Semicontinuous Emulsion Co-polymerization of Vinyl Acetate and VeoVa10

Semicontinuous Emulsion Co-polymerization of Vinyl Acetate andVeoVa10Amaia Agirre,† Inigo Calvo,†,‡ Hans-Peter Weitzel,§ Wolf-Dieter Hergeth,§ and Jose 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 Sebastian 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) theformation of PVOH-graft-poly(VAc−co-VeoVa10) leads to an overestimation of the gel content and an underestimation ofthe sol molecular weight when the standard characterization techniques are directly applied. A new method to properlycharacterize the MWD of these copolymers is presented. A mathematical model is used to analyze the effects of surfactant andinitiator on the kinetics and polymer microstructure.

■ INTRODUCTION

Vinyl acetate (VAc) copolymers are widely used for coatings.Soft co-monomers are used to decrease the glass-transitiontemperature of the copolymer to values that allow the formationof a high-quality film. In addition, in order to protect theVAc units of the copolymer against hydrolysis, hydrophobiccomonomers are used. Butyl acrylate (BA) and VeoVa10 (vinylester of neodecanoic acid) are the most commonly used co-monomers. Ethylene is another alternative but it requires the useof pressurized reactors, which increase the manufacturing costs,and the small size of the ethylene offers less steric protection tothe neighboring vinyl acetate units against hydrolysis.1 VeoVa10is more bulky than BA and, hence, it offers better protectionto VAc. This makes VAc−VeoVa10 copolymers the preferredcoating for inorganic (e.g., brick and concrete) substrates. TheVeoVa10 content is chosen to optimize the cost/performanceratio. Latexes for interior coatings contain 15−20 wt % ofVeoVa10, whereas exterior latexes contain 20−30 wt %.2 The useof VeoVa10 presents the additional advantage that it has areactivity similar than VAc. Despite the practical importanceof the VAc−VeoVa10 copolymers, relatively few studies havebeen published.Optimal polymerization strategies to maximize the production

rate and scrub resistance of VAc−VeoVa10 latexes stabilized byan anionic surfactant and produced in tank reactors with a limitedheat removal capacity were reported by Unzue et al.3 They foundthat 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 anionicsurfactants with a nondisclosed protective colloid. It was foundthat VeoVa10 presented advantages in scrub resistance, gloss andhydrophobicity, whereas BA developed better wet adhesion andhiding efficiency. 2EHA offered hiding efficiency similar to thatof BA.

Continuous loop reactors have been used to produce high-solids VAc−VeoVa10 latexes stabilized with a mixture of anionicand nonionic surfactants.5−11 The effect of mass transfer ofVeoVa10 on copolymer composition in batch and semibatchminiemulsion and emulsion polymerizations stabilized withsodium lauryl sulfate has been studied.12 It was found that (i) thecopolymers presented a single Tg value and (ii) the Tg valuewas lower for the semibatch runs, suggesting a slightly betterincorporation of VeoVa10. No influence of the polymerizationmethod (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 reportsin the open literature using PVOH to stabilize VAc−VeoVa10latexes. High-solids VAc−VeoVa10 stabilized with PVOH canbe produced via batch miniemulsion polymerization, whereasbatch emulsion polymerization results in massive coagulation.13

In addition, it has been reported that, in batch processes, theextent of grafting of PVOH strongly depends on the initiator thatis used. Grafting increases in the following order:

≈

< ‐

<

tert

benzoyl peroxide lauryl peroxide

butyl hydroperoxide/ascorbic acid

potassium persulfate

The fraction of grafting was higher in miniemulsion than inemulsion polymerization.14

It is interesting to note that the polymerizations using PVOHwere carried out in batch that cannot be used in commercialpractice because of safety problems associated with the rapid heatgeneration rate.

Special Issue: Massimo Morbidelli Festschrift

Received: October 3, 2013Revised: November 7, 2013Accepted: November 13, 2013Published: November 13, 2013

Article

pubs.acs.org/IECR

© 2013 American Chemical Society 9282 dx.doi.org/10.1021/ie4032499 | Ind. Eng. Chem. Res. 2014, 53, 9282−9295

pubs.acs.org/IECR

In this work, the semicontinuous emulsion copolymerizationof vinyl acetate and VeoVa10 was investigated under industrial-like conditions, namely, using high solids contents (57 wt %) andPVOH as a polymeric stabilizer. It was found that PVOHstrongly affects the polymer microstructure as measured usingthe classical methods. A new method to properly determine themolecular weight distribution (MWD) of these polymers ispresented. A mathematical model was developed to shed light onthe effect of PVOH and initiator type on polymerization kineticsand polymer microstructure.

■ EXPERIMENTAL SECTIONMaterials. Technical-grade monomers, vinyl acetate (VAc,

Quimidroga), and neodecanoic acid vinyl ester (VeoVa10,Hexion) were used without further purification. Poly(vinylalcohol) (PVOH 4/88; viscosity of a 4% aqueous solution at23 °C is 4 mPa s, the degree of hydrolysis is 88 mol %) was kindlysupplied by Wacker Chemie AG, nonionic emulsifier DisponilAFX4060 (Cognis, Germany) and anionic sodiumdodecyl sulfate(SDS, Aldrich) were used as emulsifiers. tert-Butyl hydroperoxide(TBHP, Aldrich), ascorbic acid (AsAc, Panreac), potassiumpersulfate (KPS, Fluka) and sodium metabisulfite (NaMS) wereused as initiators. Formic acid (Panreac) was added to acidify theinitial aqueous reactor charge and iron ammonium sulfate wasused to accelerate the generation of radicals when PVOH wasused. Deionized water was used throughout the work andhydroquinone (Fluka) was used for stopping the reaction in thesamples withdrawn from the reactor.Polymerization Process. Semicontinuous polymerizations

were carried out in a 1-L glass reactor fitted with a refluxcondenser, a sampling device, a nitrogen inlet, four feeding inlets,a thermometer and a stainless steel anchor stirrer rotating at250 rpm. Reaction temperature and the feed flow rates werecontrolled 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

solution of emulsifier was added and acidified to pH 4 withformic acid (10 wt % solution). Then, 0.7 mL of iron ammoniumsulfate (1 wt % solution) was added. A mixture of VAc andVeoVa10 was fed over a period of 5 min and the reactor washeated 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

initiator feeding rates were changed to 0.14 g/min during 30 minand then decreased again to 0.035 g/min for additional 30 min.Then, the aqueous solution of emulsifier (0.627 g/min) and themixture of monomers (1.158 g/min) were fed separately over aperiod of 3 h. At the end of the monomer feed, the initiator feedsrates were increased to 0.07 g/min and maintained for 2 h.After this period, the reactor was cooled to 40 °C and the post-

polymerization was started. The oxidant solution was fed overa period of 10 min (0.084 g/min), whereas the reductant wasadded during 30 min (0.028 g/min). This step was repeatedtwice.The final solids content of the latex was ∼57 wt%. Samples

were withdrawn at regular intervals from the reactor and thepolymerization was short-stopped with hydroquinone.Table 2 summarizes the semibatch polymerizations carried

out to study the effect of initiator and emulsifier types andconcentrations on kinetics and polymer microstructure.

Characterization. Monomer conversion was determinedgravimetrically. The copolymer composition was not measured,because the composition of the copolymer was expected to bethe same as the monomer ratio, since the values of the reactivityratios were almost equal to 1 (see Table 3, which appears laterin this work). The z-average diameter of the polymer particleswas measured by dynamic light scattering (Zetasizer Nano Z,Malvern Instruments). Samples were prepared by diluting afraction of the latex with deionized water. The particle sizedistributions were determined by using a disk centrifugephotosedimenter (BI-DCP Brookhaven Instruments). Initially,the gel content was measured by means of a classical Soxhletextraction, using tetrahydrofuran (THF) as a solvent. Theinsoluble part was considered to be gel; the MWD of the solublepart was measured via gel permeation chromatography−sizeexclusion chromatography (GPC-SEC), and as the equipmentwas calibrated using polystyrene standards. The results obtainedwere based on polystyrene.However, it was found that this method overestimated the

gel fraction because PVOH-graft-poly(VAc−co-VeoVa10) wasformed in the process, and, since PVOH is not soluble in THF,an important fraction of the graft copolymer was accounted for asgel. In order to overcome this problem, the polymers wereacetylated to transform the −OH groups into −CH3 groups,namely, transforming PVOH into pVAc, which is soluble inTHF. The acetylation process was as follows. In the presenceof 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 driedlatex and the system was allowed to react under agitation at roomtemperature for 24 h. The dried acetylated polymer was obtainedby evaporating the solvent. This product was then subjected to aSoxhlet extraction in order to separate the gel and sol parts, andthe sol MWD was measured via GPC-SEC.

Table 1. General Formulation Used in the SemibatchProcesses

compound solution (%)initial

charge (g) feed (g)PostPolym.a

(g)

vinyl acetate 166.6 187.6VeoVa10 41.72 20.86

poly(vinyl alcohol),PVOH(4/88)b

20 83.58 66.92

Disponil(AFX4060)c 6.95 5.21iron ammonium sulfateb 1 0.7

water 125.3b 45.92b

189.38c 97.37c

oxidant 0.1d−0.2e 22.0510d−5e 1.68

reductant 0.17d−0.34e 22.055d−2.77e 1.68

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

Table 2. Summary of the Reactions Performed

Redox pair

Emulsifier Pure initiator Ox./Red. (% wbm)

latex type%

wbm ox./red. semibatchpost-

polymerizationa

S1 PVOH 7.22 TBHP/AsAc 0.005/0.009 0.04/0.02S2 PVOH 7.22 KPS/NaMS 0.005/0.009 0.04/0.02S3 PVOH 7.22 KPS/NaMS 0.01/0.018 0.02/0.011S4 Disponil 2.92 TBHP/AsAc 0.005/0.009 0.04/0.02

aBoth additions are included.

Industrial & Engineering Chemistry Research Article

dx.doi.org/10.1021/ie4032499 | Ind. Eng. Chem. Res. 2014, 53, 9282−92959283

The acetylation process was validated by acetylating purePVOH (4/88). Attenuated total reflection Fourier transforminfrared spectroscopy (ATF FT-IR) was used to check that thehydroxyl groups, which are evident in the broad characteristicpeak at 3150 cm−1, disappeared in the acetylated sample (Figure 1).

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

worth pointing out that this method opens the possibility of a moredetailed characterization of themicrostructure of the PVOH, whichcurrently is given by the degree of hydrolysis and the viscosity ofa 4 wt % aqueous solution.In order to check if the VAc−VeoVa10 copolymer chains were

damaged by the acetylation process, a VAc−VeoVa10 copolymersynthesized in batch emulsion polymerization using a mixtureof SDS and Disponil AFX4060 as surfactants was subjected tothe acetylation process. This latex did not contain any gel asmeasured by the classical Soxhlet extraction. Figure 3 shows thatthe MWD did not vary during the acetylation process, namely,the VAc−VeoVa10 copolymer chains were not affected by theacetylation process.

■ EXPERIMENTAL RESULTS AND DISCUSSIONTwo polymerizations (S1 and S2) were carried out to study theeffect of the initiator type, using the general formulation givenin Table 1; TBHP/AsAc was used in run S1 and KPS/NaMS inrun S2.Figure 4 compares the evolution of the average particle size

during polymerizations S1 and S2. In both cases, the average

particle diameter increased during the process, with the oneobtained using TBHP/AsAc always being larger. At the beginningof the process, both systems exhibited a similar particle size butafter the end of monomer and emulsifier feeds, a strong increasewas observed in the average particle size with TBHP/AsAc,because of the agglomeration of polymer particles (no macro-scopic coagulum was observed). However, at the end of theprocess, a decrease in the average particle diameter was observed,which indicated the formation of new small particles at thisstage. A similar behavior was reported by Donescu et al.15 in thesemicontinuous emulsion polymerization of vinyl acetate carriedout in the presence of PVOH using H2O2/FeSO4 as a redoxinitiator.

Figure 1. Attenuated total reflection Fourier transform infraredspectroscopy (ATF FT-IR) spectra of nonacetylated (PVOH) andacetylated (AcPVOH) PVOH.

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

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

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



Figure 5 presents the bimodal particle size distribution with abroad large mode obtained with TBHP/AsAc at the end of S1polymerization. This is typical in VAc emulsion polymer-ization.15−17 The large number of small particles that appearedat the end of the process revealed the generation of new particlesby homogeneous nucleation at least during the last stages of theprocess. On the other hand, the large particles evidenced theaggregation of polymer particles. The latex formed with KPS/NaMS coagulated at the end of the reaction, not being possibleto determine the particle size distribution. This destabilizationmight be related to the increase of ionic strength due a highamount of charges incorporated to the system by the initiatorduring the post-polymerization step. This reduced the electrostaticrepulsive energy barrier, so that the latex ultimately coagulated.18

The evolution of the number of particles with conversion forruns S1 and S2 is shown in Figure 6. The number of particles

was higher with KPS/NaMS than with TBHP/AsAc during theentire polymerization. In addition, in run S2 (KPS/NaMS), thenumber of particles increased with conversion, indicating thatnew particles were formed continuously throughout the reaction.A possible reason for the higher number of particles obtainedwith KPS/NaMS is the contribution of the SO4

− groups to thestabilization of the polymer particles.

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

regardless of the initiator type used, likely because of the lowamount of initiator used. A substantial increase of the conversionwas observed for TBHP/AsAc when the initiator feed ratewas increased, but the conversion obtained in run S2 withKPS/NaMS remained low. During the addition of monomerand emulsifier (from 90 min to 270 min), the instantaneousconversion remained almost constant in both reactions showingthat polymerization rate was only slightly lower than themonomer feed rate. In the final batch process and during thepost-polymerization step, the initiator feed rates were increasedleading to higher polymerization rates in both runs. In the caseof KPS/NaMS, a temperature runaway was observed as aconsequence of the fast reaction of the high amount of monomeraccumulated into the reactor.Figure 7 clearly shows that the polymerization rate was slower

for KPS/NaMS than for TBHP/AsAc, even though the numberof particles was higher (Figure 6), which implied that the averagenumber of radicals per particle was lower for KPS/NaMS. Thiscan be due to a lower rate of radical generation or to an inefficientradical entry mechanism. The rate of radical generation for theKPS/NaMS system has been reported to be similar if not slightlyhigher than that of TBHP/AsAc.19 Therefore, the likely reasonfor the lower n is the entry of the radicals. The sulfate ion radicalsgenerated with KPS/NaMS are very hydrophilic and, hence, theycannot enter directly into the polymer particles, whereas the tert-butoxyl radicals generated from TBHP/AsAc are hydrophobicand able to readily enter into the polymer particles. Therefore,•SO4

− needs to react with themonomer dissolved in the aqueousphase to become hydrophobic enough to be able to enter into thepolymer particles. In this process, a fraction of sulfate ion radicalssuffers bimolecular termination in the aqueous phase, loweringthe radical entry rate. Furthermore, during their stay in theaqueous phase, the •SO4

− radicals and the oligoradicals formedfrom them can abstract hydrogens from the PVOH.14,16,20,21 Theradicals formed on PVOH are relatively unreactive and a fractionof them is located in the aqueous phase where the concentra-tion of monomer is low, namely, their contribution to thepolymerization rate is low. This means that the PVOH reducesthe radical entry rate. It is worth pointing out that the PVOHlocated at the surface of the particles may also act as a radical

Figure 5. Particle size distribution of the final latex obtained in run S1initiated with TBHP/AsAc and using PVOH as a stabilizer.

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

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



sink22−26 for the radical exit, but this would affect both initiatorsystems in a similar way.In order to shed light on the effect of KPS concentration

on polymerization kinetics, reaction S3 was carried out in amanner similar to that of run S2, but the initiator concentra-tion was doubled before the post-polymerization step anddecreased to half the original concentration throughout the post-polymerization step.Figures 4, 6, and 7 compare the evolutions of the particle size,

number of particles, and instantaneous conversion of run S3 withthose obtained in run S2. Surprisingly, fewer particles than inrun S2 were produced by increasing the initiator concentration.This effect was contrary to what was predicted by theory.27 Thesmaller particle size found with the lower initiator concentrationmight be due to the lower ionic strength, which reduces thecoagulation of particles during the polymerization. A similarbehavior has been reported by other authors.3,28 Latex S3 alsocoagulated at the end of the post-polymerization step, which wasattributed to the high ionic strength.Monomer conversion increased with the concentration of

KPS/NaMS, but still it was lower than with TBHP, likely becauseof 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

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

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 graftingwas higher for KPS/NaMS. This is in agreement with what wasobserved in the batch miniemulsion polymerization of VAcand VeoVa10,14 and it is confirmed by the results presentedin Figure 9. This figure compares the MWDs of the acetylatedfinal latexes obtained in processes S1 and S2. The MWD of theacetylated PVOH(4/88) is included as a reference. It can be seenthat the shoulder corresponding to unreacted PVOH was morepronounced in the reaction carried out with TBHP/AsAc. Thehigher grafting obtained with KPS/NaMS is due to the fact that•SO4

− radicals are more hydrophilic and remain in the aqueousphase longer. Therefore, they have more opportunities toabstract hydrogens from PVOH. Moreover, higher-molecular-weight chains were observed in the acetylated samples than inthe untreated ones. These longer chains were attributed to VAc−VeoVa10 copolymer chains containing grafted PVOH that werenot soluble in THF before the acetylation process. The presenceof grafted PVOH acted as an artifact when gel and sol MWD aremeasured by a classical Soxhlet extraction.Figure 10 shows the evolution of the acetylated molecular

weight distributions during reactions S1 and S2. TheMWDof theacetylated PVOH is included as a reference. It can be seen that, inboth cases, high-molecular-weight polymer is formed during thelast stages of the process, likely because of the contribution ofchain transfer to polymer and propagation to terminal doublebonds. At 90 min, in run S2, that corresponds to the end ofthe batch polymerization of the initial charge, a high amount ofunreacted PVOH was observed. This peak was even morepronounced at 150 min, because of the addition of PVOH tothe reactor and the low conversion achieved. Before the post-polymerization, after ∼30% conversion, a high amount ofunreacted PVOH still remained in the reactor. However, duringthe post-polymerization, when a fast increase in conversion wasobserved, the small-molecular-weight peak was substantiallyreduced, showing that the majority of PVOH was incorporatedto the VAc−VeoVa10 copolymer at this step. Because of thedifferences in kinetics between runs S1 and S2, direct comparisonof the peak associated to unreacted PVOH is not possible, butthe final samples show that, in both cases, a significant part ofPVOH was grafted. This result is in conflict with what wasreported by Magallanes et al.,29 who, using a complex techniqueto characterize the grafted PVOH, found that only a small fractionof PVOH was grafted.

Figure 8. Effect of the acetylation process on the measured gel (S1 andS2 were untreated samples; AcS1 and AcS2 were acetylated samples).

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



In order to shed light on the role of PVOH in the developmentof the polymer microstructure, reaction S4 was carried using anonionic emulsifier (Disponil AFX4060) and it was comparedwith reaction S1, which was carried out under the sameconditions, but with PVOH. The formulation used to performthis 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 obtainedwith Disponil AFX4060 was larger (less particles) than withPVOH. In both cases, after the monomer and emulsifier addition,particle aggregation led to the increase of the average particlediameter, but the increase observed with Disponil AFX4060was less pronounced than with PVOH. Bimodal particle sizedistributions were obtained for the final latexes (Figure 12) andplenty of small particles still remained at the end of theprocess.Figure 13 showed that, during the monomer feed, the poly-

merization rate was slower in the system stabilized by DisponilAFX4060, because of the lower number of particles obtained,but almost complete conversion was achieved during the post-polymerization step.No gel was obtained in the polymerization stabilized with

Disponil AFX4060, and themolecular weights were lower than inthe presence of PVOH (Figure 14), likely due to the combinationof two effects:

(i) On one hand, a higher frequency of radical entry,resulting from the lower number of polymer particles

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.

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

Figure 11. Effect of the emulsifier type on the evolution of the particlesize.

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

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



■ MATHEMATICAL MODELAlthough the emulsion polymerization of VAc has beenextensively modeled,30−40 relatively little work has been done inmodeling the emulsion copolymerization of VAc−VeoVa10.3,8,10,11In this work, a mathematical model was used to investigate therole of PVOH and initiator type on both radical entry and VAc−VeoVa10 polymer microstructure and its parameters estimatedfitting the data presented above.The mathematical model was developed considering the

reactions included in Scheme 1 and incorporating the followingfeatures and assumptions to the model:

(1) A monodisperse polymer particle size distribution wasconsidered. As the model focus on radical entry andpolymer microstructure, the evolution of the particle size

measured experimentally in each reaction was used as aninput.

(2) Because the majority of the polymerization occurs in thepolymer particles, for the calculation ofMWD, the amountof polymer formed in the aqueous phase was consideredto be negligible, compared to that formed in polymerparticles.

(3) Termination was assumed to occur only by disproportio-nation, since it is the most commonly acceptedtermination mechanism for VAc.11,41

(4) The pseudo-steady-state assumption was applied to thepopulation balance of radicals.

(5) The polymer particles were assumed to contain a limitednumber of free radicals (I). Thus, instantaneoustermination was assumed to occur when a radical enteredinto a polymer particle already containing I radicals.

(6) Only monomeric radicals formed by chain transfer to VAcwere able to desorb from the polymer particles to theaqueous phase.

(7) A homogeneous distribution of the inactive polymeramong particles was assumed.

(8) Because the chain transfer to polymer is proportional tothe length of the polymer chain and the PVOH chainswere much shorter and contained less abstractablehydrogens than the VAc−VeoVa10 chains, the contribu-tion of chain transfer to PVOH to the MWDis negligible and the reaction between radicals andPVOH was not considered when calculating the MWD.On the other hand, as the entering radicals should crossthe PVOH barrier surrounding the polymer particle, chaintransfer to PVOH may occur, lowering the rate of entry.The effect of PVOH on the radical entry was considered tobe included in an efficiency factor ( fentry).

Material Balances. Assuming that the rate of the redoxreaction is proportional to the concentrations of oxidant andreductant, the material balances for the components of the redoxpair in the aqueous phase are

= − ′t

FF

a kd[Ox]

d(mol/(L s)) [Ox][Red]ox

wredox

(1)

= − ′t

FF

b kd[Red]

d(mol/(L s)) [Ox][Red]Red

wredox

(2)

where [Ox] and [Red] are the oxidant and reductantconcentrations in the aqueous phase (mol/L), respectively; Foxand Fred are the respective feeding rates of oxidant and reductantto the reactor (mol/s); kredox is the characteristic rate coefficientfor the redox reaction rate (L/(mol s)); Vw is the volume ofthe aqueous phase (L); and a′ and b′ are the stoichiometriccoefficients of the oxidant and reductant, respectively. For aredox system TBHP/AsAs, the values of a′ and b′ are 2 and 1,respectively,42 and for KPS/NaMS both are considered to beequal to 1.43

The material balance for water is

=Vt

Qdd

(L/s)ww (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 andpolymer are

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

Scheme 1. Mechanism of VAc−VeoVa10 Free-RadicalEmulsion Copolymerization



= − −Mt

F R Rdd

(mol/s)ii i i

ppW

p (4)

ρ

ρ

=−

+−

V

t

R R M

R R M

d

d(L/s)

( )

( )

pol pVAcW

pVAcp

wVAc

pVAc

pVeoW

pVeop

wVeo

pVeo (5)

whereMi is the total amount of monomer i in the reactor (mol),Fi is the monomer i feed rate (mol/s), Vpol is the volume ofpolymer (L) in the reactor, Mw

VAc and MwVeo are the molecular

weights of the monomers (kg/mol), ρpVAc and ρpVeo are thedensities of VAc and VeoVa10 units in the copolymer (kg/L),and Rpi

W and Rpip are the polymerization rates of monomer i in the

aqueous phase and polymer particles (mol/s), given by

= +k P k P M R VR (mol/s) ( )[ ] [ ]i i i ipW

pA AW

pBW

BW

w w w (6)

= + k P k P MnN

NR (mol/s) ( )[ ]i i i i pp

ppA A

ppB B

p p

A (7)

where kpij are the propagation rate coefficients (L/(mol s)), Piz

the probability of i being the last monomer unit in thepropagating active chain in phase z, [Mi]z the concentration ofmonomer i in phase z (mol/L), [R]w the concentration ofradicals in the aqueous phase (mol/L), Vw the volume of theaqueous phase (L), n the average number of radicals per particle,Np the number of polymer particles in the reactor, and NA theAvogadro’s number. For copolymerization, the probabilities areexpressed as44

=+

Pk M

k M k M

[ ]

[ ] [ ]iz p

zi z

pz

i z pz

j z

ji

ji ji (8)

= −P P1jz

iz

(9)

The material balance for the terminal double bonds that areformed by the chain transfer to monomer and by bimoleculartermination by disproportionation is as follows:

∑

= +

+ +

+ −

− =

tk P k P M

k P k P MnN

N

k h hN

N V

kV

nN

N

dTDBd

(mol/s) [( )[ ]

( )[ ] ]

( 1)

TDB

tr i tr j i

tr i tr j j

tdh

Ih

mon p mon p p

mon p mon p p p

A

2 A p

pTDB

p

p

A

ii ji

ij jj

(10)

where TDB is the total amount of double bonds in the reactor(mol), ktrij

mon represents the rate coefficients for the chain transferto monomer (L/(mol s)), ktd is the effective terminationrate coefficient by disproportionation (L/(mol s)), kp

TDB isthe propagation to terminal double bonds rate coefficient(L/(mol s)), Vp is the total volume of the monomer swollenpolymer particles (L), I is the maximum number of radicals perparticle, and Ni is the number of polymer particles containingi radicals. Because of the similar reactivity of the VAc andVeoVa10 radicals, the propagation to terminal double bonds ratecoefficient, kp

TDB, was considered to be the same for both radicals.

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

= + −

−

k nN

N Vk k R

k RN

N V

0 2 [Red][Ox] 2 [ ]

[ ] (mol/(L s))

d td

a

p

A wredox

ww

2

wp

A w (11)

where ka is the entry rate coefficient (L/(mol s)), ktdw is the rate

coefficient for termination by disproportionation in the aqueousphase (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 fromthe polymer particles, and bimolecular termination in thepolymer particles. The population balance of particles containingi radicals in the reactor is

= − + + −

+ + +

+ + +− +

+

Nt

k R k i ci i N

k R N k i N

c i i N

dd

(particles/s) ( [ ] ( 1))

[ ] ( 1)

( 2)( 1)

ii

i i

i

a w d

a w 1 d 1

2 (12)

In this work, eqs 11 and 12 were solved under pseudo-steady-stateconditions by applying the iterative method proposed by Ballardet al.,45 which provides the distribution of particles with i radicals.The average number of radicals per particle, n , can be calculated as

=∑∑

=∞

=∞n

iN

Ni i

i i

1

1 (13)

The desorption rate coefficient was calculated as46

λγη

λ

λ= −

+ +−

⎛⎝⎜⎜

⎞⎠⎟⎟k

Nm

f N

f N k M k R(s ) 1

[ ] 2 [ ]td

1 A entry p

entry p pAA A ww

w (14)

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

λπ

=+ +δ

η η −⎜ ⎟⎛⎝

⎞⎠( )D R4

1

w

DD R

DD m R R

1coth( ) 1

w 1

h

w

p (15)

γ =+ ⎜ ⎟

⎛⎝

⎞⎠k P k P M

D

( )[ ]tr tr v Nmon

Ap mon

Bp

A p1

p

jAA BA p A

(16)

η =+ + −⎜ ⎟

⎛⎝

⎞⎠k M k M k

D

[ ] [ ]p tdnv NpAA A pAB B p

w 1

p

p A

(17)

where the subscript A refers to VAc; Dw, Dp, and Dh are thediffusion rate coefficients in the aqueous phase, through polymerparticles, and through the hairy layer (dm2/s), respectively; δ1 isthe thickness of the hairy layer (dm);m is the partition coefficientof the monomeric radicals between the particle and aqueousphase; R is the particle radius (dm), and fentry is an adjustableparameter of radical entry.The rate coefficient for radical entry is calculated by the

following expression:



λ=k f N(L/(mol s))a entry A (18)

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

φ φ φ= + +( )k k a b c(L/(mol s)) exp ( ) ( )td td0

pp

pp 2

pp 3

(19)

where φpp is the volume fraction of polymer, and kt

0 is thetermination by disproportionation rate coefficient in a dilutedsystem. Because of the diffusional limitations, the effectivetermination rate coefficient in not affected by the type of radicalsinvolved in the reaction; therefore,

= = = =k k k k k(L/(mol s))tij tji tii tjj td (20)

Monomer Partitioning. In a semicontinuous process, thenewly fed monomer diffuses through the aqueous phase to thepolymer particles to be polymerized. Usually, polymerization isthe rate-determining step, and, hence, the concentration of themonomers in the different phases is given by the thermodynamicequilibrium.In this model, the distribution of the monomers among

phases is calculated using partition coefficients.47 For two ormore monomers, the calculation of the concentrations of themonomers in the different phases involves the simultaneoussolution of the thermodynamic equilibrium equations and thematerial balances.

φφ

= =KV V

V V//i

d id

d

i

id

iaq

aqaq

(21)

φφ

= =KV V

V V

/

/ii

i

i

i

pp

paq

aq

p

aq(22)

∑φ φ+ = 1i

ipolp p

(23)

∑φ φ+ = 1i

iwaterw w

(24)

∑ φ = 1i

id

(25)

φ φ φ+ + =V V V Vi i i ipp

dd

ww

(26)

φ =V Vw waterw

water (27)

φ =V Vp polp

pol (28)

where Viz is the volume of monomer i in phase z (polymer

particles (p), droplets (d), and aqueous phase (aq)); φiz is the

volume fraction of monomer i in phase z; Kip and Ki

d are thepartition coefficients between the particles and aqueous phaseand the droplets and the aqueous phase, respectively; Vp, Vd, andVw are the volume (L) of monomer swollen particles, monomerdroplets, and aqueous phase, respectively; and Vi, Vpol, and Vwaterare the volumes (L) of monomer i, polymer, and water,respectively. Efficient algorithms for the solution of this system ofnonlinear algebraic equations are available.48,49

Molecular Weights. Because the length of the macro-molecules depends on the environment in which they growth,the molecular weight is controlled by the number of radicals perparticle, monomer concentration in the polymer particles and by

the presence of chain-length modifiers, such as chain-transferagents or cross-linkers, in the formulation. In VAc−VeoVa10copolymerization, the polymerization with terminal doublebonds (TDB) (resulting from termination by disproportionationor chain transfer to monomer) and chain-to-polymer trans-formation 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 andlater modified by Butte et al.51 was used. Singly distinguishedparticles are the particles with i radicals, one of which beingthe length n. For the present system, there is no need to usedouble distinguished particles (particles with i radicals, two ofwhich being lengths n and m), because termination is bydisproportionation. The population balance for singly distin-guished particles is

∑

ρ

ρυ

υδ ρ

δ ρ

= − + + − + + + − +

+ + + + + +

+ + +

+ −

− − + +

=

−−

−

− ⎜ ⎟⎛⎝

⎞⎠

N

tp ci i tr tr k i p N

pN N ci i N k iN tr nD

iN

p ND

N tr iN

II

N

d

d[( ( 1) ( 1) )]

( 1)[ ][ ]

[ ][ ]

( )

1

i ni n

i n i n i n i nn

i

h

n

i hn h

n i i

i I I n

,m p d TDB ,

, 1 1, 2, d 1, p1

TDB1

1

,0

,1 1 m

, 1 , (29)

where

∑= +−

=

p k P k P M(s ) ( )[ ]i

i i i1

1,2pA A

ppB B

pp

(30)

ρ =− k R(s ) [ ]1a w (31)

∑= +−

=

tr k P k P M(s ) ( )[ ]i

tr i tr i im1

1,2A

monAp

Bmon

Bp

p(32)

υ= ++

−tr k P k P(s ) ( )[ ]pol

pol poltr trp1

AApol

Ap

BApol

Bp

1A

A B (33)

=−⎛⎝⎜⎜

⎞⎠⎟⎟p k

V(s )

TDBTDB

1pTDB

p (34)

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

∑ ∑

∑ ∑

ρ

υ υ

= + + + −

− −

= =

= =

⎡⎣⎢⎢

⎤⎦⎥⎥

Dt

N Vtr tr iN

IN c i N

tr nD

iN pD

iN

d[ ]d

(mol/(L s))

1( )

12 ( 1)

[ ][ ]

[ ][ ]

n

i

I

i n I n di

I

i n

n

i

I

in

i

I

i

A pm p

1, ,

2,

p1 1

TDB0 1 (35)

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

∑==

−+

S Ni jn n

n

i n,

1

,

j

j 1

(36)



∑==

−+

Q Djn n

n

n

1

j

j 1

(37)

All of the polymer chains in each interval are represented by asingle chain length that is referred as pivot value and correspondsto the average chain length of the polymer chains in the interval

=∑ =

−+

nnD

Qjn nn

n

j

1j

j 1

(38)

Therefore, the quasi-continuous distributions of Ni,n and Dnare transformed to discrete distributions with the polymer chainsplaced at a limited number of pivots. Fifty (50) pivots homo-geneously distributed in the logarithm domain were used.When reactions such as propagation, chain transfer to

polymer, and propagation to terminal double bonds occur, thelength of the newly created chain (np) might fall between twocontiguous pivots n k and nk+1. In this case, the properties of thenewly created chain are shared between the two contiguouspivots by means of the following factors:52

= − −

+

+a n n

n n

n n( , )

( )k

k

k kp

1 p

1 (39)

= − −

++

b n nn n

n n( , )

( )k

k

k kp 1

p

1 (40)

where a(n p, n k) and b(np, n k+1) are the fraction of chains assignedto n k and nk+1, respectively. With this partitioning, the overallnumber of polymer chains and the overall number ofpolymerized monomer units are preserved.Because of the propagation to terminal double bonds and the

chain transfer to polymer, branched and cross-linked high-molecular-weight polymer chains are formed in the polymerparticles. The size of these high-molecular-weight polymers maygrow to form a nanogel whose size cannot exceed the size of thepolymer particles. Therefore, following Calvo et al.,57 a sizelimitation was taken into account in order to ban reactions(propagation to TDB and chain transfer to polymer) that canproduce polymer chains with a volume higher than the volume ofthe polymer particle.The population balances for the lumped variables are

described as follows:

Active polymer chains:

∑

∑

ρ

ρ

υ

δ ρ δ ρ

= − + + − + + + −

+ + + + +

+ +

+ +

+ +

+ + + −

− − − +

+

≤ + ≤

≤ + ≤

− −

−

+

⎜ ⎟

⎧⎨⎪⎩⎪

⎫⎬⎪⎭⎪

⎛⎝

⎞⎠

S

tb p ci i tr tr i k

p S pb S S ci i S

ik S tr nQ

iN

p b n n n S Q

a n n n S Q

N tr iNI

IS

d

d[( ( 1) ( 1)

)] ( 1)

[ ]

[ ]

( , ) [ ]

( , ) [ ]

( )1

i jj d

i j j i j i j i j

d i j jj

i

n n n n

p q

p q j i p q

n n n n

p q

p q j i p q

j i i i I I j

,m p

TDB , 1 , 1 1, 2,

1, p1

TDB

,

,

,

,

,0 1 m , 1 ,

j p q j

j p q j

1

1

(41)

Inactive polymer chains:

∑

∑ ∑

∑

ρ

υ

υ

= + +

+ − −

−

=

= =

=

⎡⎣⎢⎢

⎤⎦⎥⎥

Q

t N Vtr tr S

IS

c i S tr nQ

iN

pQ

iN

d[ ]

d1

( )1

2 ( 1)[ ]

[ ]

[ ]

[ ]

j

i

I

i j I j

i

I

i j jj

i

I

i

j

i

I

i

A pm p

1, ,

d2

, p1 1

TDB0 1 (42)

The direct output of the model is a discrete molecular weightdistribution (Qj) at the pivots. The continuous MWD of Dncan be obtained from the discrete distribution by assuming alinear variation for all the chain lengths between two pivotvalues:53

= −

− +

− −

≤ ≤ −

−

−−−

D Qn n

n nQ

n nn n

n n n( )n nk

k kn

k

k kk k

1

1

11k k1 (43)

where nk is the value of the pivot k (namely, the average chainlength 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

Table 3. Parameters of the Model

kinetic parameters unit ref

kpAA = 1.44544 × 107 exp((−20700/8.31)T) L/(mol s) 66

kpBB = 2.04174 × 107 exp((−22200/8.13)T) L/(mol s) 67

ktrAAmon = 4.55 × 10−4kpAA L/(mol s) 68

ktrBBmon = 4.55 × 10−4kpBB L/(mol s) 68

ktrABmon = ktrAA

mon L/(mol s) assumed

ktrBAmon = ktrBB

mon L/(mol s) assumed

ktrApol = 2.0 × 10−4kpAA L/(mol s) 68

ktrBpol = 2.0 × 10−4kpBB L/(mol s) 68

kpTDB = 800 L/(mol s) estimated

kredoxTBHP/AsAc = 7.6 × 10−2 L/(mol s) estimated

kredoxKPS/NaMS = 2.3 × 10−1 L/(mol s) estimated

ktdij0 = 3.55 × 108 L/(mol s) 69

ktdAA0 = ktdBB

0 = ktdAB0 = ktdBA

0 = ktd0 L/(mol s) assumed

ktd = ktd0 exp[aφp

p + b(φpp)2 + c(φp

p)3] L/(mol s) 69

a = −0.011 estimated

b = −0.013 estimated

c = −6.7 estimated

fentry (Run S1, PVOH,TBHP/AsAc) = 3.5 × 10−3 estimated

fentry (Run S2, S3, PVOH,KPS/NaMS) = 2.05× 10−5 estimated

fentry (Run S4, Disponil,TBHP/AsAc) = 1.0 × 10−2 estimated

rA = 0.99 2

rB = 0.99 2

Dw = 1.1 × 10−7 dm2/s 70

Dp = 1.1 × 10−8 dm2/s 70

Dh = 1.0 × 10−7 dm2/s 46

m = 29.0 71

KAd = 34.7 72

KAd = 29.5 72



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

Library, Visual Numerics, Inc., Houston, TX). The objectivefuncation was

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.



∑ ∑ ∑=−⎛

⎝⎜⎜

⎞⎠⎟⎟j

N

Z Z

Z1

N N Zpoint

exp simul

exp

2

point (44)

where N is the number of experiments, Npoint is the number ofexperimental points in each experiment, and Zexp and Zsimul are,respectively, the experimental and model predicted values for thevariable Z. In this work, monomer conversion and the molecularweight distributions were used as variable Z. As the modelfocused on the MWD, no attempt to model the particle sizewas carried out, and, hence, the experimental evolutions of thenumber of particles obtained in semicontinuous reactions S1−S4were used as an input of the model. The adjustable param-eters were the radical entry efficiency factor ( fentry), the ratecoefficients for the redox reactions (kredox

TBHP/AsAc and kredoxKPS/NaMS),

the parameters for the gel effect, and the rate coefficient forpropagation to terminal double bonds (kp

TDB).The parameter fentry takes into account the effect of several

mechanisms that might reduce the rate of radical entry such asthe resistance to radical diffusion of the monomeric radicalsthrough the hairy layer, the surface charge repulsion and thehydrogen abstraction from the polymeric stabilizer.22−26,58−60

For redox systems, the rate of radical generation is not well-known and the range of the values reported in the literatureis very broad.61−65 Hence, in this work, the TBHP/AsAc andKPS/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 growingchains. This means that they are specific of each system, andhence they were included in the set of adjustable parameters.The rate coefficient for propagation to terminal double bondswas 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 beseen that the model fits the experimental data quite well. It isinteresting to point out that, to achieve this fitting, widely differentradical entry rates were estimated. The smallest value was for runsS2 and S3 carried out with PVOH and KPS/NaMS, which mostlikely results from the combined effect of the hydrophilicity of thesulfate ion radicals that increase termination in the aqueous phaseand the high rate for chain transfer to PVOH that reduces the rateof radical entry. The extensive grafting to PVOH is supportedby the high apparent gel content measured using the classicalSoxhlet extraction (Figure 8). A higher estimated value of fentrywas obtained for TBHP/AsAc that produced hydrophobic tert-butoxyl radicals able to enter directly into the polymer particles.The effect of PVOHon the entry of tert-butoxyl radicals is evidentwhen the values of fentry for runs S1 and S4 are compared. It can beseen 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 acetylatedsamples were available for run S3. The simulated results do notinclude the unreacted PVOH, and, hence, the comparison shouldbe done with the peak corresponding to the VAc-VeoVa10copolymer. It can be seen that a good fitting was achieved andthat the model captures the formation of the high-molecular-weight polymer in the last part of the process well.

■ CONCLUSIONSIn the foregoing, the semicontinuous emulsion co-polymer-ization of VAc and VeoVa10 was investigated under industrial-like conditions, namely, using a high solids content (57 wt %)

and PVOH as a polymeric stabilizer. A mathematical modelwas used to shed light on the effect of PVOH and initiator typeon polymerization kinetics and polymer microstructure. It wasfound that PVOH reduces the rate of radical entry into thepolymer particles. This effect was attributed to the chain transferof the entering radicals to PVOH and depends on the initiatorsystem used. Thus, it is more pronounced for KPS/NaMS thanfor TBHP/AsAc. A consequence of the chain transfer to PVOHis 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 classicalSoxhlet extraction, the use of this method overestimates the gelfraction and underestimates the molecular weight of the sol,because non-cross-linked graft copolymers are wrongly includedin the gel. A newmethod based on the acetylation of the hydroxylgroups of the PVOHhas been developed to properly measure theMWD of these copolymers.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe financial support of Wacker ChemieAG is gratefullyacknowledged.

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