Figure 3: Effect of C/S ratio on the mechanical properties of C-S-H at nanoscale.

(a) C-S-H solid particle’s indentation modulus, M. The computational data (this work, orange squares) were computed via a nonreactive potential at 0K, and compared with nanoindentation and wavelength dispersive spectroscopy experiments and previous ab initio calculations on 11 and 14 Å Tobermorite¹⁹. Gray boxes surrounding experimental mean values indicate standard deviation (STDV) calculated from standard errors by noting that M and Ca/Si are normally distributed (see Supplementary Methods). (b) Indentation modulus parallel (M₁) and perpendicular (M₃) to the calcium-silicate layers. (c) C-S-H solid particle's hardness, H. The computed data (brown squares) are compared with experimental values following the same convention as in a. (d) Computed isotropic Euclidean norm as an indication of the level of anisotropy in C-S-H. Orange lines are guide for the eyes. (e) TEM image of C-S-H at C/S=0.8634. (f) TEM image of C-S-H at C/S=1.7 produced from hydration of C₃S. In both (e) and (f), TEM imaging conditions were in vacuum at 10⁻⁶ torr; the scale bar is 10nm. The error bars in atomistic simulations are calculated via computing M or H for multiple configurations along the equilibration trajectory that generated the C-S-H structures for each polymorph. For the sake of clarity, Fig. 3c shows one fewer experimental data point at C/S~1 and H~12 GPa, listed in Supplementary Table 6.