mechanismofsuspensionpolymerizationofuniform...

Mechanism of Suspension Polymerization of UniformMonomer Droplets Prepared by Glass Membrane(Shirasu Porous Glass) Emulsification Technique

HAJIME YUYAMA, TOMOHIRO HASHIMOTO, GUANG-HUI MA, MASATOSHI NAGAI, SHINZO OMI

Graduate School of Bio-Applications and Systems Engineering, Tokyo University of Agriculture and Technology,Koganei 184-8588, Japan

Receive d 22 October 1999; accepted 24 February 2000

ABSTRACT: The mechanism of the unique suspension polymerization of uniform monomerdroplets, without coalescence and breakup during the polymerization, was investigatedusing styrene (S) as a monomer mixed with water-insoluble hexadecane (HD). The glassmembrane (Shirasu Porous Glass, SPG) emulsification technique was employed for thepreparation of uniform droplets. Depending on the pore sizes of the SPG membranes (1.0,1.4, and 2.9 mm), polymer particles of an average diameter ranging from 5.6 to 20.9 mmwere obtained with the coefficient of variation (CV) being close to 10%. The role of HD wasto prevent the degradation of the droplets by the molecular diffusion process. Sodiumnitrite was added in the aqueous phase to kill the radicals desorbed from the droplets(polymer particles), thereby suppressing the secondary nucleation of smaller particles.Each droplet behaved as an isolated locus of polymerization. With the presence of HD, theinitial polymerization rate was proportional to 0.24th power of the benzoil peroxide (BPO)concentration. This peculiar behavior as compared with the ordinary suspension polymer-ization was explained by introducing the assumption that each droplet was composed ofisolated compartments (cells) in which active polymeric radicals were dissolved in an S-richphase and surrounded by a rather incompatible S/HD (continuous) phase. The averagenumber of radicals in the droplet increased initially due to the separate existence ofpolymeric radicals in compartments. As the polymerization progressed, the HD-rich phasegradually separated, eventually forming macrodomains, which were visible by an opticalmicroscope. The phase separation allowed polystyrene chains to dissolve in a more favor-able S phase, and the homogeneous bulk polymerization kinetics took over, resulting in agradual decrease of the average number of radicals in the droplet until the increase ofviscosity induced the gel effect. When no HD was present in the droplets, the polymeriza-tion proceeded in accordance with the bulk mechanism except for the initial retardation bythe entry of inhibiting radicals generated from sodium nitrite in the aqueous phase. © 2000John Wiley & Sons, Inc. J Appl Polym Sci 78: 1025–1043, 2000

Key words: suspension polymerization; SPG membrane; styrene droplet; uniformmicrosphere; phase separation

INTRODUCTION

Shirasu porous glass (SPG) emulsification is aunique technique for preparing fairly uniform

polymeric microspheres and microcapsules. Thecoefficient of variation of the diameter (standarddeviation/average diameter) is normally around10% or even less. The membrane, commerciallyavailable from a 0.1 to 18-mm pore size, was fab-ricated by Nakashima et al.1 After the base glass,composed mainly of Al2O3—SiO2—CaO—B2O3,was heated again to 1173 K, a bicontinuous struc-ture, the Al2O3—SiO2 and CaO—B2O3 phase, was

Correspondence to: H. Yuyama, Corporate Research Divi-sion, NIPPON NSC Ltd., 1-6-5, Senba Nishi, Minoo, Osaka562-8586, Japan ([email protected]).Journal of Applied Polymer Science, Vol. 78, 1025–1043 (2000)© 2000 John Wiley & Sons, Inc.

1025

induced by spinodal decomposition. The latterphase (CaO—B2O3) was removed by acid wash-ing, leaving the skeleton structure of the formerphase (Al2O3—SiO2). To prepare an oil-in-water(O/W) emulsion, the oil phase is pushed throughthe pores of the SPG membrane by applying acarefully controlled pressure. Because of the nar-row pore-size distribution, the oil droplets areformed in a uniform state. Addition of water-in-soluble substances such as hexadecane (HD) andlauryl alcohol provides further stability of thedroplets by preventing the diffusional degrada-tion process of the droplets.

The authors realized a potential versatility ofthis particular technique for the preparation ofuniform polymer particles by subsequent suspen-sion polymerization and microcapsules by em-ploying a solvent-evaporation process of the drop-lets. For example, a formulation of a monomer, acrosslinking agent, and a poor solvent yieldedporous polymer particles, whereas another con-sisting of a hydrophilic monomer and a hydropho-bic poor solvent resulted in hollow spheres byremoving the solvent afterward. Compositespheres were also prepared by dissolving an un-reactive substance in the monomer–solvent mix-ture. Relatively large spheres of several microme-ters in diameter provided an adequate scale forthe investigation of the particle morphology, aclear advantage to the submicron-scale latex par-ticles. The droplets were so stable, no breakup orcoalescence during the polymerization, that vir-tually the same number of polymer particles asthat of the initial droplets was observed, exceptfor a slight shrinkage of the diameter because ofthe density difference between the monomer andthe polymer. The emulsification of the oil-phase,suspending hydrophilic powders in it, is ratherdifficult due to the poor stability of the suspensionand the tendency of the powders plugging up thepores. Uniform magnetite microcapsules wereprepared by overcoming these obstacles by thesolvent-evaporation process. All these develop-ments and other progress have been introducedseveral times.2–5

Because the authors were so preoccupied withthe versatility of the SPG membrane for prepar-ing various kinds of sophisticated polymer parti-cles, fundamental investigations such as themechanism of uniform droplets formation6 andhow the polymerization will proceed have beenset aside until recently. Generally, the mecha-nism of suspension polymerization involving hy-drophobic monomers such as styrene (S), which isa good solvent for its polymer, have been regarded

essentially as the same as those of the bulk orsolution polymerization kinetics. Breakup and co-alescence of the droplets during polymerizationaffected only the size distribution of final polymerbeads. Karfas and Ray7,8 proposed a mathemati-cal model to simulate the evolution of suspensionpolymerization of partially water-soluble mono-mers such as methyl methacrylate (MMA) andvinyl acetate (Vac) by introducing the partition ofthe monomer between the droplets and the aque-ous phase. They confirmed that bulk polymeriza-tion kinetics is sufficient to quantify the suspen-sion polymerization of S in which the droplets ofmillimeter size normally possess 108 radicals.

One of the most significant features in ouremulsion system is that virtually no breakup orcoalescence of the droplets takes place throughoutthe suspension polymerization. This situation, al-though the droplet size is about two orders larger,reminds the authors of a unique miniemulsionpolymerization of S reported by Miller et al.9,10

They found that almost all the initial miniemul-sion droplets were converted to polymer particleswhen they dissolved polystyrene having SO4

2

groups at both ends in the droplets. They con-cluded that the droplets behaved as though theywere monomer-swollen seed polymer particles inemulsion polymerization, and the miniemulsionprocess was regarded as a growth period. A wa-ter-soluble initiator, potassium persulfate, wasused, and they did not neglect the desorption ofradicals from the polymer particles to the aque-ous phase when they tried to elucidate the reac-tion mechanism. In other words, this mechanisminvolves the exchange of radicals across the inter-face of the polymer particles.

Besides the larger droplet size, the presence ofwater-insoluble HD in our emulsion system pre-vents the desorption of radicals from the droplets,and the addition of sodium nitrite in the aqueousphase as a radical scavenger makes the reentry ofradicals from the aqueous phase practically im-possible. These unique features imply that thedroplets are regarded as the loci of the compart-mentalized polymerization system first proposedby Haward11 and later extended by Blackley12

with rigid mathematical developments. However,Blackly pointed out that the compartmentalizedpolymerization system can be applied only to theloci in which 0.01–2 radicals normally coexistwith 10 radicals utmost. In our polymer particles,the average number of radicals is 106–7, as shownin the later part.

In this article, the mechanism of this uniquesuspension polymerization that takes place in the

1026 YUYAMA ET AL.

isolated droplets was investigated. It is shownthat the initial behavior of the polymerization isdifferent depending on the presence of HD in thedroplets. The S/HD mixture was rather a poorcosolvent for polymeric radicals, and a concept ofcompartmentalized radicals was proposed to elu-cidate the peculiar mechanism. Without the pres-ence of HD, the polymerization behaved asthough it were an ordinary bulk polymerizationprocess.

EXPERIMENTAL

Materials

Sodium lauryl sulfate (SLS; Wako Pure ChemicalCo., Ltd., Tokyo, Japan) and poly(vinyl alcohol)(PVA; degree of hydrolysis, 87.8 mol %; averagedegree of polymerization, 1725; Kuraray Co., Ltd.,Tokyo, Japan), composing a mixed stabilizer,were used as received without further purifica-tion. S and HD were reagent grade and used asreceived. Benzoyl peroxide (BPO) with a 25 wt %moisture content (Kishida Chemical Co. Ltd.,Tokyo, Japan) was reagent grade and used as aninitiator. Sodium nitrite (NaNO2 ) was reagentgrade (Kanto Chemical Co., Ltd., Tokyo, Japan)and used as a water-soluble inhibitor to preventthe secondary nucleation of polymer particles inthe aqueous phase. Twice-distilled and deionizedwater (DII) was used for the preparation of aque-ous solutions. Nitrogen was a high-purity grade.

Emulsification

A particular apparatus for emulsification with amicroporous glass (MPG; Ise Chemical Co., Ltd.)module was already presented in our previousreport.3 SPG membranes were immersed in anSLS solution and treated with ultrasonification(Branson Sonic Model B-5200J-4) prior to use sothat the surface may be thoroughly wetted withthe aqueous phase. The dispersion phase, a mix-ture of S and HD dissolving a small amount ofBPO, was stored in a pressure-tight storage tankand allowed to permeate through the membraneunder an appropriate pressure in the recirculat-ing flow of the continuous phase, an aqueous so-lution of the stabilizers, and the water-solubleinhibitor. The droplets were suspended in thecontinuous phase and stored in an emulsion stor-age tank with a gradual increase of the dropletnumbers. After the half-volume of the dispersionphase was emulsified, the emulsion was with-

drawn from the storage tank and served for poly-merization. A more detailed description can befound elsewhere.1–6

Polymerization

As the initiator, BPO, was already mixed with themonomer in the dispersion phase, efficient oper-ation was required to minimize the idle time. Fivehundred grams of the emulsion was transferredto an ordinary glass separator flask, and gentlebubbling of nitrogen into the emulsion was fol-lowed with mild agitation. After 1 h, the bubblingnozzle was removed from the emulsion, the ingre-dients were heated to the reaction temperature at75°C and polymerized for 26 h under a nitrogenatmosphere. After the polymerization, the poly-mer particles were removed from the serum bycentrifugation, washed with methyl alcohol, anddried under a vacuum. A small amount of thesamples was withdrawn periodically from the re-actor and was short-stopped by adding methylethylhydroquinon as an oil-soluble inhibitor andstored in an ice bath. Table I indicates the stan-dard recipe used for all the reactions.

Analysis

Percent conversion of S was measured with head-space gas chromatography (HS-GC; HS module:

Table I Standard Recipe of Emulsification andPolymerization

1. Continuous phaseWater (DII) 450 gPoly(vinyl alcohol) (PVA) 6.02 gSodium lauryl sulfate(SLS) 0.60 gSodium nitrite (NaNO2) 0.00, 0.20g

2. Dispersion phaseStyrene (S) 20 gHexadecane (HD) 0.0, 5.0 gBenzoyl peroxide (BPO)a 0.15, 0.30, 0.45, 0.60 g

3. EmulsificationSPG membrane pore size 1.0, 1.4, 2.9 mmApplied pressureb 0.13, 0.30, 0.49 kgf/cm2

Circulation flow ratec 330 mL/min

4. PolymerizationReaction temperature 348 KReaction time 26 hAgitation rate 122 rpm

a 25 wt % moisture content.b Nitrogen pressure applied to the pressure bottle.c Recirculation rate of the continuous phase in which the

droplets were gradually released.

POLYMERIZATION OF UNIFORM MONOMER DROPLETS 1027

Perkin–Elmer HS-40; GC module: Hewlett–Pack-ard 5890 Series II). The injecting samples wereprepared by adding a known amount of toluene asan external standard and then diluted with 10mL of tetrahydrofuran (THF).

Emulsion droplets before and during the poly-merization and polymer particles were observedwith an optical microscope (Nikon Optiphoto200). Diameters of several hundred droplets orparticles were counted to calculate average diam-eters and the coefficient of variation (CV 5 stan-dard deviation/average diameter 3 100%). Gen-eral features of the polymer particles were ob-served with an SEM (Hitachi S-2500CX).

Average molecular weight and molecularweight distribution were measured with gel per-meation chromatography (GPC; Waters 510/410),employing THF as an elution solvent. The col-umns were calibrated with nine standard polysty-rene samples.

RESULTS AND DISCUSSION

Polymerization of Monomer Droplet Including HD(HD System)

Effects of Monomer Droplet Size

Average diameters and the CV of the obtainedmonomer droplets and polymer particles arelisted in Table II with the SPG pore size. Figure 1shows the conversion–time curves for polymeriza-tion, where the monomer droplet containing 10.3mol % of HD and a 0.0726 mol/L-oil phase of BPOwere prepared with different pore sizes of theSPG membrane: 1.0, 1.4, and 2.9 mm. The conver-sion–time curves show a similar conversion pro-

file regardless the average size of the monomerdroplets. All curves were found to have the samekinetics features. The polymerization rate for dif-ferent monomer droplet sizes is shown in Figure2. All runs showed the same general behaviorduring the polymerization. The rate reached amaximum, decreased slowly, increased again fora short period, and decreased gradually until theend of the reaction. The following discussion isintended to provide a basic understanding of thepolymerization rate curves, which will then be

Table II Properties of Obtained Monomer Droplets Prepared with Different SPG Pore Sizes andTheir Polymerized Particles

SPG Pore Size(mm)

Emulsion Droplets Polymer Particles

d# na

(mm)CVb

(%)No. Droplets

(/L)cd# nd

(mm)CV(%)

No. Particles(/L)c

2.9 20.9 11.9 3.73 3 109 19.6 15.7 4.53 3 109

1.4 8.9 11.7 6.25 3 1010 8.3 12.2 6.38 3 1010

1.0 5.6 8.2 2.51 3 1011 5.0 9.2 2.80 3 1011

Monomer droplets contained 10.3 mol % of HD and 0.0991 mol/L of BPO based on the dispersion phase. The continuous phasecontained 0.2 g of sodium nitrite as a water-soluble inhibitor.

a Number-average droplet size.b Coefficient of variation.c Number in the total emulsion.d Number-average particle size.

Figure 1 Conversion versus time curves for polymer-ization of S droplets in the presence of hexadecaneinitiated by 0.0726 mol/L-oil phase of BPO and at threedifferent number-average droplet sizes: (F) 20.9 mm;(L) 8.9 mm; (E) 5.5 mm.

1028 YUYAMA ET AL.

discussed in more detail in a later section. Thefirst increase in the rate of polymerization until0.1 of the fractional conversion is attributed to thegeneration and growth of the polymeric radicalsin the droplets. Let us define these droplets aspolymer particles although they are several or-ders larger than those in conventional emulsionpolymerization. This period lasted 0.5–1.0 h fromthe start. The second stage continued until 0.5–0.6 of the fractional conversion, where the poly-merization rate started to decrease as a result ofthe steady drop in the monomer concentration inthe polymer particles. This decrease in monomerconcentration in the particles continued until thefinal conversion was achieved. At the end of thisstage, the rate again increased to a second maxi-mum. This is attributed to the well-known geleffect: acceleration due to the viscosity increasewithin the growing particles. Finally, at high con-version, the polymerization rate decreased again.

In this system, the continuous phase can beregarded as a sink for active radicals since a wa-ter-soluble inhibitor was added to suppress thenucleation of secondary particles. Stability of themonomer droplets was maintained during the po-lymerization because of the uniform size and thepresence of a water-insoluble substance, HD (sol-ubility in water: 9.0 3 1028 wt % at 283 K), whichprevents the monomer from diffusing out of thedroplet. Indeed, the droplets were so stable that

all the droplets were converted to polymer parti-cles and did not serve as the reservoirs of mono-mers as in the case of conventional emulsion po-lymerization.

Virtually, neither the coalescence nor thebreakup of the droplets took place—only a smallshrinkage in volume due to the conversion ofmonomer to polymer.13 The number of polymerparticles was expected to remain equal to theinitial number of monomer droplets before thepolymerization. Table II shows that the number-average particle size and particle number are notsignificantly different. In Figure 3, the number ofpolymer particles calculated from the averageparticle size is shown as a function of the frac-tional monomer conversion, providing substantialevidence of the discussion described above. Also,Figure 4 shows that the size distributions of theinitial droplets and the final polymer particles allrevealed similar curves except the slight decreasein the size of polymer particles. These resultssuggest that the polymerization mechanism of theHD system is not dependent on the initial dropletsize ranging from 5.6 to 20.9 mm as a locus ofpolymerization.

Effects of Initiator Concentration

Figure 5 shows the conversion–time curves forthe polymerization of monomer droplets preparedwith a 1.0-mm pore size, where the initiator con-

Figure 2 Polymerization rate versus fractional con-version curves for S droplets in the presence of hexa-decane initiated by 0.0726 mol/L-oil phase of BPO andat three different number-average droplet sizes: (F)20.9 mm; (L) 8.9 mm; (E) 5.5 mm.

Figure 3 Particle number during polymerization of Sdroplets in the presence of hexadecane at three differ-ent number-average droplet sizes: (F) 20.9 mm; (L) 8.9mm; (E) 5.5 mm.


centration was varied from 0.0217 to 0.0726 mol/L-oil phase. The overall polymerization rate in-creased with the amount of initiator. Figure 6

shows logarithmic plots of the number of polymerparticles and the initial polymerization rate ver-sus the initiator concentration. The rate of poly-merization varied to the 0.24th power of the ini-tiator concentration. The number of particles did

Figure 4 Measured particle-size distribution of S droplets in the presence of hexa-decane: (a) dn 5 20.9 mm; (b) dn 5 8.9 mm; (c) dn 5 5.5 mm. (F) Before polymerization;(E) after polymerization.

Figure 5 Conversion versus time curves for polymer-ization of S droplets in the presence of hexadecane pre-pared using 1.0 mm of SPG and initiated using 0.0217,0.0433, 0.0643, and 0.0726 mol/L-oil phase BPO.

Figure 6 Log–log plot of the number of particles andfirst maximum polymerization rate versus initiatorconcentration for polymerization of S droplets in thepresence of hexadecane prepared using 1.0 mm of SPG.

1030 YUYAMA ET AL.

not change with the initiator concentration. Theresults listed in Table III indicate that both thedroplets and final polymer particle size did notsignificantly change before and after polymeriza-tion. This implies that the formation of the initialmonomer droplets slightly depended on the BPOconcentration, probably due to the minor changesinflicted to the interfacial tension, viscosity, andhydrophobicity. The low dependence of the initialpolymerization rate on the initiator concentration(0.24th power) compared to the square-root de-pendence in the case of ordinary bulk polymeriza-tion14 is discussed in the later section dealingwith the mechanism of polymerization.

The number- and the weight-average molecu-lar weight of the polymers composing the finalpolymer particles are listed in Table III. In Figure7, the number- and weight-average degree of po-lymerization is plotted against the fractional con-version when the monomer droplets were pre-pared with a pore size of 1.42 mm, and the con-centration of BPO was 0.0726 mol/L-oil phase. Itcan be seen that the degree of polymerization (P# n,P# w) decreased steadily and decreased even morerapidly after the fractional monomer conversionexceeded 0.6. The decrease of the number-averagemolecular weight during polymerization is simi-lar to that obtained by Alduncin and Asua.15 Theyreported that this decrease was due to chaintransfer to the initiator, which counteracted theinfluence of the gel effect in the study of mini-emulsion polymerization of S with HD (2 wt %)initiated by BPO.

Since there is no radical entry from the aque-ous phase because of the presence of a water-

soluble inhibitor and virtually no coalescence orbreakup of the droplets, each monomer dropletbehaves as being an isolated locus. Let us firstassume that the molecular weight was controlledby the bulk polymerization kinetics, that is, ter-mination by the combination of two polymericradicals and the chain transfer of radicals to HD;chain transfer to the monomer can be neglectedbecause the chain-transfer coefficient of S is of theorder of 1025 compared to 1022 of HD.16 From thebulk polymerization kinetics, the number-aver-

Table III Effect of BPO Concentration in the Dispersion Phase (HD System)

BPO(mol/L)a


M# nf M# w

gd# nb

(mm)CVc

(%)No. Droplets

(/L)dd# ne

(mm)CV(%)

No. Particles(/L)d

0.0726 5.6 8.2 2.51 3 1011 5.0 9.2 2.80 3 1011 2.12 3 104 2.80 3 104

0.0643 5.8 8.4 2.26 3 1011 5.3 9.1 2.39 3 1011 2.31 3 104 3.07 3 104

0.0433 6.1 8.6 1.92 3 1011 5.3 9.9 2.42 3 1011 2.11 3 104 3.15 3 104

0.0217 6.1 9.8 1.95 3 1011 5.9 10.0 1.81 3 1011 2.87 3 104 4.14 3 104

Monomer droplets were prepared with a 1.0-mm pore size and contained 10.3 mol % of HD based on the dispersion phase. Thecontinuous phase contained 0.2 g of sodium nitrite as a water-soluble inhibitor.

a Concentration in the dispersion phase.b Number-average droplet size.c Coefficient of variation.d Number in the total emulsion.e Number-average particle size.f Number-average molecular weight.g Weight-average molecular weight.

Figure 7 Degree of polymerization during the poly-merization of S droplets in the presence of hexadecaneprepared using 1.4 mm of SPG: (E) number-average; (F)weight-average.


age degree of polymerization can be estimated.The rate constants of propagation (kp 5 413 Lmol21 s21) and termination [kt 1.11(108) L mol21

s21] by recombination for S at 348 K were ob-tained from the literature.16,17 The decompositionrate constant of BPO (kd) is 1.83 3 1025 s21.17

The volume unit, L, refers to the volume of the oilphase.

From the experimental recipe, the rate of ini-tiation (ri) is 1.35 3 1026 mol L21 s21, where theinitial concentration of S, HD, and BPO are 6.58,0.757, and 0.0726 mol/L, respectively. Then, theinitial rate of polymerization (rp) is given as 3.003 1024 L21 s21. This value is in good agreementwith the observed value shown as the point lo-cated at the extreme right in Figure 6.

The initial number-average degree of polymer-ization controlled by the combination of radicals(p# n0,t) can be calculated as 444, whereas the ini-tial number-average degree of polymerizationdominated by the chain transfer to HD (p# n0,tr) isgiven as 870. With these two values being com-bined, the overall degree of polymerization can beestimated as

P# n0 > p# n0 51

1/p# n,t 1 1/p# n,tr

51

1/444 1 1/870 5 294

p# n0,t and P# n0 are larger than is the initially ob-served value of 207 as shown in Figure 7. If oneassumes that the termination in the dropletstakes place between one polymeric radical and asmall radical (initiator radical) rather than atransferred radical, then the value will be 222

and in good agreement with the observed value.The bulk polymerization mechanism was notvalid to estimate the number-average degree ofpolymerization.

Polymerization of Monomer Droplet Without HD(Non-HD System)

Effects of Monomer Droplet Size

To study the effect of HD on the polymerization,the monomer droplets without HD were polymer-ized. In this system, defined as the non-HD sys-tem, the active radicals and monomers as well aresubject to diffuse from the particles to the contin-uous phase during the polymerization; however,the continuous phase is a sink for the active rad-icals as in the case of the HD system.

The average diameter and CV of the S mono-mer droplets and the polymer particles are listedin Table IV with the SPG pore size. The absenceof HD is reflected on the high CV values when thelargest pore size (2.9 mm) was employed for theemulsification. Figure 8 shows the conversion–time curves of the polymerization, where themonomer droplets containing BPO, 0.117 mol/L-oil phase, were prepared with the same pore sizesof the SPG membranes as in the HD system.Compared with the HD system (Fig. 1), the con-version–time curves showed a different conver-sion profile. From the start to 0.3 of the fractionalconversion, it was found that the polymerizationproceeded slowly as though in an induction periodregardless of the size of the monomer droplets,and this period lasted 2.0 h from the startingtime. The polymerization rates for differentmonomer droplet sizes are shown in Figure 9. The

Table IV Properties of Obtained Monomer Droplets Without HD Prepared with Different SPG PoreSizes and Their Polymerized Particles

SPG Pore Size(mm)


d# na

(mm)CVb

(%)No. Droplets

(/L)cd# nd

(mm)CV(%)

No. Particles(/L)c

2.9 28.2 28.4 1.25 3 109 27.1 19.8 1.21 3 109

1.4 8.7 12.7 5.16 3 1010 7.4 16.0 6.11 3 1010

1.0 5.7 14.4 1.80 3 1011 5.0 16.5 1.78 3 1011

Monomer droplets contained 0.1170 mol/L of BPO based on the dispersion phase. The continuous phase contained 0.2 g ofsodium nitrite as a water-soluble inhibitor.

a Number-average droplet size.b Coefficient of variation.c Number in the total emulsion.d Number-average particle size.

1032 YUYAMA ET AL.

overall polymerization rate curves showed thesame general behavior except for the appearanceof the gel effect. The polymerization rate reachedthe maximum slower than that of the HD system,

stayed almost constant for a short period, in-creased again due to the gel effect, and decreasedgradually until the end of the reaction. From thefractional conversion 0.5–0.7, the smaller drop-lets appeared to exhibit a more prominent geleffect, and it started at a lower fractional conver-sion than that of the larger droplets.

In the liquid–liquid dispersion systems, thepossibility that the recirculating flow exists in thedroplets (hence, enhanced mobility of molecules)is governed by the bond number (gDrdp

2/g), whereg is the acceleration rate by gravity; Dr, the den-sity difference between the continuous and thedispersion phase; dp, the average diameter of thedroplet; and g, the interfacial tension. Althoughno appreciable flow may actually exist in our mi-cron-scale droplet system, still it may be reason-able to assume that the radicals in the smallerdroplets are less mobile. The consequence will bean accumulation of the radicals, inducing an en-hanced gel effect in the earlier stage of the reac-tion.

In Figure 10, the number of polymer particlesis shown as a function of the fractional monomerconversion. The number of polymer particles didnot change during the polymerization as in theHD system. Figure 11 shows the size distributionof the initial droplets and the final polymer par-ticles. Comparison of the CV values in Tables IIand IV indicates that the size distributions werebroader with the runs without HD, in particular,

Figure 8 Conversion versus time curves for polymer-ization of S droplets in the absence of hexadecane ini-tiated by 0.117 mol/L-oil phase of BPO and at threedifferent number-average droplet sizes: (F) 28.2 mm;(L) 8.7 mm; (E) 5.7 mm.

Figure 9 Polymerization rate versus fractional con-version curves for S droplets in the absence of hexade-cane initiated by 0.117 mol/L-oil phase of BPO and atthree different number-average droplet sizes: (F) 28.2mm; (L) 8.7 mm; (E) 5.7 mm.

Figure 10 Particle number during the polymeriza-tion of S droplets in the absence of hexadecane at threedifferent number-average droplet sizes: (F) 28.2 mm;(L) 8.7 mm; (E) 5.7 mm.


when the largest pore size (2.9 mm) was em-ployed. The distributions shown in Figures 4(b)and 11(b) were plotted against the same scale ofthe horizontal axis, demonstrating a broader sizedistribution of the latter. The reason for a broaderdistribution of the initial droplet size without HDwas already presented in our report.6 The dropletsize and its distribution were significantly af-fected by the hydrophobicity of the dispersionphase, which depends on the amount of HD.These results suggest that the polymerizationmechanism without HD was not dependent on theinitial droplet size from 5.7 to 21.7 mm, exceptduring the period of the gel effect.

Effects of Initiator Concentration

Figure 12 shows the conversion–time curves forthe polymerization of the monomer droplets pre-pared with a 1.0-mm pore size, where the initiatorconcentration was varied from 0.0299 to 0.1170mol/L-oil phase. The polymerization rate in-creased with the amount of initiator significantly.Figure 13 shows a logarithmic plot of the numberof final polymer particles and the initial polymer-ization rate at the point of the first maximumversus initiator concentration. This figure showsthat the polymerization rate was proportional to

the 0.48th power of the initiator concentration,except the point of the lowest concentration. Thenumber of particles did not change with the ini-

Figure 11 Measured particle-size distribution of S droplets in the absence of hexa-decane prepared by three different SPG pores: (a) 1.0 mm of SPG pore; (b) 1.4 mm of SPGpore; (c) 2.9 mm of SPG. (F) Before polymerization; (E) after polymerization.

Figure 12 Conversion versus time curves for poly-merization of S droplets in the absence of hexadecaneprepared by 1.0 mm of SPG and initiated using 0.0299,0.0589, 0.0890, and 0.1170 mol/L-oil phase BPO.

1034 YUYAMA ET AL.

tiator concentration as in the case of the HD sys-tem. Table V shows that the average diameterand CV values of the initial droplets and the finalpolymer particles did not depend on the BPO con-centration. As shown in the other tables (II–IV),the size distribution of the final polymer particlesbecame broader than those of the initial monomerdroplets.

In Figure 14, the number- and weight-averagedegree of polymerization are plotted against thefractional conversion when the monomer dropletswere prepared with a pore size of 1.42 mm, and

the concentration of BPO was 0.117 mol/L-oilphase. By comparing two pairs of figures, Figures2 and 9 and Figures 7 and 14, respectively, theeffect of HD in the droplets to the mechanism ofthe polymerization can be considered as follows:Without the presence of HD, a slow increase ofthe polymerization rate (Fig. 9) and an initialdecrease of the degree of polymerization (Fig. 14)were observed. Fitch18 suggested that NaNO2 asa water-soluble inhibitor eventually generates ni-trogen dioxide and nitric oxide which deactivate

Figure 13 Log–log plot of the number of particles andfirst maximum polymerization rate versus initiatorconcentration for polymerization of S droplets in theabsence of hexadecane prepared using 1.0 mm of SPG.

Table V Effect of BPO Concentration in the Dispersion Phase (Non-HD System)

BPO(mol/L)a


M# nf M# w

gd# nb

(mm)CVc

(%)No. Droplets

(/L)dd# ne

(mm)CV(%)

No. Particles(/L)d

0.1170 5.7 14.4 1.88 3 1011 5.0 16.5 1.78 3 1011 2.30 3 104 3.51 3 104

0.0890 5.9 12.8 1.61 3 1011 4.9 16.3 2.09 3 1011 2.45 3 104 3.87 3 104

0.0589 5.6 12.7 1.90 3 1011 4.8 13.6 2.29 3 1011 2.85 3 104 4.50 3 104

0.0299 6.0 12.9 1.18 3 1011 4.9 16.3 2.14 3 1011 2.74 3 104 6.08 3 104

Monomer droplets were prepared with a 1.0-mm pore size. The continuous phase contained 0.2 g of sodium nitrite as awater-soluble inhibitor.

a Concentration in the dispersion phase.b Number-average droplet size.c Coefficient of variation.d Number in the total emulsion.e Number-average particle size.f Number-average molecular weight.g Weight-average molecular weight.

Figure 14 Degree of polymerization during polymer-ization of S droplets in the absence of hexadecane pre-pared using 1.4 mm of SPG: (E) number-average; (F)weight-average.


water-soluble radicals. He also pointed out thatthese radicals are soluble in a hydrophobic me-dium, hence capable of inhibiting the polymeriza-tion without HD. Then, the polymeric radicals inthe S droplets will be more susceptible to be short-stopped by these species. This may explain theprofile of a gradual increase of the polymerizationrate in Figure 9 and an initial decrease of thedegree of polymerization in Figure 14. Notice thatthe initial value of the degree of polymerizationwas higher than that observed in Figure 7 (eventhough the initiator concentration was slightlyhigher, 0.117–0.0726 mol/L-oil phase, implyingthat the mechanism of the non-HD system fol-lowed the bulk polymerization mechanism exceptthe initial entry of inhibiting radicals from theaqueous phase. As the amount of polymers wasaccumulating in the droplets, the droplets gainedenough hydrophobicity as in those with HD, theentry of the inhibiting radicals became less en-hanced, and the polymerization in the dropletsproceeded similar to that of the HD system.

Effect of Sodium Nitrite on the PolymerizationWith and Without HD

As described above, it was suggested that sodiumnitrite as a water-soluble inhibitor affected thepolymerization of the monomer droplets with andwithout HD initiated by an oil-soluble initiator.In this section, the effect of NaNO2 on the poly-merization of both the HD and non-HD systemswill be discussed.

Data of the obtained monomer droplets andpolymer particles are listed in Table VI with theconnections of HD and NaNO2, which were ex-tracted from the data in Tables II and IV. Con-version–time curves for the four polymerizationsystems are shown in Figure 15, in which thecorresponding runs in Figures 1 and 8 were in-

Table VI Effect of HD Content and NaNO2 Content on Polymerization

HD(mol %)a

NaNO2

(mol/L)b


M# ng

(3104)M# w

h

(3104) Dpid# nc

(mm)CVd

(%)No. Droplets

(/L)ed# nf

(mm)CV(%)

No. Particles(/L)e

0.0 0.005 8.7 12.7 5.16 3 1010 7.4 16.0 6.11 3 1010 2.30 3.51 1.520.0 0.000 9.8 18.3 3.43 3 1010 6.0 17.9 1.11 3 1011 2.68 5.87 2.19

10.3 0.005 8.9 11.7 6.25 3 1010 8.3 12.2 6.38 3 1010 2.11 2.80 1.3310.3 0.000 9.7 13.1 4.71 3 1010 7.6 13.9 7.81 3 1010 2.34 3.98 1.69

Monomer droplets of the non-HD system contained 0.117 mol/L of BPO based on the dispersion phase. Monomer droplets of theHD system contained 0.0276 mol/L of BPO based on the dispersion phase. All monomer droplets were prepared with a 1.4-mm poresize.

a HD content based on the dispersion phase.b Concentration in the total emulsion.c Number-average particle size.d Coefficient of variation.e Number in the total emulsion.f Number-average particle size.g Number-average molecular weight.h Weight-average molecular weight.i Molecular weight dispersity of polymer (Mw/Mn).

Figure 15 Conversion versus time curves for poly-merization of S at four different recipe conditions: (E)HD 0.0 mol %, NaNO2 0.005 mol/L; (h) HD 0.0 mol %,NaNO2 0.000 mol/L; (■) HD 10.3 mol %, NaNO2 0.000mol/L; (F) HD 10.3 mol %, NaNO2 0.005 mol/L.

1036 YUYAMA ET AL.

cluded. For the runs without NaNO2 (square sym-bols), the conversion–time curve showed a similartendency, and the polymerization rates werefaster than were those in the runs with NaNO2(circular symbols) regardless the presence of HD.The number- and the weight-average molecularweight of the polymers composing the final poly-mer particles are listed in Table VI. For the runswithout NaNO2, the molecular weight distribu-tions were broader than were those prepared withNaNO2. In particular, the non-HD run revealed abroader distribution.

The sizes of the monomer droplets and polymerparticles, listed in Table VI, showed that themonomer droplet sizes and the size distributionswithout NaNO2 were larger and broader thanwere those prepared with NaNO2. This impliesthe interaction of sodium nitrite with the mixedstabilizer, although the mechanism has yet to beunderstood. The final polymer particle size of theruns without NaNO2 was somewhat smaller thanwere the runs with NaNO2. Moreover, the num-ber of particles of the runs with no NaNO2 in-creased remarkably, compared with the numberof droplets. These results imply a scenario thatwithout the addition of NaNO2 the secondary nu-cleation of polymer particles took place, resultingin the increased polymerization rate and molecu-lar weight and broadening of the molecularweight distribution.

In Figure 16, the number of polymer particlesformed without NaNO2 is shown as a function ofthe fractional conversion. The run without HDchanged significantly during the polymerization,

especially at the initial polymerization stage,from the start to 0.2 of the fractional conversion.However, for the run with HD, the number ofpolymer particles did not change remarkably asin the HD system, as shown in Figure 10. Theparticle-size distribution of the run preparedwithout HD and NaNO2 is given in Figure 17. Thefirst peak of the weight-average particle size is174 nm and the second peak is 11.5 mm, yieldinga bimodal distribution curve. It is confirmed thatthe nucleation of secondary particles occurred bythe desorption of the monomer and radicals fromthe particles to the aqueous phase at the earlystage of the polymerization.

These results indicate that the addition of awater-soluble inhibitor together with the oil-sol-uble initiator retarded the polymerization of themonomer droplets without HD in the initial stageof the polymerization. For both systems with andwithout HD, the water-soluble inhibitor caused adelay of the overall polymerization by consumingthe radicals in the monomer droplets as well as inthe aqueous phase.

Mechanism of Polymerization

From the results and the discussions above, it isapparent that the monomer droplets served asthe main loci of initiation, propagation, and ter-mination of free radicals. This situation corre-sponds closely to the approach adopted by Sudol

Figure 16 Particle number during the polymeriza-tion of S droplets in the absence of water-soluble inhib-itor: (h) HD 0.0 mol % ; (■) HD 10.3 mol %.

Figure 17 Measured polymer particle-size distribu-tion of S droplets in the absence of neither HD norNaNO2.


et al.19 to produce monodisperse latexes throughthe successive seeding processes based upon theconcept of polymerization within the locus pre-pared in advance. Furthermore, the miniemul-sion polymerization is defined as the polymeriza-tion in the monomer droplets dispersed in theinitial emulsion, where the initial droplet-sizedistribution is reflected in the final polymer par-ticle-size distribution. Tang et al.20 studied thedifferences in the polymerization kinetics of Sbetween a conventional emulsion and a mini-emulsion stabilized with SLS together with eithercetyl alcohol (CA) or HD. This work showed afaster initial rate of polymerization when HDrather than CA was used as a cosurfactant, whichresulted in a more narrow particle-size distribu-tion. The polymerization rate–conversion curvesof the miniemulsion polymerization with CA re-vealed a similar profile observed with the conven-tional emulsion polymerization. Choi et. al.21 re-ported the kinetics of S miniemulsion polymeriza-tion carried out by using both a water-soluble(potassium persulfate) and an oil-soluble [2,29-azobis-(2-methyl butyronitrile)] initiator withSLS and CA. They suggested that the polymer-ization mechanism with the oil-soluble initiatorwas similar to that observed with the persulfateinitiator even though their primary radical gen-eration sites were different. Only the radicals en-tering from the aqueous phase are capable ofpropagating radicals in the polymer particles.

In our current experiments, the polymerizationrate–conversion curves with and without HD(Figs. 2 and 9) showed a similar polymerizationrate profile to that of the miniemulsion polymer-ization with the hydrophobic additive as a cosur-factant. The mechanism of radical formation froman oil-soluble initiator influences the polymeriza-tion kinetics through the distribution of free rad-icals in the particles and, therefore, through theaverage number of radicals per particles.22 In Fig-ure 18, the average number of radicals per parti-cles, n# , obtained from the rate equation given foremulsion polymerization, is plotted against thefractional conversion for the four polymerizationsystems listed in Table VI. With an HD of content10.3 mol % as shown in Figure 18(a), n# decreasedwith increasing the fractional conversion. In ad-dition, since n# of the run with NaNO2 is far lessthan that without NaNO2, it becomes clear thatthe radicals generated from the water-soluble in-hibitor deactivate the free radicals in the parti-cles. On the other hand, in the run without HD asshown in Figure18(b), n# increased slightly until0.3 of the fractional conversion and stayed almost

constant from 0.3 to 0.55 of the fractional conver-sion. The influence of a water-soluble inhibitor isless enhanced than is the presence of HD. Theparticles with HD [Fig. 18(a)] has a larger num-ber of n# than those without HD regardless of thepresence or absence of NaNO2.

For the polymerization with HD, incompatibil-ity between the polymeric radicals and HD playsan essential role for the mechanism. In addition,the termination of radicals by a chain-transferreaction to HD will be possible to take place asdiscussed in the previous section. The probabilitythat the desorptions of initiator radicals beforereacting with monomer molecules and radicalsother than the initiator radicals will occur shouldbe lower than that in the polymerization withoutHD. In the initial stage of polymerization, thedecomposition of the initiator and the subsequentchain growth will take place in the monomerdroplets. The homogeneity of the S/HD mixturewill be soon lost after the substantial numbers ofoligomer radicals were generated because it is apoorer solvent for polystyrene than is the mono-mer itself [dS 5 9.6, dHD 5 8.2, and dpolystyrene5 8.6–9.7 (cal/cc)1/2].23 The oligomeric radicalsare apt to precipitate or exist in a coiled confor-mation, and in either state, the probability of thetermination by recombination will decrease. Itwas proved experimentally that the S oligomerswith five units or more are no longer soluble inHD.24 The accumulation of radicals, well knownfor precipitation polymerization,25 takes place inthis polymerization with HD. From the simplecalculations, n# divided by the number of initiatedradicals per second in a droplet, the average life-time of radicals is estimated as 15.2 s at thefractional conversion of 0.12, whereas the lifetimedecreases to 2.6 s at 0.49 of the conversion. Inother words, the longer lifetime of radicals ac-counts for the high number of n# in the early stageof polymerization. As the polymerizationprogresses, the number of polymer chains willprogress in parallel. Finally, the phase-separateddomains of HD become visible in an optical mi-croscopic scale as shown in Figure 19(b–d). It wasobserved that the macrodomain of HD appearedon the particle surface at the fractional conver-sion of 0.33 [Fig. 19(b)]. Notice that this kind ofphase separation was not observed in the poly-merization without HD as the photographs shownin Figure 19(f) clearly indicated. Therefore, it maybe reasonable to assume that the separation ofHD from the polystyrene/S phase started from theearlier stage of polymerization, and the polymericradicals gradually recovered a favorable extended

1038 YUYAMA ET AL.

conformation and mobility in the S-rich phase.The termination between two radicals will re-sume its intensity, leading to the gradual de-crease in n# . This trend continues until the viscos-ity in the droplet increases so high as to obstructthe mobility of the polymer chains and induce thegel effect.

At the earlier stage of the polymerization, it isassumed that the oligomeric radicals are com-partmentalized through the process of phasetransition from the homogeneous state to the mi-crophase separation states in the particles. Thissituation in the droplet is sketched in Figure 20 inthe Appendix, the droplet being composed of thetiny compartments in which polymeric radicalsare isolated (segregated) in the S-rich medium

and the surrounding S/HD medium. A stochasticapproach may be justified since the number ofradicals in the droplet is of the order of 106. Thatthe initial polymerization rate was proportionalto the 0.24th power of the initiator concentrationcan be mathematically derived as shown in theAppendix, if the following hypotheses are grant-ed:

1. The volume fraction of the compartments(cells) are small compared to that of thesurrounding (continuous) medium;

2. The termination by recombination of radi-cals is dominated in the continuous me-dium; and

3. In the cells, the termination between the

Figure 18 Average particle radical number during polymerization of S droplets: (a)HD 5 10.3 mol %; (b) HD 5 0.0 mol %. (E) NaNO2 0.000 mol/L; (F) NaNO2 0.005 mol/L.


radicals, mainly polymeric and small radi-cals, prevails rather than does the desorp-tion of the small radicals into the back-ground medium.

Although we do not have much substantial in-formation for the rate constant (ki) and the pa-

rameters (vc and Nc, at least, by considering thecompartmentalized model, we could speculateabout a possible mechanism which resulted in the0.24th power dependence of the polymerizationrate to the initiator concentration As we haveshown, the initial polymerization rate, rp0, de-pends on the number of cells in the particles

Figure 19 Optical photomicrographs of emulsion during polymerization of S particles(a–d) in the presence of HD and (e,f) in the absence of HD, where Fc is the fractionalconversion, dn 5 number-average monomer droplet or polymer particle size, and CV isthe coefficient of variation: (a) 0% of conversion; (b) 33% of conversion; (c) 74% ofconversion; (d) 95% of conversion; (e) 0% of conversion; (f) 97% of conversion.

1040 YUYAMA ET AL.

which will depend on the amount of HD. It wasproved that the rp0 for the polymerization with highHD contents was faster than that of the correspond-ing low HD content: rp0 (0 mol % HD) 5 1.03 3 1024

mol L21 s21, rp0,(5.1mol % HD) 5 2.69 3 1024 molL21 s21 (not shown in the figure), and rp0 (10.3 mol% HD) 5 3.82 3 1024 mol L21 s21; each value wasobtained from the droplet prepared with a 2.9-mmSPG pore size. As the polymerization proceeds, HDmolecules start to separate from the S/HD mediumbecause of the accumulation of polystyrene chains.Gradually, microdomains of HD are formed, gath-ering and eventually forming separated macrodo-mains in the droplets, which are visible by an opti-cal microscope.

On the other hand, in the non-HD system, thehydrophobicity of the droplets was less enhancedthan were those of the HD system. The desorptionof radicals and the minor generation of radicals bythe initiator dissolved in the aqueous phase playeda substantial role in the polymerization mechanismof the non-HD system. It can be assumed that thedesorption of radicals occurred at the initial stage ofpolymerization. In addition, the slower polymeriza-tion rate up to the fractional conversion of 0.3 (seeFig. 8) implied the entry of inhibiting radicals gen-erated from the water-soluble inhibitor (see Fig. 15).The mechanism of polymerization obeyed that ofbulk polymerization because the desorbed radicalswere deactivated by the inhibitor in the aqueousphase (NaNO2).

However, when the water-soluble inhibitor wasnot present, the number of polymer particles in-creased until 0.3 of the fractional conversion, asshown in Figure 16. Obviously, the desorbing rad-icals maintained their activity and generatedsmaller polymer particles by the mechanism ofemulsion polymerization. The bimodal particle-size distribution as shown in Figure 17 confirmedthe formation of smaller particles. Almog andLevy26 observed the same result in their suspen-sion polymerization of S with the 10-mm dropletsize by employing an oil-soluble initiator and amixed stabilizer (PVA plus SLS). The initial in-crease in n# in Figure 18(b) (without NaNO2) up tothe fractional conversion of 0.3 was attributedmainly to the generation of secondary loci ratherthan to the gradual decrease of entry of the inhib-iting radicals (with NaNO2).

CONCLUSIONS

The unique mechanism of suspension polymeriza-tion of uniform S droplets was investigated. The

homogeneous mixture of S, water-insoluble HD,and BPO was emulsified with the glass mem-brane (SPG) emulsification technique, forminguniform-sized droplets ranging from 5.6 (1.0-mgr;m pore size) to 20.9 mm (2.9-mm pore size) inaverage diameter. By the addition of HD, thedroplets were stable, without coalescence andbreakup during the polymerization. The S/HDmixture was rather incompatible with polysty-rene, implying that the polystyrene radicals wereisolated in tiny compartments (cells) dissolved inthe S-rich medium. These cells were surroundedby the S/HD phase. The initial behavior of poly-merization was speculated on by considering atheoretical prediction of n# (average number ofradicals per particle) based on the Smith–Ewarttheory (see the Appendix). As the polymerizationprogressed, the HD phase started to separatefrom the polystyrene/S phase, and the macrodo-main was formed on the surface of the droplets(polymer particles) at the fractional monomerconversion of 33% n# decreased steadily until in-crease of the viscosity induced the gel effect. Ob-viously, the termination by recombination of rad-icals gradually took over, and the polymerizationproceeded in accordance with the homogeneousbulk polymerization mechanism.

In the second series of experiments which werecarried out without the addition of HD, no phasetransition was observed, and the polymerizationbehaved as an ordinary suspension polymeriza-tion process. Smooth and homogeneous polymerparticles were obtained.

As expected, the stability of the monomer drop-lets was no longer maintained in the runs withoutthe addition of HD in the oil phase and sodiumnitrite in the aqueous phase. Some of the initialdroplets were wasted as they were consumed bysupplying monomers for the growth of secondaryparticles. These experiments made clear that thewater-insoluble substance (HD) and the water-soluble inhibitor (sodium nitrite) were both essen-tial for the preparation of uniform-sized polymerparticles by employing the SPG emulsificationtechnique.

APPENDIX: PROPOSED REACTIONMECHANISM IN ISOLATED DROPLETS INTHE EARLY STAGE OF POLYMERIZATION

The droplets are composed of an oil-soluble initi-ator (BPO), S, and HD. We may assume that theall the droplets are isolated because of the lowdesorption of radicals from them and no entry


from the aqueous phase (regarded as a sink). Sup-pose that each droplet is compartmentalized intiny cells (c) as shown in Figure A.1. These cellsmay dissolve 0, 1, or a few growing radicals in anS-rich environment. These cells are surroundedby the S/HD phase (o), which is by no means agood solvent for polystyrene and the growing rad-icals.

According to the models proposed by Ugelstadet al.27 and Kubota et al.28 based on the Smith–Ewart theory29 for the kinetics of emulsion poly-merization, equations of the radical balance canbe written for two phases. Assuming the quasi-steady-state situation for each phase,

ac 1 y 2 mcn# c 2 n# c2 5 0 (A.1)

ac 1 mcn# c 2 y 2 gy2 5 0 (A.2)

ac 5ricvcNA

ktcNA, a0 5

riovcNA

ktcNc, mc 5

kf vcNA

ktc

g 5ktckto

ki2vcNcNA

, y 5kivcNA

ktcNcRo

where ric and rio are the rate of initiation initiatedin the cell and the S/HD phase; vc, the cell volume;Nc, the number of cells in each droplet; n# c, theaverage number of radicals in the cell; Ro, theradical concentration in the S/HD phase; and ktcand kto, the rate constants of termination by therecombination of radicals that occurred in the celland the S/HD phase; kf, the rate constant of rad-ical desorption from the cell; and ki, the rate con-stant of entry of radicals to the cell.

Adding up each side of eq. (A.1) and eq. (A.2),we obtain

ac 1 ao 2 n# c2 2 gy2 5 0 (A.3)

If gy2 @ n# c2 or if the termination is the S/HD

phase prevails, then y will be expressed as

y 5 Sac 1 a0

g D 1/2

(A.4)

In eq. (A.1), if we could further assume that n# c2 .

mcnc, in other words, the radicals inside the cellprefer to terminate each other rather than desireto go into the outer phase, then n# c will be ex-pressed as

n# c 5 Fac 1 Sac 1 a0

g D 1/2G 1/2

(A.5)

Considering that in the initial stage of the poly-merization the polymer concentration is low, thenthe volume fraction of the total cells will be neg-ligible, and eventually we obtain

n# c 5 Sac 1 a0

g D 1/4

5 Sa

gD1/4

a 5rivcNA

ktcNc(A.6)

Kubota and Omi28 derived the same solution of n#for the extreme case where the termination in theaqueous phase prevails and the desorption of rad-icals from the polymer particles is low in theirattempt to derive approximate solutions of n# forthe precipitation polymerization system.

The rate of polymerization in each droplet canbe expressed as

rp,droplet 5 kp@M#oRo 1 kp@M#cn# cNc (A.7)

where [M]o and [M]c are the monomer concentra-tion in the S/HD phase and in the cell, respec-tively. Notice that the dimension of Nc is mol/L inthis discussion.

Since the HD content is 20 wt % (see Table I),[M]o and [M]c will not be so much different. If thepolymerization progresses dominantly in thecells, the polymerization rate in the total systemwill be obtained from eq. (A.7):

rp 5 rp,dropletN 5 kp@M#cn# cNcN

5 kpS ri

rtoD 1/4SkivcNA

ktcD 1/2

@M#cNcN (A.8)Figure A.1 Schematic representation of isolateddroplets in the early stage of polymerization in thepresence of HD.

1042 YUYAMA ET AL.

The dimension of N is L21. [M]o may be replacedwith the monomer concentration in the droplets;then, finally, we obtain

rp 5 kpS ri

kt0D 1/4Skivc NA

ktcD 1/2

@M#Nc N (A.9)

Under the fixed volume of the oil phase, vc (the cellvolume) may slightly decrease with increasing ini-tiator concentration, whereas Nc will increase nat-urally. Compensating for each other, vc

1/2Nc will notbe so drastically affected by the change of the initi-ator concentration. It can be said that the initialrate of polymerization is proportional to 0.25thpower of the initiator concentration.

REFERENCES

1. Nakashima, T.; Shimizu, M.; Kukizaki, M. In Mem-brane Emulsification Operation Manual; Indus-trial Research Institute of Miyazaki Prefecture:Miyazaki, Japan, 1991.

2. Omi, S.; Katami, K.; Taguchi, T.; Kaneko, K.; Iso,M. Macromol Symp 1995, 92, 309.

3. Omi, S. Colloids Surf A Physicochem Eng Aspects1996, 97, 109.

4. Omi, S.; Nagai, M.; Ma, G.-H. In 2nd World Congresson Emulsion, Bordeaux, France, 1997; Vol. 4, p 99.

5. Omi, S.; Nagai, M.; Ma, G.-H. Macromol Symp, inpress.

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11. Haward, R. N. J Polym Sci 1949, 4, 273.12. Blackley, D. C. In Emulsion Polymerization; Pi-

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17. Alduncin, J. A.; Forcada, J.; Asua, J. M. Macromol-ecules 1994, 27, 2256.

18. Fitch, R. M., personal communication, 1994.19. Sudol, E. D.; El-Aasser, M. S.; Vanderhoff, J. W. J

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M. S. J Appl Polym Sci 1991, 34, 1059.21. Choi, Y. T.; El-Aasser, M. S.; Sudol, E. D.; Vander-

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22. Asua, J. M.; Rodriguez, V. S.; Sudol, E. D.; El-Aasser, M. S. J Polym Sci Part A Polym Chem Ed1989, 27, 3569.

23. Van Krevelen, D. W.; Hoftyzer, P. J. In Propertiesof Polymers; Van Krevelen, D. W., Ed.; Elsevier:New York, 1972; Chapter 8.

24. Yuyama, H., unpublished data, 1999.25. Bamford, C. H.; Bard, W. G.; Jenkins, A. D.; Onyon,

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