Semicontinuous Emulsion Co-polymerization of Vinyl Acetate and

Article pubs.acs.org/IECR

Semicontinuous Emulsion Co-polymerization of Vinyl Acetate and VeoVa10 Amaia Agirre,† Iñigo Calvo,†,‡ Hans-Peter Weitzel,§ Wolf-Dieter Hergeth,§ and José M. Asua†,* †

POLYMAT and Departamento de Química Aplicada, Facultad de Ciencias Químicas, University of the Basque Country UPV/EHU, Joxe Mari Korta zentroa, Tolosa etorbidea 72, Donostia-San Sebastián 20018, Spain ‡ Oribay Mirror Buttons S.L. R&D Department, Portuetxe bidea 18, Donostia-San Sebastian 20018, Spain § Wacker Chemie AG, Johannes-Hess-Str. 24, 84489 Burghausen, Germany ABSTRACT: The high solids semicontinuous emulsion polymerization of VAc and VeoVa10 using poly(vinyl alcohol) (PVOH) as polymeric stabilizer is investigated. It is shown that (i) PVOH strongly affects the kinetics of the process and (ii) the formation of PVOH-graft-poly(VAc−co-VeoVa10) leads to an overestimation of the gel content and an underestimation of the sol molecular weight when the standard characterization techniques are directly applied. A new method to properly characterize the MWD of these copolymers is presented. A mathematical model is used to analyze the effects of surfactant and initiator on the kinetics and polymer microstructure.

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INTRODUCTION

Continuous loop reactors have been used to produce highsolids VAc−VeoVa10 latexes stabilized with a mixture of anionic and nonionic surfactants.5−11 The effect of mass transfer of VeoVa10 on copolymer composition in batch and semibatch miniemulsion and emulsion polymerizations stabilized with sodium lauryl sulfate has been studied.12 It was found that (i) the copolymers presented a single Tg value and (ii) the Tg value was lower for the semibatch runs, suggesting a slightly better incorporation of VeoVa10. No influence of the polymerization method (miniemulsion vs emulsion) on Tg was reported. Although PVOH is the most widely amphiphilic substance used to stabilize vinyl acetate latexes, there are only a few reports in the open literature using PVOH to stabilize VAc−VeoVa10 latexes. High-solids VAc−VeoVa10 stabilized with PVOH can be produced via batch miniemulsion polymerization, whereas batch emulsion polymerization results in massive coagulation.13 In addition, it has been reported that, in batch processes, the extent of grafting of PVOH strongly depends on the initiator that is used. Grafting increases in the following order:

Vinyl acetate (VAc) copolymers are widely used for coatings. Soft co-monomers are used to decrease the glass-transition temperature of the copolymer to values that allow the formation of a high-quality film. In addition, in order to protect the VAc units of the copolymer against hydrolysis, hydrophobic comonomers are used. Butyl acrylate (BA) and VeoVa10 (vinyl ester of neodecanoic acid) are the most commonly used comonomers. Ethylene is another alternative but it requires the use of pressurized reactors, which increase the manufacturing costs, and the small size of the ethylene offers less steric protection to the neighboring vinyl acetate units against hydrolysis.1 VeoVa10 is more bulky than BA and, hence, it offers better protection to VAc. This makes VAc−VeoVa10 copolymers the preferred coating for inorganic (e.g., brick and concrete) substrates. The VeoVa10 content is chosen to optimize the cost/performance ratio. Latexes for interior coatings contain 15−20 wt % of VeoVa10, whereas exterior latexes contain 20−30 wt %.2 The use of VeoVa10 presents the additional advantage that it has a reactivity similar than VAc. Despite the practical importance of the VAc−VeoVa10 copolymers, relatively few studies have been published. Optimal polymerization strategies to maximize the production rate and scrub resistance of VAc−VeoVa10 latexes stabilized by an anionic surfactant and produced in tank reactors with a limited heat removal capacity were reported by Unzue et al.3 They found that 40% of reduction in the process time could be achieved, maintaining the final product quality. Prior et al.4 compared the performance of copolymers of vinyl acetate with VeoVa10, BA, and 2-ethyl hexyl acrylate (2EHA). The latexes were stabilized by a mixture of nonionic and anionic surfactants with a nondisclosed protective colloid. It was found that VeoVa10 presented advantages in scrub resistance, gloss and hydrophobicity, whereas BA developed better wet adhesion and hiding efficiency. 2EHA offered hiding efficiency similar to that of BA. © 2013 American Chemical Society

benzoyl peroxide ≈ lauryl peroxide < tert ‐butyl hydroperoxide/ascorbic acid < potassium persulfate

The fraction of grafting was higher in miniemulsion than in emulsion polymerization.14 It is interesting to note that the polymerizations using PVOH were carried out in batch that cannot be used in commercial practice because of safety problems associated with the rapid heat generation rate. Special Issue: Massimo Morbidelli Festschrift Received: Revised: Accepted: Published: 9282

October 3, 2013 November 7, 2013 November 13, 2013 November 13, 2013 dx.doi.org/10.1021/ie4032499 | Ind. Eng. Chem. Res. 2014, 53, 9282−9295

Industrial & Engineering Chemistry Research

Article

initiator feeding rates were changed to 0.14 g/min during 30 min and then decreased again to 0.035 g/min for additional 30 min. Then, the aqueous solution of emulsifier (0.627 g/min) and the mixture of monomers (1.158 g/min) were fed separately over a period of 3 h. At the end of the monomer feed, the initiator feeds rates were increased to 0.07 g/min and maintained for 2 h. After this period, the reactor was cooled to 40 °C and the postpolymerization was started. The oxidant solution was fed over a period of 10 min (0.084 g/min), whereas the reductant was added during 30 min (0.028 g/min). This step was repeated twice. The final solids content of the latex was ∼57 wt%. Samples were withdrawn at regular intervals from the reactor and the polymerization was short-stopped with hydroquinone. Table 2 summarizes the semibatch polymerizations carried out to study the effect of initiator and emulsifier types and concentrations on kinetics and polymer microstructure.

In this work, the semicontinuous emulsion copolymerization of vinyl acetate and VeoVa10 was investigated under industriallike conditions, namely, using high solids contents (57 wt %) and PVOH as a polymeric stabilizer. It was found that PVOH strongly affects the polymer microstructure as measured using the classical methods. A new method to properly determine the molecular weight distribution (MWD) of these polymers is presented. A mathematical model was developed to shed light on the effect of PVOH and initiator type on polymerization kinetics and polymer microstructure.

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EXPERIMENTAL SECTION Materials. Technical-grade monomers, vinyl acetate (VAc, Quimidroga), and neodecanoic acid vinyl ester (VeoVa10, Hexion) were used without further purification. Poly(vinyl alcohol) (PVOH 4/88; viscosity of a 4% aqueous solution at 23 °C is 4 mPa s, the degree of hydrolysis is 88 mol %) was kindly supplied by Wacker Chemie AG, nonionic emulsifier Disponil AFX4060 (Cognis, Germany) and anionic sodium dodecyl sulfate (SDS, Aldrich) were used as emulsifiers. tert-Butyl hydroperoxide (TBHP, Aldrich), ascorbic acid (AsAc, Panreac), potassium persulfate (KPS, Fluka) and sodium metabisulfite (NaMS) were used as initiators. Formic acid (Panreac) was added to acidify the initial aqueous reactor charge and iron ammonium sulfate was used to accelerate the generation of radicals when PVOH was used. Deionized water was used throughout the work and hydroquinone (Fluka) was used for stopping the reaction in the samples withdrawn from the reactor. Polymerization Process. Semicontinuous polymerizations were carried out in a 1-L glass reactor fitted with a reflux condenser, a sampling device, a nitrogen inlet, four feeding inlets, a thermometer and a stainless steel anchor stirrer rotating at 250 rpm. Reaction temperature and the feed flow rates were controlled by an automatic control system (Camile TG, Biotage). The general formulation used in the semibatch process is given in Table 1. The initial charge was formed as follows: the aqueous

Table 2. Summary of the Reactions Performed Redox pair Emulsifier

vinyl acetate VeoVa10 poly(vinyl alcohol), PVOH(4/88)b Disponil(AFX4060)c iron ammonium sulfateb water oxidant reductant

initial solution (%) charge (g)

20

1

0.1d−0.2e 10d−5e 0.17d−0.34e 5d−2.77e

166.6 41.72 83.58 6.95 0.7 125.3b 189.38c

feed (g)

latex

type

% wbm

ox./red.

semibatch

postpolymerizationa

S1 S2 S3 S4

PVOH PVOH PVOH Disponil

7.22 7.22 7.22 2.92

TBHP/AsAc KPS/NaMS KPS/NaMS TBHP/AsAc

0.005/0.009 0.005/0.009 0.01/0.018 0.005/0.009

0.04/0.02 0.04/0.02 0.02/0.011 0.04/0.02

a

Both additions are included.

Characterization. Monomer conversion was determined gravimetrically. The copolymer composition was not measured, because the composition of the copolymer was expected to be the same as the monomer ratio, since the values of the reactivity ratios were almost equal to 1 (see Table 3, which appears later in this work). The z-average diameter of the polymer particles was measured by dynamic light scattering (Zetasizer Nano Z, Malvern Instruments). Samples were prepared by diluting a fraction of the latex with deionized water. The particle size distributions were determined by using a disk centrifuge photosedimenter (BI-DCP Brookhaven Instruments). Initially, the gel content was measured by means of a classical Soxhlet extraction, using tetrahydrofuran (THF) as a solvent. The insoluble part was considered to be gel; the MWD of the soluble part was measured via gel permeation chromatography−size exclusion chromatography (GPC-SEC), and as the equipment was calibrated using polystyrene standards. The results obtained were based on polystyrene. However, it was found that this method overestimated the gel fraction because PVOH-graft-poly(VAc−co-VeoVa10) was formed in the process, and, since PVOH is not soluble in THF, an important fraction of the graft copolymer was accounted for as gel. In order to overcome this problem, the polymers were acetylated to transform the −OH groups into −CH3 groups, namely, transforming PVOH into pVAc, which is soluble in THF. The acetylation process was as follows. In the presence of HCl (1 mL) to acidify the medium, a mixture of acetic acid (20 mL) and acetic anhydride (20 mL) was added to 1 g of dried latex and the system was allowed to react under agitation at room temperature for 24 h. The dried acetylated polymer was obtained by evaporating the solvent. This product was then subjected to a Soxhlet extraction in order to separate the gel and sol parts, and the sol MWD was measured via GPC-SEC.

Table 1. General Formulation Used in the Semibatch Processes compound

Pure initiator Ox./Red. (% wbm)

PostPolym.a (g)

187.6 20.86 66.92 5.21 45.92b 97.37c 22.05 1.68 22.05 1.68

a

All additions are included. bUsed in reactions S1, S2, and S3. cUsed in reaction S4. dUsed in reactions S1, S2, S4. eUsed in reaction S3.

solution of emulsifier was added and acidified to pH 4 with formic acid (10 wt % solution). Then, 0.7 mL of iron ammonium sulfate (1 wt % solution) was added. A mixture of VAc and VeoVa10 was fed over a period of 5 min and the reactor was heated until 67 °C. Once the desired temperature was reached, the oxidant and reductant solutions were fed at 0.07 g/min for 30 min. Then, the 9283

dx.doi.org/10.1021/ie4032499 | Ind. Eng. Chem. Res. 2014, 53, 9282−9295


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The acetylation process was validated by acetylating pure PVOH (4/88). Attenuated total reflection Fourier transform infrared spectroscopy (ATF FT-IR) was used to check that the hydroxyl groups, which are evident in the broad characteristic peak at 3150 cm−1, disappeared in the acetylated sample (Figure 1).

Figure 3. Molecular weight distributions of the acetylated (AcB1) and nonacetylated (B1) VAc−VeoVa10 latex stabilized with SDS and Disponil AFX4060.

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EXPERIMENTAL RESULTS AND DISCUSSION Two polymerizations (S1 and S2) were carried out to study the effect of the initiator type, using the general formulation given in Table 1; TBHP/AsAc was used in run S1 and KPS/NaMS in run S2. Figure 4 compares the evolution of the average particle size during polymerizations S1 and S2. In both cases, the average

Figure 1. Attenuated total reflection Fourier transform infrared spectroscopy (ATF FT-IR) spectra of nonacetylated (PVOH) and acetylated (AcPVOH) PVOH.

The acetylated PVOH is completely soluble in THF and the molecular weight distribution can be measured (Figure 2). It is

Figure 2. Molecular weight distribution of the acetylated PVOH (4/88).

Figure 4. Effect of the initiator type and concentration on the evolution of the particle size using PVOH.

worth pointing out that this method opens the possibility of a more detailed characterization of the microstructure of the PVOH, which currently is given by the degree of hydrolysis and the viscosity of a 4 wt % aqueous solution. In order to check if the VAc−VeoVa10 copolymer chains were damaged by the acetylation process, a VAc−VeoVa10 copolymer synthesized in batch emulsion polymerization using a mixture of SDS and Disponil AFX4060 as surfactants was subjected to the acetylation process. This latex did not contain any gel as measured by the classical Soxhlet extraction. Figure 3 shows that the MWD did not vary during the acetylation process, namely, the VAc−VeoVa10 copolymer chains were not affected by the acetylation process.

particle diameter increased during the process, with the one obtained using TBHP/AsAc always being larger. At the beginning of the process, both systems exhibited a similar particle size but after the end of monomer and emulsifier feeds, a strong increase was observed in the average particle size with TBHP/AsAc, because of the agglomeration of polymer particles (no macroscopic coagulum was observed). However, at the end of the process, a decrease in the average particle diameter was observed, which indicated the formation of new small particles at this stage. A similar behavior was reported by Donescu et al.15 in the semicontinuous emulsion polymerization of vinyl acetate carried out in the presence of PVOH using H2O2/FeSO4 as a redox initiator. 9284



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The effect of the initiator type on the evolution of the instantaneous conversion in runs S1 and S2 is presented in Figure 7. At the beginning of the process, the reaction was slow,

Figure 5. Particle size distribution of the final latex obtained in run S1 initiated with TBHP/AsAc and using PVOH as a stabilizer.

Figure 5 presents the bimodal particle size distribution with a broad large mode obtained with TBHP/AsAc at the end of S1 polymerization. This is typical in VAc emulsion polymerization.15−17 The large number of small particles that appeared at the end of the process revealed the generation of new particles by homogeneous nucleation at least during the last stages of the process. On the other hand, the large particles evidenced the aggregation of polymer particles. The latex formed with KPS/ NaMS coagulated at the end of the reaction, not being possible to determine the particle size distribution. This destabilization might be related to the increase of ionic strength due a high amount of charges incorporated to the system by the initiator during the post-polymerization step. This reduced the electrostatic repulsive energy barrier, so that the latex ultimately coagulated.18 The evolution of the number of particles with conversion for runs S1 and S2 is shown in Figure 6. The number of particles

Figure 7. Effect of the initiator type and concentration on the evolution of instantaneous conversion using PVOH as a stabilizer.

regardless of the initiator type used, likely because of the low amount of initiator used. A substantial increase of the conversion was observed for TBHP/AsAc when the initiator feed rate was increased, but the conversion obtained in run S2 with KPS/NaMS remained low. During the addition of monomer and emulsifier (from 90 min to 270 min), the instantaneous conversion remained almost constant in both reactions showing that polymerization rate was only slightly lower than the monomer feed rate. In the final batch process and during the post-polymerization step, the initiator feed rates were increased leading to higher polymerization rates in both runs. In the case of KPS/NaMS, a temperature runaway was observed as a consequence of the fast reaction of the high amount of monomer accumulated into the reactor. Figure 7 clearly shows that the polymerization rate was slower for KPS/NaMS than for TBHP/AsAc, even though the number of particles was higher (Figure 6), which implied that the average number of radicals per particle was lower for KPS/NaMS. This can be due to a lower rate of radical generation or to an inefficient radical entry mechanism. The rate of radical generation for the KPS/NaMS system has been reported to be similar if not slightly higher than that of TBHP/AsAc.19 Therefore, the likely reason for the lower n̅ is the entry of the radicals. The sulfate ion radicals generated with KPS/NaMS are very hydrophilic and, hence, they cannot enter directly into the polymer particles, whereas the tertbutoxyl radicals generated from TBHP/AsAc are hydrophobic and able to readily enter into the polymer particles. Therefore, •SO4− needs to react with the monomer dissolved in the aqueous phase to become hydrophobic enough to be able to enter into the polymer particles. In this process, a fraction of sulfate ion radicals suffers bimolecular termination in the aqueous phase, lowering the radical entry rate. Furthermore, during their stay in the aqueous phase, the •SO4− radicals and the oligoradicals formed from them can abstract hydrogens from the PVOH.14,16,20,21 The radicals formed on PVOH are relatively unreactive and a fraction of them is located in the aqueous phase where the concentration of monomer is low, namely, their contribution to the polymerization rate is low. This means that the PVOH reduces the radical entry rate. It is worth pointing out that the PVOH located at the surface of the particles may also act as a radical

Figure 6. Evolution of the number of particles in runs S1, S2, and S3.

was higher with KPS/NaMS than with TBHP/AsAc during the entire polymerization. In addition, in run S2 (KPS/NaMS), the number of particles increased with conversion, indicating that new particles were formed continuously throughout the reaction. A possible reason for the higher number of particles obtained with KPS/NaMS is the contribution of the SO4− groups to the stabilization of the polymer particles. 9285



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sink22−26 for the radical exit, but this would affect both initiator systems in a similar way. In order to shed light on the effect of KPS concentration on polymerization kinetics, reaction S3 was carried out in a manner similar to that of run S2, but the initiator concentration was doubled before the post-polymerization step and decreased to half the original concentration throughout the postpolymerization step. Figures 4, 6, and 7 compare the evolutions of the particle size, number of particles, and instantaneous conversion of run S3 with those obtained in run S2. Surprisingly, fewer particles than in run S2 were produced by increasing the initiator concentration. This effect was contrary to what was predicted by theory.27 The smaller particle size found with the lower initiator concentration might be due to the lower ionic strength, which reduces the coagulation of particles during the polymerization. A similar behavior has been reported by other authors.3,28 Latex S3 also coagulated at the end of the post-polymerization step, which was attributed to the high ionic strength. Monomer conversion increased with the concentration of KPS/NaMS, but still it was lower than with TBHP, likely because of the lower entry rate of sulfate ion radicals. Figure 8 shows that a substantial amount of apparent gel was observed when the latex samples were directly subjected to

untreated samples was an artifact created by the grafted PVOH, which is insoluble in THF. Figure 8 shows that the apparent gel fraction was greater for KPS/NaMS than for TBHP/AsAc, which suggests that grafting was higher for KPS/NaMS. This is in agreement with what was observed in the batch miniemulsion polymerization of VAc and VeoVa10,14 and it is confirmed by the results presented in Figure 9. This figure compares the MWDs of the acetylated final latexes obtained in processes S1 and S2. The MWD of the acetylated PVOH(4/88) is included as a reference. It can be seen that the shoulder corresponding to unreacted PVOH was more pronounced in the reaction carried out with TBHP/AsAc. The higher grafting obtained with KPS/NaMS is due to the fact that •SO4− radicals are more hydrophilic and remain in the aqueous phase longer. Therefore, they have more opportunities to abstract hydrogens from PVOH. Moreover, higher-molecularweight chains were observed in the acetylated samples than in the untreated ones. These longer chains were attributed to VAc− VeoVa10 copolymer chains containing grafted PVOH that were not soluble in THF before the acetylation process. The presence of grafted PVOH acted as an artifact when gel and sol MWD are measured by a classical Soxhlet extraction. Figure 10 shows the evolution of the acetylated molecular weight distributions during reactions S1 and S2. The MWD of the acetylated PVOH is included as a reference. It can be seen that, in both cases, high-molecular-weight polymer is formed during the last stages of the process, likely because of the contribution of chain transfer to polymer and propagation to terminal double bonds. At 90 min, in run S2, that corresponds to the end of the batch polymerization of the initial charge, a high amount of unreacted PVOH was observed. This peak was even more pronounced at 150 min, because of the addition of PVOH to the reactor and the low conversion achieved. Before the postpolymerization, after ∼30% conversion, a high amount of unreacted PVOH still remained in the reactor. However, during the post-polymerization, when a fast increase in conversion was observed, the small-molecular-weight peak was substantially reduced, showing that the majority of PVOH was incorporated to the VAc−VeoVa10 copolymer at this step. Because of the differences in kinetics between runs S1 and S2, direct comparison of the peak associated to unreacted PVOH is not possible, but the final samples show that, in both cases, a significant part of PVOH was grafted. This result is in conflict with what was reported by Magallanes et al.,29 who, using a complex technique to characterize the grafted PVOH, found that only a small fraction of PVOH was grafted.

Figure 8. Effect of the acetylation process on the measured gel (S1 and S2 were untreated samples; AcS1 and AcS2 were acetylated samples).

Soxhlet extraction. However, virtually no gel was observed when the latexes were acetylated. Therefore, the gel observed in the

Figure 9. MWDs of the final latexes of processes S1 and S2 before acetylation (S1 and S2) and after acetylation (AcS1 and AcS2). 9286



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Figure 10. Evolution of the MWD in runs S1 and S2.

Figure 12. Effect of the emulsifier type on particle size number distribution of the final latex.

Figure 11. Effect of the emulsifier type on the evolution of the particle size.

In order to shed light on the role of PVOH in the development of the polymer microstructure, reaction S4 was carried using a nonionic emulsifier (Disponil AFX4060) and it was compared with reaction S1, which was carried out under the same conditions, but with PVOH. The formulation used to perform this reaction is given in Table 1. Figure 11 compares the evolution of particle size for runs S1 and S4. During the monomer feed, the particle size obtained with Disponil AFX4060 was larger (less particles) than with PVOH. In both cases, after the monomer and emulsifier addition, particle aggregation led to the increase of the average particle diameter, but the increase observed with Disponil AFX4060 was less pronounced than with PVOH. Bimodal particle size distributions were obtained for the final latexes (Figure 12) and plenty of small particles still remained at the end of the process. Figure 13 showed that, during the monomer feed, the polymerization rate was slower in the system stabilized by Disponil AFX4060, because of the lower number of particles obtained, but almost complete conversion was achieved during the postpolymerization step. No gel was obtained in the polymerization stabilized with Disponil AFX4060, and the molecular weights were lower than in the presence of PVOH (Figure 14), likely due to the combination of two effects: (i) On one hand, a higher frequency of radical entry, resulting from the lower number of polymer particles

Figure 13. Effect of the emulsifier type on the evolution of the instantaneous conversion.

and perhaps the absence of restrictions due to chain transfer to surfactant, which led to a shorter kinetic chiain length. (ii) On the other hand, the lower conversion achieved during the process, which reduced the chain transfer to polymer and the propagation to terminal double bonds. 9287



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measured experimentally in each reaction was used as an input. (2) Because the majority of the polymerization occurs in the polymer particles, for the calculation of MWD, the amount of polymer formed in the aqueous phase was considered to be negligible, compared to that formed in polymer particles. (3) Termination was assumed to occur only by disproportionation, since it is the most commonly accepted termination mechanism for VAc.11,41 (4) The pseudo-steady-state assumption was applied to the population balance of radicals. (5) The polymer particles were assumed to contain a limited number of free radicals (I). Thus, instantaneous termination was assumed to occur when a radical entered into a polymer particle already containing I radicals. (6) Only monomeric radicals formed by chain transfer to VAc were able to desorb from the polymer particles to the aqueous phase. (7) A homogeneous distribution of the inactive polymer among particles was assumed. (8) Because the chain transfer to polymer is proportional to the length of the polymer chain and the PVOH chains were much shorter and contained less abstractable hydrogens than the VAc−VeoVa10 chains, the contribution of chain transfer to PVOH to the MWD is negligible and the reaction between radicals and PVOH was not considered when calculating the MWD. On the other hand, as the entering radicals should cross the PVOH barrier surrounding the polymer particle, chain transfer to PVOH may occur, lowering the rate of entry. The effect of PVOH on the radical entry was considered to be included in an efficiency factor (fentry). Material Balances. Assuming that the rate of the redox reaction is proportional to the concentrations of oxidant and reductant, the material balances for the components of the redox pair in the aqueous phase are

Figure 14. Effect of the emulsifier type on the final MWD.

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MATHEMATICAL MODEL Although the emulsion polymerization of VAc has been extensively modeled,30−40 relatively little work has been done in modeling the emulsion copolymerization of VAc−VeoVa10.3,8,10,11 In this work, a mathematical model was used to investigate the role of PVOH and initiator type on both radical entry and VAc− VeoVa10 polymer microstructure and its parameters estimated fitting the data presented above. The mathematical model was developed considering the reactions included in Scheme 1 and incorporating the following features and assumptions to the model: (1) A monodisperse polymer particle size distribution was considered. As the model focus on radical entry and polymer microstructure, the evolution of the particle size Scheme 1. Mechanism of VAc−VeoVa10 Free-Radical Emulsion Copolymerization

F d[Ox] (mol/(L s)) = ox − a′k redox[Ox][Red] dt Fw

(1)

F d[Red] (mol/(L s)) = Red − b′k redox[Ox][Red] dt Fw

(2)

where [Ox] and [Red] are the oxidant and reductant concentrations in the aqueous phase (mol/L), respectively; Fox and Fred are the respective feeding rates of oxidant and reductant to the reactor (mol/s); kredox is the characteristic rate coefficient for the redox reaction rate (L/(mol s)); Vw is the volume of the aqueous phase (L); and a′ and b′ are the stoichiometric coefficients of the oxidant and reductant, respectively. For a redox system TBHP/AsAs, the values of a′ and b′ are 2 and 1, respectively,42 and for KPS/NaMS both are considered to be equal to 1.43 The material balance for water is dVw (L/s) = Q w dt

(3)

where Qw is the water feed rate to the reactor. Taking into account the reactions in the polymer particles and the aqueous phase, the material balances for monomers and polymer are 9288



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dM i (mol/s) = Fi − R pWi − R ppi dt dVpol dt

(L/s) =

Under pseudo-steady-state conditions, the balance for the radicals in the aqueous phase is

(4)

Np 0 = kdn ̅ + 2k redox[Red][Ox] − 2ktdw[R ]w 2 NAVw Np (mol/(L s)) − ka[R ]w NAVw

W p (R pVAc )M wVAc − R pVAc

ρpVAc +

W (R pVeo

p )M wVeo − R pVeo

ρpVeo

(5)

where ka is the entry rate coefficient (L/(mol s)), is the rate coefficient for termination by disproportionation in the aqueous phase (L/(mol s)), and kd is the desorption rate coefficient (1/s). It is worth pointing out that, in order to solve eq 11, the value of the average number of radicals per particle is required. The number of radicals per particle depends on the relative rates of radical entry from the aqueous phase, radical exit from the polymer particles, and bimolecular termination in the polymer particles. The population balance of particles containing i radicals in the reactor is

where Mi is the total amount of monomer i in the reactor (mol), Fi is the monomer i feed rate (mol/s), Vpol is the volume of polymer (L) in the reactor, MwVAc and MwVeo are the molecular weights of the monomers (kg/mol), ρpVAc and ρpVeo are the densities of VAc and VeoVa10 units in the copolymer (kg/L), p and RW pi and Rpi are the polymerization rates of monomer i in the aqueous phase and polymer particles (mol/s), given by W W R pWi (mol/s) = (k pAiPAW + k pB iPB )[Mi]w [R ]w Vw

R ppi (mol/s) = (k pAiPAp + k pBiPBp)[Mi]p

(6)

nN ̅ p NA

dNi (particles/s) = − (ka[R ]w + kdi + ci(i − 1))Ni dt

(7)

+ ka[R ]w Ni − 1 + kd(i + 1)Ni + 1

where kpij are the propagation rate coefficients (L/(mol s)), Pzi the probability of i being the last monomer unit in the propagating active chain in phase z, [Mi]z the concentration of monomer i in phase z (mol/L), [R]w the concentration of radicals in the aqueous phase (mol/L), Vw the volume of the aqueous phase (L), n ̅ the average number of radicals per particle, Np the number of polymer particles in the reactor, and NA the Avogadro’s number. For copolymerization, the probabilities are expressed as44 z

Pi =

+ c(i + 2)(i + 1)Ni + 2

The desorption rate coefficient was calculated as46

ji

+

(12)

In this work, eqs 11 and 12 were solved under pseudo-steady-state conditions by applying the iterative method proposed by Ballard et al.,45 which provides the distribution of particles with i radicals. The average number of radicals per particle, n,̅ can be calculated as ∞ ∑i = 1 iNi n̅ = ∞ ∑i = 1 Ni (13)

k pz [Mi]z k pz [Mi]z ji

(11)

kwtd

k pz [Mj]z ji

(8)

Pj z = 1 − Pi z

kd (s−1) = λ

(9)

dTDB (mol/s) = [(ktrmon Pip + ktrmon Pjp)[Mi]p ii ji dt

I

+ ktd ∑ h(h − 1) h=2

TDB nN ̅ p − k pTDB Vp NA

(14)

where λ is the rate of radical diffusion, γ the rate of radical formation via chain transfer to monomer, relative to diffusion, and η is the rate of radical reaction, relative to diffusion, which is defined as

The material balance for the terminal double bonds that are formed by the chain transfer to monomer and by bimolecular termination by disproportionation is as follows:

Pip + ktrmon Pjp)[Mj]p ] + (ktrmon ij jj

⎛ ⎞ fentry λNp γNA ⎜ ⎟ 1 − w ηm ⎜⎝ fentry λNp + k pAA[MA ]w + 2kt [R ]w ⎟⎠

λ= nN ̅ p NA

1+

Nh NAVp

γ=

(10)

η=

where TDB is the total amount of double bonds in the reactor (mol), kmon trij represents the rate coefficients for the chain transfer to monomer (L/(mol s)), ktd is the effective termination rate coefficient by disproportionation (L/(mol s)), kTDB is p the propagation to terminal double bonds rate coefficient (L/(mol s)), Vp is the total volume of the monomer swollen polymer particles (L), I is the maximum number of radicals per particle, and Ni is the number of polymer particles containing i radicals. Because of the similar reactivity of the VAc and VeoVa10 radicals, the propagation to terminal double bonds rate coefficient, kTDB p , was considered to be the same for both radicals.

Dw δ1 DhR

4πDwR ⎛D ⎞ + ⎜ D wm ⎟ R ⎝ p ⎠

(

1 η coth(R η ) − 1

)

(15)

⎛ 1 ⎞ (ktrmon PAp + ktrmon P p)[MA ]p ⎜ v N ⎟ AA j BA B ⎝ p A⎠ Dp

(16)

⎛ n − 1⎞ k pAA[MA ]p + k pAB[MB]p + ktdw ⎜ v N ⎟ ⎝ p A⎠ Dp

(17)

where the subscript A refers to VAc; Dw, Dp, and Dh are the diffusion rate coefficients in the aqueous phase, through polymer particles, and through the hairy layer (dm2/s), respectively; δ1 is the thickness of the hairy layer (dm); m is the partition coefficient of the monomeric radicals between the particle and aqueous phase; R is the particle radius (dm), and fentry is an adjustable parameter of radical entry. The rate coefficient for radical entry is calculated by the following expression: 9289



Article

ka (L/(mol s)) = fentry λNA

the presence of chain-length modifiers, such as chain-transfer agents or cross-linkers, in the formulation. In VAc−VeoVa10 copolymerization, the polymerization with terminal double bonds (TDB) (resulting from termination by disproportionation or chain transfer to monomer) and chain-to-polymer transformation strongly affect the molecular weight distribution. In order to account for radical compartmentalization, the idea of singly distinguished particles developed by Lichti et al.50 and later modified by Butte et al.51 was used. Singly distinguished particles are the particles with i radicals, one of which being the length n. For the present system, there is no need to use double distinguished particles (particles with i radicals, two of which being lengths n and m), because termination is by disproportionation. The population balance for singly distinguished particles is

(18)

The gel effect was taken into account by using the expression proposed by Friis and Hamielec:32

(

ktd (L/(mol s)) = ktd0 exp aφpp + b(φpp)2 + c(φpp)3

) (19)

where φpp is the volume fraction of polymer, and k0t is the termination by disproportionation rate coefficient in a diluted system. Because of the diffusional limitations, the effective termination rate coefficient in not affected by the type of radicals involved in the reaction; therefore, ktij (L/(mol s)) = ktji = ktii = ktjj = ktd

(20)

Monomer Partitioning. In a semicontinuous process, the newly fed monomer diffuses through the aqueous phase to the polymer particles to be polymerized. Usually, polymerization is the rate-determining step, and, hence, the concentration of the monomers in the different phases is given by the thermodynamic equilibrium. In this model, the distribution of the monomers among phases is calculated using partition coefficients.47 For two or more monomers, the calculation of the concentrations of the monomers in the different phases involves the simultaneous solution of the thermodynamic equilibrium equations and the material balances. K id =

V id /Vd V iaq /Vaq

K ip =

Vip/Vp V iaq /Vaq

p φpol +

=

=

φi φi

φi

aq

∑ φi p = 1

+

∑ φi

w

= − [(p + ρ + ci(i − 1) + trm + trp + kd(i − 1) + pTDB )]Ni , n + pNi , n − 1 + ρNi − 1, n + ci(i + 1)Ni + 2, n + kdiNi + 1, n + trpn n−1

+ pTDB

∑ φid = 1 i

[Dn] iNi [υ1]

[Dn − h] + δn ,1(ρNi − 1 + trmiNi) [υ0]

⎛ I−1 ⎞ + δi , I − 1⎜ρ NI , n⎟ ⎝ ⎠ I

(29)

where p (s−1) =

(k pAiPAp + k pBiPBp)[Mi]p

∑

(30)

i = 1,2

ρ (s−1) = ka[R ]w

(21)

trm (s−1) = (22)

(27)

p Vpφpol = Vpol

(28)

polA polA + pol B

(33)

(34)

and δi,j = 1 if i = j and δi,j = 0, otherwise. [υi] is the ith moment concentration of the length distribution of inactive polymer chains. The material balance for the inactive chains (n > 0) is

(25)

w Vwφwater = Vwater

(32)

⎛ TDB ⎞ ⎟⎟ pTDB (s−1) = k pTDB⎜⎜ ⎝ Vp ⎠

(24)

(26)

p mon p (ktrmon Ai PA + k tr Bi PB )[Mi]p

trp (s−1) = (ktrpolAAPAp + ktrpolBAPBp)[υ1]

(23)

Vpφi p + Vdφid + Vwφi w = Vi

∑

(31)

i = 1,2

=1

i

∑ Ni ,h h=1

p

i

w φwater

dt

d

aq

φi

dNi , n

d[Dn] (mol/(L s)) dt I I 1 ⎡⎢ 1 (trm + trp) ∑ iNi , n + ρ NI , n + 2cd ∑ (i − 1)Ni , n = NAVp ⎢⎣ I i=1 i=2

Vzi

where is the volume of monomer i in phase z (polymer particles (p), droplets (d), and aqueous phase (aq)); φzi is the volume fraction of monomer i in phase z; Kpi and Kdi are the partition coefficients between the particles and aqueous phase and the droplets and the aqueous phase, respectively; Vp, Vd, and Vw are the volume (L) of monomer swollen particles, monomer droplets, and aqueous phase, respectively; and Vi, Vpol, and Vwater are the volumes (L) of monomer i, polymer, and water, respectively. Efficient algorithms for the solution of this system of nonlinear algebraic equations are available.48,49 Molecular Weights. Because the length of the macromolecules depends on the environment in which they growth, the molecular weight is controlled by the number of radicals per particle, monomer concentration in the polymer particles and by

− trpn

[Dn] [υ1]

I

∑ iNi − pTDB i=1

[Dn] [υ0]

I

⎤

∑ iNi⎥ i=1

⎥⎦

(35)

Equations 29−35 were solved by means of the Kumar− Ramkrishna method,52−54 taking into account the modification of Butte et al.51,55,56 In this method, the entire range of the independent variable (polymer chain length) is divided in a series of intervals and the chains in each interval aggregated as follows: nj + 1− 1

Si , j =

∑ n = nj

9290

Ni , n (36) dx.doi.org/10.1021/ie4032499 | Ind. Eng. Chem. Res. 2014, 53, 9282−9295


Article

nj + 1− 1

Qj =

∑

Inactive polymer chains: Dn

n = nj

(37)

n

nj̅ =

I 1 ⎡⎢ 1 (trm + trp) ∑ Si , j + ρ SI , j = NAVp ⎢⎣ I i=1

d[Q j]

All of the polymer chains in each interval are represented by a single chain length that is referred as pivot value and corresponds to the average chain length of the polymer chains in the interval

dt

I

+ 2cd ∑ (i − 1)Si , j − trpnj̅

−1

∑nj=+1n nDn

i=2

j

Qj

[Q j] [υ1]

I

∑ iNi i=1

⎤ [Q j] ∑ iNi⎥ − pTDB [υ0] i = 1 ⎥⎦ I

(38)

Therefore, the quasi-continuous distributions of Ni,n and Dn are transformed to discrete distributions with the polymer chains placed at a limited number of pivots. Fifty (50) pivots homogeneously distributed in the logarithm domain were used. When reactions such as propagation, chain transfer to polymer, and propagation to terminal double bonds occur, the length of the newly created chain (np̅ ) might fall between two contiguous pivots n̅k and n̅k+1. In this case, the properties of the newly created chain are shared between the two contiguous pivots by means of the following factors:52

(42)

The direct output of the model is a discrete molecular weight distribution (Qj) at the pivots. The continuous MWD of Dn can be obtained from the discrete distribution by assuming a linear variation for all the chain lengths between two pivot values:53 Dn = Q n

k̅ − 1

nk̅ − n n − nk̅ − 1 + Qn k̅ n − n nk̅ − nk̅ − 1 k̅ k̅ − 1

(nk̅ − 1 ≤ n ≤ nk̅ )

(43)

nk̅ + 1 − (n p̅ ) a(n p̅ , nk̅ ) = nk̅ + 1 − nk̅

(39)

where nk̅ is the value of the pivot k (namely, the average chain length of the pivot) and n is the chain length. Table 3 presents the values of the parameters taken from literature and those estimated in this work. Parameter estimation

(n p̅ ) − nk̅ nk̅ + 1 − nk̅

(40)

Table 3. Parameters of the Model

b(n p̅ , nk̅ + 1) =

where a(n̅p, n̅k) and b(n̅p, n̅k+1) are the fraction of chains assigned to n̅k and nk̅ +1, respectively. With this partitioning, the overall number of polymer chains and the overall number of polymerized monomer units are preserved. Because of the propagation to terminal double bonds and the chain transfer to polymer, branched and cross-linked highmolecular-weight polymer chains are formed in the polymer particles. The size of these high-molecular-weight polymers may grow to form a nanogel whose size cannot exceed the size of the polymer particles. Therefore, following Calvo et al.,57 a size limitation was taken into account in order to ban reactions (propagation to TDB and chain transfer to polymer) that can produce polymer chains with a volume higher than the volume of the polymer particle. The population balances for the lumped variables are described as follows:

= 2.0 × 10 kpBB

L/(mol s)

68

= 800 kTDB p kTBHP/AsAc = 7.6 × 10−2 redox KPS/NaMS = 2.3 × 10−1 kredox 0 ktdij = 3.55 × 108

L/(mol s) L/(mol s) L/(mol s) L/(mol s)

estimated estimated estimated 69

Active polymer chains:

k0tdAA = k0tdBB = k0tdAB = k0tdBA = k0td

L/(mol s)

assumed

ktd = k0td exp[aφpp + b(φpp)2 + c(φpp)3] a = −0.011 b = −0.013 c = −6.7 fentry (Run S1, PVOH,TBHP/AsAc) = 3.5 × 10−3 fentry (Run S2, S3, PVOH,KPS/NaMS) = 2.05 × 10−5 fentry (Run S4, Disponil,TBHP/AsAc) = 1.0 × 10−2 rA = 0.99 rB = 0.99 Dw = 1.1 × 10−7 Dp = 1.1 × 10−8 Dh = 1.0 × 10−7 m = 29.0 KdA = 34.7 KdA = 29.5

L/(mol s)

69 estimated estimated estimated estimated estimated estimated 2 2 70 70 46 71 72 72

dSi , j dt

kinetic parameters

ref

kpAA = 1.44544 × 10 exp((−20700/8.31)T)

L/(mol s)

66

kpBB = 2.04174 × 107 exp((−22200/8.13)T)

L/(mol s)

67

−4

= 4.55 × 10 kpAA

L/(mol s)

68

−4 kmon trBB = 4.55 × 10 kpBB

L/(mol s)

68

kmon trAB

=

kmon trAA

L/(mol s)

assumed

=

kmon trBB

L/(mol s)

assumed

L/(mol s)

68

kmon trAA

kmon trBA

−4 kpol trA = 2.0 × 10 kpAA

kpol trB

= − [(bjp + ρ + ci(i − 1) + trm + trp + (i − 1)kd + pTDB )]Si , j + pbj − 1Si , j − 1 + ρSi − 1, j + ci(i + 1)Si + 2, j [Q j] iNi + ikdSi + 1, j + trpnj̅ [υ1] ⎧ p,q ⎪ ∑ b(np̅ + nq̅ , nj̅ )Si ,p[Q q] + pTDB ⎨ ⎪ nj̅ − 1≤ np̅ + nq̅ ≤ nj̅ ⎩ ⎫ p,q ⎪ ∑ a(np̅ + nq̅ , nj̅ )Si ,p[Q q]⎬ + ⎪ nj̅ ≤ np̅ + nq̅ ≤ nj̅ + 1 ⎭ ⎛ I−1 ⎞ SI , j⎟ + δj ,0(ρNi − 1 + trmiNi) + δi , I − 1⎜ρ ⎝ ⎠ I

unit

7

(41) 9291

−4

dm2/s dm2/s dm2/s



Article

Figure 15. Comparison of the model simulations and experimental data for the overall conversion in runs S1, S2, S3, and S4.

Figure 16. Comparison of the model simulations and experimental data for the evolution of MWD in runs S1, S2, and S4.

was carried out by means of the DBCPOL algorithm of direct search (Library IMSL, International Mathematics and Statistics

Library, Visual Numerics, Inc., Houston, TX). The objective funcation was 9292


Industrial & Engineering Chemistry Research j=

∑∑ N Npoint

1 Npoint

⎛ Zexp − Zsimul ⎞2 ⎟⎟ ∑ ⎜⎜ Zexp ⎠ Z ⎝

Article

and PVOH as a polymeric stabilizer. A mathematical model was used to shed light on the effect of PVOH and initiator type on polymerization kinetics and polymer microstructure. It was found that PVOH reduces the rate of radical entry into the polymer particles. This effect was attributed to the chain transfer of the entering radicals to PVOH and depends on the initiator system used. Thus, it is more pronounced for KPS/NaMS than for TBHP/AsAc. A consequence of the chain transfer to PVOH is the formation of PVOH-graft-poly(VAc-VeoVa10) copolymer. As PVOH is not soluble in the solvents that are commonly used (e.g., THF) to determine gel and sol MWD by the classical Soxhlet extraction, the use of this method overestimates the gel fraction and underestimates the molecular weight of the sol, because non-cross-linked graft copolymers are wrongly included in the gel. A new method based on the acetylation of the hydroxyl groups of the PVOH has been developed to properly measure the MWD of these copolymers.

(44)

where N is the number of experiments, Npoint is the number of experimental points in each experiment, and Zexp and Zsimul are, respectively, the experimental and model predicted values for the variable Z. In this work, monomer conversion and the molecular weight distributions were used as variable Z. As the model focused on the MWD, no attempt to model the particle size was carried out, and, hence, the experimental evolutions of the number of particles obtained in semicontinuous reactions S1−S4 were used as an input of the model. The adjustable parameters were the radical entry efficiency factor (fentry), the rate coefficients for the redox reactions (kTBHP/AsAc and kKPS/NaMS ), redox redox the parameters for the gel effect, and the rate coefficient for propagation to terminal double bonds (kTDB p ). The parameter fentry takes into account the effect of several mechanisms that might reduce the rate of radical entry such as the resistance to radical diffusion of the monomeric radicals through the hairy layer, the surface charge repulsion and the hydrogen abstraction from the polymeric stabilizer.22−26,58−60 For redox systems, the rate of radical generation is not wellknown and the range of the values reported in the literature is very broad.61−65 Hence, in this work, the TBHP/AsAc and KPS/NaMS redox initiation rate coefficients were estimated. The gel effect depends on the internal viscosity of the polymer particles as well as on the molecular weights of the growing chains. This means that they are specific of each system, and hence they were included in the set of adjustable parameters. The rate coefficient for propagation to terminal double bonds was also estimated. Figure 15 presents the fitting of the experimental results of the evolution of the overall gravimetric conversion in runs S1, S2, S3, and S4 by the model using the parameters in Table 3. It can be seen that the model fits the experimental data quite well. It is interesting to point out that, to achieve this fitting, widely different radical entry rates were estimated. The smallest value was for runs S2 and S3 carried out with PVOH and KPS/NaMS, which most likely results from the combined effect of the hydrophilicity of the sulfate ion radicals that increase termination in the aqueous phase and the high rate for chain transfer to PVOH that reduces the rate of radical entry. The extensive grafting to PVOH is supported by the high apparent gel content measured using the classical Soxhlet extraction (Figure 8). A higher estimated value of fentry was obtained for TBHP/AsAc that produced hydrophobic tertbutoxyl radicals able to enter directly into the polymer particles. The effect of PVOH on the entry of tert-butoxyl radicals is evident when the values of fentry for runs S1 and S4 are compared. It can be seen that the presence of PVOH reduces the rate of radical entry. Figure 16 presents the fitting of the experimental MWD of the final latexes of runs S1, S2, and S4 by the model. No acetylated samples were available for run S3. The simulated results do not include the unreacted PVOH, and, hence, the comparison should be done with the peak corresponding to the VAc-VeoVa10 copolymer. It can be seen that a good fitting was achieved and that the model captures the formation of the high-molecularweight polymer in the last part of the process well.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The financial support of Wacker ChemieAG is gratefully acknowledged.

■

REFERENCES

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CONCLUSIONS In the foregoing, the semicontinuous emulsion co-polymerization of VAc and VeoVa10 was investigated under industriallike conditions, namely, using a high solids content (57 wt %) 9293



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