3.3.1 Water transport in cement revealed by NMR relaxometry and molecular simulations
Calcium silicate hydrates (C-S-H) are complex nano-porous materials which are responsible for the retention of radionuclides and water transport in cement. Nuclear magnetic resonance (NMR) relaxation experimentation is an effective technique for probing the dynamics of proton spins in porous media but interpretation requires the application of appropriate spin diffusion models. In collaboration with the University of Surrey (UK) within TRANSCEND FP7 Marie Curie ITN, molecular simulations were applied to predict NMR relaxation parameters using a dipolar spin–spin correlation function. Water dynamics was modeled for the interlayer (slit pore) and an external 1 nm sized pores (gel pore) in tobermorite. Diffusion in the slit pores occurs largely through discreet site hopping. While the 2D diffusion coefficient in the gel pore was of the same order of magnitude as in bulk water, it was more than two orders of magnitude smaller in the slit pores. The NMR relaxation parameters obtained in
simulations helps to improve interpretation of NMR measurement in cement and obtain better knowledge on the exchange rate of water between gel and slit pores as well as to characterize pore size distribution in C-S-H.
3.3.2 Multi-scale molecular modelling of ion sorption by C-S-H phases
During 2014, the post-doc project "Thermodynamic equilibrium in C(-A)-S-H (Calcium-(Aluminium)-Silicate-Hydrate) from molecular simulations" (L.
Pegado), a subproject of the SNF-funded Sinergia project "Stable phase composition in novel cementitious materials: C(-A)-S-H", has been continued through the project A thermodynamic model for C-S-H/C-A-S-H from a bottom-up approach”. The latter is financed mainly by NANOCEM, the Industrial-Academic Research Network on Cement and Concrete. By means of multi-scale molecular modelling, the goal is to refine a thermodynamic model for ion sorption by C-S-H at the level of a single C-S-H/C-A-S-H particle. The result can be used to support and provide input to macroscopic phenomenological thermodynamic models. The microscopic, single-particle model will incorporate a description of surface charge formation,
equilibrium with bulk electrolyte solutions, Si/Al substitution and silicate chain polymerization. Two milestones have been already reached during the reporting period:
The mechanism of Al incorporation into C-S-H at low Ca to Si ratio has been addressed through large-scale ab initio calculations, showing that having Al in bridging tetrahedra is the thermodynamically favored state (PEGADO et. al.
2014).
Ion sorption equilibrium in C-S-H was modeled through titrating Grand Canonical Monte Carlo (GCMC) simulations at the level of the Primitive Model of electrolytes but employing pKa’s for surface -OH groups previously calculated from ab initio molecular dynamics (AIMD). The model was found to satisfactorily reproduce available experimental data (Fig. 3.6). In particular, the charge-reversal of C-S-H particles, observed for high electrostatic coupling, is well reproduced (CHURAKOV et. al. 2014b).
Fig. 3.6: Simulation (lines, blind prediction) and experimental (symbols) results for the zeta-potential of C-S-H particle dispersions in equilibrium with solutions of either Ca(OH)2 alone (blue) or a mixture of Ca(OH)2 and CaCl2 (red) with a constant concentration of Ca2+ (20 mM).
Moreover, the calibration of classical polarizable force fields for Si(OH)4 and Si(OH)3O- in aqueous solution has been completed. It has been achieved by comparing with the water structure around a single molecule as obtained from first principles molecular dynamics simulations. It is now possible to calculate effective potentials (PMF’s - Potentials of Mean Force) between different ions and relevant surface
groups in C-S-H from classical atomistic molecular dynamics simulations. The PMF's will be used further, in coarse-grained GCMC simulations of ion sorption to incorporate ion specific and solvent effects into the current models.
3.3.3 Up-scaling of diffusion coefficients: Scale dependent mobility of aqueous species No single experimental or modelling technique provides data that allow a description of transport processes in clays and clay minerals at all relevant scales. Accordingly, several complementary approaches have to be combined to understand and explain the interplay between transport relevant phenomena. Molecular dynamics simulations (MD) were applied to investigate the mobility of water in the interlayer of montmorillonite, and to estimate the influence of mineral surfaces and interlayer ions on the water diffusion. Random walk (RW) simulations based on a simplified representation of pore space in montmorillonite were used to understand the effect of the arrangement of particles on the meso- to macroscopic diffusivity of water. In this way, the scale dependent diffusion of water in montmorillonite was evaluated (CHURAKOV et al. 2014a). According to the MD simulations, at very short timescales water dynamics has the characteristic features of an oscillatory motion in the cage formed by neighbors in the first coordination shell. At slightly larger, but still short times (~10-100 ps) the limited width of the interlayer leads to a decreasing diffusion coefficient perpendicular to the interlayers and thus to locally anisotropic diffusion (Fig. 3.7). The RW simulations for an idealized sample map consisting of hexagon montmorillonite particles (Fig. 3.8) show also a decrease of the diffusion coefficients at early times, and then a further decrease at a normalized time Th
that corresponds to a diffusion distance equal to the typical length of the particles (or the length of individual pores). Such a detailed understanding of transport processes is needed for the correct interpretation of experimental data. It is thus expected that experimental diffusion coefficients depend on the timescales of the measurement. This was verified with QENS (Quasi Elastic Neutron Scattering) measurements of aqueous diffusion in montmorillonite with two pseudo-layers of water.
The experiments were performed at four significantly different energy resolutions, that is, at four different observation times (Fig. 3.9). At observation times of 160 ps, local diffusion cannot be well described with an isotropic 3D diffusion model, but has features of a local 2D motion.
Fig. 3.7: Left: Scale dependent diffusion coefficients of water parallel (||) and perpendicular (|–) to a basal montmorillonite plane obtained for an interlayer with two pseudo-layers of water (~0.5 nm thick) and a larger pore (macropore, ~6 nm thick). The black curves represent the orientation-averaged diffusion coefficients for the interlayer and the macropore. Right: Snapshot of the simulated system. Na-ions are blue, oxygen atoms are red, hydrogen atoms are white, silica atoms are brown, aluminum atoms are green and magnesium atoms are black.
Fig. 3.8: Time evolution of normalized diffusion coefficients of water (left) derived from RW simulations for an idealized pore map consisting of hexagonal particles (right) with randomly oriented interlayers separated by inter-particle pores with the same width as the interlayer pores. Results for three independent simulations for different time ranges are shown with increasing color saturation. At a diffusion time Th =1, a particle has diffused a distance h, where h is the width of a hexagon (0.1 micrometer).
Fig. 3.9: Line broadening ΓT (HWHM, half width at half maximum of peak) due to translational diffusion of water molecules in montmorillonite with two pseudo layers of water measured by QENS with different observation times. The data are fitted with a jump diffusion model. The horizontal markers on the y axis show the different instrument resolutions. All data points obtained for the observation time 3 ps are below the instrument resolution. The most important feature observed at the longest observation time (160 ps) is the reduced line width at high Q values.
This feature is indicative for the transition from local 3D to apparent 2D diffusive motion of water in the interlayer.
3.3.4 Up-scaling of diffusion coefficients:
Influence of interparticle pore width distribution
Random Walk simulations are well suited to investigate the relation between pore structure and sample-scale diffusion coefficients. For that purpose, a series of large clay structure maps (16'000 by 16'000 pixels) were modelled with a previously developed algorithm (TYAGI et al. 2013). The 2D structure maps had the same types of montmorillonite particles, but differed in their interparticle pore size distributions. The mean interparticle pore width was in all cases 3 nm, but the coefficient of variation of the width distribution was varied from 1.5 (rather uniform widths) to 12 (very broad distribution). A part of two sample maps and the resulting sample-scale diffusion coefficients are shown in Fig. 3.10. A broad interparticle pore width distribution leads to a lower sample-scale diffusion coefficient, i.e. a larger tortuosity, compared to a narrow distribution.
Fig. 3.10: Left: A small part (1/16) of the clay structure maps with a CV of the interparticle pore width distribution of 2 and of 10. Right: Sample-scale diffusion coefficients in x and y direction, normalized by the local water diffusion coefficient D0, and the corresponding anisotropy ratio obtained for different coefficients of variation of the interparticle pore width distribution.
3.4 Benchmarking and validation of coupled