Previous: Description of microstructure
To analyze the results of the aggregate study, various phase fractions were measured as a function of distance in pixels from the aggregate surface by adding up the pixels in concentric squares around the aggregate, and averaging over 5-10 independent realizations of the cement paste-aggregate system. In each realization, the cement particles were "parked" using a different set of random numbers. The initial work was done using circular particles with the same 21 pixel diameter, like those shown on Fig. 1a, in a unit cell with an edge length of 500 pixels. Figs. 2a and 2b show the results of the phase fraction measurements. In Fig. 2a, porosity, as a function of distance in pixels from the aggregate edge, is plotted. The upper curve, marked, "Original", is the porosity of the original packing, before any simulated hydration has taken place. A large porosity peak can be seen close to the aggregate surface, due to the fact that particles cannot be packed as efficiently near an edge as in bulk space. In this case, the aggregate surface is acting as the edge. The porosity then decreases to its bulk value, with some oscillations due to the discrete nature of the cement particles. The lower curve, marked "Hydrated", is the porosity after = 0.855 hydration. A higher-porosity peak is clearly visible, and extends approximately 10-15 pixels until the final bulk value of the porosity is reached. Using the scale of the problem previously mentioned, that means that the interfacial zone in the model is of the order of 10-15 micrometers wide. This width is in reasonable agreeement with experimental results of 10-50 micrometers for the interfacial zone width [4,5].
Figure 2a: Showing the porosity of the structures shown in Figs. 1a and 1b plotted against distance from the aggregate edge.
Fig. 2b shows all the phase fractions, after hydration, plotted as functions of distance from the aggregate surface. It is clear that the fraction of CH increases near the aggregate surface, in agreement with experiment [6,7]. This arises naturally in the model, as CH pixels have a uniform probability to nucleate anywhere in the pore space, so that there would tend to be more in regions of high porosity. Also, there is more room for the CH clusters to grow in the higher-porosity interfacial zone. The small dip in the amount of CH shown in Fig. 2b, at distances less than 3-4 pixels from the aggregate edge, can be explained by the fact that CH clusters very near to the aggregate have their growth limited on that side by the presence of the aggregate itself. The amount of C3S is low near the aggregate surface, due to the original packing, and the C-S-H fraction is consequently low in that region as well.
Figure 2b: Showing all the phase fractions of the hydrated structures shown in Fig. 1b plotted against distance from the aggregate edge.
Figs. 3a and 3b are the equivalent of Figs. 2a and 2b, but for a mixture of four different size cement particles, where the 21 pixel diameter particles used previously are now the largest of the four sizes used. The cement particles were placed in order of decreasing size, as in a real mixing process the larger particles could always push the smaller particles aside. This enables the larger particles to go anywhere, with the smaller particles filling in around them. The results are basically the same, with the width of the interfacial zone porosity peak in of Fig. 3a slightly reduced when compared to of Fig. 2a. The height of the porosity peak is also reduced, from a value of 50% down to 44%, because of the smaller particles that can fill in some of the spaces between the larger particles near the aggregate edge. The width of the peak is still clearly controlled by the largest particles, however, since the width is only slightly reduced from part a) of Fig. 2a.
Figure 3a: Showing the porosity of structures similar to those shown in Figs. 1a and 1b, but with a distribution of four different size cement particles, plotted against distance from the aggregate edge. The curve marked "Original" is averaged over five original unhydrated structures, and the curve marked "Hydrated" is averaged over five structures after hydration.
Figure 3b: Showing all the phase fractions of a structure similar to that shown in Fig. 1, but with a distribution of four different size cement particles, plotted against distance from the aggregate edge.
By comparing the original and hydrated porosities, it is clear that the initial placement of cement particles around the aggregate plays a large role in the formation of the interfacial zone. This has been suggested before  as the main cause of the interfacial zone porosity. The initial particle placement effect has certainly been corroborated in the model results described above. However, after watching the actual simulations take place, another factor that could play a role in interfacial zone formation suggested itself.
Consider a typical point in the pore space of the hydrating cement paste, far enough away from the aggregate surface to be well outside the interfacial zone. On average, this point has new material (C-S-H and CH) growing into it from all directions, due to the isotropy of the random packing and random growth processes. Now consider a point in the pore space that is close to the aggregate surface. There is no growth towards this point from the direction of the aggregate, as the aggregate is non- reactive and does not supply dissolved species, so that the net supply of new material into this point is reduced from that of the previous case. We call this the "one-sided growth" effect. This effect should also contribute to the higher porosity in the interfacial zone, although to a lesser extent than the initial particle placement effect. Experimentally, it would be impossible to separate the two effects. However, this becomes possible, using the digital simulation model, in the following way.
Figure 4b: Same as Fig. 4a but after completion of the hydration simulation. White represents the aggregate, the remaining unhydrated cement is red, blue represents CH, yellow represents C-S-H, and the remaining water-filled pore space is black.
If the effect of the aggregate edge on the particle placement could be eliminated, then any interfacial zone present after hydration would be due only to the one-sided growth effect. To accomplish this, the initial structure was generated in a different way. The cement particles were placed in the box first, and then the aggregate particle was added in the center. Any cement particle pixels that were overlaid by the aggregate were then turned into aggregate pixels. This totally eliminates the edge effect of the aggregate, as the cement particles were placed completely independently of the position of the aggregate. Fig. 4a shows the initial packing for one realization of this version of the model, and Fig. 4b shows the same system after = 0.807 hydration. Fig. 5 clearly shows that the edge effect of the aggregate was totally eliminated, as the porosity of the original system, marked "Original", is completely flat, except for the small amount of noise remaining after averaging over ten independent configurations. There can be no contribution to an enhanced interfacial zone porosity from the original packing. However, the one-sided growth effect, if real, would be unaffected. In Fig. 5, the porosity after hydration is shown in the curve marked "Hydrated", which clearly shows a small enhanced-porosity interfacial zone peak, due entirely to the one-sided growth effect. This peak is much narrower than the porosity peaks shown in Figs. 2a and 3a, but has approximately half the height. Therefore, the one-sided growth effect makes an important contribution to the interfacial zone only on small length scales, say 0-5 micrometers, while the aggregate edge effect on cement particle packing dominates the larger (5-50 micrometers) length scales.
Figure 5: Showing porosity versus distance from aggregate edge averaged over ten original and hydrated cement paste structures like those shown in Figs. 4a and 4b.