Structuring of a foam concrete matrix from the perspective of fractal percolation theory on RLA, DLA, DLCA models

Introduction. Foam concrete is a complex highly porous system, the structuring process of which (sol-gel transition) determines its physical, mechanical, and operational characteristics. Fractal percolation theory is a modern tool for describing and modeling the formation of the fractal pore structure and the cement matrix.
Aim. To analyze the phase transition of the foam concrete matrix from a colloidal solution to a solid body from the perspective of fractal percolation theory using computer aggregation models (RLA, DLA, DLCA), as well as to experimentally study the effect of surfactants on the setting time.
Materials and methods. The experimental part used Portland cement CEM I 42.5N, technical water, and a synthetic silicone foaming agent “Penta Pav 430A”. Cement paste (W/C=0.24) was prepared in a control mix and with a surfactant additive. Setting times were determined according to GOST 30744–2001 using a Vicat device. The theoretical part was based on the analysis of diffusion-limited (DLA) and reaction-limited (RLA, DLCA) aggregation models.
Results. It was established that the introduction of a synthetic foaming agent in the range of 0.3–3 % increases the setting time of the cement paste by an average of 30 minutes. It is shown that the percolation transition (onset of setting) occurs when the concentration of chemically bound particles reaches 22 to 30 %. The presence of surfactants shifts the onset of setting, but the critical ratio of free to bound particles remains practically unchanged.
Conclusions. It is concluded that to prevent sedimentation and form a strong framework, it is necessary to control the setting kinetics through the water-solid ratio and the introduction of chemical additives.  

1. Morgun L.V. Foam concrete. The monograph. Rostov-on-Don: Publishing House of the Russian State University of Civil Engineering, 2012. 154 p.

2. Savenkov A.I., Shustov P.A., Gorbach P.S., Ploskonosova A.O. Evaluation of the strength of foam concrete under axial uniaxial compression. Izvestiya vuzov. Investment. Construction. Realty, 2020, vol. 10, no. 1 (32), pp. 100–107. 454 с. DOI: 10.21285/2227-2917-2020-1-100-107 EDN: KYMNTY

3. Akhverdov I.N. Fundamentals of concrete physics. Moscow: Stroyizdat, 1981. 454 p.

4. Maekawa K., Ishida T., Kishi T. Multiscale modeling of concrete characteristics: integrated materials science and construction mechanics. J. Adv. Concr. Tech., 2003, vol. 1, no. 2, pp. 91–126.

5. Kondo R., Ueda S. Kinetics and mechanism of cement hydration. 5th International Conference. Symposium on Cement Chemistry, Tokyo, 1968, pp. 230–255.

6. Holmes N., Kelliher D., Tyrer M. Modeling of cement hydration using HYDCEM. Constr. Build., 2020, vol. 239, pp. 117811. DOI: 10.1016/j.conbuildmat.2019.117811 EDN: ONHOFP

7. Mengutina N.V., Ivanov S.I., Lebedev I.V., Tyrtinnikov A.H. Creation of algorithms FOR and during the development of architectural projects. Software products and systems, 2017, no. 4(30), pp. 758–764. EDN: YMUFON

8. Babu S., Gimel J.K., Nicolai T. Diffusion-limited aggregation of clusters with irreversible slippery bonds. European Journal of Physics, 2008, E 27, pp. 297–308.

9. Porshnev S.V. Computer modeling of physical processes in the MATLAB package. St. Petersburg: Lan, 2011. 736 p.

10. Mikin P. Formation of fractal clusters and networks by irreversible diffusion-limited aggregation. Phys. Rev. Lett., 1983, vol. 51, p. 1119.

11. Li Kai, Zhao Wen, Shi Caijun. The use of computer modeling to study cement hydration and the evolution of the microstructure of its products. Cement and its application. Information portal about cement. Production, science, technology, 2024, issue no. 3. https://jcement.ru/magazine/vypusk-3-24/primenenie-kompyuternogo-modelirovaniya-dlya-izucheniya-gidratatsii-tsementa-i-evolyutsii-mikrostruk/

12. Virchenko Yu.P., Tolmacheva Yu.A. Method of sequential approximative estimates in the theory of discrete percolation. Research in mathematical Physics / ed. By Charles W. Benton. New York: Nova Science Publishers, Inc., 2004. pp. 155–175.

13. Nguyen V., Thermodynamic inequalities for percolation. General. Mathematics, Physics, 1985, 99, iNo. 2, 253–269 (RGMat, 1985, 12B270)

14. Ebert H.-P. Thermal properties of aerogels. Handbook of Aerogels Springer, 2011, pp. 537–564.

15. Blaszynski T., Shlosarczyk A., Morawski M. Synthesis of silica aerogel by supercritical drying. Procedural Engineering, 2013, vol. 57, pp. 200–206.

16. Menshutina N.V., Kolnochenko A.V., Katalevich A.M. Structural analysis and modeling of inorganic aerogels. Theoretical foundations of chemical engineering, 2014, vol. 48, no. 3, pp. 344–348.

17. Carnpanino M., Russo L. The upper bound of the probability of critical percolation for a three-dimensional cubic lattice. Ann. Probab., 1985, 13, vol. 2, pp. 478–491.

18. Vasher R., Vounye T., Falippu J., Pelous J., Courtens E. Fractal structure of silicon dioxide aerogels catalyzed by a base and compacted on its basis. Journal of Non-crystalline solids, 1988, vol. 106, no. 1, pp. 161–165.

19. Wei G., Zhang Y., Xu S., Du H., Yang Y. Investigation of thermal conductivity of aerogels with a two-porous distribution of powdered silica. Currently. Heat and mass transfer. 2017, vol. 108, pp. 1297–1304.

20. Allegre S.J., Le Mouel J.L., Provost A. Scaling rules for rock destruction and possible consequences for earthquake forecasting. Nature, 1982, 297, no. 5861, pp. 47–49.

21. Li S., Cheng H., Li Z., Pan Yu., Huang Yu., Gong L. Mechanical, thermal and ignitable properties of glass fiber film and silica aerogel composites. Journal of non-crystalline solids, 2017, vol. 457, pp. 52–59.

22. Amaral-Labat G., Shchurek A., Fierro V., Masson E., Pizzi A., Selzard A. Influence of pressure reduction rate on aerogel porosity. Microporous and mesoporous materials, 2012, vol. 152, pp. 240–245.

23. Antonova E.S., Virchenko Yu.P. Monotony of percolation probability for Bernoulli random fields on periodic graphs //Journal of Mathematical Sciences. 2011. Volume 175, No. 1. pp. 86–90. DOI: 10.1007/s10958-011-0335-5 EDN: HJDRSA