Modeling of the Inhibition Mechanism of Acrylic Acid Polymerization

Mar 15, 2006 - Kinetics and Modeling of Free-Radical Batch Polymerization of Nonionized Methacrylic Acid in Aqueous Solution. Michael Buback , Pascal ...
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Ind. Eng. Chem. Res. 2006, 45, 3001-3008

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Modeling of the Inhibition Mechanism of Acrylic Acid Polymerization Rujun Li and F. Joseph Schork* School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst DriVe, N.W., Atlanta, Georgia 30332-0100

Inhibitors such as MEHQ (monomethyl ether hydroquinone) and PTZ (phenothiazine) are added to acrylic acid in the shipping and storage process to prevent its spontaneous polymerization. Dissolved oxygen is also an strong inhibitor, and its presence in the solution enhances the inhibition effects of MEHQ. In this work, we developed a comprehensive mathematic model for the inhibition of acrylic acid polymerization and simulated the inhibition effects of oxygen and MEHQ on the polymerization of acrylic acid in batch and semibatch processes. The key kinetic parameters were obtained from the literature or estimated from experimental data in the literature. The model was able to predict most of the effects of inhibitors. Although the literature data we used failed to predict the synergistic inhibition effects of oxygen and MEHQ, the model was able to predict the effects. Simulation results show that oxygen is a strong inhibitor in both batch and semibatch reactors and does not act as a retarder as expected. MEHQ has a much stronger effect on polydispersity than on polymerization rate, especially in a semibatch reactor. Thus, MEHQ can be used to narrow the molecular weight distribution (MWD) without compromising too much on the monomer conversion and weight average molecular weight. 1. Introduction Poly(acrylic acid) is widely used commercially in the manufacture of coatings and flocculants. Due to its tendency to polymerize in shipping and storage, polymerization inhibitor is added to the monomer to prevent spontaneous polymerization. Among the types used, MEHQ (monomethyl ether hydroquinone) and PTZ (phenothiazine) are most common. When polymerized on a commercial scale, the monomer may or may not be purified to remove the inhibitor. The oxygen dissolved in the solution also acts as a strong inhibitor.1,2 It is found that without oxygen, the inhibition effect of MEHQ is very week. In the presence of oxygen, the inhibition of MEHQ is enhanced.3 PTZ itself is a much stronger inhibitor than MEHQ, and its effectiveness as an inhibitor is independent of oxygen level.3,4 The inhibition mechanism of oxygen on acrylic acid polymerization has been studied since the 1950s. Researchers proposed the mechanism for the inhibition of oxygen as three steps:5-7 (i) Oxygen reacts with the primary (carbon) radicals produced by the initiator and forms peroxy radicals. The rate constant of the reaction, kin,O2,1, is greater than that of propagation, kp. (ii) Monomer adds to the peroxy radicals in a much slower rate to form a random copolymer; at a higher oxygen level, the copolymer is essentially an alternating copolymer.8 (iii) The peroxy radicals easily terminate each other, produce dead copolymer, and release an oxygen molecule. MEHQ and other similar phenols react weakly with carbon radicals to inhibit the polymerization. MEHQ is therefore treated as a retarder.9 However, MEHQ is more likely to react with peroxy radicals and to form more stable radicals that may further terminate peroxy radicals. Thus, MEHQ prevents the formation of long oxygen-monomer copolymer chains and, therefore, reduces the consumption rate of oxygen and enhances the inhibition of oxygen. This is the so-called synergistic inhibition effect. * To whom correspondence should be addressed. Tel.: +1-404-8943274. Fax: +1-404-894-2866. E-mail: [email protected].

Kurland found that MEHQ can reduce the chain length of the copolymer from 30 to about 6.6 PTZ, on the other hand, has no enhancing effect on oxygen. Levy3 found that carbon radicals react with PTZ faster than with oxygen, and thus, PTZ is a stronger inhibitor than oxygen. The presence of oxygen accelerates the consumption rate of PTZ due to some inhibitionunrelated reactions between oxygen and PTZ. Gladyshev et al.10 estimated from steady state the associated kinetic parameters for the oxygen inhibition mechanism with 12 possible reaction paths. Schulze and Vogel7 obtained the live oxygen-monomer concentration by assuming the radicals are in a quasi-steady state. They also obtained the critical oxygen concentration when the addition rates of oxygen and monomer, the primary radicals, are equal. However, a detailed model which includes oxygen, MEHQ, and/or PTZ has not been published. The purposes of this work are to develop a detailed mathematical modeling and simulation based on the accepted inhibition mechanism, to obtain key parameter values from available experiment data, and to investigate the effects of the inhibitors on the polymerization process. 2. Mechanism Acrylic acid polymerization is a typical free radical polymerization. It involves the following typical steps:11 (i) activation and initiation. Persulfate is a popular thermal initiator. It decomposes into two free radicals at high temperature, which can be represented as kd

I 98 2R

(1)

where I represents persulfate and R represents the primary radical SO/4 produced by thermal decomposition of persulfate. The monomer reacts with the radical to initiate a live chain: ki

R + M 98 P1

10.1021/ie0512439 CCC: $33.50 © 2006 American Chemical Society Published on Web 03/15/2006

(2)

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where M and P1 are monomer and a live chain with one monomer unit, respectively. (ii) propagation. Monomer units add to the live chain: kp

Pi + M 98 Pi+1

ktd

Pi1(O2)l1 + Pi2 98 Mi1(O2)l1 + Mi2

(12)

ktd

Pi1(O2)l1M + Pi2 98 Mi1(O2)l1M + Mi2

(3)

(13)

ktd

where i is the number of monomer units in the chain. (iii) termination. A radical or live polymer chain can be terminated by disproportionation, where the β hydrogen of one radical is transferred to another radical, forming one saturated dead polymer and one unsaturated dead polymer, or more rarely by combination, when two radicals react to form one dead polymer. Termination by Disproportionation

Pi1(O2)l1M + Pi2(O2)l2M 98 Mi1(O2)l1M + Mi2(O2)l2M (14) (ii) Inhibition by MEHQ in the presence of oxygen6,12 kin,MEHQ,1

Pi[R] + MEHQ 98 Q

(15)

kin,MEHQ,2

ktd

Pi1 + Pi2 98 Mi1 + Mi2

Pi(O2)l + MEHQ 98 Q/

(4)

(16)

kin,MEHQ,3

Pi(O2)l + Q/ 98 Q

Termination by Combination ktc

Pi1 + Pi2 98 Mi1+i2

(5)

where Mi is a dead chain with i units of monomer. (iv) chain transfer. The radical center can transfer to the monomer, the solvent, or another polymer chain to start a new radical, while the old radical becomes a dead polymer. Chain transfer reactions are important for some polymers at higher conversion, have little to do with inhibition, which takes place at the beginning of the reaction, and therefore are not considered in this work. (v) inhibition. Oxygen reacts with radicals and produces a peroxy radical or an oxygen-ended live monomer-oxygen copolymer Pi(O2)l. Here, i and l are the numbers of monomer and -OO- units in the copolymer, respectively. This copolymer reacts slowly with monomer to form Pi+1(O2)lM, a monomer-ended live monomer-oxygen copolymer, but terminates faster to form dead copolymers and to release an oxygen molecule. MEHQ itself reacts with carbon radicals at a very small rate, but it can react much faster with peroxy radicals to form a relatively stable radical Q*; thus, its inhibition is enhanced in the presence of oxygen. Q* can further react with peroxy radicals and becomes inactive. On the other hand, oxygen can react with PTZ in some inhibition-unrelated reactions and consume PTZ. The detailed inhibition mechanism for oxygen, MEHQ, and PTZ is as follows: (i) Inhibition by oxygen6 Propagation

where Q/ is a MEHQ radical and Q is a dead species. (iii) Inhibition by PTZ3,4 kin,PTZ,1

Pi(R) + PTZ 98 Q

Pi[R] + O2 98 Pi(O2)1[P0(O2)1]

(6)

kin,O

2,1

Pi(O2)lM + O2 98 Pi+1(O2)l+1

(7)

kp

Pi(O2)lM + M 98 Pi+1(O2)lM

(8)

(18)

kin,PTZ,2

PTZ + O2 98 Z

(19)

3. Mathematic Model The model equations for batch and semibatch solution polymerization reactors can be derived for the mechanism. For batch reactors, the feed flow terms for the monomer, initiator, and inhibitors Fi are set to zero. 3.1. Reactants. Monomer

dCM

)-

dt

CM dV

∞ FM CM,i - [kiCR + kp( Pi + V i)0

∑

+

V dt ∞ ∞

∑ ∑ i)0 l)0

∞ ∞

Pi(O2)lM) + kin,O2,2

∑ ∑Pi(O2)l]CM i)0 l)0

(20)

Initiator

CI dV FI dCI )+ CI,i - kdCI dt V dt V

kin,O

2,1

(17)

(21)

Primary radical R

dCR CR dV )+ 2kdfCI - kiCRCM - (kin,O2,1CO2 + dt V dt kin,MEHQ,1CMEHQ + kin,PTZ,1CPTZ)CR (22) Inhibitor O2

kin,O

2,2

Pi(O2)l + M 98 Pi(O2)lM

(9)

Termination

dCO2 dt

kin,O

2,3

Pi1(O2)l1 + Pi2(O2)l2 98 Mi1(O2)l1-1OH + Mi2(O2)l2-1 ) O + O2 (10)

)-

CO2 dV

+

V dt ∞ ∞

∑ ∑ i)0 l)0

∑

∞ ∞

Pi(O2)lM] + 1/2kin,O2,3[

∑ ∑Pi(O2)l]2 i)0 l)1 kin,PTZ,2CO2CPTZ (23)

ktd

Pi1(O2)l1 + Pi2(O2)l2M 98 Mi1(O2)l1 + Mi2(O2)l2M (11)

F O2 ∞ CO2,i - kin,O2,1CO2[CR + Pi + V i)0

Inhibitor MEHQ

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dCMEHQ

)-

CMEHQ dV

dt

V (CR +

∞

dt

+

FMEHQ CMEHQ,i - kin,MEHQ,1CMEHQ V

3.3. Moment Equation. We define the moments where µ0, ∞

∞ ∞

Pi) - kin,MEHQ,2CMEHQ∑∑Pi(O2)l ∑ i)0 i)0 l)1

µm )

(24)

im P i ∑ i)0

(31)

Inhibitor PTZ

dCPTZ

)-

dt

∞

CPTZ dV

FPTZ + CPTZ,i - kin,PTZ,1(CR + dt V

V

λm )

2

(25)

3.2. Population Balance Equations. The population balance equations for the live and dead polymers, as well as the monomer-oxygen copolymer, can also be derived. Live polymer

)-

Pi dV

dt

V dt

∞

∑ i)0

Pi -

∞ ∞

∑ ∑[Pi(O2)l + Pi(O2)lM] i)0 l)1

ktdPi

(26)

Dead polymer

)-

dt

∞ ∞ 1 Pi-i1 + ktdPi Pi + ktcPi1 V dt 2 i1)0 i)0

Mi dV

∑

∑

(27)

Monomer-oxygen copolymer that ended with oxygen, Pijk(O2)l

dPi(O2)l

)

dt -

Pi(O2)l dV V

dt

+ kin,O2,1CO2Pi-1(O2)l-1M - kin,O2,2CMPi(O2)l ∞

∞

∞

∞

∞

Pi +∑∑Pi(O2)lM] ∑ ∑Pi(O2)l - ktdPi(O2)l[∑ i)0 l)1 i)0 i)0 l)1

-kin,O2,3Pi(O2)l

-(kin,MEHQ,2CMEHQ + kin,MEHQ,3CQ/)Pi(O2)l

(28)

Monomer-oxygen copolymer that ended with monomer, Pijk(O2)mM

dPi(O2)lM

Pi(O2)lM dV

- kpCM[Pi(O2)lM dt V dt Pi-1(O2)l] - kin,O2,1CO2Pi(O2)lM + kin,O2,2CMPi-1(O2)l )-

∞

∞ ∞

Pi + ∑∑(Pi(O2)l + Pi(O2)lM)] ∑ i)0 i)0 l)1

ktdPi(O2)lM[

(29)

The population balance equation for Q/

dCQ/ dt

)-

∞ ∞

µO,mn )

lminPi(O2)l ∑ ∑ i)0 l)0

(33)

∞ ∞

µM,mn )

lminPi-1(O2)lM ∑ ∑ i)0 l)0

(34)

+ kpCM(Pi-1 - Pi) - (kin,O2,1CO2 +

kin,MEHQ,1CMEHQ + kin,PTZ,1CPTZ)Pi - (ktc + ktd)Pi

dMi

(32)

∞

Pi)CPTZ - kin,PTZ,2CO CPTZ ∑ i)0

dPi

im M i ∑ i)0

CQ/ dV V dt

+ (kin,MEHQ,2CMEHQ ∞ ∞

kin,MEHQ,3CQ/)

∑ ∑Pi(O2)l i)0 l)1

(30)

λ0, µO,00, and µM,00 are the concentrations of live homopolymer, dead homopolymer, oxygen-ended copolymer, and monomerended copolymer, respectively. The terms µ1 and λ1 are the total monomer concentrations (masses) of the live and dead homopolymers. The terms µO,10 and µO,01 are the oxygen and monomer concentrations of the oxygen-ended copolymer. The terms µM,10 and µM,01 are the oxygen and monomer concentrations of the monomer-ended copolymer. We obtain the moment equations by summing up the corresponding population balance equations (PBEs) from zero to infinity.

µ0 dV dµ0 )- (kin,O2,1CO2 + kin,MEHQ,1CMEHQ + dt V dt kin,PTZ,1CPTZ)µ0 - (ktc + ktd)(µ0)2 - ktdµ0(µO,00 + µM,00) (35) µ1 dV dµ1 )- (kin,O2,1CO2 + kin,MEHQ,1CMEHQ + dt V dt kin,PTZ,1CPTZ)µ1 + kpµ0CM - (ktc + ktd)µ1µ0 - ktdµ1(µO,00 + µM,00) (36) dµ2 µ2 dV )- (kin,O2,1CO2 + kin,MEHQ,1CMEHQ + dt V dt kin,PTZ,1CPTZ)µ2 + kp(µ0 + 2µ1)CM - (ktc + ktd)µ2µ0 ktdµ2(µO,00 + µM,00) (37) dλ0 λ0 dV )+ (1/2ktc + ktd)(µ0)2 dt V dt

(38)

dλ1 λ1 dV )+ (ktc + ktd)µ1µ0 dt V dt

(39)

dλ2 λ2 dV )+ ktc[µ2µ0 + (µ1)2] + ktdµ2µ0 dt V dt

(40)

dµO,00 µO,00 dV )+ kin,O2,1CO2(µM,00 + CR + µ0) dt V dt kin,O2,2CMµO,00 - kin,O2,3(µO,00)2 - ktdµO,00(µ0 + µM,00) (kin,MEHQ,2CMEHQ + kin,MEHQ,3CQ/)µO,00 (41)

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dµO,10 µO,10 dV )+ kin,O2,1CO2(µM,10 + µM,00 + CR + dt V dt µ0) - kin,O2,2CMµO,10 - kin,O2,3µO,10µO,00 - ktdµO,10(µ0 + µM,00) - (kin,MEHQ,2CMEHQ + kin,MEHQ,3CQ/)µO,10 (42) dµO,01 µO,01 dV )+ kin,O2,1CO2(µM,01 + CR + µ1) dt V dt kin,O2,2CMµO,01 - kin,O2,3µO,01µO,00 - ktdµO,01(µ0 + µM,00) (kin,MEHQ,2CMEHQ + kin,MEHQ,3CQ/)µO,01 (43) µM,00 dV dµM,00 )- kin,O2,1CO2µM,00 + kin,O2,2CMµO,00 dt V dt ktdµM,00(µ0 + µO,00 + µM,00) (44) dµM,10 µM,10 dV )- kin,O2,1CO2µM,10 + kin,O2,2CMµO,10 dt V dt ktdµM,10(µ0 + µO,00 + µM,00) (45) µM,01 dV dµM,01 )- kin,O2,1CO2µM,01 + kin,O2,2CM(µO,01 + dt V dt µO,00) - ktdµM,01(µ0 + µO,00 + µM,00) (46) dCQ/ CQ/ dV )+ (kin,MEHQ,2CMEHQ dt V dt kin,MEHQ,3CQ/)µO,00 (47) 3.4. Polymer Properties. Polymer properties such as molecular weights and polydispersity can be computed from the moments. The number and weight average molecular weights M h n and M h w can be calculated from the first three moments of the dead polymer

M hn)

λ1 λ0

(48)

M hw)

λ2 λ1

(49)

and the polydispersity (Pd) is the ratio of M h w and M h n. Another important property is the chain length of the monomer-oxygen copolymers. The number of oxygen units in the oxygen-ended copolymer is µO,10/µO,00, and the number of monomer units is µO,01/µO,00. Similarly, the number of oxygen units in the monomer-ended copolymer is µM,10/µM,00, and the number of monomer units is µM,01/µM,00. 4. Simulation The resultant ordinary differential equations (ODEs) then can be solved with known initial and/or feed conditions for batch and/or semibatch reactors and kinetic parameters using an appropriate ODE solver. We used Matlab/Simulink with the “ode15s” solver, which is a variable-order stiff-ODE solver based on the numerical differentiation formulas, and found it most efficient for this problem. 4.1. Recipe. In this work, we studied the polymerization of acrylic acid in aqueous solution. There are few papers with experimental data in the open literature. For instance, the experiments of Schulze and Vogel7 and Levy3,4 mimic the effects of inhibitors under storage conditions of acrylic acid where an initiator is not added into the system, while the experiments of Kurland6 and Cuite et al.12 are for normal batch

polymerization, with AIBN and Na2(SO4)2 as initiators, respectively. The emphasis of this paper is on the actual polymer manufacturing process not on the storage or shipping of the monomer. We were not able to find experiment data for the effects of PTZ in such a process, so this paper will focus on oxygen and MEHQ only. Cutie et al.12 performed comprehensive experiments on the inhibition of oxygen and MEHQ, so their experimental data can be used to estimate key kinetic parameters. The simulated polymerization process in this paper follows those of Cutie et al.12 and two other papers from the same group with similar experiment conditions.13,14 The base solution is a 33% solid (based on neutralized monomer), 65% neutralization (by sodium carbonate), and 1600 ppm initiator (sodium persulfate, based on monomer) solution. Sodium persulfate and MEHQ concentrations were varied from the base solution to demonstrate the effect of the two species, while other conditions remained constant. The reactor temperature was 55 °C and was held constant. The reactor was purged with pure nitrogen throughout the reaction so that the monomer has no contact with oxygen other than that originally dissolved in the water. 4.2. Estimation of Oxygen Concentration for the Deoxygenated Solution. The base solution was aerated in oxygen for 70 min to allow the solution to be saturated with oxygen. It was also deoxygenated by bubbling in nitrogen for 15, 30, and 60 min, respectively, to test the effect of different oxygen levels on the monomer conversion.12 Cutie et al. showed that the conversion vs time curve is essentially the same for 15-, 30and 60-min deoxygenation, with an unexpected induction time of approximately 4 min. The causes for the induction not vanishing with deoxygenation might be the following: (i) oxygen was not completely removed from the solution, possibly due to leakage or (ii) there were other unknown species and/or factors acting as inhibitors. Here, we assumed that the first was the main cause and ignore the second one. Because typical industrial practice utilizes a deoxygenation process, it is important to have an estimate of the residual oxygen after the deoxygenation process. We determined this parameter by matching our simulation to the experimental data of Cutie et al. (Figure 4 of Cutie et al.12). In our simulation, we assumed that the oxygen saturation and deoxygenation processes take place at 25 °C and that oxygen only dissolves in water, not in the monomer. Thus we can compute the oxygen concentration from the oxygen solubility data. The kinetic parameters essential to the simulation are kd, kp, ktc + ktd, kin,O2,1, and kin,O2,2. The first three parameters affect the shape of the conversion vs time curve, while the last two determine the induction time, the time shift of the curve from the origin. The term kin,O2,3 is believed to be the same as ktc + ktd,7 and was not adjusted. Henton et al.13 (the same research group as Cutie et al.) estimated kd at 55 °C to be 9.15 × 10-4 min-1 for the same condition. The ktc + ktd value was adopted from Gromov et al.,15 and it is 8 × 108 L‚mol-1‚s-1. The kz value (kin,O2,1/kp) for a similar monomer methacrylic acid is about 33 000.9 In this work, we used a close number 30 000 and kept it unadjusted. The terms kp and kin,O2,2 were first varied to match the shape and induction time of the experimental conversion vs time curve for the saturated oxygen case (squares in Figure 1). When a set of kp and kin,O2,2 values were found to match the curve, then the oxygen concentration was varied to match the deoxygenated curve (diamonds in Figure 1). It was found that when kp and kin,O2,2 were 6.1 × 106 L‚mol-1‚min-1 and 105 L‚mol-1‚min-1, respectively, with 18% of saturated oxygen, the simulation (dotted line in Figure 1) yielded a good fit to the experimental conversion vs time curve for the deoxygenated solution case (diamonds in Figure 1). The

Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006 3005 Table 1. Estimated Parameters from Cutie et al.12 kd 9.15 × 10-4 kin,O2,1 (3 × 104)kp kin,MEHQ,1 (2.7 × 10-5)kp kp 2.32 × 106 kin,O2,2 60 kin,MEHQ,2 200kin,O2,2 ktc + ktd 1.94 × 1010 kin,O2,3 1.94 × 1010 kin,MEHQ,3 (104)kin,O2,3 a

Figure 1. Estimation of residual oxygen concentration for the deoxygenated solution. In the figure, squares and diamonds are experimental data for saturated oxygen and 60-min deoxygenation, respectively.12 Solid, dashed, dashed-dotted, and dotted lines are simulation results without oxygen, without oxygen shifted by 4 min, with saturated oxygen, and with 18% oxygen, respectively.

simulated 18% oxygen conversion vs time curve overlapped with that of the case in the absence of oxygen shifted by 4 min (dashed line), the induction time for the deoxygenated case, and both curves matched the experimental data nicely for lower conversion where induction matters. The residual oxygen level might be overestimated due to the aforementioned reasons; however, it is a good approximation of the combined effect of oxygen and other unknown inhibition factors. Therefore, this value was used for the rest of the simulation for the deoxygenated solution case. 5. Simulation Results and Discussion 5.1. Estimation and Effects of Kinetic Parameters. Cutie et al.12 performed several experiments for different initiator and MEHQ concentrations for the polymerization of deoxygenated acrylic acid solution. Unfortunately, their data in Figures 4 (plot of conversion vs time at different deoxygenation levels for the base recipe) and 5 (plot of conversion vs time with 30-min deoxygenation for three other persulfate concentrations) of the paper12 do not agree. In Figure 4 of the paper,12 the initial persulfate concentration is 1600 ppm (based on acrylic acid), or 0.001 66 mol‚L-1. When we inserted the conversion vs time curve for the 60-min deoxygenated solution in Figure 4 of the paper12 into Figure 5 of the paper,12 the curve falls between the curves of persulfate concentrations 0.014 and 0.002 67 M, rather than between those of 0.002 67 and 0.000 665 M, where it should be. Without any knowledge of the causes of this inconsistency, we re-estimated the kinetic parameters using the data from Figures 5 (for kp, ktc + ktd, and oxygen-related inhibition parameters) and 6 (for MEHQ-related parameters) of Cutie et al.12 and used the newly estimated parameter values, together with the residual oxygen level of 18% estimated from Figure 4 of Cutie et al.,12 in the rest of the simulation. The residual oxygen level could not be re-estimated due to the lack of experimental data with saturated oxygen for the aforementioned reaction conditions. Therefore, we still use 18%, the value estimated from Figure 4 of Cutie et al.,12 as the residual oxygen level in the deoxygenated case. Only two curves in Figure 5 of Cutie et al. with persulfate concentrations of 0.006 65 and 0.002 67 M, respectively, were used for the estimation, and the third curve with a persulfate concentration of 0.0141 M was

The units of the displayed values are moles, liters, and minutes.

not used because the persulfate concentration was so high that the reaction time was too short to be estimated accurately from the figure. The nominal values for the key kinetic parameter values were taken from the literature where they were available and believed to be accurate. The value for kd is taken from Henton et al.,13 which was done by the same group and for the same condition used in Cutie et al.12 and in this work. The term kin,O2,1 was taken from Odian9 for a similar monomer, methyl methacrylate, and was rounded up. The value for this parameter from Schulze and Vogel7 was not used because their value was almost 6 orders of magnitude larger than kp, more than 1 order of magnitude larger than Odian.9 We did not attempt to adjust the above parameters. They were kept constant because we believe that the data sources are reliable, and experiment data can be matched without adjusting them. The initial values of kp and ktc + ktd were from Gromov.15 The initial values of kin,O2,2 and kin,O2,3 were taken from Schulze and Vogel.7 The initial values for the MEHQ-related kinetic parameters were determined based on the analysis of the kinetics which yields the following inequalities.

kin,MEHQ,1 , kp , kin,O2,1

(50)

kin,MEHQ,2 . kin,O2,2

(51)

kin,MEHQ,2 . kin,MEHQ,1

(52)

These parameter were adjusted to match the shape and induction time of the monomer conversion vs time curve. We found that kin,O2,3 has no effect on the conversion. The parameter kin,MEHQ,1, the rate constant for the MEHQ-alone inhibition, affects the shape of the monomer conversion vs time curve. The larger the value of kin,MEHQ,1, the smaller the conversion because MEHQ will react faster with the primary radicals. The parameter kin,MEHQ,2 determines the synergistic inhibition effect, and it was found that it has insignificant effects on conversion when it is of the same magnitude as kin,O2,2, where the inhibition of oxygen alone still dominates, and that it will affect the induction time when it is much larger than kin,O2,2. The ratio of kin,O2,2 and kin,MEHQ,2 determines the magnitude of the synergistic inhibition effect. Because the monomer concentration is much larger than that of MEHQ, the synergistic inhibition effect, shown as increased induction time, can only be seen when kin,MEHQ,2 . kin,O2,2. However, the data from Figure 5 of Cutie et al.12 (shown in Figure 3 of this paper as the experimental data) failed to show this effect even when the MEHQ concentration is 4844 ppm, about 24 times higher than the commercial standard. Therefore, only a range of kin,MEHQ,2, rather than a value, can be estimated and the synergistic effect cannot be predicted. The estimated range is 2kin,O2,2 to 200kin,O2,2. We used the maximum value 200kin,O2,2. For a system with pronounced synergistic inhibition effects, a much larger kin,MEHQ,2 is expected. We also found that kin,MEHQ,3 has no significant effects on the monomer conversion, and therefore, it was not adjusted. The newly estimated parameter values are listed in Table 1. We found that our simulation matched the experiment well using these parameters for the cases without MEHQ (Figure 2) and with 4844 ppm MEHQ (based on monomer, Figure 3).

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Figure 2. Effects of initiators on the monomer conversion.

Figure 4. Effects of kin,MEHQ,2 on the oxygen concentration and monomer conversion for a batch reactor with an initial initiator concentration 0.001 29 M. The reaction conditions are the same as those in Figure 3 except that the initial MEHQ level is 200 ppm.

Figure 3. Effects of MEHQ on the monomer conversion. The MEHQ concentration is 4844 ppm.

Because the experimental data do not show the effect of MEHQ on the induction time, the set of parameters listed in Table 1 is not able to predict the synergistic inhibition effect, which contradicts other researchers’ findings. However, our model can predict this effect if a larger kin,MEHQ,2 is used. If kin,MEHQ,2 is increased, for instance, to (2 × 104)kin,O2,2, this effect is noticeable, and when kin,MEHQ,2 is increased to (2 × 105)kin,O2,2, the effect is very strong. Figure 4 shows that when kin,MEHQ,2, at a 200-ppm MEHQ concentration, the oxygen consumption rate can be reduced by almost half when kin,MEHQ,2 increases from 2kin,O2,2 to 200kin,O2,2 (Figure 4a). From Figure 4b, we see that kin,MEHQ,2 only changes the induction time without changing the shape of the conversion curve. 5.2. Chain Length of the Oxygen-Monomer Copolymer. Both copolymers Pi(O2)l and Pi(O2)lM are basically alternating copolymers, and they can change back and forth from each other by adding oxygen or monomer to the chain. So essentially, the two copolymers should have the same chain length and composition, except the one monomer or oxygen molecule difference. This is verified by the simulation. The effect of MEHQ on the chain length or the numbers of oxygen and monomer units of the copolymer chain can be illustrated in Figure 5. In the figure, curves 1, 1′, and 1′′ refer to the numbers of -O-O- units per chain in the oxygen-ended copolymer, the number of monomer units per chain in the oxygen-ended

Figure 5. Effects of kin,MEHQ,2 on the copolymer chain lengths for a batch reactor with an initial initiator concentration 0.001 29 M. The reaction conditions are the same as those in Figure 3 except that the initial MEHQ level is 200 ppm.

copolymer, and the number of monomer units per chain in the monomer-ended copolymer for the case of kin,MEHQ,2 ) 0. The number of -O-O- units per chain in the monomer-ended copolymer is the same as curve 1. Curves 2, 2′, and 2′′ are for kin,MEHQ,2 ) (2 × 104)kin,O2,2, and 3, 3′, and 3′′ are for kin,MEHQ,2 ) (2 × 105)kin,O2,2. A larger kin,MEHQ,2 reduces the number of oxygen or monomer units in a chain by transferring the live copolymer to a species Q/ that could not have the capability of further growth. The numbers of oxygen and monomer units in oxygen-ended copolymers are essentially the same before oxygen is depleted, and the difference increases dramatically when oxygen is depleted because reaction 8 begins to dominate over reaction 7. The results agree with the experimental data of Kurland.6 5.3. Effects of Oxygen and MEHQ on the Polymerization in a Semibatch Process. Commercially, poly(acrylic acid) is manufactured in a semibatch process, with monomer, initiator, and/or neutralizer continuously feeding into the reactor. We simulated a semibatch process using the same recipe as for the batch reactor. The reactor is started empty, and three feed flows of monomer, initiator, and neutralizer are regulated to keep the

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Figure 6. Comparison of oxygen (a) and monomer conversion (b) profiles for batch and semibatch reactors at three different oxygen levels. In the figure, 1, 2, and 3 indicate oxygen free, 18% oxygen, and fully saturated with oxygen conditions in a batch reactor, respectively, and 1′, 2′, and 3′ indicate the same oxygen levels for a semibatch reactor. The solid lines are for the batch reactor, and the dashed lines are for the semibatch reactor.

flow rate ratios constant throughout the reaction. The feed time is 40 min. The reaction is carried out for another 100 min after the end of the feed interval. The total reaction time is, then, 140 min, consistent with the batch reactor. Because a batch process is the limiting case of a semibatch process when feed flow rates reach infinity, we should expect slower dynamics for a semibatch process. 5.3.1. Effects of Oxygen. Three different cases were simulated to compare the inhibition effects of oxygen on polymerization in batch and semibatch processes: oxygen free, 18% oxygen, and fully saturated oxygen. In a semibatch reactor, oxygen, as well as other species, is consumed slower than in a batch reactor, despite the fact that oxygen is fed into the reaction continuously; when the oxygen level in the feed is 18%, its concentration still goes to zero before the the feed interval is completed (Figure 6a). Thereafter, the oxygen dissolved in the water is reacted instantaneously by excessive primary radicals once it is fed into the reactor. Therefore, oxygen does not act as a retarder in a semibatch reactor as we expected and still acts as an inhibitor as in a batch reactor. For the same oxygen level, a semibatch reactor has a higher induction time due to its slow dynamics. The slower the flow rate, the longer the induction time. From the conversion vs time plot (Figure 6b), we can see that the discontinuation of feeds causes the conversion to increase faster for the 18% oxygen level case. This is because the fresh feed has a larger monomer concentration and a lower free radical concentration than the solution already in the reactor. For the saturated oxygen case, the polymerization does not start until the feeds are stopped, so the discontinuation of feeds has no effects on the polymerization. The initial weight average molecular weight of the polymer (M h w) in a semibatch reactor is similar to that is a batch reactor(Figure 7a), and it will yield a similar final value as the batch reactor if the reaction time is long enough. The polydispersity (Pd) of the polymer, on the other hand, is greatly affected by the oxygen level and the type of reactor. For both reactors, oxygen suppresses the increase of Pd. In a semibatch reactor, Pd increases much slower than that in a batch reactor (Figure 7b), and the longer the reaction time, the larger the difference. Deoxygenation will enhance the difference. So, using the same recipe with the same total reaction time, semibatch reactors may

Figure 7. Comparison of M h w (a) and Pd (b) profiles for batch and semibatch reactors at three different oxygen levels. In the figure, 1, 2, and 3 indicate oxygen free, 18% oxygen, and fully saturated with oxygen conditions in a batch reactor, respectively, and 1′, 2′, and 3′ indicate the same oxygen levels for a semibatch reactor. The solid lines are for the batch reactor, and the dashed lines are for the semibatch reactor.

Figure 8. Comparison of oxygen (a) and monomer conversion (b) profiles for batch and semibatch reactors at three different oxygen levels and two different MEHQ levels (0 and 200 ppm). In the figure, 1, 2, and 3 indicate oxygen free, 18% oxygen, and fully saturated with oxygen conditions in a batch reactor, respectively, and 1′, 2′, and 3′ indicate the same oxygen levels for a semibatch reactor. The solid, dashed, dashed-dotted, and dotted lines are for batch without MEHQ, semibatch without MEHQ, batch with MEHQ, and semibatch with MEHQ processes, respectively.

yield a similar M h w but a much smaller Pd, and the higher the oxygen level, the lower the value of Pd. 5.3.2. Effects of MEHQ. As mentioned earlier, the parameters obtained from the experimental data of Cutie et al. failed to show the synergistic inhibition effects of MEHQ and oxygen for a batch reactor, although the retardation of the polymerization can be clearly seen. For a semibatch reactor, if the same kinetic parameters are used, similar conclusions can be drawn. Figure 8 plots the effects of MEHQ on oxygen concentration and monomer conversion for a concentration of 200 ppm MEHQ, the typical commercial usage level, while the other conditions are the same as in Figures 6 and 7. The oxygen concentration is not affected by MEHQ due to the aforementioned reason. Monomer conversion, however, is reduced by MEHQ, a clear indication of retardation. Another simulation not shown here

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not able to predict the synergistic inhibition effects of MEHQ and oxygen; these effects can be predicted by the model if kin,MEHQ,2 is allowed to be much larger than kin,O2,2. Simulation results show that oxygen exerts a strong inhibition on both batch and semibatch reactors and does not act as a retarder in semibatch reactors as was expected. MEHQ has a much stronger effect on polydispersity than on the polymerization rate, especially in a semibatch reactor. MEHQ can be used to narrow the MWD without compromising too much on the monomer conversion and M h w. Literature Cited

Figure 9. Comparison of M h w (a) and Pd (b) profiles for batch and semibatch reactors at two different oxygen (18% and saturation) and MEHQ (0 and 200 ppm) levels. In the figure, 2 and 3 indicate 18% oxygen and fully saturated with oxygen conditions in a batch reactor, respectively, and 2′ and 3′ indicate the same oxygen levels for a semibatch reactor. The solid, dashed, dashed-dotted, and dotted lines are for batch without MEHQ, semibatch without MEHQ, batch with MEHQ, and semibatch with MEHQ processes, respectively.

with 4844 ppm MEHQ shows that when the reaction ends the monomer conversion can be reduced by half for all cases. The reactor type has no significant effect on the magnitude of the retardation. The effects of MEHQ on M h w and Pd are more significant (Figure 9). MEHQ increases M h w for all cases because it destroys radicals and live polymer chains. The M h w at the end of the reaction is about 20 higher with MEHQ than that without it for both batch and semibatch reactors. MEHQ reduces Pd more significantly. A concentration of 200 ppm MEHQ reduces the final Pd from 3.2 to 2.5 for the semibatch reactor with 18% oxygen, while, without MEHQ, the final Pd is reduced from 3.2 to 2.7 when the oxygen level changes from 18% to saturation. Due to both the slower dynamics of the semibatch reactor and the effect of MEHQ, the Pd for the final polymer is much smaller. Thus, MEHQ can be used to narrow the molecular weight distribution (MWD) without compromising too much on the monomer conversion and M h w. 6. Conclusion A comprehensive model for oxygen and MEHQ inhibition was developed, and the inhibition effects of oxygen and MEHQ on acrylic acid free radical polymerization in batch and semibatch reactors were studied through simulation. The key kinetic parameters were obtained from the literature and from matching experimental data. The model was able to predict most of the effects of the inhibitors. Although due to the limitation of the obtained experimental data, the estimated parameters were

(1) Barnes, C. E. Mechanism of vinyl polymerization. I. Role of oxygen. J. Am. Chem. Soc. 1945, 67, 217. (2) Barnes, C. E.; Elofson, R. M.; Jones, G. D. Role of oxygen in vinyl polymerization. II. Isolation and structure of the peroxides of vinyl compounds. J. Am. Chem. Soc. 1950, 72, 210. (3) Levy, L. B. Inhibition of acrylic-acid polymerization by phenothiazine and para-methoxyphenol. J. Polym. Sci. Polym. Chem. 1985, 23, 1505-1515. (4) Levy, L. B. Inhibition of acrylic-acid polymerization by phenothiazine and para-methoxyphenol. 2. Catalytic inhibition by phenothiazine. J. Polym. Sci. Polym. Chem. 1992, 30, 569-576. (5) Schulz, G. V.; Henrici, G. Kinetik der polymerisationsreaktionen. 22. Reaktionskinetik der polymerisationshemmung durch molekularen sauerstoff (versuche mit methylmethacrylat). Makromol. Chem. 1956, 189, 437-454. (6) Kurland, J. J. Quantitative aspects of synergistic inhibition of oxygen and para-methoxyphenol in acrylic-acid polymerization. J. Polym. Sci. Polym. Chem. 1980, 18, 1139-1145. (7) Schulze, S.; Vogel, H. Aspects of the safe storage of acrylic monomers: Kinetics of the oxygen consumption. Chem. Eng. Technol. 1998, 21, 829-837. (8) Mayor, F. R.; Miller, A. A. The oxidation of unsaturated compounds. VII. The oxidation of methacrylic esters. J. Am. Chem. Soc. 1958, 80, 24932496. (9) Odian, G. Principles of Polymerization, 4th ed.; John Wiley & Sons: New York, 2004. (10) Gladyshev, G. P.; Kitaeva, D. K.; Popov, V. A.; Penkov, E. I. Increase of weak inhibitor effectiveness in processes of deep polymerization in the presence of oxygen. Proc. Acad. Sci. USSR 1974, 215, 898-901. (11) Schork, F. J.; Deshpande, P. B.; Leffew, K. W. Control of Polymerization Reactors; Marcel Dekker Inc.: New York, 1993. (12) Cutie, S. S.; Henton, D. E.; Powell, C.; Reim, R. E.; Smith, P. B.; Staples, T. L. The effects of mehq on the polymerization of acrylic acid in the preparation of superabsorbent gels. J. Appl. Polym. Sci. 1997, 64, 577589. (13) Henton, D. E.; Powell, C.; Reim, R. E. The decomposition of sodium persulfate in the presence of acrylic acid. J. Appl. Polym. Sci. 1997, 64, 591-600. (14) Cutie, S. S.; Smith, P. B.; Henton, D. E.; Staples, T. L.; Powell, C. Acrylic acid polymerization kinetics. J. Polym. Sci., Part B: Polym. Phy. 1997, 35, 2029-2047. (15) Gromov, V. F.; Galperina, N. I.; Osmanov, T. O.; Khomikovskii, P. M.; Abkin, A. D. Effect of solvent on chain propagation and termination reaction-rates in radical polymerization. Eur. Polym. J. 1980, 16, 529535.

ReceiVed for reView November 9, 2005 ReVised manuscript receiVed February 10, 2006 Accepted February 20, 2006 IE0512439