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The behavior of the dielectric constant as a function of decreasing temperature is very similar to the behavior of the conductivity, as shown by Fig. 5. The value of log k is relatively constant with change in temperature down to about −5 ºC, where it drops sharply by two orders of magnitude. Beyond this point, log k is again relatively constant with change in temperature. Log k of samples cooled below −100 ºC remained relatively unchanged in the temperature region below the drop, as shown by Fig. 8.
Figure 8: Logarithm of the relative dielectric constant vs. temperature for an 0.4 w/c ratio cement paste hydrated 18 hours, and taken to lower temperatures.
When tap water is frozen, k drops from a value of about 80 at room temperature, to a value of about 5 at temperatures below 0 ºC. In previous studies, the dielectric constant of extracted pore solution at room temperature was found to be similar to that of water [2,4]. However, the dielectric constant of frozen pore solution is difficult to determine because the solution does not freeze completely at a specific temperature. Multiple arcs appear in the impedance spectra at low temperatures, which suggests that multiple phases precipitate during freezing. For example, a pore solution extracted from a cement paste hydrated for 15 hours and then tested at −50 ºC displays four separate arcs, as shown in Fig. 9. The phase separation, with its resulting multiple arc response, makes it impossible to estimate the dielectric constant accurately. Because of the small size of pores, phase separation may not occur during freezing of cement paste. According to Yoon et al. , freshly-mixed cement paste with a w/c ratio of 0.4 has a dielectric constant of about 24 at −30 ºC, so it is safe to assume that the dielectric constant of frozen pore solution is on the same order as the dielectric constant of frozen tap water.
Figure 9: Impedance response of frozen pore solution at −50 ºC.
Although the dielectric constant of pore solution decreases when it freezes, this cannot be the only cause for the drop in the dielectric constant of cement paste. The drop in k for the pore solution is at most about one order of magnitude, compared to the largest drop in k for cement paste being up to three orders of magnitude* [28,29], measured for an 0.7 w/c ratio cement paste. This result is strong evidence for the dielectric amplification mechanism proposed in Part II  of this series. This dielectric amplification mechanism is clearly almost eliminated when the capillary pores freeze and lose their high conductivity. When this happens the microstructure changes from one in which the layers of C-S-H gel act as capacitors within the conductive capillary porosity to one in which the interconnected C-S-H gel becomes the most conductive pathway, embedded in the much less conductive capillary pores. The relative value of the conductivity of frozen pore solution and C-S-H are discussed in Sec. 5 below.
Figure 10 is a plot of log(k) vs temperature for four pastes of w/c ratio 0.4 with hydration times of 15 hours, 26 hours, 200 hours, and 40 days. Notice how Δ log(k) decreases with time until at about 40 days there is only a minimal drop. The behavior of Δ logk′ essentially tracks that of Δ log(σ). After the capillary pores become disconnected, the dielectric amplification mechanism loses its effectiveness. Turning off the conductivity of the capillary pores by freezing then has relatively little effect on the value of k.
Figure 10: Logarithm of the relative dielectric constant vs. temperature for an 0.4 w/c ratio cement paste hydrated 15 hours, 26 hours, 8 days, and 40 days.
*Two-point IS measurements tend to give somewhat higher low-frequency dielectric constants than do four-point measurements. The two-point measurements can give up to a three order of magnitude drop in k upon initial freezing, while the four-point measurements give closer to a two order of magnitude drop.