*3.2. Compressive and Flexural Strength*

The compressive and flexural strength results obtained for each mixture are shown in Figure 3. The maximum failure load and its failure pattern is noted and results are presented in Table 5 below.

**Figure 3.** Compressive (**a**) and flexural strength (**b**) of MWCNT-mortar specimens.


**Table 5.** Compressive and flexural loads and strength.

The results confirm an increase in compressive strength in all the specimens with MWCNT content in the cement matrix for the two curing periods, in agreement with related works which also studied low CNT loading [17,43,44]. In particular, all mortars manufactured with 0.01 wt.% MWCNT showed 1.6% and 4.1% higher compressive strength values than those manufactured with ordinary cement (control) for 28 and 90 days curing periods, respectively. Furthermore, the improvements were significant in mortars prepared with 0.015 wt.% MWCNT, which showed 3.0% and 4.7% increases in compressive strength at 28 and 90 days curing period respectively. This increase in strength can be explained by the CNTs-induced formation of highly dense zones in the cement microstructure, as seen in the strength-density relationship shown in Figure 4. The densification of cement, forming virtual aggregate clusters (cement-MWCNTs) with presumably rounded shapes, minimizes crack initiation, propagation and distribution [45]. More remarkable effect was shown in cement mortars with 0.02 wt.% MWCNT loading at the age of 90 days, that exhibited an improvement of 25.4% in compressive strength.

Flexural strength results show the same trends in increasing flexural strength when low MWCNT loading in present in mortar. MWCNT 0.02 wt.% demonstrates to be the optimum dosage in accommodating in the cement matrix, achieving improvements up to 20.3% in flexural strength at 90 days curing period. Additions 0.01 and 0.015 wt.% also showed satisfactory results, with an increase of the ultimate strength of about 8.8% and 11.3%, respectively, at the same curing period of 90 days.

**Figure 4.** Relationship between compressive strength and density of MWCNT-mortar specimens.

These findings show that the modification of cement microstructure after inclusion of low dosage of MWCNTs results in an increase in the ultimate strength, both compressive and flexural, specially at long curing time. These results also lead to the importance of caring cement paste hydration parameters at long ages, when microstructure development is almost completed, and CNTs can contribute to a filled porous structure with enhanced strength properties. If mortar curing has developed properly under cared curing conditions, hardened material can take advantage of CNTs for an improved loads distribution.

#### *3.3. Electrical Resistivity Analysis*

Figure 5 shows the average results of the electrical surface resistivity of MWCNTmortars versus the amount of MWCNTs for each curing time. In agreement with Konsta-Gdoutos and Aza [46], a decrease in resistivity is observed with the presence of MWCNTs in the cement matrix even for very low nanomaterial additions. In general, similar decrement range is observed regarding the curing times, regardless of the MWCNT loading. For example, in the case of mortar specimens with 0.01 wt.%, the registered resistivity values were 3.32 kΩ · cm and 3.82 Ω · cm, at curing times of 28 and 90 days respectively, which corresponds to a decrease of 11% and 6%, respectively. A similar behavior happened in the case of mortar specimens with 0.015 wt.% MWCNT, where electrical resistivity values reached decrements of 8% and 5% at curing times of 28 and 90 days respectively. Thus, in the case of both MWCNT loadings, average values of electrical resistivity are in a similar range, although our findings demonstrate that the curing time does have an influence on the electrical resistivity of the specimens. This statement is in agreement with relevant works where findings on nearly linear increment of resistivity as degree of hydration increases are reported [47,48]. Surprisingly, the sample with the addition of MWCNTs 0.02%, manages to increase the resistivity by 27% at 90 days curing time. These very MWCNT-mortar specimens did show a remarkable increase in compressive strength test at 90 days curing time, which in indeed should explain this different trend at electrical resistivity variation, that is presumed to be a physical property related to mechanical performance of cement-based materials.

**Figure 5.** Average electrical surface resistivity of MWCNTs-mortar samples.

Regarding the variation of resistivity with respect to the MWCNTs content in the samples, it is clear from the results that there is a slight detriment in conductivity as the addition of MWCNTs increases. No significant improvement in conduction properties is obtained from an increasing loading of MWCNTs. Once electrical conduction is established in the material, the presence of a greater amount of nanomaterial does not imply a gain in electrical flux. Although in this work we cannot warranty good MWCNTs dispersion within the matrix of our samples, we can derive, however, that good dispersion was achieved from the fresh properties results. Therefore, we believe that conduction paths do not break due to bad MWCNT dispersion, but that resistivity increases due to polarization effects caused by the amount of water and the dissolved ions in the mixes [46], as consistency results proved large water retention in our samples.

Measurements of the dependence of resistivity with temperature are presented in Figure 6a. All samples were tested at the age of 90 days. Temperature significantly influences the measured resistivity, with higher temperatures leading to lower resistivity values, as demonstrated in Figure 6a. From these experimental findings, it is clear that all the profiles of resistivity versus temperature follow a trend of exponential decay, as previously reported [49].

To reach a better insight in this topic, we analyze the activation energy as provided by the Arrhenius equation, given by Equation (3)

$$\rho = A \cdot \exp \frac{E\_d}{R\_{\%}T} \tag{3}$$

where *ρ* is the electrical resistivity measured at temperature *T*(*K*), *A* is the pre-exponential factor and represents the nominal resistivity at infinite temperature, *Rg* is Universal Gas constant (8.314 J · mol−<sup>1</sup> · <sup>K</sup><sup>−</sup>1), and *Ea* is the activation energy for the conduction process (J · mol<sup>−</sup>1). In Figure 5b below, natural logarithm of the inverse of resistivity (natural logarithm of conductivity *σ*), is plotted against 1000/T, therefore multiplying the slope of the plot by the Universal Gas constant *Rg*, *Ea* is obtained in kJ · mol<sup>−</sup>1. Results of the calculated activation energy of MWCNT-mortar specimens are presented in Table 6.

**Figure 6.** Thermal evolution of electrical resistivity of MWCNT-mortar at 90 days curing time (**a**), and Arrhenius plots for MWCNT-mortar at 90 days curing time presented over the temperature range 20–55 ◦C (**b**).

**Table 6.** Summary of activation energy values, calculated with Arrhenius equation of MWCNTsmortar at 90 days curing time. Conductivity of the MWCNT-mortar at 20 ◦C, *σ*<sup>20</sup> is also presented.


The above figures are in agreement with resistivity results as plotted in Figure 6a; high resistivity correlates with high activation energy and vice versa. The activation energy slightly decreases for mortars containing MWCNTs 0.01 and 0.015 wt.%, which implies that in these mortars the energy barrier that must be overcome for an ion to conduct is lesser than the control specimen.

Further understanding of the above facts can be obtained from the analysis of electrical resistivity behavior in porous materials, as mortar, which can be described by using the following Equation (4):

$$
\rho\_T = \rho\_o \frac{1}{\Phi \beta} \tag{4}
$$

where *ρ<sup>T</sup>* is the total resistivity, *ρ<sup>o</sup>* is the resistivity of the pore solution, which in turns is a function of the ions composition and concentration in solution; *φ* is the porosity of the system that is accessible to fluids, and *β* is the connectivity of the pores in the system [48]. The term 1/*φβ* is ofter called Formation Factor *F*, which comprises the material microstructural characteristics, such as the water-to-cement ratio, volume of paste, and degree of hydration.

Since electrical conduction through saturated cement mortar occurs via ions in the continuous (percolated) aqueous phase between the electrodes [50]; the fact that samples with MWCNT 0.01 wt.% loading show better conductivity than samples with 0.015 wt.% could, in part, be attributed to microstructural changes resulting from further hydration in sample 0.01 wt.% (being hydration reactions thermally activated processes). Another plausible explanation could be the effect of a smaller formation factor in this specimens, which reflects either a higher porosity or a higher connectivity. Higher porosity directly comes out of a more hydrated mortar, as introduced before. Higher connectivity, however, can only be explained by the presence of MWCNTs in the microstructure. From the results, it seems that 0.01 wt.% be more efficient in developing conductive paths within the microstructure. Nevertheless, these findings indicate that the MWCNT loadings studied in this work are insufficient to produce conductive cement mortar.

Similarly, the increase in activation energy, and subsequently increased resistivity, with respect to the control sample for mortars with MWCNT 0.02 wt.% wt can be explained considering that these specimens have better developed their hydration products, as confirmed by the results of mechanical resistance, therefore the formation factor has been enlarged as result of decrease porosity.

#### **4. Conclusions**

The effect of 0.01, 0.015 and 0.02 wt.% MWCNT loading on mechanical strength and electrical resistivity of cement mortar is studied in the present work. MWCNTs are dispersed in mortar microstructure and tested through mechanical performance analysis at 28 and 90 curing period. The electrical resistivities of MWCNT-mortar are measured at different temperatures up to 60 ◦C, using the four point probe Wenner setup and dynamic temperature test (DTT). Activation energies corresponding to different MWCNT loadings are calculated using Arrhenius equation.

It is found that an increase in both compressive and flexural strength is achieved in mortars with MWCNT contents. Remarkable improvements of 25.4 and 20.3% at 90 days are found in compressive and flexural strength respectively, for an addition of 0.02 wt.% MWCNTs. Shorter initial and final setting times are obtained for 0.02 wt.% MWCNT loading, which implies a denser microstructure and finer porous structure.

The resistivity measurements in mortars with 0.01 and 0.015 wt.% MWCNT loading result up to 10% decrement to respect to control mortar at both 28 and 90 days curing. Mortar with 0.02 wt.% MWCNTs, however, depicts a sudden 27% increase in resistivity at 90 days curing time, due to well hydrated microstructure as confirmed by the mechanical tests. Activation energy calculations show fully accordance with these statements, resuming

that 0.01 wt.% MWCNT seems to be the most effective loading scheme to produce certain conductivity enhancement in cement mortar.

**Author Contributions:** Conceptualization, E.C.-P.; Data curation, F.V.; Formal analysis, E.C.-P.; Funding acquisition, F.V.; Investigation, E.C.-P. and R.P.-T.; Methodology, E.C.-P., F.V. and R.P.-T.; Resources, E.C.-P. and R.P.-T.; Validation, E.C.-P. and R.P.-T.; Writing original draft preparation, E.C.-P. and R.P.-T., writing review and editing, E.C.-P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.
