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

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 .

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