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Results

Based on the interpretation of SANS data provided in [12], diameters of 5 and 40 nm were selected for the spheres in the micro and macro-level models of C-S-H respectively. More recent SANS results [30] have confirmed this 5 nm diameter, suggesting a particle diameter on the order of 6 nm which is achieved very early in the cement hydration and changes very little thereafter. Also, Jennings and Tennis arrived at a diameter of 5.4 nm for the C-S-H gel particles based on a simple analysis of the density and surface area of the gel [26]. The value of 40 nm chosen for the macro-level model is also based on SANS data [12], but could vary with sample age and composition, as some TEM images suggest a value closer to 100 nm [14].

It is also necessary to decide the distribution of porosity between these two levels. The total internal porosity of the C-S-H gel was set at 28%, a generally accepted value for this parameter. The macro-level model was assigned a porosity of 7.6% with the solids in this model being assigned a porosity of 22.3% at the micro-level, for a total porosity of 28.2%. This distribution of porosity was chosen such that the volume of pores in the micro-level model would equal that indicated by measured sorption isotherms [31]. Details of the two models are summarized in Table 1.

As described in the computational techniques section, a composite TEM image of the model C-S-H was produced. A direct comparison against a TEM image of the C-S-H gel in a tricalcium silicate (C₃S) paste [14] is provided in Figure 3. While contrast differences exist and the macro particles are larger in the real image, the model appears to capture much of the structure of the real C-S-H at the presented scale.

Figure 3a. Simulated TEM images of C-S-H macro-level structure. Simulated image is 500 nm by 500 nm.

Figure 3b. Real TEM images of C-S-H macro-level structure. Real image is 1200 nm by 1800 nm (courtesy of Dr. R. Maggion [14]).

By counting solid/pore interfaces in the pixel-based representation of the nanostructure of the model C-S-H, one arrives at a surface area estimate of about 220 meters squared per gram D- dried paste. Using water as an adsorbate, values typically presented in the literature are on the order of 200 meters squared per gram [29]. The model value would be expected to be slightly higher since the 0.125 nm pixel resolution of the micro-level C-S-H model is smaller than the size of a water molecule. Thus, a value within 10% of that measured experimentally seems reasonable.

Figures 4a and 4b present measured sorption isotherms for two cement paste systems [31]. Several points are worth noting from the experimental curves. First, the curves are

Figure 4a. Experimental water adsorption/desorption isotherms for a hardened cement paste sample with a w/c ratio of 0.348.

Figure 4b. Comparison of experimental and model water sorption isotherms for a system with 10% silica fume and a water/binder ratio of 0.196.

practically identical for water contents below 7%. Thus, while the capillary porosities of the two samples are different (due to their different starting water:cement (w/c) ratios), the porosities at the nanolevel are quite similar. Stoichiometric calculations [32] indicate that these two samples would contain approximately the same volume fractions of C-S-H gel, which suggests that in terms of behavior during water sorption, the C-S-H gel is identical in the two pastes. This is an interesting conclusion since it is well known that the Ca/Si molar ratio of the C-S-H gel and polymerization of the silicate ions are different with (Fig. 4b) and without (Fig. 4a) silica fume [16]. Thus while the chemical structure of the gel is altered by the presence of pozzolans (silica fume, fly ash, etc.), its physical structure at the nanometer level may be the same, as suggested previously [33].

A second point of interest is the large drop in the desorption curves observed between 33 and 44% RH, particularly for the system shown in Fig. 4b. Based on the Kelvin-Laplace equation, this would correspond to a pore diameter between 2.0 and 2.5 nm. If surface adsorption is included in the calculation, one obtains a pore diameter between 2.6 and 3.5 nm. Similar to a threshold diameter in mercury intrusion [21,25], this value is taken to indicate the maximum size of pores that are continuous across a volume of the C-S-H gel. This means that to traverse a volume of the C-S-H gel, one must consider at least pores of this size and larger. If only pores larger than this are considered, the C-S-H gel is discontinuous, i.e. a sphere larger than this critical size cannot pass through the pore structure. For the system shown in Fig. 4b, the pronounced drop in the desorption curve in this RH range is due to the existence of isolated capillary pores which can undergo desorption (empty) only when the surrounding C-S-H gel can do the same.

For the system shown in Fig. 4b, a comparison was also made between sorption isotherms computed for the model C-S-H and those measured on the cement paste. Here, the following assumptions were made: the paste contains 58% C-S-H by volume, 7% capillary porosity, and has a specific gravity of 2.29. While not an exact match, the agreement between experimental and model curves is promising. The difference in the adsorption branches at high RH is due to the presence of the small isolated capillary pores (0.01 to 0.1 micrometers) in the paste which are not considered in a model based strictly on the C-S-H. Thus, the ultimate value achieved in the adsorption branch for the model is below that observed experimentally. In this very low water:binder ratio paste with silica fume, one would expect these pores to be isolated as the capillary porosity would become disconnected early in the hydration process [32]. Thus, for the desorption branch, we have included this capillary porosity (7% or 3 kg/ 100 kg) and assumed that these isolated capillary pores are detected (empty) only when the surrounding macro-level C-S-H structure empties, between RHs of 41 and 57% for the model structure. This range partially overlaps the RH range of 33-44% observed experimentally.

Jennings and Tennis have measured the degree of hydration and pore volume accessible to a series of molecules
(H₂O, CH₃OH, C₃H₇OH, and C₆H₁₂) for a cement paste at five different w/c ratios [26]. Their results are shown in Fig. 5a. To compare these results to those for the model, estimates of the volumes of C-S-H and capillary pores present in each sample are necessary. To obtain these, the assumption was made that the cement paste is pure C₃S, the main component of Portland cement. Knowing the w/c ratio and measured degree of hydration [26], these needed volumes can be calculated for a C₃S paste [32]. While the exact sizes of the real molecules used on the abscissa in Fig. 5a are somewhat questionable [29], the model results shown in Fig. 5b clearly indicate the same trends as those observed experimentally. Once again, measurements computed on the model structures are considered to exhibit a reasonable agreement with those determined experimentally for the real material.

Figure 5. Comparison of (a) experimental (top) and (b) model (bottom) pore volumes vs. molecule size. From left to right, experimental points are for water, methanol, isopropanol, and cyclohexane.