Toward Understanding of Branching in RAFT Copolymerization of

Jan 26, 2016 - †State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, and ‡Key Lab of Biomass Chemical ...
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Toward Understanding of Branching in RAFT Copolymerization of Methyl Methacrylate through a Cleavable Dimethacrylate Shaoning Liang,† Xiaohui Li,† Wen-Jun Wang,*,†,‡ Bo-Geng Li,† and Shiping Zhu§ †

State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, and ‡Key Lab of Biomass Chemical Engineering of Ministry of Education, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou, Zhejiang, P. R. China 310027 § Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7 S Supporting Information *

ABSTRACT: We report the reversible addition−fragmentation chain transfer (RAFT) solution copolymerization of methyl methacrylate (MMA) with a cleavable divinyl comonomer, bis(2methacryloyl)oxyethyl disulfide (BMAODS). 2-Cyano-2-propyldodecyl trithiocarbonate was used as a RAFT chain transfer agent and 2,2′-azobis(2-methylpropionitrile) as an initiator. The selective cleavage of BMAODS disulfide bonds was used to collect primary chains for the determination of the branching density (BD). The effects of initial monomer concentration, vinyl/divinyl ratio, and primary chain length on the branching and cyclization reactions were thoroughly investigated. It was found that more than 50% pendent double bonds from BMAODS were consumed in cyclization rather than in branching. The BD increased linearly with the conversion up to approximately 60% conversion. The monomer concentration was found to be the most efficient parameter in promoting branching. Increasing divinyl monomer ratio and primary chain length favored cyclization over branching. The work provides experimental evidence to support the random branching mechanism in RAFT copolymerization of vinyl and divinyl monomers.

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INTRODUCTION Over the past few decades, polymer gels have been of great research interest.1−3 This interest has resulted in many applications in such areas as tissue engineering, biomedicine, and catalysis.4−11 Polymer gels are typically synthesized via a free radical copolymerization (FRP) of vinyl and divinyl monomers.12 During such reactions, the resulting polymers cross-link gradually, with a change from complete soluble sols to insoluble but swellable gels. The study on branching reactions prior to gelation is therefore of great importance to fully understanding the process of gel formation. During the gelation process, divinyl monomers are involved in branching/cross-linking to form cross-linkages, intra/ interchain cyclization for cycle formation, or copolymerization of one of vinyl groups to preserve another pendent double bond (PDB) on the polymer chain. Two branching points (“T”-type) form one cross-linkage unit (“H”-type). The branching density (BD) is defined as the number of branching points divided by the total number of monomeric units, while the cyclization density (CD) is the number of cycle points divided by the total number of monomeric units bound in the polymer chains. In the FRP of vinyl and divinyl monomers, the gelation begins when the number of branching units per primary polymer chain reaches unity. However, a delay in the onset of gelation (referred to as the gelation point) is often observed.13,14 This delay is due to the formation of cyclic structures of primary chains, which competes with branching/ cross-linking reactions. The nature of FRP mechanism also results in heterogeneity of the gel structure. The homogeneity © XXXX American Chemical Society

of cross-linkage units in gels can be improved by using controlled/“living” radical copolymerization (CLRP), such as nitroxide-mediated copolymerization (NMP),15 atom transfer radical copolymerization (ATRP),16 and reversible addition− fragmentation chain transfer (RAFT) copolymerization.17 In CLRP, all propagating primary chains undergo a reversible activation/deactivation process, which allows the pendent double bonds in primary chains to have sufficient time to interact with other macromolecules, thus minimizing microgel formation.18−20 The critical gelation point in CLRP processes can be well described by Flory−Stockmayer theory, suggesting a homogeneous network formation.21,22 The resulting gels from CLRP have lower stresses of material shrinkage and higher deswelling rates than their counterparts prepared by FRP.23,24 Prior to the formation of cross-linked networks, the polymers are highly branched yet soluble. Gelation can be suppressed by employing a large quantity of chain transfer agent (CTA) in FRP or by controlling the initiator or CTA to divinyl monomer ratio greater than 0.5 in CLRP in order to achieve highly branched polymers (HBPs).25−28 A number of theoretical studies on cross-linking reactions have been carried over the past several decades. Such theories generally fall under one of the three categories: statistical, percolation, and kinetic.29,30 Statistical theory was developed by Flory and Stockmayer, who pioneered studies on branching and gelation.31,32 The theory was later extended with conditional Received: November 30, 2015 Revised: January 18, 2016

A

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Table 1. Summary of Polymerization Conditions and Characterization of Branched Poly(methyl methacrylate) (b-PMMA) Samples runa [M1]0/[M2]0b 1 2 3 4 5 6 7

50/0.5 50/1 50/1.5 50/1 50/1 50/1 50/1

[CTA]0/[M1]0

c0 c (wt %)

Xd (%)

Mn,be (kg/mol)

PDIbe

Mn,lf (kg/mol)

PDIlf

λpg

BDn C/1000 C

n1h

n2h

nPDBh

CDn C/1000 C

1/50 1/50 1/50 1/75 1/100 1/50 1/50

30 30 30 30 30 15 45

97.9 96.2 99.8 90.9 97.1 80.3 99.6

6.84 8.20 9.90 12.5 19.6 5.60 11.1

2.6 5.5 4.2 4.1 8.0 1.7 7.5

5.21 5.40 5.37 7.10 9.95 4.69 5.61

1.2 1.3 1.4 1.4 1.3 1.3 1.3

0.48 0.68 0.92 0.86 0.98 0.33 0.99

4.6 6.3 8.5 6.1 4.9 3.5 8.8

68.4 82.0 99.0 125 196 56 111

0.67 1.69 2.98 2.51 4.06 1.14 2.19

0.06 0.14 0.21 0.16 0.15 0.15 0.14

4.2 11.8 18.1 11.9 14.2 13.5 9.0

CPDTTC and AIBN were used as RAFT chain transfer agent (CTA) and initiator (I), respectively, [M1]0/[I]0 = 50/0.2, T = 70 °C. b[M1]0/[M2]0: initial mole ratio of MMA (M1) and BMAODS (M2). cc0 is initial monomer concentration. dOverall monomer conversions X were determined gravimetrically. eMn,b and PDIb are number-average molecular weight and polydispersity index of b-PMMAs. fMn,l and PDIl are number-average molecular weight and polydispersity index of PMMA primary chains, respectively. gλp is average number of branching units per primary chain calculated by λp = 2(1 − Mn,l/Mn,b). hn1, n2, and nPDB are number of M1, M2, and unreacted pendent double bond units in polymer chains estimated from 1H NMR spectra, respectively. a

assumptions by Gordon,33 Macosko and Miller,34,35 Pearson and Graessley,36 and others. Statistical theory is based on meanfield theory because only average properties are considered in the polymerization system. Based on simulation in n-dimensional space, percolation theory was proposed by de Gennes37 and Doi and Edwards38 and further developed by Mannevile and de Seze,39 Simon et al.,40 Bowman and Peppas,41 Chiu and Lee,42 and others in FRP. The percolation theory can consider spatial correlation, but it is difficult to introduce the mobility of polymer chains due to its use of fixed lattice structure. Despite some successes in the polycondensation system, it is challenging to apply the mean-field theory to predict gelation in FRP. This limitation is mainly attributed to the inherent heterogeneous characteristics in FRP. The problem could be resolved by the kinetic modeling approach. Mikos et al.43 proposed a kinetic model for cross-linking reaction in the FRP system, where the kinetics in pregelation and postgelation could both be well described. Tobita and Hamielec44 proposed a pseudokinetic model for the polymer network development in FRP by considering primary chains whose birth times are different, and each experiences a different cross-linking history. Zhu45 further developed the model for prediction of molecular weight distribution and sol/gel fraction of polymers in FRP. There have been also many other kinetic models developed by a number of researchers, such as Dusek and Somvarsky,46 Okay et al.,47 Elliott and Bowman,48 and others. More recently, branching/cross-linking modeling has been extended to CLRP systems through kinetic or stochastic approaches. Zhu and co-workers studied the cross-linking in RAFT copolymerization of vinyl/divinyl monomers.49 Developments in molecular weight, branching density, and gelation point with respect to various monomer concentrations, divinyl monomer ratios, and CTA concentrations were systematically investigated using a pseudokinetic-based model. The model was further extended to branching studies in a semibatch RAFT copolymerization of acrylamide/N,N′-methylenebis(acrylamide) in solution and styrene/butyl acrylate in miniemulsion.50−52 Poly et al.53 used a semiempirical method to distinguish inter- and intramolecular cross-linking for the evolution of branching density and gelation point. Perrier et al.54 applied a random branching theory for the model development. The authors argued that the model agreed well with experiment data when no nanogels were formed. Using the method of moment, a model for molecular weight development before gelation was developed by Hernández-

Ortiz et al. 55−57 By using the Monte Carlo method, Matyjaszewski and co-workers predicted gel points by considering polymer topologies and cyclization under dilute condition.58−60 Armes and co-workers assumed a random addition of double bonds into the primary chains during the ATRP of vinyl and divinyl monomers for the prediction of the onset of gelation.61 The random branching distribution along with the polymerization is assumed to be a characteristic of the CLRP of vinyl and divinyl monomer systems, which is commonly used in modeling the cross-linking reactions. Although the Flory− Stockmayer theory has been used to examine if the crosslinking reactions possess a randomness behavior,13,62 there is no experimental evidence reported to elucidate the characteristics of branching/cross-linking reactions at the pregelation stage. In addition, branching behaviors around the gel point often deviate dramatically from the classical gelation theories and are difficult to determine due to polymer solubility issues. Many techniques have been employed for quantitative studies on BD and its distribution, including viscometer, nuclear magnetic resonance (NMR), and online viscometer and lightscattering detectors with gel permeation chromatography (GPC). However, viscometer and light-scattering techniques are insensitive to determination of polymer chains having low molecular weight.63−71 In this work, a cleavable divinyl monomer, bis(2methacryloyl)oxyethyl disulfide (BMAODS), is used for an investigation of the branching behavior in RAFT copolymerization with methyl methacrylate (MMA). Highly branched poly(methyl methacrylate) (b-PMMA) samples are synthesized using this approach. The disulfide bonds in polymer chains could be cleaved to convert the branched chains into linear primary chains, which provide an opportunity to quantitatively estimate BD by comparing the molecular weight of the branched polymers before and after the S−S cleavage. Branching behaviors including BD and CD at various monomer concentrations, vinyl/divinyl ratios, and monomer/CTA ratios (control over primary chain length) are investigated. The experimental results are compared to kinetic models to gain a better understanding of the branching processes. The characteristics of random branch formation during the RAFT copolymerization of vinyl/divinyl monomers are elucidated by studying weight fraction distributions of i-chains in b-PMMA samples. B

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Scheme 1. Synthesis of b-PMMAs via RAFT Copolymerization of MMA and BMAODS and Their Degradation to Primary Chains

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EXPERIMENTAL SECTION

varying divinyl monomer ratio ([M1]0/[M2]0), primary chain length ([CTA]0/[M1]0), and monomer concentration (c0) on the branching formation were studied. The b-PMMA samples had the number-average molecular weights (Mn,b) of 5.6−19.6 kg/mol and polydispersity indexes of 1.7−20.2. Since the meansquare radius of gyration (Rg) was beyond detectability of the online light scattering (Mn,b’s for all the samples were lower than 20 kg/mol),60 the contract factors from Rg values could not be obtained. This limited the application of the Zimm and Stockmayer equation for the determination of branching density (BD).74 Instead, an estimate of BD was made by comparing b-PMMA molecular weight with that of its primary chains obtained from the degradation of the b-PMMA disulfides. Since tributylphosphine (Bu3P) is an efficient reductant for cleaving the disulfide bonds in the presence of trace amount water, it was used for the degradation of b-PMMA. Structural changes prior to and after degradation were determined by the 1 H NMR and GPC measurements. The b-PMMA samples at various conversions in run 7 are taken as an example. Figure 1

Materials. MMA (99%) from Aldrich was purified by washing twice with a 5% NaOH solution and deionized water, drying with Na2SO4 overnight, and distilling under vacuum to remove the inhibitor. BMAODS (99%) and 2-cyano-2-propyldodecyltrithiocarbonate (CPDTTC, 99%) were synthesized according to the literature procedures.72,73 2,2′-Azobis(isobutyronitrile) (AIBN, 99%) was purchased from Aladdin Industrial Co. and recrystallized twice against methanol. Toluene (AR, Sinopharm) was distilled prior to use. Nitrogen (99.999%) was supplied by Jingong Air Co. Tributylphosphine (Bu3P, 95%) from Aladdin Industrial Co. was used as received. Synthesis of Hyperbranched PMMA (B-PMMA). The polymerization conditions are summarized in Table 1. Taking run 2 as an example: MMA (1, 15.00 g, 0.15 mol), BMAODS (2, 0.89 g, 3.07 × 10−3 mol), CPDTTC (1.04 g, 3.02 × 10−3 mol), AIBN (99.0 mg, 0.6 × 10−3 mol), and dried toluene (35 g) were added into a 100 mL flask sealed with a rubber septum and purged by N2 for 40 min. The flask was then immersed in an oil bath at 70 °C with intense agitation to start the polymerization. The reaction systems were homogeneous during the polymerization. Periodically b-PMMA samples were taken and quenched with 3% hydroquinone THF solution immediately. After removing toluene under vacuum, the resulting light yellow bPMMA was dissolved in approximately 3 mL of THF and precipitated out by adding n-hexane (n-hexane:THF = 3:2 in volume) to remove residual monomers. The b-PMMA samples were dried at 50 °C for approximately 24 h under vacuum. Cleaving Disulfide Cross-Linkage in B-PMMA by Tributylphosphine. The b-PMMA sample (0.30 g) was dissolved in 5 mL of THF and then mixed with 0.23 g of Bu3P and 0.02 g of deionized water. The mixture was blanketed with N2 and stirred at room temperature overnight. The resulted b-PMMA sample was precipitated out by adding an excess of n-hexane and dried under vacuum. Characterization. 1H NMR spectra of the b-PMMAs were acquired on a Bruker Advance 400 MHz spectrometer with CDCl3 as solvent. Molecular weight distributions were determined using an integrated Waters Alliance GPC system with a Waters e2695 separation module. Three 7.8 × 300 mm Waters Styragel 3 THF columns were equipped in series after Styragel 4.6 × 30 mm guard column. A Waters 2414 reflective index (RI) detector, Wyatt DAWN EOS multiangle light scattering (LS) detector, and Wyatt ViscoStar II intrinsic viscosity (DP) detector were equipped after the columns. The GPC characterization was conducted at 35 °C with THF as eluent at a flow rate of 1.0 mL/min. Nine narrow PMMA standards (MW from 875 to 625 500 g/mol) purchased from Polymer Laboratories were used for calibration. A dn/dc value of 0.08 was used for LS.

Figure 1. GPC traces of run 7 samples collected at different conversions (a) before and (b) after disulfide bond degradation.

shows their molecular weight distributions prior and subsequent to the cleavage. It can be seen that the molecular weight distribution of b-PMMA after degradation became significantly narrower. The overlapping of GPC traces from light scattering, refractive index, and intrinsic viscosity detectors of the cleaved PMMA (Figures S1 and S2 in the Supporting Information) demonstrates a complete cleavage of the disulfide bonds in b-PMMA after Bu3P treatment. The disappearance of the resonances at 2.9 and 4.2 ppm in the 1H NMR spectrum, attributed to protons adjacent to the disulfide bonds (see Figure S3), further supports the fully degradation of b-PMMA. Narrow molecular weight distribution and linear increment of molecular weight with conversion for the cleaved PMMA samples as shown in Figure 1b suggest system livingness in the RAFT copolymerization of MMA and BMAODS.

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RESULTS AND DISCUSSION The experimental conditions and characterization results for the b-PMMA samples from RAFT copolymerization of MMA (M1) and BMAODS (M2) are summarized in Table 1. The experiments were conducted in toluene at 70 °C with the CPDTTC as RAFT chain transfer agent (CTA). The effects of C

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Macromolecules The divinyl monomer BMAODS participates in chain propagation to introduce pendent double bonds (PDBs) in the polymer chains. The PDBs continue taking part in either branching reaction or cyclization. A branched structure is formed when a PDB on a polymer chain reacts with another propagating chain, while a cyclic structure is generated via the reaction of a PDB with a radical on the same growing chain or on a different propagating chain, which is already cross-linked with the polymer chain having the same PDB. In comparing the molecular weights of b-PMMA samples prior to and after the S−S cleavage, the branching density (BD, Cs/1000 C) can be is expressed as ⎛ 1 1 ⎞ ⎟⎟m1 BD = 1000 × ⎜⎜ − M n,b ⎠ ⎝ M n,l

Figure 2. Number-average molecular weight development in RAFT copolymerization of MMA (1) and BMAODS (2) at various [M1]0/ [M2]0 (run 1 = 50/0.5, run 2 = 50/1, and run 3 = 50/1.5). (a) bPMMAs and (b) their primary chains. Lines give the model prediction values.

(1)

where Mn,l is the number-average molecular weight of linear PMMA primary chain and m1 is the molecular weight of MMA. The cyclization density (CD, Cs/1000 C) can be expressed as n − nPDB CD = 1000 × 2 − BD 2n2 + n1 (2) where n1, n2, and nPDB are the average number of MMA, BMAODS, and pendent double bond units in polymer chains, respectively. For better understanding of cross-linking and cyclization reactions in the RAFT copolymerization of MMA and BMAODS, a kinetic model has been developed based on the terminal model and the pseudokinetic rate constant method. The details for modeling are presented in the Supporting Information. The experimental data and modeling correlation results are discussed here. Effect of Initial Vinyl/Divinyl Monomer Ratio. The initial vinyl/divinyl ratio [M1]0/[M2]0 was varied from 50/0.5 to 50/1.5 (runs 1−3) at a fixed [M1]0/[CTA]0/[I]0 = 50/1/0.2 and 30 wt % monomer concentration. In run 1, BD = 4.6 Cs/ 1000 C and CD = 4.2 Cs/1000 C (see Table 1), suggesting approximately half of the divinyl monomer BMAODS contributed to branching. Changing [M1]0/[M2]0 to 50/1 (run 2) and to 50/1.5 (run 3) increased the BD to 6.3 and 8.5 and CD to 11.8 and 18.1 Cs/1000 C, respectively. More BMAODS were consumed in cyclization than in branching with the increased amount of divinyl monomer. The data of number-average molecular weight Mn,b, BD, CD, average number of branching units per primary chain (λp), number-average branching frequency (BF, branching or crosslinkage units per polymer molecule), number-average cyclization frequency (CF, cyclization units per polymer molecule), and overall conversion X as well as their model predictions in runs 1−3 are shown in Figures 2a and 3 (as well as Figure 4S), respectively. The BF and CF can be expressed as BF =

CF =

Figure 3. (a) Number-average branching density (BD), (b) numberaverage cyclization density (CD), (c) average number of branching units per primary chain (λp), (d) number-average branching frequency (BF), and (e) number-average cyclization frequency (CF) as a function of overall monomer conversion in RAFT copolymerization of MMA (1) and BMAODS (2) at various [M1]0/[M2]0 (run 1 = 50/0.5, run 2 = 50/1, and run 3 = 50/1.5). Curves are model predicted values.

cyclization was favored. The BD increased linearly with conversion up to approximately 60%, indicating the formation of b-PMMA having homogeneous branch distribution. As the copolymerization progressed, the BD leveled off, while the CD increased substantially. More pendent double bonds from BMAODS participated in cyclization than in branching, leading to inhomogeneous branch distribution in b-PMMA. With the increased amount of BMAODS from [M1]0/[M2]0 = 50/0.5 (run 1) to 50/1.5 (run 3), the ratio of cyclic to branch structures increased, particularly at the late stage of copolymerization. Note that the CD data provided here are the accumulated values, suggesting a majority of pendent double bonds from BMAODS consumed for cyclization. The BF and CF had similar evolution tendency to BD and CD as shown in Figure 3d,e. The diffusion control effect on branching became severe with an increased divinyl monomer ratio. Although different vinyl/divinyl ratios were used for runs 1−3, little effect on the primary PMMA chain length was observed, as shown in Figure 2b.

BD × M n,b 1000 × m1

(3)

CD × M n,b 1000 × m1

(4)

The number-average molecular weights of primary linear PMMA after cleavage of b-PMMA (Mn,l’s) are also given in Figure 2b. It can be seen that more BMAODS participated in cyclization than contributed to branching, suggesting that D

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Macromolecules Effect of Primary Chain Length. The primary chain length is believed to be one of the most important parameters determining gelation. Control of primary chain length facilitates the synthesis of soluble highly branched polymers. Here, three targeted primary chain lengths were studied by controlling [CTA]0/[M1]0 = 1/50 (run 2), 1/75 (run 4), and 1/100 (run 5), corresponding to the final primary chain length L = 50, 75, and 100 monomer units. The [M1]0/[M2]0/[I]0 was 50/1/0.2, and the monomer concentration was 30 wt %. Plots of Mn,b, BD, CD, λp, BF, and CF versus X for runs 2, 4, and 5 are shown in Figures 4a and 5 as well as Figure 5S, along

primary chains bear more PDB, which is also confirmed with the higher average number of branching units per primary chain, as shown in Figure 5c, allowing for more cyclization reactions between primary chains. Effect of Monomer Concentration. With the increase of monomer concentration in the polymerization system, the concentration of polymer chains bearing pendent double bonds increases, enhancing the formation of branched and cyclic structures. We carried out the runs with the initial monomer concentrations of 15 (run 6), 30 (run 2), and 45 wt % (run 7) at [M1]0/[M2]0/[CTA]0/[I]0 = 50/1/1/0.2. The numberaverage molecular weight of b-PMMA and primary chain, BD, CD, BF, and CF as well as their model predicted values for runs 2, 6, and 7 are plotted against the overall monomer conversion X in Figures 6 and 7, respectively. Figure 6S provides the

Figure 4. Number-average molecular weight development in RAFT copolymerization of MMA (1) and BMAODS (2) at various primary chain lengths by controlling [CTA]0/[M1]0 at 1/50 (run 2), 1/75 (run 4), and 1/100 (run 5). (a) b-PMMAs and (b) their primary chains. Curves are model predicted values.

Figure 6. Number-average molecular weight development in RAFT copolymerization of MMA (1) and BMAODS (2) at various initial monomer concentrations of 15 (run 6), 30 (run 2), and 45 wt % (run 7). (a) b-PMMAs and (b) their primary chains. Curves are model predicted values.

overall monomer conversion during polymerization. It can be seen that run 7 with the highest monomer concentration (c0 = 45 wt %) had BD of 8.8 Cs/1000 C and CD of 9.0 Cs/1000 C,

Figure 5. (a) Number-average branching density (BD), (b) numberaverage cyclization density (CD), (c) average number of branching units per primary chain (λp), (d) number-average branching frequency (BF), and (e) number-average cyclization frequency (CF) as a function of overall monomer conversion in RAFT copolymerization of MMA (1) and BMAODS (2) at various primary chain lengths by controlling [CTA]0/[M1]0 at 1/50 (run 2), 1/75 (run 4), and 1/100 (run 5). Curves are model predicted values.

with their model predictions. The linear increase of Mn,l of the primary chains after cleavage of b-PMMA, shown in Figure 4b, confirms good control of the copolymerization system. Run 5 sample had the longest primary chain and an average number of branching units of 0.98, close to the gel point, at the overall conversion of 97.1%, while it still maintained its solubility. The BD and BF decreased but the CD and CF increased with the primary chain length. This is due to the fact that the longer

Figure 7. (a) Number-average branching density (BD), (b) numberaverage cyclization density (CD), (c) average number of branching units per primary chain (λp), (d) number-average branching frequency (BF), and (e) number-average cyclization frequency (CF) as a function of overall monomer conversion in RAFT copolymerization of MMA (1) and BMAODS (2) at various initial monomer concentrations of 15 wt % (run 6), 30 wt % (run 2), and 45 wt % (run 7). Curves are model predicted values. E

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Macromolecules respectively, compared to 6.3 (BD) and 11.8 (CD) Cs/1000 C for run 2 (c0 = 30 wt %) and 3.5 (BD) and 13.5 (CD) Cs/1000 C for run 6 (c0 = 15 wt %). Comparable evolution trend existed with BF and CF as shown in Figure 7d,e. The high monomer concentration clearly favored branching over cyclization. This suggests that at the higher monomer concentrations PDBs were more likely to be involved in intermolecular branching reactions. Run 7 sample at X = 99.6% possessed an average number of branching units of 0.99, suggesting the b-PMMA system was close to its gel point but still remained soluble. Branching Behavior in RAFT Copolymerization of MMA and BMAODS. RAFT copolymerization of vinyl and divinyl monomers is useful for preparing highly branched polymers due to their slow chain growth feature. Assuming random branching reactions with this mechanism, the molecular weight distribution of polymer chains should follow the following equation derived by Zhu:75 σi i−1 [(σ + 1)i − 1]! ⎛ σ ⎞ ⎛ λp ⎞ ⎜ ⎟ ⎜ ⎟ ω(i) = (σi) ! (i − 1)! ⎜⎝ σ + λp ⎟⎠ ⎜⎝ σ + λp ⎟⎠

Figure 8. Evolution of weight fraction of polymers containing iprimary chains synthesized by RAFT copolymerization of MMA (1) and BMAODS (2) at (a) various [M1]0/[M2]0 (run 1 = 50/0.5, run 2 = 50/1, and run 3 = 50/1.5); (b) various primary chain lengths by controlling [CTA]0/[M1]0 at 1/50 (run 2), 1/75 (run 4), and 1/100 (run 5); and (c) various initial monomer concentrations of 15 (run 6), 30 (run 2), and 45 wt % (run 7). The lines are theoretical calculation results using eq 3, which is a discrete function, but shown in the form of continuous curves to allow for better comparisons.

(5)

where i is the number of primary chains cross-linked in the polymer, which has the molecular weight equal to i times of the primary chain, and ω(i) is the weight fraction of i-chains. The σ can be calculated by PDI p = (σ + 1)/σ

primary chains were converted to branched structures, resulting in the existence of more single chains.

(6)

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where PDIp is the polydispersity index of the primary chains obtained after cleavage of the disulfide linkages of the branched polymer. The experimentally determined λp and σ values thus allow us to estimate the weight fraction distribution of branched polymers containing a variety of i-primary chains. On the basis of molecular weight distribution of the primary chain, the GPC trace of the b-PMMA samples could be deconvoluted into several i-chain populations. The weight fraction of i-chains ω(i) in the branched polymer could thus be estimated. The comparison of ω(i) values from the peak deconvolution of the b-PMMA samples and the theoretical calculation using eq 5 for runs 1−7 are shown in Figure 8. Note that eq 5 is a discrete function, and the calculation results are shown in the form of lines for better comparison. It can be seen that all experimental results agree well with the theoretically calculated results from the equation. This appears to be the first experimental evidence to support the random branching characteristic during the RAFT copolymerization of vinyl and divinyl monomers. In the case of changing vinyl/divinyl ratio, the weight fraction of polymer chains comprising more i-chains increased with the divinyl fraction. This was expected, but it is worth noting that although intramolecular cyclization is preferred in the case of longer primary chains, the weight fraction of polymer chains having more i-chains increased. This is due to the fact that longer primary chains contain more PDBs and thus favor the formation of polymer chains with higher branching frequencies. This result also suggests that the gels synthesized at high RAFT chain transfer agent concentrations or short primary chains have a fluffy and soft structure, owing to less cross-linked dangling primary chains containing lower molecular weights. This is evident from the studies, in which the initial monomer concentrations were varied. Taking run 6 sample at c0 = 15 wt % as an example, the weight fraction of single chains (i = 1) was 0.41 compared with 0.12 for run 7 at c0 = 45 wt %. Fewer

CONCLUSIONS

A comprehensive understanding of the branching mechanisms in the vinyl/divinyl RAFT copolymerization was reported by employing a cleavable disulfide-based dimethacrylate BMAODS as a cross-linker in the copolymerization with MMA. The branch formation in b-PMMA was found to be directly competitive with cyclization. More than 50% of the pendent double bonds from BMAODS were consumed in cyclization, as opposed to branching. The BD increased linearly with monomer conversion and the b-PMMA had a homogeneous branch distribution up to approximately 60% conversion. With the progress of polymerization, the percentage of PDBs participating in branching decreased, resulting in an inhomogeneous branch distribution in b-PMMA. Under the studied experimental conditions, the monomer concentration was found to be most efficient variable for promoting branching. Varying the initial monomer concentration from 15 to 45 wt % increased BD from 3.5 to 8.8 Cs/1000 C while decreasing CD from 13.5 to 9.0 Cs/1000 C. The soluble b-PMMA having 0.99 points per primary chain with an almost complete conversion of divinyl monomer was synthesized at the high monomer concentrations. Increasing the initial divinyl monomer ratio by changing [M1]0/[M2]0 from 50/0.5 to 50/1.5 resulted an increase of the CD/BD ratio, particularly for the conversions over 60%. More PDBs from BMAODS favored cyclization over branching at high divinyl/vinyl monomer ratios. The extension of primary chain length from 50 to 100 promoted the intramolecular cyclization by offering more PDBs to react with radicals of the same chain. Moreover, for the first time, the experimental evidence supported the random branching characteristic during the RAFT copolymerization of vinyl and divinyl monomers. F

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b02596. Details about GPC traces and 1H NMR spectra of bPMMA samples before and after cleavage, kinetic model for RAFT copolymerization of vinyl/divinyl monomer system with branching, evolution of overall conversions in RAFT copolymerization, and deconvolution of GPC trace of b-PMMA sample (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(W.-J.W.) Tel +86-571-8795-2772; Fax +86-571-8795-2772; e-mail [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank National Natural Science Foundation of China (Grants 21420102008, 21074116, and 20936006), Chinese State Key Laboratory of Chemical Engineering at Zhejiang University (Grant SKL-ChE-14D01), and the Program for Changjiang Scholars and Innovative Research Team in University in China (IRT0942) for financial support.

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DOI: 10.1021/acs.macromol.5b02596 Macromolecules XXXX, XXX, XXX−XXX