**3. Materials and methods**

In the course of our experimental studies, we considered the possibility and efficiency of using 12 additives attributable [15, 16] to three groups on the basis of size: (1) the group of nano-sized ones are specially synthesized particles SiO2∙nH2O, sols of aluminum hydroxide particles and iron hydroxide, montmorillonite, NaX type zeolite, chrysotile nanotubes, and fulleroid-type carbon nanotubes; (2) the group of ultrafine silica fume (waste of ferroalloy production), carbon pipes of the type "Astralen—C," and a departure from the combustion of high-energy fuel; and (3) the group of microdisperse natural montmorillonite, tripoli, and shungite.

These additives were monitored by the effect of their type, dosage, and methods of introduction into the cement-water suspension on the structure formation processes [16–20]. In experiments with changes in W/C, the introduction in some cases of superplasticizers (C-3 based on naphthalene lignosulfonate; GLENIUM® ACE 30 и Sika® ViscoCrete® 20HE based on polycarboxylate esters; Sikament FF based on melamine sulfonate) fixed the degree of hydration in time and the kinetics of cement strength. The study of the hydration kinetics and strength of the modified cement stone was carried out based on the comparison of the reference cement system without additives.

When varying the dosage of nano-additives from 1 to 0.0001% of the mass of cement, it was shown that its optimal value corresponds to hundredths of a percent [16, 18]. Based on the monitoring, a different measure of the effect of the studied additives was revealed, and it was found that the most effective of them can be considered as a complex additive of SiO2 nanoparticles in combination with Sika®ViscoCrete®20HE (additive CND) as well as individual addition of chrysotile or carbon nanotubes.

Below are experimental data on the use of this complex (additive CND) and the addition of carbon nanotubes of the fulleroid type of the brand "Nanocyl-7000," treated with ultrasound (additive CNT in the accepted designation) for the nanomodifying structure of the cement stone.

Portland cement CEM I 42.5 and these nano-additives with a dosage of 0.01% were used in the experiments for the production of cement paste with a W/C = 0.33. Studies of the parameters of the kinetics of the cement hydration process were carried out under thermostatic conditions at temperatures of 0, 20, 40, and 60°С (with, respectively, 273, 293, 313, 333 K), with the duration of the process implementation for 1, 3, 7, 12 hours and 1, 3, 7, 14, 28 days. The phase composition of the reference and nano-modified cement paste was monitored by an X-ray method (CuKα radiation, λ = 1.541788 Å, ARL X'TRA diffractometer). The processing of diffractometric data was carried out automatically using the PDWin 4.0 computer program. The hydration degree Dh (C3S) was calculated [21–23] by the formula:

$$D\_h\{C\_9S\} = \left(\mathbf{1} - \frac{I\_m}{I\_0}\right) \cdot \mathbf{100}\,\%,\tag{1}$$

where **Im** is the diffraction intensity *of* 3СаО⋅SiO2 (C3S) (*d = 2.75 Å*) *phase for* hardening cement paste samples and **I0** is the diffraction intensity *of* 3СаО⋅SiO2 (C3S) (*d = 2.75* Å) for cement.

The hydration kinetics was formally described by the kinetic equation [24, 25]:

$$D\_h(\mathcal{C}\_\mathcal{S}\mathcal{S}) = (k \cdot \pi)^n,\tag{2}$$

where *Dh*(*C3S*) is the *cement hydration degree* (g/g) to the point in time τ (hour), *k* is the *hydration rate constant*, and *n* is the *exponent of the kinetic equation*.

Taking into account Eq. (2), for all the above conditions, isotherms of the hydration degree were obtained and, on their basis, *n*ср was calculated considering this quantity based on the logarithmic equation

$$
\ln \left( D\_h \right) = \overline{n} \cdot \ln \left( \overline{k} \right) + \overline{n} \cdot \ln \left( \tau \right) \tag{3}
$$

We also determined *ln*(*k*¯) for each of the temperatures and then considered the Arrhenius dependence *lnk*¯ *= ƒ*(*1/T*), by which the calculation found the effective activation energy (EEA) as an indicator characterizing the energetics of hydration process development in terms of the use of structure formation nano-modifiers. To draw a conclusion about the limiting kinetic or diffusion components of the cement hydration process, the temperature coefficients of its speed were determined. In this case, the calculation was carried out according to the van't Hoff rule using the kinetic dependences of the cement hydration degree on temperature obtained for different compositions.

#### *Strength of Materials*

The compressive strength of the hardened cement paste was determined after 1, 3, 7, 14, and 28 days in water-curing conditions; tests of samples with a size of "5 × 5 × 5 cm" were conducted on an INSTRON Sates 1500HDS test system; to ensure the statistical reliability of the results of physical and mechanical tests, the number of samples in the series ranged from 9 to 12. It was determined that the intra-serial coefficient of variability of the results of the strength assessment did not exceed 7–10%.
