Diffusion-limited reaction in one dimension

2006 ◽  
Vol 222 (1-2) ◽  
pp. 159-163 ◽  
Author(s):  
Grant Lythe
Keyword(s):  
One Dimension ◽  
Diffusion Limited ◽  
Diffusion Limited Reaction

scholarly journals Diffusion-limited reaction in one dimension: Paired and unpaired nucleation

2001 ◽  
Vol 115 (1) ◽  
pp. 73-89 ◽  
Author(s):  
Salman Habib ◽  
Katja Lindenberg ◽  
Grant Lythe ◽  
Carmen Molina-Parı́s
Keyword(s):  
One Dimension ◽  
Diffusion Limited ◽  
Diffusion Limited Reaction

Experimental Investigations of the Kinetics of a Catalytic Trapping Reaction in Confined Spaces

1996 ◽  
Vol 464 ◽  
Author(s):  
Mark S. Feldman ◽  
Anna L. Lin ◽  
Raoul Kopelman
Keyword(s):  
Reaction Front ◽  
Rate Coefficient ◽  
Capillary Tube ◽  
One Dimension ◽  
Experimental Investigations ◽  
Confined Spaces ◽  
Diffusion Limited ◽  
Kinetics Of ◽  
Oxidation Of Glucose ◽  
Theoretical Results

AbstractWe investigate the anomalous kinetics in one dimension of a diffusion limited catalytic trapping reaction, A + T → T, by measuring the oxidation of glucose. The reaction is carried out in a thin capillary tube, and the depletion of oxygen in the vicinity of the reaction front is monitored by the fluorescence of a Ru(II) dye. Theoretical results and simulations have predicted an asymptotic t1/2 dependence for the rate coefficient. We observe a depedence on t0.56, with what appears to be an asymptotic behavior approaching t1/2.

Diffusion-reaction in one dimension

1988 ◽  
Vol 25 (04) ◽  
pp. 733-743 ◽  
Author(s):  
David Balding
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Particle Systems ◽  
Diffusion Reaction ◽  
One Dimension ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Special Cases ◽  
Initial Arrangement ◽  
Number Of Particles

One-dimensional, periodic and annihilating systems of Brownian motions and random walks are defined and interpreted in terms of sizeless particles which vanish on contact. The generating function and moments of the number pairs of particles which have vanished, given an arbitrary initial arrangement, are derived in terms of known two-particle survival probabilities. Three important special cases are considered: Brownian motion with the particles initially (i) uniformly distributed and (ii) equally spaced on a circle and (iii) random walk on a lattice with initially each site occupied. Results are also given for the infinite annihilating particle systems obtained in the limit as the number of particles and the size of the circle or lattice increase. Application of the results to the theory of diffusion-limited reactions is discussed.

Diffusion-reaction in one dimension

1988 ◽  
Vol 25 (4) ◽  
pp. 733-743 ◽  
Author(s):  
David Balding
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Particle Systems ◽  
Diffusion Reaction ◽  
One Dimension ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Special Cases ◽  
Initial Arrangement ◽  
Number Of Particles

One-dimensional, periodic and annihilating systems of Brownian motions and random walks are defined and interpreted in terms of sizeless particles which vanish on contact. The generating function and moments of the number pairs of particles which have vanished, given an arbitrary initial arrangement, are derived in terms of known two-particle survival probabilities. Three important special cases are considered: Brownian motion with the particles initially (i) uniformly distributed and (ii) equally spaced on a circle and (iii) random walk on a lattice with initially each site occupied. Results are also given for the infinite annihilating particle systems obtained in the limit as the number of particles and the size of the circle or lattice increase. Application of the results to the theory of diffusion-limited reactions is discussed.

Glancing Angle X-Ray Study of Crystallization of Amorphous Ge at the Ge-A1 Interface

1990 ◽  
Vol 202 ◽  
Author(s):  
S. M. Heald ◽  
J. K. D. Jayanetti ◽  
R. C. Budhani
Keyword(s):  
Initial Period ◽  
Time Characteristic ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffusion Limited ◽  
Glancing Angle ◽  
Lower Temperature ◽  
Kinetics Of ◽  
Diffusion Limited Reaction ◽  
Good Agreement

ABSTRACTThe amorphous to crystalline transformation of Ge in Al/Ge thin film couples has been studied using glancing angle EXAFS, x-ray reflectivity and diffraction. It was found that crystallization occurs at a much lower temperature (118-150 °C) than for bulk Ge, and initiates at the Al/Ge interface. X-ray diffraction studies were made at 152 °C to study the kinetics of the reaction. After an initial period we find good agreement with a square root dependence of the time, characteristic of a diffusion limited reaction.

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