Targeting Copolymer Composition Distribution via Model-Based

Article pubs.acs.org/IECR

Targeting Copolymer Composition Distribution via Model-Based Monomer Feeding Policy in Semibatch RAFT Mini-Emulsion Copolymerization of Styrene and Butyl Acrylate Xiaohui Li,† Wen-Jun Wang,*,†,‡ Feiyin Weng,† and Bo-Geng Li† †

State Key Laboratory of Chemical Engineering, ‡Key Laboratory of Biomass Chemical Engineering of Ministry of Education, Department of Chemical & Biological Engineering, Zhejiang University, Hangzhou 310027, Zhejiang People’s Republic of China

Shiping Zhu* Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7 ABSTRACT: Copolymer composition distribution (CCD) is an important parameter of chain microstructure that has significant impact on the material properties of polymer products. Controlled/living radical polymerization (CLRP) has provided a great opportunity in producing polymers with predesigned CCDs through a model-based monomer feeding policy (MMFP) in homogeneous systems. In this work, the MMFP has been expanded to heterogeneous systems. Reversible addition− fragmentation transfer (RAFT) mini-emulsion polymerizations of styrene (St) and butyl acrylate (BA) were carried out with 3benzyltrithiocarbonyl propionic acid (BCPA) used as a RAFT agent. A kinetic model was developed and correlated to the batch St/BA RAFT mini-emulsion experimental data for parameter estimation. The MMFP was then developed by combining the kinetic model with a semibatch reactor model and applied to the semibatch St/BA RAFT mini-emulsion copolymerization for the synthesis of targeted CCDs. The model agreed well with the polymerization kinetics. A series of St/BA copolymers with predesigned CCDs were successfully synthesized.

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INTRODUCTION The properties of polymer materials are, to a large extent, determined by polymer chain architectures. It is essential to exercise a good control over polymer architectures to produce polymers with tailor-made properties. Free radical polymerizations are an important technology for commercial polymer production. However, in a conventional free radical polymerization process, the chain propagation is rapid with individual chains (from initiation to termination) being completed a few seconds, making it nearly impossible to control the microstructure along the polymer backbone. The recently developed controlled/living radical polymerization (CLRP)1−8 has provided great potential for the control over polymer architectures. In a CLRP process, the chain propagation is relatively slow, requiring hours for individual chains to grow. Furthermore, almost all of the chains grow simultaneously, resulting in polymer products that have a narrow molecular weight distribution (MWD). Meanwhile, irreversible termination and chain transfer reactions are limited and chains have high chain-end functionality, which can be efficiently extended to block copolymers. It has been demonstrated that the CLRP technologies are effective means for producing polymers with defined molecular weight (MW), narrow MWD, and well-controlled polymer architectures.9−13 The slow chain propagation in the CLRP system is particularly useful for the control over CCDs and copolymer sequence distributions (CSD) along polymer backbones. Studies on the CSD control have been published previously,14,15 and will not be discussed here. It has been demonstrated that varying the CCD (i.e., copolymer © 2014 American Chemical Society

composition from one chain end to the other along the backbone) provides an effective means for polymer product innovation.16−19 Design and control of the CCD could lead polymer products with tailor-made properties. In chemistry, the CCD is determined by the mole ratio of two monomers and their reactivity ratios. In a batch process, there exists a “composition drifting”, because of the different reactivity ratios. Gradient copolymers are thus produced, with the monomeric unit composition varying from one chain end to the other along the chain backbones, following the “composition drifting”. The copolymer products synthesized using a batch process have such gradients, which are determined purely by the monomer reactivity ratios. Thus, batch processes lack the versatility to produce copolymers having predesigned desired gradients targeted for specific properties. Take a targeted uniform CCD as an example. Batch processes cannot produce a uniform CCD if two monomers have different reactivity ratios. One may resort to the use of a continuous stirred tank reactor (CSTR) system. When operated at a steady state, it produces a uniform CCD. However, the residence time distribution (RTD) of the CSTR results in a broad MWD, which is undesirable in CLRP systems. It is well-known that the narrow MWD is one of the Special Issue: John Congalidis Memorial Received: Revised: Accepted: Published: 7321

August 26, 2013 April 10, 2014 April 10, 2014 April 10, 2014 dx.doi.org/10.1021/ie402799u | Ind. Eng. Chem. Res. 2014, 53, 7321−7332

Industrial & Engineering Chemistry Research

Article

important advantages of the CLRP. A plug flow tubular reactor (PFTR) would be more efficient at producing narrow MWD, but the kinetics are similar to those of the batch reactor and the copolymer composition drifts along the PFTR, following monomer reactivity ratios. Theoretically, the polymer composition could be adjusted by varying the monomer composition along the PFTR through multiple inlets to feed monomers; however, in practice, this approach is impractical. Semibatch processes are the best choice for the CCD control. In a semibatch process, the monomer composition in the reactor can be readily changed by co-monomer feeding. For a targeted CCD, the required co-monomer feeding rate can be calculated through modeling. A model-based monomer feeding policy (MMFP) provides a powerful tool to produce polymer products with predesigned CCDs via the semibatch copolymerization. With established relationships between polymer architecture and properties, careful design and precise control of polymer architecture is the most effective means for achieving desired properties. Digital synthesis and precision production of polymer materials represents the future for the polymer production industries. There have been several reports on the preparation of copolymers by applying the MMFP to semibatch CRLPs.20−24 The feasibility of the MMFP for targeted CCDs is wellestablished through experiments both in RAFT22,23 and ATRP 24 solution systems. However, there are several disadvantages of the solution systems that limit their developments, such as long polymerization times and high product separation costs. Compared to the CLRP solution systems, heterogeneous counterparts have the advantages of high polymerization rate, green environment, and low separation costs. Reactions involving mini-emulsions have attracted much attention in recent years.25−27 Farcet et al.28 synthesized PSt-bPBA block co-polymers by feeding BA after the completion of mini-emulsion polymerization of St, using C6F13I as a transfer agent; and synthesized PSt-b-P(BA-co-St) block co-polymers by feeding BA at the late stage of St homopolymerization (at a conversion of ca. 80%−90%). Luo and Liu29 synthesized PSt-bP(St-co-MMA) block co-polymers by feeding St after the complete RAFT mini-emulsion copolymerization of St and MMA. Similar to Farcet et al.’s work, Zhang et al.30 synthesized PBMA-b-PDFMA block copolymers by feeding DFMA after the complete RAFT mini-emulsion homopolymerization of BMA. Min et al.31 prepared a series of gradient copolymers by feeding co-monomers at the beginning of ATRP mini-emulsion polymerization. However, the constant monomer feeding policies lacked precise control of CCDs. To date, the precise control of predesigned CCDs by the MMFP in heterogeneous systems has not been reported, although online measurement techniques and optimal monomer feed policies have been used for the CCD control in conventional emulsion copolymerization systems.32−39 The precise control of CCDs in heterogeneous systems turns out to be more challenging than in homogeneous solution systems, because of the existence of multiple phases and mass transfer issues. Many modeling efforts have been made to CLRP miniemulsion systems. Ma et al.40−42 developed a model to investigate the kinetics of NMP mini-emulsion polymerization of St in alkoxyamine- and persulfate-initiated systems. Luo et al.43 studied the kinetics of RAFT mini-emulsion polymerization of St by modified Smith−Ewart equations, and developed a method for estimating the RAFT equilibrium

constants. Zetterlund et al. investigated the effects of compartmentalization in dispersed NMP44,45 and ATRP46,47 systems using modified Smith−Ewart equations. Thomson and Cunningham48 described the compartmentalization effects on polymerization rate, livingness, and PDI of polymers in a dispersed ATRP system by modified Smith−Ewart equations. Tobita49−53 highlighted the characteristics of polymerization rate and MWDs in RAFT mini-emulsion systems, and they also investigated the effects of fluctuation and segregation on the kinetics in an ATRP mini-emulsion system through Monte Carlo simulations. Jung and Gomes54 developed a kinetic model for RAFT mini-emulsion in pseudo-bulk systems and targeted minimization of the number-average molecular weight through a semibatch operation. In this work, a RAFT mini-emulsion copolymerization model is first developed and then correlated with batch experimental data of St/BA copolymerization for estimating kinetic parameters. The model is then combined with the semibatch reactor model to describe the semibatch RAFT mini-emulsion copolymerization. Here, the model is functioning as an important tool determining the MMFP. The MMFP was then developed to target CCDs, and the rate of co-monomer feeding was controlled by a computer. A series of St/BA copolymers with predesigned CCDs were produced by the MMFP via semibatch RAFT mini-emulsion copolymerization.

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MODEL DEVELOPMENT Polymerization Scheme and Mass Transfer Events. As shown in Table 1, the initial free radicals in aqueous phase (P•0,aq) are generated by the decomposition of a water-soluble initiator (I). When P•0,aq enters a monomer droplet, it becomes the initial propagating radical in the particle (P•0 ). Droplet nucleation occurs when P•0 initiates the RAFT reaction. The monomer droplet then becomes a polymer particle. The Table 1. Elementary Reactions and Mass Transfer Involved in the RAFT Mini-Emulsion Copolymerization in the aqueous phase initiation

f , kd

I ⎯⎯⎯→ 2P0,• aq

absorption of radicals into particles

P0,• aq + particle ⎯→ ⎯ P0• + particle

droplet nucleation

P0,• aq + droplet ⎯→ ⎯ particle

in the particle phase propagation

kap

kad

k p , in

P0• + Mj ⎯⎯⎯→ P1,•j k p , ijk

Pr•, ij + Mk ⎯⎯⎯⎯→ Pr•+ 1, jk

7322

RAFT pre-equilibrium

Pr•, ij + TP0 ←⎯⎯⎯⎯→ Pr , ijTP0 ←⎯⎯⎯⎯⎯⎯→ P0• + TPr , ij

RAFT core-equilibrium

Pr•, ij + TPs , kl ←⎯⎯⎯⎯→ Pr , ijTPs , kl ←⎯⎯⎯⎯⎯→ Ps•, kl + TPr , ij

chain transfer to monomer

Pr•, ij + Mk ⎯⎯⎯⎯⎯→ Pr , ij + P1,•k

termination by disproportionation

Pr•, ij + Ps•, kl ←→ ⎯ Pr + Ps

termination by recombination

Pr•, ij + Ps•, kl ←→ Pr + s

cross-termination

Pr•, ij + Ps , klTPt , mn ←→ Pr + s + t

desorption of radicals in particles

P1,•i ⎯⎯⎯⎯→ P1,•aq

•

ka , j / k f , j

ka , j / k f , j

ka ,0/ k f ,0

•

ka , l / k f , l

k fm , jk

k td , jl

k tc , jl

•

kct , j

kdes , i

dx.doi.org/10.1021/ie402799u | Ind. Eng. Chem. Res. 2014, 53, 7321−7332


Article

• process by which P 0,aq enters the droplet/particle is appropriately termed absorption, while the opposite process in which the propagating radical escapes from the particle to the aqueous phase is desorption. A monomeric radical generated from the transfer of propagating radical to monomer has a high probability of desorption. In this work, an implicit penultimate model (IPUM) is employed, which is appropriate for acrylate systems.55,56 In a typical RAFT copolymerization system, there are five chain species, as shown in Table 1. Their detailed notations can be found in the reference.22 Mj is j-type monomer, with M1 as St and M2 as BA. Polymerization Rate. In this work, the polymerization rate of type-i monomer in the particle is calculated based on a pseudo-homopolymerization approach,

R p , i = (kp1iϕ1 + kp2iϕ2)[Mi]p

k dm̅ = −k f m̅ + ka[RAFT]n ̅ − ct mn dt VsNA ̅ ̅

In eqs 3 and 6, Vs is the swollen volume of particles (L), [RAFT] is the concentration of RAFT agent in particles (mol L−1), ktp, ka, kf, and kct represent pseudo-kinetic rate constants of self-termination of propagating radicals (L mol−1 s−1), addition of propagating radicals to RAFT agent (L mol−1 s−1), fragmentation of intermediate radicals (s−1), and crosstermination between propagating and intermediate radicals (L mol−1 s−1), respectively: i

ka =

(1)

kf =

dt

kdes = kdes ,1 + kdes ,2

(2)

(i = 1, 2)

(8a)

Koi βi Koi + kpi1[M1]p + kpi2[M 2]p (8b)

where kf1i (or kf 2i) is the rate constant of a propagating radical transferring to type-i monomer (L mol−1 s−1) in the particle; βi is the probability of propagation or termination by a type-i desorbed monomer radical in aqueous phase. Koi is the desorption rate coefficient of type-i monomeric radicals:59 Koi =

(12Dwi /mdidsp2) 1 + (2Dwi /mdiDpi)

(9)

where Dwi represents the diffusion coefficient of type-i monomeric radicals in the aqueous phase, while Dpi represents the diffusion coefficient of type-i monomeric radicals in particle (dm s−1); mdi is the ratio of type-i monomeric radical concentration in particles over that in the aqueous phase; and dsp is the swollen particle diameter (dm). Free Radicals in the Aqueous Phase. Free radicals in the aqueous phase are generated by initiator decomposition and the desorption of monomeric radicals in particles, consumption by termination, and capture by monomer droplets and polymer particles:

(3)

where σ is the entry rate of free radicals from aqueous phase to particles (s−1), given by (4)

P•0,aq

and kap is the rate constant of captured by particles (Lw mol−1 s−1) . The coefficient c is defined as a function of σ, kdes, and ktp in the work of Li and Brooks,57

kdesNpn ̅ kap[R]w Np k [R] N d[R]w = 2fkd[I] + − − ad w d NA NA NA dt − 2ktw[R]w 2

2(2σ + kdes) ktp VsNA

(7d)

The overall desorption rate constant kdes (s−1) is calculated, following Forcada and Asua’s work,58

cktp 2 k dn ̅ = σ − kdesn ̅ − n ̅ + k f m̅ − ka[RAFT ]n ̅ − ct mn dt VsNA VsNA ̅ ̅

2σ + kdes +

∑ kct ,iϕi

kdes , i = (k f 1iϕ1 + k f 2iϕ2)[Mi]p

σ = kap[R ]w

(7c)

i

Vw ∑i = 1 MWR i p,i ρp

(7b)

∑ kf ,iϕi

kct =

where MWi is the molecular weight of type-i monomer (g mol−1), and ρp is the polymer density (g L−1). Free Radicals in Particle. In a RAFT system, there are two types of free radicals (propagating radical and intermediate radical) possessing very different kinetic properties. Calculating n̅ in this study is an extension of the work by Li and Brooks.57 n̅ is generated by free radicals entering particles in aqueous phase, the fragmentation of intermediate radicals, and the escape of propagating radicals from particles into water phase, selftermination between propagating radicals, cross-termination between propagating and intermediate radicals, and addition to RAFT agents, as follows:

c=

∑ ka ,iϕi i

2

=

(7a)

i

i

where [Mi]p is the concentration of monomer i in the particle (mol L−1); Np is the number of particles per volume water (L−1 w ); n̅ is the average number of propagating radical per particle; NA is Avogadro’s number (mol−1); kpij (i,j = 1, 2) are the apparent propagation rate constants (L mol−1 s−1) in IPUM, and ϕi is the probability of a propagating chain with an ultimate unit i (i = 1 or 2) in the particle. The increase in polymer volume can be calculated by dVpol

∑ ∑ kt ,ijϕϕ i j

ktp =

Npn ̅ NA

(6)

(10)

where f is an initiator efficiency; kd represents the rate constant of initiator decomposition (s−1); kad is the rate constant of radicals in aqueous phase captured by monomer droplets (Lw mol−1 s−1); Nd is the number of monomer droplets per volume water (L−1 w ); [I] is the initiator concentration in the aqueous phase (mol Lw−1):

(5)

Similarly, the average number of intermediate radicals per particle (m̅ ) is generated by the addition of propagating radicals to RAFT agent and consumption by self-fragmentation and cross-termination with propagating radicals, 7323



d[I] = −kd[I] dt

Article

Y0T =

(11)

Polymer Particles. In this work, the generation of polymer particles is through droplet nucleation. Micellar nucleation is ignored because most surfactants are adsorbed to the surface of the monomer droplets, because of their high surface area in the mini-emulsion system.60,61 Homogeneous nucleation can also be ignored, given that St and BA have a lower water solubility than MMA.62 Droplet nucleation occurs when P•0,aq enter monomer droplets to initiate polymerization, and the generation rate of polymer particles are calculated by dNp

= kad[R]w Nd

dt

(12)

∞

1 2

YiT =

r=0

∞

YiT, j =

r=0 s=0

∑ r i[TPr ] r=0

r=0

(19b)

(19c)

d(Vρ) = Vf , iρf , i dt

(20)

(21a)

that is, Vf , iρf , i dV V dρ = − dt ρ ρ dt

(21b)

where Vf,i is the volumetric feeding rate of monomer i (L s−1) and ρf,i is the density of feeding monomer i (g L−1). V (L) and ρ (g L−1) are the total volume and density in the reactor, respectively, which are mainly contributed by monomer and polymer. The change of the concentration of monomer i and any other species k, respectively, are calculated by

(16a)

(16b)

(17)

i

∑ r [Pr ]

Y1 + Y1T + Q 1T + Q 1

where Fci is the cumulative copolymer composition of monomer i. Semibatch Reactor Model. The semibatch reactor model has been well-described by Zhu et al.20−24 We aim to control CCDs using a MMFP. Only monomers are fed into the reactor and the total mass balance can be written for the semibatch operation as follows:

(14)

∞

Qi =

Y2 + Y2T + Q 2T + Q 2

i=1

∞

Q iT =

(19a)

2

∞

̇ s] ∑ ∑ r is j[PTP r

Y0 + Y0T + Q 0T + Q 0

Mn = rN̅ ∑ FciMWi

(15)

s=0

Y1 + Y1T + Q 1T + Q 1

Thus, the number-average molecular weight (Mn) is given as

r

∑ r i ∑ [Pr− sTṖ s]

(16e)

r PDI = W̅ rN̅

∞

r=0

T T Y2T = Y2,0 + Y1,1

rW̅ =

where kF is the rate constant of droplet−particle coalescence (Lw s−1). MW and MWD. The method of moments63,64 and the pseudo-kinetic rate constant method65 were employed in calculating MW and PDI of polymers in the RAFT copolymerization system. The moments of propagating radical chains (Yi), intermediate radical chains (YTi , YTi,j), dormant chains (QTi ), and dead chains (Qi) are respectively defined as follows:

∑ r i[Pr•]

(16d)

(13)

Coalescence is a common phenomenon in mini-emulsion systems. Droplet−droplet and droplet−particle coalescence reduces the number of droplets during polymerization.60,61 In this work, only ∼40% of droplets were actually nucleated with the rest consumed by the droplet−particle coalescence. The droplet−particle coalescence does not reduce the number of particles, but the number of droplets decreases until they are fully consumed, increasing the monomer concentration in the particle. Thus, the consumption rate of monomer droplets is given by

Yi =

T Y1T = Y1,0

rN̅ =

8⎜

dNd = −kad[R]w Nd − kFNpNd dt

(16c)

The derivation of these moment equations are given in detail in Zhu et al.63,64 The moment equations are applied to the miniemulsion system by replacing termination rate constant of propagating radicals kt with ckt, where c is a coefficient calculated from eq 5. The zeroth moment of propagating radical chains Y0 is equal to the concentration of propagating radicals in the particle since each particle can be considered as an isolated microreactor.49,50 With the help of methods of moments, the number-average chain length (rN̅ ), weightaverage chain length (rW̅ ), and PDI can be calculated as follows:

The diameter of unswollen particles dp (nm) is calculated based on the “monodispersed” approximation: ⎛ 6Vpol ⎞1/3 ⎟⎟ dp = 1.0 × 10 ⎜ ⎝ πNpVw ⎠

1 T Y0,0 2

(18)

dCi 1⎛ dV ⎞ = ⎜Vf , iCi , f − Ci ⎟ + R i dt V⎝ dt ⎠

(22a)

dC k 1⎛ dV ⎞ = ⎜ − Ck ⎟ + R k ⎝ dt V dt ⎠

(22b)

where Ci,f represents the concentration of monomer i in the feed (mol L−1); Ci and Ck are the concentrations of monomer i and any other species k in the reactor (mol L−1), respectively;

where eq 16b is needed for closure of the differential moment equations, and the relationships between YTi and YTi,j are 7324



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Table 2. Recipes Used in the Experimental RAFT Mini-emulsion Polymerizations of St/BAa run

St (g)

BA (g)

initial St mole fraction, f10

1a 1b 1c 1d 2a 2b 3a 3b

3.380 6.760 10.14 15 1.758 6.925 6.760 20.28

12.48 8.320 4.160 0 24.96 16.64 0 0

0.25 0.50 0.75 1.0 0.0798 0.3387 1.0 1.0

amount of St(BA) added in the second stage (g)b

total St mole fraction, Fn1

KPS (g)

RAFT (g)

5.002 6.595 8.320 8.320

0.25 0.50 0.75 1.0 0.25 0.50 0.50 0.75

0.0351 0.0351 0.0351 0.0389 0.0702 0.0702 0.0351 0.0702

0.1061 0.1061 0.1061 0.1177 0.2122 0.2122 0.1061 0.2122

For all runs, SDS and HD were both 5 wt % of total monomer mass and the solid content was fixed at 20 wt %. bThe recipe for semibatch copolymerization.

a

Ri and Rk are the intrinsic reaction rate of monomer i and any other species k (mol L−1 s−1), respectively. Therefore, the total volume evolution of organic phase is given by dV0 = dt

2

2

i=1

i=1

⎞ 1 1 − ⎟⎟ ρp ⎠ ⎝ ρmi

distillation. 3-Benzyltrithiocarbonyl propionic acid (BCPA) was synthesized following the literature.66 Hexadecane (HD, Aladdin Chemistry Co., Ltd.), sodium dodecyl sulfate (SDS, Xilong Chemical Co., Ltd.), and potassium persulfate (KPS, Sinopharm Chemical Reagent Co., Ltd.) were commercially obtained and used without purification. Polymerization Recipes. In all experiments, the total molar ratio of [M]0:[BCPA]0:[KPS]0 was 1000:3:1 and the polymerization temperature was 70 °C. HD and SDS were both set to 5 wt % of monomers, and the solid content of latex was kept at 20 wt % of the total mass. All the experimental recipes were summarized in Table 2. Runs 1a−1d were designed to study batch kinetics at different initial monomer ratios; runs 2a and 2b were designed to target uniform (U) CCDs, while runs 3a and 3b were designed to target linear gradient (LG) CCDs. Batch Mini-Emulsion Polymerization. The procedure for the mini-emulsion preparation is as follows. Using run 1d as an example, the organic phase was prepared by magnetically mixing 15 g of St with 0.1177 g of RAFT agent and 0.7653 g of HD for 10 min. The aqueous phase was formed by mixing 60 g of water with 0.8824 g of SDS with magnetic stirring for 10 min. The emulsion mixture was formed by adding the organic phase to the aqueous phase with magnetic stirring for 10 min, and then ultrasonified for 7 min using a Model JY92-2D Sonifier (amplitude 60%, 600 W) in an ice-water bath. The initial mini-emulsion was transferred to a 250-mL four-necked flask. The mini-emulsion in the flask was deoxygenated by N2 purging for half an hour with magnetic stirring at room temperature and then immersed in a 70 °C oil bath. KPS (0.0389 g) in 5 g of water was added to initiate the polymerization. The samples were withdrawn regularly and quenched by quickly cooling them in an ice bath and adding hydroquinone. These samples were divided into two parts: one part was used for the measurements of conversion (gel permeation chromatography (GPC) and 1H NMR spectroscopy), and the other part was used for particle size measurement. Semibatch Mini-Emulsion Polymerization. The procedure for the mini-emulsion preparation is similar to that for the batch process. The initial mini-emulsion was transferred to a 500-mL four-necked flask. Scheme 1 shows the experimental setup for the semibatch mini-emulsion polymerization using the MMFP. The co-monomer was fed with a model-optimized feeding rate profile using a computer-controlled metering pump. Sample Characterization. The monomer conversion was measured gravimetrically. The latex particle diameter was measured using dynamic light scattering (DLS) (Zetasizer Model 3000HSA). The number of latex particles was calculated as follows:

⎛

⎜ ∑ Vf ,i − ∑ MWR i p , iVw ⎜

(23)

and the overall monomer weight conversion and cumulative copolymer composition of monomer i in the copolymer are given by the following expressions: overall monomer weight conversion, x: 2

x=

∑i = 1 (Mi0 − Mit − Mir )MWi 2

∑i = 1 Mi0MWi

(24)

cumulative copolymer composition, Fci: Fci =

Mi 0 − 2 ∑ j = 1 (M j 0

Mit − Mir − Mjt − Mjr )

(25)

where Mi0 represents the total number of moles of monomer i of the recipe; Mit represents the number of moles of monomer i in the feeding tank; and Mir represents the number of moles of monomer i in the reactor. Strategy for CCD Control. The mass balance equations of various species combined with the reactor model can form semibatch RAFT mini-emulsion copolymerization model. Targeting CCDs under the constraint condition of eq 26, we use the monomer feeding rate as an operation variable. Fi = fun( rN̅ )

(26)

where Fi is the instantaneous copolymer composition of type-i monomer in the copolymer, which is given by Fi =

R p,i 2 ∑ j=1 R p,j

(27)

f un is the targeted relationship between Fi and rN̅ . The monomer feeding rates are determined by solving the ordinary different equations (ODEs) under constraint conditions as shown in eq 26. The ode 15i program in MATLAB is used to solve fully implicit ODEs. The detailed calculation process for the monomer feeding rates is described elsewhere.23

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EXPERIMENTAL SECTION Materials. Styrene (St, >99%) and butyl acrylate (BA, >98%) were purchased from Shanghai Lingfeng Chemical Reagent Co., Ltd. and purified using a reduced pressure 7325



Article

while ka was obtained by fitting the PDI data. The rest batch experimental data were used to verify the model correlation. All the kinetic parameters are summarized in Table 3.

Scheme 1. Schematic Experimental Setup for the Semibatch RAFT Mini-Emulsion Polymerization

Table 3. Model Parameters Used in Modeling the St/BA RAFT Mini-Emulsion Polymerization

Np =

6MT x 3

πdw̅ ρp

(28)

Lw−1);

where MT is the monomer mass per volume water (g x is the total monomer weight conversion; and d̅w is the volumeaverage diameter. The experimental data of n̅ was then given as follows:

n̅ =

R pNA kp[M]p Np

(29)

where Rp is the total polymerization rate calculated from x (mol Lw s−1); kp is the apparent propagation rate constant (L mol−1 s−1); and [M]p is the total monomer concentration in particle calculated from x (mol L−1). The MW and MWD of the polymers were measured using a Polymer Laboratory Model PL-GPC 50 GPC system, which is equipped with three types of detectors: laser light scattering (LS), differential refractive index (RI), and viscometry (IV). The detection angle and laser wavelength of LS were, respectively, 90° and 650 nm. Two PL gel linear columns with MW values from 5 × 102 g mol−1 to 7 × 107 g mol−1 were selected, and one PL gel 500 Å column with a MW value of 1 × 102 to 3 × 104 g mol−1 was also used. Tetrahydrofuran was used as an eluent at a flow rate of 1.0 mL min−1 at 30 °C. A series of narrow PSt standards (MW values from 5.75 × 102 g mol−1 to 2.85 × 106 g mol−1) were used for calibration. The dn/dc values of PSt and PBA were 0.180 and 0.065 mL/g, respectively.67 The copolymer composition analysis for the St/BA copolymers, as determined by 1H NMR spectroscopy, followed the literature.22,23

parameter

value

reference

kd (s−1) kp11 (L mol−1 s−1) kp22 (L mol−1 s−1) ka1 = ka2 (L mol−1 s−1) kf1 (s−1) kf 2 (s−1) ktc11 (L mol−1 s−1) ktc22 (L mol−1 s−1) ktd11 (L mol−1 s−1) ktd22 (L mol−1 s−1) kt12 = kt21 (L mol−1 s−1) kct1 (L mol−1 s−1) kct2 (L mol−1 s−1) ktw (Lw mol−1 s−1) r1 r2 s1 s2 kfm11 (L mol−1 s−1) kfm22 (L mol−1 s−1) kfm12 = kfm21 (L mol−1 s−1) kap (Lw mol−1 s−1) kad (Lw mol−1 s−1) md1 = md2 Dw1 = Dp1 (dm2 s−1) Dw2 = Dp2 (dm2 s−1) kF (Lw s−1) ρm1 (g cm−3) ρm2 (g cm−3) ρp (g cm−3)

8.0 × 1015 exp(−16237.67/T) 4.266 × 107 exp(−3909.61/T) 7.37 × 105 exp(−1156.90/T) 3.4 × 104 9.0 × 103 5.0 × 102 2.0 × 1010 exp(−1553.01/T) 2.57 × 108 exp(−292/T) 0 0 (kt11kt22)1/2 3.0 × 107 6.5 × 108 1.0 × 108 exp(0.05919 − 131.6/T) exp(1.351−1034.1/T) 1 0.1 0.0173 0.0147 0.0159 6.0 × 107 9.0 × 104 1600 5.0 × 10−8 1.7 × 10−7 1.5 × 10−21 0.9193 − 6.65 × 10−4(T − 273.15) 0.9211 − 1 × 10−3(T−273.15) 1.05

68 69 70 this work this work this work 71 72 73 74 75, 76 this work this work 43, 77 78 78 55, 56 55, 56 79 80 79 this work this work 81 81 82 this work 75 75 75

The experimental data of BA RAFT mini-emulsion homopolymerization was not available. The BA homopolymerization system was not stable, because the R group of the initial RAFT agent easily escaped from the monomer droplet. Figure 1a shows the effects of the initial St monomer composition ( f10) at four levels on the polymerization rate of St (1)/BA (2) RAFT mini-emulsion polymerization. The polymerization rate increased with the decrease of f10 due to kp11 < kp22. Figure 1b shows the cumulative St mole fraction in the St/BA copolymers (Fc1) vs the total monomer conversion (x) at three f10 levels. The “composition drifting” was more severe with the decrease of f10. Figure 1c shows a rapid increase of dp before 10% conversion, and a linear increase later. Furthermore, the increase of dp was more rapid with the increase of f10. As shown in Figure 1d, Np increased slowly from the beginning to ∼35% conversion and then remained constant, indicating that the nucleation period completed at ∼35% conversion. Figure 1e gives the trends of n̅ as the polymerization proceeded. The n̅ value increased with the increase of f10 due to lower possibilities of termination in larger particles; n̅ also decreased gradually with the monomer conversion. The reasons for this decrease were 2-fold. First, the radical concentration in aqueous phase decreased as the polymerization proceeded. Second, the radicals in particle were more likely to be stored as intermediate radicals

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RESULTS AND DISCUSSION Batch Copolymerization of St/BA and Model Correlation. Our objective of this work is to develop the MMFP for targeting co-polymers with predesigned composition profiles via semibatch RAFT mini-emulsion copolymerization. A kinetic model was first developed and correlated to the batch experimental data of St/BA RAFT mini-emulsion polymerization for various parameter estimations. Parameters kf, kct, and kap were obtained by fitting the batch conversion data; kad and kF were obtained by fitting the batch experimental data of Np, 7326



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observed and it was attributed to the continuous accumulation of dead chains as explained by the model simulation. Programmed Synthesis of the Copolymers with Uniform Composition. It is difficult to produce copolymer products with uniform composition profiles in a batch process, because of the different reactivity ratios of the monomers, as shown in Figure 1b. In this part, we targeted two uniform CCDs at Fn1(U) = 0.25 and Fn1(U) = 0.50, respectively. Equation 30 shows the constraint conditions for targeting the uniform CCDs. F1 =

R p ,1 R p ,1 + R p ,2

= 0.25 or 0.50 (30)

Figure 2a gives the monomer feeding rates obtained through the model simulation. For the targeted uniform CCDs, all of the BA and a part of the St must be fed into the reactor at the start of polymerization, as shown in Table 3. The Mayo−Lewis equation was used to calculate the initial masses of St in the reactor with the targeted uniform CCDs. The remaining St was continuously fed to the reactor by a programmed metering pump, following the simulated feeding profiles. It should be pointed out that monomer, not monomer droplets, was directly fed into the reactor in this work. Large-sized monomer droplets were formed and dispersed under continuous magnetic stirring, acting as monomer reservoirs. The monomer molecules in the droplets then diffused into aqueous phase and then polymer particles for polymerization. The model predicted the semibatch RAFT mini-emulsion copolymerization kinetics well. Figure 2b shows the monomer conversion versus time for Fn1(U) = 0.25 and Fn1(U) = 0.50. The polymerization rate of Fn1(U) = 0.25 was higher than that of Fn1(U) = 0.50, because of the lower St mole composition of the former. As shown in Figure 2c, the agreement between the experimental and theoretical Fc1 values was very good, suggesting that the composition drifting was controlled by the MMFP. Figures 2d−f give the developments of dp, Np, and n̅ versus the total monomer conversion, respectively. Figures 2g and 2h show those of Mn and PDI, suggesting good livingness and control of the polymerization system. Programmed Synthesis of the Copolymers with Linear Gradient Composition. Gradient copolymers, as a type of emerging polymer material, have unique properties and have attracted great attention in recent years. For copolymers produced in batch CLRP processes, their gradients (i.e., the variation of monomeric composition along a chain backbone from one end to the other) are solely determined by monomer reactivity ratios, following the “composition drifting” pattern. The gradients of these as-synthesized copolymers lack any design. Batch processes cannot produce gradient copolymers with predesigned gradients. In this part, we demonstrated the synthesis of two linear gradient (LG) CCDs at Fn1(LG) = 0.50 and Fn1(LG) = 0.75. For the targeted LG CCDs, the following constraint conditions applied:

Figure 1. Batch RAFT mini-emulsion polymerization of St and BA with different initial mole ratios of the monomers: (a) total monomer conversion, (b) cumulative styrene copolymer composition, (c) diameter of unswollen particles, (d) number of particles per volume water, (e) average number of propagating radicals per particle, (f) number-average molecular weight, and (g) polydispersity index. [Experimental conditions: molar ratio [M]/[RAFT]/[I] = 1000/3/1, m[SDS] and m[HD] = 5 wt % [M], and solid content = 20% at 70 °C. The points are experimental data while the lines are model simulations.]

and/or consumed by cross-termination (kf 2 < kf1, kct2 > kct1) as the propagating radicals with the BA (2) terminal unit increased. It should be pointed out that a slightly large deviation existed between the model predictions and the experiment results for RAFT miniemulsion polymerization of St ( f10 = 1.0). This might be caused by the model overprediction in the number of PS particles formed. Figure 1f shows a linear development of Mn versus the total monomer conversion, suggesting good livingness and control of the polymerization. The experimental Mn values were larger than their theoretical values because of incomplete initiation of the initial RAFT agents. Figure 1g gives the development of PDI versus total monomer conversion. The PDI ranged from 1.1 to 1.5, indicating narrow MWDs. It should be noted that a small increase in the PDI at the late stage of polymerization was

F1 = 1 −

rN̅ rN̅ , t

for Fn1(LG) = 0.50

(31a)

and F1 = 1 − 7327

0.5 × rN̅ rN̅ , t

for Fn1(LG) = 0.75

(31b)



Article

Figure 3. Semibatch St/BA RAFT mini-emulsion copolymerization targeting for linear gradient CCDs with different mole ratios of the monomers: (a) programmed volumetric feeding rate, (b) total monomer conversion, (c) cumulative styrene copolymer composition, (d) diameter of unswollen particles, (e) number of particles per volume water, (f) average number of propagating radicals per particle, (g) number-average molecular weight, and (h) polydispersity index. [Experimental conditions: molar ratio [M]/[RAFT]/[I] = 1000/3/1, m[SDS] and m[HD] = 5 wt % [M], and solids content = 20% at 70 °C. The points are experimental data while the lines are model simulations.]

Figure 2. Semibatch St/BA RAFT mini-emulsion copolymerization targeting for uniform CCDs with different molar ratios of the monomers: (a) programmed volumetric feeding rate, (b) total monomer conversion, (c) cumulative styrene copolymer composition, (d) diameter of unswollen particles, (e) number of particles per volume water, (f) average number of propagating radicals per particle, (g) number-average molecular weight, and (h) polydispersity index. [Experimental conditions: molar ratio [M]/[RAFT]/[I] = 1000/3/1, m[SDS] and m[HD] = 5 wt % [M], and solid contents = 20% at 70 °C. The points are experimental data while the lines are model simulations.]

1.0 to 0.50 and 0.75, respectively, suggesting successful control of the LG CCDs by the MMFP. Figures 3d−f show the developments of dp, Np, and n̅ as the polymerization proceeded. Figures 3g and 3h present those of Mn and PDI. The Mn increased linearly with the monomer conversion, and the PDI ranged from 1.1 to 1.2 for both Fn1(LG) = 0.50 and Fn1(LG) = 0.75.

where rN̅ ,t is the targeted number-average chain length, set to 333 in this work. The entire amount of St was charged to the reactor at the start of polymerization. BA was continuously fed to the reactor following the feeding rate profiles shown in Figure 3a. Figure 3b shows the total monomer conversion versus polymerization time at Fn1(LG) = 0.50 and Fn1(LG) = 0.75. At the early stage, the polymerization rate of Fn1(LG) = 0.50 was lower than that of Fn1(LG) = 0.75, because of a higher RAFT agent concentration in the former. However, at the later stages, the polymerization rate of Fn1(LG) = 0.50 became higher than that of Fn1(LG) = 0.75 as the model simulated, because the cumulative BA in the reactor with Fn1(LG) = 0.50 promoted the rate. Figure 3c shows good agreement of the experimental Fc1 to the targeted LG CCDs. The Fc1 decreased linearly from

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CONCLUSIONS Model-assisted design and control provides a powerful tool for digital synthesis and precision production of polymer materials. For the first time, a model-based monomer feeding policy (MMFP) approach was applied to a heterogeneous polymerization system, which demonstrates the ability to design and control of copolymer composition distribution (CCD) in the RAFT mini-emulsion polymerization of St/BA. A kinetic model 7328



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kp = propagation rate constant, L mol−1 s−1 ktc = termination by combination rate constant, L mol−1 s−1 ktd = termination by disproportionation rate constant, L mol−1 s−1 ktp = apparent termination rate constant in particle phases, L mol−1 s−1 ktw = termination rate constant in water phases, L mol−1 s−1 m̅ = average number of intermediate radicals per particle mdi = type-i monomeric radical partition coefficient between particle and water phase MWi = molecular weight of monomer i, g mol−1 Mi0 = total number of moles of monomer i of the recipe, mol Mir = number of moles of monomer i in the reactor, mol Mit = number of moles of monomer i in the tank, mol Mn = number-average molecular weight, g mol−1 [Mi]p = concentration of monomer i in particles, mol L−1 n̅ = average number of propagating radicals per particle NA = Avogadro’s number, mol−1 Nd = number of monomer droplets per volume water, L−1 w Np = number of polymer particles per volume water, L−1 w PDI = polydispersity index P•0 = primary radical in the particles P•0,aq = primary radical in aqueous phase Pr = dead chain with length r • Pr,ij = propagating radical with chain length r, i-type penultimate unit, and j-type terminal unit Pr,ijṪ P0 = primary intermediate radical with chain length r, itype penultimate unit, and j-type terminal unit Pr,ijṪ Ps,kl = intermediate radical that has two “arms” with chain lengths r and s, adjacent penultimate units i and k, adjacent terminal units j and l Qi = moment of dead chain QTi = moment of dormant chain ri = reactivity ratio for monomer i rN̅ = number-average chain length rN̅ ,t = targeted number-average chain length rW̅ = weight-average chain length Rp,i = intrinsic propagation rate of monomer i, mol L−1 s−1 [R]w = concentration of free radicals in aqueous phase, mol L−1 w si = radical reactivity ratio for monomer i TPr,ij = dormant chain with chain length r, i-type penultimate unit, and j-type terminal unit Vf,i = volumetric feeding rate of monomer i, L s−1 Vo = total volume of organic phase, L x = overall monomer weight conversion Yi = moment of propagation radical chain YTi , YTi,j = moments of intermediate radical chain

was first developed and correlated to the batch experimental data of St/BA RAFT mini-emulsion polymerization for model verification and parameter estimation purposes. The batch model was then combined with a semibatch reactor model. The MMFP was developed for several targeted uniform and linear gradient CCDs with the monomer feeding rate in the semibatch processes as an operation variable. A series of St/ BA copolymers with the predesigned CCDs were successfully produced by the MMFP. The model predicted the semibatch kinetics well. In particular, the experimental St/BA copolymer compositions (Fc1), that is, the variation of ST/BA composition along the polymer backbone, agreed well with the targeted profiles, demonstrating the power of precise production of the approach.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (W.-J. Wang). *E-mail: [email protected] (S. Zhu). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by National Natural Science Foundation of China (Key Grant No. 20936006, Grant No. 21074116), Chinese State Key Laboratory of Chemical Engineering at Zhejiang University (Grant Nos. SKL-ChE08D02 and SKL-ChE-12T05), and the Program for Changjiang Scholars and Innovative Research Team in University in China (No. IRT0942).

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NOMENCLATURE Ci = concentration of species i in reactor, mol L−1 Ci,f = concentration of species i in feed, mol L−1 dp = diameter of unswollen particle, dm dsp = diameter of swollen particle, dm d̅w = volume-average diameter, dm Dpi = diffusion coefficient of type i monomeric radical in particle, dm s−1 Dwi = diffusion coefficient of type i monomeric radical in aqueous phase, dm s−1 f = initiator efficiency f10 = initial St mole fraction Fci = cumulative copolymer composition of monomer i Fi = instantaneous copolymer composition of monomer i Fn1 = total St mole fraction ka = addition rate coefficient, L mol−1 s−1 kad = rate constant of radical captured by monomer droplets, Lw mol−1 s−1 kap = rate constant of radical captured by polymer particles, Lw mol−1 s−1 kct = cross-termination between propagation and intermediate radicals, L mol−1 s−1 kd = initiator decomposition rate constant, s−1 kdes = overall desorption rate constant, s−1 Kdwi = partition coefficient for monomer i between monomer droplet and water phases kf = fragmentation rate coefficient, s−1 kf m = chain transfer to monomer rate constant, L mol−1 s−1 kF = rate constant of droplet-particle coalescence, Lw s−1 Koi = desorption rate coefficient of monomeric radical of type i, s−1

Abbreviations

BA = butyl acrylate BCPA = 3-benzyltrithiocarbonyl propionic acid CCD = co-polymer composition distribution CLRP = controlled/living radical polymerization CSD = co-polymer sequence distributions CSTR = continuous stirred tank reactor DLS = dynamic light scattering GPC = gel permeation chromatography HD = hexadecane I = initiator IPUM = implicit penultimate model IV = viscometry KPS = potassium persulfate LG = linear gradient 7329



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LS = light light scattering M = monomer MMFP = model-based monomer feeding policy MWD = molecular weight distribution ODE = ordinary differential equation PDI = polydispersity index PFTR = plug flow tubular reactor RAFT = reversible addition-fragmentation transfer RI = refractive index RTD = residence time distribution SDS = sodium dodecyl sulfate St = styrene U = uniform Greek Letters

βi = probability of a monomeric radical of type i experiencing propagation or termination in the aqueous phase ϕi = probability of a propagating chains with ultimate unit i σ = absorption rate of radicals into particles, s−1 ρ = density of reaction mixture, g L−1 ρf,i = density of feeding monomer i, g L−1 ρmi = density of type-i monomer, g L−1 ρp = density of polymer, g L−1 Subscripts

mi = monomer i p = polymer 1 = St 2 = BA

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