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Introduction

Impedance spectroscopy (IS) is an electrical technique that has been used to characterize the microstructure of cement paste, providing useful information about the relationships between microstructure, electrical properties, and chemical processes during the hydration of cement paste [1,2,3,4,5,6,7,8,9]. The IS experiment consists of applying an alternating current, of small enough amplitude to be in the linear response regime, to a cement paste sample and measuring the impedance as a function of frequency. The measurement of impedance can be made rapidly and easily while the sample is hydrating, without altering its microstructure or drying the sample.

Parts I [10] and II [11] of this series studied the relationships between the D.C. conductivity σ [10] and low frequency relative dielectric constant k (the dielectric constant normalized by the dielectric constant for vacuum) [11], and the microstructure of cement paste, using IS measurements interpreted by digital-image-based computer models. One main experimental finding was that the value of ik for cement paste can be very high [11]. The value of k increases sharply during the first 10-15 hours of hydration to a value as high as 10⁴−10⁵, then decreases gradually to a value near 10³, as shown by Figure 1 [2,4,11].

Figure 1: Relative dielectric constant vs. hydration time for a portland cement paste of w/c ratio 0.4. The dotted line represents a slight uncertainty in the early measurements due to the high frequency required to obtain the data (taken from Refs. [2,4, 11]).

The high values are surprising, since none of the components of the cement paste have such high values. The aqueous phase (dissolved inorganic ions in water), which is the single pure phase with the highest value of k, has k ≈ 80. Calcium silicate hydrate (C-S-H) gel contains small water-filled pores, and although its overall dielectric constant is relatively high, perhaps about k = 10³ [2,4], it cannot account for cement paste values on the order of k = 10⁵, especially at early stages of hydration where not much C-S-H is present.

In Part II of this series, a "dielectric amplification" mechanism was proposed [11] based on a geometric amplification within the microstructure on a micrometer scale. The proposed mechanism is a microstructure of interlocking C-S-H gel and pore water with a structure in some ways similar to that of a grain boundary ceramic [12], where the interconnecting layers of C-S-H act as low σ, high k grain boundaries, and the capillary pores act as high σ, low k grains, as shown schematically in three dimensions in Fig. 2. Since the current is carried mainly by the pore fluid (σ_o = 4-16 S/m⁻¹ for typical portland cement pastes), a large capacitance could result from thin layers of C-S-H gel within the capillary pore network. Porous rocks saturated with an electrolytic solution, having microstructures in some respects similar to that of hardened cement paste, also display high dielectric constants [13]]. Similarly, porous alumina saturated with brine solution has a low frequency relative dielectric constant on the order of 10⁶ [14].

Figure 2: Schematic diagram of the brick layer model of a grain boundary ceramic and its relationship to cement paste [12].

Figure 3: (a) A schematic diagram of a parallel plate capacitor, where D = the distance between the plates, b = thickness of the dielectric substance, and d = the space between the dielectric substance and the plates [3]. (b) A schematic diagram of the arrangement of C-S-H and capillary pores in cement paste, in analogy to Figure 3a (taken from [11]).

This amplification mechanism can be demonstrated in the following simple example. A composite parallel plate capacitor, shown in Fig. 3a, has a capacitance that is controlled by its D/d ratio, as given by

where C = capacitance, D = distance between the plates, b = thickness of the conducting material between the plates, k_s = relative dielectric constant of the substance in the d/2 width gaps, ε_o = permittivity of free space, k = effective dielectric constant of the entire composite parallel plate capacitor, and A = cross-sectional area of the electrodes [2]. The resulting overall relative dielectric constant,

can be very large, depending on the D/d ratio. This is the type of amplification observed in grain boundary ceramics, where D = the grain size of the conductive grains and d = the thickness of the more insulating grain boundaries.

The dielectric constant of each "C-S-H capacitor" in the microstructure of cement paste is also controlled by its D/d ratio, as shown by the schematic diagram in Fig. 3b, where d = the thickness of the C-S-H layer and D = the size of the capillary pore. Initially, as C-S-H is produced and projects into the capillary network, the dielectric constant of the paste increases. At some point, however, the D/d ratio of each capillary pore:C-S-H "capacitor" begins to decrease. This is due both to the increase of the value of d, via hydration growth of C-S-H, and the corresponding reduction in the value of D, as pore water is consumed and porosity and pore size decreases. Reducing the value of D/d causes the dielectric constant of the entire sample to also decrease. Part II showed that, unlike grain boundary ceramics, the high conductivity phase, which in cement paste is the capillary pore space, did not need to be disconnected in order to generate a high dielectric constant. It was also suggested that this same mechanism, acting at the nanometer scale in the nanometer-size C-S-H pores, was responsible for the relatively high value of k ≈ for C-S-H.

The electrical coupling between the pore fluid in the capillary pores and the high values of k assumed to be taking place in the proposed dielectric amplification mechanism implies a method of independently checking the validity of this mechanism. Since the freezing point of pore fluid depends on the size of the pore it occupies [15], a phenomenon associated with freezing point depression in small pores, changes in electrical properties with decreasing temperature can be attributed to specific size classes of pores. In the present study the pore solution in the capillary pores was frozen in order to change the main conducting path from the capillary porosity to the C-S-H gel. The smaller pores in the C-S-H phase freeze at lower temperatures than the larger capillary pores, so that the conductivity of the C-S-H phase, while still lower than its value at room temperature, becomes significantly higher than the conductivity of the capillary pores filled with frozen pore fluid. "Turning off" the high conductivity of the capillary pores should then have a substantial effect on the value of k, if the proposed dielectric amplification mechanism is valid.