Internal Relative Humidity

The autogenous relative humidity readings with time for the four cements studied are provided in Fig. 5. It should be noted that the spike observed at a time of about 500 h for the 212 m²/kg curve was due to a temperature drop during a short power outage in the building, during which data continued to be collected since the datalogger runs on batteries. Each curve in Fig. 5 exhibits a similar behavior, with an initial rise (as the humidity sensor equilibrates with the cement paste)

**Figure 5:** Internal relative humidity vs. time as a function of cement fineness.
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to a plateau region (98 % RH to 98.5 % RH) followed by a significant decrease with time. The initial observed rise in RH doesn't reach 100 % RH due to the reduction in RH caused by the dissolved ions (Ca⁺⁺, Na⁺, etc.) present in the cement pore solution [22]. The coarser cements (254 m²/kg and 212 m²/kg) remain at their plateau level for a longer period of time and also subsequently decrease at a much slower rate than the finer ones (387 m²/kg and 643 m²/kg), for RH values between 98 % and 96%, as hypothesized.

Of course, some of the differences in the curves shown in Fig. 5 could be due to the differing hydration kinetics of the four cements, as it is well known that hydration rates are significantly influenced by cement PSD [23,24]. This could be preliminarily examined by plotting the internal relative humidity against the measured chemical shrinkage (directly proportional to degree of hydration at early times [4,5,6]), the only problem being that the chemical shrinkage specimens are basically saturated while the internal relative humidity specimens experience sealed curing. One way around this minor discrepancy is to utilize the NIST cement hydration model executed under both sealed and saturated curing conditions [6,18]. Figure 6 shows a comparison of the model-predicted (saturated conditions) and the experimentally observed chemical shrinkage results for the four different cement finenesses. As expected, the two finer cements are observed to hydrate at a significantly faster rate than the coarser ones. For calibration of model hydration cycles to real time [6], a simple linear calibration factor of 0.125 h/cycle was employed for these specimens hydrated at 30 ºC. This means that at a temperature of 30 ºC, the hydration behavior of these cements is better described by the linear as opposed to the parabolic kinetic model of Knudsen [24], the latter being typically employed for room temperature hydration in past studies [6,10,25]. Previous measurements of chemical shrinkage have indicated that some cements better follow the linear model, while others are better characterized using the parabolic model [5]. Using this single calibration, good agreement is observed between all four experimental curves and their model counterparts (particularly for times between 10 h and 200 h). This suggests that the hydration and microstructure differences due to cement PSD are adequately captured by the NIST microstructure model, as observed in previous studies [6,25]. It is observed that the two finer cements exhibit similar hydration kinetics, while the two coarser ones hydrate at a significantly slower rate.

**Figure 6:** Experimental (data points) and model-predicted (solid lines) chemical shrinkage as a function of cement fineness. In all cases, model was executed under saturated conditions and hydration cycles were converted to time in hours simply by multiplying by a factor of 0.125 h/cycle.
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Next, the same calibration factor of 0.125 h/cycle was used for the simulated hydrations conducted under sealed conditions to determine their degree of hydration vs. time behavior. For each of the four systems, the achievable hydration after 5000 cycles (625 h) of model hydration, α₅₀₀₀, under sealed and saturated conditions are provided in Table 2. As would be expected, the finer cements are able to achieve a higher degree of hydration, and also exhibit a larger difference between sealed and saturated conditions. The sealed degree of hydration vs. time was then used to plot the experimental relative humidity vs. degree of hydration, as shown in Fig. 7. Now, interestingly, the plateau regions for all four finenesses extend to the same degree of hydration, α=0.4. Beyond this, the curves basically diverge into two subsets, for the finer and coarser cements, respectively. The divergence is maximal at about α=0.47 and then the two subsets of curves approach one another once again.

**Figure 7:** Internal relative humidity vs. model-predicted degree of hydration as a function of cement fineness.
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The curves in Fig. 7 can actually be interpreted as pore size distribution curves in the following manner. First, as shown in Fig. 1 and Table 1, there is a direct relationship between RH and the size of the largest water-filled pore in the cement paste microstructure. Second, since the volume of empty porosity in a sealed system is directly proportional to the degree of hydration (after setting), the abscissa in Fig. 7 can be equivalently viewed as a measure of empty pore volume. Thus, Fig. 7 can be thought of as a plot of pore size vs. (empty) pore volume. With this interpretation (and neglecting the effects of dissolved salts on RH), the sharp drop in RH with increasing hydration observed at α=0.4 for the two finer cements would indicate that these two microstructures contain very few "coarse" pores in comparison to the ones based on the coarser cements, in good agreement with the 3-D spherical intrusion results in Fig. 4. In fact, an obvious similarity between Figs. 4 and 7 can be observed, realizing that higher RH values correspond to larger empty pore sizes. As hydration proceeds, the curves eventually approach one another, since the overall capillary porosity of the four systems is identical and the pores are reduced to equivalent sizes in the four pastes by the ongoing hydration.

While the differences in the RH vs. $\alpha$ curves in Fig. 7 may seem rather subtle, their implications are extremely significant. This is because the tensile strain capacity and elastic moduli of cement-based materials change drastically during the first several hundred hours of hydration [7,8]. Thus, delaying the development of "fine" water menisci and their associated stresses for just a few days should have a significant impact on minimizing autogenous shrinkage and cracking. At a fixed capillary stress (pore size), a microstructure that has hydrated more will have a higher elastic modulus and will have had a longer time for any stress relaxation and creep to manifest themselves. Thus, such a microstructure should exhibit less shrinkage. The autogenous deformation results presented next will indeed validate this conjecture.