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Diffusivity of Cement Paste

Building on the percolation and pore size results given above, the dependence of the diffusivity of cement paste on pore structure can now be qualitatively outlined. Early in the hydration process the capillary pore space is fully percolated. These pores are much larger than the C-S-H gel pores (which are themselves also fully connected fairly early in the hydration process [19]) and so dominate the transport. As the capillary porosity decreases, the capillary pores become smaller and only partially connected, so for porosities near but above the percolation threshold, pure capillary pore paths have only slightly more influence on flow than the hybrid paths that are made up of isolated capillary pockets linked by C-S-H gel pores. The capillary pores are still somewhat bigger than the gel pores, but their connectivity is decreasing. Below the critical capillary porosity, all flow must now go through C-S-H gel pores, but flow will be dominated by paths that still contain some isolated capillary pore regions, and are not just made up of pure C-S-H gel pores. If this were not true, then after a certain point, the diffusivity would begin going up with increasing hydration, since more C-S-H, and thus more gel pores, were being formed. This has not been observed in cement paste [30].

The same microstructure model used to predict the connectivity results shown in Figs. 5 and 6 can also be used to compute the diffusivity of cement paste by solving Laplace's equation in the pore space with a finite difference method [30]. Because of the Nernst-Einstein relation [30,31], relating diffusivity and conductivity, the same mathematical apparatus can be used for both, so that solutions to the time-independent Laplace's equation apply equally well to diffusivity or conductivity. If D_o is the ionic diffusivity in free water, σ_o is the conductivity of the electrolytic pore solution, D is the measured diffusivity of the porous material, and σ is the measured conductivity of the porous material, then the physical content of the Nernst-Einstein relation is that D/D_o = σ / σ_o. This computational procedure can be done for the DC and also for the frequency-dependent AC conductivity [32,33]. Computational results confirm the above microstructural picture, and compare reasonably well to experimental measurements [30,32,33,34].

Figure 8 shows comparisons between experiment and model results for an 0.5 w/c cement paste [34]. The quantity Γ = σ / σ_o is called the relative conductivity or diffusivity [30,34].

The value of σ_o was found by first squeezing out the elecrolytic pore solution in a high-pressure press, and then measuring the conductivity of the pore solution in an impedance spectrometer [34]. A reasonably good comparison exists between simulation and experiment over a wide range of capillary porosity, indicating that the capillary pore space of the model compares well to that of real cement paste. The model results are from an equation that was fit to the results shown in Fig. 9 [30]. They were determined from fairly low porosities, and so are not expected to fit well at high porosities. The agreement across all porosities is within a factor of two, however. The φ^1.5 power line shown is the result for suspensions of insulating, reasonably spherical objects suspended in a conducting medium. When hydration begins, ions are released into the mixing water, turning it conductive, while the cement simply acts as suspended insulating particles, which grow in size with hydration and so increase in volume fraction 1 − φ. However, as can be seen in the figure, the hydrating cement paste quickly changes its topology as the solid phase connects (set point), and the measured conductivities drop below the φ^1.5 curve.

Figure 9 shows a collection of model results for Γ for different w/c values, all plotted against capillary porosity. Notice how all the data falls on a single master curve, as did the capillary pore space percolation data, when plotted against capillary porosity [30].

Such a qualitative result has been observed experimentally as well [35], lending support to the basic correctness of the model and the percolation picture of cement paste pore structure. A recent review (and references therein) may be referred to for more details of the electrical conductivity/ionic diffusivity of cement paste [36].