Next: Freeze-thaw cycling experiment Up: Main Previous: Effect of freezing

Electrical properties of frozen cement paste at −40 ºC

The conductivity and the dielectric constant of frozen cement paste, at temperatures lower than −8 ºC, increased with hydration time, as shown in Figs. 7 and 10. Assuming that in the frozen paste the C-S-H gel has the highest conductivity and the highest dielectric constant, these electrical properties of the paste would be expected to increase with time, as the degree of hydration and therefore the amount of C-S-H has increased.

To enable quantitative comparison between experimental and computational results for the D.C. conductivity, the normalized conductivity was used. This is defined as σ / σ_CSH, where σ_CSH is the conductivity of the pure C-S-H phase at -40 ºC, as determined below. The quantity σ is the measured electrical property at −40 ºC of the frozen pastes. The temperature of −40 ºC was chosen because it is the point at which most of the capillary porosity is frozen, but most of the gel porosity is still unfrozen. This leaves the C-S-H gel as the only conducting phase, and the frozen capillary porosity as an insulating phase. No significant changes in σ or k were observed between −5 and −40 ºC, because the remaining unfrozen capillary porosity is disconnected after the larger capillary pores freeze.

The volume fraction of C-S-H gel (φ_CSH), which is then expected to be the primary variable, was calculated as follows:

where w_o/c = initial water to cement ratio, and α = degree of hydration [30]. The degree of hydration was approximated using data in Ref. [4]. As shown by Fig. 11, the experimental normalized conductivity increases with the volume fraction of C-S-H gel for frozen pastes of w/c ratios 0.4 and 0.7. If C-S-H gel is indeed the most conductive phase in the matrix, the conductivity of the paste would be expected to increase as hydration proceeds and more C-S-H gel is produced, as observed. Note, too how the conductivity of the frozen paste is independent of w/c ratio, also indicating that the conductivity depends on the C-S-H content only.

Interestingly, the normalized conductivity of frozen paste does not begin to increase significantly until the C-S-H gel reaches a volume fraction of about 0.20. The percolation threshold for the C-S-H phase has previously been predicted to be about 17-18% [24]. If, in the frozen paste, the conductivity of the C-S-H gel is much greater than the frozen pore solution, then the overall D.C. conductivity should appear to go to nearly zero near the true percolation threshold. Below this threshold, the C-S-H is disconnected, and the overall conductivity is dominated by the much smaller frozen pore fluid conductivity. In this case, the experimental threshold is in good agreement with the theoretical prediction. This threshold could also be the point at which the C-S-H network is physically strong enough to resist the stresses associated with freezing so that it is not broken apart and remains interconnected in the frozen cement paste. In this case, the true geometric percolation threshold for the C-S-H phase would be somewhat lower than the 17-18% theoretical prediction.

As shown by Fig. 12, the dielectric constant increases with the volume fraction of C-S-H gel for frozen pastes of w/c ratios 0.4 and 0.7, an indication that the C-S-H gel has the highest dielectric constant in the matrix. Moreover, the results for different w/c ratios are the same, further indicating that the dielectric behavior of frozen cement paste depends only on its C-S-H content. This is another indication in support of the proposed dielectric amplification mechanism. In the frozen system, with the capillary pores "turned off", the values of σ / σ_CSH and possibly that of k follow a simple function of φ_CSH, without amplification of the value of k at the micrometer cement paste level. However, there is almost certainly still amplification at the C-S-H nanometer scale, as will be discussed further below.

Figure 12: Relative dielectric constant at −40 ºC vs. the volume fraction of C-S-H for portland cement pastes of w/c ratio 0.4 and 0.7.

In Ref. [26], it was found that for the different cement paste phases, the percolation probabilities (fraction of a given phase that is connected) for each phase at different w/c ratios all fell on the same curve when plotted against the volume fraction of that phase. The connectivity of each phase was independent of w/c ratio. Since the conductivity of a phase depends sensitively on how well it is connected, Ref. [32] predicted that the conductivity of unfrozen pastes would depend only on capillary porosity, the main conducting phase at room temperature, not w/c ratio. Figures 11 and 12 show that this is true also for the frozen pastes, when plotted against the volume fraction of C-S-H gel, the main conducting phase in the frozen state.

Figure 11 also shows finite-difference computations from the NIST/NU cement paste microstructure model [31] for σ / σ_CSH , which are in excellent agreement with the experimental results. The C-S-H percolation threshold, and the arrangement of C-S-H vs. the arrangement of capillary pores are built right into this model, lending support for the above microstructural deductions from the electrical data. Effective medium theories like the general effective medium theory (GEM) [32] are not suitable for this material since there are three phases involved, two conducting and one insulating, and the GEM, at present, is set up for only two conducting phases. Both model and experimental results are under the Hashin/Shtrikman (H-S) exact upper bound for a three phase material [33]. The corresponding H-S lower bound is identically zero. The H-S lower bound has a series-like microstructure built into it, so that the whole lower bound becomes zero if any one phase has zero conductivity [4]. In this case, we are assuming that the insulating phases actually have zero conductivities.

The actual values of the conductivity of each phase can be determined by a combination of experimental and model results. There are two parameters to be determined, expressed in the following way: 1) the ratio of the conductivity of pore fluid, σ_pf, to the conductivity of C-S-H, σ_CSH, at −40 ºC, and 2) the actual value of σ_CSH at −40 ºC. The value of the ratio needed to make the computations agree with experimental results was estimated by comparing the conductivity of frozen extracted pore solutions to the frozen cement paste. The frozen cement paste conductivities were much larger than that of the frozen pore solution. The value of σ_CSH / σ_pf was found to be about 100, which was then the value chosen to calculate the H-S bound and with which to run the digital-image-based microstructure model computation. Having this ratio is enough to compute the value of σ / σ_CSH in both cases, since normalizing the overall conductivity by σ_CSH reduces the number of parameters needed to only one. However, to extract the actual value of σ_CSH required the use of the experimental data, as follows.

The conductivity data at −40 ºC was preliminarily normalized by the conductivity of the sample with the longest hydration time, having therefore the largest degree of hydration. This degree of hydration is known [4]. The model results were then also normalized by the model result at this same degree of hydration, and compared to the normalized experimental results. The agreement was extremely good, as good as in Fig. 11. The experimental value of σ / σ_CSH was then known accurately, from the model results, for each degree of hydration of the cement paste samples. Knowing σ experimentally for each sample then allowed σ_CSH to be determined for each sample at −40 ºC. This calculated value did not vary more than 20% or so, over different degrees of hydration and the two different w/c ratios, 0.4 and 0.7, lending validity to this procedure. The value of σ_CSH at −40 ºC was found to be 6 x 10⁻⁵ S/m, which was then used to normalize the experimental data at −40C.

In similar fashion, it should be possible to estimate the relative dielectric constant of C-S-H from the frozen paste data and the NIST/NU cement paste microstructure model. This work is in progress and will be reported separately. Nevertheless, the order of magnitude can be estimated based upon the data in Fig. 10. Concentrating at −10 ºC, which insures that all the gel porosity is unfrozen, the relative dielectric constant increases steadily with hydration time, from 650 at 15 hours to 1250 at 26 hours, 2800 at 200 hours, and finally 4000 at 40 days, where C-S-H makes up approximately 50% of the microstructure by volume. These large values indicate that C-S-H gel is itself a microstructure that amplifies its dielectric constant. Gel pores and intervening C-S-H layers achieve amplification on the nanometer scale after the model in Fig. 3. The dielectric constant is amplified from 10 (solid phase) or 80 (pore fluid) to several thousand (C-S-H gel). Subsequently, above the melting point of the large capillary pores, the dielectric constant can be amplified further from 1000 (C-S-H gel) to as high as 100,000 in pastes with a low degree of hydration. Here the large capillary pores and intervening C-S-H product layers achieve dielectric amplification on the micrometer scale, again after the model in Fig. 3.