An old kinetic method for a new polymerization mechanism: … · 2020. 6. 16. · these processes, excess ligand acts as an electron donor. In general ATRP process, initiation, propagation,

An Old Kinetic Method for a New Polymerization Mechanism:Toward Photochemically Mediated ATRP

Yin-Ning Zhou and Zheng-Hong LuoDept. of Chemical Engineering, School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University,

Shanghai 200240, P.R. China

DOI 10.1002/aic.14792Published online March 29, 2015 in Wiley Online Library (wileyonlinelibrary.com)

With the idea of “an old method for a new mechanism,” a detailed kinetic insight into photochemically mediated atom-transfer radical polymerization (photo ATRP) was presented through a validated comprehensive model. The simulationmimics the experimental results of the model system using optimized photochemically mediated radical generation ratecoefficients. The activator and radical (re)generated from the photo mediated reactions endow the photo ATRP withunique features, such as rapid ATRP equilibrium and quick consumption of initiator with a small amount of residual.The effect of the reaction parameters on ATRP behaviors was also investigated. Results showed that the acceleration ofpolymerization rate follows the square root law in the following three cases: the overall photochemically mediated radi-cal generation rate coefficients (kr), the free ligand concentration, and the initiator concentration. However, the inde-pendence of the apparent propagation rate coefficient (kappp ) on the square root of catalyst concentration might beattributed to the result of the synergy between the activators regenerated by electron-transfer ATRP and the initiatorsfor continuous activator regeneration ATRP mechanism. The photo ATRP is able to design and prepare various poly-mers by carefully tuning the conditions using the model-based optimization approach.VC 2015 American Institute of Chemical Engineers AIChE J, 61: 1947–1958, 2015Keywords: photochemically mediated ATRP, kinetic model, parameter estimation, model-based optimization

Introduction

The increasing demand of polymer production in our soci-ety has led to significant development in macromolecularreaction engineering.1 As a branch of chemical reaction engi-neering that plays an important function in various industrialfields, macromolecular reaction engineering follows similarprinciples to produce and process the polymeric materials.Specifically, three major questions need to be answered:“How far?,” “How fast?,” and “How to?”1,2 For each spe-cific reaction, the first question is commonly based on aclarified reaction mechanism and can be answered by ther-modynamics. Subsequently, kinetic studies are carried out toanswer the second question. Using a well-built kinetic modelwith proper kinetic rate coefficients, one can design andoperate reactor systems, and discriminate the reaction mech-anisms including new, pendent, or controversial mechanism.Finally, the model-based optimization of reaction conditionsand the choice of reactor can determine how a structurallywell-defined and cost-effective product is prepared.2 Theaforementioned core knowledge indicates that kinetic investi-gation remains an important issue in the chemical reactionengineering field, although it is an old method.3

The development of the chemistry field has led to the emer-gence of numerous new experimental and analytical methods thathelp scientists to discover new chemical reactions. An exampleof a research focused on macromolecular chemistry is the reversi-ble deactivation radical polymerization (RDRP) techniques,which have been studied since their discovery a couple of deca-des ago.4,5 Among these techniques, atom-transfer radical poly-merization (ATRP) has been researched extensively because oftheir brilliant ability in preparing polymers with well-defined andcomplex architectures.6–8 However, the industrialization ofATRP technique still has a long way to go, which includes mech-anism and kinetics study, although a few achievements havealready been made.9 In ATRP, the use of low oxidation statetransition-metal catalyst (commonly CuI salt) inevitably leads tocontamination of products and time-consuming deoxygenationprocess.9–11 Scientists have been focusing on diminishing the cat-alyst dosage and applying high oxidation state catalytic complexor metallic copper through experimental and kinetic modelinginvestigations.12–26 For example, initiators for continuous activa-tor regeneration (ICAR) ATRP,13–16 activators regenerated byelectron transfer (ARGET) ATRP,17–19 single electron transfer-living radical polymerization (SET-LRP),20–22 supplemental acti-vator and reducing agent (SARA) ATRP,23–25 and electrochemi-cally mediated ATRP (eATRP)26 have been investigated.Previous studies have indicated that well-constructed mathemati-cal models are useful for kinetics studies, and can be applied tosimulation,15,19,22 optimization,15,22 parameter estimation,16 con-trol,19 and mechanistic investigation24,25 of polymerizationprocesses.

Additional Supporting Information may be found in the online version of thisarticle.

Correspondence concerning this article should be addressed to Z. H. Luo [email protected].

VC 2015 American Institute of Chemical Engineers

AIChE Journal 1947June 2015 Vol. 61, No. 6

Photo ATRP have attracted significant attention becauseof its facile operation and minimal addition of catalyst.27–52

Among the non-copper photo ATRP techniques, Hawkeret al. developed an efficient and facile technique for poly-merization of methyl methacrylate (MMA) and a series ofacrylate monomer using an Ir-based photoredox catalyst.31,32

More recently, an important development of light-inducedliving polymerization was presented almost simultaneouslyby Hawker and coworkers and Miyake et al., which realizeda metal-free ATRP with an organic visible-light photocata-lyst.36,37 In traditional Cu-mediated ATRP, Guan and Smartdiscovered that the rate and livingness of ATRP can be sig-nificantly improved under visible light irradiation.39 Yagciand coworkers reported UV light-induced ATRP of MMAthrough directly reduction of CuIIX2/L to Cu

IX/L complex.41

In addition, polymerization was enhanced by using methanolas solvent, causing the reaction to proceed in a homogeneoussystem.42 Mosn�aček and Ilč�ıkov�a carried out UV light-mediated ATRP in a system with low Cu catalyst.44 Subse-quently, Matyjaszewski and coworkers investigated the effectof light sources on photoinduced ATRP by applying blue,violet LEDs, or even sunlight.45 At that time, the mechanismheld in these works were subject to a hybrid system ofICAR ATRP and ARGET ATRP in the presence of a stoi-chiometric ligand.41–45 However, detailed investigations pub-lished by Haddleton and Matyjaszewski showed that a well-controlled polymerization should be carried out in a systemwith excess ligand, and the light-induced ATRP is anARGET-dominated system with limited contribution fromthe ICAR mechanism.46–49 Overall, with the merit of light inthe temporal and spatial control of polymerization, photoATRP has attracted increasing interest and has been used tosynthesize the multiple-block copolymers and surface micro-patterns.50–52 However, no detailed kinetic study for thismechanism based on a well-built model has been conducted.

According to the above descriptions, kinetics and its mod-eling are old topics in chemical engineering, but remain acore issue in polymerization engineering. Furthermore, pho-tochemically mediated ATRP with newly clarified reactionmechanism needs a thorough investigation for its application.Accordingly, with the idea of “an old method for a newmechanism,” a comprehensive kinetic model of photo ATRP

was developed in this work for the first time using themethod of moments. The proposed photo ATRP mechanismis illustrated in Scheme 1. The presented model was vali-dated by experimental data, and then used as a convenientand powerful tool to estimate the rate coefficients of photo-chemically radical (re)generation reactions based on methylacrylate (MA) model system, which was carried out indimethyl sulfoxide (DMSO) at 25�C. A kinetic simulation,as a supplement to the experiments, described the detailedinformation of all the species and reactions during the poly-merization. Finally, the effects of reaction conditions, includ-ing the strength of light-induced reactions and theconcentrations of free ligand, catalyst, and initiator on thekinetic behavior of photo ATRP were determined to under-stand and optimize the reaction process.

Kinetic Model and Computational Method

According to the proposed mechanism, all the relevantreactions and original rate coefficients are listed in Table 1.In the case of this specific system, the radicals generatedfrom photochemical reactions include several parallel path-ways, such as the reduction of CuIIX2/L deactivator(CuIIX2 5 CuBr2, L 5 Me6TREN) in the presence of excessligand (free L), the photochemical SET reaction betweeneither an alkyl halide initiator [P0X 5 ethyl 2-bromoisobutyrate (Eib-Br)] or a macroinitiator (PrX 5 PMA-Br) with excess ligand, the unimolecular P0X photochemicalhomolytic cleavage of the carbon-halogen bond, or the pho-tochemical SET between excess ligand and monomer. Inthese processes, excess ligand acts as an electron donor. Ingeneral ATRP process, initiation, propagation, activation–deactivation equilibrium, chain transfer to ligand or initiator,and termination were considered in the kinetic model. How-ever, chain transfer to the monomer, solvent, and polymerthat led to branch formation was neglected under the presentpolymerization conditions.20,24,25 Aside from the conven-tional radical termination, the reaction of CuIX/L mediatedradical loss for secondary radicals was previously confirmedas the reason for the additional end functionality loss, andwas thus taken into account.56 Although the small radicals(re)generated from the photochemical and transfer reactionswere essentially different, they are assumed to have similarreactivity in this work to simplify the simulations. It shouldbe noted that an updated new propagation rate coefficient ofMA (1.30 3 104 M21 s21 at 298 K) estimated by Barner-Kowollik et al.59 is lower than that used in this work (1.563 104 M21 s21 at 298 K), which will slow down the overallrate of polymerization. However, to compare our simulationresults with previous work reported by Ribelli et al.,48 theused value of kp was the same as that in Ribelli et al.’swork.

Molar balance equations for all species in the reactionscan be established, as listed in Table 2. Pr

�(l), PrX(k), andPr(s) denote the propagating radical chain, dormant chain,and dead chain species with the length of chain (r),respectively.

The numerical analysis of the kinetic equations listed inTable 2 can be easily conducted on a well-developedapproach, that is, the method of moments. This method is aclassical one that is suitable for kinetic study of the radicalpolymerization processes, as published in previous works byZhu, D’Hooge, and our group.1,18,25,60–68 The methodologyis implemented by defining the moments for the chain

Scheme 1. The proposed mechanism of the photo-chemically mediated ATRP.

[Color figure can be viewed in the online issue, whichis available at wileyonlinelibrary.com.]

1948 DOI 10.1002/aic Published on behalf of the AIChE June 2015 Vol. 61, No. 6 AIChE Journal

http://wileyonlinelibrary.com

species first, and then a set of moment equations can beobtained accordingly. Detailed information is provided inSupporting Information Tables S1 and S2. By calculating themodel equations in MATLAB 2012b (8.0), the concentra-tions of all reaction species, reaction rates, and a series ofpolymerization properties can be obtained as follows:

Reaction rates

Rred;CL5kr;C2L CuIIX2=L

� �L½ � (1)

Rred;IL5kr;I2L P0X½ � L½ � (2)

Rred;MIL5kr;MI2L PrX½ � L½ � (3)

Rred;I5kr;I P0X½ � (4)

Rred;LM5kr;L2M P0X½ � L½ � (5)

Rp5kp½M�½Pr �� (6)

Ra5ka½CuIX=L�½PrX� (7)

Rd5kd½CuIIX2=L�½Pr �� (8)

Rtr5ktr;L P�r

� �L½ �1ktr;I P�r

� �P0X½ � (9)

Rt5kt0 P�0

� �P�0� �

1ktR P�r

� �P�0� �

1kt P�r

� �P�s� �

1kt;C P�r

� �CuIX=L� �

(10)

Number-average molecular weight (Mn)

Mn5Mmonomer

Xk11l11s1� �

Xk01l01s0� � (11)

Weight-average molecular chain length (Mw)

Mw5Mmonomer

Xk21l21s2� �

Xk11l11s1� � (12)

Molecular weight distribution (Mw=Mn)

Mw=Mn5

Xk21l21s2� �

Xk01l01s0� � (13)

Chain-end functionality (Ft)

Ft5k0� �

P0X½ �1 P�0� �

r;C2L1 P�0� �

r;L2M1 P�0� �

tr;L

(14)

Results and Discussion

Simulation of photochemically mediated ATRP

The experimental data (black circle) were obtained fromthe work as reported by Ribelli et al.48 under the followingconditions: [MA]0:[Eib-Br]0:[CuBr2]:[Me6TREN]0 5 300:1:0.03:0.18, [MA] 5 7.4 M, MA/DMSO 5 2/1 (v/v), with 392-nm UV light irradiation and at 25�C. The simulations werefirst conducted at the identical conditions, which can becompared with the results presented in Ribelli’s work. Usingthe original rate coefficients listed in Table 1, the simulationresults in Figure 1 (blue dash lines) shows slower polymer-ization rate and lower conversion than the experimental datawithin 25,000 s. The conversion of MA reached 98% whenthe simulation time was prolonged to 80,000 s, as shown inSupporting Information Figure S1. The evolution trends ofthe polymerization outcomes (i.e., ln([M]0/[M]t), Mn, Mw/Mn,and Ft) are similar to those in previous work,

48 which implythe reliability of the model developed in this study.

A linear semilogarithmic kinetic plot is expected to beobserved in a well-controlled ATRP system, which indicates

Table 1. Reactions for Photochemical ATRP Used in Simulation

Type of Reaction Scheme Rate Coefficient at 298 Ka Reference

Photochemical radical (re)generationbCuIIX2=L1L��!kr;C2L CuIX=L1L1�1X2 1:0 3 1023 48P0X 1 L��!kr;I-L P�01L1�1X2 6:2 3 1026 48PrX 1 L��!kr;Ml-L P�r1L1�1X2 1:4 3 1026c 48P0X��!kr;I P�01X� 2:9 3 1029 48L1M��!kr;L-M L1�1M2� 1:5 3 1029 48

Initiation P0X1CuIX=L�ka0

kd0P�r1Cu

IIX2=L 2:0 3 103 24,53

5:0 3 107

P�01M�!kin P�1 7:3 3 102 54,55Propagation P�r1M�!kp P�r11 1:56 3 104 54ATRP equilibrium PrX1Cu

IX=L�ka0kd0

P�r1CuIIX2=L 2:0 3 10

2 242:8 3 108

Transfer P�r1L��!ktr;L Pr1L� 2:8 3 103 48P�r1P0X��!ktr;I Pr1P0X� 2:3 3 102 48

Conventional radical terminationd P�01P�0�!kt0 P0P0 2:0 3 109 58

P�r1P�0�!ktr PrP0 2:0 3 109 58

P�r1Ps � ��!kt5ktd1ktc PrH1P5s or Pr1s 1:0 3 108 58Catalytic radical termination P�r ��!kt ;CCuIX=L PrH or P5r 4:0 3 103 48

aThe units for all rate coefficients are M21 s21, except that of kr,I is expressed in s21.

bThe rate coefficients of photochemical radical (re)generation were also estimated in this work for comparing with those from Ref. 48.cIn the case of MA system, because secondary PMA-Br chain end closely resembles methyl 2-bromopropionate (MBP), kr,MI-L of PMA-Br uses the kr,I-L ofMBP by analogy.48dktc and ktd represent the combination and disproportionation termination rate coefficients with the values of 0.9kt and 0.1kt, respectively.

56,57

AIChE Journal June 2015 Vol. 61, No. 6 Published on behalf of the AIChE DOI 10.1002/aic 1949

the constant concentration of radicals through the reaction.However, an apparent induction period was observed beforethe rapid polymerization for this specific system, whichmight be attributed to the slow reduction of CuBr2/L inresponse to UV light and the slow initiation of monomer bythe EibBr initiator. In the case wherein original rate parame-ters were used, the time to complete the induction is nearly5 h, as clearly shown in Supporting Information Figure S3A,which is longer than that observed in the experimental result.According to the mechanism shown in Table 1, the rate ofthe photochemical generation of radicals in the system isslower than that of the initiation reaction; thus, the light-induced reactions can be thought of as the rate-controllingsteps. Therefore, the increase in photochemically mediatedreaction rate can shorten the induction period.

With the idea in mind, a preliminary attempt was pro-posed in two steps. The four photochemical reduction ratecoefficients (i.e., kr;I2L, kr;MI2L, kr;I, and kr;L2M) werederived from the model experiments with no Cu based onthe steady-state approximation, and proportionated to anassumed radical termination rate coefficient (kt).

48 Conse-quently, the value of kt significantly affected the results ofthe derived rate coefficients. In addition, the radical termina-tion was predominated by the termination involving smallmolecular radical during the reaction. In the first attempt, thevalues of these four rate coefficients increased to 20 times aslarge as the original values according to the kt value(2:0 3 109 M21 s21) used in this work, which is 20 times aslarge as that (1:0 3 108 M21 s21) used in previous work.48

As shown in Figure 1 (green dash-dot lines), the induction

period of polymerization was shortened to approximately2.5 h, and the conversion reached 68% after 7 h. However,the polymerization rate was still slower than the experimen-tal result. In addition to the above four rate coefficientsrelated to the termination rate coefficient, kr;C2L denotes thereduction of CuBr2/L with excess ligand and derived fromthe semilogarithmic kinetic plot for the model experimentsin the presence of Cu.48 Herein, kr;C2L was considered anindependent variable that can be adjusted to the experimentaldata. In the second step, an encouraging result showing arapid polymerization rate and meeting the experimentalresults was achieved by doubling the value of kr;C2L, asshown in Figure 1 (red lines). Notably, the induction periodwas further decreased (2 h), which cannot be avoided totallybecause of the utilization of CuBr2/L and the relatively slowrate of the photochemically mediated radical generation. Inaddition, the chain-length dependent termination might be afactor of the deviation of simulation results from experimen-tal data in this system at high conversion. This complicateddescription is usually included in the detailed models of, forexample, D’hooge and Zhu et al.1,61,63,64,69,70

Figure 1B shows the linear evolutions of Mn with conver-sion for the three cases from the start of polymerization tothe end. The simulation results matched well with the experi-mental data, although the conversions within the simulationtime scale were different. The evolutions of Mw/Mn shownin Figure 1C were similar and decreased quickly after estab-lishment of ATRP equilibrium. Addition of CuBr2/L led toan inevitable induction period, but can considerably changethe polymerization behavior and improve the property of the

Table 2. Kinetic Equations for All Species in Photochemical ATRP

Type Mass Balance Equations

MacromoleculesPropagating radical

chainsd Pr

�½ �dt

5kp Pr21�½ � M½ �2kp Pr �½ � M½ �1ka PrX½ � CuIX

� �2 kd Pr

�½ � CuIIX2� �

1kr;MI-L½PrX�½L�2ktr; L½Pr ��½L�2

ktr; I½Pr ��½P0X�2ktR½Pr ��½P0 ��2X1s51

ktc1ktdð Þ Pr �½ � Ps �½ �2kt; C Pr �½ � CuIX� �

Dormant chains d½Pr X�dt 5kd½Pr ��½Cu

IIX2�2ka½PrX�½CuIX�2kr;MI-L½PrX�½L�

Dead chains d Pr½ �dt

5ktr; L½Pr ��½L�1ktr; I½Pr ��½P0X�1ktR Pr �½ � P0 �½ �1X1s51

ktd Pr�½ � Ps �½ �1

1

2

Xrs51

ktc Ps�½ � Pr2s �½ �1kt; C Pr �½ � CuIX

� �

Small molecules

Monomer d M½ �dt 52kr; L-M L½ � M½ �2kin P0 �½ � M½ �2kp Pr �½ � M½ �

Initiator d P0X½ �dt

52kr; I-L L½ � P0X½ �2kr; I P0X½ �1kd0 CuIIX2� �

P0�½ �2ka0 CuIX

� �P0X½ �2ktr; I Pr �½ � P0X½ �

Primary radical d P0�½ �

dt5kr; C-L Cu

IIX2� �

L½ �12kr; I-L P0X½ � L½ �1kr; MI-L PrX½ � L½ �12kr; I P0X½ �1

2kr; L-M L½ � M½ �2kin P0 �½ � M½ �1ka0 CuIX� �

P0X½ �2kd0 CuIIX2� �

P0�½ �1

ktr; L Pr�½ � L½ �1ktr; I Pr �½ � P0X½ �22kt0 P0 �½ � P0 �½ �2ktR Pr �½ � P0 �½ �

Activator d½CuIX�dt

5kr; C-L CuIIX2

� �L½ �1kd0 CuIIX2

� �P0�½ �2ka0 CuIX

� �P0X½ �1

kd CuIIX2

� �Pr�½ �2ka CuIX

� �PrX½ �

Deactivator d½CuIIX2�dt

52kr; C-L CuIIX2

� �L½ �1ka0 CuIX

� �P0X½ �2kd0 CuIIX2

� �P0�½ �1ka CuIX

� �PrX½ �2kd CuIIX2

� �Pr�½ �

Ligand d L½ �dt

52kr; C-L CuIIX2

� �L½ �2kr; I-L P0X½ � L½ �2kr;MI-L PrX½ � L½ �2kr; L-M L½ � M½ �2ktr; L Pr �½ � L½ �


resulting polymer.24,25 On one hand, no polymer with longchain-length formed at the start of the reaction because ofthe sufficient deactivator that can suppress the irreversibleradical termination and govern the reaction based on persis-tent radical effect.71 On the other hand, the time to attainATRP equilibrium decreased significantly compared withthose of other ATRP systems that used CuBr/L as catalyst;the polydispersity index can reach as low as 1.02. The devia-tion between the simulation and experimental results at lowconversion region is mainly caused by the adoption of idealconditions during simulation. In addition, the test error mightbe another factor for this result. Figure 1D demonstrates thefraction of polymer chains with livingness. A high conver-sion causes the decrease of end functionality; however, thepolymer chains still have high livingness (>96%) because ofthe mechanism of all RDRP techniques involving irreversibleradical termination. Even in photo ATRP, that is only mini-mized. In practice, rate coefficients depend not only on reac-tion temperature, but also on the property of reactant. Forexample, radical termination rate coefficient has beendescribed as chain-length dependence composite model.69,70

Overall, a set of accurate rate coefficients is important forsimulation, although obtaining such coefficients is a formida-ble task. The preliminary attempt based on a well-builtkinetic model causes the simulation to meet well with practi-cal experiment under polymerization conditions, indicatingthat an appropriate adjustment of photochemically mediatedradical generation rate coefficients improves the fitness ofsimulation without disrupting the ATRP equilibrium.

Estimation of photochemically mediated radicalgeneration rate coefficients

From the chemical engineering perspective, parameterestimation through a well-built kinetic model is a useful andefficient method, especially in situations wherein experi-ments cannot be carried out easily. In this study, all of thefive photochemical reduction rate coefficients were estimatedfrom the kinetic experimental data [ln([M]0/[M]t) vs. time]from the open report.48 To ensure the accuracy of the result-ing parameters, five sets of data at different conditions werechosen for the estimation based on least-square error calcula-tion method. The standardized residual analysis of rate coef-ficients estimation is shown in Supporting InformationFigure S2. In Figures 2A–C, the fitting curves describe wellthe characteristics of photo ATRP under specific conditionsand are consistent with the experimental data, with one criti-cal exception (black triangular symbol). The estimatedkinetic parameters with the corresponding 95% confidenceintervals are summarized and listed in Figure 2D. By com-parison, these constants and the above adjusted parametersare in the same order of magnitude. The following kineticinvestigations were carried out using the present rateparameters.

Concentration of reactants and rate of reactions forphotochemically mediated ATRP

Using the developed model and estimated rate coefficients,the overall variation of the reactants and the relevant reaction

Figure 1. Comparison of the simulation results with the experimental data for photo ATRP of MA from Ref. 48: (A)semilogarithmic kinetic plot; (B) evolution of Mn with conversion; (C) evolution of Mw/Mn with conversion;(D) evolution of end functionality with conversion.

[Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]



rates were determined under the following conditions:[MA]0:[Eib-Br]0:[CuBr2]:[Me6TREN]0 5 300:1:0.03:0.18, [MA]5 7.4 M, MA/DMSO 5 2/1 (v/v), with 392-nm UV light irradia-tion at 25�C.

In response to UV light irradiation, a series of photo-chemically mediated radical generation reactions was trig-gered, as proposed in Table 1. The activator Cu(I) wasgenerated through the reduction of deactivator Cu(II) withfree L, followed by the activation of initiator (P0X) (Figure3A). The radical generated from the photochemical reactionand ATRP activation initiated the monomer (M) to begin thepropagation [formation of growth radical species (Pr

�)]. Therate of propagation (Rp) first increased and then sloweddown at the end of the reaction because of the consumptionof monomer, as shown in Figure 3B. However, the existenceof deactivator Cu(II) can effectively deactivate both P0

� andPr�. Hence, it will maintain the Pr

� concentration at anextremely low level, which is typical to conventional ATRP,and leads to a small amount of P0X residual, which is aunique trait for photo ATRP (Figure 3A). Moreover, theexistence of Cu(II) can act with these continuously generatedphotochemical radicals (all have similar reactivity) to regen-erate P0X. With the proceeding of reaction and the establish-ment of ATRP equilibrium, the concentration of totalradicals (P0

� and Pr�) maintains at a low level, which leads

to a small amount of P0X residual. Another important char-acteristic of photo ATRP that benefited from excess Cu(II) isthe rapid establishment of ATRP equilibrium, which can beclearly confirmed by the evolution of [PrX] and the rates of

activation and deactivation, as depicted in Figure 3. In gen-eral, the time to reach steady state at a constant value of[PrX] is the transition period, which is needed to attain theATRP equilibrium. Based on the result, the time to reachsteady-state is as early as the start of polymerization. Therate of PrX activation (Ra) overlaps that of Pr

� deactivation(Rd) nearly from the beginning to the end of the reaction,which also demonstrates that the equilibrium is establishedquickly. From Figure 3A, the concentration of L decreasesslowly because of the relatively slow rates of the photochem-ical reactions (Rred,CL, Rred,IL, Rred,MIL, and Rred,LM) andtransfer reaction (Rtr), which are commonly five to sevenorders of magnitude slower than those of the ATRP reac-tions. Finally, given the unavoidable irreversible radical ter-mination and chain transfer, dead polymer accumulates withthe conversion, but its fraction is as low as 4.6%. As awhole, the detailed information of the photo ATRP systemwas vividly illustrated by the simulation, which is useful tounderstand the characteristics of photo ATRP.

Effect of overall photochemically mediated radicalgeneration rate coefficients on ATRP behaviors

In this specific system, the relevant reactions regulated byUV light are the five photochemically mediated radical gen-eration reactions. The light intensity might affect the ratecoefficients of these reactions and thus affect the polymeriza-tion. Using the developed model, the simulation of photoATRP under different overall photochemically mediated rad-ical generation rate coefficients (kr) was carried out and

Figure 2. The corresponding fitted results for the experimental data under different conditions from Ref. 48 usingthe developed model: (A) semilogarithmic kinetic plot; (B) evolution of Mn with conversion; (C) evolutionof Mw/Mn with conversion; (D) estimated results.




shown in Figure 4. The conditions are the same as thoseused in Figure 3. The kr value with 100% means that esti-mated coefficients (Figure 2D) were used and the kr valueswith 50, 75, 125, and 150% mean that all five coefficientswere simultaneously changed by the corresponding ratio.

From Figure 4A, the increase in kr not only shortens theinduction period but also increases the polymerization rate atsteady state, which is caused by the increase of the radicalgeneration rate. Specifically, the induction periods for differ-ent kr values with 50, 75, 100, 125, and 150% are 168, 150,132, 120, and 102 min, respectively. The evolution of induc-

tion time is inversely proportional to the square root of krmagnitude, as illustrated in Supporting Information FigureS3A. The polymerization rate at steady state can be deter-mined from the slope of the linear semilogarithmic kineticplot (after induction period), which indicates that the concen-tration of the radicals in the system is constant (see Eq. 15).The plot of the apparent propagation rate coefficient (kappp )with the square root of the kr magnitude in Supporting Infor-mation Figure S3B shows that the polymerization rate atsteady state is proportional to the square root of the kr mag-nitude. Actually, the square root relationship between the

Figure 3. Reactant concentrations (A) and reaction rates (B) for photo ATRP of MA.


Figure 4. Simulation of photo ATRP using different overall photochemically mediated radical generation rate coeffi-cients: (A) semilogarithmic kinetic plot; (B) evolution of Mn with conversion; (C) evolution of Mw/Mn withconversion; (D) evolution of end functionality with conversion.



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reaction rate and the reaction parameters are commonlyapplied to other ATRP24,25,48

Rphoto ATRP52d½M�

dt5kp½P��½M� ) ln

½M�0½M�t

� �5kp½P��t5kappp t

(15)

Figures 4B, C show that the evolutions of Mn and Mw/Mnwith conversion are overlapped. The linear evolution of Mnis consistent with theoretical Mn. Moreover, the evolution ofMw/Mn is lower than 1.5 at the start of polymerization andrapidly levels off to 1.04. The slight increase in Mw/Mn athigh conversion might be due to the lack of monomer, andthe regenerated radical can be mainly consumed through rad-ical termination. Finally, the end functionality thus decreasesto certain extent, but it is still as high as 94%. The abovesimulation results indicate that the change of kr within aproper range can increase the polymerization rate withoutthe loss of controllability.

Effect of the free ligand concentration on photo ATRPbehaviors

Previous experimental studies have indicated that the freeligand concentration ([free L]0) has an important role inphoto ATRP system.46,48 The most important result obtainedfrom the two pioneer works is that the free ligand is essen-tial for photo ATRP. No polymerization was observedthrough the simulation (Figure 2) at the condition that[CuBr2]0:[L]0 5 1:1 (i.e., no free ligand exists in the system).

Herein, the effect of the free ligand concentration on the out-come of photo ATRP was investigated by simulation, andthe results were depicted in Figure 5. The simulation condi-tions are similar to those used in Figure 3, except the freeligand concentration.

Figure 5A indicates that the increase in free ligand concen-tration has a positive effect on the polymerization rate. Theinduction period is suppressed with the increase in polymeriza-tion rate. Supporting Information Figure S4A shows that theinduction time almost linearly decreases from 270 to 90 minas [free L]0 increase. In addition, the linear relationship of k

appp

with the square root of the free ligand concentration, whichcan be observed in Supporting Information Figure S4B, is con-sistent with the experimental results.48 However, Mn andMn/Mw were found to be affected by the increase in [free L]0,which was ignored in the experimental study because of theexperimental errors. Based on the simulation results shown inFigures 5B, C, the evolution of Mn slightly deviates from theo-retical Mn at high conversion, and the polydispersity with high[free L]0 is relatively higher than that with low [free L]0 dur-ing polymerization. The drawbacks might be due to the gener-ation of nonliving polymer chains, such as those initiated bysmall molecular radical, the transfer to ligand, and the termina-tion by radicals. From the evolution of end functionality shownin Figure 5D, the lower the [free L]0 is, the higher is the endfunctionality. The main reason is that increasing ligand con-centration affects livingness through the transfer to ligand reac-tion shown in Table 1. As a whole, the investigation of thefree ligand concentration indicates that the polymerization rate

Figure 5. Simulation of photo ATRP using different free ligand concentrations: (A) semilogarithmic kinetic plot; (B)evolution of Mn with conversion; (C) evolution of Mw/Mn with conversion; (D) evolution of end functional-ity with conversion.




can be increased by increasing the [free L]0, but the controll-ability of the polymerization system would be slightly weak-ened. In addition, one can find that the polymerization rateshows the same functional response to the radical generationrate coefficients (Figure 4) and the ligand concentration (Fig-ure 5). This can be explained as radical generation rate is pro-portional to the product of the above two factors (Eqs. 1–5).

Effect of the catalyst concentration on photo ATRPbehaviors

The effect of catalyst concentration on ATRP system is amain concern in polymer science that needs to be addressed.Figure 6 shows the simulation results of photo ATRP usingdifferent catalyst concentrations. The simulation was per-formed by varying the catalyst concentration from 10 to 200ppm with respect to the monomer concentration.

Figure 6A and Supporting Information Figure S5A demon-strate that diminishing the catalyst concentration results in thedecrease of the polymerization induction time. Therefore, thecorresponding conversion increases at the same reaction time(Figure 6B). However, the reaction rates reflected by the slopeof the kinetic plot are nearly the same at different catalystconcentrations, as shown in Supporting Information FigureS5B. The result indicates that the polymerization rate does notdepend on the catalyst concentration, which is similar to theconventional ATRP without deactivator, but different from theother ATRP systems with deactivator, such as ICAR ATRPand ARGET ATRP. Generally, the absolute amount of cata-

lyst (commonly Cu species) in ATRP can be decreased undernormal ATRP conditions without affecting the rate of poly-merization, which is ultimately governed by a ratio of theconcentrations of Cu(I) to Cu(II) species.12 However, theunavoidable irreversible radical termination and the accumula-tion of persistent radical [Cu(II) deactivator] in practical poly-merization system leads to about 1–10% loss of polymericend functionality, unless there is larger enough catalyst con-centration (commonly> 1000 ppm).12 It is well known that adecrease in deactivator concentration causes an increase in thepolymerization rate of ICAR ATRP14 but slows downthe reaction rate of ARGET ATRP.19 For the former one, theactivator is continuously generated from the activation of thedeactivator by conventional initiator radical. If the amount ofthe initial deactivator is too low, the propagating radicalwould not be effectively deactivated by the deactivator,thereby accelerating of the polymerization rate and increasingpolydispersity index at the early stage of polymerization. Forthe latter one, the activator is gradually generated from thereduction of the deactivator by excess reducing agent. Thehigher the deactivator loading is, the higher is the amount ofthe activator. Therefore, the polymerization rate speeds up,and the controllability of polymerization is improved. Basedon the results in this system, the independence of kappp on theinitial catalyst concentration, (Figure 6A and Supporting Infor-mation Figure S5B), the higher polydispersity index at lowconversion (Figure 6C), and the loss of end functionality (Fig-ure 6D) might be the consequences of the synergistic effect ofARGET ATRP and ICAR ATRP. In this regard, the reduction

Figure 6. Simulation of photo ATRP using different catalyst concentrations: (A) semilogarithmic kinetic plot; (B)evolution of Mn with conversion; (C) evolution of Mw/Mn with conversion; (D) evolution of end functional-ity with conversion.




of CuBr2/L in the presence of excess ligand through UV lightstimuli resembles the ARGET ATRP process, and the photo-chemical SET reaction between either Eib-Br or PMA-Brwith excess ligand is similar to ICAR ATRP process. Herein,a bold but rational speculation is proposed that the mechanismof photo ATRP is a combination of ARGET ATRP andICAR ATRP, which coincides with the result obtained in aprevious work.48

Effect of the initiator concentration on photo ATRPbehaviors

A simulation was conducted to study the kinetic behaviorsof photo ATRP under different initial initiator concentration.Figure 7 shows that the initiator concentration has a signifi-cant effect on the polymerization kinetics.

As depicted in Figure 7A, the induction time is shortenedand the reaction rate speeds up as the initiator concentrationincreases. Interestingly, a linear relationship between kapppand the square root of the initiator concentration was alsoobserved in Supporting Information Figure S6B. In termsof this acceleration, the increase in [EibBr]0 (shorter tar-geted chain-length) causes the high radical concentration byshifting the ATRP equilibrium, and thus increases the poly-merization rate, which is the same as that in ICAR ATRPand ARGET ATRP processes.15,16,72 In addition, the photo-chemical reactions that involve the initiator might also con-tribute to this speed up. However, the relationship betweenthe polymerization rate and initiator concentration is to the

half power, which is an interesting point in this specificsystem as theoretically derived in Ribelli et al.’s work.48

Figure 7B shows that the evolution of Mn with conversionmatches the theoretical Mn well, and the long polymerchain-length is as expected because of the low [EibBr]0.The development of Mw/Mn in Figure 7C also indicates thatlow initiator concentration helps establish the ATRP equi-librium. This can be explained as a lower [EibBr]0 usuallyimplies a faster ATRP initiation, which is helpful forinstantaneously propagation.16 Based on the evolution ofend functionality, the result wherein low [EibBr]0 with lowradical concentration can lead to the decrease in end func-tionality seems impossible. According to Eq. 14, thedecrease in Ft is mainly due to the low dormant speciesconcentration, which is a determinant in the denominator(in the system, the concentration of the radical species ordead polymer species is extremely low). The above simula-tion results illustrate that the characteristics of photo ATRPunder different initiator concentrations are similar to butnot the same as those of ATRP processes with low initialCu loading.

Conclusion

To sum up, a case study of the kinetics of photochemi-cally mediated ATRP was carried out based on a newlyclarified mechanism through simulation approach. A compre-hensive kinetic model was developed using the method of

Figure 7. Simulation of photo ATRP using different initiator concentrations: (A) semilogarithmic kinetic plot; (B)evolution of Mn with conversion; (C) evolution of Mw/Mn with conversion; (D) evolution of end functional-ity with conversion.




moments, which is not only used to study the polymerizationbehaviors but also to estimate the uncertain reaction ratecoefficients.

In this specific case, the photochemically mediated radicalgeneration rate coefficients were first adjusted to the experi-mental data through the trial and error method. The as-developed model was then used to estimate five coefficients.The results indicate that the original coefficients derivedfrom the experiments are lower than the adjusted or esti-mated results and thus cause the simulation results to deviatefrom the experimental data. The evolution of reactants andthe rates of each reaction in photo ATRP system show theunique characteristics of photo ATRP, such as rapid ATRPequilibrium and quick consumption of small initiator with asmall amount of residual.

Simulations on the effects of overall photochemicallymediated radical generation rate coefficients (kr), as well asthat of the concentrations of the free ligand, catalyst, and ini-tiator on ATRP behaviors were also investigated. The resultsshow that the acceleration of polymerization rate can beachieved by increasing the kr, the free ligand concentration,or the initiator concentration. The development of kappp withthe square root of these three parameters is linear, which is atypical law followed by other ATRP processes. However,the independence of kappp on the square root of [CuBr2/L]was observed in this work. These results indicate that themechanism of photo ATRP is a combination of ARGETATRP and ICAR ATRP.

Overall, through the kinetic modeling (old method) ofphoto ATRP (new mechanism), the underlying mechanismand the optimization of polymerization condition were dem-onstrated in detail.

Acknowledgment

The authors thank the National Natural Science Foundationof China (No. 21276213), the Research Fund for the DoctoralProgram of Higher Education (No. 20130073110077), and theNational High Technology Research and Development Pro-gram of China (No. 2013AA032302) for supporting thiswork.

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Manuscript received Jan. 11, 2015, and revision received Feb. 27, 2015.


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An old kinetic method for a new polymerization mechanism: … · 2020. 6. 16. · these processes, excess ligand acts as an electron donor. In general ATRP process, initiation, propagation,