Free Radical Polymerizatio Referece: Aspe Polymers: Uit Operatios ad Reactio Models, Aspe Techology, Ic., 2013.
1. Itroductio The free-radical bulk/solutio polymerizatio model is applicable to bulk ad solutio polymerizatio processes. Some examples of applicable polymers are: - Geeral purpose polystyree - Made by polymerizatio of styree moomer with or without solvet fed cotiuously to reactor. - High impact polystyree - Made by polymerizatio of a usaturated rubber dissolved i styree i a solutio process. Also produced i suspesio processes. - Poly(viyl chloride) - Produced i bulk polymerizatio usig moomer soluble free radical iitiators. Most of the homopolymers ad copolymers of viyl chloride, however, are produced by suspesio polymerizatio. - Poly(viyl acetate) - Produced idustrially by the polymerizatio of viyl acetate i bulk or solutio processes. Also produced i suspesio ad emulsio processes. Both batch ad cotiuous processes are used. - Poly(methyl methacrylate) - The vast majority of commercially prepared acrylic polymers ad methacrylic polymers are copolymers. Commercially they are prepared by solutio polymerizatio. They are also produced by emulsio ad suspesio polymerizatio. - Low desity polyethylee - Made by high pressure, free radical processes i either a tubular reactor or a stirred autoclave. Typical commercial processes iclude staged compressio, iitiator ijectio, partial coversio of ethylee to polymer, separatio of ethylee from polymer, extrusio of molte polymer, ad coolig of ethylee. The Free-Radical model may also be used to simulate suspesio polymerizatio processes i which the polymer is completely soluble i the orgaic (moomer) phase. Two reactio models ca be applied together to represet reactios i each liquid phase. A example of this process is: productio of Poly(styree) i a cotiuous suspesio process i a series of CSTR type reactors.
2. Reactio Kietic Scheme Most free-radical polymerizatios have at least four basic reactio steps: - Iitiatio - Propagatio - Chai trasfer to aother molecule (i.e. moomer, solvet, polymer or trasfer aget) - Termiatio These reactios occur simultaeously durig the polymerizatio. For brached polymers additioal reactios for log ad short chai brachig ca also be preset. A comprehesive kietic scheme for the free-radical homo- ad copolymerizatio of up to N m moomers has bee built ito Aspe Polymers. The scheme icludes most of the reactios commoly used for modelig free radical polymerizatio. The model also icludes several optioal reactios: - Termial double bod polymerizatio - Pedet double bod polymerizatio (for diee moomers) - Head-to-head propagatio (for asymmetric moomers) - Cis- ad tras- propagatio (for diee moomers) - Primary ad secodary decompositio of bifuctioal iitiators Reactios such as depropagatio ad radom chai scissio are ot icluded i the curret model. 2.1. Polymer Chai Terms The term live polymer chai, P[, refers to growig polymer chais cotaiig segmets, with a radical attached to a segmet of type i, i.e., segmet formed from moomer i. The term dead polymer chai, D, refers to termiated polymer chais that do ot have a attached radical. The term bulk polymer chai is used to refer to
the sum of the live ad dead polymer chais. The subscript refers to the chai legth i terms of the umber of segmets or moomer uits icorporated i the polymer chai. Live chais are reactive ad ca participate i the polymerizatio reactios while dead chais are usually cosidered iert, except whe log chai brachig reactios are importat (such as termial double boud polymerizatio). The radical attached to oe ed of a live polymer chai is cosidered to be mobile ad moves away from the iitiator fragmet with every additio of a moomer molecule. It is believed that after a few moomer additios the chemistry of the iitiator fragmet ad developig chai microstructure will ot have a strog ifluece o the mode of moomer additio. The free-radical kietic model assumes that the reactivity of a live polymer chai depeds oly o the active segmet cotaiig the radical, ad is idepedet of the polymer chai legth ad other structural properties. For example, i the propagatio reactio, the rate of propagatio, Rpij, is idepedet of the polymer chai legth. It depeds oly o the cocetratio of moomer j ad the cocetratio of live polymer chais with active segmets of type i. Models usig this assumptio are referred to as termial models i the polymerizatio literature. The rate costats for each reactio i the built-i kietics is calculated at the reactio temperature ad pressure usig the modified Arrheius equatio show below with user specified parameters: pre-expoetial (or frequecy) factor, activatio eergy, activatio volume, ad referece temperature: (1) Where: k o = Pre-expoetial factor i 1/s for first order reactios, ad m 3 /(kmol s) for secod order reactios
Ea = Activatio eergy i mole-ethalpy uits ΔV = Activatio volume i volume/mole uits P = Reactio pressure R = Uiversal gas costat T ref = Referece temperature f g = Gel effect factor from optioal built-i or user-defied gel effect correlatio The secod term i the expoetial fuctio cotais a activatio volume that is importat for high pressure polymerizatio systems. For low to moderate pressures, the activatio volume is typically set to default value of zero. This term is used to accout for the pressure depedece of the reactio rate costat. The free-radical model allows the rate expressio to be modified by a gel effect term, f g. The gel effect term ca be calculated usig oe of several built-i correlatios or it ca be calculated by a optioal user-defied gel effect subroutie. 2.2. Iitiatio The iitiatio step ivolves the geeratio of reactive free-radicals followed by the additio of a moomer molecule (chai iitiatio) to form chai radicals of uit legth, P 1 [. The o-chai or primary radicals (R * ) may be geerated by the thermal decompositio of a chemical iitiator, a catalyzed iitiatio reactio ivolvig electro trasfer from ios, or by thermal/radiatio iduced mechaisms. Three types of stadard iitiatio reactios are icluded i the built-i kietics: - Iitiator decompositio reactio - Iduced iitiatio reactio - Catalyzed iitiatio reactio
The iitiator decompositio reactio accouts for primary radical geeratio from the thermal decompositio of chemical iitiators. The iduced iitiatio reactio ca be cofigured to accout for the geeratio of radicals by thermal ad radiatio iduced mechaisms from the moomers themselves, with or without the use of a coiitiator or promoter. The catalyzed iitiatio reactio ca be used to accout for redox iitiatio, which has foud wide applicatio i aqueous emulsio polymerizatio systems. Iitiator decompositio reactio The most commoly used radical geeratio method is the thermal decompositio of chemical iitiators (usually peroxide or azo compouds) which decompose to form radicals whe heated to a appropriate temperature. Oly small amouts of the chemical iitiator (less tha 1 wt. % based o moomer) are eeded. The iitiator decompositio reactio is modeled as a first order thermal decompositio reactio: kd * I N R aa bb, Rd k C (2) d I Where: C I = Iitiator cocetratio k d = Iitiator decompositio rate costat ε = Iitiator efficiecy N = Number of produced primary radicals (1 or 2) A ad B = By-product molecules Primary chai iitiatio The reactive primary radicals (R * ) react with moomer by the primary chai iitiatio reactio to form polymer chai radicals of uit legth, as show below:
R * I * M, P[, R [ k R C (3) k i i 1 I I, i Mi Where: C Mi = Cocetratio of moomer of type i k I,i = Chai iitiatio rate costat The chai radicals grow by successive additio of moomer molecules to form log chai polymer molecules. It is commo practice to set the chai iitiatio rate costats equal to the propagatio rate costat of each moomer. 2.3. Propagatio The chai radicals grow or propagate by the additio of moomer molecules to form log polymer chais of legth, P[. The propagatio reactio is represeted by: k [ j 1 P, ij P, ij, ij P M P P [ j], R k C P[ (4) Mj where moomer j is beig added to a polymer chai of legth, with a active segmet of type i. The resultig polymer chai will be of legth +1 ad the active segmet will be of type j. The active segmet type usually represets the last moomer icorporated ito the polymer chai. For copolymerizatio, there will be (o of moomers) 2 propagatio reactios havig differet reactivities. For example, with two moomers, four reactio exist with four rate costats (k P11, k P12, k P21, k P22 ) where the first subscript refers to the active segmet type while the secod subscript refers to the reactig moomer type. 2.4. Chai trasfer Chai trasfer to small molecules such as moomer, solvet or chai trasfer aget usually ivolves the abstractio of hydroge from the small molecule by the chai
radical ad leads to the termiatio of the live chai. At the same time, a ew primary trasfer radical is formed which ca start chai polymerizatio. The effect of chai trasfer o the polymerizatio kietics depeds o the reactivity of the trasfer radical. Whe the trasfer radical is very reactive, as is the case whe the chai iitiatio rate costat is greater tha the propagatio rate costat, chai trasfer will ot lower the polymerizatio rate or coversio, but will reduce the molecular weight of the polymer. However, if the trasfer radical is less reactive tha the moomer based propagatig radical, as i the case of low chai iitiatio rate costat, both the coversio ad molecular weight of the polymer will be lowered. Chai trasfer to solvet or aget Chai trasfer to solvet ad chai trasfer to a trasfer aget have the followig rate expressios: k, i * P S TS D R, R k C P[ (5) [ TS, i TS, i [ TA, i TA, i S k, i * P TA D R, R k C P[ (6) TA For trasfer to aget or solvet the trasfer radicals are assumed to have the same reactivity as the primary radicals formed by iitiatio. Chai trasfer to moomer Geeratio of termial double bods I the chai trasfer to moomer reactio, the live polymer ed P abstracts a hydroge from a moomer molecule, resultig i a dead polymer chai D. The moomer, which loses a hydroge, becomes a live polymer ed group with a ureacted double bod P 1 [i = ]. Subsequet propagatio reactios geerate log-chai polymer radicals with a termial double-bod segmet at the opposite ed of the chai P =. These iitial reactio steps are show below:
The chai trasfer to moomer reactio does ot always geerate a termial double bod. The termial segmet may udergo a re-arragemet reactio, which destroys the double bod site. The model parameter TDB fractio, f TDB,ij ca be used to specify the fractio of chai trasfer to moomer reactios that geerate a termial double bod. The reactio rate of the chai trasfer to moomer reactio is defied as: k P[ M TM ij j D (1 ftdbij, ) P1 [ ftdbij, P1 [ i ], RTM, ij k, C P[ ], i TM ij Mj (7) Chai trasfer to polymer The radical i oe polymer chai ca trasfer to a repeat uit i a secod polymer chai. This chai trasfer to polymer reactio always geerates a log chai brach, sice subsequet propagatio from the live site causes the backboe molecule to grow a ew brach. The chai trasfer to polymer reactio ca be writte as: k [ m m TP, ij TP, ij, ij P D TP D P [ j], R k m D P[ (8) Where m j represets the umber of repeat groups of type j i the molecule to which the radical is trasferred. Each trasfer reactio geerates oe log chai brach. The optioal polymer compoet attributes LCB ad FLCB are used to track the molar flow rate of log chai braches ad the log chai brachig frequecy (brach poit per thousad repeat uits). j m
2.5. Termiatio Itermolecular termiatio occurs by oe of two mechaisms, combiatio (couplig) ad disproportioatio. May moomers (e.g. MMA) show both types of termiatio while other moomers (e.g. styree) termiate predomiatly by combiatio. The mode of termiatio has a strog ifluece o the average polymer chai legth ad chai legth distributio, especially whe chai trasfer is ot sigificat. Whe the combiatio reactio is domiat, the polydispersity (i a sigle CSTR) will approach 1.5. The polydispersity approaches 2.0 whe disproportioatio is domiat. Termiatio by combiatio I termiatio by combiatio, two live polymer ed groups react with each other, formig a sigle dead chai with a head-to-head segmet pair. Each of these reactios, o average, doubles the molecular weight of the polymer. The reactio rate depeds o the cocetratio of the live ed groups: k, ig P P [ j] TC D, R k P[ P [ j] (9) [ m m TC, ij TC, ij The formatio of head-to-head segmet dyads ca be tracked by icludig the optioal HTHFLOW ad HTHFRAC (head-to-head flow ad head-to-head fractio) attributes i the attribute list o the Polymers. Head-to-head sequeces ca cotribute to thermal istability ad may cause degradatio durig storage or subsequet processig. Termiatio by disproportioatio I disproportioatio reactios, the radical at the ed of oe chai attacks a hydroge atom at the secod-to-last carbo atom i the secod chai, formig two dead polymer molecules with o et chage i molecular weight. The reactio rate depeds o the cocetratio of the live ed groups: k [ m TDBij, TDBij, m TM, ij TD, ij P P [ j] TD, ij f D [ i ] (1 f ) D D, R k P[ P [ j ] (10) m m
The formatio of termial double bods ca be tracked by icludig the TDBFLOW ad TDBFRAC (termial double bod flow ad fractio) i the list of attributes o the Polymers. Termial double bods ca cotribute to thermal istability ad may cause degradatio, brachig ad gelatio durig storage or subsequet processig. 2.6. Gel effect Bimolecular termiatio reactios betwee chai radicals become diffusio cotrolled at high polymer cocetratios or high coversio leadig to a icrease i the polymerizatio rate ad molecular weight. This coditio is kow as the gel effect or Trommsdorff effect. At high polymer cocetratios, the icreased viscosity of the reactio medium imposes a diffusioal limitatio o the polymer chais, which leads to lower effective termiatio rates. Typically the termiatio rate coefficiets are affected first by the gel effect because they ivolve diffusio of two bulky polymer radicals. Evetually at high eough coversios, eve the propagatio, iitiatio, chai trasfer reactios, ad the iitiator efficiecy are lowered by the gel effect. Hece, i geeral it may be ecessary to allow gel/glass effects for all the polymerizatio reactios i the built-i kietic scheme. The diffusioal limitatio is usually modeled by multiplyig the low coversio reactio rate coefficiets, k o, by a gel effect factor, GF, that decreases with icreasig coversio. Hece the effective rate coefficiet for a reactio is give by: k eff = k o GF (11) Several empirical ad semi-empirical correlatios relatig the gel effect factor to coversio ad operatig coditios are available i the literature. Curretly two of these have bee implemeted as built-i correlatios i Aspe Polymers. Users will be able to use these gel effect correlatios simply by specifyig the correlatio umber ad the parameters.