Hostname: page-component-7bb8b95d7b-cx56b Total loading time: 0 Render date: 2024-10-06T12:33:18.053Z Has data issue: false hasContentIssue false
  • English
  • Français

Concentration Influence on Diffusion Limited Cluster Aggregation

Published online by Cambridge University Press:  03 September 2012

ST.C. Pencea  and
M. Dumitrascu
ST.C. Pencea
Affiliation:
Romanian Academy, Institute of Physical Chemistry, Department of Colloids, Spl.Independentei 202, 79611 Bucharest sect. 6, Romania
M. Dumitrascu
Affiliation:
Biotehnos SA, Department of Automation, Str. Dumbrava Rosie 18, Bucharest sect. 2, Romania
Get access

Abstract

Diffusion-limited cluster aggregation has been simulated on a square two dimensional lattice. In order to simulate the brownian motion, we used both the algorithm proposed initially by Kolb et all. and a new algorithm intermediary between a simple random walk and the ballistic model.

The simulation was performed for many values of the concentration, from 1 to 50%. By using a box-counting algorithm one has calculated the fractal dimensions of the obtained clusters. Its increasing vs. concentration has been pointed out. The results were compared with those of the classical diffusion-limited aggregation (DLA).

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 367: Symposium P – Fractal Aspects of Materials , 1994 , 373
Copyright
Copyright © Materials Research Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Witten, T.A. and Sander, L.M., Phys. Rev. Lett. 47, 1400 (1980); Phys. Rev. B 27, 5696 (1983).Google Scholar
2. Meakin, P., Phys. Rev. A 27, 1495 (1983).Google Scholar
3. Stanley, H.E., Bunde, A., Halvin, S., Lee, J., Roman, E. and Schwartzer, S., Physica A 168, 23 (1990).Google Scholar
4. Meakin, P., Stanley, H.E., Coniglio, A. and Witten, T.A., Phys. Rev. A 32, 2364 (1985).Google Scholar
5. Nittman, J. and Stanley, H.E., Nature 321, 663 (1986).Google Scholar
6. Meakin, P., Phys. Rev. Lett. 51, 1119 (1983).Google Scholar
7. Kolb, M., Botet, R. and Jullien, R., Phys. Rev. Lett. 51, 1123 (1983).Google Scholar
8. Wicsek, T., Fractal Growth Phenomena, 2nd ed., World Scientific Publishing Co. Pte. Ltd., Singapore, 1992.Google Scholar
9. The percolation threshold depends on the lattice dimension, because the clusters are fractals. At any given concentration, when the lattice dimension increases, the fractal dimension remains quite constant, until that lattice dimension at which percolation firstly occurs. Above this dimension we expect that the fractal dimension will obviously increase with the dimension of the lattice, having a limit equal to 2 for an infinite lattice. Please note that at concentration greater or equal to 50% one must observe incipient percolation even for small latices. The first author wishes to thank A.E. Gonzales and T. Odagaki for their comments who gave a new light on our conclusions.Google Scholar