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AGGREGATION OF NANOPARTICLES IN 1D. The C-S-H gel. RAQUEL GONZALEZ Low dimensional curse 22 February 2009. OUTLINE. Introduction - The cement based materials. C-S-H gel: - Structural models Colloidal models Aggregation Brownian Cluster Dynamics: Isotropic interactions
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AGGREGATION OF NANOPARTICLES IN 1D The C-S-H gel. RAQUEL GONZALEZ Low dimensional curse 22 February 2009
OUTLINE • Introduction • - The cement based materials. • C-S-H gel: • - Structural models • Colloidal models • Aggregation • Brownian Cluster Dynamics: • Isotropic interactions • Non-isotropic interactions • Preliminar results • Conclusions and perspectives
NANOPARTICLES Wide range of properties Improving our life
STRUCTURAL MODEL Calcium Silicon Oxygen Hydrogen Ca-O layer Silicate chain
COLLOIDAL MODELS JENNINGS MODEL 5 nm sized Rounded particles Single Basic Building Block Basic Building Block HD C-S-H LD C-S-H
JENNINGS MODEL Drawbacks: • Link between structural models and colloidal models • Inner and Outer product TEM images 3D 1D
AGGREGATION IN C-S-H GEL Existence of Inner and Outer product Two type of forces: Isotropic: V d W Directional a b Geometrical restrictions!!
Stochastic processes Brownian Dynamics DESPLACEMENT PROPORTIONAL TO TIME
BROWNIAN CLUSTER DYNAMICS APPROACH V(r) Square well potential a 0 1 r b u Algorithm: • clusters are built by forming randomly rigid bonds between neighboring particles with a probability P = 1-exp(u/kT) • monomers/clusters move with no bond breaking nor overlap • clusters are rebuilt at each time step
β α Ea Enl ∆E=E1-Enl E1 Thermodinamic relation
ISOTROPIC INTERACTIONS: DLCA AND RLCA LIMITS Depending on the probability α that particles form a bond at each collision. DLCA α = 1 RLCA α→ 0 (b) [11]
ANISOTROPIC SYSTEM directional interaction + isotropic interaction rotational +translational diffusion
ANISOTROPIC SYSTEM Ω θ Ω the interaction takes place
Isotropic interactions p= 0.37 AMORFUS 3D [9]
Non isotropic interactions: α1=1 β1=0.331 α2=1 β2=0 CRYSTALINE 1D [9]
The method allows passing from a 3D structure to a 1D structure as we can see in the results. • In cementitious materials there are two types of systems, the Inner and the Outer product, which correspond with the aggregation of particles in 1D or 3D. • These preliminary results point out that the Basic Building Blocks are not a unique “black” particle they must be have something inside which makes them different. Some MD calculations point out that for similar morphology there are different structures formed.
CSH aggregation My work
REFERENCES [1] J.H. Liao, K.J. Chen, L.N. Xu, C.W. Ge, J. Wang, L. Huang, N. Gu, Appl. Phys. A, 76 (2003)541. [2] H.F.W. Taylor, “Cement chemistry”, Ed.Thomas Telford, 2nd Edition (1998). [3] E. Bonaccorsi, S. Merlino and H.F.W. Taylor, “The crystal structure of jennite, Ca9Si6O18(OH)6·8H2O”, Cement and Concrete Research, 34 (9) 1481-1488 (2004). [4] E. Bonaccorsi, S. Merlino and A.R. Kampf, “The Crystal Structure of tobermorite 14 Å (plombierite), a C–S–H phase”, Journal of the American Ceramic Society, 88 (3) 505-512 (2005). [5] H.M. Jennings, “A model for the microstructure of calcium silicate hydrate in cement paste”, Cement and Concrete Research, 30 (1) 101-116 (2000). [6] A.J. Allen, R.C. Oberthur, D. Pearson, P.Schofield, C.R. Wilding, Development of the fine porosity and gel structure of hydrating cement systems, Phil mag B 56 (1987) 263-268. [7] H.F. Taylor, proposed structure for calcium silicate hydrate gel, J Am Ceram Soc 69(6) (1986) 464-467. [8] E. Allen, J. Henshaw, P. Smith,” A Review of Particle Agglomeration” , Issue1, (2001) [9] J.C. Gimel “Static and dynamical study of aggregating processes using a novel simulation technique: The Brownian Cluster Dynamics” (2007) [10] J. S Dolado, “A molecular Dynamics study of cementitious calcium silicate hydrate gels” Ceram.Soc. 90, 3938 (2007). [11] D.A. Weitz and J.S. Huang. Self similar structures and the kinetics of aggregation of gold colloids. Kinetic of aggregation and gelation. F.Family and D.P.Landau, Elsevier Science publishers, 19, (1984)