7 Emulsion Polymerization 7.1 INTRODUCTION Emulsion polymerization is a technique of polymerization where polymer formation occurs in an inert medium in which the monomer is sparingly soluble (not completely insoluble). Traditionally, water is the inert medium and the initiator is chosen such that it is water soluble. Monomers undergoing step- growth reaction do not require any initiation and are not polymerized by this method. Emulsion polymerization is commonly used for vinyl monomers under- going addition polymerization and, even among these, those that polymerize by the radical mechanism are preferably polymerized by this method. Water-based emulsions for ionic polymerizations are uncommon because of high-purity requirements. This discussion is therefore restricted to the polymerization of monomers following the radical mechanism only. The water-soluble initiator commonly used is potassium or sodium persul- fate, and the usual recipe for emulsion polymerization is 200 parts by weight of water, 100 parts by weight of the monomer, and 2–5 parts by weight of a suitable emulsifier [1,2]. The monomer should be neither totally soluble nor totally insoluble in the water medium and must form a separate phase. The emulsifier is necessary to ensure that the monomer is dispersed uniformly as in a true emulsion [3–8]. The polymer that is formed from emulsion polymerization is in the form of small particles having an average diameter around 5 mm. The particles form a stable emulsion in water. Their separation can be effected only through the 299 Copyright © 2003 Marcel Dekker, Inc. evaporationofwater,andoncethewaterisevaporated,theseparticlescoalesceto asolidmass.Therateofemulsionpolymerization,r p ,isfoundexperimentallyto bemuchgreaterthanthatforthecorrespondingbulkpolymerization,andthe averagemolecularweightofthepolymerformedissimultaneouslyveryhigh—a propertythatisnotachievedinbulkpolymerization. 7.2AQUEOUSEMULSIFIERSOLUTIONS Emulsifiersareknowntoplayaveryimportantroleinemulsionpolymerization. Toappreciatetheroleofanemulsifier,wemustunderstandthephysicochemical propertiesofemulsifiersolutions.Whenanemulsifierisdissolvedinwater, severalphysicalpropertiesofthesolution(e.g.,osmoticpressure,conductivity, relativeviscosity,andsurfacetension)change.Figure7.1showsthesechangesas afunctionofthemolarconcentrationoftheemulsifier.Beyondaparticularlevel ofconcentration,thereisasuddenchangeintheslopeofthesephysicochemical properties,asshowninthefigure.Thisconcentrationiscalledthecriticalmicelle concentration(CMC). Anemulsifiermoleculeconsistsofalonghydrocarbonchain,whichis hydrophobicinnature,andasmallhydrophilicend,asshowninFigure7.2.For verysmallconcentrationsoftheemulsifier,moleculesofthelatterarrange themselvesonthefreesurfaceofwatersuchthatthehydrophobicendspoint FIGURE7.1Changesinphysicalpropertiesofwaterasafunctionoftheconcentration ofthesodiumdodecylsulfateemulsifer. 300Chapter7 Copyright © 2003 Marcel Dekker, Inc. outwardandthehydrophilicendsareburiedinthewater.Inthisway,thetotalfree energyofthesystemisminimized.Whenmoremoleculesoftheemulsifierare presentthannecessarytoformamonolayeronthefreesurface,theytendtoform aggregates,calledmicelles,soastominimizetheenergyofinteraction.This aggregateformationstartswhentheemulsifierconcentrationincreasesabovethe criticalmicellarconcentration.Theidealizedlamellaeandsphericalaggregates areshowninFigure7.2.BeyondtheCMC,theemulsifiermoleculesstay primarilyinmicellarform.Thesemicellesareresponsibleforthechangesin thephysicalpropertiesthatcanbeobservedinFigure7.1. Whenanemulsifier(ordetergent)isaddedtowaterandasparinglysoluble monomerisdissolved,thesolubilityofthemonomersisfoundtoincrease.The apparentlyhighersolubilityisattributedtothepresenceofmicelles,whichreally becomeakindofreservoirfortheexcessmonomer,asshowninFigures7.2band 7.2c. At the beginning of the emulsion polymerization, therefore, an emulsifier acts as the solubilizer of the monomer, thus giving a higher rate of emulsion polymerization. FIGURE 7.2 Schematic representation of micelle formation in emulsion polymeriza- tion. Emulsion Polymerization 301 Copyright © 2003 Marcel Dekker, Inc. 7.2.1PolymerizationinWaterEmulsion Itmayberecognizedthatthewater-solubleinitiator(say,sodiumpersulfate) decomposestogiveahydrophilicradicalthatcannotenterthemonomerphase duetothermodynamicconstraints.Wehavealreadypointedoutthatthemonomer issparinglysolubleintheaqueousphase,whichmeansthatonceinitiationoccurs inwater,thepolymerradicalbeginstogrowinchainlength.Ifthepolymer radicalgrowstoacertaincriticalchainlength(say,n*),itnucleatesintoprimary particles,butinthemeantimethereisafiniteprobabilityofbeingtrappedby monomer-swollenmicelles,already-existingpolymerparticles(throughcoagula- tion),ormonomerdroplets.Iftheradicalistrappedinamonomerdroplet,the monomer–waterequilibriumistotallydisturbed,andthereisatendencytoejectit andformasmallermonomerdropletandprimaryparticles,asshowninFigure 7.3.Primaryparticlescansimilarlybeformedfromthemonomer-swollen micelles. Whenemulsionpolymerizationisstarted,physicalchangesoccurinthe mediumasthereactionprogresses.Forexample,itisfoundthatbeyondabout5% conversion,thesurfacetensionincreasessuddenly.Becausemicelleformation involvesasharpdecreaseinsurfacetension,emulsifiermoleculesarenotpresent intheformofmicellesbeyondabout5%conversion.Theregionbeforethispoint isreferredtoasthefirststageofpolymerization,whereastheregionbeyondis referredtoasthesecondstage.Thethirdstageoftheemulsionpolymerizationis thestageinwhichmonomerisnotavailableasdroplets.Whateverthemonomer ispresentinthereactionmass,itisavailablein(monomer)swollenpolymer particles.ThesestagesaredepictedinFigure7.4. Figure7.4,asummaryofvariousstudies,revealsthatinthesecondstage, fewerprimaryparticlesareformedandpolymerizationoccursessentiallybythe growthofpolymerparticles.Asthepropagationcontinues,monomermolecules fromtheemulsifiedmonomerdroplets(seeFig.7.5)diffusetowardthepropagat- ingchainswithinthepolymerparticles.Thediffusionofthemonomertothe polymerparticlescontinuesatafairlyrapidratetomaintainconstantmonomer concentrationinthepolymerparticles. Wewillfirstdiscussthemodelingofthesecondstageofemulsion polymerization,becausemostofthepolymerizationoccursinthisstage.One ofthesimplest(andoldest)modelsexistingisthatofSmithandEwart.This modelwasthefirsttoexplaingrossexperimentalobservations.Itmaybeadded thattheSmithandEwarttheoryassumesthatprimaryradicals(SO 4 À2 )canenter intothepolymerparticles.Althoughwehavealreadyexplainedthatthisisnot possiblebecauseofthermodynamicconstraints,itisanimportantsimplifying assumptionofthistheory. 302Chapter7 Copyright © 2003 Marcel Dekker, Inc. FIGURE 7.4 Various phases in different stages of emulsion polymerization. FIGURE 7.3 The overall polymerization process in emulsion polymerization. Emulsion Polymerization 303 Copyright © 2003 Marcel Dekker, Inc. 7.3 SMITH AND EWART THEORY FOR STATE II OF EMULSION POLYMERIZATION [1,2] This theory is based on the observation that no new polymer particles are formed in the second stage of emulsion polymerization. As depicted in Figure 7.5, monomer-swollen polymer particles exist in this stage in the form of a stable emulsion. It is assumed that initiator radicals formed in the water phase can enter into these particles to start or stop polymerization. Thus, polymer radicals lie only within these polymer particles. The total number of polymer particles per unit volume of emulsion in the second stage of the emulsion polymerization is assumed to be N t . Out of these, N 0 particles are assumed to have no polymer radicals, N 1 to have one polymer radical each, N 2 to have two polymer radicals, and so forth. Therefore, N t ¼ P 1 i¼0 N i ¼ N 0 þ N 1 þ N 2 þÁÁÁ ð7:3:1Þ If n t is the total number of polymer radicals per unit volume in the reaction mass, then n t ¼ P 1 i¼0 iN i ¼ N 1 þ 2N 2 þ 3N 3 þÁÁÁ ð7:3:2Þ FIGURE 7.5 Representation of physical processes in emulsion polymerization in stage 2. Monomer concentration within polymer particles is maintained constant through diffusion. 304 Chapter 7 Copyright © 2003 Marcel Dekker, Inc. The upper limit on these summations would theoretically be infinity. It is assumed that r primary radicals are generated in the aqueous phase per unit time per unit volume. These primary radicals enter the polymer particles and generate polymer radicals therein. These polymer radicals can also diffuse out of the particle or undergo a mutual termination with other polymer radicals in the particle. Because primary radicals are generated in the aqueous phase at a rate of r radicals per unit volume per unit time and there are N t polymer particles per unit volume, r=N t primary radicals per unit time (on average) enter a given particle. Polymer radicals can diffuse out of a particle at a rate r 1 , given by r 1 ¼Àk 0 a n v ð7:3:3Þ where a is the surface area of the polymer particle, v is its volume, k 0 is the mass transfer coefficient, and n is the number of polymer radicals in it. It is assumed that all particles are of equal size. The polymer radicals are also destroyed by mutual termination and the rate, r 2 , at which this happens is given by r 2 ¼À 2k 2 nðn À 1Þ v ð7:3:4Þ This form of the equation appears because the polymer radical cannot react with itself. The term nðn À 1Þ=v is proportional to the total number of collisions between the radicals per unit volume. The rate of generation of particles having n radicals can now be written as follows. A particle having n polymer radicals is formed when one primary radical enters into a particle having n À 1 polymer radicals, one radical diffuses out from a particle having n þ 1 radicals, or two polymer radicals undergo a mutual termination in a particle having n þ 2 radicals. Similarly, the population of particles having n radicals is reduced when a primary radical enters into them or any one radical diffuses out or there is a mutual termination. At steady state, the rate of increase of N n equals the rate of decrease of N n ; that is, N nÀ1 r N t þ N nþ1 k 0 a n þ 1 v þ N nþ2 k 2 ðn þ 2Þðn þ 1Þ v ¼ N n r N t þ N n k 0 n v þ N n k 2 n nðn À 1Þ v ð7:3:5Þ This equation is valid if the number of particles is large. The factor of 2 does not appear with k 2 because only one particle having n radicals is formed from one having n þ 2 radicals. Equati on (7.3.5) is the basic recursion relation for emulsion polymerization derived by Smith and Ewart. Many refinements to this equation have been suggested by several authors, but their net result is similar Emulsion Polymerization 305 Copyright © 2003 Marcel Dekker, Inc. to that of Smith and Ewart. It is difficult to solve Eq. (7.3.5) in its general form; the following discussion develops a few simplified forms. 7.3.1 Case I: Number of Free Radicals per Polymer Particle Is Small Compared with Unity It is clear that polymer radicals of one polymer particle cannot undergo a mutual termination with polymer radicals of another polymer particle. Therefore, when the number of polymer radicals per particle is on average less than 1, there would not be any mutual termination and the corresponding term in Eq. (7.3.5) should be dropped; that is, N nÀ1 r N t þ N nþ1 k 0 a n þ 1 v ¼ N n r N t N n k 0 a n v ð7:3:6Þ This equation is valid only when the diffusion of free radicals out of the particle is much higher than the mutual termination of radicals within it. In general, there are some particles having more than one polymer radical, but such cases are rare because as soon as more radicals are formed, they are transported out of the particle. As a good approximation, therefore, Eq. (7.3.1) can be modified for this case to N t ffi N 0 þ N 1 ð7:3:7Þ where it is assumed that the number of particles having more than one polymer radical is small (i.e., N 2 ¼ N 3 ¼ N 4 ¼ÁÁÁffi0). Then, N 1 k 0 a v ¼ N 0 r N t ð7:3:8Þ from which N 1 can be determined as follows: N 1 ¼ N t 1 þðk 0 a=r v ÞN t ð7:3:9Þ If N 1 is small, N 0 ¼ N t and Eqs. (7.3.8) and (7.3.9) give N 1 ffi r v k 0 a ð7:3:10Þ Therefore, the overall rate of polymerization, r p , per unit volume of the aqueous phase is given by r p ¼ k p ½MN 1 ¼ k p ½Mrv k 0 a ð7:3:11Þ 306 Chapter 7 Copyright © 2003 Marcel Dekker, Inc. where [M] is the local monomer concentration within the polymer particles. Procedures to obtain this value are discussed later. 7.3.2 Case II: No Transfer of Polymer Radicals out of the Particle Through Di¡usion Combined with a High Termination Rate This occurs when polymer radicals are intertwined in the particles and k 0 ¼ 0. In this case, the recursion relation, Eq. (7.3.5), becomes N nÀ1 r N t þ N nþ2 k 2 ðn þ 2Þðn þ 1Þ v ¼ N n r N t þ N n k 2 nðn À 1Þ v ð7:3:12Þ which can be written as N nÀ1 N n þ N nþ2 N n bðn þ 2Þðn þ 1Þ¼1 þ bn ðn À1Þð7:3:13Þ where b ¼ k 2 N t vr ð7:3:14Þ The following can now be defined: x ¼ N nþ1 N n x 1 ¼ N n N nþ1 ð7:3:15Þ x 2 ¼ N nþ1 N nþ2 as a result of which Eq. (7.3.13) can be written as follows x ¼ 1 þ bnðn À 1Þ 1 À 1 x 1 x 2 ðn þ 2Þðn þ 1Þ nðn À 1Þ ð7:3:16Þ If we examine the convergence of the series P 1 n¼0 N n and P 1 n¼0 nN n , it is clear that for n t and N t to be finite, these series must be such that x, x 1 , and x 2 are each greater than 1. Because b and n can take on only positive values, the following expression can be deduced from Eq. (7.3.16) to be valid for x > 1: 1 À 1 x 1 x 2 ðn þ 2Þðn þ 1Þ nðn À 1Þ > 0 ð7:3:17Þ Emulsion Polymerization 307 Copyright © 2003 Marcel Dekker, Inc. If this difference is defined as D, D 1 À 1 x 1 x 2 ðn þ 2Þðn þ 1Þ nðn À 1Þ > 0 ð7:3:18Þ where D is a positive quantity; then, Eq. (7.3.16) becom es x ¼ 1 þ bnðn À 1ÞD ð7:3:19Þ For any arbitrary positive value of D,asn or b tends to very large values, x also tends to a very large value. Consequently, x 1 and x 2 also take on large values. Therefore, in the limit of large b or large n, the factor ð1=x 1 x 2 Þ ½ðn þ 2Þðn þ 1Þ=nðn À 1Þ goes to zero and the following approximation can be made: x N nÀ1 N n % 1 þ bnðn À 1Þð7:3:20Þ which is true for large b or large n. From Eq. (7.3.20), N 0 N 1 ¼ 1 for n ¼ 1 ðand large bÞð7:3:21Þ N 1 N 2 ¼ 1 þ 2b for n ¼ 2 ð7:3:22Þ N 2 N 3 ¼ 1 þ 6b for n ¼ 3 ð7:3:23Þ and so on. From these results the values of N 1 , N 2 , and so forth can be solved as follows: N 1 ¼ N 0 ð7:3:24aÞ N 2 ¼ N 0 1 þ 2b ð7:3:24bÞ N 3 ¼ N 0 ð1 þ 2bÞð1 þ 6bÞ ð7:3:24cÞ The average number of polymer radicals per polymer particle can now be determined as follows: n t N t ¼ N 1 þ 2N 2 þ 3N 3 þÁÁÁ N 0 þ N 1 þ N 2 þÁÁÁ ð7:3:25Þ 308 Chapter 7 Copyright © 2003 Marcel Dekker, Inc. [...]... (7.3.4) within the polymer particles] We define the following: Nw ¼ number of latex particles per liter H2O N0 ¼ number of latex particles having no radicals N1 ¼ number of particles having one radical N2 ¼ number of particles having two radicals Nt ¼ sum of the number of radicals in the latex particles and in the water phase per liter of H2O Copyright © 2003 Marcel Dekker, Inc Emulsion Polymerization... decrease in [M] within polymer particles One of the assumptions in the Smith and Ewart theory is that no new polymer particles are generated in the second stage of emulsion polymerization The rate of polymerization per particle has been experimentally measured in the F IGURE 7 .8 Polymerization of isoprene in aqueous emulsion with 0.3 g K2S2O8 initiator per 100 g monomer and potassium laurate emulsifier... assume that dead polymer chains do not get desorbed, even though polymer radicals (i.e., Pn ) Copyright © 2003 Marcel Dekker, Inc 320 Chapter 7 F IGURE 7.9 Formation of branched polymer in the emulsion polymerization of vinyl acetate and vinyl chloride could If Vp is the total volume of polymer particles within the reaction mass, the rate of formation of polymer molecules, Mn , within the particle is given... all i and j ð7 :8: 5bÞ for all j Rmp1 À MD þ MD À * MD )À À ð7 :8: 5cÞ Rmd1 With the model presented in Eqs (7 .8. 1)–(7 .8. 5) it is possible to model the transience of emulsion polymerization As an example, let us derive the rate of formation of polymer particles as follows If Nt represents the total number of particles in the reaction mass, then 1 dN t ¼ ½Nucleation in aqueous phase by Eq: ð7 :8: 2aÞ þ ½Nucleation... initiating polymerization therein Radical desorption from the particles can be written as kei Paj Ki À Paj þ a Pi ! ð7 :8: 4Þ for all j The coagulation of polymer particles [Eq (7 .8. 5a)], micelle disappearance to cover newly formed particle surface [Eq (7 .8. 5b)], and the coalescence and breakage of monomer droplets [Eq (7 .8. 5c)] can be represented as follows: Kfij Pai þ Paj À Paiþj ! Rmp ! MC þ Paj À Paj ð7 :8: 5aÞ... volume fractions of monomer and polymer in the particle, respectively, XFH is the Flory–Huggings interaction constant (whose value is known for a monomer polymer system), Vm is the partial molar volume of the monomer, g is the interfacial tension, and r is the radius of the polymer particle The first term in the brackets in Eq (7.5.1) is the chemical potential of the monomer in the absence of surface tension... 69, 14 28, 1943 Copyright 1943 American Chemical Society.) Copyright © 2003 Marcel Dekker, Inc 3 18 Chapter 7 second stage and is found to be flat for Nt between 1012 and 1014 particles per milliliter of water solution However, for larger concentrations of particles, Nt has been observed to change with conversion [8] It was believed earlier that the nucleation of particles in stage I of emulsion polymerization... is t À t The volume, Vt , of this particle at time t is Vt;t ¼ mðt À tÞ ð7:4:2Þ assuming that the size of the particle at birth is negligible The term at;t is the surface area of this particle at time t and is given by 2=3 3mðt À tÞ at;t ¼ 4p ¼ ½ð4pÞ1=2 3mðt À tÞ2=3 ð7:4:3Þ 4p To determine the total area, At , of all polymer particles at time t, the rate at which polymer particles are formed must... subscript or superscript d), or polymer particles As soon as one of the former two happens, the micelle (MC) and the droplet (MD) become particles with one radical in them: a Kmd ð7 :8: 3aÞ Kmc ð7 :8: 3bÞ Kc ð7 :8: 3cÞ Pi þ MD À Pa1 ! a Pi þ MC À Pa1 ! a Pi þ Paj À Pajþ1 ! Copyright © 2003 Marcel Dekker, Inc 3 28 Chapter 7 In writing Eq (7 .8. 3c), we assume that, on average, a polymer particle has mostly dead chains... statistical arguments as given in Ref 2 Each of the polymer particles can be imagined as having at most one growing polymer radical at a given time Because kt is large, as soon as an initiator radical enters a polymer particle, it terminates the polymer radical if there is any present If there are no polymer radicals, the entry of any initiator radical into the polymer particle starts the propagation step . clear that polymer radicals of one polymer particle cannot undergo a mutual termination with polymer radicals of another polymer particle. Therefore, when the number of polymer radicals per particle. polymerization. Thus, polymer radicals lie only within these polymer particles. The total number of polymer particles per unit volume of emulsion in the second stage of the emulsion polymerization is. polymer particles. One of the assumptions in the Smith and Ewart theory is that no new polymer particles are generated in the second stage of emulsion polymerization. The rate of polymerization per particle