Chemical characterization by Inelastic Neutron Scattering-INS
Figure 1 shows the INS spectra of M0, M1, CM2 and CM3 mortar composites after subtraction of the backgrounds from dry cement and empty container. As the main contribution to the spectra comes from hydrogen atoms involved in cement hydration, data were compared with a deionised H2O sample measured at the same temperature, also shown in Figure 1. From the bulk-H2O spectrum, it is possible to recognize the translational (below 400 cm-1) and vibrational (around 600 cm-1) modes arising from the intermolecular interactions and the hydrogen-bonding network. By comparison, it is noticed how the sharp vibrational feature in bulk H2O is clearly broadened and red-shifted in the mortar samples, as a consequence of the different interactions that coordinated water molecules experience within the mortar structure. The overall shift of the vibrational bands to lower frequencies corresponds to a picture whereby some H2O molecules undergo rotations that are less hindered than in the bulk, due to the breaking of the hydrogen-bonding network. At lower energies, the sharp translational features in bulk water at 50 cm-1, 220 cm-1, and 305 cm-1 disappear, replaced by more complex lattice and translational motions between 70 cm-1 and 400 cm-1 in the hydrated cements, resulting from the coordination of water to the cement, as well as the creation of new Calcium Silicate Hydrated species. In particular, the strong peak at ca. 330 cm-1 corresponds to the Ca-OH bond . Molecular modelling  and far-IR spectra  of CSH systems also showed peaks in the same region, related to the vibrations of Ca(OH)2 grains forming in the mesopores of the cementitious material. Apart for minor differences related to NR, discussed below, one can notice how the spectra from the four mortar samples, with and without fillers and NR, closely resemble each other. This brings to the conclusion that the average structure and dynamics of hydrogen within the mortars is not affected by the inclusion of rGO, MWCNT, and NR at the investigated concentrations. The same conclusion can be drawn from the spectra of filler dispersions that well reproduced that of bulk H2O (the spectra are not shown for sake of brevity).
The two mortar systems including the NR dispersions, of which the main component is polyisoprene (PIP), manifest an additional intensity clearly visible around 200 cm-1 in Figure 1, likely related to the CH3 torsion mode in PIP . The signal from PIP in the two composites was isolated by subtraction of the corresponding sample prepared without natural rubber. The results are shown in Figure 2 and compared to the spectra from Adams et al.  available from the TOSCA INS Database . Despite some noise in the resulting spectra, related to the small amount of natural rubber in the sample (about 1%wt), one can appreciate how the features from PIP in both mortar samples, with and without carbonaceous fillers, closely resemble those from bulk PIP. A slight shift in the first peak (200 cm-1) is likely related to the fact that the reference spectrum was measured on a previous version of the TOSCA spectrometer (TFXA), with lower resolution at the elastic line (0 cm-1) providing a larger background below 200 cm-1. Because of such background, it is difficult to infer if the clear feature at around 100 cm-1 was absent in bulk PIP. However, over the entire range of intermolecular vibrations, the peak positions in both mortar samples closely match those from Adams et al. . Such similarities in the region of intermolecular vibrations highlight that negligible interactions take place between NR with the rest of cementitious-based hydration phases and other components of the mortar matrix.
Structural and morphological characterization
Figure 3 shows the crystalline phases present in each composite sample at the end of the hydration process. M0 and M1 samples show quartz as main crystalline phase (silica sand, ICCD #01-083-2465) and presented also traces of un-hydrated calcium silicate (C3S, ICCD #01-086-0402) (see the most intense reflection at 2q = 26.63° and 29.40° respectively). Otherwise, CM2 and CM3 composites did not revealed any unreacted phases. In fact, besides the quartz peaks, traces of typical hydrated products such as Hydrate calcium silicate-CSH (ICCD # 00-033-0306, the main peak is tobermorite at 2q = 28.40° and the amorphous band around 30-31° [26, 27, 38]) for CM2 and CM3 and calcium hydroxide, CH (ICCD # ICCD # 00-033-0306, the main peak is at 2q = 36.55°) for CM3 (reflection at 35°) were clearly detected . These diffraction features confirm that the carbonaceous fillers, both MWCNTs and rGO are able to increase the hydration kinetics of the cementitious phases in the mortar, as already verified by Lin et al. , who observed that graphene oxide speed-up the cement hydration enhancing the assembly of the CH crystals produced during the hydration (mainly for the CM3) process .
The morphological structure of mortar samples is shown in Figure 4. The utilization of the D2 and D3 aqueous dispersions significantly affected the morphological structure of mortars (Figure 4c and 4d respectively) as compared with the control sample (M0, Figure 4a) and M1 (produced with D1 dispersion, Figure 4b). For instance, from SEM micrographs in Figure 4a1, 4b1, 4c1, 4d1 and 4a2, 4b2, 4c2 and 4d2, the presence of a diffuse porosity [42, 43] is observed in the structure of the M1 and CM3 (which could be ascribed to the presence of NR latex dispersions) and CM2 samples (which could be ascribed to a poor interaction between the carbonaceous filler with cementitious matrix), conversely M0 composite looks like more compact. Furthermore, M0 and M1 highlighted the typical amorphous structure of cement-based materials whereas the hydrated products (CSH and Hydrated Aluminate-CA) were not clearly highlighted (see the SEM pictures in Figure 4a2 and 4a3) [26, 27, 44]. As also evidenced by WAXD analysis, the addition of carbonaceous fillers (D2 and D3 aqueous dispersions) promoted, speeding-up, the formation of hydrated phases, and the characteristic star-like structure of CSH was observed for CM2 (see the SEM microstructure in Figure 4c2 and 4c3) and CM3 (see the SEM microstructure in Figure 4d2) [26, 27]. In addition, for the composite mortars the presence of MWCNTs was clearly detected (see the inset in the Figure 4c3 and 4d3) . More difficult is to detect the presence of rGO which was dispersed as nanoparticles in the matrix and get confused among the several phases present in the composite mortars. In particular, MWCNTs present in CM3 (Figures 4d2 and 4d3) are more homogenously dispersed, mainly as single carbon nanotubes or small bundles and intertwined with the hydrated phases of the cement and some rGO platelets. On the other side, for the CM2 sample (Figures 4c2 and 4c3) the MWCNTs appear mainly as coarse aggregates, evidencing their difficulties to homogeneously disperse in the hydrophilic environment of composite mortars. The results confirm the beneficial effect of the NR latex dispersion to endow a better distribution of the carbonaceous filler throughout the volume of hydrated cementitious phases, avoiding the formation of detrimental coarse aggregates.
Mechanical and piezoresistive characterization
To investigate piezoresistive behavior of cement-based composites, the time-dependent electrical resistance (R) variations, over 100 mechanical compression cycles for CM2 and CM3 samples was measured. The composites were submitted to a relatively small compressive deformation (strain < 0.6%) in order to study mechanical and piezoresistive properties in the linear elastic region (Figure 5a).
Compressive elastic modulus values (EC) of composite mortars were calculated from compressive strain-curves of Figure 5b. EC values of 294 ± 15 MPa and 209 ± 27 MPa were assessed for CM2 and CM3 systems respectively, after 5 loading/unloading cycles. Furthermore, CM3 composite show lower value of the compressive stress (σC) at strain of ~ 0.6% than CM2 composite. Hence, the introduction of the NR latex in the mortar matrix induces a decrease of EC and σC values, although the filler aqueous dispersions induce a better hydration of cementitious anhydrous phases as confirmed by WAXD and SEM analysis. Finally, it is worth noting that for the composite mortar CM2, the stress-strain curves after 5 and 60 loading/unloading compression cycles slightly differ each other, highlighting a reduction of the mechanical performances above all up to 0.2% strain which increase with the compression cycles. This difference is markedly reduced for the samples CM3, highlighting the capability of natural rubber inclusions to improve the strain deformation of the composite mortar, avoiding the localization of internal microcracks. In fact, the NR, due to the poor bonds with cement matrix, influences the mechanical behaviour of specimens, since it contributes to weakness the interfacial transition zone  between the aggregated and the hydrated phases of cement and promote the formation of voids (as confirmed by SEM images in Figure 4). Turki et al. found a decrease of EC and σC values of mortar-rubber composites as increasing the rubber content, and ascribed it to the weak interactions of the interfacial transition zone between rubber aggregates and the cementitious structures . Moreover, the decrease of the compressive modulus is also associated to the intrinsic elastic properties of the NR. Indeed, Turatsinze et al. demonstrated that the incorporation of rubber particles in cement paste, if on the one hand reduces the compressive modulus and stress of the cement-based composites, on the other hand, it is beneficial in terms of strain and toughness capacity. The rubber material acts as crack arrester and gives rise to cementitious mortars which adsorb more of the compression energy before macrocracking localization and consequent structural collapse. Finally, they also pointed out to the beneficial effect of rubber on the reduction of cracking extent from shrinkage, which significantly contributes to the mechanical properties of composite mortars.  Similar results were also recently obtained by Gampanart Sukmak et al., who published on the positive effect of addition of NR latex to improving the flexural strength and toughness of composite mortar through the formation of a rubber-based film which permeate the structure, whilst retarding the setting time and hydration. .
Piezoresistive results of Figure 6 show that CM2 (Figure 6a) does not have a reproducible electrical trend; in fact, the electrical resistance increases with the number of loading/unloading cycles. This increase may be ascribed to both an electric polarization of fillers in the cement-based composite [49, 50] and to a modification of the MWCNTs and rGO fillers spatial distribution in the mortar matrix. Indeed, during loading/unloading compressive cycles, local cracks and slips may occur, as also confirmed by the mechanical results (see Figure 5b). The microcracks modify the spatial arrangement of carbon fillers in the cement-based binding phase and, some carbonaceous nanoparticles, i.e. MWCNTs and rGO, irreversibly separated or disconnected from each other, due to the increased distance between the cracked surfaces, with a consequent increase of the electrical resistance. [51, 52]
On the contrary, the CM3 (Figure 6b) composite, which has a better strain capability due to the presence of rubber phase, exhibits a regular resistance variation over loading and unloading cycles, without any performance degradation. That suggests that the mortar composite modified with rubber has a relative high reliability in strain-sensing process. As shown in Figure 6b, the electrical resistance decreases with the increasing compressive strain and increases as the compressive strain decreases, changing between the maximum and minimum values at different cycles. This behavior confirms that the carbonaceous filler densifies during compression, realizing more effective contacts which improve the electrical conductivity. When the compression load is released, the carbonaceous fillers recover their initial spatial distribution, and that brings the electrical resistance to its initial value. So the piezoresistive behavior of the composite mortars, both CM2 and CM3 is connected with the re-construction and de-construction of the conductive network, over loading/unloading compressive cycles. Moreover, the variation of the electrical resistance for the CM3 composite, after a single compression cycle at ~ 0.6% strain, is higher than that of the CM2 composite. These results suggest that the presence of the NR in the CM3 sample generates a better spatial arrangement of the carbonaceous filler, contributing to increase the sensitivity and piezoresistive properties of the composite. Similar conclusions have been already found by Wang et al  for MWCNTs/polydimethylsiloxane nanocomposites with a segregated structure of the carbon filler. The sensitivity of piezoresistive material can be evaluated by the gauge factor, GF, defined as the ratio of relative resistance change (ΔR/R0) to applied strain. GF values of 0.34 and of 0.70 have been found for CM2 and CM3 respectively. The higher piezoresistive sensitivity of the CM3 sample is ascribed to a more efficient de-construction and re-construction of the fillers network during compression cycles.
Finally the presence of NR coupled with the carbonaceous fillers plays a double effect in the composite mortars: i) it contributes to reducing both the compressive modulus of the sample CM3 compared to that of the sample CM2 and the occurring of local cracks and slips during repeated compression cycles, thus avoiding irreversible modifications in the spatial arrangement of fillers; ii) it contributes to building-up a more effective conductive fillers spatial segregated arrangement within the mortar matrix, which facilitates the re-construction and de-construction of conductive percolation paths as compared with the randomly filler structure obtained in the CM2 system without NR. The effect of segregated carbon filler structures in enhancing piezoresistive properties of polymer and natural rubber-based composites has already been investigated, [54, 55] while, as far as we know, it has never been highlighted in cement-based composites.
Hence, the presence of the NR latex, inducing better segregated structures of the rGO/MWCNTs fillers increase the sensitivity and electrical conductivity of mortar composites, indicating that the utilization of rubber-based filler composite dispersion as raw material for the preparation of composite mortars is a valuable method in developing effective mortar-based piezoelectric sensors, which can be potentially used for developing smart buildings and infrastructures.