Next: Experimental Results
Several papers have been published recently relating the impedance response of cement paste to certain aspects of the microstructure [1,2,3,4,5,6,7,8,9]. These reports have focused on the observed offset resistance, bulk resistance, and the origin of the dielectric response of cement paste. However, the effective dielectric constant associated with the bulk arc has not been reported. Part I of this paper , studied the bulk resistance and the apparent "offset resistance" found in Nyquist plots of the impedance response of cement paste, using computer modelling. In Part II of this paper, we now use computer modelling to help understand the dielectric response of cement paste, and in particular the low frequency effective dielectric constant.
Using impedance spectroscopy techniques [10,11], we have measured the low frequency effective dielectric constant, keff, associated with the bulk arc of the Nyquist impedance plot. We have found keff to be a function of the water:cement ratio (w/c = weight ratio of water to cement in the original mixture), and the age or degree of reaction of the paste. The quantity keff is defined in the following way . A Nyquist plot that is perfectly circular in the complex impedance plane, with its center on the real axis, can be fit to a circuit containing a perfect resistor R and a perfect capacitor, C, connected in parallel. The value of R is the DC resistance of the material, and the value of C, normalized for the geometry, gives the dielectric constant ε = k εo.
We have found [1,10] that the Nyquist plots for cement paste can be successfully fit by "constant phase elements", or CPE's [10,11], which are circular arcs but with their center depressed below the real axis. In these circuit elements, a parameter Q takes the place of C in the parallel RC circuit. If the arcs are not depressed below the axis very much, as is usually the case for cement paste, then we can define an effective dielectric constant keff = Q' / εo, where Q' is just Q but normalized for sample geometry . The parameter Q reduces to the regular capacitance C when the center of the arc is on the real axis. This is the quantity reported and discussed in this paper. In the area of composites, quantities reflecting the response of an entire sample are also often denoted as "effective" or "average" quantities . This same meaning also applies to the effective dielectric constant we have measured, as cement paste is a composite material, and we are measuring the dielectric response of the entire composite.