Kinetics and Modeling of Semi-Batch RAFT Copolymerization with

For LS, the detection angle was 90° and the laser wavelength was 650 nm. .... by batch RAFT copolymerization were 19.3 and 36.7 C/1000Cs, respectivel...
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Kinetics and Modeling of Semi-Batch RAFT Copolymerization with Hyperbranching Dunming Wang, Xiaohui Li, Wen-Jun Wang,* Xue Gong, and Bo-Geng Li State Key Laboratory of Chemical Engineering, Institute of Polymerization and Polymer ngineering, Department of Chemical & Biological Engineering, Zhejiang University, Hangzhou, Zhejiang, P.R. China 310027

Shiping Zhu* Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7 S Supporting Information *

ABSTRACT: This work reports a kinetic model developed to provide insight into branching mechanisms and control of gelation by semibatch controlled radical copolymerization processes. The semibatch RAFT copolymerization of acrylamide (AM) and N,N′-methylenebis(acrylamide) (BisAM) in the presence of 3benzyltrithiocarbonyl propionic acid (BCPA) as chain transfer agent (CTA) was carried out for the model validation. The BisAM was fed to the reactor at a constant rate to yield hyperbranched polyacrylamide (b-PAM) without gelation. Different feeding rates and [BisAM]0/[CTA]0 ratios were theoretically simulated and experimentally investigated to optimize the instantaneous BisAM concentration in the reactor for branching formations. No gel was formed in the semibatch operation up to 99% total monomer conversion, in contrast to gel occurrence at 70% conversion in its corresponding batch operation. The polymer molecular weight and polydispersity as well as branching density increased slowly throughout the semibatch polymerization. Cyclization reactions were significant and helped to suppress the gelation. The model simulations correlated the experimental data very well.

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INTRODUCTION Controlled radical polymerization (CRP) has attracted much attention over the past decade.1−3 It provides a powerful tool for the synthesis of a large variety of polymers having tailormade molecular weight (MW) and narrow molecular weight distribution (MWD), as well as well-defined chain architectures such as block, graft, brush, star, and hyperbranched polymers.4−7 Compared with dendrimers having monodisperse and highly symmetric structure, hyperbranched polymers are polydisperse and possess intrinsic defects in the built-in linear segments.8 The hyprebranched polymers were normally synthesized by step-growth polymerization of ABn type monomers.9−11 Fréchet et al. introduced self-condensing vinyl polymerization (SCVP) for the preparation of hyperbranched polymers in 1995, employing chain-growth mechanism of vinyl inimers through propagation of the double bond and addition of the initiating site to the double bond.12 This approach was adopted and combined with group transfer polymerization13,14 and CRPs that included nitroxide-mediated radical polymerization (NMP),19 atom transfer radical polymerization (ATRP),16−18 and reversible addition−fragmentation chain transfer (RAFT) polymerization.19−27 The slow growth in the CRPs gives individual chains sufficient time for chain relaxation and diffusion, which facilitates intermolecular cross-linking and thus makes the CRPs advantageous for the preparation of hyperbranched polymers. Another approach for synthesizing © 2011 American Chemical Society

hyperbranched polymers was via copolymerization of a vinyl monomer with a di- or multivinyl comonomer. Sherrington and co-workers28−32 reported that branched PMMA could be synthesized by the copolymerization of MMA with di- or multivinyl comonomer in the presence of chain transfer agent such as mercaptans. Using RAFT copolymerization, Armes and co-workers33−35 synthesized branched methacrylic copolymers using disulfide-based dimethacrylate as the branching agent. It was found that the living character of RAFT chemistry was retained under branching conditions, as confirmed by gel permeation chromatography (GPC) analysis of the degraded copolymer chains after selective cleavage of disulfide bonds. Branching in RAFT polymerization of divinylbenzene36 and copolymerization of methyl methacrylate with ethylene glycol dimethacrylate,37,38 acrylic acid or acrylamide with N,N′methylenebis(acrylamide)39 was also investigated. Because of the importance of branched/cross-linked polymers, various theories have been developed for free radical copolymerization with branching/cross-linking. Flory40 and Stockmayer41 pioneered the theoretical development with their famous recursive theory of gelation based on a statistical argument, which assumed an equal reactivity for all functional Received: October 3, 2011 Revised: December 5, 2011 Published: December 22, 2011 28

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groups and free of intramolecular cyclization reactions. While readily satisfied in condensation types of polymerization, these assumptions are clearly violated by chain growth processes and free radical copolymerization of vinyl/divinyl comonomers in particular. The reactivities of various vinyl groups (those on monomer, comonomer and pendant to polymer chain) are usually different. Cyclization reactions are unavoidable and often significant. Since Flory and Stockmayer, there have been many statistical models developed for branching/cross-linking processes with efforts to remove these assumptions. For example, Dusek42 accounted for nonequal reactivity, Doston43 included molecular weight drifting of primary chains, Scranton44 modified cyclization reactions, and so on. However, the branching/cross-linking processes in the free radical polymerization are inherently kinetically controlled. Tobita45−47 applied a pseudokinetic rate constant method to simplify the kinetic treatment of a multicomponent polymerization to homopolymerization and demonstrated the inhomogeneous nature of polymer networks formed in free-radical polymerization. Zhu48−50 investigated the radical trapping, the validities of the monoradical assumption, and the stationary-state hypothesis using the method of moments. However, the kinetic approaches are disadvantageous in dealing with the postgelation period, many researchers combined kinetic and statistical approaches in deriving gelation theories, such as Tobita,51 Ogus,52 Zhu,48 and so on. Compared to slow initiation and fast propagation of the conventional radical polymerization, controlled radical polymerization such as NMP, ATRP, and RAFT is characteristic of fast initiation and slow propagation of polymer chains. The slow propagation gives individual chains sufficient time to relax and diffuse, thus in favor of formation of homogeneous branching or network structures and limiting microgels. Recently, Wang et al.53 developed a kinetic model for branching and gelation in batch RAFT copolymerization of vinyl/divinyl systems, as an extension of Zhu’s previous work on conventional vinyl/divinyl copolymerizaton.49 Other research groups, such as Matyjaszewski,54,55 Poly,56 Armes,57 Lona,58 and Perrier59 also conducted kinetic modeling study on gelation and/or branching in CRP vinyl/divinyl cross-linking copolymerization. However, semibatch models of controlled radical vinyl/divinyl copolymerization have not been developed. Semibatch processes are particularly useful in synthesis of hyperbranched polymers that are free of gels. In our previous work,60 we prepared hyperbranched polyacrylamide (PAM) via a semibatch RAFT copolymerization by continuous feeding of the branching agent (BA) N,N′-methylenebis(acrylamide) (BisAM) and the chain transfer agent (CTA) 3-benzyltrithiocarbonyl propionic acid (BCPA). Low CTA levels with the ratios of BCPA/BisAM < 0.05 were used and the systems were free of gels. In contrast, the literatures reported that batch ATRP used initiator/BA ratios >1,61−67 and batch RAFT polymerization used CTA/BA ratios >0.533,34,68−71 in order to minimize gelation. In a semibatch process, the instantaneous BisAM concentration in the reactor was controlled at a relatively low level, resulting in a high instantaneous CTA/BA ratio to effectively suppress cross-linking reactions. In this work, we developed a kinetic model to describe semibatch RAFT copolymerization of vinyl/divinyl systems. The model was experimentally verified and correlated to RAFT AM/BisAM data at various CTA/BA levels. The work provided good insight into the synthesis of gel-free hyperbranched polymers through semibatch CRP processes.

Article

MODEL DEVELOPMENT FOR RAFT BRANCHING PROCESS

Polymerization Scheme and Kinetic Equations. The elementary reactions involved in a batch RAFT copolymerization of vinyl/divinyl monomers are shown in Table 1. Table 1. Elementary Reactions Involved in the AM/BisAM RAFT Copolymerization

Pn,r,c denotes the macromolecule containing n monomeric units, r radical centers, and c RAFT moieties. I and Mi represent initiator and monomer-i, respectively with M1 as vinyl monomer AM and M2 as divinyl monomer BisAM. The pseudokinetic rate constant method45 was adopted in this work. The kinetic parameters listed in Table 1 are thus functions of radical fractions ϕi, which can be calculated from the instantaneous monomer composition f i. The pseudorate constants of propagation (kp,i), transfer (ktr), termination (kt), intermolecular cross-linking (kinter), and intramolecular crosslinking (kintra) are expressed as

kp , i =

∑ kp, ji ϕj (1a)

j

k tr =

∑ k tr , jϕj (1b)

j

kt =

∑ ∑ k t , ijϕiϕj i

kinter =

(1c)

j

∑ k*inter , j ϕj( F2 − C̅ − D̅ ) (1d)

j

kintra =

∑ k*intra , j ϕj( F2 − C̅ − D̅ ) j

(1f)

where F̅2 is the cumulative composition of divinyl monomeric units in copolymer chains, C̅ is the density of intermolecular cross-linkages, and D̅ is the density of intramolecular crosslinkages. In the simulation, we used the kinetic parameters as summarized in Table 2, assuming polymerization at 60 °C. 29

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The population balance for Pn,r,c is dPn , r , c dt

=

∑ rkp, iMiPn − 1, r , c − ∑ rkp, iMiPn , r , c i

∞

+

Table 2. Kinetic Rate Constants Used in the Simulation of AM/BisAM RAFT Copolymerization parameter

i ∞

∑ ∑ ∑ (r + 1)dk trPn , r + 1, c − 1Pm, s , d

kp11 (L·mol−1·s−1)

m=0 s=0 d=1 ∞ ∞ ∞

− +

−1 −1

kp12 (L·mol ·s )

∑ ∑ ∑ rdk trPn , r , cPm, s , d m=0 s=0 d=1 ∞ ∞ ∞

kp22 (L·mol−1·s−1)

∑ ∑ ∑ s(c + 1)k trPn , r − 1, c + 1Pm, s , d

kp21 (L·mol−1·s−1)

m=0 s=1 d=0 ∞ ∞ ∞

−

ktc11 (L·mol−1·s−1)

∑ ∑ ∑ sck trPn , r , cPm, s , d

ktc22 (L·mol−1·s−1)

m=0 s=1 d=0 ∞ ∞ ∞

+

∑ ∑ ∑ (r + 1)sk tdPn , r + 1, cPm, s , d

kt12,kt21 (L·mol−1·s−1) ktr1 (L·mol−1·s−1)

m=0 s=1 d=0 ∞ ∞ ∞

−

∑ ∑ ∑ rsk tdPn , r , cPm, s , d

ktr2 (L·mol−1·s−1)

m=0 s=1 d=0 n r+1 ∞

+

∑ ∑ ∑ s(n − m)kp, interPm, s , dPn − m, r − s , c − d

k*p,interl (L·mol−1·s−1) k*p,inter2 (L·mol−1·s−1) k*p,intra1 (L·mol−1·s−1) k*p,intra2 (L·mol−1·s−1)

m=0 s=0 d=0 ∞ ∞ ∞

that is

1 ∑ ∑ ∑ (r + 2 − s)sk tcPm, s , dPn − m, r + 2 − s , c − d 2 m=0 s=1 d=0 ∞

−

∞

∞

∑ ∑ ∑ rsk tcPn , r , cPm, s , d m=0 s=1 d=0 n r c

+ −

∑ ∑ ∑ rmkp, interPn , r , cPm, s , d ∑ ∑ ∑ snkp, interPn , r , cPm, s , d m=0 s=1 d=0

(2)

Method of Moments. We define the moments of Pn,r,c as ∞

Yi , j , k =

∞

∑ ∑ ∑ nir jc kPn, r , c (3)

⎛ ⎞ 1 1⎟ ⎜ ∑ mwiR p, i⎜ − ⎟V ρp ⎠ ⎝ ρi i=1

4.2 × 103

73

1.2 × 10

estimated from r1 = 0.35 =kp12

4

1.2 × 104 6 × 103 1 × 106

estimated from r2 = 2 73

1 × 106

=ktc11

(kt11 × kt22)1 74 1 × 107

this work

1 × 107

=ktr2

3.2 × 103

this work

3.2 × 103

=k*p,interl

70

this work

70

=k*p,intral

(6a)

(6b)

where Ci and Ci,f are the concentrations of species i in the reactor and in the feed, respectively; Ri is the intrinsic reaction rate of species i. The reactor model, together with the mass balance equations of various species, form a complete set of equations for the semibatch RAFT copolymerization. Three different monomer conversions are defined as follows. Conversion of AM (X1):

n

X1 =

(4)

M10 − M1r M10

(7)

Instant conversion of BisAM (X2):

where Vf is the volumetric feeding rate, mwi is the molecular weight of monomer i, ρi is the density of monomer i, ρp is the density of polymer, and Rp,i is the reaction rate of monomer i converted to polymer. The evolution of density in the reactor can be obtained through applying a mass balance to all entities:

d(V ρ) = Vf ρf dt

reference 72

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

After some mathematical manipulations, a complete set of moment equations can be derived as summarized in Table 3. With these moments, we can readily describe the chain properties as listed in Table 4. Semibatch Reactor Model. A well-mixed isothermal tank reactor is assumed in this work, and only monomer, polymer, and solvent significantly contribute to the volume V and density ρ, because the initiator and chain transfer agent are in trace amounts. The evolution of reaction volume follows

dV = Vf − dt

value 0.6 × 10−5

d(VCi) = Vf Ci , f + VR i dt that is,

∞

n=0 r=0 c=0

decomposition rate constant propagation rate constant of AM cross propagation rate constant of BisAM propagation rate constant of BisAM cross propagation rate constant of AM recombination termination rate constant of AM recombination termination rate constant of BisAM cross termination rate constant chain transfer rate constant of AM chain transfer rate constant of BisAM intermolecular cross-linkage rate constant of AM intermolecular cross-linkage rate constant of BisAM intramolecular cross-linkage rate constant of AM intramolecular cross-linkage rate constant of BisAM

Vf ρf dρ ρ dV = − (5b) dt V V dt where ρf is the density of feeding materials. The mass balance equations for species i are

m=0 s=0 d=0 ∞ ∞ ∞

−

description

kd (s−1)

∞

X2 =

M20 − M2r − M2t M20 − M2t

(8a)

Cumulative conversion of BisAM (X2cum):

X2cum =

(5a) 30

M20 − M2r − M2t M20

(8b)

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Table 3. Moment Equations Developed for RAFT Copolymerization

Diffusion-Controlled Termination Model. In free-radical polymerization, when the polymerization of branching/crosslinking proceeds to a high conversion, the system becomes viscous. In this work, we consider diffusion-controlled termination reactions, and the termination rate constant is expressed as75−77

Total monomer conversion (Xtotal):

M X + M20X2cum X total = 10 1 M10 + M20 The cumulative copolymer composition (F̅2) is then: M20 − M2r − M2t F2 = M10 − M1r + M20 − M2r − M2t

(9)

1 1 1 = + k tii k tii , C k tii , D

(10)

(i = 1, 2) (11)

where ktii,C is the chemical termination rate constant, ktii,D is the diffusion-controlled termination rate constant, which can be

Here Mi0 is the total mole of monomer i, Mit and Mir are the moles of monomer i in the tank and in the reactor, respectively. 31

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Table 4. Definitions of the Important Chain Structural Properties

calculated from the following semiempirical free-volume expressions78

k tii , D = k tii0 , D(rn)−2 exp( − 1/vf )

Table 5. Physical and Transport Properties in the AM/ BisAM RAFT Copolymerization parameter

(12)

0 where ktii,D is an adjustable parameter to correlate the experi0 0 mental data. In our work, kt11,D = 3 × 1016 and kt22,D = 1 × 1014 are estimated based on the batch monomer conversion data. The free volume fraction vf is expressed by79

vf = [0.025 + α p(T − Tgp)]∂p + [0.025 + αm1(T − Tgm1)]∂m1 + [0.025 + αm2(T − Tgm2)]∂m2 + [0.025 + αs(T − Tgs)]∂s

(13)

where α is the thermal expansion coefficient, ∂ is the volume fraction, and Tg is the glass-transition temperature. The subscripts p, mi, and s denote polymer, monomer, and solvent, respectively. The parameters of all physical and transport properties are listed in Table 5. Primary Cyclization and Secondary Cyclization. Cyclization reactions are important in a free-radical copolymerization with cross-linking and can be divided into two groups: primary and secondary cyclization. Primary cyclization occurs when a radical propagates through pendant double bonds on its own chain; while secondary cyclization occurs when a radical reacts with pendant double bonds on different chains of the same macromolecule.87−89 Note: a branched macromolecule can contain many primary chains that are connected by crosslinkages. The primary cycles are considered to be ineffective for elastic properties of gel molecules because they are formed by small numbers of monomeric units. However, the secondary cycles are elastically effective since they are formed between primary chains, similar to intermolecular cross-linking.87 Both intermolecular cross-linking and secondary cycles contribute to the experimental branching density (BD) because the experimental BD is estimated from GPC data. The primary cyclization reaction rate is assumed to be proportional to the consumption rate of divinyl monomer BisAM, which is expressed as88

dM dCP = − kcp 2 dt dt

value

reference

ρm1 (g·cm−3) 1100 ρm2 (g·cm−3)

1200

ρp (g·cm−3)

1300

αm1 (K−1) αm2 (K−1) αp1 (K−1) αp2 (K−1) αp (K−1) αs (K−1) Tgm1 (K) Tgm2 (K) Tgp1 (K) Tgp2 (K) Tgp (K) Tgs (K)

1 × 10−3 1 × 10−3 4.8 × 10−4 4.8 × 10−4 (1 − F̅2)αp1 + F̅2αp2 1.5 × 10−3 250 250 438 438 (1 − F̅2)Tgp1 + F̅2Tgp2 153

estimated 30 °C estimated 30 °C estimated 23 °C estimated =αm1 estimated =αp1 81 estimated estimated =Tgm1 84 =Tgp1 85 86

from ρm1 = 1122 g·cm−3 at from ρm2 = 1240 g·cm−3 at from ρ1 = 1302 g·cm−3 at from ref 80 from ref 80

from ref 82 from refs 80, 83

where kcp is a constant and CP is the concentration of pendant double bond to form the primary cycles. The secondary cyclization reaction rate is assumed to be proportional to the rate of intermolecular cross-linking reaction,88

dCS dC = kcs (15) dt dt where kcs is the average number of secondary cycles per crosslink, which is considered as a constant, and CS is the concentration of pendant double bond to form the secondary cycles. In this work, kcp = 0.125 and kcs = 4.8 are estimated from the batch experimental branching and cyclization density data. The kcp and kcs values are in the same range as those reported for the copolymerization systems of styrene/divinylbenzene51,90 and methyl methacrylate/ethylene glycol dimethacrylate.88 With these considerations, the fraction of primary cyclization (P) is CP CP + CS The branching density BD is P=

BD = 2000 × (14) 32

C Y1,0,0

(16)

+ (1 − P) × CD′ (17)

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pure nitrogen for at least 30 min. Meanwhile, BisAM was continuously fed into the reaction system at a constant rate of 17.5−7.8 mmol/h over 2 to 4.5 h. Aliquots were taken at predetermined time intervals and quenched by cooling before testing. After complete feeding of BisAM, the polymerization was continued at 60 °C for another 30 min, prior to termination by cooling. The polymer samples were dialyzed for 5 days in a Spectra/Por Dialysis Membrane with molecular weight cutoff of 1000 g/mol. Characterization. Monomer conversions were determined from the residual monomer concentration in the samples and determined using Agilent 6890N gas chromatograph equipped with a capillary column (HP-5, 30 m × 0.32 mm × 0.25 μm). The PAM samples were characterized using Polymer Laboratory PL-GPC 50 gel permeation chromatography (GPC) with differential refractive index (RI), viscometer (IV), and laser light scattering (LS) triple detectors. The detectors were installed in a series of LS, RI, and IV. For LS, the detection angle was 90° and the laser wavelength was 650 nm. A set of three columns of two Ultrahydrogel linear columns (MW ranged from 1 to 7000 kg/mol) and a PL-aquagel-20 column (MW ranged from 100 to 10,000) were equipped in the GPC. Then, 1.0 N NaNO3 aqueous solution was used as eluent at a flow rate 0.8 mL/min and 30 °C. PEO standards (MW1 = 1190 kg/mol, PDI1 = 1.21; MW2 = 885.5 kg/mol, PDI2 = 1.10; MW3 = 77.35 kg/mol, PDI3 = 1.05; as well as a PEO mixed standard having MW from 2 to 162 kg/mol) were used for calibrations. The dn/dc values for PAM and PEO were 0.170 and 0.133 mL/g, respectively,73 which were measured using various PAM and PEO samples at different concentrations. The delay volumes between the detectors were determined by PEO standards with 0.163 mL for LS and −0.557 mL for IV. 1H NMR spectra were recorded on a Bruker Advance 400 spectrometer with D2O as solvent.

and the cyclization density (CD) is (18) CD = P × CD′ where CD′ is the sum of the densities of primary and secondary cyclizations, which can be expressed by D×V CD′ = 2 × (M20 − M2t − M2r ) + M10 − M1r

× 1000 The branching frequency (BF) is thus BD × MW BF = 71000

■

(19)

(20)

EXPERIMENTAL SECTION

Materials. Acrylamide (AM, ≥98.5%) was purchased from Lingfeng Chemical Reagent Co. Ltd., China. Ammonium persulfate (APS, ≥98%) and N,N′-methylenebis(acrylamide) (BisAM, ≥98%) were obtained from Sinopharm Chemical Reagent Co. Ltd., China. AM and BisAM were recrystallized in acetone and ethanol, respectively, before use. APS was used as received. 3-Benzyltrithiocarbonyl propionic acid (BCPA) was synthesized according to the literature.91 Synthesis of b-PAM by Batch RAFT Polymerization. Batch RAFT copolymerization of AM and BisAM was conducted in sodium acetate/acid acetate buffer solution at pH = 5 with solid content of 4.99 wt % using BCPA as CTA and APS as initiator at 60 °C. Then 0.1 mol of AM and 0.167 mmol of BCPA were added to a 250 mL three-neck flask equipped with a mechanical stirring mixer and contained 100 g buffer solution, and 35.0 mmol BisAM was dissolved in 50 g of deionized water and then transferred into the flask. After deoxygenation with pure nitrogen for about 30 min, 0.083 mmol of APS was injected to initiate the polymerization. The temperature remained at 60 °C. Aliquots were taken at predetermined time intervals. The monomer conversions were determined by gas chromatography. Synthesis of b-PAM by Semibatch RAFT Polymerization. Semibatch RAFT polymerization was used to synthesize hyperbranched PAM as shown in Scheme 1 in a 1000 mL jacketed reactor

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RESULTS AND DISCUSSION Hyperbranched polyacrylamide was synthesized via batch or semibatch RAFT copolymerization of AM and BisAM. The instantaneous content of BisAM in the copolymerization system significantly influenced the branching parameters of b-PAMs. In our work, the instantaneous BisAM content was adjusted by changing the total ratio of [BisAM]0/[AM]0 and/or feeding rate (rf). For all experiments, [AM]0/[BCPA]0/ [APS]0 = 600/1/0.5 and [AM]0 = 0.667 M. Figure 1 shows a

Scheme 1. Synthesis of Hyperbranched Polyacrylamide (b-PAM) Using Batch or Semibatch Reversible Addition− Fragmentation Chain Transfer (RAFT) Copolymerization of Acrylamide with N,N′-Methylenebisacrylamide (BisAM)

Figure 1. GPC traces of b-PAM samples synthesized by semibatch RAFT polymerization under the condition: [AM]0/[BisAM]0/ [BCPA]0/[APS]0 = 600/30/1/0.5 and [AM]0 = 0.667 M in pH = 5 sodium acetate/acid acetate buffer solution at 60 °C and feeding rate of 11.7 mmol/h of BisAM.

equipped with a condenser, a nitrogen inlet, a thermometer, a mechanical stirrer, and a syringe pump. Then 0.7 mol of AM and 1.167 mmol of BCPA were dissolved in 700 g of buffer solution and then charged into the reactor. BisAM (11.7−35.0 mmol) was dissolved in 350 g of deionized water and equipped in constant flow pump. The system was heated to 60 °C by cycling water. Then, 0.583 mmol of APS was injected to initiate the polymerization after deoxygenation by

typical evolution of the molecular weight of b-PAM samples during the polymerization. As the reaction proceeded, the polymer molecular weight increased and the distribution became broader, indicating branching formation. 33

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The b-PAM samples were also characterized with an NMR spectrometer. In the 1H NMR spectrum (see the Supporting Information), the peaks at 6.8 and 7.5 ppm were the pendant double bonds of BisAM with one vinyl moiety reacted. This suggested that not all the reacted BisAM contributed to branching. The content of the unreacted pendant double bonds (cp) allowed us to estimate the percentage of pendant double bonds over the total BisAM converted and that of BisAM with both vinyl moieties converted for branching and/or cyclization, following the published procedure.60 Branched polymers have a lower root mean-square gyration radius ((⟨Rg2⟩1/2)) and a lower intrinsic viscosity ([η]).92 The level of branching density could be described by the contraction factors g and g′ as

g=

g′ =

Figure 3. g′ of b-PAMs at different reaction times as a function of molecular weight under the condition: [AM]0/[BisAM]0/[BCPA]0/ [APS]0 = 600/30/1/0.5 and [AM]0 = 0.667 M in pH = 5 sodium acetate/acid acetate buffer solution at 60 °C and feeding rate of 11.7 mmol/h of BisAM.

⟨R g 2⟩br ⟨R g 2⟩lin

(21)

[η]br [η]lin

(22)

density BD:92

⎤−1/2 ⎡⎛ ⎛ BF ⎞ ⎞ 4 × BF ⎥ g = ⎢⎜ 1 + ⎜ ⎟ ⎟ + ⎝ 6 ⎠⎠ 3π ⎥⎦ ⎢⎣⎝

60 2 1/2 In our previous work, the relationship of ⟨Rg ⟩ ∼ MW and 2 1/2 [η] ∼ MW were determined as ⟨Rg ⟩ = 1.70 × 10−2 M0.583 and [η] = 1.12 × 10−4 M0.769. Further, the quantitative relationship between g and g′ was also determined as

g′ = g ε

BD =

(23)

where the exponential factor ε was 0.74 and it was used for further estimation of branching density from g′. Figure 2 present

35500 × BF ×2 M

(24)

(25)

where the g data were obtained through converting g′ in Figure 3 using eq 23. CD could be calculated using eq 26

CD =

mBisAM − mBisAM , p 2mBisAM + mAM

× 1000 − BD (26)

where mBisAM and mAM were the moles of BisAM and AM incorporated into the polymer and could be determined by their conversions, respectively. mBisAM,p is the mole of BisAM with one vinyl reacted and the other pendant in the polymer Effect of Feeding Rate. The feeding period of the same BisAM aqueous solution quantity was varied to adjust the instantaneous BisAM concentration in the copolymerization system from 0 (batch) to 4.5 h to investigate the semibatch effects on MW, PDI, and branching structure. It was found that a shorter feeding period or higher feeding rate increased the instantaneous BisAM concentration and resulted in higher BF and BD.60 Parts a−c of Figure 4 show good agreement between the experimental data and the theoretical model for the conversion histories of both AM and BisAM, which were insensitive to instantaneous BisAM concentration. A low feeding rate reduced the BisAM amount copolymerized with AM. Figure 4d shows the MW of the b-PAM samples, determined by triple-detector GPC, plotted as a function of total monomer conversion. In the batch operation, the MW experienced a sudden increase at 70% conversion prior to gelation. However, in the semibatch processes, MW increased slowly up to 90% conversion, followed by sudden increase to about 1.5 × 106 g/mol without gelation, as agreed with the model prediction. Figure 4e shows the same trend of PDI as MW. The PDI increased to 4.33 before gelation in the batch, while it reached 6.85−8.15 in the semibatch processes without gelation.

Figure 2. Intrinsic viscosity of b-PAMs at different reaction times as a function of molecular weight under the condition: [AM]0/[BisAM]0/ [BCPA]0/[APS]0 = 600/30/1/0.5 and [AM]0 = 0.667 M in pH = 5 sodium acetate/acid acetate buffer solution at 60 °C and feeding rate of 11.7 mmol/h of BisAM.

the [η] versus molecular weight correlations for the b-PAM samples, with the linear PAM data included as reference. All the [η] values of b-PAMs were substantially lower than their linear counterpart. Figure 3 plots the contraction factor g′, estimated by eq 22, against molecular weight. For these b-PAMs, the branching units were expected to be distributed randomly along primary chains.1 The reacted BisAM units served as bridges and connected primary chains forming H-type cross-linkages. The Zimm-Stockmayer equation was applied to estimate the branching frequency BF and branching 34

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Figure 4. Hyperbranched polyacrylamides synthesized by RAFT copolymerization with different feeding rates of BisAM: (a) AM conversion, (b) instantaneous conversion of BisAM, (c) cumulative conversion of BisAM, (d) MW versus the total monomer conversion, (e) PDI, (f) BF, (g) BD, and (h) CD. Experimental conditions: [AM]0/[BisAM]0/[BCPA]0/[APS]0 = 600/30/1/0.5 and [AM]0 = 0.667 M in pH = 5 sodium acetate/acid acetate buffer solution at 60 °C. The points are experimental data while the lines are theoretical simulations.

The most important parameters of branched polymers are BF and BD, which can be estimated by eqs 24 and 25. The weight-average BF and BD of all the b-PAM samples were calculated from ∑iBFiCi/∑iCi and ∑iBDiCi/∑iCi, respectively, where Ci is the polymer concentration at each GPC elution fraction. Parts f and g of Figure 4 show the BF and BD values plotted as a function of the total monomer conversion. Both the experimental data and theoretical model showed that shorter feeding time gave higher BF and BD. The BFs of b-PAMs from batch RAFT copolymerization were much higher than those from semibatch operation. It is clear that the higher

instantaneous BisAM concentration in the batch process was advantageous for branching. However, the system could be readily gelled at a low to intermediate conversion. For comparison, in the semibatch processes, the final BFs reached up to 250 to 300 per molecule at high conversions but still free of gels. The BD of b-PAMs from the batch process, unlike BF, MW and PDI, increased in the early stage followed by a decrease to the final value of 19.3 C/1000Cs at gelation. In the semibatch processes, the BDs increased slowly with conversion and reached 8.81−12.3 C/1000Cs at nearly complete conversion without gelation. 35

dx.doi.org/10.1021/ma202215s | Macromolecules 2012, 45, 28−38

Macromolecules

Article

Figure 5. Hyperbranched polyacrylamides synthesized by RAFT copolymerization with different [BisAM]0/[CTA]0 ratios: (a) AM conversion, (b) instantaneous conversion of BisAM, (c) cumulative conversion of BisAM, (d) MW versus the total monomer conversion, (e) PDI, (f) BF, (g) BD, and (h) CD. Experimental conditions: [AM]0/[BCPA]0/[APS]0 = 600/1/0.5 and [AM]0 = 0.667 M in pH = 5 sodium acetate/acid acetate buffer solution at 60 °C. The points are experimental data while the lines are theoretical results.

The experimental BD values were substantially lower than those calculated based on the assumption that all the incorporated BisAM with both vinyl groups reacted contributed to branching through intermolecular reactions. This discrepancy suggested significant intramolecular cyclization reactions occurred. That is, a fraction of the incorporated BisAM formed cyclic structures. Figure 4h shows that, in the batch process, CD increased in the early stage and decreased slowly to 36.7 C/

1000Cs just before gelation. However, in the semibatch processes, it increased steadily with conversion to a final value of 17.6−28.5 C/1000Cs. With the feeding rate of 7.8−17.5 mmol/hs, 39.0−60.5% of all double bonds from BisAM were consumed for cyclization and 17.0−26.8% for branching, with the remainder as pendant double bonds. This suggested that cyclization played an important role in postponing gelation. 36

dx.doi.org/10.1021/ma202215s | Macromolecules 2012, 45, 28−38

Macromolecules

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Effect of BisAM content. Hyperbranched polymers could be prepared by increasing the branching agent BA concentration but at the risk of gelation. Chain transfer agent (CTA) was often added to suppress the network formation. Low BA/CTA levels (