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Introduction

Portland cement paste is a porous, chemically bonded ceramic which results from the reaction of an initial suspension of portland cement powder and water. Portland cement is a manufactured material, consisting primarily of calcium silicates, with fairly minor amounts of aluminates, ferrites, and sulfates [1]. The hydration reaction between cement and water in time produces a multi-phase, rigid material. After initial mixing, the water originally between the cement particles gradually becomes a highly conductive pore fluid, due to the dissolution of Ca and alkali ions from the cement. The main product of reaction is a poorly crystalline or amorphous calcium silicate hydrate commonly referred to as C-S-H (standard cement chemistry notation is: C = CaO, S = SiO₂, and H = H₂O), with the hyphens denoting a varying C/S ratio non-stoichiometric compound. This phase is conductive as well, because its nanometer-size pores are filled with conductive pore fluid. Another important product is calcium hydroxide, CH, which forms in crystals and is an insulator. Since the total reaction products have a higher specific volume than the reactants (cement and water), the volume originally containing the pore fluid, termed capillary porosity, is reduced and becomes increasingly tortuous. The capillary pores control properties such as permeability, strength, toughness, and durability. With respect to electrical properties, which this paper focuses on, the only phases of importance are capillary porosity and C-S-H. Other phases are insulators [2].

Analysis of porosity by methods like scanning electron microscopy (SEM) or gas adsorption is complicated by the fact that the high vacuum necessary for these measurements remove water, which is an integral part of the cement paste structure. Recently, impedance spectroscopy (IS) [3] has been used to study the microstructure of cement paste [4,5,6,7,8,9,10,11,12]. IS, as it is commonly practiced, is a technique in which an alternating voltage at a single frequency is applied to a sample, and the magnitude and phase of the current measured [3]. Impedance spectra are then given by the behavior of the impedance (or other quantities derived from the impedance and the frequency [3]) as a function of frequency. It has been shown that the impedance spectra of cement pastes depend strongly on the amount of porosity present in the microstructure, and, perhaps more importantly, on the arrangement and connectivity of the porosity [2]. By studying the impedance response at different times during the reaction, information about the arrangement and interconnectivity of the microstructure in the undried state can be obtained.

It is very common to study the cement paste made from pure tricalcium silicate (C₃S) and water, since C₃S is the major component of portland cement. This reaction serves as a useful, somewhat simpler approximation for the hydration of portland cement. The electrical properties of C₃S paste are qualitatively very similar to portland cement paste, however, since both capillary porosity and C-S-H are still the main phases. Figure 1 shows an impedance curve of a tricalcium silicate paste. The impedance curve is in the form of a Nyquist plot [3], with -Z'' plotted vs. Z', and where Z'' and Z' are the imaginary and real parts, respectively, of the impedance Z. Applied frequency parameterizes the plot, with frequency increasing from right to left in Fig. 1. The paste was mixed with an initial weight ratio of water to cement (denoted w/c) of 0.45, and has reacted for 14 days. The degree of hydration or reaction, α, is defined as the fraction of cement that has hydrated. The impedance curve in Fig. 1 exhibits a large electrode arc on the low frequency (right hand) side of the plot. This arc is due to the interface between the ionically conducting sample and the electronically conducting electrode, and is not a response of the bulk cement paste. The bulk arc to the left of the electrode arc is the response of the paste. The point where the bulk and electrode arcs intersect on the real axis ( 470 ohms on Fig. 1) is the bulk resistance of the sample, and is equivalent to the DC resistance of the sample. The separation of bulk and electrode effects in IS is a much more reliable way of measuring the true DC resistance than single frequency electrical measurements. Higher frequency measurements that would be located to the left of those shown on Fig. 1 are currently unattainable due to experimental limitations, which make the maximum reliable frequency to be about 5-10 MHz [2].

Figure 1: Nyquist plot of a C₃S paste with water to cement ratio of 0.45, reacted for 14 days.

While initial efforts to explain IS spectra in terms of microstructure have had some success [4,5,6,7,8,9,10,11,12,13], some implications of the experimental results have been hard to reconcile with prevailing theories of microstructural development. The purpose of this paper is to explain these puzzling features, described below, using a computer model.