Detailed Modeling of Multicomponent Emulsion Polymerization Systems

Chapter 30

Detailed Modeling of Multicomponent Emulsion Polymerization Systems G. Storti , M . Morbidelli , and S. C a r r à 1

1

Dipartimento

2

3

di Chimica Inorganica, Metallorganica ed Analitica, Università di Padova, Via Marzolo, 1-35131, Padua, Italy

2

Dipartimento di Ingegneria Chimica e Materiali, Universitàdi Cagliari,

Downloaded by UNIV OF ARIZONA on January 16, 2013 | http://pubs.acs.org Publication Date: August 29, 1989 | doi: 10.1021/bk-1989-0404.ch030

Piazza d'Armi, 09123 Cagliari, Italy 3

Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133, Milan, Italy A comprehensive Kinetic model, suitable for simulating multicomponent emulsion polymerization batch reactors, i s presented An efficient solving procedure i s applied, reducing the computational effort to that of an equivalent one-component system, the so-called "pseudo-homopolymer". Multivariate distributions of the polymer particles in terms of particle size, number and type of contained active chains are typical model outputs: this corresponds to a system description suitable for microstructural investigations.

I n e i n d u s t r i a l i n t e r e s t i n new p o l y m e r i c m a t e r i a l s i s c o n t i n u o u s l y increasing, p a r t i c u l a r l y w i t h r e s p e c t t o multicomponent p r o d u c t s , where t h e p o l y m e r e x h i b i t s a w i d e r a n g e o f a p p l i c a t i o n properties m a i n l y depending u p o n i t s c o m p o s i t i o n . Ine preparation o f t a i l o r made m a t e r i a l s r e q u i r e s knowledge o f t n e r e l a t i o n between p o l y m e r s t r u c t u r e a n d p r o p e r t i e s , a n d t h e r e a c t i o n p a t h s t o be f o l l o w e d so as t o make t h e " d e s i r e d " p r o d u c t , i . e. with required integral composition, particle s i z e d i s t r i b u t i o n (PSD), molecular weight distriïxrtion (IMD), chain composition d i s t r i b u t i o n (CCD). Tnis work i s f o c u s e d o n t h e s e c o n d a s p e c t , namely, a model i s p r e s e n t e d whose m a i n g o a l i s t o p r o v i d e a d e t a i l e d d e s c r i p t i o n o f t h e s y s t e m suitable for microstructural investigation. Many comprehensive models have b e e n p r o p o s e d w i t h reference t o e m u l s i o n , s i n g l e component systems, w h i c h h a v e b e e n e x t e n s i v e l y r e v i e w e d i n t h e l i t e r a t u r e (i) (2) (3). The most d e t a i l e d a n d u p to-date model f o r h o m o p o l y m e r i z a t i o n systems h a s b e e n recently r e p o r t e d b y R a w l i n g s a n d Ray (4), w i t h r e f e r e n c e t o c o n t i n u o u s reactors i n b o t h the t r a n s i e n t and the s t e a d y - s t a t e regime. T h e f u l l PSD i s e v a l u a t e d t h r o u g h a p o p u l a t i o n b a l a n c e e q u a t i o n (PBE) in t h e p a r t i c l e age, w h i l e t h e a v e r a g e number o f a c t i v e chains within t h e p a r t i c l e s i s c a l c u l a t e d according to the classical 0097-6156/89/0404-0379$07.00/0 ο 1989 American Chemical Society

In Computer Applications in Applied Polymer Science II; Provder, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.


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s t e a d y - s t a t e s o l u t i o n o f the Smith-Ewart equation. E m u l s i f i e r and monomer p a r t i t i o n i n g i n t h e system are accounted f o r and a detailed d e s c r i p t i o n o f the reactions i n the latex a n d aqueous ptoses i s given. F i n a l l y , an e f f i c i e n t s o l v i n g procedure, based on t h e o r t h o g o n a l c o l l o c a t i o n method o n f i n i t e elements, i s developed. An optimal choice o f the numerical computation technique is required, due t o t h e i n t r i n s i c b r o a d n e s s o f t h e PSD i n a continuous reactor. On t h e o t h e r hand, very few models f o r multicomponent systems h a v e b e e n r e p o r t e d i n t h e l i t e r a t u r e . Apart from models for binary systems, usually r e s t r i c t e d to "zero-one" systems (5) (6), t h e most d e t a i l e d model o f t h i s t y p e h a s b e e n p r o p o s e d b y Hamielec et al. (7), w i t h reference t o batch, semibatch and continuous emulsion polymerization reactors. Notably, besides the u s u a l K i n e t i c i n f o r m a t i o n s (monomer, conversion, PSD), t h e model a l l o w s f o r t h e e v a l u a t i o n o f IM), long and s h o r t c h a i n branching f r e q u e n c i e s a n d g e l c o n t e n t . Comparisons between model p r e d i c t i o n s and experimental data are l i m i t e d to bulK and s o l u t i o n binary p o l y m e r i z a t i o n systems. In t h i s work, a comprehensive k i n e t i c model, suitable for s i m u l a t i o n o f multicomponent e m u l s i o n p o l y m e r i z a t i o n r e a c t o r s , is presented. A we 11-mixed, isothermal, batch r e a c t o r i s considered with illustrative purposes. Typical model outputs a r e : PSD, monomer c o n v e r s i o n , multivariate d i s t r i b u t i o n o f the polymer p a r t i c l e s i n terms o f number a n d t y p e o f c o n t a i n e d a c t i v e chains, and polymer composition. Model p r e d i c t i o n s a r e compared with experimental data f o r the ternary system acrylonitrile-styrenemethyl methacrylate. Model

Development

Ine following k i n e t i c scheme, u s u a l l y adopted i n polymerization studies, i s considered:

initiation

I

>

propagation

R +Mj

free

R

radical

(1)

KpRj

,Jj,n

> r

+

^Ji 1

Mi

> P

(2)

i

>

n

+

(3)

1

^^trji chain transfer

Pj

Pj,n

termination

P

+ M^

> n

+

+ Ρ

i > n

Pj,n

Τ

+

> P *trj

> Τ

*tji 1 ι Π 1

Pl,m

*t P

> Pn

(5)

n

n

+

W

+

m

%


(6)

7

STORTI ET AL.

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Multicomponent Emidsion Polymerization Systems

381

Usually, r e a c t i o n s 1 a n d 2 t a k e p l a c e i n t h e aqueous phase, w h i l e a l l t h e o t h e r k i n e t i c e v e n t s c a n o c c u r b o t h i n t h e aqueous a n d in t h e p o l y m e r phases. Note t h a t P j , i n d i c a t e s the concentration of active polymer c h a i n s w i t h η monomer u n i t s a n d t e r m i n a l u n i t of type j (i.e. o f monomer j ) ; M i i s t h e c o n c e n t r a t i o n o f monomer i a n d Τ i s t h e c o n c e n t r a t i o n o f t h e c h a i n t r a n s f e r agent. Reactions 4 and 5 are r e s p o n s i b l e f o r c h a i n d e s o r p t i o n from the polymer particles; reactions 6 and 7 d e s c r i b e b i m o l e c u l a r t e r m i n a t i o n by combination and d i s p r o p o r t i o n a t i o n , r e s p e c t i v e l y . A l l the k i n e t i c constants a r e dependent u p o n t h e l a s t monomer u n i t i n t h e chain, i . e. t e r m i n a l model i s assumed


n

Polymer P a r t i c l e B a l a n c e s (PEE)• I n t h e c a s e of multicomponent emulsion polymerization, a multivariate d i s t r i b u t i o n of particle p r o p e r t i e s i n terms o f m u l t i p l e i n t e r n a l c o o r d i n a t e s i s required: in t h i s work, t h e p o l y m e r volume i n t h e p a r t i c l e , ν (continuous coordinate), a n d t h e number of active chains of any type, n n g , . . , nm ( d i s c r e t e coordinates), are considered. Therefore nl,n2, , nm (v, t ) d v i n d i c a t e s t h e number o f p a r t i c l e s c o n t a i n i n g n^ a c t i v e c h a i n s o f t y p e 1, ng o f t y p e 2 o f t y p e m, whose p o l y m e r volume l i e s between ν a n d v+dv, a t time t . The f u l l PBEs f o r t h i s d e t a i l e d d i s t r i b u t i o n f u n c t i o n a r e q u i t e complex a n d h a v e been r e p o r t e d i n d e t a i l i n the case m-3 elsewhere (8). The n u m e r i c a l s o l u t i o n o f s u c h a s e t o f e q u a t i o n s becomes practically impossible when m > 2 a n d t h e maximum number o f a c t i v e c h a i n s p e r particle i s g r e a t e r t h a n about f i v e , i . e. at low termination rates. An approximation procedure has been proposed in (ô) for reducing the f u l l PBEs f o r a multicomponent s y s t e m t o the PBEs t y p i c a l o f a s i n g l e component system, w i t h o u t any s i g n i f i c a n t l o s s of accuracy. This i s the s o - c a l l e d pseudo-homopolymerization approach, which i s based on the w i d e l y d i f f e r e n t time s c a l e s of the k i n e t i c events involved. In p a r t i c u l a r , the c h a i n propagation processes are l a r g e l y f a s t e r than the processes determining the active chain distribution: therefore, a l l terms i n t h e P E E w i t h respect to those r e l a t i v e t o the c r o s s propagation processes can be neglected, so that the d i s t r i b u t i o n of the types of active c h a i n s c a n be e v a l u a t e d as f o l l o w s : l f

f

l,

f

(v, t ) n^.ng rim ηι+η£>+,.. +n - η

=

M

f

Ρ

(v,t)

1,2,...,m

(8)

η

m

where f ( v , t ) is the d i s t r i b u t i o n o f the polymer p a r t i c l e s in terms o f t h e t o t a l number o f a c t i v e c h a i n s a n d p o l y m e r particle volume, t y p i c a l o f a homopolymer. Ρ\ ζ ,, m p r o b a b i l i t y of a particular d i s t r i b u t i o n of a c t i v e ' c h a i n type i n the particle c o n t a i n i n g η c h a i n s , a n d i t i s e v a l u a t e d as f o l l o w s : n

i

n

Ρ

1,2, . . . , m

(η; η , η , . . . , η ) 1 2 m

Ρ l

l

s

n

2 ...

Ρ 2

Ρ

(9) m


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where the term within brackets indicates the nultinomial c o e f f i c i e n t , while P± i s the p r o b a b i l i t y associated with an active chain of type i . Such P± can be evaluated by solving a l i n e a r system of m equations, i n which the cross propagation terms appear, k p j j Mpj, i . e. the k i n e t i c events determining the terminal monomer u n i t i n the chain. The d e t a i l e d treatment i s reported i n the above mentioned work; here, i t i s worthwhile mentioning that, through the pseudo -homopo 1 ymer i zat i on approach, the full multicomponent PBEs are reduced to those of an equivalent homopo 1 ymer:


ôf dt

n

ô + — (g n f ) = ρ(ν) (f - f ) + k(v) dv n n-1 n

[(n+l)f - n f ]+ n+1 n

+ c(v)[(n+2) (n+1) f - n(n-l) f ] + r p, i s assumed, independent of polymer composition and correspondent to the average of the homopolymer density values. 2. Monomer S o l u b i l i t y Laws. The d e s c r i p t i o n of the monomer p a r t i t i o n i n g i n a three-phases system such as a polymer latex can be pursued according to the thermodynamics of solutions with largely d i f f e r e n t molecular weight components (19), accounting f o r the c o l l o i d a l nature of the dispersed phases, the polymer p a r t i c l e s and the o i l droplets (20) (21). However, due to the large amount of involved parameters (monomer-monomer interactions, monomer-polymer interactions, i n t e r f a c i a l tension between o i l droplets and aqueous phase and between polymer p a r t i c l e s and aqueous Fhase) and to t h e i r d i f f i c u l t a p r i o r i " evaluation, empirical approaches have been u s u a l l y adopted i n the modeling literature, i n p a r t i c u l a r with reference to the evaluation of the M


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Table I. Numerical Values of tne Parameters

1. monomer and polymer densities 3

p =0. 806; p =0. 909; PM=0. 894; pp= 1.107 A

[gr/cm ]

S

2. monomer s o l u b i l i t y laws — o i l droplets-water phase a

A

A

°A = aiMwA/^-^MwA) » S = 3**wS > °M =4?*wM a - 249. 2; a = 429. 7; a = 2. 7 1 0 ; a^ = 6. 3 1 0 c


5

t

2

—

3

3

[mol/cm ]

3

o i l droplets-polymer p a r t i c l e s - «i/aj; i , j = A, M, S; = 0.665 (maximum swelling r a t i o )

3. propagation r a t e constants and r e a c t i v i t y r a t i o s pAA = i 1 0 ; k p s s - 2. 5 9 1 0 ; k ^ - 5. ô 1 0 r u s = 0.46 ; r ^ = 0. 52 ; r ^ = 1. 3 5 Α Μ = °î r ^ g = 0. 0 4 ; r ^ = 0. 4 0

K

6

5

Γ

1

5

[cn^/mol sec]

0

4. bimolecular termination r a t e constants °tAA = î ° t S S = · 97 1 0 ; K ^ = 3. 29 1 0 [cmVmol sec] ° t S S = fctSS «ΧΡ[2( -0.939 X -3. 875 Xg* +0.494 X ) ] °tMM = *tMM ^3Φ[2( "6. 59 % -1. 90 Χγ£ )) where Xj indicates the conversion of the monomer j

K

1

l o i 0

K

5

10

0

1 0

K

3

s

s

K

5. r a d i c a l entry, ρ j (v) = k j P j N v n=2 ; k = kys = k ^ = ky = 1 10" v

A

n p

4

[cm/sec]

v A

6. r a d i c a l desorption, k j (v) = equation 38 — chain t r a n s f e r to monomer rate constants 2150

2 3

2

KtrAA '» 1^^35=6.824; * Η Γ Μ Μ = · — effective diffusion coefficients D = 1 10~ ; I£ = 2 10" ; % = 1 10~ 7

9

[cn^/mol sec] 7

[cn^/sec]

k

7. m i c e l l a r nucleation r a t e constants, r ^ j = k ^ P j N = % 5 = KrnM = *v = ~ 1

1

0

4

8. i n i t i a t o r and r a d i c a l r a t e constants k j = 1. 18 10" KpRi = p i i î t R i = (^twii K-tER) î i=A,S,M ktRR - 1 1 0 6

K

K

A

[cm/sec]

[1/sec] [cm^/mol sec] [cm^/mol sec]

1/2

1 1

9. e m u l s i f i e r c h a r a c t e r i s t i c s CMC = 1.77 10" [mol/cm ] C - a C / ( l + b C ) S p ; a=4. 74 1 0 " cmÊ/mol ; b=8.0 10 cm^/mol % = em s m A'» s m - 9. 2 1 0 ~ cmP/molecule; v«v =2. 2 1 0 ~ cm 6

3

1 0

e a

ew

c

a

6

ew

N

a

1 6

1 0

m


3


30. STORTI ET AK

Multicomponent Emuhion Polymerization Systems

391

monomer concentrations i n polymer p a r t i c l e s i n batch reactors (22) (23). In t h i s work, oversimplified s o l u b i l i t y laws have been considered Namely, a nonlinear equation r e l a t i n g the volume f r a c t i o n of the monomer i n the o i l droplets to i t s molar concentration i n water Fhase has been considered i n the case of acrylonitrile, due to i t s h i g h water s o l u b i l i t y , while simple l i n e a r laws have been adopted f o r the other components. Note that the parameter values i n Table I have been evaluated by f i t t i n g the experimental data reported by Smith (24) r e l a t i v e to the binary system acrylonitrile-styrene; the extension of t h i s law to the ternary system has been made without any adjustment, assuming chemical i d e n t i t y between the other monomers with respect to the interactions with a c r y l o n i t r i l e . About the t o t a l monomer concentration i n the polymer p a r t i c l e s , i t has been evaluated assuming constant "maximum swelling r a t i o " , independent of polymer and monomer mixture composition and equal to the average value between those corresponding to styrene and methyl methacrylate homopolymers. The p a r t i t i o n i n g f o r each component has been assumed equal to the equivalent value i n o i l droplets. This corresponds to neglect any chemical difference between the monomers with respect to t h e i r i n t e r a c t i o n with the polymer; the r e l i a b i l i t y of t h i s assumption has been v e r i f i e d f o r both the binary systems a c r y l o n i t r i l e - s t y r e n e (25) and styrene-methyl methacrylate (6). 3. Propagation Rate Constants and R e a c t i v i t y Ratios. The liomopolymer k values have been taken d i r e c t l y from the l i t e r a t u r e (ref. (26-28) with the usual A, S,M order). The same i s true f o r the r e a c t i v i t y ratios, where, due to the presence of some discrepancies i n the l i t e r a t u r e values (6) (23) (29-31), the values reported by Ham (29) have been chosen The same numerical values have been used both i n aqueous and p a r t i c l e Fhases; note that the same r e a c t i v i t y r a t i o s have been assumed f o r the reactions of chain transfer to monomer. p i i

4. Bimolecular Termination Rate Constants. The homopolymer k ^ values at zero conversion (k°tu) have been taken d i r e c t l y from the l i t e r a t u r e f o r styrene and methyl methacrylate (32) (28); i n the case of a c r y l o n i t r i l e , due to the large scatter i n the l i t e r a t u r e values (26), an a r b i t r a r y value i n the range of the other components has been adopted The same values have been considered both i n aqueous and i n p a r t i c l e phases. In the second case, the dependence of the homopolymer k on the monomer conversion (the so-called "gel effect") has been accounted f o r through the empirical laws d e t a i l e d i n Table I and suggested by F r i i s and Hamielec (32). Note that the same dependence has been neglected f o r a c r y l o n i t r i l e , due to the lack of data i n the current l i t e r a t u r e . F i n a l l y , the cross termination r a t e constants, ktij, have been estimated as the geometric mean of the correspondent homopolymer values Q9). However, comparing these values with available l i t e r a t u r e values (binary system styrenemethyl methacrylate; (6) ) s i g n i f i c a n t discrepancies are evident. t i i

5. Radical Entry Rate. The rate of transport of the active oligomers from the aqueous phase to the p a r t i c l e s have been


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evaluated according to the simple " c o l l i s i o n a l " model (33), i.e. proportional to the p a r t i c l e surface. Note that, even though various other mechanisms have been proposed (34) (35), the adopted model i s a common choiche i n the modelling l i t e r a t u r e (4). The correspondent k i n e t i c constant, k , has been evaluated by f i t t i n g the model predictions to the experimental data, assuming the same value f o r each component.


v

6. Radical De sorption Rate. I t i s evaluated, according to the law proposed by Nomura (36), as the r e s u l t of three stages i n series: chain transfer of a growing chain to monomer, d i f f u s i o n of the active, low molecular weight product to the p a r t i c l e surface and d i f f u s i o n i n the aqueous phase. The r e s u l t i n g expression has been extended to the multicomponent case as follows: m 3Z>j ( Σ ktpijHpjPi) i=l kj(v) = (36) m 3Pj + r ( Σ k Mpi) i=l where D$ indicates an e f f e c t i v e d i f f u s i o n c o e f f i c i e n t of the active oligomer of type j i n the p a r t i c l e and i n the aqueous phases, k^ j j i s the r a t e constant f o r chain transfer to monomer and r i s the radius of the p a r t i c l e . The numerical values f o r kt υ each component have been d i r e c t l y taken from the literature (18), while the cross terms have been estimated assuming r e a c t i v i t y r a t i o values equal to those f o r chain propagation Some d i f f i c u l t i e s have been found f o r the "a p r i o r i " evaluation of Dy Namely: f o r styrene and methyl methacrylate the values suggested by Nomura and F u j i t a (6) have been adopted, despite of some scatter i n the l i t e r a t u r e values (4) (37); f o r acrylonitrile a numerical value equal to that f o r methyl methacrylate has been assumed In a l l cases, any dependence of the d i f f u s i o n c o e f f i c i e n t s of conversion and composition has been neglected 2

p

p J i

P|

p

i

o

r

P j

7. Nucleation Rates. Due to the large amount of emulsifier used i n a l l the considered cases, only the m i c e l l a r nucleation mechanism has been considered (38). The c o l l i s i o n a l model f o r evaluating the r a d i c a l entry into the emulsifier micelles has been adopted and the correspondent rate constant, has been assumed independent of the component and equal to the value f o r k , the rate constant f o r r a d i c a l entry into the p a r t i c l e s . v

8. Rate constants f o r i n i t i a t o r decomposition and r a d i c a l reactions i n aqueous phase. The r a t e c o e f f i c i e n t f o r KgSgOg thermal decomposition has been calculated at the relevant temperature according to K o l t h o f f and Miller (39). The r e a c t i v i t i e s f o r the r a d i c a l s produced by the i n i t i a t o r have been considered equal to the correspondent homopolymer values f o r the oligomers; f o r the bimolecular termination between r a d i c a l and radical, an average value w i t h i n the range t y p i c a l f o r s o l u t i o n polymerization has been adopted (18).


II

30.

STORTIETAL.

Multicomponent Emuhion Polymerization Systems

393

E m u l s i f i e r Characteristics. The values f o r CMC, adsorption isotherm parameters and. m i c e l l a r s p e c i f i c surface f o r sodium lauryl sulphate as previously reported (13) have been used Finally, note that the coalescence of polymer p a r t i c l e s has been neglected, due to the large amount of emulsifier used i n a l l the considered experimental runs. In conclusion, i t i s worthwhile stressing that: (i) only one parameter has been f i t t e d on the experimental data under consideration, the rate constant f o r r a d i c a l entry i n p a r t i c l e s and micelles, K ; ( i i ) several a r b i t r a r y decisions o r assumptions have been taken i n assembling Table I. Thus, the simulations reported below substantiate more the r e l i a b i l i t y of the computational procedure proposed than any conclusion about the detailed mechanism of the process and i t s experimental verification. Results of t h i s k i n d would require further experimental work with reference to the ternary and to each of the r e l a t e d binary subsystems, with deeper characterization of the product and more accurate models f o r each of the elementar processes occurring i n the system, which presently are not available i n the literature.


v

Simulation Results. A ternary run with the same amount o f each monomer (33. 33 gr. of A, S and M, respectively) i s f i r s t examined In Figures 1 and 2, the experimental and c a l c u l a t e d o v e r a l l conversion and polymer composition values (expressed as amount o f reacted monomer), are shown. A f i n a l number of p a r t i c l e s of 5.4 10 1/crn i s c a l c u l a t e d vs. an experimental value of 4. 6 1 0 1/cm . The s a t i s f a c t o r y agreement between experimental and c a l c u l a t e d data i s not surprising, because the adjustable parameter of the model, k , has been f i t t e d on t h i s experimental run (see value i n Table I). In Figure 3, the time evolutions of monomer volume f r a c t i o n w i t h i n the polymer p a r t i c l e s f o r each monomer are shown. The d i s c o n t i n u i t i e s i n the slopes of the c a l c u l a t e d curves correspond to the disappearance of the monomer droplets, while the d i f f e r e n t behaviour i n the h i g h conversion range (40 to 200 min. ) i s due to the d i f f e r e n t r e a c t i v i t i e s and water s o l u b i l i t i e s of the monomers. In Figure 4, the p a r t i c l e s i z e d i s t r i b u t i o n function i n terms of polymer volume computed at three d i f f e r e n t time values during the r e a c t i o n are shown. In Figure 5, the complete time evolutions of the average polymer p a r t i c l e and average t o t a l p a r t i c l e volume are presented F i n a l l y , i n Figure 6, the time evolution of the average number of active chains f o r each type of terminal u n i t i s shown; as expected, the complex behaviour of the c a l c u l a t e d curves r e f l e c t s the differences i n r e a c t i v i t y and concentration among the components. Note that the t o t a l average number of active chains i s always v e i y low (

Detailed Modeling of Multicomponent Emulsion Polymerization Systems

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