Modelling the process of synthesis of low molecular mass polyacrylic acid

Polymer Science U.S.S.R. Vol. 32, No. 11, pp. 2211-2216, 1990 Printed in Great Britain.

0032-3950/90 $10.00 + .00 © 1991 Pergamon Press plc

MODELLING THE PROCESS OF SYNTHESIS OF LOW MOLECULAR MASS POLYACRYLIC ACID* S. A. KULIKOV, N. V. YABLOKOVA, V. N. KOKOREV, L. V. MOL'KOVA and Y u . A. ALEKSANDROV Chemistry Research Institute at the Lobachevskii State University, Gorkii (Received 16 October 1989)

A mathematical model of solution polymerization of acrylic acid initiated by the system H202--Cu 2+ accompanied by the formation of low molecular mass polyacrylic acid is considered. It has been established that termination of the polymerization chain comes about in the main on the Cu 2+ ions. Increase in the concentration of H202 and Cu E+ promotes a fall in the MM of polyacrylic acid. Cu 2+ ions are both a component of the initiating system and a regulator of the MM of polyacrylic acid. The mathematical model of the process considered helps in the selection of the requisite concentrations of the starting reagents and the conditions of conducting the experiment for obtaining polyacrylic acid of specified MM.

MATHEMATICAL modelling of real polymerization processes is of theoretical and practical interest. The present paper is concerned with the creation of a model of solution polymerization initiated by the redox system H202 + Cu 2+ in relation to acrylic acid (AA). Redox H202-Mt n+ systems are often used as sources of free radicals in solution polymerization in an aqueous medium. Decomposition of H202 under the influence of iron salts is the subject of much work; the state of this problem is detailed in a number of reviews and monographs [1-3]. The H202-Cu 2+ system especially in conditions of the polymerization process has been far less studied. The patterns obtained for H202-Fe 3+ may apparently be extended in large measure to the initiating H 2 0 2 - - C u 2+ system. A A was purified by repeated recrystallization; the content of the main substance was not less than 99.6% (GLC method: Tsvet 104 chromatograph with a heat conductivity detector; column 100 x 0.4 cm filled with polysorb-1; Tc = 150°C; speed of the gas carrier helium 50 ml/min). P A A was synthesized in a glass reactor with stirrer and reflux condenser at 353 K in an argon atmosphere with single loading of the components. The loss of H202 was checked by iodometric titration [4]. From the results of titration we constantly subtracted the blank value corresponding to the volume of the Na2S203 solution expended on titration of Cu 2+. Three hours after the start of synthesis the reaction mixture was cooled and water and the monomer residues driven off in vacuo. From the viscosity of the 1% aqueous solution of the dry residue we determined the mean molecular mass of PAA from the calibration graph plotted from the GPC results. The published data on polymerization of acrylic monomers on redox systems [2, 3] and also the experimental findings allowed us to choose an acceptably simplified scheme of the process of obtaining P A A (Table 1). The right part of Table I indicates the published rate constants of the elementary reactions klit [2, 3, 5]. Among the elementary reactions presented in Table 1 it is necessary to take a closer look at the reaction (13). According to the findings of Kochi [6, 7] the high reactivity of Cu 2+ in relation to the alkyl radicals R" is related to the formation of an intermediate * Vysokomol soyed. A32: No. 11, 2309-2313, 1990.

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S . A . KULIKOV et al.

TABLE1. REACrZONSOCCURRINGDURINGSOLUTIONPOLYMERIZATIONOFACRYLICACID Reaction* H202-~2"OH H202 + "OH--~ HO2 + H 2 0 H202 + HO2"--~ "OH + 02 + H 2 0 "OH + "OH---~ H 2 0 + O HO2" + Cu2+--'~ Cu + + 02 + H + H202 + Cu +--~ C a 2+ + "OH + O H Cu + + "OH--~ Cu 2+ + O H Cu + + HO2"--)Cu 2+ + HO2"OH + M--~ R" HOE" + M--+ R" R" + M - o R" R" + R ' - o p o l y m e r R" + Cu2+---~ Cu + + polymer

]Cexp, I/mole s

5x 10-11 (s -1) 2 x 108 45 10l° 4 x 109 2 x 107

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

3 x 108

3 x 109 3 x 109 2 x 108 105 4 × 107 2.5 X 10s

]tilt, I/mole s

4x 10 -7 4 X 10 7 4 8 X 10 9 2 x 108 104 3 x 108 3 × 109 ~109 ~ 108 4105 ~ 107 ~10 s

* R" is the generalized polymer radical; M = A A . organocopper compound; the alkyl radical replaces water in the coordination sphere of the copper ion Cu(H20)6'+ + R"

--H~O

) [Cu(H20)6s+R]

> Cu(HsO)6S+"4- R+.

As a result the radical R" oxidizes to R + and Cu 2+ reduces to CuZ+--active catalyst of the breakdown of H202 (reaction (13)). Thus, the scheme (1)-(13) details the dual role of Cu2+; on the one hand, this is a component of the redox system and, on the other, a regulator of the MM of the polymer formed. It has been established experimentally that change in the initial concentration of Cu 2+ and H202 influences the rate of polymerization of A A and the MM of the P A A formed (Fig. 1). With rise in the Cu 2+ concentration the polymerization rate and the MM of the polymer drop (Fig. 1, curves 2, 4, 5). Probably with increase in the Cu 2+ concentration the rate of chain termination on copper ions rises to a higher degree than the rate of initiation of polymerization (Table 2). With rise in the H202 concentration the polymerization rate grows but the MM drops (number of active polymerization centres rises) (Fig. 1, curves 1-3). ~,% J qo

xq

20

5

60

120

Time, min

FIG. 1. Change in conversion a on polymerization of A A (1 mole/l). [H202], mole/l: (1) 0.08; (2) (4) (5)

0.17; (3) 0.33. [Cu2+], mole/l: (1)-(3) 0.003; (4) 0.01; (5) 0.03. MpAA = 10500 (1), 9000 (2), 5100 (3), 6000 (4) and 3400 (5). T = 353 K.

Synthesis of low MM polyacrylic acid

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Figure 2 shows how the ratio of components of the initiating system influences the MM of the polymer formed at a constant concentration of AA. The graph demonstrates how in different variants of the ratio of the components of the redox system PAA of specified MM may be obtained. Cc. 2+ x 102 mole/I

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FIG. 2. Influenceof the concentration ratio of Cu2+ and on the molecular mass of PAA. M p A A = 3000 (1); 5000(2) and 10000(3). [AA] = 1 mole/l. T = 343 K.

The above experimental findings served as the basis for a mathematical analysis, refining and final confirmation of the scheme (1)-(13) of obtaining PAA. The generalized scheme (1)-(13) includes the reactions (1)-(4) of spontaneous and induced breakdown of H202 in water, the reactions (5)-(8)--catalytic decomposition of H202 on copper ions and the reactions (9)-(13)--radical chain polymerization of AA. For most elementary reactions (2)-(8) the k values are known. They have been determined by different methods, as a rule, at room temperature [5]. For the reactions (9)-(13) the exact value of k is not known but the order of these magnitudes is [2, 3]. The system of differential equations (1)-(13) was integrated by the Geer method using the modified and functionally expanded program complex K81 [8] realized on the Amstrad PC. Operating in stages we evaluated k for the reactions where these magnitudes were absent and also found the optimum values kopt ensuring the best agreement of the experimentally measured kinetic magnitudes and the known published k values for the reactions (1)-(13). Varying the initial concentrations of H202 and Cu 2+, measuring them at each moment of time and also using the k2, k3 and k4 values at first we more closely defined, by the selection method, the magnitudes k 2 - k 4 and determined kl. Then in a similar way we more closely defined the magnitudes k5 - ks for the catalytic breakdown of H 2 0 2 and, finally, varying the concentration of AA, H 2 0 2 and Cu 2+ we evaluated kopt for the reactions (9)-(13) (Table 1). The kopt values optimally reproduce within the proposed scheme (1)-(13) the experiment presented in Figs 1 and 2 and Table 3. The solution of the forward kinetic problem [8] using kopt allowed us to give the time dependence of the concentrations of all the components of the system in the interval 0-180 min (Tables 2 and 3). Table 3 gives the results making it possible in different experimental conditions to evaluate the "steady" concentration of the active catalytic particle Cu 1+ and also compare the molecular mass of P A A calculated from the scheme (1)-(13) with that determined experimentally. The satisfactory agreement between the experimental and calculated values of the molecular mass of PAA allows

Synthesis of low MM polyacrylic acid

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TABLE3. EXPERIMENTALAND CALCULATEDPARAMETERSOF SOLUTION POLYMERIZATIONOF AA AT 353 K [H202]II x 10

[Cu 2+ Ill X 102

[AA]II

mole/l 3 3 3 3 3.3 3.3 1.7 1.7 3.3 3.3

[Cu I+ ]c~lcx 1013

MpAA cxp

MpAA talc

--->106 1800 5100 2600 9000 850 9600

---8 × 107 1900 5200 2060 10000 900 10000

mole/l 0 0.3 1.0 0 1.1 0.3 1.1 0.3 1.1 1.1

0 0 0 1.1 1.1 1.1 1.1 1.1 0.5 5.6

0 1.2 x 103 1.6 x 103 -5.6 1.6 7.7 2.1 5.6 5.5

one to select from Table 3 the necessary concentrations of the starting reagents to obtain P A A of specified MM. Mathematical analysis makes it possible from the overall scheme (1)-(13) to choose the minimum number of reactions adequately describing the kinetics of obtaining low molecular mass PAA. Table 2 compares the rates v of reactions (1)-(13) for t = 60 rain and different concentrations of A A and Cu 2+ and also the reaction rates (1)-(8) of breakdown of H202 for t = 7 s in absence of AA. From it it follows that the contribution of the reactions (3), (4), (7) and (8) to the overall process is negligibly small and they may be omitted in the calculations. For [AA] ~>0.5 mole/l its concentration does not influence the rate of expenditure of H202 on the reactions (2) and (6). The reaction rate (13) is 104-105 times higher than the reaction rate (12) and, therefore, for the given concentration ratio of n 2 0 2 and Cu 2+ termination of the polymerization chain comes about not through reaction (12) but through reaction (13) on the Cu 2+ ions. Taking all this into account the molecular mass of P A A was calculated from the formula MpAA ----"MAA 1"11/~'13where Vn and v13 are respectively the chain propagation and termination rates. The scheme of the process considered (reactions (1), (2), (5), (6) and (9)-(13)) is the scheme of the mechanism adequately reflecting the set and stage sequence of the reactions of the real process of obtaining low molecular mass PAA. It should be noted that the elementary reaction constants presented in Table I correspond to the temperature at which the experiment was run (353 K). For wider use of the scheme for calculating the MM of a polymer, knowledge of the energy parameters of the reactions (1)-(13) is required. The scheme describes the process of synthesis of a polymer in an inert atmosphere. In practice, synthesis is often conducted in air. In presence of 02 the polymerization rate drops through the reaction R" + O2--> R O E "

(14)

This leads to fall in the MM of the polymer. In air the rate of loss of peroxide oxygen in the mixture also decreases which is connected with accumulation of new peroxide derivatives RO2" + M--~ RO2M',

(15)

and also with fall in the concentration of Cu 1+ with fall in the concentration of R" radicals (reaction

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S . A . KULIKOVet al.

(13)). To allow for all these factors in conducting the process in presence of oxygen the reactions (14) and (15) need to be introduced into the scheme. The scheme presented (1)-(13) may be used for the approximate calculation of the MM of other polymers obtained on polymerization of water-soluble monomers (AN, MAA, MA, etc.). For this it is necessary to specify more closely on the basis of the experiment the constants of the reactions (9)-(13). Translated by A. Cnozv

REFERENCES 1. Kataliz. Issledovaniye gomogennykh protsessov (Catalysis. Investigation of Homogeneous Processes) (Ed. N. Balandin) p. 96, Moscow, 1957. 2. B. A. DOLGOPLOSK and Ye. I. TINYAKOVA, Okislitel'no-vosstanovitel'nye sistemy kak istochniki svobodnykh radikalov (Redox Systems as Free Radical Sources) p. 240, Moscow, 1972. 3. Idem, Generirovaniye svobodnykh radikalov i ikh reaktsii (Generation of Free Radicals and their Reactions) p. 252, Moscow, 1982. 4. A. K. BABKO and N. V. PYATNITSKH, Kolichestvennyi analiz (Quantitative Analysis) p. 401, Moscow, 1962. 5. K. T. DENISOV, Konstanty skorosti gomoliticheskikh zhidkofaznykh reaktsii (Rate Constants of Homolytic Liquid Phase Reactions) p. 711, Moscow, 1971. 6. J. K. KOCHI, Account. Chem. Res. 7: 351, 1974. 7. I. V. KHUDYAKOV and V. A. KUZ'MIN, Usp. khim. 47: 39, 1978. 8. L. S. POLAK, M. Ya. GOL'DENBYERG and A. A. LEVITSKII, Vychisliternye metody v khimicheskoi tekhnike (Computational Methods in Chemical Technology) p. 280, Moscow, 1984.