European Polymer Journal 46 (2010) 2164–2173

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European Polymer Journal

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Kinetic modeling of two-step RAFT process for the production of novelfluorosilicone triblock copolymers

Yin-ning Zhou, Cheng-mei Guan, Zheng-hong Luo ⇑Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005,People’s Republic of China

a r t i c l e i n f o

Article history:Received 17 June 2010Received in revised form 9 August 2010Accepted 6 September 2010Available online 17 September 2010

Keywords:PDMS-b-PHFBMA-b-PSTwo-step RAFT polymerizationModelingPolymerization kinetics

0014-3057/$ - see front matter � 2010 Elsevier Ltddoi:10.1016/j.eurpolymj.2010.09.002

⇑ Corresponding author. Tel.: +86 592 2187190; faE-mail address: luozh@xmu.edu.cn (Z.-h. Luo).

a b s t r a c t

Well-defined poly(dimethylsiloxane)-b-poly(2,2,3,3,4,4,4-heptafluorobutylmethacryl-ate-b-poly(styrene) (PDMS-b-PHFBMA-b-PS) triblock copolymers were prepared bytwo-step reversible addition–fragmentation chain transfer (RAFT) polymerization. Acomprehensive mathematical model for the two-step RAFT polymerization in a batchreactor was presented using the method of moments. The model described molecularweight, monomer conversion and polydispersity index as a function of polymerizationtime. Good agreements in the polymerization kinetics were achieved for fitting thekinetic profiles with the suggested model. In addition, the model was used to predictthe effects of initiator concentration, chain transfer agent concentration and monomerconcentration on the two-step RAFT polymerization kinetics. The simulated resultsshowed that for the two-step RAFT polymerizations, the effects initiator concentration,chain transfer agent concentration and monomer concentration are identical and theinfluence degrees are different yet.

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1. Introduction

Poly(dimethylsiloxane, DMS)-b-poly(2,2,3,3,4,4,4-hep-tafluorobutyl methacrylate, HFBMA)-b-poly(styrene, St)(PDMS-b-PHFBMA-b-PS) combines the unique propertiesof silicone polymers with those of fluorinated polymers[1–3]. Incorporation of siloxane moieties and fluorinatedgroups into synthetic materials/fluorosilicone polymersopens a way to various industrial applications. Thecomprehensive properties of these fluorosilicone (block)polymers are excellent, including weather resistance, lowsurface energy, chemical resistance, etc. [1–5]. On the otherhand, various fluorosilicone block copolymers have beenachieved mainly by living anionic polymerization [6–7]and atom transfer radical polymerization (ATRP) [8–9].No detailed research was done using the RAFT techniqueto prepare the PDMS-b-PHFBMA-b-PS copolymers. Accord-

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ingly, it is desirable to develop a novel approach to directlysynthesize PDMS-b-PHFBMA-b-PS copolymers.

Recently, a series of PDMS-b-PHFBMA-b-PS triblockcopolymers were prepared by two-step reversibleaddition–fragmentation chain transfer (RAFT) polymeriza-tion in our group [10], namely, the RAFT polymerization ofHFBMA using a PDMS-macro RAFT agent and the RAFTpolymerization of St using PDMS-b-PHFBMA-macro RAFTagent in succession. Our primary results showed thatPDMS-b-PHFBMA-b-PS triblock copolymers with well-defined structures were successfully synthesized via thetwo-step RAFT polymerization. The copolymer molecularweights measured by 1H NMR and GPC are close to thoseas predicted, and we can confirm that the two-step poly-merization proceeded in a controlled manner. It providesan applicable approach to the preparation of PDMS-containing block copolymers using a PDMS-macro RAFTagent with a xanthate group. However, the two-step RAFTpolymerization kinetics was not investigated [10]. In addi-tion, the effects of polymerization conditions, such as initiatorconcentration and feed composition, etc. on the two-step

Scheme 1. Synthetic scheme of the PDMS-b-PHFBMA-PS triblock copoly-mers via two-step RAFT polymerization.

Y.-n. Zhou et al. / European Polymer Journal 46 (2010) 2164–2173 2165

RAFT polymerization kinetics were not investigated. Inpractice, the polymerization kinetics is an important pro-portion of polymerization engineering, which describesthe changes of polymerization activity and polymer prop-erties dependent on polymerization time [11–12]. Thepolymerization kinetics can be described using modelequations. Moreover, the kinetic model can be used topredict the effects of polymerization conditions on thepolymerization kinetics [10].

Several papers [11–15] have been published concerningthe kinetic modeling of RAFT polymerization processes.Although interest in the RAFT polymerization is great, thereappear to be no models reported in the open literature atpresent to address the modeling of the two-step RAFTprocess using a functional PDMS-macro RAFT agent to pre-pare PDMS-b-PHFBMA-b-PS block copolymers. In addition,no studies have been reported that consider the influence ofpolymerization condition choice on the two-step RAFTpolymerization using a functional PDMS-macro RAFTagent. This paper aims to develop the RAFT polymerizationkinetics and to use these model equations to predict theeffects of polymerization conditions, such as initiator con-centration, chain transfer agent concentration and mono-mer concentration, etc. on the polymerization kinetics.

2. Experimental

The experimental section in this work is close to thatreported in our previous work [10]. Here, in order to keepthe study complete, the experimental section was stilldescribed in brief.

2.1. Syntheses of PDMS-b-PHFBMA-b-PS diblock copolymers

Syntheses of PDMS-b-PHFBMA-b-PS triblock copoly-mers were described previously [10]. The PDMS-b-PHFBMA-b-PS triblock copolymers were prepared bytwo-step RAFT polymerization from dithioester groupend-capped PDMS (PDMS-macro RAFT agent, T1) (seeScheme 1). As shown in Scheme 1, PDMS-macro RAFTagent was prepared from bromine end-capped PDMS(PDMS-Br) and PDMS-Br was obtained via the esterifica-tion reaction of 2-bromoisobutyrylbromide with a com-mercially available PDMS-OH. The polymerization ofHFBMA (M1) using AIBN (I) as initiator was used to preparethe PDMS-b-PHFBMA diblock copolymers, which are usedas PDMS-b-PHFBMA-macro RAFT agent (T2) for the nextRAFT polymerization of St (M2). In addition, the secondstep RAFT polymerization of St used AIBN (I) as initiatorand was used to prepare the PDMS-b-PHFBMA-b-PStriblock copolymers.

As described above, AIBN was used as the initiator ofthe typical RAFT polymerization of HFBMA or St. AIBNand the RAFT agent were charged into a dry two-neck flaskalong with a magnetic stirrer bar. Vacuum was then ap-plied and the flask was flushed with nitrogen, which wasrun for three times. Monomer (HFBMA or St) and toluenewere added to the flask using degassed syringes. The solu-tion was flushed with nitrogen as described above, and washeated to 60 �C by an oil bath. Samples were taken period-

ically with a syringe. The reaction was stopped after 5 h.The reaction mixtures were diluted with THF, and precipi-tated in methanol. The obtained polymer was rinsed withmethanol for several times and dried to constant weightunder vacuum at 50 �C. Concerning the syntheses andcharacterizations of PDMS-b-PHFBMA-b-PS triblock copoly-mers, readers are encouraged to refer to our previous work[10].

2.2. Measurements

The polymer conversion was recorded as a function oftime and the polymerization rate was calculated by furtherdifferentiation. The monomer conversion was measured bygravimetry via drying the samples to constant weight invacuum at 50 �C. Besides, Fourier transform infrared (FTIR)spectra were recorded from KBr pellets on a Nicolet Avatar360 FTIR spectrophotometer. The polymers sampled weremeasured by nuclear magnetic resonance (1H NMR) on aBruker AV400 NMR spectrometer in deuterated chloro-form. The molecular weight (Mn) and molecular weightdistribution (Mw/Mn, PDI) of the polymers sampled weredetermined at 40 �C by gel permeation chromatographyGPC. GPC was carried out using tetrahydrofuran (THF) ata flow rate of 1 ml/min, with a Waters 1515 isocratic HPLCpump equipped with a Waters 2414 refractive index detec-tor and three Waters Styragel HR columns (1 � 104,1 � 103, and 500 Å pore sizes). Monodisperse polystyrenestandards were used for calibration.

3. Kinetic modeling of the two-step RAFT process

3.1. Polymerization scheme

As described in Scheme 1, the present polymeriza-tion process to prepare PDMS-b-PHFBMA-b-PS triblock

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copolymers composes of two steps of RAFT polymeriza-tions, namely, the RAFT polymerization of HFBMA usingPDMS-macro RAFT agent and the next RAFT polymeriza-tion of St using PDMS-b-PHFBMA-macro RAFT agent. Boththe two steps of polymerizations involve the RAFT reactionin the presence of a macromolecular RAFT agent. Therefore,the above two polymerization schemes are still similar tothose of the classical RAFT processes reported in Ref.[16–20,21]. According to Refs. [16–20,21], the followingpolymerization scheme is applied in this work:

I!f ;kd 2P�0; ð1Þ

P�r þM!kp

P�rþ1 r ¼ 0;1;2; . . . ; ð2Þ

P�r þ TPs!ka Pr

_TPs!kf

TPr þ P�s ; ð3Þ

P�r þ P�s!ktd Pr þ Ps; ð4Þ

P�r þ P�s!ktc Prþs; ð5Þ

Pr_TPs þ P�t !

kct Prþsþt; ð6Þ

where, I is the initiator (AIBN), Pr_TPs is the intermediate

radical chain, TPr is the dormant chain, P�r is the propagat-ing radical chain, M is the monomer (HFBMA or St) and Pr

is the dead chain. In addition, Eq. (1) is the chain initiationwith kd as the rate constant and with f as the initiator effi-ciency due to cage effect. The factor 2 in Eq. (1) accountsfor the fact that one initiator molecule normally generatestwo radicals. Eq. (2) is the chain propagation with kp as thechain propagation rate constant. The subscript r representsthe number of monomeric units that have been incorpo-rated into the chain. In addition, one can know that thevalue of the rate constant for above each step is indepen-dent on the chain length. Eq. (3) is the addition and frag-mentation reactions. T represents the chain-transfer-agentunit; ka and kf are the addition and fragmentation rate con-stants, respectively. Eqs. (4)–(6) are the bimolecular radicaltermination by disproportionation (ktd), combination (ktc)and cross-combination (kct).

3.2. Defining chain moments and deriving moment equations

We use the method of moments [14,20–21]. There arefour types of chain species involved in the RAFT system:P�r , Pr

_TPs, TPr and Pr . Their corresponding moments aredefined as follows:

Yi ¼X1

r¼0

ri½P�r �; ð7Þ

YTi ¼

12

X1

r¼0

riXr

s¼0

½Pr�s_TPs�; ð8Þ

YTi;j ¼

X1

r¼0

X1

s¼0

risj½Pr_TPs�; ð9Þ

Q Ti ¼

X1

r¼0

ri½TPr�; ð10Þ

Q i ¼X1

r¼0

ri½Pr �; ð11Þ

On the other hand, for the species including the fourtypes of chain species, the initiator and the monomerinvolved in the RAFT system, the following mass balanceequations can be derived:

for P�r ;d½P�r �

dt¼ kp½P�r�1�½M� þ

12

kf

X1

s¼0

½Pr_TPs� � kp½P�r �

� ½M� � ka½P�r �QT0 � ktd½P�r �Y0

� ktc½P�r �Y0 � kct½P�r �YT0; ð12Þ

for Pr_TPs;

d½Pr_TPs�

dt¼ ka½P�r �½TPs� þ ka½P�s �½TPr �

� kf ½Pr_TPs� � kct½Pr

_TPs�Y0; ð13Þ

forTPr;d½TPr �

dt¼ 1

2kf

X1

s¼0

½Pr_TPs� � ka½TPr �Y0; ð14Þ

forPrd½Pr �

dt¼ ktd½P�r �Y0 þ

12

ktc

Xr

s¼0

½P�s �½P�r�s� � kct

�Xr

s¼0

½P�r�s�12

Xs

t¼0

½Pt_TPs�t �; ð15Þ

forI;d½I�dt¼ �kd½I�; ð16Þ

forM;d½M�

dt¼ �kp½M�Y0; ð17Þ

Based on the method of moments and Eqs. (1)–(17)[14,20–21], the following moment equations can beobtained:

dY0

dt¼ R1 þ kf YT

0 � kaY0Q T0 � ktdY0Y0 � ktcY0Y0

� kctY0YT0; ð18Þ

dYT0

dt¼ kaY0Q T

0 � kf YT0 � kctY0YT

0; ð19Þ

dQT0

dt¼ kf Y

T0 � kaY0Q T

0; ð20Þ

dQ0

dt¼ ktdY0Y0 þ

12

ktcY0Y0 þ kctY0YT0; ð21Þ

dY1

dt¼ kpY0½M� þ

12

kf YT1 � kaY1QT

0 � ktdY0Y1

� ktcY0Y1 � kctY1YT0; ð22Þ

dYT1

dt¼ kaY1Q T

0 þ kaY0QT1 � kf YT

1 � kctY0YT1; ð23Þ

Fig. 1. Comparison between experimental and simulated data of mono-mer conversion versus polymerization time for the RAFT polymerizationof HFBMA. (Experimental data 1 stands for the RAFT polymerization withmolar ratio of each component of [M1]/[T1]/[I] = 50:1:1; Experimentaldata 2 stands for the RAFT polymerization with molar ratio of eachcomponent of [M1]/[T1]/[I] = 30:1:1).

Y.-n. Zhou et al. / European Polymer Journal 46 (2010) 2164–2173 2167

dQT1

dt¼ ktdY0Y1 þ ktcY0Y1 þ kctY1YT

0 þ kctY0YT1; ð24Þ

dQ1

dt¼ 1

2kf YT

1 � kaY0Q T1; ð25Þ

dY2

dt¼ kpY0½M� þ 2kpY1½M� þ

12

kf YT2;0 � kaY2Q T

0

� ktdY0Y2 � ktcY0Y2 � kctY2YT0; ð26Þ

dYT2

dt¼ kaY2Q T

0 þ 2kaY1QT1 þ kaY0QT

2 � kf YT2 � kctY0YT

2;

ð27Þ

dQT2

dt¼ 1

2kf YT

2;0 � kaY0Q T2; ð28Þ

dQ2

dt¼ ktdY0Y2 þ ktcY0Y2 þ ktcY1Y1 þ kctY0YT

2

þ 2kctY1YT1 þ kctY2YT

0; ð29Þ

dYT2;0

dt¼ kaY2QT

0 þ kaY0QT2 � kf YT

2;0 � kctY0YT2;0; ð30Þ

In addition, the number-average chain lengths (rN;tot , Mn),weight-average chain lengths (rW;tot , Mw) and polydispersityindex (PDI) for the total chain population can be describedas follows [19–21]:

rN;tot ¼Y1 þ YT

1 þ Q1 þ QT1

Y0 þ YT0 þ Q0 þ QT

0

; ð31Þ

rW;tot ¼Y2 þ YT

2 þ Q 2 þ Q T2

Y1 þ YT1 þ Q 1 þ Q T

1

ð32Þ

PDI ¼ rW ;tot

rN;tot: ð33Þ

Corresponding initial conditions are described via thefollowing equations:

YT0 ¼ 0; ð34Þ

Q T0 ¼ ½CTA�0; ð35Þ

Q 0 ¼ 0; ð36Þ

Y1 ¼ 0; ð37Þ

YT1 ¼ 0; ð38Þ

Q T1 ¼ 0; ð39Þ

Q 1 ¼ 0; ð40Þ

Y2 ¼ 0; ð41Þ

YT2 ¼ 0; ð42Þ

Q T2 ¼ 0; ð43Þ

Q 2 ¼ 0; ð44Þ

YT2;0 ¼ 0; ð45Þ

½I� ¼ ½I�0; ð46Þ

½M� ¼ ½M�0; ð47Þ

The model, i.e., Eqs. (12)–(47), consists of a set of stiff,ordinary differential equations for the RAFT process ofHFBMA or St. The ODE23S-function provided in Matlab6.5 software is used to solve the ordinary differentialequations.

4. Results and discussion

4.1. Kinetic constant estimation and model verification

As to the two steps of polymerization, many kineticexperiments at different polymerization conditions, includ-ing initiator concentration, chain transfer agent concentra-tion, monomer concentration, etc., are accomplished [22].Corresponding experimental data are obtained. However,the kinetic constant estimation results obtained by fittingthe experimental data with Eqs. (12)–(47) according toleast-square method are similar. In addition, we also findthat the errors between the fitting data obtained via Eqs.(12)–(47) and the experimental data are almost equal. Cor-responding correlation coefficients for the experimentaldata are also almost equal (>0.98). Here, four of the repre-sentative sets of the results are shown in Figs. 1–4 due tolimited space. The obtained model parameters are shownin Table 1.

Figs. 1–4 illustrate that the comparisons between theexperimental data and the simulated results during thetwo RAFT polymerizations at two feed compositions. Thesimulated results meet experimental data well. The corre-lation coefficients of Eqs. (12)–(47) for corresponding

Fig. 2. Comparison between experimental and simulated data of Mn

versus monomer conversion for the RAFT polymerization of HFBMA.(Polymerization conditions same as Fig. 1).

Fig. 3. Comparison between experimental and simulated data of mono-mer conversion versus polymerization time for the RAFT polymerizationof St. (Experimental data 1 stands for the RAFT polymerization with molarratio of each component of [M2]/[T2]/[I] = 100:1:1; Experimental data 2stands for the RAFT polymerization with molar ratio of each componentof [M2]/[T2]/[I] = 200:1:1).

Fig. 4. Comparison between experimental and simulated data of Mn

versus monomer conversion for the RAFT polymerization of St. (Poly-merization conditions same as Fig. 3).

Table 1Optimal rate constants for the two-step RAFT polymerization.

RAFTpolymerization k

RAFT polymerizationof HFBMA

RAFT polymerizationof St

kd/s 1.12 � 10�5 1.00 � 10�5

kp/(L/(mol s)) 5.21 � 103 5.02 � 103

ka/(L/(mol s)) 0.92 � 107 1.00 � 107

kf/s 5.00 � 104 5.00 � 104

ktd/(L/(mol s)) 1.03 � 108 1.01 � 108

ktc/(L/(mol�s)) 0.98 � 108 1.00 � 108

kct/(L/(mol�s)) 1.12 � 108 1.00 � 108

Fig. 5. The simulated monomer conversion versus polymerization time atdifferent initiator concentrations for the RAFT polymerization of HFBMA.

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experimental data all exceed 0.98. The above resultsindicate that the kinetic model provide a reasonable fit ofthe experiment data.

When the model was testified, it was used to investi-gate the effects of initiator concentration, chain transferagent concentration and monomer concentration, etc. onthe RAFT polymerization kinetics. In this work, asdescribed in Scheme 1, the model was used to the RAFTpolymerizations of HFBMA and St, respectively.

4.2. Model application in the RAFT polymerization of HFBMA

4.2.1. The effects of initiator concentrationFigs. 5–7 describe the simulated effects of initiator con-

centration on the polymerization kinetics. From Figs. 5 and

6, one can know that the monomer conversion increasesand the number-average molecular weight of polymerskeeps unchanged basically with the increase of initiatorconcentration, which is consistent with that described byEqs. (1)–(6). Eqs. (1, 2) show that the increase of initiator

Fig. 6. The simulated Mn versus monomer conversion at differentinitiator concentrations for the RAFT polymerization of HFBMA.

Fig. 7. The simulated PDI versus polymerization time at different initiatorconcentrations for the RAFT polymerization of HFBMA.

Fig. 8. The simulated monomer conversion versus polymerization time atdifferent chain transfer agent concentrations for the RAFT polymerizationof HFBMA.

Fig. 9. The simulated Mn versus monomer conversion at different chaintransfer agent concentrations for the RAFT polymerization of HFBMA.

Y.-n. Zhou et al. / European Polymer Journal 46 (2010) 2164–2173 2169

concentration leads to the increase of monomer consum-ing and number-average molecular weight of polymers.However, the increase of initiator concentration also leadsto the increase of occurrence probabilities of the chaindeactivation as described in Eqs. (4)–(6), which leads tothe decrease of number-average molecular weight of poly-mers. Combined effects of Eqs. (1)–(6) leads to the nearlyconstant change of number-average molecular weight ofpolymers. Furthermore, with the increase of initiatorconcentration, the polydispersity index decreases in theearly period of polymerization (t 6 2� 103s) and increasessince then (t 6 2� 103s) as shown in Fig. 7.

On the other hand, one can also obtain some messagesregarding the RAFT polymerization kinetics via any onecurve including in Figs. 5–7. For instance, Fig. 5 shows thatthe monomer conversion increases with the polymeriza-tion proceeding at constant polymerization condition.The linearity of Fig. 6 and the narrow molecular weight

distributions (PDI < 1.2) at t P 2� 103 of Fig. 7 stronglyimply that the polymerization of HFBMA proceeds in aliving controlled/living manner, which can also obtainedin the following simulated results.

4.2.2. The effects of chain transfer agent concentrationThe chain transfer agent plays a key role in the RAFT

polymerization. In addition, as described in Sections 2and 3, different from ordinary RAFT processes, the RAFTprocess of HFBMA reported in this work uses the PDMS-macro RAFT agent as a RAFT agent. Here, the effect ofPDMS-macro RAFT agent concentration on the polymeriza-tion kinetics is simulated via the above model. Correspond-ing simulated results are illustrated in Figs. 8–10.

Fig. 8 shows that the monomer conversion increaseswith the polymerization proceeding at constant polymeri-zation condition. In addition, Fig. 8 also shows that themonomer conversion decreases with the increase of chaintransfer agent concentration. From Fig. 9, one can observe

Fig. 11. The simulated monomer conversion versus polymerization timeat different monomer concentrations for the RAFT polymerization ofHFBMA.

Fig. 12. The simulated Mn versus monomer conversion at differentmonomer concentrations for the RAFT polymerization of HFBMA.

Fig. 10. The simulated PDI versus polymerization time at different chaintransfer agent concentrations for the RAFT polymerization of HFBMA.

2170 Y.-n. Zhou et al. / European Polymer Journal 46 (2010) 2164–2173

the linearity and the number-average molecular weight ofpolymers decreases with the increase of chain transferagent concentration. However, Fig. 9 also shows that thelinearity of kinetic curve decreases with the decrease ofchain transfer agent concentration, which proves that thechain transfer agent concentration has important influenceon the living ability of the RAFT polymerization. Further-more, It can be seen from Fig. 10 that the polydispersityindex increases in the early period of polymerization(t 6 7� 103) and decreases since then with the increaseof chain transfer agent concentration. The above simulatedresults are similar to those obtained by Wang and Zhu [21].In addition, Wang and Zhu also explained the results basedon Eqs. (1)–(6). Therefore, here, we do not discuss theabove results.

4.2.3. The effect of monomer concentrationIn the present study, the effect of monomer concentra-

tion on the polymerization kinetics is also simulated via

Fig. 13. The simulated PDI versus polymerization time at differentmonomer concentrations for the RAFT polymerization of HFBMA.

Fig. 14. The simulated monomer conversion versus polymerization timeat different initiator concentrations for the RAFT polymerization of St.

Y.-n. Zhou et al. / European Polymer Journal 46 (2010) 2164–2173 2171

the above model and the simulated results are shown inFigs. 11–13.

Fig. 11 shows that the monomer conversion keepsunchanged basically with the increase of monomer con-centration. As described in Fig. 12, at the same monomerconversion, the number-average molecular weight of poly-mers increases with the increase of the monomer concen-tration. Furthermore, it can be seen from Fig. 13 that withthe increase of initiator concentration, the polydispersityindex first increases and then decreases. However, thewhole change is low. In practice, the above results can bedescribed via Eqs. (1)–(6).

4.3. Model application in the RAFT polymerization of St

4.3.1. The effects of initiator concentrationFigs. 14–16 describe the simulated effects of initiator

concentration on the polymerization kinetics for the RAFT

Fig. 15. The simulated Mn versus monomer conversion at differentinitiator concentrations for the RAFT polymerization of St.

Fig. 16. The simulated PDI versus polymerization time at differentinitiator concentrations for the RAFT polymerization of St.

polymerization system of St. The same results as thoseobtained from Figs. 5–7 based on the RAFT polymerizationof HFBMA can be observed from Figs. 14–16. In practice, forthe RAFT polymerizations of HFBMA and St, their mecha-nisms described in Eqs. (1)–(6) are the same. Correspond-ingly, their rate constants described in Table 1 obtainedby least-square method are the same. Therefore, the effectsof initiator concentration on the two polymerizationsystem are the same although the chain transfer agentsused in the two systems are different.

4.3.2. The effects of chain transfer agent concentrationAs described earlier, for the RAFT polymerizations of

HFBMA and St, their chain transfer agents are PDMS-macroRAFT agent and PDMS-b-PHFBMA-macro RAFT agent,respectively. In addition, the effects of PDMS-macro RAFTagent on the RAFT polymerization of HFBMA are simulated

Fig. 17. The simulated monomer conversion versus polymerization timeat different chain transfer agent concentrations for the RAFT polymeri-zation of St.

Fig. 18. The simulated Mn versus monomer conversion at different chaintransfer agent concentrations for the RAFT polymerization of St.

2172 Y.-n. Zhou et al. / European Polymer Journal 46 (2010) 2164–2173

and shown in Figs. 8–10. Here, the effects of PDMS-b-PHFBMA-macro RAFT agent on the RAFT polymerizationof St are simulated via the above model. Figs. 17–19describe the simulated effects of chain transfer agent con-centration on the polymerization kinetics for the RAFTpolymerization system of St.

Comparing Figs. 17–19 with Figs. 8–10, one can knowthat the effects of the two chain transfer agents are similarand their influence degrees are different yet. Here, theeffect of the chain transfer agent on the polydispersityindex is emphasized. It can be seen from Fig. 19 that thepolydispersity index increases in the early period of poly-merization (t 6 5� 103) and decreases since then withthe increase of chain transfer agent concentration. How-ever, Fig. 10 shows that the polydispersity index increasesin the early period of polymerization (t 6 7� 103) anddecreases since then with the increase of chain transferagent concentration. Namely, at the same concentrationof chain transfer agent concentration, the change of

Fig. 19. The simulated PDI versus polymerization time at different chaintransfer agent concentrations for the RAFT polymerization of St.

Fig. 20. The simulated monomer conversion versus polymerization timeat different monomer concentrations for the RAFT polymerization of St.

polydispersity index comes at a faster rate for the RAFTpolymerization of St than that of HFBMA.

4.3.3. The Effect of monomer concentrationFigs. 20–22 describe the simulated effects of monomer

concentration on the polymerization kinetics for the RAFTpolymerization system of St. The same results as thoseobtained from Figs. 11–13 based on the RAFT polymeriza-tion of HFBMA can be observed from Figs. 20–22. As de-scribed in Section 4.3.3, for the RAFT polymerizations ofHFBMA and St, both their mechanisms described in Eqs.(1)–(6) and rate constants described in Table 1 obtainedby least-square method are identical. Therefore, the effectsof monomer concentration on the two polymerizationsystem are identical although the chain transfer agentsused in the two systems are different. In addition, we alsopoint out that the influence degrees of the two monomersare different.

Fig. 21. The simulated Mn versus monomer conversion at differentmonomer concentrations for the RAFT polymerization of St.

Fig. 22. The simulated PDI versus polymerization time at differentmonomer concentrations for the RAFT polymerization of St.

Y.-n. Zhou et al. / European Polymer Journal 46 (2010) 2164–2173 2173

5. Conclusions

The PDMS-b-PHFBMA-b-PS triblock copolymers wereprepared by two-step RAFT polymerization in a batch reac-tor. A comprehensive mathematical model for the two-step RAFT polymerization was presented using the methodof moments. Good agreements in the polymerizationkinetics were achieved for fitting the kinetic profiles withthe suggested model. In addition, the model was used topredict the effects of initiator concentration, chain transferagent concentration and monomer concentration on thetwo-step RAFT polymerization kinetics.

The simulated results showed that for the two-stepRAFT polymerizations, the effects initiator concentration,chain transfer agent concentration and monomer concen-tration are identical and the influence degrees are differ-ent. The simulated results showed that the monomerconversion increases and the number-average molecularweight of polymers keeps unchanged basically, the poly-dispersity index first decreases and then increases withthe increase of initiator concentration for the two-stepRAFT polymerizations. The simulated results also showedthat the monomer conversion and the number-averagemolecular weight of polymers are both decrease and thepolydispersity index first increases and then decreaseswith the increase of chain transfer agent concentrationfor the two-step RAFT polymerizations. Finally, the simu-lated results proved that the monomer conversion keepsunchanged basically and the number-average molecularweight of polymers increases, the polydispersity index firstincreases and then decreases with the increase of themonomer concentration for the two-step RAFT polymer-izations. More detailed results are shown in Sections 4.2and 4.3.

Acknowledgement

The joint financial supports for this research wereprovided by the National Natural Science Foundation ofChina (No. 20406016), Nation Defense Key Laboratory ofOcean Corrosion and Anti-corrosion of China (No.51449020205QT8703), and Fujian Province Science andTechnology Office of China (No. 2005H040). The authorsacknowledge the State Key Laboratory of Physical Chemis-try of Solid Surfaces at Xiamen University for providingAFM facilities and assistance.

References

[1] Grunlan MA, Mabry JM, Weber WP. Synthesis of fluorinatedcopoly(carbosiloxane)s by Pt-catalyzed hydrosilylation copolymeri-zation. Polymer 2003;44:981–7.

[2] Ameduri B, Boutevin B. Well-architectured fluoropolymers:synthesis, properties and applications. Amsterdam: Elsevier; 2004.p. 103.

[3] Ameduri B, Boutevin B, Caporiccio G, Guida-Pietrasanta F,Ratsimihety A. Fluoropolymers. New York: Kluwer Academic Press;1999. p. 67.

[4] Guida-Pietrasanta F, Boutevin B, Ratsimihety A. Silcon containingpolymers: the science and technology of the synthesis andapplications. New York: Kluwer Academic Press; 2001. p. 54.

[5] Luo ZH, He TY. Synthesis and characterization of poly(dimethy-lsiloxane)-b-poly(2,2,3,3,4,4,4-heptafluorobutylmethacrylate) diblockcopolymers with low surface energy prepared by atom transferradical polymerization. React Funct Polym 2008;68:931–42.

[6] Bellas V, Iatrou H, Hadjichristidis N. Controlled anionicpolymerization of hexamethylcyclotrisiloxane: model linear andmiktoarm star co- and terpolymers of dimethylsiloxane with styreneand isoprene. Macromolecules 2000;33:6993–7.

[7] Saam JC, Gordon DJ, Lindsey S. Block copolymers ofpolydimethylsiloxane and polystyrene. Macromolecules 1970;3:1–4.

[8] Luo ZH, He TY, Yu HJ, Dai LZ. A novel ABC triblock copolymer withvery low surface energy: poly(dimethylsiloxane)-block-poly(methylmethacrylate)-block-poly(2,2,3,3,4,4,4-heptafluorobutyl methacrylate).Macromol React Eng 2008;2:398–406.

[9] Luo ZH, Yu HJ, Zhang W. Microphase separation behavior on thesurfaces of poly(dimethylsiloxane)-block-poly(2,2,3,3,4,4,4-heptaflu-orobutyl methacrylate) diblock copolymer coatings. J Appl Polym Sci2008;113:4032–41.

[10] Guan CM, Luo ZH, Qiu JJ, Tang PP. Novel fluorosilicone triblockcopolymers prepared by two-step RAFT polymerization: synthesis,characterization, and surface properties. Eur Polym J2010;46:1582–93.

[11] Wang R, Luo Y, Li BG, Zhu S. Control of gradient composition in ATRPusing semibatch feeding policy. AIChE. J. 2007;53:174–86.

[12] Sun X, Luo Y, Wang R, Li BG, Liu B, Zhu S. Programmed synthesis ofcopolymer with controlled chain composition distribution viasemibatch RAFT copolymerization. Macromolecules 2007;40:849–59.

[13] Russum JP, Jones CW, Schork FJ. Continuous reversible addition–fragmentation chain transfer polymerization in miniemulsionutilizing a multi-tube reaction system. Macromol Rapid Commun2004;25:1064–8.

[14] Wang R, Luo Y, Li BG, Sun XY, Zhu SP. Design and control ofcopolymer composition distribution in living radical polymerizationusing semi-batch feeding policies: a model simulation. MacromolTheory Simul 2006;15:356–68.

[15] Soriano-Moro G, Jaramillo-Soto G, Guerrero-Santos R, Vivaldo-LimaV. Kinetics and molecular weight development of dithiolactone-mediated radical polymerization of styrene. Macromol. React. Eng.2009;3:178–84.

[16] Zhang M, Ray WH. Modeling of ‘‘living” free-radical polymerizationprocesses. I. Batch, semibatch, and continuous tank reactors. J ApplPolym Sci 2002;86:1630–62.

[17] Altarawneh IS, Gomes VG, Srour MS. The influence of xanthate-basedtransfer agents on styrene emulsion polymerization: mathematicalmodeling and model validation. Macromol. React. Eng. 2008;2:58–79.

[18] Tobita H. Fundamental molecular weight distribution of RAFTpolymers. Macromol. React. Eng. 2008;2:371–81.

[19] Zargar A, Schork FJ. Copolymer sequence distributions in controlledradical polymerization. Macromol React Eng 2009;3:118–30.

[20] Zhang M, Ray WH. Modeling of ‘‘living” free-radical polymerizationwith RAFT chemistry. Ind Eng Chem Res 2001;40:4336–52.

[21] Wang AR, Zhu SP. Modeling the reversible addition–fragmentationtransfer polymerization process. J Polym Sci Pol Chem 2003;41:1553–66.

[22] Guan CM. Synthesis of fluorosilicone block copolymers by RAFTpolymerization and kinetic simulation. Master Dissertation, XiamenUniversity, Xiamen, China, 2010.