Creep in reactive colloidal gels: A nanomechanical study of cement hydrates

From soft polymeric gels to hardened cement paste, amorphous solids under constant load exhibit a pronounced time-dependent deformation called creep. The microscopic mechanism of such a phenomenon is poorly understood in amorphous materials and constitutes an even greater challenge in densely packed and chemically reactive granular systems. Both features are prominently present in hydrating cement pastes composed of calcium silicate hydrate (C-S-H) nanoparticles, whose packing density increases as a function of time, while cement hydration is taking place. Performing nanoindentation tests and porosity measurements on a large collection of samples at various stages of hydration, we show that the creep response of hydrating cement paste is mainly controlled by the interparticle distance and results from slippage between (C-S-H) nanoparticles. Our findings provide a unique insight into the microscopic mechanism underpinning the creep response in aging granular materials, thus paving the way for the design of concrete with improved creep resistance.

Figure 1

Sketch depicting the hydration process of cement particles in water (a), which results in the formation of hardened cement paste consisting of nonhydrated cement particles, C-S-H phases, CH phases, and pores of different size and content [(b) and (c)]; due to the hydration process, cement particles dissolve, and C-S-H and CH precipitate in the solvent in a less densely packed manner outside the (former) particle surface and in a tighter manner within the bounds of the former particle surface (which was dissolved) (d). Gel pores designate voids between the C-S-H particles; capillary pores designate voids formerly occupied by the solvent. (e) Zoom area in (d) of a bricklike C-S-H particle.

Figure 2

(a) Scanning electron microscope (SEM) backscattered image of the surface of a sample of hardened cement paste. Spatial distributions: (b) map of the CaO-to-${\mathrm{SiO}}_2$ ratio determined via wavelength-dispersive x-ray spectroscopy (WDS) element mapping of Ca and Si and converted into an oxide ratio, and (c) map of the indentation modulus $M$ determined by nanoindentation. Data were measured on a cement sample with a degree of hydration ${\xi }_{\mathrm{NMR}}=0.6$.

Figure 3

Mechanical properties as a function of the degree of hydration. (a)–(c) Indentation hardness $H$, indentation modulus $M$, and creep modulus $C$ for LD-C-S-H and HD-C-S-H phases determined by statistical nanoindentation as a function of degree of hydration ${\xi }_{\mathrm{NMR}}$ determined by ${}^{29}\mathrm{Si}$ NMR spectroscopy. Both phases are identified by a statistical analysis based on $H$, $M$, and $C$ (index HMC, open symbols) or based on $H$, $M$, and $C$ and the chemical composition in calcium, silicon, and aluminum at the locus of the indents (index HMC-chem, half-filled symbols) as input values. Solid lines are logarithmic functions, which serve as guides to the eye. (e)–(g) Same data, $H$, $M$, and $C$, as in (a)–(c) vs packing density $\eta$ computed by micromechanical modeling (see text) of C-S-H particles in the respective phases. Dotted lines correspond to the best linear fit of the data. (d) Volume (Vol.) fraction $f$ and (h) packing density $\eta$ of LD- and HD-C-S-H phases vs degree of hydration ${\xi }_{\mathrm{NMR}}$. The blue dashed line corresponds to a packing density of 0.74, and solid lines serve as guides to the eye. In all the graphs, the error bars stand for twice the standard deviation of the considered observable.

Figure 4

(a) Creep modulus $C$ as a function of $r/d$, the ratio of the distance between C-S-H nanoparticles in LD- and HD-C-S-H phases normalized by the nanoparticle size. (b) Interparticle spacing $r/d$ for LD- and HD-C-S-H phases and (c) difference between LD- and HD-C-S-H interparticle distance $\mathrm{\Delta }(r/d)$ as a function of the degree of hydration ${\xi }_{\mathrm{NMR}}$. The dashed line in (c) corresponds to the best linear fit of the data.

Figure 5

(a) Fraction of C-S-H dimers and silicate end groups (designated $Q^1$) and polymeric units of silicate $\mathrm{tetrahedra}$ $(Q^2$), including sites bound to tetrahedral Al in the chains $\left[Q^2\left(1\mathrm{Al}\right)\right]$, relative to the total amount of C-S-H phases formed multiplied by the degree of hydration ${\xi }_{\mathrm{NMR}}$ and plotted as a function of ${\xi }_{\mathrm{NMR}}$. (b) Average (Av.) aluminosilicate chain lengths (CLs) of the C-S-H polymers (see Appendix pp4 for calculations) as a function of ${\xi }_{\mathrm{NMR}}$. The average standard deviation is estimated to be $\pm 0.15$ for the chain length values. (c) Creep modulus $C$ vs average aluminosilicate chain length of the C-S-H polymers, for both LD- and HD-C-S-H data.

Figure 6

Contribution to the cement paste total porosity of LD-C-S-H, HD-C-S-H, and both phases as determined by statistical nanoindentation as a function of the degree of hydration ${\xi }_{\mathrm{NMR}}$. Results are compared with direct porosity measurements performed by nitrogen adsorption at 77 K and mercury intrusion porosimetry (MIP). BET stands for Brunauer, Emmett, and Teller.

Figure 7

(a) Example of indentation depth-vs-time curve afflicted with discontinuities (jumps). (b) Cumulative probability (Cum. probab.) of discontinuities and their contribution to the total creep deformation during the indentation creep phase for the investigated degrees of hydration (DOH) ${\xi }_{\mathrm{NMR}}$..

Figure 8

Sketch of the microstructure of hardened cement paste in (a) the unloaded stage and (b) the loaded stage. Different areas of the sample show different packing densities (LD- and HD-C-S-H) associated with the spaces formerly occupied by particles prior to their dissolution (see dashed red lines). Deformation of the individual C-S-H particles [see inset (c)] subjected to loading as proven in molecular dynamics simulations might facilitate reorganization of the densely packed system and thus allow creep.