In self-assembly, building blocks consisting of colloidal particles with anisotropy in shape and interaction drive the formation of mesoscopic structures during aggregation, strongly influencing the transport and mechanical properties of the material. An example is the binding phase of cement, calcium silicate hydrate (C-S-H). Several questions persist on its structure and rheology during hydration. Early models of C-S-H proposed a building block of a few nanometers, which forms larger units up to 100 nm [1]. Experimental evidence has resolved the structure of these colloidal particles as calcium silicate sheets bound together by water, hence resembling narrow disks that stack together to form larger globules with size polydispersity [2].

Using computer simulations, we explore the rheological properties of a colloidal suspension targeting the characteristics of C-S-H aggregates. Due to the large colloid-solvent size ratio, full atomistic simulations are ruled out and here we focus on mesoscopic simulations of colloids with spherical or aspherical shape and with interactions that can be anisotropic. The solvent is modelled using stochastic rotation dynamics (SRD) [3]. This method includes thermal fluctuations, as well as hydrodynamic interactions, an important driving force in the dynamics of colloidal aggregation. SRD particles and colloids are coupled by means of collisions that impart a force and a torque. We show that in the implementation, care must be taken to avoid artificial depletion forces induced by the SRD fluid and finite size effects. The shear viscosity is computed using a reverse nonequilibrium method that allows us to explore the dependence of the shear viscosity on the inter-particle interactions, the composition of the suspension, and the shear rate.

We confirm that the nonequilibrium method can be used to compute the shear viscosity of hard spheres, modelled through a repulsive power law. We recover the well-known Einstein relation between shear viscosity and volume fraction at low concentrations, and its asymptotic behaviour near the jamming transition. The shear viscosity shows a strong dependence on the velocity gradient, with both shear thinning and shear thickening regimes. For binary mixtures of spheres with size ratios 1.2-5, we find a non-linear behaviour in the viscosity as a function of the concentration of the components, an effect connected to the increase in the maximum packing fraction before reaching the jamming transition [4]. We find that the shear viscosity of the mixture decreases with respect to the pure systems, as a function of the volume fraction and relative sizes of colloids.

Tailoring the effective potentials of the colloids with organic molecules and the composition of the suspension can lead to a desired rheological response. This investigation provides insight on the impact of additives on surface functionalization. The effective potentials between the colloids can be constructed from full atomistic simulations, bridging together the molecular and mesoscopic scales.

[1] Jennings (2000), Cem. Concr. Res., 30, 101-116.

[2] Chiang, Fratini, Baglioni, Liu & Chen (2012), J. Phys. Chem. C, 116 (8), 5055-5061.

[3] Malevanets and Kapral (1999). J. Chem. Phys, 110, 8605-8613.

[4] Dörr, Sadiki and Mehdizadeh (2013) J. Rheol. 57 (3) 743-756.

Engineered self-assembly , Non-equilibrium thermodynamics