Cluster–cluster aggregation with mobile impurities

  • Anwar HasmyEmail author
  • Juan Primera
  • Thierry Woignier
Original Paper: Modelling, computational tools and theoretical studies of sol-gel and hybrid materials


We considered the diffusion-limited cluster–cluster aggregation (DLCA) model in the presence of inert template (mobile impurities) for the simulation of mesoporous materials obtained through sol–gel processes. A computer algorithm based on the off-lattice version of the two-dimensional DLCA model with moving impurities is introduced. If the density of monomers is large enough, a porous matrix results at the end of the aggregation mechanism. Impurities are removed at the final stage of the simulation, assuming that the porous structure is not altered as in some experiments. We are interested in the modification of the resulting porous structure due to the presence of moving inert impurities during aggregation. The resulting porous material consists of a homogeneous structure of interconnected fractal clusters. Such structure is characterized by computing the correlation length and the fractal dimension of these clusters. The numerical analysis of the pore size distribution reveals a strong dependence with the density and sizes of mobile impurities. Compared to the DLCA model, the curve distribution becomes bimodal when impurities are introduced, i.e., it appears a first maximum at small pore sizes (of the order of the monomer dimension), and a second maximum around the impurity size. For large monomer densities the amplitude of the peak around the impurity size becomes larger than the peak of the smallest pore size.


  • We simulate the mesoporous materials obtained through so–gel process by a cluster–cluster aggregation model in the presence of impurities.

  • We show that the porous material consists of interconnected fractal clusters.

  • The pore size distribution is strongly dependent on the concentration and the size of impurities.


Cluster–cluster aggregation Numerical simulation Template Pore size distribution 



  1. 1.
    Hasmy A, Anglaret E, Foret M, Pelous J, Jullien R (1994) Small-angle neutron-scattering investigation of long-range correlations in silica aerogels: Simulations and experiments. Phys Rev B 50:6006–6016CrossRefGoogle Scholar
  2. 2.
    Woignier T, Phalippou J. (2016) Glasses: sol–gel methods. In: Hashmi S. (ed) Reference module in materials science and materials engineering. Elsevier Inc., Amsterdam p 3581–3585Google Scholar
  3. 3.
    Sabín J, Prieto G, Ruso JM, Messina P, Sarmiento F (2007) Aggregation of liposomes in presence of La 3+: a study of the fractal dimension. Phys Rev E 76:011408CrossRefGoogle Scholar
  4. 4.
    Gao J, Qu R, Tang B, Wang C, Ma Q, Sun C (2011) Control of the aggregation behavior of silver nanoparticles in polyurethane matrix. J Nanopart Res 13:5289–5299CrossRefGoogle Scholar
  5. 5.
    Fuller GT, Considine T, Golding M, Matia-Merino L, Mac Gibbon A, Gillies G (2015) Aggregation behaviour of crystalline oil-in-water emulsions: Part II – effect of solid fat content and interfacial film composition on quiescent and shear stability. Food Hydrocoll 43:521–558. 2015CrossRefGoogle Scholar
  6. 6.
    Nishihara H, Iwamura S, Kyotani T (2008) Synthesis of silica-based porous monoliths with straight nanochannels using an ice-rod nanoarray as a template. J Mater Chem 18:3662–3670CrossRefGoogle Scholar
  7. 7.
    Wa L, Fengyunb L, Fanlua Z, Mengjing C, Qianga C, Jueb H, Weijunc Z, Mingweia M (2015) Preparation of silica aerogels using CTAB/SDS as template and their efficient adsorption. Appl Surf Sci 353:1031–1036CrossRefGoogle Scholar
  8. 8.
    Vareda JP, Maximiano P, Cunha LP, Ferreira AF, Simões PN, Durães L (2018) Effect of different types of surfactants on the microstructure of methyltrimethoxysilane-derived silica aerogels: a combined experimental and computational approach. J Colloid Interface Sci 512:64–76CrossRefGoogle Scholar
  9. 9.
    Zhang W, Tao Y, Li C (2018) Effects of PEG4000 template on sol-gel synthesis of porous cerium titanate photocatalyst. Solid State Sci 78:16–21CrossRefGoogle Scholar
  10. 10.
    Thomson KT, Gubbins KE (2000) Modeling structural morphology of microporous carbons by reverse Monte Carlo. Langmuir 16:5761–5773CrossRefGoogle Scholar
  11. 11.
    Family F, Landau DP (eds) (1984) Kinetics of aggregation and gelation. Elsevier, AmsterdamGoogle Scholar
  12. 12.
    Jullien R, Botet R (1987) Aggregation and fractal aggregates. World Scientific, SingaporeGoogle Scholar
  13. 13.
    Jullien R, Hasmy A, Anglaret E (1997) Effect of cluster deformations in the DLCA modeling of the sol-gel process. J Sol Gel Sci Techn 8:819–824Google Scholar
  14. 14.
    Primera J, Woignier T, Hasmy A (2005) Pore structure simulation of gels with a binary monomer size distribution. J Sol Gel Sci Techn 34:273–280CrossRefGoogle Scholar
  15. 15.
    Sorensen CM (2011) The mobility of fractal aggregates: a review. Aerosol Sci Technol 45:765–779CrossRefGoogle Scholar
  16. 16.
    Meakin P, Djordjevic Z (1986) Cluster-cluster aggregation in two- monomer systems. J Phys A 19:2137–2153CrossRefGoogle Scholar
  17. 17.
    Stoll S, Pefferkorn E (1996) Monte Carlo simulation of controlled colloid growth by homo- and heterocoagulation in two dimensions. J Colloid Interface Sci 177:192–197CrossRefGoogle Scholar
  18. 18.
    Anderson ML, Morris CA, Stroud RM et al. (1999) Colloidal gold aerogels: preparation, properties, and characterization. Langmuir 15:674–681CrossRefGoogle Scholar
  19. 19.
    AlSunaidi A, Lach-hab M, Gonzalez AE, Blaisten-Barojas E (2000) Cluster-cluster aggregation in binary mixtures. Phys Rev E 61:550–556CrossRefGoogle Scholar
  20. 20.
    AlSunaidi A, Lach-hab M, Blaisten-Barojas E, Gonzalez AE (2000) Colloidal aggregation with mobile impurities. Phys Rev E 61:6781–6788CrossRefGoogle Scholar
  21. 21.
    Woignier T, Primera J, Hasmy A (2006) Application of the diffusion limited cluster agregation model to natural gels: the allophanic soils. J Sol Gel Sci Techn 40(2-3):201–207CrossRefGoogle Scholar
  22. 22.
    Meakin P (1983) Diffusion-controlled cluster formation in 2—6-dimensional space. Phys Rev Lett 51:1119–1122CrossRefGoogle Scholar
  23. 23.
    Kolb M, Botet R, Jullien R (1983) Scaling of kinetically growing clusters. Phys Rev Lett 51:1123–1126CrossRefGoogle Scholar
  24. 24.
    Hasmy A, Jullien R (1995) Sol-gel process simulation by cluster-cluster aggregation. J Non Cryst Solids 186:342–348CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidad Simón BolívarCaracasVenezuela
  2. 2.Facultad de Ingeniería AgricolaUniversidad Técnica de ManabíPortoviejoEcuador
  3. 3.Departamento de Física, FECUniversidad del ZuliaMaracaiboVenezuela
  4. 4.Aix Marseille Univ, Univ Avignon, CNRS, IRDIMBEMarseilleFrance
  5. 5.IRD UMR 237Campus Agro Environnemental CaraïbesLe LamentinMartinique

Personalised recommendations