Assessment of the elastic properties of amorphous calcium silicates hydrates (I) and (II) structures by molecular dynamics simulation

Based on Hamid model of 11Å tobermorite, amorphous calcium silicates hydrates (or C-S-H) structures (Ca₄Si₆O₁₄(OH)₄•2H₂O as the C-S-H(I) and (CaO)_1.67(SiO₂)(H₂O)_1.75 as the C-S-H(II)) with the Ca/Si ratio of 0.67 and 1.7 are concerned. Then, as the representative ‘globule’ C-S-H, two amorphous C-S-H structures with the size of 5.352 × 4.434 × 4.556 nm³ during the stretch process are simulated at a certain strain rate of 10⁻³ ps⁻¹ by LAMMPS program for molecular dynamics simulation, using ClayFF force field. The tensile stress–strain curves are obtained and analysed. Besides, elastic modulus of the ‘globule’ C-S-H is calculated to assess the elastic modulus of C-S-H phases (the low-density C-S-H – LD C-S-H – and the high-density C-S-H – HD C-S-H), where the porosity is a critical factor for explaining the relationship between ‘globule’ C-S-H at nanoscale and C-S-H phases at microscale. Results show that: (1) The C-S-H(I) structure has transformed from crystalline to amorphous during the annealing process, Young’s moduli in x, y and z directions are almost the same. Besides, the extent of aggregation and aggregation path for water molecules in the structure is different in three directions. (2) Young’s modulus of both amorphous C-S-H(I) and C-S-H(II) structures with a size of about 5 nm under strain rate of 10⁻³ ps⁻¹ at 300 K in three directions is averaged to be equal, of which C-S-H(II) structure is about 60.95 GPa thus can be seen as the elastic modulus of the ‘globule’ C-S-H. (3) Based on the ‘globule’ C-S-H, the LD C-S-H and HD C-S-H can be assessed by using the Self-Consistent Scheme (separately 18.11 and 31.45 GPa) and using the Mori–Tanaka scheme (29.78 and 37.71 GPa), which are close to the nanoindentation experiments by Constantinides et al. (21.7 and 29.4 GPa).