It should be stressed that other transport parameters can be strongly affected, however, by the presence of the ITZ, properties like permeability and sorptivity, which are measures of fluid, rather than ionic, transport. Halamickova et al. have measured the hydraulic permeability of both mortars and pastes and found that the presence of aggregate particles significantly increased the coefficient of permeability in the mortar samples. In fact, the hydraulic permeability of a mortar with 55 volume % of sand was 40 times higher than that of a paste with the same water/cement ratio and degree of hydration.
To show this graphically, the mortar permeabilities of Halamickova et al. 15 were normalized by a paste of the same water/cement ratio and degree of hydration and are shown in Fig. 13. These data are overlaid on a plot of the normalized mortar conductivity from the present study, all plotted as a function of sand content. Clearly the mortars show a marked increase in permeability, while the conductivity decreases as sand is added.
Figure 13: Normalized permeability and conductivity data. Permeability data are adapted from Halamickova (degree of hydration = 0.6), conductivity data are from the present work (degree of hydration approx. 0.7).
The contrast in conductivity between the ITZ and matrix paste conductivities in mortars and concrete is apparently not large enough for the ITZ to overcome the effect of the aggregate. This is because the conductivity is not a very strong function of the porosity, as seen in Fig. 11. However, fluid flow is different. The case of flow through a tube of circular cross-section and radius r shows this clearly. For conduction, the electrical flow through such a tube is proportional to the total cross-sectional area r2. In the same tube, fluid flow is proportional to r4. Therefore, fluid flow, and thus permeability, is a much more sensitive function of pore size than is conductivity. Because of the larger pores and higher porosity in the ITZ compared to the matrix paste, the contrast between the permeabilities of the ITZ and matrix paste are thought to be much larger than for conductivity, perhaps 10-100 times as much. For such a large contrast, the positive effect of transport through the ITZ will dominate the negative effect of the blocking aggregate particles and the densified matrix paste. Thus, as in Fig. 13, permeability increases with additional sand content.
One way to approximately elucidate the effect of the ITZ on the permeability is to use the Katz-Thompson equation 42 and an MIP intrusion curve of a neat OPC paste and mortar.26 The Katz-Thompson equation is,
where dc is the critical pore diameter associated with the inflection point in the MIP intrusion curve, σ and σ o are the sample and pore fluid conductivities, respectively, and kp is the hydraulic permeability. 42, 43 The derivative of two mercury intrusion curves are shown in Fig. 14. These curves are generated from two of the intrusion curves from Fig. 3 and indicate a bi-modal distribution of pores for the mortar. The coarser pores are associated with the ITZ and the finer pores are assigned to the matrix cement paste. According to the term in the Katz-Thompson equation (assuming similar values for σo) , the larger ITZ pores (dc = 0.49 µm) will have a higher permeability than the smaller matrix pores (dc = 0.030 µm), and although the ITZ volume fraction is relatively low, it will have a significant influence on the overall permeability. It is also interesting to note that the paste portion of the two MIP curves indicates a slight shift to smaller pore diameters for the mortar. This is consistent with both the results of the model and of Scrivener et al. 5 which indicate that the water/cement ratio and thus the average pore size in the matrix is reduced when aggregate is present.
Figure 14: The derivative of an MIP curve for a neat paste and a cement mortar showing approximate pore size distribution (adapted from Winslow). Note the bi-modal distribution of the mortar porosity.
The applicability of the Katz-Thompson equation can be determined by looking at the critical pore diameters of an MIP intrusion curve for a paste and a mortar (e.g., Fig 14). If the ITZ is percolated through the sample, the mortar can be roughly modeled as a parallel, three-phase composite, especially when the contrast between the ITZ and matrix is large.41 The volume fraction of the ITZ and matrix pastes are determined by the multi-scale model shown in Fig. 7. The MIP intrusion data, as measured by Winslow et al.,26 shows a bimodal distribution of pores, with a critical pore diameter for the ITZ paste of 0.49 µm. The paste has a single pore-size distribution and a critical pore diameter of 0.030 µm. According to the Katz-Thompson equation, the two factors that influence the permeability are the normalized conductivity (σ/σo) and critical pore diameter (). It was demonstrated earlier that the conductivity of the ITZ and matrix are different by about a factor of two late in the hydration. Therefore, the ratio of the permeability of a mortar and a paste can be calculated by the following equation:
According to this calculation, the ITZ is predicted to be approximately 500 times more permeable than the paste. However, not all of the mortar is comprised of ITZ paste. Therefore, the result from Eqn. 2 needs to be multiplied by the volume fraction of ITZ in the mortar (10 % at 55 volume % sand, according to the model). Thus, assuming all the transport is through the ITZ, the mortar permeability is predicted to be about 50 times higher than that of a paste. This prediction can be compared to the experimental value in Fig. 13 of about 40. As can be seen in the figure, the agreement is reasonable. It should be noted that it is valid to use the MIP data by Winslow et al.26 and the permeability data of Halamickova et al. 15 together for this comparison because the work of Halamickova was designed to follow the work of Winslow. (A similar comparison using the multiscale model can be found elsewhere)41
It is also interesting to note in Fig. 13 that there seems to be a sharp up-turn in the permeability of the mortar between 35 volume % and 45 volume % sand. In agreement with the results of Winslow et al.,26 this is an indication that the ITZ has become percolated. The conductivity does not show such an upturn because the contrast between the ITZ and matrix paste is too small. The upturn for the permeability is another piece of evidence for the higher contrast in permeabilities between ITZ and matrix paste. Further experimental and theoretical work is needed on the fluid flow properties of mortar and concrete as compared to cement paste.