Keywords: cement, cohesion, Monte Carlo simulation, ion-ion correlations, overcharging, atomic force microscopy.

Cement paste is a complex heterogeneous, polyphasic and reactive material with a relatively low stability range in the different phases. The pH and ionic concentrations of the pore solution are high, circumstances that have made it difficult to set up accurate experiments. The nanometric dimensions of the main hydrate of cement pastes, i.e. calcium silicate hydrate (C-S-H), has also added to the experimental difficulties. As a consequence, it is only recently that the molecular interactions responsible for the cohesion of hydrated cement were elucidated.

In this paper we show that the physical chemistry of the C-S-H/water interface and the interactions of the C-S-H particles in an early cement paste can be described with a simple electrostatic model in the grand canonical ensemble. The model was solved using Monte Carlo simulations. This model makes three predictions regarding the charge formation, the apparent charge and the interactions of the C-S-H particles dispersed in dissolved Ca(OH)₂ solutions.

The surface of the C-S-H becomes highly negatively charged in saturated lime solution, i.e. high pH (>12) and calcium ion concentration (~20 mM). The charge formation is promoted by the screening of calcium ions that accumulate in the region just next to the C-S-H surface. An excellent agreement is obtained between the titration experiments and simulations.

The overcharging of the C-S-H particles results from both the occurrence of high negative surface charge and of accumulation of calcium counterions to the surface. In perfect agreement with the electrophoretic mobility experiments the model predicts an overcharging for concentrations of Ca(OH)₂ higher than 2 mM. Therefore, the overcharging is a consequence of electrostatic interactions alone (ion-ion correlations) and does not reflect a chemical binding of calcium ions to the surface.

The interactions of the C-S-H particles result from a delicate balance between an ionic entropic repulsion and an electrostatic attraction due to the correlations between the ions. For small Ca(OH)₂ concentrations in the pore solution, the surface silanol groups are weakly ionized and the C-S-H particles repel each other as a consequence of a strong ionic entropic pressure. On contrary, for saturated Ca(OH)₂ solutions, the C-S-H surfaces are almost fully ionized and accumulate a huge amount of Ca²⁺ counterions which lead to the collapse of the entropic pressure. As a consequence the correlation force dominates the interaction. In these conditions the C-S-H particles aggregate and form a cohesive network. At later stages, short-range attractive forces may control the maximum strain of the C-S-H network. The medium range attraction between the C-S-H particles observed through the atomic force microscopy experiments is shown to be controlled by the coupling of the system, that is the ionized state of the surface silanol groups (or equivalently the surface charge density) and the concentration of Ca²⁺ counterions in the pore solution.

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