# On the Stability of Graphene-Based Aqueous Dispersions and Their Performance in Cement Mortar
## 3 Results and Discussion
### Porosimetry  
In order to explain the findings obtained by CWA, both MIP and \(N_{2}\) adsorption/desorption isotherm analyses were carried out [59]. Cementitious materials are heterogeneous systems mainly characterized by mesopores and macropores. Based on the nature of pore formation, gel pores (\(\rho\leq 10\) nm) and capillary pores (\(10\) nm \(\leq\rho\leq 10\) um) can be distinguished [60]; in relation to the hazardousness of pores based on their size, [PERSON] et al. [60] defined four ranges of pore sizes as: harmless (\(\rho<20\) nm); less harmful (\(20\) nm \(\leq\rho\leq 50\) nm); harmful (\(50\) nm \(\leq\rho\leq 200\) nm); and multi-hazardous (\(\rho>200\) nm). MIP is known to give information on pore sizes ranging from tens of micrometers down to a few nanometers (small mesopores), but it fails to access micropores (\(\rho<2\) nm). Furthermore, previous studies have shown that this investigation technique can be potentially  
Figure 6: Calculated sorptivity values for: (**a**) GO and C; (**b**) Gr-TG, Gr-SG and C mortars. (**c**) Comparison between CWA measurements of 1 TG and C mortars. harmful to cementitious materials due to the high pressures applied, the need for a preliminary drying step, and the ink-bottle effect, which might alter its outcome [61; 62; 63]. On the other hand, \(N_{2}\) porosimetry provides more detailed surface information when focusing on micropores (\(\rho<2\) nm) and small mesopores (2 nm \(\leq\rho\leq 50\) nm) [63; 64]. Both techniques have access only to open pores. Considering the observations made above, results obtained from both methods were combined to study the PSD over the wide range [0-12,000] nm. The isotherms of \(N_{2}\) adsorption and desorption of the investigated mortars are reported in Figure 7a-c. They can be classified as type IIb, as there is no indication of a plateau at high \(P/P_{0}\), with a H3 hysteresis loop. The narrow loop and the forced closure of the hysteresis loop near \(P/P_{0}=0.45\) that characterize all the mortars suggest that some constrictions are present in these samples at the nanometric scale due to the presence of pore network effects, with interconnected larger pores emptying through pores with smaller diameters. The isotherms are the result of interparticle capillary condensation and indicate the presence, in the microstructure of the mortars, of aggregates of particles giving rise to slit-shaped pores that provide them with meso and macro-porosity. In order to further confirm the evidence, data from \(N_{2}\) adsorption/desorption isotherms were analyzed using the Barrett-Joyner-Halenda (BJH) theory. Specifically, the pore size distribution (PSD) was determined using the adsorption branch and the pore entrance size distribution (PESD) using the desorption branch of the curve, based on the Harkins and Jura equation with Faas Correction [65]. The PSD and PESD for each mortar are shown in Figure 7d-f. The curves of PESD were corrected, taking into account the tensile strength effect produced by the forced closure of the hysteresis loop around \(P/P_{0}=0.45\)[66]. All tested samples showed unimodal PSD and PESD distribution with peaks volume centred around 17.8 and 13.5 nm, respectively, indicating in all cases that pore entrance sizes were smaller than pore sizes in the investigated range. Cumulative pore volume (CPV) was thus obtained as a function of the pore entrance width by considering data obtained from \(N_{2}\) adsorption isotherms for porosities below 50 nm and those obtained by MIP analysis for porosities above 50 nm up to 12,000 nm (see Figure A1 in Appendix A) [64]. Figure 7: \(N_{2}\) adsorption/desorption isotherms for: (**a**) C, (**b**) 1 TG and (**c**) IGO samples. PSD and PESD obtained for: (**d**) C, (**e**) 1 TG and (**f**) IGO samples. The result of the combination is reported in Figure 8a, while the obtained pore volumes (PV) contribution per unit of mass in each pore size range is reported in Figure 8b.