on an external electric field leads to nonequilibrium steady states for the four models. By performing computer simulations we study the probability density, the conductivity and the attractor in nonequilibrium. The results are compared to the Gaussian thermostated Lorentz gas and to the Lorentz gas as thermostated by deterministic scattering. We find that slight modifications of the Nosé–Hoover thermostat lead to different dynamical properties of our models. However, in all cases the attractor appears to be multifractal.     

Renormalized diffusion coefficients for electron-hole plasmas in crossed fields

The diffusion and drift of an excess plasma in a semiconductor is described with magnetohydrodynamic two-fluid equations including the fluctuating electric field produced by the equilibrium plasma in the sample. Using the weak coupling limit an equation of motion for the mean density of the excess plasma is established with renormalized drift and diffusion coefficients. With the aid of the fluctuation dissipation theorem these coefficients are expressed in terms of the dielectric function and discussed in detail for stable systems. The renormalized diffusion coefficient differs from the bare one by an additional term with thet ^–3/2-long time dependence. It is shown that this term in addition represents an anomalous diffusion rate proportionalB ^–1 which overweights the classical ambipolar diffusion for sufficiently strong fields, but decreases with increasing external electric field. The results are compared with experimental data.     

Radiation enhanced diffusion in face centered cubic cu-zn alloys

The enhancement of diffusion by neutron irradiation has been investigated on a Cu-36 percent Zn alloy for various neutron fluxes and irradiation temperatures by means of in-pile measurements of electrical resistivity. For fresh samples the diffusion rate depends on temperature with an activation energy of 0.35 eV. During repeated irradiations the diffusion rate decreases and becomes nearly temperature independent. The variation of the concentration of interstitials and vacancies with irradiation time has been numerically calculated for various neutron fluxes, irradiation temperatures and sink concentrations. A comparison of the experimental and theoretical results shows that the point defects annihilate in fresh samples mainly by pair recombination and in samples which had been repeatedly cycled by pair recombination and at fixed sinks. Point defect clusters acting as sinks are created during the course of the irradiation as shown by electron microscope investigations. The radiation enhanced diffusion rate was found to depend on interstitials only, the activation energy of which was determined to 0.70 eV.     

Diffusion thermopower due to interface roughness-induced piezoelectric scattering in lattice-mismatched semiconductor quantum wells

We calculate the diffusion thermopower for a degenerate two-dimensional electron gas in real lattice-mismatched semiconductor quantum wells (QWs) at low temperatures. We consider explicitly two scattering mechanisms: (i) the surface roughness-induced piezoelectric effect, a new important scattering source, arising due to a large fluctuating density of roughness-induced piezoelectric charges and (ii) the surface roughness. The scattering parameter p of energy dependence of the momentum relaxation time and the diffusion thermopower S^d, of each of the mechanisms separately and also when both the mechanisms are combined, are calculated as a function of electron concentration and well width. The diffusion thermopower, as a function of electron concentration, due to piezoelectric field shows a change in sign for lower concentrations. Interestingly, the diffusion thermopower, due to this mechanism, as a function of well width also shows a change in sign and it is dominant for larger well widths. The numerical calculations are presented for In_0.2Ga_0.8As/GaAs and AlN/GaN QWs. The piezoelectric mechanism is expected to be very important in systems with large piezoelectric constant and lattice mismatch.     

Anomalous plasma phenomena of hollow cathode arc discharge

Magnetically confined argon plasma produced by hollow cathode arc discharge has been studied in different experimental conditions, with discharge current from 10–50 A, vessel argon pressure between 10^–3 and 10^–4 torr (1 torr=133·32 Pa) and axial magnetic field up to 0·12 T. The plasma density measured by a cylindrical Langmuir probe is found to be 10¹⁹ to 4 × 10¹⁹ m^–3 and the electron temperatureT _e varies between 2·5 and 4·8 eV. When an external axial magnetic field is applied the plasma temperature decreases with the increase in the magnetic field intensity until it reaches a minimum value at 0·075T and then increases with the same rate. This has been interpreted as high frequency waves excitation due to electron beam-plasma interaction, which explains the electron density jumps with the magnetic field intensity. Enhanced plasma transport across the magnetic field is studied and classified as anomalous diffusion.     

Magnetoresistance of the compound CeRu2Ge2

In this work we present a magnetoresistance study on the CeRu₂Ge₂ compound. We analyze the ρ(T) curves for several applied magnetic fields using the electron–magnon scattering model for a ferromagnetic spin arrangement. From this analysis, the field dependence of the energy gap of the magnon spectrum is obtained. The magnetoresistance ρ(H) at various temperatures arises from a normal metal contribution with an additional scattering mechanism due to electron–magnon interaction.     

Dynamics of nonspecific adsorption of insulin to erythrocyte membranes

Molecules may arrive at targets (receptors, enzymes, etc.) localized on a membrane surface by first adsorbing onto the surface and then surface diffusing to the targets. The flux rate of molecules arriving at targets via this mechanism depends on the surface diffusion coefficient of the molecules and, in some circumstances, on the adsorption/desorption kinetics. The technique of total internal reflection with fluorescence recovery after photobleaching (TIR-FRAP) was used here to study these rate parameters of fluorescein-labeled insulin (f-insulin) interacting with erythrocyte ghosts. Ghosts were adhered to polylysine coated slides for TIR illumination. Some ghosts became flattened and unsealed on the polylysine so that both extracellular and cytoplasmic sides of the membrane were openly exposed to the solution. An aluminum thin film between the polylysine and the fused silica of a slide quenched background fluorescence from f-insulin adsorbed directly onto the polylysine. An interference fringe pattern from two intersecting and totally internally reflecting laser beams provided surface-selective excitation with a spatial variation of illumination intensity across a ghost for surface diffusion measurements. Measured characteristic values of desorption rate constants ranged from 0.043 to 270 s^–1. According to a preexisting theoretical model, the largest desorption rate constant in this range would result in some increase in the total flux rate to a perfect sink target due to capture from the surface, provided that the surface diffusion coefficient was about 10^–8 cm²/s. However, based on TIR-FRAP measurements on our system, we estimate that the surface diffusion coefficient is less than about 5×10^–10 cm²/s. The combination of novel techniques presented here may prove valuable to other workers seeking to make diffusive and chemical kinetic rate parameter measurements of biomolecules at biological cell membranes.