# Американский Научный Журнал OPTIMIZATION OF THE PROCESSES OF DISAGGREGATION OF PIGMENTS AND FILLERS USING THE METHODS OF PROBABILISTIC DETERMINISTIC MODELING

An important technological characteristic of
paintwork materials, which determine the coverage and
protective properties of their coatings, is the degree of
disaggregation of pigments and fillers [1,2]. In freshly
prepared suspensions of paintwork materials the
development of aggregation and disaggregation
processes depends both on the surface properties of the
solid-phase components themselves and on the
qualitative and quantitative composition of coverformers, solvents and surfactants. To optimize the
composition of coatings, it is necessary to know how
the set of all these components will affect the dispersion
processes, which involves the construction of a
generalized mathematical model of the system under
study Скачать в формате PDF

54 American Sci entific Journal № ( 28) / 20 19

OPTIMIZATION OF THE PROCES SES OF DISAGGREGATIO N OF PIGMENTS AND FIL LERS

US ING THE METHODS OF P ROBABILIS TIC DETERMINISTIC MO DELING

Antonina Dyuryagina 1,

Candidate of Chemistry,

associate profess or of the Department of Che mistry and Chemical Technology of the North Kazakhstan

State University named after M. Kozybaev.

Aida Lutsenko 1,

Graduate student of th e Department of Chemistry and Chemical Te chnology of the North Kazak hstan State

University named after M. Kozybaev.

Roman Tarunin 1,

Third -year student of the Department of Chemistry and Chemical Technology of the North Kazakhstan

State University named after M. Kozybaev. 1M. Kozybaev North -Kazakh stan State University,

18, Abay street, Petropavlovsk, 150000, Republic of Kazakhstan.

An important technological characteristic of

paintwo rk materials, which determine the coverage and

protective properties of their coatings, is the degree of

disaggregati on of pigments and fillers [1,2]. In freshly

prepared suspensions of paintwork materials the

development of aggregation and disaggregation

processes depends both on the surface properties of the

solid -phase components themselves and on the

qualitative and quantitative composition of cover -

formers, solvents and surfactants. To optimize the

composition of coatings, it is necessary to know how

the set of all these components will affect the dispersion

processes, which involves the construction of a

generalized mathematical model of the system under

study [3,4].

We attempted withdrawal of multifactor models of

the dispersion process of the pigment of titanium

dioxide (R -02), and filler, calcite (M -20), i n the coating

system on the basis of the varnish PF -060, wh ite spirit,

surface -active substances (surfactants) AS (an amine

derivative with the number of carbon atoms in the chain

6-8, TU 655 -RK 056 006434 -002 -2000) on the basis of

the principles of probabi listic and deterministic

simulation.

During the experiments , a modified plan -matrix of

the four -factor experiment was used at three levels,

which was achieved by taking the factor C TiO2 (pigment

con centration) beyond its limits. As the main factors

affecti ng the indicators of pigment and filler

disaggregation, the quantitative content of th e added

solvent in suspensions (CP,%, 10÷50 volume relative

to PF -060,%), surfactant (C surfactant , in terms of t he total

mass of solid -phase components, — 0÷16%), the

rel ative content of titanium dioxide with a constant

mass cont ent of pigment and filler i n suspensions —

16% (C TiO2 , 0÷100% RH) was determined.).

The method of preparation of suspensions of

paintwork m aterials with different content of cover -

forming substance was the preliminary dilution of

white spirit varnish PF -06 0 in the following volume

ratios: 1:9, 3:7, 1:1. The resulting solutions

(hereinafter -A) were directed to the preparation of

suspensions, w hich was carried out at 20 °C in a

hermetic reactor (volum e 0.2 dm 3), equipped with a

mixing device (impeller agitato r, frequency — 700

rpm). Th e duration of the operation, in which the

stabilization of the equilibrium characteristics of

suspensions and th e fractional composition of the

pigment and filler was fix ed, was 1 hour.The relative

pigment contents varied due to changes in its mass

concent ration in the solid phase. To estimate the

disaggregating effect of surfactants, the calculated

index — its conc entration (in mass, %) by mass of

pigment. For this purpos e, a series of solutions with

different surfactant content (from 0 to 16%) was pre -

pre pared by dissolving the surfactant in a fixed volume

of solution A. The resulting solution (hereinafter — B)

was sent to the preparation of suspensions. The method

of pre paration of modified suspensions using solution

B is simila r to the above.

The studied samples of paint suspensions were

placed on a slide, fixed with a cover glass and

maintained for a certain time under load with the help

of a microdispenser (the volume of the drop was 0.02

ml). As it is known, as the solvent ev aporates (in time),

due to the tightening effect (in height and in plane), the

development of deformation processes that affect the

charact eristics (geometric, structural) of the films

themselves, as well as the width of the gap between the

object and cove r glasses, increases. The r esults of

preliminary tests carried out on samples of different

compositions showed that the load regime should be

p≥10 g/cm 2. At the same time, the period of holding the

samples under load was optimized, which was set

according to the time required to sta bilize the

deformation processes in the films. For the system

under study, the static load period was 5 minutes.

The response function was the total number of

solid phase particles (N) falling on a fixed area of the

substrate:

The values of N in the sam ples were determined at

a given magnification ratio (X350) using a computer -

optical control system [4 -6], which calculates the

number of particles at S = 0.38 mm 2.

After the implementation of the active experiment

the experimenta l array was sampled for eac h level of

each factor within the two -dimensional matrix Yx :

American Scientific Journal № ( 28) / 20 19 55

m – number of levels; z - number of functional

expressions for each level.

Particular dependences N = f (C i)

for each individual factor are shown in Fig

From the analysis of particular dependences

follows a natural increase in the number of particles as

the total concentration of solid -phase com ponents in

the paintwork system increases (Fig. 1, a); at the same

time, the positive contribution of the as surf acta nt

concentration to the cha nge in N is consistent with its

disaggregating effect previously established for other

pigments [5,8]. Reducing the degree of disaggregation

of the pigment and filler as dilution of the cover -former

by solvent indicates a pos itiv e (surface -active) role of

functional groups (hydroxy -, carboxy -) in the

pentaphthalic resin [9,10].

After approximation of partial depende nces using

standard programs "Advanced Grapher" and

"Microsoft Excel", one -parameter equations

characterizing the eff ect on the response functio n of

each factor separately (equations 1 -3) are obtained.

To build a generalized model, we used a

multivariate equation of nonlinear multiple correlation,

which in an implicit form has the look [2]:

x1, x 2,..., x n — facto rs; n — number of factors;

gaverage — general average. Values of g average were

calculated by the formula:

Yexp. - the set of experimental dat a in the matrix;

M - the number of rows in the matrix. After substituting

56 American Sci entific Journal № ( 28) / 20 19

the approximated expressions (1 -3) into equ ation (4),

we obtain a gene ralized equation that takes into account

the joint contribution of all factors:

The adequacy of the obtaine d model (for the 95th

significance level) was estimated on the basis of the

correlation coefficients (R) and signific ance (t R),

which were calculat ed by the equations:

The calculations showed a satisfactory

convergence of the experimental and calculated

(according to equation 6) values of the response

function:

Based on the solution of the generalized equation,

the opti mal expenditure of the surf actant, solvent and

pigment in the suspension of paintwork materials were

determined, providing the required degree of

disaggregation of titanium dioxide. The joint

contribution of the two factors to N is repres ented by

nomograms (Fig. 2) obtained by equat ion 6.

The analysis of the obtained dependences shows

that in order to stabilize the indices of pigmen t

disaggregation at a fixed level, providing, for example,

N = 1800, required to increase the surfactant

consumption or reduc e the relative pigment cont ent as

the paintwork composition is diluted with a solvent.

Calculations according to equation (6) showe d that if

Cp = 10%, then the given N = 1800 in paintwork

materials is achieved at C surfactant = 6,95% and C TiO2 =

70% (relati vely); a similar indicator of the degree of

dispersion can be achieved by reducing the relative

pigment content to 68.2%, but this will require an

increase in surfactant expenditure to 12%. According to

the results of balance experiments performed with

pai ntwork compositions of thes e two compositions, a

satisfactory convergence in the predicted and practical

values of N was establishe d; the mean -square deviation

for the two examples considered does not exceed 1.2%.

Thus, the use of probabi listic -determinist ic

methods of modeling with an extended plan -matrix

provides an adequate multifactorial mathematical

model of the processes of disa ggregation of pigments

and fillers and, as a consequence, the solution of

applied problems in the optimizat ion of the

composi tion of paintwork materials .

REFERENCES

1. Bolatbaev K.N., Dyuryagina A.N., Ostrovnoy

K.A. Modification of composites by surfactan ts.

Petropavlovsk: NKZU Publishing House, 2005. 184 p.

2. Malyshev V.P. Planning of probabilistic

determinis tic experiment. Al ma -Ata: Science of AN

Kaz. SSR, 1981. 161 p.

3. Bolatbaev K.N., Lugovitskaya T.N., Tukachev

A.A., Rustem R.S. Computer -micro -optic al complex

for the analysis of powders and suspensions /

Certificate of registration of intellectual product 0806

RK 00075 fro m 01. 06. 2006

4. Lugovits kaya T.N., Bolatbaev KN,

Naboichenko S.S., Rustem R.S. Investigation of the

dispersing effect of thiolig nins in suspensions of

elemental sulfur and zinc sulphide by optical

American Scientific Journal № ( 28) / 20 19 57

microscopy methods / BULLETIN of the KA RGU.

Karaganda, № 3, 2006, 5 p.

5. Dyuryagin a A.N., Bolatbaev K.N.,

Demyanenko A.V. The study of the adsorption of

surfactants on pigments in paint compositions. Paints

and varnishes and their use. Moscow, 2002, № 10, pp.

36 –38.

6. A.M. Al -Sabagh, M.I. Abd ou, M.A. Migahed,

A.M. Fadl, Ahmed A. Farag, M.M. Mohammedy, S.

Abd -Elwanees, A. Deiab. Influence of ilmenite ore

particles as pigment on the antico rrosion and

mechanical performance properties of polyamine cured

epoxy for internal coating of gas transmiss ion

pipelines. Egy ptian Journal of Petroleum , 2018, vol. 27,

Issue 4, pp. 427 –436.

7. Nurudeen Yekeen, Muhammad A. Manan,

Ahmad Kamal Idris, Ali Mo hamed Samin. Influence of

surfactant and electrolyte concentrations on surfactant

adsorption and foaming char acteristics. Journ al of

Petroleum Science an d Engineering, 2017, vol.149, pp.

612 –622.

8. Grażyna Para, Agnieszka Hamerska -Dudra,

Kazimiera Anna Wi lk, Piotr Warszyński. Surface

activity of cationic surfactants, influence of molecular

structure. Colloids an d Surfaces A: Phys icochemical

and Engineerin g Aspects, 2010, vol. 365, pp. 215 –221.

9. M.A.Deyab, Rachid Ouarsal, A.M. Al -Sabagh,

Mohammed Lachkar, B.El Bali. Enhancement of

corrosion protection performance of epoxy coating by

introducing new hydrogenphosp hate compound.

Pro gress in Organic Coatings, 2017, Vol. 107, pp. 37 –

42.

10. Xianming Shi, Tuan Anh Nguyen, Zhiyong

Suo, Yajun Liu, Recep Avci. Effe ct of nanoparticles on

the anticorrosion and mechanical properties of epoxy

coating. Surface and Coatings Tec hnology, 2009, Vol .

204, Issue 3, pp. 237 –24 5.

OPTIMIZATION OF THE PROCES SES OF DISAGGREGATIO N OF PIGMENTS AND FIL LERS

US ING THE METHODS OF P ROBABILIS TIC DETERMINISTIC MO DELING

Antonina Dyuryagina 1,

Candidate of Chemistry,

associate profess or of the Department of Che mistry and Chemical Technology of the North Kazakhstan

State University named after M. Kozybaev.

Aida Lutsenko 1,

Graduate student of th e Department of Chemistry and Chemical Te chnology of the North Kazak hstan State

University named after M. Kozybaev.

Roman Tarunin 1,

Third -year student of the Department of Chemistry and Chemical Technology of the North Kazakhstan

State University named after M. Kozybaev. 1M. Kozybaev North -Kazakh stan State University,

18, Abay street, Petropavlovsk, 150000, Republic of Kazakhstan.

An important technological characteristic of

paintwo rk materials, which determine the coverage and

protective properties of their coatings, is the degree of

disaggregati on of pigments and fillers [1,2]. In freshly

prepared suspensions of paintwork materials the

development of aggregation and disaggregation

processes depends both on the surface properties of the

solid -phase components themselves and on the

qualitative and quantitative composition of cover -

formers, solvents and surfactants. To optimize the

composition of coatings, it is necessary to know how

the set of all these components will affect the dispersion

processes, which involves the construction of a

generalized mathematical model of the system under

study [3,4].

We attempted withdrawal of multifactor models of

the dispersion process of the pigment of titanium

dioxide (R -02), and filler, calcite (M -20), i n the coating

system on the basis of the varnish PF -060, wh ite spirit,

surface -active substances (surfactants) AS (an amine

derivative with the number of carbon atoms in the chain

6-8, TU 655 -RK 056 006434 -002 -2000) on the basis of

the principles of probabi listic and deterministic

simulation.

During the experiments , a modified plan -matrix of

the four -factor experiment was used at three levels,

which was achieved by taking the factor C TiO2 (pigment

con centration) beyond its limits. As the main factors

affecti ng the indicators of pigment and filler

disaggregation, the quantitative content of th e added

solvent in suspensions (CP,%, 10÷50 volume relative

to PF -060,%), surfactant (C surfactant , in terms of t he total

mass of solid -phase components, — 0÷16%), the

rel ative content of titanium dioxide with a constant

mass cont ent of pigment and filler i n suspensions —

16% (C TiO2 , 0÷100% RH) was determined.).

The method of preparation of suspensions of

paintwork m aterials with different content of cover -

forming substance was the preliminary dilution of

white spirit varnish PF -06 0 in the following volume

ratios: 1:9, 3:7, 1:1. The resulting solutions

(hereinafter -A) were directed to the preparation of

suspensions, w hich was carried out at 20 °C in a

hermetic reactor (volum e 0.2 dm 3), equipped with a

mixing device (impeller agitato r, frequency — 700

rpm). Th e duration of the operation, in which the

stabilization of the equilibrium characteristics of

suspensions and th e fractional composition of the

pigment and filler was fix ed, was 1 hour.The relative

pigment contents varied due to changes in its mass

concent ration in the solid phase. To estimate the

disaggregating effect of surfactants, the calculated

index — its conc entration (in mass, %) by mass of

pigment. For this purpos e, a series of solutions with

different surfactant content (from 0 to 16%) was pre -

pre pared by dissolving the surfactant in a fixed volume

of solution A. The resulting solution (hereinafter — B)

was sent to the preparation of suspensions. The method

of pre paration of modified suspensions using solution

B is simila r to the above.

The studied samples of paint suspensions were

placed on a slide, fixed with a cover glass and

maintained for a certain time under load with the help

of a microdispenser (the volume of the drop was 0.02

ml). As it is known, as the solvent ev aporates (in time),

due to the tightening effect (in height and in plane), the

development of deformation processes that affect the

charact eristics (geometric, structural) of the films

themselves, as well as the width of the gap between the

object and cove r glasses, increases. The r esults of

preliminary tests carried out on samples of different

compositions showed that the load regime should be

p≥10 g/cm 2. At the same time, the period of holding the

samples under load was optimized, which was set

according to the time required to sta bilize the

deformation processes in the films. For the system

under study, the static load period was 5 minutes.

The response function was the total number of

solid phase particles (N) falling on a fixed area of the

substrate:

The values of N in the sam ples were determined at

a given magnification ratio (X350) using a computer -

optical control system [4 -6], which calculates the

number of particles at S = 0.38 mm 2.

After the implementation of the active experiment

the experimenta l array was sampled for eac h level of

each factor within the two -dimensional matrix Yx :

American Scientific Journal № ( 28) / 20 19 55

m – number of levels; z - number of functional

expressions for each level.

Particular dependences N = f (C i)

for each individual factor are shown in Fig

From the analysis of particular dependences

follows a natural increase in the number of particles as

the total concentration of solid -phase com ponents in

the paintwork system increases (Fig. 1, a); at the same

time, the positive contribution of the as surf acta nt

concentration to the cha nge in N is consistent with its

disaggregating effect previously established for other

pigments [5,8]. Reducing the degree of disaggregation

of the pigment and filler as dilution of the cover -former

by solvent indicates a pos itiv e (surface -active) role of

functional groups (hydroxy -, carboxy -) in the

pentaphthalic resin [9,10].

After approximation of partial depende nces using

standard programs "Advanced Grapher" and

"Microsoft Excel", one -parameter equations

characterizing the eff ect on the response functio n of

each factor separately (equations 1 -3) are obtained.

To build a generalized model, we used a

multivariate equation of nonlinear multiple correlation,

which in an implicit form has the look [2]:

x1, x 2,..., x n — facto rs; n — number of factors;

gaverage — general average. Values of g average were

calculated by the formula:

Yexp. - the set of experimental dat a in the matrix;

M - the number of rows in the matrix. After substituting

56 American Sci entific Journal № ( 28) / 20 19

the approximated expressions (1 -3) into equ ation (4),

we obtain a gene ralized equation that takes into account

the joint contribution of all factors:

The adequacy of the obtaine d model (for the 95th

significance level) was estimated on the basis of the

correlation coefficients (R) and signific ance (t R),

which were calculat ed by the equations:

The calculations showed a satisfactory

convergence of the experimental and calculated

(according to equation 6) values of the response

function:

Based on the solution of the generalized equation,

the opti mal expenditure of the surf actant, solvent and

pigment in the suspension of paintwork materials were

determined, providing the required degree of

disaggregation of titanium dioxide. The joint

contribution of the two factors to N is repres ented by

nomograms (Fig. 2) obtained by equat ion 6.

The analysis of the obtained dependences shows

that in order to stabilize the indices of pigmen t

disaggregation at a fixed level, providing, for example,

N = 1800, required to increase the surfactant

consumption or reduc e the relative pigment cont ent as

the paintwork composition is diluted with a solvent.

Calculations according to equation (6) showe d that if

Cp = 10%, then the given N = 1800 in paintwork

materials is achieved at C surfactant = 6,95% and C TiO2 =

70% (relati vely); a similar indicator of the degree of

dispersion can be achieved by reducing the relative

pigment content to 68.2%, but this will require an

increase in surfactant expenditure to 12%. According to

the results of balance experiments performed with

pai ntwork compositions of thes e two compositions, a

satisfactory convergence in the predicted and practical

values of N was establishe d; the mean -square deviation

for the two examples considered does not exceed 1.2%.

Thus, the use of probabi listic -determinist ic

methods of modeling with an extended plan -matrix

provides an adequate multifactorial mathematical

model of the processes of disa ggregation of pigments

and fillers and, as a consequence, the solution of

applied problems in the optimizat ion of the

composi tion of paintwork materials .

REFERENCES

1. Bolatbaev K.N., Dyuryagina A.N., Ostrovnoy

K.A. Modification of composites by surfactan ts.

Petropavlovsk: NKZU Publishing House, 2005. 184 p.

2. Malyshev V.P. Planning of probabilistic

determinis tic experiment. Al ma -Ata: Science of AN

Kaz. SSR, 1981. 161 p.

3. Bolatbaev K.N., Lugovitskaya T.N., Tukachev

A.A., Rustem R.S. Computer -micro -optic al complex

for the analysis of powders and suspensions /

Certificate of registration of intellectual product 0806

RK 00075 fro m 01. 06. 2006

4. Lugovits kaya T.N., Bolatbaev KN,

Naboichenko S.S., Rustem R.S. Investigation of the

dispersing effect of thiolig nins in suspensions of

elemental sulfur and zinc sulphide by optical

American Scientific Journal № ( 28) / 20 19 57

microscopy methods / BULLETIN of the KA RGU.

Karaganda, № 3, 2006, 5 p.

5. Dyuryagin a A.N., Bolatbaev K.N.,

Demyanenko A.V. The study of the adsorption of

surfactants on pigments in paint compositions. Paints

and varnishes and their use. Moscow, 2002, № 10, pp.

36 –38.

6. A.M. Al -Sabagh, M.I. Abd ou, M.A. Migahed,

A.M. Fadl, Ahmed A. Farag, M.M. Mohammedy, S.

Abd -Elwanees, A. Deiab. Influence of ilmenite ore

particles as pigment on the antico rrosion and

mechanical performance properties of polyamine cured

epoxy for internal coating of gas transmiss ion

pipelines. Egy ptian Journal of Petroleum , 2018, vol. 27,

Issue 4, pp. 427 –436.

7. Nurudeen Yekeen, Muhammad A. Manan,

Ahmad Kamal Idris, Ali Mo hamed Samin. Influence of

surfactant and electrolyte concentrations on surfactant

adsorption and foaming char acteristics. Journ al of

Petroleum Science an d Engineering, 2017, vol.149, pp.

612 –622.

8. Grażyna Para, Agnieszka Hamerska -Dudra,

Kazimiera Anna Wi lk, Piotr Warszyński. Surface

activity of cationic surfactants, influence of molecular

structure. Colloids an d Surfaces A: Phys icochemical

and Engineerin g Aspects, 2010, vol. 365, pp. 215 –221.

9. M.A.Deyab, Rachid Ouarsal, A.M. Al -Sabagh,

Mohammed Lachkar, B.El Bali. Enhancement of

corrosion protection performance of epoxy coating by

introducing new hydrogenphosp hate compound.

Pro gress in Organic Coatings, 2017, Vol. 107, pp. 37 –

42.

10. Xianming Shi, Tuan Anh Nguyen, Zhiyong

Suo, Yajun Liu, Recep Avci. Effe ct of nanoparticles on

the anticorrosion and mechanical properties of epoxy

coating. Surface and Coatings Tec hnology, 2009, Vol .

204, Issue 3, pp. 237 –24 5.