Abstract.
Lattice and off-lattice Monte Carlo simulations of diffusion-limited cluster aggregation and gelation were done over a broad range of concentrations. The large-scale structure and the size distribution of the clusters are characterized by a crossover at a characteristic size (\(m_{\rm c}\)). For \(m < m_{\rm c}\), they are the same as obtained in a dilute DLCA process and for \(m \gg m_{\rm c}\) they are the same as obtained in a static percolation process. \(m_{\rm c}\) is determined by the overlap of the clusters and decreases with increasing particle concentration. The growth rate of large clusters is a universal function of time reduced by the gel time. The large-scale structural and temporal properties are the same for lattice and off-lattice simulations. The average degree of connectivity per particle in the gels formed in off-lattice simulations is independent of the concentration, but its distribution depends on the concentration.
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References
M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, Phys. Rev. A 42, 7347 (1990).
T. Nicolai, S. Cocard, Eur. Phys. J. E 5, 221 (2001).
G. Kruif, M. Hoffmann, Faraday Discuss. 101, 185 (1995).
S.H. Chen, J. Rouch, F. Sciortino, P. Tartaglia, J. Phys. Condens. Matter 6, 10855 (1994).
T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1989).
P. Meakin, Phys. Scr. 46, 295 (1992).
M. Kolb, R. Botet, R. Jullien, Phys. Rev. Lett. 51, 1123 (1983).
A. Hasmy, M. Foret, J. Pelous, R. Jullien, Phys. Rev. B 48, 9345 (1993).
M. Lattuada, P. Sandkuhler, H. Wu, J. Sefcik, M. Morbidelli, Adv. Colloid Interface Sci. 103, 33 (2003).
P. Meakin, F. Family, Phys. Rev. A 38, 2110 (1988).
A.E. Gonzalez, G. Ramirez-Santiago, J. Colloid Interface Sci. 182, 254 (1996).
R. Jullien, M. Kolb, R. Botet, J. Phys. (Paris) Lett. 45, L211 (1984).
J.C. Gimel, T. Nicolai, D. Durand, J. Sol-Gel Sci. Technol. 15, 129 (1999).
D. Stauffer, A. Aharony, Introduction to Percolation Theory, second edition (Taylor and Francis, London, 1992).
M. Lattuada, H. Wu, A. Hasmy, M. Morbidelli, Langmuir 19, 6312 (2003).
M. Rottereau, J.C. Gimel, T. Nicolai, D. Durand, this issue p. \(\bullet\).
J.C. Gimel, D. Durand, T. Nicolai, Phys. Rev. B 51, 11348 (1995).
M. Rottereau, J.C. Gimel, T. Nicolai, D. Durand, Eur. Phys. J. E 11, 61 (2003).
S. Torquato, Phys. Rev. Lett. 74, 2156 (1995).
T. Nicolai, D. Durand, J.C. Gimel, in Light Scattering: Principles and Development, edited by W. Brown (Clarendon Press, Oxford, 1996) p. 201.
R. Klein, D.A. Weitz, M.Y. Lin, H.M. Lindsay, R.C. Ball, P. Meakin, Prog. Colloid Polym. Sci. 81, 161 (1990).
T. Nicolai, D. Durand, J.C. Gimel, Phys. Rev. B 50, 16357 (1994).
P. Sandkuhler, J. Sefcik, M. Lattuada, H. Wu, M. Morbidelli, AIChE J. 49, No. 6, 1542 (2003).
G. Odriozola, A. Schmitt, J. Callejas-Fernandez, R. Martinez-Garcia, R. Hidalgo-Alvarez, J. Chem. Phys. 111, 7657 (1999).
M. Von Smoluchowski, Z. Phys. Chem. 92, 129 (1917).
S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
M. Lattuada, H. Wu, M. Morbidelli, J. Colloid Interface Sci. 268, 96 (2003).
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Received: 27 April 2004, Published online: 26 October 2004
PACS:
64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 02.70.Uu Applications of Monte Carlo methods
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Rottereau, M., Gimel, J.C., Nicolai, T. et al. Monte Carlo simulation of particle aggregation and gelation: I. Growth, structure and size distribution of the clusters. Eur. Phys. J. E 15, 133–140 (2004). https://doi.org/10.1140/epje/i2004-10044-x
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DOI: https://doi.org/10.1140/epje/i2004-10044-x