Peculiarities of diffusion-controlled recombination kinetics at long time and/or for great initial reagent concentrations

1985 ◽  
Vol 35 (5) ◽  
pp. 541-548 ◽  
Author(s):  
V. Kuzovkov ◽  
E. Kotomin
Keyword(s):  
Initial Reagent ◽  
Diffusion Controlled ◽  
Long Time ◽  
Recombination Kinetics

THOMPSON's METHOD APPLIED TO THE BROWNIAN AND NON-BROWNIAN DIFFUSION-CONTROLLED REACTIONS OF TYPE kA → lA (l < k)

2002 ◽  
Vol 16 (17) ◽  
pp. 601-613 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Renormalization Group ◽  
Good Description ◽  
Wave Length ◽  
Group Scheme ◽  
Single Species ◽  
Critical Dimension ◽  
Stationary Regime ◽  
Brownian Diffusion ◽  
Diffusion Controlled ◽  
Long Time

The diffusion-controlled reactions of type kA → lA, with l < k, including the case of the annihilation reaction kA → 0, are studied by using Thompson's method, both in the case of Brownian (γ = 2) as in the case of anomalous (γ ≠ 2) diffusion conditions. These reactions are known to be strongly dependent on fluctuations below some critical dimension dc. We find dc = γ/(k-1) and the asymptotic behavior of density [Formula: see text]. At d = dc, the density goes as <∊> ~ ( ln t/t)1/k-1. For γ = 2, the scaling results obtained here are in agreement with the renormalization group calculations of Lee15 and a more recent work of Oliveira.8 We go further by also studying the case of an external homogeneous source (h) of single species particles A in the case of the stationary regime. Then we obtain the critical exponent δ in [Formula: see text], the dynamical exponent for the relaxation time Δ′ in (τh ~ hΔ′) and the exponent for the concentration decay ξ in (∊ ~ τ- ξ), with all these quantities evaluated in the limit h → 0. We get relations of scaling among critical indexes, and, in the special case of γ = 2, we recover those results previously obtained by Rácz.30 Thompson's method is a simple alternative way to the renormalization group scheme and has been shown to be a good description for the long-time (long wave-length) regime.

Long-time behavior of the diffusion-controlled A+B→0 reaction with hopping energy relaxation

1997 ◽  
Vol 106 (8) ◽  
pp. 3157-3158
Author(s):  
S. D. Baranovskii ◽  
F. Hensel ◽  
J. E. Golub ◽  
P. Thomas
Keyword(s):  
Energy Relaxation ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Diffusion Controlled ◽  
Long Time ◽  
Hopping Energy

A+B→0 ENHANCED DIFFUSION-CONTROLLED REACTIONS UNDER STATIONARY REGIME CONDITION THROUGH THOMPSON'S APPROACH

2004 ◽  
Vol 18 (09) ◽  
pp. 345-353
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Good Description ◽  
Group Scheme ◽  
Stationary Regime ◽  
Brownian Diffusion ◽  
Zero Field ◽  
Enhanced Diffusion ◽  
Diffusion Controlled ◽  
Simple Alternative ◽  
Time Regime ◽  
Long Time

In this work, Thompson's method is used to study the A+B→0 reactions controlled by anomalous and brownian diffusion in the case of an external homogeneous source (h) of particles A and B under sthequiometric condition (the same input rate h) and also in the special case of the stationary regime. So the novelty in the present work is that we are able to obtain for such kind of reactions (σ=1) the static critical exponent δ of concentration [Formula: see text], the dynamical exponent for the relaxation time Δ'(τh~h-Δ') and the exponent for the concentration decaying ξ(∊~τ-ξ), with all these quantities evaluated in the limit h→0 (zero-field-rate). We also get scaling relations among new critical indexes. After we go further by obtaining more general results for such exponents so that we are able to include also the case of A+A→0(A) reactions within an unified scheme as already made before by introducing a general effective action (Aσ,γ). Thus, when we consider the case σ=0 (A,+A→0(A) reactions) we recover those critical exponents (δ,Δ',ξ) for anomalous coalescence reactions of type kA→lA(l<k). And when we even make γ=2 (brownian diffusion) we get the exponents previously given by Rácz, and also some results obtained by Lee and Oliveira. Thompson's method is a simple alternative way to the renormalization group scheme and has been shown to be a good description for long-time regime.

A TEM investigation of a hyper-eutectic lead-tin alloy

1988 ◽  
Vol 46 ◽  
pp. 562-563
Author(s):  
John A. Sutliff
Keyword(s):  
Volume Diffusion ◽  
Eutectic Mixture ◽  
Precipitation Reaction ◽  
Directionally Solidified ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Diffusion Controlled ◽  
Discontinuous Precipitation Reaction ◽  
Controlled Precipitation

Near-eutectic Pb-Sn alloys are important solders used by the electronics industry. In these solders, the eutectic mixture, which solidifies last, is the important microstructural consituent. The orientation relation (OR) between the eutectic phases has previously been determined for directionally solidified (DS) eutectic alloys using x-ray diffraction or electron chanelling techniques. In the present investigation the microstructure of a conventionally cast, hyper-eutectic Pb-Sn alloy was examined by transmission electron microscopy (TEM) and the OR between the eutectic phases was determined by electron diffraction. Precipitates of Sn in Pb were also observed and the OR determined. The same OR was found in both the eutectic and precipitation reacted materials. While the precipitation of Sn in Pb was previously shown to occur by a discontinuous precipitation reaction,3 the present work confirms a recent finding that volume diffusion controlled precipitation can also occur.Samples that are representative of the solder's cast microstructure are difficult to prepare for TEM because the alloy is multiphase and the phases are soft.

200kv superconducting cryo electron microscope

1987 ◽  
Vol 45 ◽  
pp. 642-643
Author(s):  
M. Iwatsuki ◽  
Y. Kokubo ◽  
Y. Harada ◽  
J. Lehman
Keyword(s):  
Electron Microscope ◽  
Structure Analysis ◽  
Organic Materials ◽  
Strong Interactions ◽  
Specimen Preparation ◽  
Great Effort ◽  
Electron Microscopic ◽  
Crystal Fields ◽  
Special Skill ◽  
Long Time

In recent years, the electron microscope has been significantly improved in resolution and we can obtain routinely atomic-level high resolution images without any special skill. With this improvement, the structure analysis of organic materials has become one of the interesting targets in the biological and polymer crystal fields.Up to now, X-ray structure analysis has been mainly used for such materials. With this method, however, great effort and a long time are required for specimen preparation because of the need for larger crystals. This method can analyze average crystal structure but is insufficient for interpreting it on the atomic or molecular level. The electron microscopic method for organic materials has not only the advantage of specimen preparation but also the capability of providing various information from extremely small specimen regions, using strong interactions between electrons and the substance. On the other hand, however, this strong interaction has a big disadvantage in high radiation damage.

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