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A percolation threshold that is more important for transport processes is the point at which the capillary pore space no longer percolates. Such a percolation threshold can exist, because as hydration products are formed, pieces of the capillary pore space will be trapped and cut off from the main pore network, thus reducing the fraction of the pores that form a connected pathway for transport. As this process continues, the capillary pore space can lose all long-range connectivity, so that fast transport of water or ions through the relatively large capillary pore system would end, and slow transport would then be regulated by the smaller C-S-H gel pores (pore product).
Computer simulation of cement hydration in 3-D is a means of computing such a percolation threshold. Fig. 5 shows the Fraction Connected of the capillary pore space vs. degree of hydration for several w/c ratios, as computed by a computer simulation model of cement paste microstructure [19]. The quantity Fraction Connected is defined as the volume fraction of capillary pores that make up a connected path through the sample, divided by the total volume fraction of capillary pores.
Immediately after mixing, the cement particles are totally isolated, assuming adequate dispersion, and so the connected fraction of the capillary pore space is one. As hydration occurs the connected fraction decreases gradually. If continuity is lost at some critical degree of hydration, the Fraction Connected will go to zero. Such a percolation threshold can be seen in all of the w/c ratio results plotted, except for 0.6 and 0.7. We have found in the model that w/c ratios of 0.6 and above always have a continuous (or percolated) capillary pore system. This prediction is in good agreement with experiment [25]. It is clearly seen in Fig. 5 that as the w/c ratio decreases below 0.6, less and less hydration is required to close off the capillary pore system.
In order to unify the previous results, we have re-plotted all the data from Fig. 5 in Fig. 6 against capillary porosity. All the connectivity data now falls on one curve, and it is clearly seen that there is a common percolation threshold at a critical value of capillary porosity of about 0.18.
Even the 0.6 and 0.7 water:cement ratio data fall on this curve, and now it is clear why these pastes always have an open capillary pore space: there is not enough cement present originally to be able to bring the capillary porosity down to the critical value, even after full hydration. The capillary pore space percolation threshold for cement paste will have some sensitivity to cement particle size distribution and degree of dispersion, so that the critical value of capillary porosity for percolation should be considered to be about 18 + 5%. This range of values is a rough estimate of finite system size and particle size distribution effects, based on computation on different systems.
The percolation threshold is also sensitive to the morphology of the reaction products, reminscent of the simple overlapping object percolation problem [8]. For example, in a simple dissolution/reaction model, in which only a pore product is formed, capillary porosity percolation thresholds have been computed that are on the order of 20% for totally random morphology products, 25% for 1-D needle-like products, and 30% for plate-like products [26].
