Monitoring Fiber Dispersion in Fiber-Reinforced Cementitious Materials: Comparison of AC-Impedance Spectroscopy and Image Analysis. Paper by Nilufer Ozyurt, Leta Y. Woo, Thomas O. Mason, and Surendra P. Shah/AUTHORS' CLOSURE

APPROACH OF AUTHORS

The authors' notion that steel fibers are insulating under DC and conductive under AC is flawed. The use of NaCl solution (an ionic conductor) for passing current, so electron injection is impossible and the electrons' role is limited. Because steel is an electronic conductor, the sensitivity for the fiber is low. Even at high frequencies that hinder the ionic response, electronic conduction is limited. At low frequencies, ions contribute, making the relative role of electrons even less. The oxide on the steel and the polarization layer at the fiber-matrix interface are ineffective ionic conductors. If an electronic conductor is used for passing current, electronic conduction will be more significant and the method will be more sensitive. Silver paint functions after drying. Aqueous solutions are wet. Thus, conductive pastes are more practical than solutions.

The fiber dispersion is particularly poor for 1 vol.% fiber (with regions without fibers, Fig. 3(a)). The authors cannot distinguish dispersion degrees corresponding to different fiber contents, as shown by dispersion factor (DF) data and their scatter (Table 2 and Fig. 7).

The oxide on the fiber may interact with ions. The interaction depends on the frequency and may help ionic conduction.33 Ozone treatment of carbon fiber provides functional groups,34 thereby helping DC ionic conduction.33 Moreover, the dielectric constant is increased by carbon fiber.35 A small dielectric effect is indicated by the effect of the steel fiber on the imaginary part of the impedance (Fig. 1). The higher the frequency is, the smaller the skin depth is. Thus, the fiber's electronic conduction ability diminishes with increasing frequency.

Mechanisms may include: 1) the frequency-dependent interaction of the fiber surface with the ions; 2) the decreasing role of ionic conduction and the consequent increasing role of electronic conduction (hence increasing the contribution of the fiber to conduction) as the frequency increases; and 3) the decreasing conduction ability of the fiber as the frequency increases.

DC ELECTRICAL RESISTIVITY

The DC contact resistivity (silver paint) of the fiber-cement interface is 106 O.cm2 (105 O.in.2) for steel fiber (diameter 60 µm [2.4 × 10-3 in.])36-38 and 105 O.cm2 (104 O.in.2) for carbon fiber (diameter 15 µm [5.9 × 10-4 in.]).34,39,40 For the interface between steel reinforcing bar and concrete, it is 107 O.cm2 (106 O.in.2).41,42 These values are above 10-2 O.cm2 (10-3 O.in.2) for the interface between adhesively bonded steel surfaces43 and 10-4 O.cm2 (10-5 O.in.2) for the interface between bonded copper surfaces.44,45 Nevertheless, the interface is not insulating. This is consistent with the DC volume resistivity decreasing with increasing fiber content.46-48

The authors imply that the DC method is insensitive to the fiber dispersion. The DC volume resistivity (silver paint) is sensitive, as shown for steel and carbon fibers.33,49-52 For steel fiber (diameter 60 µm [2.4 × 10-3 in.]) below the percolation threshold, the resistivity is decreased by silica fume.50 For steel fiber (diameter 60 µm [2.4 × 10-3 in.]) below the percolation threshold, the resistivity is decreased by silane.49 Thus, DC resistivity reflects the effect of admixtures. DC is also attractive in its simpler instrumentation compared with AC.

Below the percolation threshold, the lower the resistivity is, the better the fiber dispersion. Above the threshold, the resistivity is not reliable for indicating fiber dispersion because percolation may be enhanced or degraded by fiber segregation. Below the threshold, differences in the fiber dispersion due to admixtures, fiber surface treatments, and curing ages have been shown by DC resistivity (silver paint).33,49-52 The authors' percolation threshold is not reported. Equation (1), however, suggests the assumption that the threshold is not exceeded.

DISPERSION FACTOR CALCULATION LIMITATION

The authors describe DF as an upper limit for the fraction of dispersed fibers and calculate it based on AC results and Eq. (1), (2), and (4). The measured AC conductivity relative to that of the matrix is not reported, though this ratio is in the calculation. The DC resistances of cements with and without fiber are close (Fig. 1), suggesting that the fiber contributes little to conduction.

The ratio of the composite (high-frequency cusp) AC conductivity to the matrix DC conductivity is 1.4 (Fig. 1), which is low compared with the ratio of the DC composite conductivity (silver paint) to the DC matrix conductivity given in the following for other steel fibers.50,53

For silica fume cement paste containing 0.03 vol.% (below the percolation threshold of 0.3 vol.%53) steel fiber of diameter 8 µm (3.2 × 10-4 in.), DC conductivity ratio equals 7.653 and DF equals 0.56. At 0.06 vol.% fiber, the ratio equals 1453 and DF equals 0.52. At 0.09 vol.% fiber, the ratio equals 13653 and DF equals 6.8, which exceeds 1. Thus, the DF calculation is invalid when the conductivity ratio exceeds a value between 14 and 136 and is not useful for applications that require high conductivity.