Kinetics and Modeling of Free-Radical Batch Polymerization of

Sep 30, 2008 - and Department of Chemical Engineering, Dupuis Hall, Queen's UniVersity, ... partially neutralized methacrylic acid (MAA) in solution,6...
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Ind. Eng. Chem. Res. 2008, 47, 8197–8204

8197

Kinetics and Modeling of Free-Radical Batch Polymerization of Nonionized Methacrylic Acid in Aqueous Solution Michael Buback,*,† Pascal Hesse,† Robin A. Hutchinson,*,§ Peter Kasa´k,‡ Igor Lacı´k,‡ Marek Stach,‡ and Inga Utz§ Institute of Physical Chemistry, UniVersity of Go¨ttingen, Tammannstrasse 6, D-37077, Go¨ttingen, Germany, Polymer Institute of the SloVak Academy of Sciences, Du´braVska´ cesta 9, 842 36, BratislaVa, SloVak Republic, and Department of Chemical Engineering, Dupuis Hall, Queen’s UniVersity, Kingston, Ontario K7L 3N6, Canada

The batch free-radical polymerization of nonionized methacrylic acid (MAA) in aqueous solution has been investigated at 50 °C and initial monomer concentrations up to 30 wt % MAA. The rate of conversion increases as the initial weight fraction of MAA decreases, a result explained by the dependence of the propagation rate coefficient, kp, on monomer concentration. The conversion profiles measured at different MAA and initiator levels are represented by a polymerization model with conversion-dependent kp taken from literature, and the termination rate coefficient, kt, represented by a function including terms for segmental diffusion, translational diffusion, and reaction diffusion. The model includes chain transfer to monomer and is capable of representing polymer molecular weight averages and distributions, with the better fit obtained assuming that the transfer rate coefficient also varies with monomer concentration. Introduction Water-soluble polymers are of high technical importance, finding widespread application in hydrogels, flocculants, thickeners, coatings, etc.1,2 These materials are typically produced by free-radical polymerization in aqueous solution. In addition, aqueous-phase polymerization kinetics is important for emulsion systems that incorporate carboxylic monomers such as acrylic or methacrylic acid as an in situ stabilizer and as a component to improve final product properties, including adhesion characteristics and mechanical properties of paints and paper coatings.3,4 Kinetic and modeling studies of the production of water-soluble polymers, however, are scarce. Gu et al. have examined the bulk and aqueous-phase polymerization of N-vinyl formamide,5 Shoaf and Poehlein studied the polymerization of partially neutralized methacrylic acid (MAA) in solution,6 and Cutie´ et al.7 and Li and Schork8 examined aqueous-phase polymerization of acrylic acid (AA). None of these studies, however, considers the complexity of how rate coefficients are affected by the action of hydrogen bonds between monomer, polymer, growing radical, and water. Early studies indicated that AA and MAA polymerization rate varies strongly with pH and degree of ionization, with the rate effects attributed to changes in propagation rather than termination kinetics (e.g., 9-11 for a more thorough discussion of this previous work, see ref 12). Some of the early work found also that polymerization rate in aqueous solution showed an unusual dependence on monomer concentration.2,7,13,14 This finding has been more recently confirmed for a number of water-soluble monomers in aqueous solution using the PLP-SEC method, which combines pulsed laser initiated polymerization (PLP) with polymer analysis by size-exclusion chromatography (SEC) to measure propagation rate coefficients (kp).12,15-22 For example, kp of nonionized MAA increases by more than 1 order of magnitude in passing from the bulk system to a highly dilute * To whom correspondence should be addressed. E-mail: robin. [email protected]; [email protected]. † University of Go¨ttingen. § Queen’s University. ‡ Polymer Institute of the Slovak Academy of Sciences.

monomer solution.12,15,16 The same trend of higher kp for lower monomer concentrations was found for N-iso-propyl acrylamide,17 acrylamide,18 acrylic acid,15,19,20 and N-vinyl pyrrolidone.21The significant lowering in kp upon increasing the monomer concentration is attributed to a reduction in the Arrhenius pre-exponential factor, A(kp), resulting from the intermolecular interactions between the transition state (TS) structure for propagation and a monomer environment being significantly stronger than the ones between this TS structure and an H2O environment.12,16,22 More recently, PLP-SEC studies have also shown that kp increases with monomer conversion during a polymerization, as the relative concentration of water and monomer changes.21,22 It is expected that these changes in kp with initial monomer concentration and conversion will have a strong effect on polymerization kinetics in batch reactors, affecting both rate and polymer molecular weight (MW). We have selected nonionized MAA polymerization in aqueous solution at 50 °C to systematically investigate this effect. In addition, a mechanistic model is developed to represent the system, with predictions compared to the experimental conversion and MW data. Experimental Details Chemicals. Methacrylic acid (MAA, Fluka, > 98.0% stabilized with 0.025% hydroquinone monomethyl ether) was purified by passing the monomer through a column filled with inhibitor-remover (Aldrich). The thermally decomposing initiator 2,2′-azobis (2-methylpropionamidine) dihydrochloride (V-50, Fluka, g 98%) was used as received. Demineralized water was used for preparation of polymerization mixtures as well as of eluent for aqueous SEC. The organic solvents and other chemicals were of analytical grade. Chemically Initiated Polymerizations. Monomer, V-50 initiator, and water were mixed in a 5 mL flask and purged with nitrogen under ice cooling for 3 min; experience with other water-soluble monomers suggests that a longer purge time can induce polymerization. The mixture was put into the polymerization cell consisting of a Teflon tube closed by a cylindrical quartz window on each side. This internal cell was fitted into a

10.1021/ie800887v CCC: $40.75  2008 American Chemical Society Published on Web 09/30/2008

8198 Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008

preheated stainless steel cell of a transmission type equipped with two sapphire windows. Details of the experimental setup including heating and temperature control are given elsewhere.23 The autoclave was filled with n-heptane to transmit a pressure of about 50 bar in order to fix the internal cell and to promote heat transfer. The stainless steel cell was immediately inserted into the sample chamber of the FT-IR/NIR spectrometer (Bruker IFS-88) and FT-NIR spectra were taken every 60 s until MAA conversion was complete. As detailed previously,24 the first overtone of the C-H-stretching vibration at the CdC double bond is used to monitor MAA conversion as a function of polymerization time. Polymerizations in aqueous solution of MAA were carried out at 50 °C, with initial V-50 concentrations of 5.0, 2.5, and 0.50 mmol · L-1, and initial MAA contents of 10, 20, and 30 wt % in water. The system became heterogeneous during polymerization at higher initial levels of MAA. In some of the experiments, polymerization was stopped at intermediate conversions by removing the internal cell from the high-pressure cell and subsequent cooling of the reaction mixture in liquid nitrogen. Polymerization was quenched by addition of hydroquinone monomethyl ether. The polymer was isolated by removing solvent and, eventually, unreacted monomer via drying under high vacuum. Molecular Weight Characterization. Molecular weight characteristics of polyMAA were determined on their esterified form of poly(methyl methacrylate), polyMMA. The esterification was performed as follows: 5-7 mg of polyMAA samples were dissolved in 2 mL of distilled water followed by addition of 1 mL of tetrahydrofuran (THF). The yellow solution of methylation agent diazomethane in toluene prepared according to Arndt25 was added dropwise. Addition of diazomethane was stopped as soon as the yellow coloration persisted and there was no more nitrogen gas formation. The reaction medium was stirred for an additional 5 hours until the yellow coloration disappeared by evaporation of nonreacted diazomethane. The solvents were removed under vacuum at room temperature followed by washing of polyMMA in hexane and drying under vacuum. The molecular weight of polyMMA samples was determined using organic-phase SEC in THF. The SEC setup consists of a Waters system (degasser, autosampler 717, pump 515, DRI detector model 2410) with 8 × 50 mm PSS SDV 5 µm guard column and three 8 × 300 mm PSS SDV 5 µm columns (Polymer Standards Service, Mainz) of pore sizes 102, 103, and 105 Å contained in a Waters column heater module set to 40 °C. PolyMMA solutions were prepared at concentrations of 3 mg · mL-1. The sample injection volume was 100 µL and the eluent flow rate of 1.0 mL · min-1 was controlled by toluene as a flow marker. Molecular weight calibration was established via narrow polydispersity polyMMA standards (Polymer Standards Service, Mainz) between 505 and 2 740 000 g · mol-1 applying a third order polynomial fit. Data acquisition and analysis was performed with WinGPC7 software (Polymer Standards Service, Mainz). The measured M values of polyMMA were multiplied by a factor of 0.86, which is the ratio of the molar mass of monomer units of methacrylic acid (86 g · mol-1) and methyl methacrylate (100 g · mol-1), to directly compare the experimental MWDs with the simulated ones as well as to report the weight and number average molecular weights for polyMAA. The SEC methodology described above differs from that used for the PLP-SEC studies of the propagation kinetics of (meth)acrylic acid,16,19 for which aqueous-phase SEC was found to be a precise technique for determining the position of the inflection points related to the kp values. In this work, the indirect

Figure 1. Comparison of MWD for a polyMAA sample measured using aqueous SEC with the MWD of the same sample after esterification to polyMMA and SEC analysis in THF. The arrow indicates a kink seen in the aqueous SEC analysis. The abscissa molecular weight values were recalculated to the monomer unit of MAA.

method of methyl esterification to polyMMA followed by SEC analysis in THF was used, so as to obtain a better measure of the entire MWDs, which in this work significantly exceed the molecular weight range covered by the available narrow distribution polyMAA standards (between 1200 and 1 027 000 g · mol-1).16 When aqueous-phase SEC was employed to examine the samples produced in this study, the extrapolation of the calibration curve (constructed with a third order polynomial) leads to a kink in the MWD distributions corresponding to the end point of the calibration curve, shown as an arrow in Figure 1. This led to an ambiguity whether such an evaluation gives reasonable information about the molecular weight characteristics of these polyMAA samples and, consequently, we decided to carry out the esterification of polyMAA. The esterification of polyMAA to polyMMA is well established and has been used previously for characterization of PLP-prepared polyMAA samples.15,26 The available narrow distributed polyMMA standards sufficiently cover the range of resulting MWDs of polyMAA samples esterified to polyMMA. As demonstrated in Figure 1, the MWDs of esterified polyMAA samples were close to those obtained by aqueous SEC using direct calibration with polyMAA standards and third polynomial fit. The M values in Figure 1 correspond to the molecular weight of the monomer unit of methacrylic acid equal to 86 g · mol-1 calculated from the M values of sodium methacrylate 108 g · mol-1 and methyl methacrylate 100 g · mol-1, respectively, which are the monomer units of standards used in aqueous and THF SEC. Figure 2 depicts the close agreement between the molecular weight averages of polyMAA samples using both modes of SEC by plotting the Mw and Mn values obtained by aqueous SEC against those for polyMAA esterified to polyMMA. In spite of this agreement, the esterification procedure is recommended for evaluation of the molecular weight characteristics for polyMAA samples that contain a significant portion of the MWD at MWs greater than 1 × 106 g · mol-1. Results and Discussion Figure 3 shows the time-conversion profiles obtained for varying initial MAA fractions (10, 20, and 30 wt % in water) at two different concentrations of V-50 initiator, 0.05 and 0.005 mol · L-1. Repeat reactions were run at ostensibly the same conditions to provide a measure of experimental reproducibility. While some variability is seen, it can be concluded that the initial slopes of the profiles at a constant initiator concentration differ depending on the initial monomer concentration in the batch. As summarized in Table 1, there is an increase in slope by a factor of roughly 1.4-1.6 as monomer content is lowered from

Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 8199

( )

1

fkd[I] 2 dxp ) kp (1 - xp) dt kt

Figure 2. Correlation between weight-average (Mw, circles) and numberaverage (Mn, squares) molecular weights for polyMAA samples obtained by aqueous SEC on polyMAA samples and organic SEC in THF on polyMMA samples after esterification of polyMAA samples. The molecular weight values, in kg · mol-1, were recalculated to the monomer unit of MAA. The dashed line represents an exact match between MW average values obtained by both techniques.

(2)

From eq 2 it is evident that the slope of the conversion-time profile depends on the rate coefficients kp, fkd, and kt, but not explicitly on the actual monomer concentration. At low conversions, these coefficients do not show a marked solvent effect for polymerization of common monomers such as styrene and methacrylates in organic solvents.27 However, there is a clear effect for polymerization of MAA in aqueous solution that indicates that one or more of these rate coefficients has a dependence on monomer concentration. Decomposition kinetics of persulfate initiators can vary greatly with monomer concentration and pH due to induced decomposition.28 The same, however, is not true for watersoluble azo initiators such as V-50, for which kd and its temperature dependence remains constant below a pH of 7.29,30 Previous aqueous-phase polymerization studies of MAA10,13 report that polymerization rate is dependent on the concentration of azo initiator to a power that is very close to 0.5, as expected for free-radical polymerization and as can also be seen by inspection of the data in Table 1. Thus, there is no reason to suspect that a variable initiation rate is responsible for the increase in conversion rate observed in Figure 3. The singlepulse PLP method with NIR detection (SP-PLP-NIR) has been recently used to measure the conversion dependence of kt for aqueous-phase MAA polymerization at 50 °C,24 demonstrating that kt at low conversions is not significantly dependent on initial monomer concentration. Thus, the variation in kp with weight fraction MAA in aqueous solution, as measured by the PLP-SEC technique, remains as the most likely explanation for the nonstandard kinetics observed. A large body of PLP-SEC kp data16 measured at low pressure has been fit by the following generalized equation as a function of temperature, initial weight fraction of MAA in solution (w0MAA), and fractional monomer conversion:24

(

0 kp(wMAA , T, xp) (L · mol-1 · s-1) ) 3.3 × 105 + 3.8 ×

(

106 exp -

Figure 3. Monomer conversion vs time plots for chemically initiated batch polymerizations of methacrylic acid (MAA) in aqueous solution at 50 °C with [V-50] ) 0.005 mol · L-1 (A) and [V-50] ) 0.05 mol · L-1 (B). The initial monomer levels are 10 (2,4), 20 ([,]), and 30 (9,0) wt %; open and filled symbols refer to repeat experiments under ostensibly the same conditions.

30 to 20 wt %, and a further increase by a factor of 1.3-1.8 as monomer level is decreased to 10 wt %. This increase, seen at all initiator levels, is a remarkable observation, as can be appreciated by considering the rate equation for an isothermal free-radical batch polymerization with negligible volume contraction: -

( )

fkd[I] d[M] ) kp[M] dt kt

1 2

(1)

Expressing monomer concentration as [M] ) [M]0(1 - xp), where [M]0 is the initial concentration at the start of the batch and xp is fractional conversion of monomer to polymer such that d[M]/dt ) -[M]0dxp/dt, eq 1 becomes

0 5.3wMAA (1 - xp) 0 1 - wMAA xp

))

(

exp -

)

1.88 × 103 (3) (T (K))

As can be seen from Table 1, the predicted increase in kp with decreasing initial MAA level calculated by eq 3 matches the observed increase in the initial slope of the time-conversion plots: kp increases by a factor of 1.5 as monomer content is Table 1. Average Values ((Standard Deviation) of the Slope (dxp/dt) of the Time-Conversion Profiles during the First 600 s of Methacrylic Acid (MAA) Batch Polymerization at 50 °C in Water as a Function of Initial MAA Weight Fraction and Concentration of V-50 Initiatora dxp/dt (s-1 × 104) initial wt % MAA

[V-50] ) 0.005 mol · L-1

[V-50] ) 0.025 mol · L-1

[V-50] ) 0.05 mol · L-1

kp (L · mol-1 · -1 s )

10

1.6 ( 0.8 2.7 ( 0.3 1.3 ( 0.3 1.5 ( 0.5 1.0 ( 0.2 1.0 ( 0.2

5.1 ( 0.6 8.0 ( 0.8 3.2 ( 0.4 4.2 ( 0.4

9.1 ( 1.3 7.0 ( 0.7 7.0 ( 0.5 5.8 ( 0.6 3.8 ( 0.3 4.3 ( 0.4

7700

20 30

4900 3300

a The values are calculated from the derivatives of the smoothed conversion profiles; multiple entries indicate repeat experiments. Values of the propagation rate coefficient (kp) are calculated according to eq 3.

8200 Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008

Figure 4. Dependence of the termination rate coefficient, kt, on monomer conversion, as estimated from batch polymerization of methacrylic acid (MAA) at 50 °C: (A) initial MAA content of 20 wt % with [V-50] levels at 0.005 (b,O), 0.025 (2,4), and 0.05 (9,0) mol · L-1. (B) [V-50] ) 0.005 mol · L-1 with initial MAA fraction at 10 (b,O,s), 20 (2,4,- - -), and 30 (9,0, · · · ) wt %. Open and closed symbols refer to repeat experiments under ostensibly the same conditions, and curves are calculated using the kt correlation in eq 6 with parameters from eq 7. The gray line in panel B is from the SP-PLP-NIR study of termination kinetics of 30 wt % MAA at 50 °C and 2000 bar,24 shifted higher by a factor of 3.05 to account for the difference in pressure.

lowered from 30 to 20 wt % and increases further by a factor of 1.6 as initial monomer level is decreased to 10 wt %. With the variation in the initial slope of the time-conversion profiles with wt % MAA explained by a consideration of propagation kinetics, the experimental data are used to estimate how kt varies with conversion for the batch polymerizations run at different monomer and initiator concentrations. Rearrangement of eq 2 leads to the following expression: k0.5 t ) kp

(fkd[I]0.5) (1 - xp) dxp dt

(4)

It is assumed that the initiator efficiency f is constant at 0.8, a value typical for azo initiators, and that V-50 initiator decomposes according to the first-order rate expression: [I] ) [I]0 exp(-kdt) -1

-6

(5)

with kd (s ) ) 8.3 × 10 at 50 °C. The value for kp is not only a function of initial monomer level, but for the same physical reason also a function of conversion, as given by eq 3. Finally, the first derivative of the conversion vs time plot is estimated after smoothing the conversion profiles using fivepoint averaging. Typical kt profiles estimated using this approach are shown as Figure 4. As one can see in Figure 4, the curves at different initiator concentrations and different initial monomer concentrations overlap when plotted against conversion. The observed sigmoi29

dal shape of kt vs monomer conversion dependence is typical for methacrylate monomers. For monomer conversions up to 20-30%, segmental diffusion (SD) is dominant and the kt values stay at a constant plateau level that is independent, within experimental scatter, of initial conditions. In the intermediate conversion range, 30 to 70%, kt decreases more than an order of magnitude, attributable to translational diffusion (TD) limitations due to the increase in system viscosity. At higher conversions, the decrease in kt slows, an effect often attributed to reaction diffusion (RD), where the polymer chain ends move more quickly via monomer addition (propagation) than centerof-mass diffusion; even though the highest content of polymer in solution is 30 wt %, the resulting polymer solution has high viscosity. The overall decrease in kt with conversion is similar in shape to that observed for bulk methyl methacrylate,27 and also as measured for MAA polymerization in aqueous solution using the SP-PLP-NIR technique.24 The gray line shown in Figure 4B represents the fit reported in ref 24 for the kt vs conversion data measured by SP-PLP-NIR at 50 °C and 2000 bar for 30 wt % MAA in aqueous solution. To extrapolate this data to ambient pressure, the entire curve has been shifted higher by a constant factor of 3.05 corresponding to an activation volume of 15 cm3 · mol-1, a typical value for methacrylate monomers.27 The close agreement between kt values estimated in this batch polymerization study with the previous SP-PLP-NIR study24 for 30 wt % MAA is quite satisfying. The decrease in kt through the TD regime is observed to be quite similar for the batch experiments run with 10 and 20 wt % MAA in solution (see Figure 4B). This result is surprising, as the weight fraction of polymer in solution at a particular conversion (and thus solution viscosity) increases with increasing MAA level. The SPPLP-NIR study24 for 30 and 60 wt % MAA in aqueous solution found that the kt curves overlapped when plotted against weight fraction polymer rather than polymer conversion. The difference between the two results may be related to the different MAA concentration regions examined (10-30 wt % MAA in this study; 30-60 wt % MAA by SP-PLP-NIR). With respect to the scatter in the high conversion region, it may be that the kp prediction for higher degrees of monomer conversion are not overly accurate, as experimentally the effect of conversion could only be examined for a system containing 10 wt % polymer and 10 wt % MAA, i.e., 50% conversion.22 As the calculated values of kt are proportional to (kp)2 (cf. eq 4), any deviation between the actual kp value at higher conversion and that predicted by eq 3 will result in errors in the estimated kt values. An examination of Figure 4 indicates that there may be some systematic variation in kt with initiator and monomer levels in the higher conversion regime. It must be remembered that the estimated kt value should be considered as an average value over the complete radical distribution, as some chain-length dependency is expected.27 Thus, the increase in kt at high conversions observed for higher initiator levels (Figure 4A) could result from the shorter radicals and lower MW polymer produced at higher [V-50]. (MW data for the experiments are presented later.) The increase in kt at high conversions observed at lower monomer concentrations may also result from lower radical chain lengths and might be influenced by the increased chain-end flexibility that occurs at lower monomer concentrations due to decreased system viscosity. Also, as mentioned previously, any differences between the actual kp value at higher conversion and that predicted by eq 3 will lead to errors in the estimated kt values.

Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 8201

Despite these kinetic questions, the kt profiles shown in Figure 4 are encouraging from a modeling perspective, as they indicate that a single correlation may be used to represent kt as a function of conversion for the experimental ranges of initiator and monomer concentrations examined in this work. Equation 6 was introduced to model kt behavior where the three types of diffusion control (SD, TD, and RD) are operating31 and is the same functional form as that used to fit the MAA kt data obtained by the SP-PLP-NIR technique.24 kt )

1 + CRDkp(1 - xp) exp(Cηxp) + kt,SD kt,TD 1

(6)

As a first estimate, the parameters were set to the following values based on a rough fit to the experimental kt vs conversion plots: kt,SD ) 3.19 × 107 L · mol-1 · s-1, kt,TD ) 1.0 × 109 L · mol-1 · s-1, CRD ) 530 and Cη ) 12.8. A simple kinetic model was implemented in Predici, including initiation, propagation, termination, and chain transfer to monomer mechanisms, with the variation in kp and kt with conversion represented by eq 3 and eq 6, respectively. The parameter estimation capabilities of Predici were then used to fit the complete set of timeconversion profiles obtained experimentally. The set of coefficients obtained, with 95% confidence intervals, were kt,SD ) (3.53 × 107 ( 8.47 × 106) L · mol-1·s-1 Cη ) 10.9 ( 4.72 kt,TD ) (2.79 × 108 ( 4.52 × 108) L · mol-1·s-1 CRD ) 517 ( 212 (7) The high uncertainty in kt,TD reflects the fact that this estimate is highly coupled to Cη, and the uncertainty in CRD results from the variation of estimated kt values at higher conversions noted previously. The values summarized by eq 7 were used to generate the curves in Figure 4; while there is some mismatch to the specific kt vs conversion data shown, the parameters provide the best fit to the overall conversion vs time data set. Simulations of the batch polymerizations are compared to the complete set of experimental time-conversion plots in Figure 5. Although some mismatch is observed at higher conversions, there are no systematic deviations observed with initial wt % MAA or [V-50] levels. It can be concluded that rate data for aqueous-phase polymerization of nonionized MAA are reasonably represented by a standard free-radical polymerization model, as long as the variation in kp with monomer concentration is properly accounted for. In the next step, the ability to model polymer MW averages and MWDs is examined. Figure 6 compares MWDs calculated with the Predici model, assuming no chain transfer in the system, to the experimental distributions. The Predici software calculates complete MWDs using a discrete weighted Galerkin method on an adaptive grid, as described by Wulkow.32 (Simulations were done assuming the fraction of termination by disproportionation is 0.8, a typical value for methacrylate systems.33) The simulated MWDs exhibit the same general shape as the experimental traces, but the absolute MW averages are higher by 40% for the experiment with 0.05 mol · L-1 V-50 and by 90% for the experiment with 0.005 mol · L-1 V-50. Thus, it can be concluded that some additional chain-forming mechanism must be occurring, such as chain transfer. Scant information regarding H-abstraction in aqueous-phase polymerization systems could be found in the literature, although a study of freeradical induced polyMAA degradation in aqueous solution concludes that the primary site for radical attack is the monomer methyl group rather than the methylene or carboxylic groups.34

Figure 5. Monomer conversion vs time profiles for chemically initiated methacrylic acid (MAA) batch polymerizations in aqueous solution at 50 °C with [V-50] ) 0.005 mol · L-1 (A), [V-50] ) 0.025 mol · L-1 (B), and [V-50] ) 0.05 mol · L-1 (C). The initial monomer levels are 10 (2, 4, s), 20 ([, ], - - -), and 30 (9, 0, · · · ) wt %; open and filled symbols refer to repeat experiments under ostensibly the same conditions. Lines are the simulated profiles calculated using the kt parameters from eq 7.

Figure 6. Simulated and experimental (with replicates) polymer molecular weight distributions obtained from batch polymerizations with 30 wt % MAA in aqueous solution and [V-50] at 0.005 (gray) or 0.05 mol · L-1 (black). The dotted and dashed curves refer to experimental data, the solid lines to the simulated MWD, calculated assuming no chain transfer.

Thus, chain transfer to monomer has been added to the model. The unresolved issue is whether the transfer rate coefficient should be set to a constant value, as for typical free-radical polymerization systems, or is expected to vary with monomer

8202 Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 Table 2. Experimental and Simulated Number (Mn) and Weight-Average (Mw) Molecular Weights, in kg · mol-1a reaction conditions

simulation: ktr ) 0.353 L · mol-1 · s-1

experimental

simulation: ktr /kp ) 5.37 × 10-5

% error -1

% error

initial wt % MAA

[V-50] (mol · L )

xp

Mw

Mn

Mw/Mn

Mw

Mn

Mw/Mn

Mw

Mn

Mw

Mn

Mw/Mn

Mw

Mn

10

0.005

2.25

461 213

2.07 2.33

885 471

431 204

2.05 2.31

477 332 339

228 142 161

2.09 2.34 2.11

54.5 147.1 66.3 29.9 36.5 -1.6 -11.8 10.0 7.8

403

956 496

30.0 66.1 44.2 16.7 25.3 -15.6 -11.7 7.4 -5.5

905

0.05

2.72 3.40 2.39 2.59 2.54 2.44 2.34 2.16 2.41

2.29

10

283 177 277 164 156 232 161 146 149

437

0.025

769 602 663 425 396 565 376 316 359

1000

10

full full 52 full full 53 full 64 65

458 321 329

221 138 157

2.07 2.33 2.10

17.7 50.4 33.5 10.8 18.9 -18.9 -14.6 4.1 -8.3

42.4 127.6 55.6 24.4 30.8 -4.8 -14.0 7.3 5.2

20

0.005

2.20

537 319

2.14 2.33

1153 716

552 313

2.09 2.29

650 535

301 228

2.16 2.35

172.7 225.6 251.8 57.4 19.4 11.1 27.6 21.3

553

1148 742

69.4 103.7 100.8 23.5 -4.5 -2.2 21.9 14.8

1219

0.05

3.57 3.55 3.89 2.73 2.91 2.64 2.26 2.48

2.22

20

209 175 162 341 267 287 236 188

570

0.025

747 621 630 930 777 759 533 466

1265

20

full full full 59 full full 53 full

653 521

306 225

2.13 2.32

63.2 96.3 93.5 24.0 -7.9 -5.7 22.4 11.8

164.5 215.9 241.2 61.8 17.4 9.2 29.8 19.7

30

0.005

full full 68 27 full full full 72 52 38

1330 1273 1114 819 617 524 591 424 449 471

516 500 610 401 236 244 247 175 207 197

2.58 2.55 1.83 2.04 2.61 2.15 2.39 2.42 2.17 2.39

1304

558

2.34

607

2.21

519 365 240

2.25 2.01 2.43

1302 898 591

606 448 249

2.15 2.00 2.37

549 446 357

234 200 172

2.35 2.23 2.08

8.1 11.5 -14.9 -9.0 1.5 -1.8 -3.0 33.5 -3.2 -12.8

1342

1166 733 583

-1.9 2.4 4.7 -10.5 -5.6 11.2 -1.4 29.6 -0.8 -24.3

575 480 387

250 217 187

2.30 2.21 2.07

0.9 5.4 16.9 9.6 -4.2 12.8 0.0 35.6 6.8 -17.8

17.6 21.4 -0.7 11.7 5.7 2.2 1.0 43.0 5.0 -5.0

30

a

0.05

The % error is calculated as (Mw,sim - Mw)/Mw ×100.

concentration as kp does. Both possibilities have been examined: case 1 with constant ktr, and case 2 with constant ktr/kp (with kp varying according to eq 3). In both cases, the rate coefficient was adjusted using Predici parameter estimation capabilities to fit the MWDs measured for polymerizations with 30 wt % MAA and [V-50] ) 0.05 mol · L-1. For case 1, the best fit is achieved with ktr ) 0.353 L · mol-1 · s-1, and case 2 is best fit with ktr/kp ) 5.37 × 10-5. The value of ktr/kp is similar to accepted transfer to monomer rate coefficients for methyl methacrylate.35 Table 2 compares the experimental number- and weightaverage-MW values to the simulation results for the two cases. In addition to MW data at full conversion, some values at intermediate conversions were obtained by quenching the reaction at shorter times. Experimentally, the following trends can be noted: (1) Polymer MW increases with decreasing [V-50] at constant initial weight fraction of MAA in the batch. Mw (weight-average MW) values at full conversion increase by a factor of 2 to 3 as [V-50] is decreased from 0.05 to 0.005 mol · L-1 for 10 and 30 wt % MAA in solution. This increase, which is the expected behavior according to free-radical polymerization kinetics, is less evident for the experiments with 20 wt % MAA. (2) Polymer MW increases with increasing initial monomer concentration. For [V-50] ) 0.05 mol · L-1, Mw values decrease from 5–6 × 105 g · mol-1 to 3-4 × 105 g · mol-1 as initial fraction of MAA decreases from 30 to 10 wt %. With [V-50] ) 0.005 mol · L-1, Mw values are in the range of 6-7 × 105 g · mol-1 at full conversion for experiments with 10 and 20 wt % MAA, but are greater than 1 × 106 g · mol-1 for an initial MAA concentration of 30 wt %. (3) The trends in polymer MW with conversion are more difficult to summarize. With an initial fraction of MAA at 30 wt %, Mw values tend to increase with increasing conversion

in the system, with [V-50] at 0.05 or 0.005 mol · L-1. The results for 10 and 20 wt % MAA are not consistent, with MW increasing with conversion for some conditions, but decreasing for others. (4) Weight-average MW values have been used when discussing these experimental trends, as it is felt that this average provides a better representation of the MWD than numberaverage molecular weights, Mn. However, it is instructive to examine the polydispersity (PDI ) Mw/Mn) of the distributions. These vary from 1.8 to 3.9, with the majority of the values between 2.4 and 3.0. It is difficult to see systematic trends with experimental conditions, although it can be argued that PDI values increase slightly with conversion. It is important to consider the experimental uncertainty associated with the reported MW values, relative to the trends noted above. There is some variability in time-conversion profiles from repeat experiments (cf. Figure 3) that is most likely caused by differences in effective radical concentrations related to the presence of oxygen or other inhibitor in solution.8 This variation in radical concentration would also affect polymer MW. The experimental MW trends are better matched by assuming that the ratio of ktr/kp remains constant rather than the absolute value of ktr, as can be seen in Table 2 by comparing the error between simulation and experiment for the two cases. However, the improvement in the root mean squared error estimates for Mw and Mn is minor and does not conclusively indicate that the rate coefficient for chain transfer is affected by the acid to water ratio, as is kp. We adopt the constant ktr/kp ratio, as the basic kinetics behind the explanation of the kp dependence on monomer concentration16 should apply more or less similarly to the transition state of the transfer-to-monomer step.

Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 8203

Figure 7. Simulated (top) and experimental (bottom, with replicates) polymer molecular weight distributions obtained from batch polymerizations with 30 wt % MAA in aqueous solution and [V-50] 0.005 or 0.05 mol · L-1. In the simulation the ratio between ktr and kp is set to 5.37 × 10-5.

Figure 9. Simulated (top) and experimental (bottom) polymer molecular weight distributions obtained from batch polymerizations with [V-50] ) 0.05 mol · L-1 and 10, 20, or 30 wt % MAA in aqueous solution. In the simulation the ratio between ktr and kp is set to 5.37 × 10-5.

initial MAA fraction (Figure 9). Furthermore, the shapes of the experimental distributions are close to the simulated distributions. While perhaps not capturing the full complexity of MWD evolution during aqueous-phase MAA polymerization, the simple kinetic model is capable of representing the important experimental tendencies. Conclusion

Figure 8. Simulated (top) and experimental (bottom) polymer molecular weight distributions obtained at different conversion levels during batch polymerizations with 30 wt % MAA in aqueous solution and [V-50] ) 0.005 mol · L-1. In the simulation the ratio between ktr and kp is set to 5.37 × 10-5.

When ktr/kp is set to match MWDs for the 30 wt % MAA and [V-50] ) 0.05 mol · L-1 experiments, the model provides a reasonable match to MWs measured for 20 and 10 wt % MAA with [V-50] ) 0.05 or 0.025 mol · L-1. Although the model overpredicts the MW values for experiments conducted with [V-50] ) 0.005 mol · L-1 and initial MAA fractions of 10 and 20 wt %, for all other cases the calculated Mw values are generally within 20% of experiment. Experimental and simulated MWDs are shown in Figures 7–9. The trends in the simulations and the experiment are similar with varying initiator concentration (Figure 7), conversion (Figure 8) and

This systematic investigation into the batch polymerization of nonionized methacrylic acid (MAA) in aqueous solution illustrates the similarities and differences of the system compared to free-radical polymerization in nonaqueous solution. The major difference between the two is the strong dependence of the propagation rate coefficient, kp, on monomer concentration (and thus conversion) in the aqueous system. This behavior leads to an increased rate of conversion as the initial weight fraction of MAA in the batch decreases. Once this significant deviation from “ideal” free radical polymerization kinetics is properly accounted for, the functional form commonly used to represent the change in termination rate coefficient with conversion for polymerization of methacrylates, acrylates, and styrene in nonaqueous systems can be used for aqueous-phase polymerization of MAA. The variation of kt for MAA is similar to polymerization behavior of methyl methacrylate in nonaqueous solution. Furthermore, the changes in MW with experimental conditions are largely captured by a simple model that includes chain transfer to monomer, with a slightly better fit obtained assuming that the transfer rate coefficient varies with monomer concentration following the same functional form as does kp. Work is underway to extend this experimental and modeling study to other water-soluble monomers, such as N-vinyl pyrrolidone,21 and to contrast and compare free-radical polymerization in aqueous and nonaqueous systems. Acknowledgment P.H. acknowledges a fellowship by the Fonds der Chemischen Industrie, and I.U. acknowledges support from Deutscher

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ReceiVed for reView June 5, 2008 ReVised manuscript receiVed August 7, 2008 Accepted August 12, 2008 IE800887V