Conceptual Model: 100 % RH Environment

Here, it is conjectured that the Inter-LD C-S-H forms on the walls of both the capillary pores and the inter-capillary spaces, and a schematic of the CM is shown in Fig. 11. Initially, the inter-LD C-S-H thickness is far smaller than either the capillary pores or the inter-capillary spaces. As a result, for water to freeze within the capillary pores, the advancing ice front has to penetrate only the inter-capillary pore space, manifesting itself as a DSC peak at -20 ºC. This situation is depicted in Fig. 11(a).

Figure 11: Schematic of capillary pores, each lined with Inter-LD C-S-H. (a) Capillary pores are continuous. (b) Capillary pores are accessible only via regions filled with Inter-LD C-S-H.

Upon further hydration, the inter-LD C-S-H continues to fill both the capillary pores and the inter-capillary spaces. Eventually, the inter-capillary pore space becomes filled with inter-LD C-S-H, and the capillary pores are no longer percolated via the inter-capillary pore space. For water to freeze within the existing capillary pores, the advancing ice front must now pass through the inter-LD C-S-H pores. As a result, DSC data no longer exhibit a peak at -20 ºC, but at -30 ºC instead. This situation is depicted in Fig. 11(b). Unfortunately, in this experiment, measures were not taken to eliminate supercooled surface water through the use of silver iodide [27], so the physical interpretation of the -20 ºC peaks cannot be stated definitively in this experiment.

As seen in Figures 1-3, 20 % capillary porosity (based on Eqn. 2) and the appearance of the -30 ºC peak give different estimates for the age at which the capillary pores are no longer percolated. There are a number of explanations for this difference. In a pixel-based model, percolation is a well-defined quantity, and has a binary value. By contrast, in a hydrating cement paste there is a critical pore diameter d_c [32] that, conceptually, defines the diameter of the largest sphere that can pass through the system. For these systems, there will always be a critical pore diameter, even if the length scale of d_c must approach atomic dimensions, so there is no definite point at which porosity is no longer percolated. Therefore, in cementitious systems, percolation can only be defined with respect to a given threshold pore diameter.

In addition, the permeability of the system can be approximated by $d_{c}^{\,2}$ [32]. If at early ages the critical capillary pore diameter has dimensions of micrometers, the permeability has a value that is on the order of 10^-12 m². When the -30 ºC peak appears, the critical pore diameter has decreased to the range 1 nm to 10 nm, and the permeability has fallen to approximately 10^-18 m², which is typical for cementitious systems. This is consistent with the dramatic change in permeability that Powers originally observed and attributed to the cessation of capillary pore percolation [21].

There are three possible explanations for the subsequent disappearance of the -30 ºC peak: loss of water from the capillary pores; collapse (and densification) of the phase containing inter-LD C-S-H pores; or cessation of percolation of the inter-LD C-S-H phase. Loss of water from the capillary pores (due to hydration) is unlikely to occur within 7 d in a SWVE 0.40 w/c paste (the age at which the -30 ºC peak disappears in this experiment). Given that the SWVE specimens hydrated at virtually the same rate as saturated specimens, water imbibition through chemical shrinkage probably occurred at a sufficient rate to keep the pores saturated with water. Alternatively, a physical collapse of the inter-LD C-S-H phase would suggest a freezing peak near -30 ºC that slowly moves toward lower temperatures, but this was not observed here.

The cessation of inter-LD C-S-H pore percolation is plausible if continued hydration could fill in the inter-LD pores with a regular microstructure, possibly LD C-S-H, until the freezable capillary pore water is only accessible via LD C-S-H pores; similar to the argument for the appearance of the -30 ºC peak. If this were to happen, available freezable water would not freeze until -45 ºC, as was observed. The rate at which this occurs would also depend on the initial solids fraction (w/c ratio), as was also observed in this experiment.

The disappearance of the -30 ºC peak in SWVE specimens suggests the critical pore diameter d_c decreases from the size of the inter-LD pores (1-10 nm) down to the size of LD C-S-H pores (approx. 1.2 nm). The corresponding decrease in permeability would be one to two orders of magnitude. Based on this assumption, extremely low permeability concretes can only be achieved in those systems for which the -30 ºC peak has disappeared.

Upon studying Figs. 1-3, the disappearance of the -30 ºC freezing peak appears to coincide with the age at which the capillary porosity is approximately equal to 20 %. One could argue that the disappearance of the -30 ºC peak corresponds to a significant reduction in the critical pore diameter d_c and accounts for the dramatic change in permeability that Powers et al. [21] based their conclusions. The agreement between the age when the peak first appears and the predicted minimum curing duration by Powers et al. may have only been coincidental, attributed to changes in cement production in the intervening decades. The only definitive way to resolve this question would be to perform simultaneous DSC and permeability measurements.