3.3.1. Specimens without Treatment of TX10

Similar to the compressive strength of non-TX10-treated specimens, the flexural strength decreased with the increase of the concentration of SWWCNTs. Figure 8 shows the increase of flexural Strength of non-TX10-containing mortar prisms as a function of curing time. SWCNT-containing mortars could reach high flexural strength at early stage (seven days). After seven days of curing, the flexural strength reached stable value and continued curing gained little increase in flexural strength. The reason is that, with the addition of SWCNTs, the rapid hardening phenomenon of mortar was more obvious, even though early hardening cement was used. At 28 days of curing, SWCNT0S showed 6.75% increase in flexural strength compared to the seven-day strength, but, for SWCNTXS (where X equals 2, 4, and 6), the increase was little, only from 0.91% to 2.17%. This might be the crack-bridging effect in cement/CNTs composites produced by CNTs. CNTs have the ability to prevent the development of

cracks [65,69]. TEM is needed for further works to analyze the crack-bridging effect of CNTs and to study the effect of CNTs on hydration products of cement/CNTs composites.

**Figure 8.** Flexural strength of non-TX10-added mortar prisms.

In addition, Figure 9 shows that the flexural strength decreased with the increase of the concentration of SWCNTs. It can also be observed that, when SWCNTs were added, the values of flexural strength after 7 and 28 days of curing were close for all concentrations of SWCNTs used.

**Figure 9.** Flexural strength as a function of concentration of SWCNTs (No TX10).

## 3.3.2. Specimens with Treatment of TX10

When TX10 was added and mixed, the variation pattern of flexural strength changed. Figure 10 shows that the flexural strength was high initially, adding SWCNTs caused a slight reduction, and then the flexural strength increased with the increase of the concentration of SWCNTs. After 28 days of curing, flexural strength of SWCNT6S reached 5.31 MPa, 19.77% and 10.92% higher compared to flexural strength of SWCNT2S and SWCNT0S at 28 days of curing, respectively. This variation pattern was different to that when TX10 was not added, as shown in Figures 9 and 10. The dispersed CNTs showed positive effect on flexural strength of mortars.

Figure 11 shows that the flexural strength increased with the increase of concentration of SWCNTs, although the value of flexural strength of SWCNT0S was between those of SWCNT2S and SWCNT4S. By comparing Figures 8 and 11, it can be observed that, with the addition of TX10, the flexural strength of mortar with 0.06 wt% CNTs was the highest, resulting from the positive effect of CNTs. This finding was opposite to that of non-TX10-added mortars, where plain mortar presented the highest level.

**Figure 10.** Flexural strength as a function of concentration of SWCNTs (TX10).

**Figure 11.** Flexural strength of TX10-added mortar prisms.

## *3.4. Relationship between Strength and Bulk Density of Cement Based Specimens*

In the experiments, the mass of each tested cube and prism was recorded. According to the size of mortars and prisms, the bulk density of each specimens could be calculated. Table 13 shows the average bulk density of each set of mortars.


**Table 13.** Average bulk density of mortar specimens.

Table 13 shows that for non-TX10-added mortars, the bulk density was around 2.102–2.141 g/cm3, higher than those of TX10-treated mortars (1.884–1.998 g/cm3). This result proves that the porosity of mortars was increased due to the addition of TX10, which caused the reduction of strength of mortars. In addition, the strength of mortars was related to the bulk density of mortars. For instance, Figure 12 shows the variation of 28-day compressive strength and bulk density of TX10-treated specimens as a function of the concentration of SWCNTs. The average bulk density of plain cube mortars (no SWCNTs added) was 1.934 g/cm3, which was reduced to 1.873 g/cm3 with the increase of the concentration of CNTs to 0.02 wt%, and then increased to 1.893 and 1.963 g/cm<sup>3</sup> when the concentration of CNTs was increased to 0.04 wt% and 0.06 wt%, respectively. The variation pattern of 28-day compressive

strength was similar to the variation of bulk density of specimens, i.e., the higher was the bulk density, the higher was the compressive strength.

**Figure 12.** Variation of 28-day compressive strength and bulk density of TX10-treated specimens as a function concentration of SWCNTs.

Therefore, the strength (MPa)/mass of specimens (g) ratio was considered to standardize the law. It was found that the compressive and flexural strengths were related to the mass of the mortar cube/prism. Table 14 shows some of the data: average compressive and flexural strengths after seven days of curing are listed as illustration.


**Table 14.** Compressive (flexural) strength/mass ratio of cubes (prisms) at seven days of curing.

Comp represents compressive strength, and Flex represents flexural strength.

Table 14 shows that both the compressive strength and the flexural strength was related to the mass of the specimens. When SWCNTs were directly used, the general trend of strength/mass ratio was downward, which was same trend as for strength. When TX10 was added to pretreat SWCNTs, the ratio saw a slight increase when the concentration of SWCNTs increased, also similar to the variation pattern of strength.

The value of comp/mass of cubes ratio was close to the flex/mass ratio of prisms. The differences between the two ratios were generally less than 5%. Therefore, this relationship can be used to estimate the compressive strength (flexural strength) when the mass of the specimens and flexural strength (compressive strength) are known. However, in some cases, the difference reached 8–15%, which could be observed from results of SWCNTXS (where X equals 0, 2, 4, or 6) at three days of curing (Table 15). Its cause might be the errors in the process of preparing the specimens

Generally, it can be concluded that, when SWCNTs and MWCNTs were directly used to prepare mortars, specimens' strength decreased with the increase of concentration of CNTs due to the increase of CNTs' agglomerates. It was found that MWCNT-added specimens showed better strength properties than SWCNT-added specimens due to MWCNTs having better mechanical properties, although the differences of the strength of the cement composites were small. The effect of SWCNTs on strength properties of cement composites was mainly studied. When TX10, as a surfactant, was applied, the variation pattern was changed. The compressive and flexural strengths generally increased with the increase of concentration of SWCNTs, although TX10 produced a negative effect on cement composites by increasing porosity, causing a decrease in the bulk densities of mortar specimens. It was found that SWCNTs could help cement composites gain high strength more quickly at the early stage. In addition, it was found that the strength was related to the mass of the specimens.


**Table 15.** Compressive (flexural) strength/mass ratio of cubes (prisms) at three days of curing.

Where the comp represents compressive strength, and the flex represents flexural strength.
