**3. Development of sol silicate paint**

Sol silicate paint were used a filler microcalcite MK-2 (TU 09 5743-001- 91892010-2011) and talc MT-GShM (GOST 19284-79) and a pigment titanium dioxide 230 rutile form (TU 2321-001-1754-7702-2014), ocher (GOST 8019-71), iron red oxide (GOST 8135-74), ultramarine UM-1 (OST 6-10 - 404 - 77), and chromium oxide OHP-1 (GOST 2912-79). To determine the content of the pigment (filler), the viscosity was measured using a viscometer VZ-4. To obtain different shades, titanium dioxide is mixed with an appropriate pigment [14].

**Figure 7** shows the dependence of viscosity of paint on the content of pigment and filler. As can be seen from the obtained data, when filling in the range of about 0 < φ < 0.12, the viscosity increase is insignificant, and the polymer matrix only partially passes into the film state. With a low concentration of pigment (filler), the boundary layers of distant particles do not constitute an independent phase in the bulk of the material that can influence its properties. With further filling (φ > 0.12), there is a significant change in the ratio of bulk and film phases of the matrix, and a sharp increase in the viscosity of the composition is observed.

In **Figure 8** the dependence of viscosity on the volume fraction of pigment in the coordinates lg - C (where C is the concentration of pigment and filler in the system) is shown. This dependence consists of two intersecting straight lines.

#### **Figure 7.**

*The dependence of the viscosity of the sol of silicate paint on the content of pigment and filler: (1) sol silicate paint; (2) sol silicate paint with glycerin.*

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

**Figure 8.**

*Rp* <sup>¼</sup> *Ah<sup>b</sup>* (8)

*Rp* <sup>¼</sup> <sup>5</sup>*:*030*h*�0*:*<sup>37</sup> (9)

*Rp* <sup>¼</sup> <sup>0</sup>*:*886*h*�1*:*<sup>3</sup> (10)

Mathematical data processing (curves 1 and 2, **Figure 6**) showed that they are

The correctness of the equations was checked by Fisher's criterion.

Sol silicate paint were used a filler microcalcite MK-2 (TU 09 5743-001- 91892010-2011) and talc MT-GShM (GOST 19284-79) and a pigment titanium dioxide 230 rutile form (TU 2321-001-1754-7702-2014), ocher (GOST 8019-71), iron red oxide (GOST 8135-74), ultramarine UM-1 (OST 6-10 - 404 - 77), and chromium oxide OHP-1 (GOST 2912-79). To determine the content of the pigment (filler), the viscosity was measured using a viscometer VZ-4. To obtain different

**Figure 7** shows the dependence of viscosity of paint on the content of pigment and filler. As can be seen from the obtained data, when filling in the range of about 0 < φ < 0.12, the viscosity increase is insignificant, and the polymer matrix only partially passes into the film state. With a low concentration of pigment (filler), the boundary layers of distant particles do not constitute an independent phase in the bulk of the material that can influence its properties. With further filling (φ > 0.12), there is a significant change in the ratio of bulk and film phases of the matrix, and a

In **Figure 8** the dependence of viscosity on the volume fraction of pigment in the coordinates lg - C (where C is the concentration of pigment and filler in the system) is shown. This dependence consists of two intersecting straight lines.

*The dependence of the viscosity of the sol of silicate paint on the content of pigment and filler: (1) sol silicate*

shades, titanium dioxide is mixed with an appropriate pigment [14].

sharp increase in the viscosity of the composition is observed.

where *h* is the film thickness.

*Engineering Steels and High Entropy-Alloys*

For films based on polymer silicate paint

**3. Development of sol silicate paint**

**Figure 7.**

**260**

*paint; (2) sol silicate paint with glycerin.*

well described by the expression: For silicate-based films

*The dependence of viscosity on the volume fraction of pigment in the coordinates* lgη*-* C*: (1) red iron oxide; (2) ocher; (3) ultramarine; (4) chromium oxide.*

The point of intersection projected on the x-axis will be the critical volume concentration of the pigment (CVCP) [4, 15].

As the results in **Figure 7** show, the viscosity of the paint increases during filling, while its change at low degrees of filling can be described by the Einstein equation:

$$
\rho = \rho\_O(\mathbf{1} + \mathbf{2.5}\rho) \tag{11}
$$

where η<sup>0</sup> is the viscosity of the unfilled system and φ is the volume fraction of the pigment (filler).

With increasing concentration of the dispersed phase (more than 0.08), the interaction between particles increases, and deviations from the Einstein equation have been detected. These deviations are apparently due to the interaction of the particles and the formation of a structure in which the particles of the dispersed phase are oriented relative to each other in a certain way (structuring systems). The results of the calculations show that the model changes the viscosity of the paint from the volume concentration of the pigment (filler) which can be described by a polynomial

$$
\eta = \eta\_o \left( a + b\rho + c\rho^2 + d\rho^3 \right) \tag{12}
$$

where η<sup>0</sup> is the viscosity of the unfilled system and φ is the volume fraction of the pigment (filler).

The following equations were obtained:

$$\eta = \eta\_o \left( 0.334 + 119\rho - 2110.47\rho^2 + 12217.83\rho^3 \right) \text{-for sol slice point} \tag{13}$$

Testing the adequacy of the model showed that Eq. (2) is valid in the filling region up to φ = 0.16.

In view of the foregoing, the cohesive properties and the ability of the polysilicate binder to wet the surface of the pigment (filler) were also investigated. In the work, polysilicate solutions were obtained by the interaction of stabilized solutions of colloidal silica (sols) with aqueous solutions of alkaline silicates (liquid glasses). A sodium liquid glass with a modulus M = 2.78 was used, and a potassium liquid glass with a modulus M = 3.29.

We was calculated the work of adhesion of liquid glass and polysilicate solution to the pigment (filler). The contact angle of wetting was determined on the KRUSS DSA-30 [13].

To determine the wetting contact angle, tablets are mixed from the mixture of pigment and filler with the automatic hydraulic press Vaneox-40 t, with a pressure of 18 tons for 11 seconds. The powder compressed in a dry state, without further processing. The surface tension of the solutions is determined by the stalagmometric method. The stalagmometric method based on measuring the number of droplets formed when a liquid flows out of a vertical tube of a small radius.

Analysis of the data (**Table 1**) shows that for the potassium polysilicate solution, a large work of adhesion to the filler (pigment) is characteristic. Thus, the work of adhesion of the potassium polysilicate solution to the filler (pigment) is 103.85 mN/ m, while the work of adhesion of potassium liquid glass is 87.74 mN/m. Similar regularities are observed when using sodium liquid glass and sodium polysilicate solution. A potassium polysilicate solution is also characterized by a large wetting work of 39.786 mN/m.

In determining the wetting contact angle, it was found that sodium glass droplets on the surface of the sample formed an angle much larger than that of the potassium and for 5 minutes remained unchanged on the surface, while the drops from the potassium for half a second remained in shape and then blurred. Drops based on the sodium polysilicate solution were quickly absorbed into the material, forming a pyramidal shape. Drops based on the potassium polysilicate solution are more stable and retained on the sample for up to 2 minutes.

paint after 35 cycles is estimated as AD1 and AZ1, which corresponds to the state of coating with no discoloration, chalking, and dirt retention. Silicate-based coatings are more susceptible to degradation. The condition of coating based on silicate paint is estimated as AD3 and AZ3. The test results showed that the "failure" of coating based on silicate paint occurred after 40 freeze-thaw cycles, while the state of the coating based on polysilicate solution was evaluated as AD2 and AZ2. The "failure" of the coating based on the polysilicate solution occurred after 50 test cycles. Adhesion strength after 50 test cycles in accordance with GOST 31149 "Paint and varnish materials. Determination of adhesion by the lattice cut method" for silicate

*Change in the relative deformations when tensile samples based on: (1) sol silicate paint; (2) silicate paint.*

coatings and for coatings based on polysilicate solution was by 1 point.

the interfacial interaction at the solid-solution interface.

equation

**Figure 9.**

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

with air.

**263**

sol silicate paints [17].

Hamaker constant A\*.

The surface energy of the coatings was calculated using the critical surface tension of the liquid at the boundary with a solid (method of Zisman). The dispersion contribution to the intermolecular interaction between the particles of the coatings was estimated, for which the value of the complex Hamaker constant A\* was additionally determined, which takes into account the complex action of the two components—the interparticle interaction between homogeneous particles and

The measurement data of the contact angle showed that for all samples studied,

a linear dependence cosθ =f(σlig) is observed (**Figure 9**). By extrapolating the dependence cosθ = f(σlig) by cosθ = 1, we obtained value of the critical surface tension of a solid surface (coating). The energy of interaction between particles of the coating was estimated by value of the Hamaker constant calculated by the

cos *<sup>θ</sup>* � <sup>1</sup> <sup>¼</sup> *<sup>А</sup>*<sup>∗</sup>

where hmin is the smallest membrane thickness, which corresponds to the van der Waals distance (0.24 nm); σж is the surface tension of the liquid; and A\* is the complex constant of Hamaker in interaction of a liquid with a solid at the boundary

To calculate the complex Hamaker constant, functional dependences cosθ-1 = f (1/σlig) were built. **Figures 10**–**12** present results for coatings based on silicate and

**Table 2** presents the calculated values of the surface tension of coatings and the

12*h*min*σ<sup>ж</sup>*

(14)

The availability of more complete wetting of the surface of the filler and the pigment in the case of the use of a potassium polysilicate solution promotes the formation of a denser coating structure and an increase in the physicomechanical properties. This is evidenced by data on the change in the tensile strength of films based on colorful compositions.

It was found that the cohesive strength of membranes based on sol silicate paint is 2.65 MPa and based on silicate paint 1.8 MPa (**Figure 9**). An increase in the relative deformations is observed, which is 0.06 mm/mm for membranes based on sol silicate paint and 0.033 mm/mm based on silicate paint.

In continuation of further research, frost resistance tests were carried out by alternate freezing and thawing painted mortar samples. The samples were painted with silicate and sol with silicate paint with intermediate drying for 20 minutes. After the coatings were cured, frost resistance tests were carried out. Evaluation of the appearance of the coatings was carried out according to GOST 6992-68 "Paint coatings. Test method for resistance to atmospheric conditions". The status of coating, assessed as AD3 and AZ4, was taken as a "failure" [7]. The energy of interaction between particles of the coating was estimated by value of the Hamaker constant [16]. It was established that the condition of the coating based on silicate


#### **Table 1.**

*The work of adhesion of a polysilicate binder to a filler.*

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

To determine the wetting contact angle, tablets are mixed from the mixture of pigment and filler with the automatic hydraulic press Vaneox-40 t, with a pressure of 18 tons for 11 seconds. The powder compressed in a dry state, without further

stalagmometric method. The stalagmometric method based on measuring the number of droplets formed when a liquid flows out of a vertical tube of a small radius. Analysis of the data (**Table 1**) shows that for the potassium polysilicate solution, a large work of adhesion to the filler (pigment) is characteristic. Thus, the work of adhesion of the potassium polysilicate solution to the filler (pigment) is 103.85 mN/ m, while the work of adhesion of potassium liquid glass is 87.74 mN/m. Similar regularities are observed when using sodium liquid glass and sodium polysilicate solution. A potassium polysilicate solution is also characterized by a large wetting

In determining the wetting contact angle, it was found that sodium glass droplets on the surface of the sample formed an angle much larger than that of the potassium and for 5 minutes remained unchanged on the surface, while the drops from the potassium for half a second remained in shape and then blurred. Drops based on the sodium polysilicate solution were quickly absorbed into the material, forming a pyramidal shape. Drops based on the potassium polysilicate solution are

The availability of more complete wetting of the surface of the filler and the pigment in the case of the use of a potassium polysilicate solution promotes the formation of a denser coating structure and an increase in the physicomechanical properties. This is evidenced by data on the change in the tensile strength of films

It was found that the cohesive strength of membranes based on sol silicate paint

In continuation of further research, frost resistance tests were carried out by alternate freezing and thawing painted mortar samples. The samples were painted with silicate and sol with silicate paint with intermediate drying for 20 minutes. After the coatings were cured, frost resistance tests were carried out. Evaluation of the appearance of the coatings was carried out according to GOST 6992-68 "Paint coatings. Test method for resistance to atmospheric conditions". The status of coating, assessed as AD3 and AZ4, was taken as a "failure" [7]. The energy of interaction between particles of the coating was estimated by value of the Hamaker constant [16]. It was established that the condition of the coating based on silicate

> **°Angle of wetting, °**

**Adhesion work, mJ/m<sup>2</sup>**

64.064 51.6 103.85 39.786

55.22 62.5 80.73 25.51

**Wetting operation, mN/m**

is 2.65 MPa and based on silicate paint 1.8 MPa (**Figure 9**). An increase in the relative deformations is observed, which is 0.06 mm/mm for membranes based on

processing. The surface tension of the solutions is determined by the

more stable and retained on the sample for up to 2 minutes.

sol silicate paint and 0.033 mm/mm based on silicate paint.

**tension, mN/m**

Water 72.8 46.2 123.18 50.38

Potassium liquid glass 55.22 53.9 87.74 32.52

Sodium liquid glass 51.66 74.7 65.3 13.64

work of 39.786 mN/m.

*Engineering Steels and High Entropy-Alloys*

based on colorful compositions.

**Name of film-forming Surface**

*The work of adhesion of a polysilicate binder to a filler.*

Potassium polysilicate solution

Sodium polysilicate solution (15% Nanosil 20)

(15% Nanosil 20)

Binder

**Table 1.**

**262**

**Figure 9.** *Change in the relative deformations when tensile samples based on: (1) sol silicate paint; (2) silicate paint.*

paint after 35 cycles is estimated as AD1 and AZ1, which corresponds to the state of coating with no discoloration, chalking, and dirt retention. Silicate-based coatings are more susceptible to degradation. The condition of coating based on silicate paint is estimated as AD3 and AZ3. The test results showed that the "failure" of coating based on silicate paint occurred after 40 freeze-thaw cycles, while the state of the coating based on polysilicate solution was evaluated as AD2 and AZ2. The "failure" of the coating based on the polysilicate solution occurred after 50 test cycles. Adhesion strength after 50 test cycles in accordance with GOST 31149 "Paint and varnish materials. Determination of adhesion by the lattice cut method" for silicate coatings and for coatings based on polysilicate solution was by 1 point.

The surface energy of the coatings was calculated using the critical surface tension of the liquid at the boundary with a solid (method of Zisman). The dispersion contribution to the intermolecular interaction between the particles of the coatings was estimated, for which the value of the complex Hamaker constant A\* was additionally determined, which takes into account the complex action of the two components—the interparticle interaction between homogeneous particles and the interfacial interaction at the solid-solution interface.

The measurement data of the contact angle showed that for all samples studied, a linear dependence cosθ =f(σlig) is observed (**Figure 9**). By extrapolating the dependence cosθ = f(σlig) by cosθ = 1, we obtained value of the critical surface tension of a solid surface (coating). The energy of interaction between particles of the coating was estimated by value of the Hamaker constant calculated by the equation

$$\cos \theta - \mathbf{1} = \frac{A^\*}{12h\_{\text{min}} \sigma\_{\text{xc}}} \tag{14}$$

where hmin is the smallest membrane thickness, which corresponds to the van der Waals distance (0.24 nm); σж is the surface tension of the liquid; and A\* is the complex constant of Hamaker in interaction of a liquid with a solid at the boundary with air.

To calculate the complex Hamaker constant, functional dependences cosθ-1 = f (1/σlig) were built. **Figures 10**–**12** present results for coatings based on silicate and sol silicate paints [17].

**Table 2** presents the calculated values of the surface tension of coatings and the Hamaker constant A\*.

*The dependence cosθ =f(σlig): (1) on coating based on silicate paint; (2) on coating based on sol silicate.*

#### **Figure 11.**

*Functional type dependency cosθ-1 = f (1/σlig) before testing coatings based on: (1) silicate paint; (2) sol of silicate paint.*

Analysis of experimental data shown in **Figures 10**–**12** indicates that the critical surface tension of the coatings is almost the same, which is apparently explained by the almost identical nature components of coating. The value of the Hamaker constant for coatings based on polysilicate solution, amounting to 4.09 <sup>10</sup><sup>20</sup> J, is higher than the coatings based on silicate paints. This is confirmed by data on the higher strength of coatings based on polysilicate solutions. A higher value of the Hamaker constant for coatings based on polysilicate solution after frost resistance testing, equal to 1524 <sup>10</sup><sup>20</sup> J, indicates a greater preservation of interparticle

] No more 2

Frost resistance, brand F35

**Type of paint coating Value critical surface tension**

*\**

*the test.*

**Table 2.**

*Surface tension values of silicate coatings.*

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

Based on potassium liquid glass 28.4 2.85

Based on potassium polysilicate solution 28.7 4.09

**Name indicators Values** Portability Good Class of quality of appearance of coatings IV Viscosity to ВЗ-4 [s] 17–20 Shrinkage, the presence of cracks No Viability [day] More 90 Drying time [minute], to degree 5 15–25 Adhesion [points] 1 Adhesion [MPa] 1.1–1.3 Coefficient of vapor permeability [mg/m hPa] 0.00878 Relative hardness 0.47 Impact strength [kgcm] 50

*Above the line is the value of the Hamaker constant for coatings prior to frost resistance test, below the line—after*

**of the coating [mN/m]**

**Constant value**

1048

1524

**10<sup>20</sup> [Дж\* ]**

**Hamaker A\***

Absence of white matte spots, flaking, rashes, bubbles

**Table 3** shows the values of the properties of coatings based on sol silicate paint.

The temperature-time dependence of the strength of paint and varnish materials

interaction in the coating.

Washability [g/m<sup>2</sup>

water)

**Table 3.**

**265**

Water resistance (appearance after 24 hours in

*Properties of the paint composition and coatings based on it.*

**4. Long-lasting durability of paint coatings**

can be described by the Zhurkov Equation [18, 19]:

#### **Figure 12.**

*Functional dependence of the form cosθ-1 = f (1/σlig) after 50 test cycles of coatings based on: (1) silicate paint; (2) sol of silicate paint.*

### *Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*


*\* Above the line is the value of the Hamaker constant for coatings prior to frost resistance test, below the line—after the test.*

#### **Table 2.**

**Figure 10.**

*Engineering Steels and High Entropy-Alloys*

**Figure 11.**

*silicate paint.*

**Figure 12.**

**264**

*(2) sol of silicate paint.*

*The dependence cosθ =f(σlig): (1) on coating based on silicate paint; (2) on coating based on sol silicate.*

*Functional type dependency cosθ-1 = f (1/σlig) before testing coatings based on: (1) silicate paint; (2) sol of*

*Functional dependence of the form cosθ-1 = f (1/σlig) after 50 test cycles of coatings based on: (1) silicate paint;*

*Surface tension values of silicate coatings.*


#### **Table 3.**

*Properties of the paint composition and coatings based on it.*

Analysis of experimental data shown in **Figures 10**–**12** indicates that the critical surface tension of the coatings is almost the same, which is apparently explained by the almost identical nature components of coating. The value of the Hamaker constant for coatings based on polysilicate solution, amounting to 4.09 <sup>10</sup><sup>20</sup> J, is higher than the coatings based on silicate paints. This is confirmed by data on the higher strength of coatings based on polysilicate solutions. A higher value of the Hamaker constant for coatings based on polysilicate solution after frost resistance testing, equal to 1524 <sup>10</sup><sup>20</sup> J, indicates a greater preservation of interparticle interaction in the coating.

**Table 3** shows the values of the properties of coatings based on sol silicate paint.

### **4. Long-lasting durability of paint coatings**

The temperature-time dependence of the strength of paint and varnish materials can be described by the Zhurkov Equation [18, 19]:

$$\mu = \iota\_o \exp\left[ (U\_o - \chi \sigma) / RT \right] \tag{15}$$

where γ is the structural-sensitive factor characterizing overstrain of bonds in the structure of the material; *Uo* is the activation energy of the process of destruction; *R* is the universal gas constant; and *T* is the absolute temperature.

The values of the activation energy of the fracture process and the structuresensitive factor for polyvinyl acetate cement PVAC, organosilicon KO-168, and silicate coatings were calculated.

**Figures 13**–**17** in semilogarithmic coordinates show the experimental dependence of the long-term cohesive strength of coatings from the value of tensions and temperatures for the coatings under study. The values of the structure-sensitive factor and the activation energy of the process of destruction of coatings are given in **Table 4.**

**Figure 13.**

*The temperature dependence of* lg*τ (σ): (1) coating of PVAC, σ = 0.166 MPa; (2) coating of PVAC, σ = 0.124 MPa; (3) coating of KO-168, σ = 0.144 MPa; (4) coating of KO-168, σ = 0.17 MPa.*

Analysis of the data in **Table 4** shows that the activation energy of cohesive destruction of coatings decreases with increasing stresses acting on the coatings. A higher value of the activation energy and a lower value of the structurally sensitive

*Dependence of the long-term strength of coatings from tensions: (1) coating of PVAC; (2) coating of KO-168.*

*The temperature dependence of coating based on sol silicate paint lgτ (σ): (1) stress σ = 0.14 MPa; (2) stress*

*σ = 0.28 MPa; (3) stress σ = 0.42 MPa; (4) stress σ = 0.56 MPa.*

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

The duration of maintaining the cohesive strength of coatings during operation is also determined by the resistance to periodic exposure to environmental factors: wetting, drying, freezing, thawing, etc. It was determined the change in cohesive strength as a function of wetting time. To this end, stretched film samples were sprinkled.

The duration of preservation of cohesive strength of coatings during operation is

also determined by the resistance to periodic effects of environmental factors: wetting-drying, freezing-thawing, etc. In this connection, the influence of humidification on the change in the duration of cohesive strength was assessed. To this

factor indicate high strength of polyvinyl acetate cements compared with

organosilicon coatings.

**Figure 15.**

**Figure 16.**

**267**

#### **Figure 14.**

*The temperature dependence of coating based on silicate paint lgτ(σ): (1) stress σ = 0.14 MPa; (2) stress σ = 0.28 MPa; (3) stress σ = 0.42 MPa; (4) stress σ = 0.56 MPa.*

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

#### **Figure 15.**

*ι* ¼ *ι<sup>o</sup>* exp ½ð Þ *Uo* � *γσ =RT* (15)

where γ is the structural-sensitive factor characterizing overstrain of bonds in the structure of the material; *Uo* is the activation energy of the process of destruc-

The values of the activation energy of the fracture process and the structuresensitive factor for polyvinyl acetate cement PVAC, organosilicon KO-168, and

**Figures 13**–**17** in semilogarithmic coordinates show the experimental dependence of the long-term cohesive strength of coatings from the value of tensions and temperatures for the coatings under study. The values of the structure-sensitive factor and the activation energy of the process of destruction of coatings are given

*The temperature dependence of* lg*τ (σ): (1) coating of PVAC, σ = 0.166 MPa; (2) coating of PVAC, σ = 0.124 MPa; (3) coating of KO-168, σ = 0.144 MPa; (4) coating of KO-168, σ = 0.17 MPa.*

*The temperature dependence of coating based on silicate paint lgτ(σ): (1) stress σ = 0.14 MPa; (2) stress*

*σ = 0.28 MPa; (3) stress σ = 0.42 MPa; (4) stress σ = 0.56 MPa.*

tion; *R* is the universal gas constant; and *T* is the absolute temperature.

silicate coatings were calculated.

*Engineering Steels and High Entropy-Alloys*

in **Table 4.**

**Figure 13.**

**Figure 14.**

**266**

*The temperature dependence of coating based on sol silicate paint lgτ (σ): (1) stress σ = 0.14 MPa; (2) stress σ = 0.28 MPa; (3) stress σ = 0.42 MPa; (4) stress σ = 0.56 MPa.*

Analysis of the data in **Table 4** shows that the activation energy of cohesive destruction of coatings decreases with increasing stresses acting on the coatings. A higher value of the activation energy and a lower value of the structurally sensitive factor indicate high strength of polyvinyl acetate cements compared with organosilicon coatings.

The duration of maintaining the cohesive strength of coatings during operation is also determined by the resistance to periodic exposure to environmental factors: wetting, drying, freezing, thawing, etc. It was determined the change in cohesive strength as a function of wetting time. To this end, stretched film samples were sprinkled.

The duration of preservation of cohesive strength of coatings during operation is also determined by the resistance to periodic effects of environmental factors: wetting-drying, freezing-thawing, etc. In this connection, the influence of humidification on the change in the duration of cohesive strength was assessed. To this

#### **Figure 17.**

*Values of the activation energy of the process of destruction of coatings depending on tensions: (1) coating based on silicate paint; (2) coatings based on sol silicate paint.*


#### **Table 4.**

*The values of U and γ of coatings.*

end, stretched coating samples were subjected to sprinkling. The results of the tests are shown in **Figure 18**.

Consider the condition of brittle cracking of polymer coatings under investigation under the action of internal tensions. In the case of brittle failure, the cracking condition has the form

$$
\sigma \ge 0.\text{SR} \tag{16}
$$

Consider the change in internal stresses and the strength of coatings in the aging

**Cohesive at strength of coatings, MPa**

> 0.38 0.13 0.09

0.21 0.47 0.9

observed after 18 days of humidification on level σ = 0.062 MPa. The value of short-

Consider the kinetics of changes in the short-term strength of coatings during aging from the perspective of the kinetic concept of the strength of solids. It is known that the number of structural bonds N determines the strength of a material

During operation, there is a change in the number of structural bonds.

where *u0* is the unit bond breaking energy and *γ* is the structurally sensitive

The state of the material structure at a time *t1* is characterized by the value of the

The increase in the number of severed bonds at time due to the increase *dU* will

During long-term operation, short-term strength is reduced in proportion to the

where τ is the durability of the coating and t is the operating time.

The polyvinyl acetate cement coating after 2 months of moistening did not have

*R* ¼ *f N*ð Þ (17)

*σ=R* **Time of occurrence cracks, day**

> Not observed 27 30

*n*1*uo* ¼ *γσ* (18)

*Ut* ¼ *Uo* � *γσ* ¼ *Uo* � *n*1*uo* (19)

*dn*1*=No* ¼ *αdU* (20)

*n*<sup>1</sup> ¼ *No* exp ð Þ �*αN*<sup>1</sup> (21)

*n*<sup>1</sup> ¼ *No* exp ½ � �*α*ð Þ *Uo* � *γσ* (22)

*Rt=Ro* ¼ ½ � ð Þ *No* � *n*<sup>1</sup> *=No* : ½ � ð Þ *τ* � *t =τ* (23)

term strength after 60 days of moistening is given in **Table 5.**

**Internal stresses, MPa**

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

> 0.08 0.062 0.075

*Physicomechanical properties of coatings after moistening.*

cracks; the ratio *σ=R* for such coatings does not exceed 0.21.

coefficient, characterizing the overvoltage of bonds.

Integration of Eq. (20) leads to the form

activation energy of bond breaking:

In view of Eq. (18),

number of broken bonds *n1*:

be equal to

**269**

**Name of coatings**

PVAC Polymer-lime Lime

**Table 5.**

process on the example of humidification. It was found that at the first instant, humidification, a sharp increase in internal stresses, and then their slow decrease, i.e., an effect of the time factor, are observed. For example, for PVAC coatings, stabilization of internal stresses on level σ = 0.08 MPa is observed after 20 days of moistening, and stabilization of internal stresses in polymer-lime coatings is

#### **Figure 18.**

*Dependence of the long-term strength of coatings in the process of humidification: (1) coating of PVAC; (2) coating of PVAC with surface hydrophobization; (3) coating of KO-168.*


**Table 5.**

*Physicomechanical properties of coatings after moistening.*

Consider the change in internal stresses and the strength of coatings in the aging process on the example of humidification. It was found that at the first instant, humidification, a sharp increase in internal stresses, and then their slow decrease, i.e., an effect of the time factor, are observed. For example, for PVAC coatings, stabilization of internal stresses on level σ = 0.08 MPa is observed after 20 days of moistening, and stabilization of internal stresses in polymer-lime coatings is observed after 18 days of humidification on level σ = 0.062 MPa. The value of shortterm strength after 60 days of moistening is given in **Table 5.**

The polyvinyl acetate cement coating after 2 months of moistening did not have cracks; the ratio *σ=R* for such coatings does not exceed 0.21.

Consider the kinetics of changes in the short-term strength of coatings during aging from the perspective of the kinetic concept of the strength of solids. It is known that the number of structural bonds N determines the strength of a material

$$R = f(\mathbf{N})\tag{17}$$

During operation, there is a change in the number of structural bonds.

$$n\_1 u\_\vartheta = \chi \sigma \tag{18}$$

where *u0* is the unit bond breaking energy and *γ* is the structurally sensitive coefficient, characterizing the overvoltage of bonds.

The state of the material structure at a time *t1* is characterized by the value of the activation energy of bond breaking:

$$U\_t = U\_o - \chi \sigma = U\_o - n\_1 u\_o \tag{19}$$

The increase in the number of severed bonds at time due to the increase *dU* will be equal to

$$d n\_1 / N\_o = a d U \tag{20}$$

Integration of Eq. (20) leads to the form

$$n\_1 = N\_o \exp\left(-aN\_1\right) \tag{21}$$

In view of Eq. (18),

$$n\_1 = N\_o \exp\left[-a(U\_o - \gamma \sigma)\right] \tag{22}$$

During long-term operation, short-term strength is reduced in proportion to the number of broken bonds *n1*:

$$R\_t/R\_o = \left[ (N\_o - n\_1)/N\_o \right] : \left[ (\tau - t)/\tau \right] \tag{23}$$

where τ is the durability of the coating and t is the operating time.

end, stretched coating samples were subjected to sprinkling. The results of the tests

**Type of coating** *Uo* **γ** Polyvinyl acetate cement 122.81 27.98 Silicone KO-168 102.53 42.86 Silicate 84 11.14 Sol silicate 87 8.55

*Values of the activation energy of the process of destruction of coatings depending on tensions: (1) coating based*

Consider the condition of brittle cracking of polymer coatings under investigation under the action of internal tensions. In the case of brittle failure, the cracking

*Dependence of the long-term strength of coatings in the process of humidification: (1) coating of PVAC; (2)*

*coating of PVAC with surface hydrophobization; (3) coating of KO-168.*

*σ* ≥0*:*5*R* (16)

are shown in **Figure 18**.

*The values of U and γ of coatings.*

*on silicate paint; (2) coatings based on sol silicate paint.*

*Engineering Steels and High Entropy-Alloys*

*Note: For coatings ι<sup>о</sup> = 10<sup>13</sup> s.*

**Table 4.**

**Figure 18.**

**268**

**Figure 17.**

condition has the form

After the transformation, Eq. (23) has the form

$$R\_l = \{ R\_o \tau \exp\left(U/RT\right) [1 - \exp\left(-aU\right)] \} / \left( \tau\_o \exp\left(U/RT\right) \right) - t \tag{24}$$

Thus, the cracking condition has the form

$$
\sigma\_{\text{max}} = 0.5 \{ R\_o \tau \exp\left( U/RT \right) [1 - \exp\left( -aU \right)] \} / \left( \tau\_o \exp\left( U/RT \right) \right) - t \tag{25}
$$

The obtained cracking condition (25) was used in the analysis of coating cracking due to wind load.

Consider the work of the coating in the pore zone, unfilled with a colorful composition. Suppose that the distance with pores that are not filled with a colorful composition is larger than the size of the pores themselves. Such a coating can be considered as a thin round plate pivotally supported along the contour, while the load is evenly distributed over the area. The coating thickness does not exceed 1/5 of the smallest pore size. The calculations established that the deflection boom does not exceed 1/5 of the coating thickness; therefore, such a plate can be considered rigid.

In accordance with the theory of plates, the magnitude of the stresses arising in the coatings can be determined by the formula


$$
\sigma = \left( \mathbf{1.5} - \mathbf{0.262}a^2 - \mathbf{1.95} \ln a \right) q \left( d/h \right)^2 \tag{26}
$$

where *h* is the coating thickness; *d* is the pore diameter; and *q* is the load. The external wall self-supporting panel of the building experiences the effect of horizontal wind load. In accordance with SNiP 2.01.07 "loads and impacts," the normative value of the average component of the wind load was selected. The results of calculating the stresses arising in thin-coat paint coatings during operation

*Choosing the optimal coating thickness taking into account the duration of the voltage: (1) current voltage;*

Given the influence of the scale factor and the condition of brittle fracture of the

Line 1 characterizes the numerical values of the acting tensions. Curve 2 characterizes the change in the short-term strength of PVAC coatings from the coating thickness in accordance with Eq. (21). Since the coating is in a brittle state, the steadystate long-term strength for each thickness is 0.5 of the short-term, i.e., curve 3. An analysis of the data, (**Figure 19**), indicates that under the short-term effect of the wind load, destruction of the PVAC coatings will occur when the coating thickness is more than 850 μm, since for them σ > 0,5 *R* with long exposure to wind load, destruction will occur at a thickness of 300–850 μm. Coatings less than 300 microns thick are resistant to cracking, as σ<*R* and σ<0,5 *R*. Each type of coating has its own critical pore size, exceeding which leads to cracking of the coatings.

The received results of research of a roughness of a surface of coverings confirm the assumption that quality of a substrate, namely, the degree of its uniformity, presence or absence of pollution on its surfaces, and its porosity render essential influence on quality of appearance of formed coverings that determines their

Studies have been conducted to evaluate the long-term strength of coatings. The values of the structurally sensitive factor are calculated. The condition for coating cracking is obtained, depending on the activation energy and operating time. Given the influence of the scale factor and the conditions for the destruction of coatings, a methodology is proposed for selecting the optimal thickness of the coatings. It is established that for each type of coating, there is a critical pore size, exceeding

from the action of the wind load are given in **Table 6**.

*(2) short-term strength; (3) long-lasting strength.*

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

**5. Conclusion**

**271**

**Figure 19.**

stability while in service.

which leads to cracking of the coatings.

coatings, the optimum coating thickness was selected (**Figure 19**).

*Note: Above the line are voltage values for PVAC coatings with a thickness of 200 μm and below the line for coating XB-161 with a thickness of 80 μm.*

#### **Table 6.**

*Tensions in coatings due to wind load.*

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

#### **Figure 19.**

After the transformation, Eq. (23) has the form

Thus, the cracking condition has the form

*Engineering Steels and High Entropy-Alloys*

the coatings can be determined by the formula

3 6 12

3 6 12

3 6 12

ing due to wind load.

considered rigid.

Moscow 1–2

Penza 1–2

Vladivostok 1–2

*XB-161 with a thickness of 80 μm.*

*Tensions in coatings due to wind load.*

**Table 6.**

**270**

*Rt* ¼ f g *Roτ* exp ð Þ *U=RT* ½ � 1 � exp ð Þ �*αU =*ð*τ<sup>o</sup>* exp ð Þ *U=RT* Þ � *t* (24)

*σ*max ¼ 0*:*5f g *Roτ* exp ð Þ *U=RT* ½ � 1 � exp ð Þ �*αU =*ð*τ<sup>o</sup>* exp ð Þ *U=RT* Þ � *t* (25)

The obtained cracking condition (25) was used in the analysis of coating crack-

In accordance with the theory of plates, the magnitude of the stresses arising in

0.03 0.01 0.04 0.02 0.05 0.03 0.06 0.03

0.04 0.02 0.05 0.03 0.06 0.04 0.08 0.05

0.07 0.04 0.1 0.07 0.13 0.08 0.16 0.1

*Note: Above the line are voltage values for PVAC coatings with a thickness of 200 μm and below the line for coating*

*<sup>σ</sup>* <sup>¼</sup> <sup>1</sup>*:*<sup>5</sup> � <sup>0</sup>*:*262*α*<sup>2</sup> � <sup>1</sup>*:*95 ln *<sup>α</sup> q d*ð Þ *<sup>=</sup><sup>h</sup>* <sup>2</sup> (26)

**Pore diameter, mm** 0.1 0.2 0.5 1.0 2.0 3.0

> 0.71 0.44 0.93 0.57 1.21 0.75 1.57 0.96

0.93 0.58 1.21 0.75 1.58 0.99 2.04 1.27

1.86 1.16 2.41 1.83 3.16 1.97 4.09 2.55

2.85 1.77 3.73 2.31 4.84 3.00 6.26 3.86

3.71 2.32 4.83 3.01 6.31 3.94 8.17 5.10

7.43 4.64 9.66 7.34 12.63 7.89 16.34

6.41 4.00 8.33 5.20 10.89 6.80 14.09 8.70

8.36 5.22 10.86 6.78 14.21 8.87 18.38 11.49

16.76 10.40 21.73 16.50 28.41 17.70 36.77 22.90

0.18 0.11 0.23 0.14 0.30 0.18 0.39 0.24

0.23 0.14 0.30 0.18 0.39 0.24 0.51 0.39

0.46 0.29 0.6 0.45 0.79 0.49 1.02 0.63

Consider the work of the coating in the pore zone, unfilled with a colorful composition. Suppose that the distance with pores that are not filled with a colorful composition is larger than the size of the pores themselves. Such a coating can be considered as a thin round plate pivotally supported along the contour, while the load is evenly distributed over the area. The coating thickness does not exceed 1/5 of the smallest pore size. The calculations established that the deflection boom does

not exceed 1/5 of the coating thickness; therefore, such a plate can be

**Name cities Floor Tension, <sup>σ</sup>**�**10**�**<sup>1</sup> MPa**

0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.01

0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.01

0.02 0.01 0.02 0.01 0.03 0.01 0.04 0.01

*Choosing the optimal coating thickness taking into account the duration of the voltage: (1) current voltage; (2) short-term strength; (3) long-lasting strength.*

where *h* is the coating thickness; *d* is the pore diameter; and *q* is the load.

The external wall self-supporting panel of the building experiences the effect of horizontal wind load. In accordance with SNiP 2.01.07 "loads and impacts," the normative value of the average component of the wind load was selected. The results of calculating the stresses arising in thin-coat paint coatings during operation from the action of the wind load are given in **Table 6**.

Given the influence of the scale factor and the condition of brittle fracture of the coatings, the optimum coating thickness was selected (**Figure 19**).

Line 1 characterizes the numerical values of the acting tensions. Curve 2 characterizes the change in the short-term strength of PVAC coatings from the coating thickness in accordance with Eq. (21). Since the coating is in a brittle state, the steadystate long-term strength for each thickness is 0.5 of the short-term, i.e., curve 3.

An analysis of the data, (**Figure 19**), indicates that under the short-term effect of the wind load, destruction of the PVAC coatings will occur when the coating thickness is more than 850 μm, since for them σ > 0,5 *R* with long exposure to wind load, destruction will occur at a thickness of 300–850 μm. Coatings less than 300 microns thick are resistant to cracking, as σ<*R* and σ<0,5 *R*. Each type of coating has its own critical pore size, exceeding which leads to cracking of the coatings.

#### **5. Conclusion**

The received results of research of a roughness of a surface of coverings confirm the assumption that quality of a substrate, namely, the degree of its uniformity, presence or absence of pollution on its surfaces, and its porosity render essential influence on quality of appearance of formed coverings that determines their stability while in service.

Studies have been conducted to evaluate the long-term strength of coatings. The values of the structurally sensitive factor are calculated. The condition for coating cracking is obtained, depending on the activation energy and operating time. Given the influence of the scale factor and the conditions for the destruction of coatings, a methodology is proposed for selecting the optimal thickness of the coatings. It is established that for each type of coating, there is a critical pore size, exceeding which leads to cracking of the coatings.

*Engineering Steels and High Entropy-Alloys*

**References**

1995. p. 234

1980. p. 216

p. 240

411241

**273**

[1] Loganina VI, Orentlikher LP.

Association of Construction Universities; 2001. p. 104

[2] Orentlicher LP, Loganina VI. Protective and Decorative Coatings of Concrete and Stone Walls. Handbook. Moscow: Stroyizdat; 1993. p. 136

[3] Andrianov KA. Organosilicon Compounds. Goskhimizdat: Moscow;

[4] Karyakina MI. Physico-Chemical Foundations of the Formation and Aging of Coatings. Moscow: Chemistry;

[5] Sukhareva LA. The Durability of Coatings. Moscow: Chemistry; 1984.

[6] Loganina VI. Durability of paint and varnish coatings depending on the quality of their appearance. IOP Conference Series: Materials Science and Engineering. 2016;**471**:022044

[7] Andryushenko EA. Lightfastness of Paint and Varnish Coatings. Moscow:

[8] Bartenev GM, Zuev YS. Strength and Destruction of Highly Elastic Materials. Moscow-Leningrad: Chemistry; 1984

[9] Loganina VI. The influence of surface quality of coatings on their deformation properties. Contemporary Engineering Sciences. 2014;**7**(36):

[10] Bykhovsky AA. Distribution. Kiev:

Science, Dumka; 1983. p. 191

[11] Loganina VI, Skachkov Yu P. Assessment of the stress state of the coating in depending on the porosity of

Chemistry; 1986. p. 187

Persistence of Protective and Decorative Coatings of the Exterior Walls of Buildings. Moscow: Publishing House

*Building and Architecture Paints and Coatings DOI: http://dx.doi.org/10.5772/intechopen.90498*

the cement substrate. Key Engineering

[12] GOST R 8.700–2010. State system

measurements by means of scanning probe atomic force microscope

[13] Zisman GA, Todes OM. The Course of General Physics. Moscow: Chemistry;

Construction Materials. 2018;**9**:e00173

Seredenko MM. Optical Properties of Paint Coatings. Leningrad: Chemistry;

[16] Ajzenshtadt AM, Frolova MA, Tutygin AS. Fundamentals of

Systems of Rocks for Building Composites (Theory and Practice). Arkhangelsk: CPI NarFU; 2013. p. 113

[18] Zhurkov SN, Narzulaev BN. Temporal dependence of solids. Journal of Technical Physics. 1953;**23**:1677

[19] Bokshitsky MN. Long-Lasting Polymer Strength. Moscow: Chemistry;

Thermodynamics of Highly Dispersed

[17] Loganina VI, Mazhitov YB. Research of inter-phase interaction in ZOLsilicate paints. International Journal of Engineering & Technology. 2018;**7**(4.5):

[14] Loganina VI, Kislitsyna SN, Mazhitov Ye B. Development of solsilicate composition for decoration of building walls. Case Studies in

[15] Gurevich MM, Itsko EF,

1984. p. 120

605-607

1978. p. 309

Materials. 2016;**737**:179-183

for ensuring the uniformity of measurements. Methods of surface

roughness effective height

1968
