## 3 Results and Discussion
### Structure and Properties of Polymer-Sand Protective Coatings  
The treatment of quartz sand with the above formulations was carried out according to a procedure discussed in [43] to form a protective soil coating. The preparation of polymer-sand coatings involved deposition of the polymer formulations as 1 wt.% aqueous solutions (or dispersions) over the sand layer in Petri dishes. To visualize the stability of a protective coating, Petri dishes with dried polymer-sand samples were placed vertically, and a splitting of sand from the dishes was controlled. Note that, for samples studied, no loss of dried sand was detected (Figure 4a). This result evidences that, in this case, the stable protective coatings or crusts are formed at the sand surface. In all cases, polymer-sand crusts were easily separated from the sand surface as shown in Figure 4b. For comparison, the virgin sand, treated with water and dried, moved to the opposite edge of the dish when the Petri dish was lifted by one edge at an angle of 25 degrees (Figure 4c). Figure 3: Dependence of elastic modulus E\({}_{0}\) and ultimate strain \(\varepsilon_{f}\) of BSMs–PDADMAC films on the weight fraction of PDADMAC in formulation W.  
The strength of polymer-sand crusts (P\({}_{f}\)), quantified by the penetration method, is shown in Table 1 (column 6). The crust composed of sand and virgin BSMs (sample 1, Table 1) is characterized by a low strength P\({}_{f}\) = 0.8 MPa. Note that this crust is rather flexible and could be bent to an angle of about 15\({}^{\circ}\) without cracking. The saturation of the BSMs surface with PDADMAC chains at W\({}_{\rm sat}\) = 0.036 results in the growth in strength of the crust to 1.1 MPa (sample 2, Table 1), with the increment Q = dP\({}_{f}\)/dW = 8 MPa. Further addition of the cationic PDADMAC to BSMs suspension is accompanied by the noticeable growth in the strength up to 18 MPa for the crust with a W = 0.5 formulation (sample 8, Table 1). Note that in the 0.059 \(<\) W \(<\) 0.50 range, polymer-sand crusts demonstrate slight elasticity with the bending angle of 5-7\({}^{\circ}\) (samples 3-8, Table 1). The crust based on pure cationic PDADMAC is characterized by the highest strength of 45 MPa (sample 9, Table 1) and well-pronounced brittle fracture under bending. For a detailed discussion of the influence of composition on the crust strength, let us consider the strength-composition dependence P\({}_{f}\) = \(f\)(W) (Figure 5a). This dependence demonstrates inflection at the initial portion of the curve. The treatment of this plot in semi-logarithmic coordinates: P\({}_{f}\) = \(f\)(lnW) (Figure 5b) showed that this inflection takes place at lnW\({}_{\rm in}\) = 2.05, which corresponds to W\({}_{\rm in}\) = 0.077. An analysis of the results presented in Figure 5 and in Table 1 (column 6) evidences that in the W\({}_{\rm sat}\) (0.036) \(<\) W \(<\) W\({}_{\rm in}\) (0.077) region, the appearance of unbound PDADMAC in the saturated PDADMAC-BSMs complex provided the marked increase of the crust strength with the increment Q = 32 MPa. At W \(>\) W\({}_{\rm in}\), the efficacy of unbound PDADMAC still grows up to a Q value of 48. Figure 4: A Petri dish with sand treated by the W = 0.2 formulation and dried (**a**), the polymer-sand crust took out of the dish (**b**), and a Petri dish with sand treated by water and dried (**c**), reference sample. Figure 5: Dependence of the strength of polymer-sand crust P\({}_{f}\) on the weight fraction of PDADMAC in formulation W (**a**) and ln W (**b**). Before discussing a possible mechanism of the fixing action of the PDADMAC-BSM mixtures, let us recall an important detail that the sand was always treated with the same amount of the mixtures. In other words, an increase in the PDADMAC content in the mixture was accompanied by a decrease of an equal amount of BSM. Taking into account the above results, the mechanism of the influence of BSMs-PDADMAC formulations on the mechanical properties of polymer-sand crusts can be presented as follows.