on photoinduced miniemulsion polymerization of butyl acrylate with clay

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This article was downloaded by: [University of Chicago] On: 29 June 2012, At: 07:43 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Designed Monomers and Polymers Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tdmp20 On photoinduced miniemulsion polymerization of butyl acrylate with clay Ignác Capek a a Slovak Academy of Sciences, Polymer Institute, Institute of Measurement Science, Bratislava, Slovakia Version of record first published: 28 Jun 2012 To cite this article: Ignác Capek (2012): On photoinduced miniemulsion polymerization of butyl acrylate with clay, Designed Monomers and Polymers, DOI:10.1080/1385772X.2012.686681 To link to this article: http://dx.doi.org/10.1080/1385772X.2012.686681 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-and- conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

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This article was downloaded by: [University of Chicago]On: 29 June 2012, At: 07:43Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Designed Monomers and PolymersPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/tdmp20

On photoinduced miniemulsionpolymerization of butyl acrylate withclayIgnác Capek aa Slovak Academy of Sciences, Polymer Institute, Institute ofMeasurement Science, Bratislava, Slovakia

Version of record first published: 28 Jun 2012

To cite this article: Ignác Capek (2012): On photoinduced miniemulsion polymerization of butylacrylate with clay, Designed Monomers and Polymers, DOI:10.1080/1385772X.2012.686681

To link to this article: http://dx.doi.org/10.1080/1385772X.2012.686681

PLEASE SCROLL DOWN FOR ARTICLE

Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representationthat the contents will be complete or accurate or up to date. The accuracy of anyinstructions, formulae, and drug doses should be independently verified with primarysources. The publisher shall not be liable for any loss, actions, claims, proceedings,demand, or costs or damages whatsoever or howsoever caused arising directly orindirectly in connection with or arising out of the use of this material.

On photoinduced miniemulsion polymerization of butyl acrylate with clay

Ignác Capek*

Slovak Academy of Sciences, Polymer Institute, Institute of Measurement Science, Bratislava, Slovakia

The miniemulsion polymerizations (MiEPs) of butyl acrylate (BA) initiated by UV-lighthave been studied. The oil-soluble dibenzoyl peroxide was used as a photoinitiator. Further-more, the effect of sodium montmorillonite on kinetics and BA miniemulsion stabilized byanionic sodium dodecylsulfate (SDS) and anionic cetyltrimethylammonium bromide(CTAB) was studied. The polymerization rate vs. conversion curve of the photoinducedMiEP of BA was described by two and four nonstationary rate intervals. Two rate intervalswith one rate maximum was observed with CTAB and four nonstationary rate intervalswith two rate maxima appeared with SDS. Variation of the rate of polymerization withconversion was discussed in terms of types of initiating radicals and the gel effect.

Keywords: photoinduced miniemulsion polymerization; clays; kinetics; compositenanoparticles

Introduction

For the past 20 years, there has been increased attention paid to the synthesis of nanocompositesbased on either intercalated or exfoliated clay dispersed into various matrix polymers [1–5].

There are also some studies on the formation of composite nanoparticles by the dispersionpolymerization of monomers with clays as was reviewed by Capek [6]. As an alternative tothe procedures described above, the preparation of nanocomposites using UV-curingtechnology has only recently been reported as summarized below.

There are also several studies. Monomer polarity, monomer functionality, and the func-tional groups on the organoclay surfaces significantly impact both the degree of clay exfolia-tion and photopolymerization kinetics. The addition of polymerizable organoclays increasesphotopolymerization rate in sufficiently exfoliated clay systems, whereas the rate decreaseswith lower degrees of clay exfoliation. With clay exfoliation, the effective surface area isincreased, resulting in immobilization of a greater number of the propagating radicals anddecreased termination [7].

A photoinitiator intercalated into montmorillonite had high photoinitiation efficiency, evenonly 1/100 (w/w) modified clay could initiate the radical polymerization with the 87%acrylate conversion on UV-light exposure. The d spacing could be enlarged to 13.9 nm afterphotopolymerization with organoclay loading. This approach provided a novel pathway forusing the highly exfoliated clay–polymer composites for designing intercalating agentscapable of introducing different functional groups [8,9].

The functionalization of the sodium montmorillonite (MMTNa) surface with glycidyl-propyl-triethoxysylane allows to obtain a new modified clay mineral which can be dispersed

*Email: [email protected]

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ISSN 1568-5551 online� 2012 Taylor & Francishttp://dx.doi.org/10.1080/1385772X.2012.686681http://www.tandfonline.com

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in the UV-curable epoxy resin. By photopolymerization of the modified clay mineral–epoxyresin dispersion, it is possible to obtain a nanocomposite coating having a mixed intercalated/exfoliated structure [10].

A reaction system containing a photoinitiator, quaternary ammonium cations, andunsaturated monomer, was used to modify clays, such as MMTNa clay and prepare via radi-cal photoinduced cross-linking polymerization organic–inorganic nanocomposite resins [11].

The effect of clay on the photopolymerization kinetics and coating properties of alkylacrylate systems in the presence of novel dicarylate and dimethacrylate crosslinkers isreported [12,13]. In the presence of clay, earlier onset of autoacceleration was observed, highrates of polymerization were achieved, and high-final overall conversions were reached.Higher rates and increase in conversions were also observed as the clay content increased inthe medium.

A vast majority of the studies on dispersion (microemulsion, miniemulsion, and emulsion)polymerization processes focus primarily on thermally initiated polymerization [14–18].However, there have been several photoinduced polymerizations in microemulsion [19,20],emulsion [21,22], and in micellar media [10–13,23–25]. Monomer microemulsions and micel-lar systems are thermodynamically stable and form spontaneously with an appropriate combi-nation of a surfactant and a costabilizer [26]. Their low droplet size in the tenth nanometersize range (10–50 nm) affording optical transparency in the UV–vis region makes them partic-ularly suitable for photochemical reactions.

A first use of the photoinduced miniemulsion (fine emulsions) polymerization was men-tioned in 1999 by Capek who investigated the free-emulsifier (co)polymerization of alkyl(acrylates) [26,27]. The more-detailed photoinduced miniemulsion polymerization (MiEP)was mentioned in 2009 by Tonnar et al. [28], who investigated the controlled radical poly-merization of vinyl acetate in the presence of an iodinated macrophotoinitiator. Despiteincomplete conversion and long polymerization times, the controlled character of the reactionwas demonstrated. Chemtob et al. [29] have presented an interesting approach which is verydifferent from those in above, since conventional free radical photopolymerization in mini-emulsion was investigated with a formulation including simply conventional acrylate mono-mers (butyl acrylate [BA], methyl methacrylate, and acrylic acid) and a commercial type Iradical photoinitiatiors (BAPO). The formation of nanosized acrylate droplets encapsulatingthis hydrophobic photoinitiator was first achieved by sonication. UV irradiation was subse-quently applied to the monomer miniemulsion, to produce quantitatively at high-rates polymernanoparticles of similar size to the monomer droplets [29].

A miniemulsion process is also compatible with high solids contents [30] and its distinc-tive feature compared to emulsion polymerization is a predominant droplet nucleation.Accordingly, the high number of droplets combined with a large droplet surface area isexpected to maximize the fraction of polymer particles generated by droplet nucleation. In anideal situation, monomer droplets under 100–150 nm are all nucleated, each one becoming aparticle in the absence of any other form of particle formation [31].

The synthesis of nanoclay composites from miniemulsion and emulsion systems exhibitsan increased interest in the last years. The main reasons include the encapsulation of layeredsilicates, nanolayer stabilization, in situ polymerization of the monomers in intergalleries ofthe layered silicates and the possibility of obtaining hybrid particles and nanoparticles [32].

Concerning the layered silicates – initiator interactions the overall view of the processmust take into account at least some aspects: the modification of polarity brought by the claypresence in the dispersion media; the possibility of adsorption on the clay surface of theemulsifier counterion or the interaction of the sulfate ion on acid bridges of the middle crystalof the aluminosilicate structure [33]. These interactions could be interesting for the formation

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of radicals in the photoinduced MiEP and the increased encapsulation of silicates in thepolymer matrix.

A polar BA is expected to show large basal spacing before polymerization and produceintercalated or exfoliated polymer-MMT nanocomposites (Scheme 1). Emulsifier and MMTinteraction could modify the polymerization environment and the partitioning of monomerbetween the bulk and clay phases. The increased or decreased penetration of monomer into theinterlayer space is expected to change the overall rate of photoinduced polymerization. Further-more, the more complex fate of radicals formed by the photoinduced events within the clayinterlayer spaces is discussed here. The photoinduced mechanism of nanocomposite formationis also discussed in terms of variations of the maximum polymerization rate (Rp,max), particledimensions (dp), number of polymer particles (Np), and average number of radicals per particle(n) with the reaction conditions, the clay concentration, and the type of emulsifier.

Experimental

Materials

Commercially available BA was purified by usual methods [34]. The analytical-gradeinitiators dibenzoyl peroxide (DBP) was used as supplied (Fluka). The emulsifiers used were

Scheme 1. The mechanistic routes of polymer-clay (montmorillonite, MMT) nanocomposites formationin the photoinduced miniemulsion polymerizations of polar and nonpolar monomers. PP – polymerparticle, MD – monomer droplet.

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the reagent grade sodium dodecyl sulfate (SDS) and cetyltrimethylammonium bromide(CTAB) (both Fluka). Sodium montmorillonite (MMTNa, Cloisite Na+, and clay) from FlukaClay Products. Twice distilled water was used as the polymerization medium.

Polymerization procedure

The polymerization experiments were performed on an optical bench using UV light of wave-lengths λ= 365 nm with intensity Io = 3.5 × 10

�6 Einstein dm�3 s�1 at 23 °C. In all runs, therecipe comprises 100 g water, 10 g BA, 0.266 g SDS, or 0.3 g CTAB. Amounts of DBP(0.19 g) were used as shown later. The polymerization technique, conversion determination(dilatometric and gravimetric techniques), and the estimation of polymerization rate were thesame as described earlier [35].

Polymer and latex characterization

The measurements of average particle size (a static and dynamic light scattering – LS), theestimation of particle number, and the measurements of light intensity were the same asdescribed earlier [36,37].

Results and discussion

Variation of monomer conversion in the photoinduced MiEP of BA with the reaction time forvarious concentrations of clay is summarized in Figure 1. The monomer droplets and polymerparticles were stabilized by anionic emulsifier SDS. The curves are concave downward andthe polymerization is found to be relatively slow. The data indicate that the conversion of c.60% is reached in c. 250min. Besides, the polymerization reaches the limiting conversion c.at 60–70%. The limiting conversion cannot be ascribed to the consumption of initiator

Figure 1. Variation of monomer conversion of photoinduced miniemulsion polymerization of BA withreaction time and MMTNa concentration (SDS runs). 0.19 g DBP, (1) without clay, (2) without clay andDBP, (3) 0.185 g MMTNa, (4) 0.37 g MMTNa, and (5) 0.74 g MMTNa.

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because the half time of DBP is much above 50 h at 23 °C [38]. The low Tg for poly(butylacrylate) (PBA) disfavors the glassy state approach. The appearance of the limiting conver-sion can be discussed in terms of the low monomer concentration at the reaction loci (particlesurface) and the low radical formation.

Under the similar reaction conditions, the thermally initiated microemulsion polymeriza-tion of BA reaches much higher final conversions and the reaction is much faster [5]. In thepresent photoinduced MiEP, the radicals are formed due to the penetration of light into themonomer droplets or monomer/polymer particles. The decreased penetration of light into themonomer/polymer particles (here above c. 40% conversion) disfavors the formation of radi-cals, and therefore the polymerization gradually stops. In our earlier work, we have observedthat the polymerization can proceed even in the post-polymerization interval (the light is cutoff) and the conversion can increase in this interval by c. 15–20% conversion [35]. This isnot the case in the thermally induced MiEP where the radicals are formed during the wholepolymerization process (even at conversion much above 90%). In all present experiments, thecolloidally stable polymer latexes were formed.

In our irradiation conditions (λ= 365 nm), the DBP photoinitiator, which exhibits a absorp-tion at about 365 nm, is expected to be the main source of initiating radicals in the presentruns. In contrast, the BA monomer and the surfactants are characterized by a main absorptionband at λ < 300 nm, which limits their probability of UV decomposition. However, the possi-bility of self-intitiated photopolymerization of acrylate monomers cannot be neglected as pos-sible secondary source of radicals, as recently proved by Brown et al. [39]. Indeed, the self-photopolymerization is operative in the runs with SDS. This was attributed to the interactionbetween SDS and BA, which was proved experimentally in our earlier work [40].

Although the monomer miniemulsions are relatively light scattering (droplet diameter c.120 nm), this might not appear to be detrimental to the efficiency of the polymerization pro-cess. In agreement with this, Ballauff et al. even suggested that during the grafting photopoly-merization at the surface of preformed latex particles, a turbid dispersed medium could beeven beneficial to the photochemical process since light is scattered many times, which mightincrease the quantum yield of the photoinitiator [41].

The synergistic effect of BA which acts as a co-emulsifier, increases with SDS concentra-tion [40]. Under the present reaction condition, the co-emulsifier properties of BA are nearlycomparable with those of 1-pentanol. This can enhance the monomer concentration in thedroplet shell. The excitation of SDS…BA complex is expected to contribute to the whole for-mation of initiating radicals and the photoinduced polymerization:

fSDS. . .BAg–hc ! fSDS. . .BAg� ! radicals

Indeed, the initiating radicals which appeared in the blank (without DBP) experiment startedthe polymerization and the formation of polymer nanoparticles. Thus, the second source ofradicals can be an excited {SDS…BA}⁄ complex. At low conversion, the high monomer con-tent in the interfacial zone favors the formation of radicals by the decomposition of {SDS…BA}⁄. The accumulation of polymer within the monomer/polymer particles increases thehydrophobic interaction of SDS with PBA due to which decreases the contribution of{SDS…BA}⁄ complex. If the concentration of monomer in the particles is below a certaincritical level then the radicals are not formed via the decomposition of excited {SDS…BA}⁄

complex. The blank experiments shows that the radicals derived from excited SDS…BAcomplex are responsible for the total conversion of c. 10–15%.

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Variations of the polymerization rates of BA with conversion in presence of clay are dem-onstrated in Figure 2 and Table 1. The data indicate that this dependence is described by thefour rate intervals with two rate maxima (Figure 2). The observed behavior is very similar tothat reported by El-Aasser et al. [42] and Reimers et. al. [43] for the classical MiEPs of sty-rene and MMA in the presence of low and high molecular weight hydrophobe such as hexa-decane (HD), polymer, etc. and homogenized by a uniform shear device. In the classicalMiEP using an effective hydrophobe, the second maximum is more pronounced [44]. Thepresence of LPO and continuous accumulation of hydrophobic oligomers promote the forma-tion of highly monomer swollen particles, additional reaction loci, and the appearance of fourrate intervals [45]. The blank experiment (without DBP) shows two rate intervals and the onemaximum rate. Thus, the rate maximum can be attributed to the second source of radicals(the decomposition of excited {SDS…BA} complex). After the consumption of these radi-cals, the rate decreases and the polymerization stops (Figure 2, curve 2). The addition ofDBP increases the rate of polymerization because the first-rate maximum is the sum of boththe primary (radicals derived from DBP) and secondary sources. Radicals derived from DBPdominate the polymerization process in medium and high conversions. These data indicatesthat the present systems have two types of radicals. We cannot exclude the contribution ofgel effect which in the acrylate polymerizations starts at c. 30–40% conversion (Figure 2,curves 1 and 3). The presence of a larger amount of clay decreases the rate of polymerizationincluding the gel effect (Figure 2, curves 4 and 5).

Variation of monomer conversion in the photoinduced MiEP of BA with the reaction timefor various concentrations of clay in the presence of CTAB is summarized in Figure 3. Themonomer and polymer particles were stabilized by a cationic emulsifier CTAB. The curvesare concave downward and the polymerization is found to be relatively slow. The data indi-cate that the final conversions of c. 20% are reached in c. 50min. In this system, the excited

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Figure 2. Variation of the rate of photoinduced miniemulsion polymerization of BA with conversionand MMTNa concentration (SDS runs). 0.19 g DBP, (1) without clay, (2) without clay and DBP, (3)0.185 g MMTNa, (4) 0.37 g MMTNa, and (5) 0.74 g MMTNa.

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{CTAB…BA}⁄ did not appear and therefore the blank run (without DBP) did not lead to theformation of polymer or polymer nanoparticles. Thus, the {BA…CTAB} complex does notform in both the basic and excited states, and therefore the free radicals are not formed andthe blank polymerization does not start either.

The polymerization reaches the limiting conversion c. at 20%. The conversions are muchlower than those obtained with the above SDS system. The limiting conversion can be dis-cussed in terms of deactivation of reaction loci via interaction of radicals with CTAB and for-mation od stable transferred radicals. Figure 3 shows that the secondary source of radicals isabsent. That is, the initiation events are governed by radicals derived from DBP. Furthermore,the one type of radicals or one type of reaction locus is connected by the appearance of one

Table 1. Variation of kinetic and colloidal parameters with the MMTNa concentration in thephotoinitiated miniemulsion polymerization of BA (SDS runs).

MMTNa (g) Con.f (%)

Rp,max × 104/

conv:Rp;max2

(mol dm�3 s�1)/%dp (nm) Np × 10

�17 (dm3)�n/particle

(1a) (2a) (1b) (2b)

0 55 2.6/15 1.0/40 123 0.98 0.018 0.010.185 56 1.7/15 0.75/35 129 0.84 0.014 0.0080.370 54 1.25/7 1.0/– 132 0.79 0.01 –0.740 46 1.25/7 5.0/– 133 0.77 0.01 –

The number of radicals per particle (�n) were calculated using kPBA= 7.37 × 105 exp (�1157/T) Lmol�1 s�1

[46], Np number of polymer particles (= monomer droplets), and [BA]bulk = 6.93mol dm�3,½BA�Rp;max

¼ ½6:93� XRpmax � mol dm�3 (where X is a conversion at Rp,max),(1a) Rp,max1/conv:Rp;max1 , (2a) Rp,max2/conv:Rp;max2 , (1b) �n at Rp,max1, (2b) �n at Rp,max2.

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1

Con

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/ %

Time / min

Figure 3. Variation of monomer conversion of photoinduced miniemulsion polymerization of BA withreaction time and MMTNa concentration (CTAB runs). 0.19 g DBP, (1) without clay, (2) 0.185 gMMTNa, (3) 0.37 g MMTNa, and (4) 0.74 g MMTNa.

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maximum of the polymerization rate – conversion curve (Figure 4 and Table 2). This figurealso indicates that the rate of polymerization vs. conversion is described by a curve with amaximum at very low conversion and the polymerization also stops at relatively low conver-sions.

The cationic emulsifier molecules such as CTAB can penetrate into the interfacial zone ofclay, strongly modify the original clay, and accelerate the thermally initiated polymerizationof styrene [47]. However, the present results show that the reverse is true, that is, the pres-ence of MMTNa decreases both the rate of polymerization and the final conversion (Figure 3and Table 2).

Similar behavior in the photopolymerization of alkyl diacrylates with MMTNa wasobtained by Owusu-Adom and Guymon in the photopolymerization of alkyl diacrylates withMMTNa in the presence of quaternary ammonium surfactants [13]. The dependence of poly-merization rate vs. the reaction time obtained by DSC was described by the two rate intervalswith one rate maximum. On the contrary, the polymerization was very fast and the maximumrate of polymerization was reached much below 1min. The reaction conditions and the shapeof the polymerization rate vs. reaction time curves were in the favor of the dispersion

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Figure 4. Variation of the rate of photoinduced miniemulsion polymerization of BA with conversionand MMTNa concentration (CTAB runs). 0.19 g DBP, (1) without clay, (2) 0.185 g MMTNa, (3) 0.37 gMMTNa, and (4) 0.74 g MMTNa.

Table 2. Variations of kinetic and colloidal parameters in the photoinitiated miniemulsionpolymerization of BA with the MMTNa concentration (CTAB runs).

MMTNa (g) Con.f (%) Rp,max × 104 (mol dm�3 s�1) dp (nm) Np × 10

�17 (dm3) �n (particle)

0 19 1.80(7) 139 0.847 0.0130.185 16 1.25(4) 125 0.930 0.0080.370 15 0.75(3) 132 0.790 0.0060.740 13 0.80(3) 150 0.540 0.009

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(microemulsion) polymerization. The mechanism of polymerization was, however, discussedin terms of bulk polymerization, that is, the dependences of propagation and termination rateparameters were evaluated from DSC data and the free radical polymerization model. Propa-gation and termination rate parameters were reported to decrease with conversion and theconcentration of Clays and surfactants. The decrease in termination and propagation rates wasattributed to the immobilization of radicals and monomers which also supports our data anddiscussion.

Tables 1 and 2 show that the particle size slightly increases and the number of polymerparticles decreases with increasing concentration of clay. This behavior indicates that the claydecreases the particle nucleation and the formation of polymer particles. PBA latexes wereproduced with a size similar to that of monomer droplets, demonstrating that a droplet nucle-ation predominantly occurred.

It is interesting to observe that the number of radicals per particle is very low anddecreases with increasing concentration of clay (Table 2). The decrease in �n is more pro-nounced in the runs with CTAB. The low radical concentration is usually ascribed to thestrong desorption of radicals due to the small nanoparticles. However, the present size ofpolymer particles is relatively large to favor the desorption of monomeric radicals from parti-cles. The pseudo-bulk polymerization in particles could explain the very low radical concen-tration in particles. Under such conditions, the biradical termination is expected to govern thetermination mechanism of primary and growing radicals.

Conclusion

This study shows that the MiEP of BA leads to the formation of composite PBA/claynanoparticles via a photochemical way. A commercial oil-insoluble radical photoinitiator(DBP) proved to be well suited to initiate the polymerization of a nanosized BA miniemul-sion in the presence of a conventional anionic surfactant (SDS). A stable PBA latex wasproduced with a size similar to that of monomer droplets, demonstrating that a dropletnucleation predominantly occurred. On the contrary, the photopolymerization of BA in thepresence of cationic emulsifier CTAB led to the very low conversions around and below20%. The polymerization rate vs. conversion curve of the MiEP of BA photoinitiated byDBP was described by two and four nonstationary rate intervals. Two rate intervals withone maximum were observed with CTAB and four nonstationary rate intervals with tworate maxima appeared with SDS. The two rate maxima were attributed to two types ofreaction loci while the one type of radicals led to the one rate maximum. In the runs withSDS, the initiating radicals were derived from both the excited SDS…BA complex andphotoinitiator (DBP). In the runs with CTAB, the initiation radicals were generated onlyfrom DBP. The presence of clay decreased the rate of polymerization and the decreaseincreased with increasing the MMTNa concentration. These changes in photopolymerizationbehavior could be a result of changes in the termination mechanism as discussed earlier orpotentially due to changes in scattering with greater organophilic nature of the clay. Fur-thermore, the gel effect can contribute to the whole polymerization process at conversionabove c. 30–40% conversion.

AcknowledgementsThis research was supported by the VEGA projects No. 2/0037/10 and 2/0160/10 and APVV projectNo. APVV-0125-11.

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AbbreviationsBA butyl acrylateCTAB cetyltrimethylammonium bromideDBP dibenzoyl peroxidedp particle dimensionsHD hexadecaneLPO lauroyl peroxideMiEP miniemulsion polymerizationMMTNa sodium montmorilloniten number of radicals per particleNp number of polymer particlesRp,max maximum polymerization rateSDS sodium dodecylsulfate

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