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Calculation of kinetic parameters of amino-formaldehyde polymers formation in the presence of calcium ions.

UDC 678.652+661.842

Introduction. Calcium carbonate is on of widely used fillers of composite materials. The main characteristics defining possibility of its use as a filler are dispersion and particle shape. Calcium carbonate modification by high-molecular polymers allows changing its characteristics (dispersion, phase structure, particle shape) and properties of surface with the broad range. The widespread amino-formaldehyde polymers (AFP) have been used for modification. Carrying out of polycondensation process and hardening of AFP under certain conditions leads to sludge formation with the developed surface and reactionary and active functional groups on it. Such structure of AFP allows applying them for coprecipitation with non-organic substances with further use of precipitations in various composition structures.

The polycondensation mechanism of AFP is complex and depends on many factors (pH of environment, temperature, concentration of reagents, availability of catalysts and ions of metals or inhibitors) [1 ... 4]. The equation of carbamide reaction with formaldehyde at equimolecular ratio of components, leading to formation of linear structure prepolymers (monomethylol ureas) has the following form:

[H.sub.2] N-CO-N[H.sub.2] + C[H.sub.2]O [right arrow] [H.sub.2]N-CO-NHC[H.sub.2]OH.

Further polycondensation of monomethylol urea with formation of polimetilenmochevina courses in the following way:

n[H.sub.2]N-CO-NHC[H.sub.2]OH [right arrow] H[-HN-CO-NHC[H.sub.2]-]nOH + (n-1)[H.sub.2]O.

Small excess of formaldehyde (25% of stoichiometry) leads to formation of dimethylol ureas which are also pass polycondensation process:

[H.sub.2]N-CO-NHC[H.sub.2]OH + C[H.sub.2]O [right arrow] HOC[H.sub.2]HN-CO-NHC[H.sub.2]OH; nHOC[H.sub.2]HN-CO-NH-C[H.sub.2]OH [right arrow] H[-HOC[H.sub.2]N-CO-NHC[H.sub.2]-]nOH+(n-1)[H.sub.2]O; nHOC[H.sub.2]HN-CO-NH-C[H.sub.2]OH [right arrow] H[-HOC[H.sub.2]N-CO-NH-]nOH+(n-1)C[H.sub.2]O+(n-1)[H.sub.2]O.

Further increase in amount of formaldehyde leads to formation of three- and tetramethylol ureas, but the speed of these products formation is significantly lower than the formation speed of the first two polymers, therefore their influence on polycondensation process is insignificant. The formed polycondensates either turn into carbamide-formaldehyde resins at pH [greater than or equal to] 5, or, at pH < 5, are emitted from solutions in the form of insoluble high-disperse powders (hardening).

The pH value of the reactionary environment significantly influences not only on the type of the formed product, but also influences on the speed of formation and polycondensation of polymers, which has the minimum values in the pH range from 4 to 8 [1]. Considerable decrease of pH leads to sharp reduction of the metilol groups, that are promote binding of inorganic precipitation due to formation of donor-acceptor connection of polymer with cations (calcium ions) or due to physical interaction, and at pH > 5 the hard products are not formed. Therefore, the pH values during the experiments were used in the range of 2 ... 5, that have been recommended for AFP coprecipitations processes with metal hydroxides [5 ... 8].

As it has been established earlier [9, 10], the presence of amino-formaldehyde polymers at solution allows increasing of transformation degree of calcium ions that can demonstrate formation of the weak bonds arising between calcium ions and amino-formaldehyde polymers by electrostatic attraction or on the donor-acceptor mechanism. Availability of such bonds also influences on poly-condensation process of AFP, therefore it was necessary to establish the influence of calcium ions on the speed of this process.

The aim of the research is to determine the kinetic characteristics of polycondensation process of amino-formaldehyde polymers in the presence of calcium ions.

Materials and Methods. Polycondensation of AFP took place under following conditions: the temperature is 20, 30, 60[degrees]C; the molar ratio of carbamide to formaldehyde is 1:1.25; the polycondensation duration is 2 hours; the concentration of calcium chloride (considering on calcium ions)--[C.sub.0]([Ca.sup.2+]) = 0; 22.5; 40; 45; 70; 90 g/l (0; 0.565; 1.0; 1.125; 1.75; 2.25 mol/l); the mass ratio of CaC[O.sub.3]:AFP = 1:1. The poly condensation process was carried out in calcium chloride solution with pH = 2.5.5.

Results. During the polycondensation process rather fast formation of white precipitation is observed (during 2.5 min.) that demonstrates that process of AFP polycondensation and their hardening proceeds in parallel. During the polycondensation process the concentration of free formaldehyde were defined. It characterizing the course of reaction completeness of the methylol ureas and metilol groups formation, characterizing stitching degree at polycondensation in the solution containing [Ca.sup.2+] and in control solution without [Ca.sup.2+]. Dependences of the free formaldehyde and metilol groups concentration on polycondensation time at different pH values are presented on Fig. 1.

[FIGURE 1 OMITTED]

In the presence of [Ca.sup.2+] cations the acceleration of the first two stages is observed: the maximum concentration of metilol groups (the minimum concentration of free formaldehyde) at the first stage is reached in 40 minutes at presence of [Ca.sup.2+] and in 55 minutes without [Ca.sup.2+]; duration of the second stage--15 minutes at presence of [Ca.sup.2+] and 20 minutes without [Ca.sup.2+]. The similar accelerating influence of cations on polycondensation process has been described by other researchers [4], however the data about the influence of calcium ions and its mechanism are absent in literature.

Reduction of the solution pH from 5.5 to 2 leads to reduction of free formaldehyde concentration more than by 1.5 times that confirms expediency of the pH value equal 2 accepted earlier for initial stage of AFP obtaining. So, the further calculations were carried out for pH = 2.

The quantitative measure characterizing completeness and speed of all stages of AFP polycondensation (methylol ureas formation, their polycondensation and hardening) is the concentration of the general formaldehyde in solution. Therefore, kinetic parameters of polycondensation process are determined by processing of the general formaldehyde concentration dependences in solution on polycondensation time.

The preliminary analysis of experimental data has shown that the kinetics of the general formaldehyde expenditure in the reactionary environment is described by the kinetic equation of direct reaction of the second order with reverse reaction of the first order [11]:

[omega] = -dx/dt = [k.sub.1] ([a.sub.0] - x) ([b.sub.0] - x) - [k.sub.2] ([c.sub.0] + x), (1)

where [k.sub.1] and [k.sub.2]--constants of direct and return reactions speeds;

[tau]--reaction time;

[omega]--reaction speed;

[a.sub.0], [b.sub.0], [c.sub.0]--initial concentration of carbamide, formaldehyde and derivatives of methyleneurea, mol/l;

([a.sub.0] - x), ([b.sub.0] - x), ([c.sub.0] + x)--current concentration of carbamide, formaldehyde and derivatives of methyleneurea;

x--amount of the reacted substance, mol/l.

Equilibrium constant of the process (K = [k.sub.1]/[k.sub.2]) is:

K = [C.sub.0] + [bar.x]/([a.sub.0] - [bar.x]) ([b.sub.0] - [bar.x]), (2)

where x--equilibrium value x.

The [bar.x] value is defined by solution of quadratic equation:

K([a.sub.0] - [bar.x])([b.sub.0] - [bar.x]) - ([C.sub.0] + [bar.x]) = 0, (3)

or

K x [[bar.x].sup.2] - [bar.x] x (K x [a.sub.0] + K x [b.sub.0] + 1) + (K x [a.sub.0] x [b.sub.0] - [c.sub.0]) = 0. (4)

Taking into account that [a.sub.0] < [b.sub.0], the gain cannot be more than [a.sub.0]. Thus, only those values of [bar.x] are physically sensible which are in the range from [a.sub.0] to -[c.sub.0]. The values of the trinomial standing, put in the left side of the equation (4), at the ends of this interval, i.e. in points [bar.x] = [a.sub.0] and [bar.x] = - [c.sub.0], are equal respectively:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

If to designate the second root of trinomial as the [??], then it is possible to write down:

F(x) = K([bar.x] - x)([bar.x'] - x).

At the same time [bar.x] and [bar.x'] are also connected among themselves by:

[bar.x] + [bar.x'] = K x [a.sub.0] + K x [b.sub.0] + 1/K.

Then the equation (1) takes the following form:

dx/dt = [k.sub.1] ([bar.x] - x) ([bar.x'] - x). (5)

where [bar.x]--equilibrium value of x, defined from experimental data, at known composition of original and equilibrium stock;

[bar.x'] and [k.sub.1]--the sizes, determined of the solution of the differential equation using the formulas given below.

The solution of the differential equation (5) gives the straight line equation in coordinates:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The [k.sub.1] ([bar.x'] - x) and [k.sub.1] are determined by tangent of inclination angle of this straight line to abscissa axis. The equilibrium constant and reverse kinetic constant are defined of the equations (2) and (5).

The example of dependence of the 1g [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on reaction time at concentration of [C.sub.0]([Ca.sup.2+]) = 0,565 mol/l is presented on Fig. 2.

[FIGURE 2 OMITTED]

The examples result for the calculation of the kinetic constants and balance of polycondensation process are presented in table 1. The calculation results of effective kinetic constants of direct and reverse reaction of AFP polycondensation ([k.sub.1ef], [k.sub.2ef]) for different conditions (initial ion concentrations of [Ca.sup.2+] are 0; 0.565; 1.13; 1.695 respectively; 2.26 mol/l, formaldehyde--1.0 mol/l, carbamide--0.8 mol/l; temperature 20, 30, 60[degrees]C; pH=2) are presented in Table 2.

Based on the obtained data, the activation energy and preexponential multipliers for direct ([E.sub.1]) and the reverse ([E.sub.2]) reaction in solution without presence of [Ca.sup.2+] has been defined:

[E.sub.1] = 30.2 kJ/mol; [B.sub.1] = 4.13 l/(mol x s); [E.sub.2] = 4.3 kJ/mol; [B.sub.2] = 5.55 x [10.sup.-4] [s.sup.-1].

The Arrhenius equations for process of AFP formation in solution without presence of [Ca.sup.2+] takes the following form:

--for direct reaction

[k.sub.1] = 4.13 x e 30200/RT,

--for reverse reaction

[k.sub.2] = 5.55 x [10.sup.-4] x [e.sup.-4300/RT.

According to the obtained data, the addition to the reactionary [Ca.sup.2+] environment leads to sluggishness of both direct and inverse reactions. The dependences of efficient kinetic constants of a direct and reverse reaction on concentration of [Ca.sup.2+] (Fig. 3) in a general view are described by the following equations:

1/[k.sub.1ef] = 1/[k.sub.1] - [k.sub.1]' x C([Ca.sup.2+]), 1/[k.sub.2ef] = 1/[K.sub.2] - [k.sub.2'] x C([Ca.sup.2+),

where [k.sub.1]' and [k.sub.2']--coefficients of proportionalities for a direct and reverse reaction, that are temperature-dependent.

Processing of the dependences presented in Fig. 3 results in the following dependences for co-efficients of proportionalities for direct and inverse reactions calculation:

[k'.sub.1] = 1/2.4 x [10.sup.-3] - 0.688 x [T.sup.-1],

[k'.sub.2] = 1/4 x [10.sup.-6] x [T - 1.92 x [10.sup.-4].

[FIGURE 3 OMITTED]

Thus, the dependences of efficient kinetic constants on concentration of [Ca.sup.2+] and on temperature can be written down in the following form:

[k.sub.1ef] = [(0.242 x exp(3628/T) + [(2.42 x [10.sup.-3] - 0.688/T).sup.-1 x C([Ca.sup.2+]).sup.-1],

[k.sub.2ef] = (0.1802 x exp(515.4/T) + [(4 x [10.sup.-6] x T - 1.92 x [10.sup.-4].sup.-1]. x C([Ca.sup.2+]).sup.-1].

The common speed of AFP formation process in the presence of calcium ions is described by the following equation

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

The relative deviation of the experimental and calculated kinetic constants of reactions does not exceed 5.0% for a forward reaction, and 11% for inverse one. I.e. the received results are agree within an experiment error--3 ... 10%.

Conclusions. The analysis of equation (6) shows that polycondensation process of AFP in the presence of [Ca.sup.2+] ions at their concentration from 0 to 2.25 mol/l (0 ... 90 g/l) leads to acceleration of process more than by 1.8 times at temperature of 20[degrees]C. Further increase of [Ca.sup.2+] concentration leads to reduction of process speed. At temperature of 30[degrees]C the speed of process almost does not change in the range of [Ca.sup.2+] concentration from 0 to 2.25 mol/l and further decreases slightly. For all range of [Ca.sup.2+] concentration at temperature of 60 [degrees]C the reduction of process speed is observed. Influence of [Ca.sup.2+] on process of polycondensation confirms assumption made earlier of formation of weak bonds between AFP and calcium ions which at low temperatures interfere with hydrolysis of methyleneurea and collapse at increasing of process temperature.

Therefore, it is expedient to conduct the process of AFP obtaining at a temperature of 20[degrees]C in solutions with [Ca.sup.2+] concentration within 1.2.25 mol/l (40.90 g/l).

The question of plastics properties studying that use the amino-formaldehyde polymers modified by lime carbonate as an excipient can be considered as a subject of further researches.

DOI 10.15276/opu.1.48.2016.15

[TEXT NOT REPRODUCIBLE IN ASCII]

[1.] Grassmann, O. Biomimetic nucleation and growth of CaC[O.sub.3] in hydrogels incorporating carboxylate groups / O. Grassmann, P. Lobmann // Biomaterials.--2004.--Vol. 25, Issue 2.--PP. 277--282.

[2.] Effects of PAA additive and temperature on morphology of calcium carbonate particles / J. Yu, M. Lei, B. Cheng, X. Zhao // Journal of Solid State Chemistry.--2004.--Vol. 177, Issue 3.--PP. 681-689.

[3.] Kim, I.W. Effects of some nonionic polymeric additives on the crystallization of calcium carbonate / I.W. Kim, R.E. Robertson, R. Zand // Crystal Growth & Design.--2005.--Vol. 5, Issue 2.--PP. 513-522.

[4.] Brydson, J.A. Plastics materials / J.A. Brydson.--7th Ed.--Oxford: Butterworth-Heinemann, 2000.--920 p.

[5.] Badanie procesu precypitacji weglanu wapnia odmiany aragonitowej / M. Trypuc, U. Kielkowska, Z. Torski, G. Lyjak // Chemik.--1999.--Nr. 1.--PP. 11-15.

[6.] Effect of filler treatments on rheological behavior of calcium carbonate and talc-filled polypropylene hybrid composites / M.S.F. Samsudin, Z.A. Mohd Ishak, S.S. Jikan, et al. // Journal of Applied Polymer Science.--2006.--Vol. 102, Issue 6.--PP. 5421-5426.

[7.] Study of dispersion of nano-CaCO3 in polymer HDPE and mechanical properties of HDPE/nano-CaCO3 composite / Q.-J. Li, Y.-J. Wu, H.-J. Yang, Q.-T. Li // Journal of Guizhou University of Technology. Natural Science Edition.--2005.--Issue 6.--PP. 25-28.

[8.] [TEXT NOT REPRODUCIBLE IN ASCII].

[9.] [TEXT NOT REPRODUCIBLE IN ASCII].

[10.] [TEXT NOT REPRODUCIBLE IN ASCII].

[11.] Denisov, E.T. Chemical kinetics: Fundamentals and new developments / E.T. Denisov, O.M. Sarkisov, G.I. Likhtenshtein.--Amsterdam; Boston: Elsevier, 2003.-547 p.

References

[1.] Grassmann, O., & Lobmann, P. (2004). Biomimetic nucleation and growth of CaC[O.sub.3] in hydrogels incorporating carboxylate groups. Biomaterials, 25(2), 277-282. D0I:10.1016/S0142-9612(03)00526-X

[2.] Yu, J., Lei, M., Cheng, B, & Zhao, X. (2004). Effects of PAA additive and temperature on morphology of calcium carbonate particles. Journal of Solid State Chemistry, 177(3), 681-689. DOI:10.1016/j.jssc.2003.08.017

[3.] Kim, I.W., Robertson, R.E., & Zand, R. (2005). Effects of some nonionic polymeric additives on the crystallization of calcium carbonate. Crystal Growth & Design, 5(2), 513-522. DOI:10.1021/cg049721q

[4.] Brydson, J.A. (2000). Plastics Materials (7th Ed.). Oxford: Butterworth-Heinemann.

[5.] Trypuc, M., Kielkowska, U., Torski, Z., & Lyjak, G. (1999). Badanie procesu precypitacji weglanu wapnia odmiany aragonitowej. Chemik, 1, 11-15.

[6.] Samsudin, M.S.F., Mohd Ishak, Z.A., Jikan, S.S., Ariff, Z.M., & Ariffin, A. (2006). Effect of filler treatments on rheological behavior of calcium carbonate and talc-filled polypropylene hybrid composites. Journal of Applied Polymer Science, 102(6), 5421-5426. DOI:10.1002/app.25054

[7.] Li, Q.-J., Wu, Y.-J., Yang, H.-J., & Li, Q.-T. (2005). Study of dispersion of nano-CaC[O.sub.3] in polymer HDPE and mechanical properties of HDPE/nano-CaC[O.sub.3] composite. Journal of Guizhou University of Technology: Natural Science Edition, 6, 25-28.

[8.] Melnikov, B.I., Perekhrest, O.A., Smotrayev, R.V., & Tarasenko, V.A. (2000). The study of molybdenum ions sorption by the carbamideformaldehyde polymers. Odes'kyi Politechnichnyi Universytet. Pratsi, 2, 212-216.

[9.] Melnikov, B.I., & Arkhipova, V.V. (2007). Investigation of the possibility of deposition of chalk in the presence of urea-formaldehyde polymers. In Proceedings of the 3rd International Scientific and Technical Conference of Students and Young Scientists "Chemistry and Modern Technologies" (p. 24). Dnipropetrovsk: Ukrainian State University of Chemical Technology.

[10.] Arkhipova, V.V., Smotrayev, R.V., & Melnikov, B.I. (2009). The investigation processes of calcium carbonate precipitation in the presence of carbamide formaldehyde polymers. Issues of Chemistry and Chemical Technology, 5, 97-100.

[11.] Denisov, E.T., Sarkisov, O.M., & Likhtenshtein, G.I. (2003). Chemical Kinetics: Fundamentals and New Developments. Amsterdam; Boston: Elsevier.

Received January 14, 2016

Accepted February 24, 2016

V.V. Arhipova, PhD, R.V. Smotraiev, PhD, Assoc.Prof., O.V. Gruzdeva, PhD, Assoc.Prof.

Ukrainian State University of Chemical Engineering, 8 Gagarin Ave., 49005 Dnipropetrovsk, Ukraine; e-mail: RV1006@rambler.ru
Table 1
Example of calculation of the AFP formation process kinetic parameters

t, [degrees]C   [C.sub.0](Ca),   [tau], min     K      x'
                    mol/l

20                    0             0.5       0.189   6.977
                                     5
                                     15
                                     25
                                     40
                                     55
                                     75
                                    110
                                    125

20                  0.565           0.5       0.206   6.522
                                     5
                                     15
                                     25
                                     40
                                     55
                                     75
                                    110
                                    125

                      lg          [k.sub.1ef],
                [[bar.x'] - x /    [M.sup.-1]    [k.sub.2ef]
t, [degrees]C    [bar.x] - x]     [min.sup.-1]   [min.sup.-1]

                                              x [10.sup.3]

20                   1.784           1.049          5.552
                     2.102
                     2.158
                     2.189
                     2.248
                     2.311
                     2.299
                     2.530
                     3.110

20                   1.726           0.922          4.467
                     2.062
                     2.102
                     2.125
                     2.125
                     2.179
                     2.203
                     2.479
                     2.779

Table 2
The calculation results of effective kinetic constants
of direct and reverse reaction of AFP polycondensation

                              [k.sub.1ef],
                 [C.sub.0]     [M.sup.-1]    [k.sub.2ef]
t, [degrees]C   (Ca), mol/l   [min.sup.-1]   [min.sup.-1]

                                     x [10.sup.3]

20                   0           1.049          5.552
                   0.565         0.922          4.467
                   1.125         0.866          3.676
                   1.75          0.703          3.504
                   2.25          0.640          3.398

30                   0           1.543          6.255
                   0.565         1.311          5.880
                   1.125         1.240          4.165
                   1.75          1.228          3.712
                   2.25          1.095          3.679

60                   0           4.615          7.093
                   0.565         4.260          6.547
                   1.125         3.565          5.108
                   1.75          3.394          4.830
                   2.25          3.105          4.481
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Author:Arhipova, V.V.; Smotraiev, R.V.; Gruzdeva, O.V.
Publication:Odes'kyi Politechnichnyi Universytet. Pratsi
Article Type:Report
Date:Mar 1, 2016
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