Article pubs.acs.org/IECR
Modeling of the Atom Transfer Radical Copolymerization Processes of Methyl Methacrylate and 2‑(Trimethylsilyl) Ethyl Methacrylate under Batch, Semibatch, and Continuous Feeding: A Chemical Reactor Engineering Viewpoint Wei Wang, Yin-Ning Zhou, and Zheng-Hong Luo* Department of Chemical Engineering, School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China S Supporting Information *
ABSTRACT: A kinetic model was developed for the atom transfer radical copolymerization (ATRcoP) of methyl methacrylate (MMA) and 2-(trimethylsilyl) ethyl methacrylate (HEMA-TMS) in tank reactors under three typical feeding modes, namely, batch, semibatch, and continuous feeding. The kinetic parameters for ATRcoP equilibrium were estimated from the model using the experiment data obtained under the batch mode. The simulation results were validated using the experimental data for the semibatch process. An excellent agreement between experiment and simulation data suggests that the model is suitable for simulating the copolymerization. The effects of different operating modes on the ATRcoP characteristics were investigated. The results demonstrated that each reactor possesses its own advantages and disadvantages. Furthermore, this study offers thorough polymerization characteristics comparison with the use of a constant ATRcoP system, and the results show a promising design in determining the optimal operating conditions of quasiliving copolymerization, such as ATRcoP, in varying reactors.
1. INTRODUCTION The capacity of controlling the sequence structure of macromolecules is importance in polymer science. This capacity has been reflected in quasiliving radical polymerizations,1 such as nitroxide-mediated radical polymerization (NMP), reversible addition−fragmentation chain transfer polymerization, and atom transfer radical polymerization (ATRP).2−6 Among them, ATRP is known as a robust method to well control the polymer chain structure.7−10 In general, three typical reactor operation modes, i.e., batch, semibatch, and continuous feeding, can be applied for any polymerization in stirred tank reactors.11 The combination of ATRP and reactor operation mode provides a flexible polymer production policy that has synergy between the polymer structure and production yield. Different processes with varied operation modes yield different polymer products and production yields even at the same copolymerization system.12,13 Therefore, quantitative evaluation of the influence of the reactor operation mode on copolymerization kinetics, polymer structure, and production yield is important. These parameters are significant in industries, particularly in the ATRP reactors. Many studies have focused on the ATRP engineering field,13−30 especially on the ATRP kinetics in a laboratory-scale batch reactor.14−21 However, batch reactors are unsuitable for scale-up because an increase in reactor size decreases the ratio of surface area to volume. Semibatch mode provides better temperature control and superior management of copolymer composition by controlling the monomer feed.22−27 The combination of the semibatch mode with ATRP is hindered by inherently slower polymerization kinetics. Luo, Li, and Zhu at Zhejiang University and McMaster University, and Cunningham and Hutchinson at Queen’s University, have conducted studies using semibatch ATRP technology by experiment and simulation approaches.28−31 © XXXX American Chemical Society
In addition, continuous feeding mode in tank reactors provides more consistent product quality and higher reactor productivity than the batch mode. Moreover, long reaction time becomes less of a disadvantage, and the higher space/time yield makes it more feasible to employ ATRP on an industrial scale.32,33 Recently, an overview of solution ATRPs performed in batch, semibatch, and continuous tubular and stirred tank reactor systems has been Table 1. Elementary Reactions of ATRcoP Initiation ka , kda
RX + C ←⎯⎯→ R• + CX k in,i
R• + Mi ⎯⎯⎯→ RM•i,1 Propagation k p, ij
RM•i , r + Mj ⎯⎯⎯→ RM•j , r + 1 ka, i , kda, i
RMi , rX + C ←⎯⎯⎯⎯⎯→ RM•i , r + CX Termination k tc,ij
RM•i , r + RM•j , s ⎯⎯⎯→ RM r + sR k td, ij
RM•i , r + RM•j , s ⎯⎯⎯⎯→ RMi , r + RMj , s Transfer k tr,, ij
RM•i , r + Mj ⎯⎯⎯⎯→ RMi , r + M•j
Received: April 10, 2014 Revised: July 2, 2014 Accepted: July 9, 2014
A
dx.doi.org/10.1021/ie501467g | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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ethyl methacrylate (HEMA-TMS) is used as the model system because such system has been previously studied experimentally (previous ATRcoP experiments were performed in semibatch tank reactors).27,35 First, the kinetic parameters for ATRP equilibrium are estimated from the model correlations based on the experimental data obtained from the batch mode. Second, the kinetic model is validated via the semibatch mode experiments. Finally, the kinetic model, with the use of the same system and from the reactor engineering viewpoint, is applied to thoroughly investigate the effect of the feeding model on the ATRcoP characteristics under batch, semibatch, and continuous tank operating modes.
Table 2. Moment Definitions for Different Types of Polymer Chains type of chains
definition of moment ∞
RMi,r
μim =
∑ r m[RM•i ,r] r=1 ∞
RMi,rX
λ im =
∑ r m[RMi ,rX] r=1
∞
RMi+sR
ψm =
∑ r m[RM r+ sR] r=1 ∞
RMi,r
ϕm =
∑ r m[RMi ,r] r=1
2. MODEL DEVELOPMENT 2.1. Reaction Mechanism and Kinetic Equations of ATRcoP. Several accepted assumptions that simplify the model are listed as follows:27,28,36−41 (1) The terminal model is considered while the penultimate effect is neglected. (2) The rate constants are assumed as chain length independent, i.e., chain length does not affect the reaction rate constants. (3) Only coupling and disproportion termination reactions are considered. (4) Only chain transfer to monomer is considered. (5) Side reactions such as thermal initiation and elimination reaction are neglected. Table 1 shows the considered elementary reactions of ATRP process based on the assumptions. 2.2. Method of Moments. The kinetic equations for each type of reaction components are listed in Table S1 (Supporting Information). The method of moments is used to simplify the calculation. The kinetic equations of polymer chains can be replaced by limited moment equations based on the definition of moments. Meanwhile, the average properties of the copolymers such as number-average chain length (rn), polydispersity index (PDI), instantaneous copolymer composition (Fi), and chain-end functionality (Ft) can then be described. Four types of polymer chains exist in the system: (1) living chains (RM•i,r); (2) dormant chains (RMi,rX); (3) dead chains formed by coupling termination (RMr+sR); and (4) dead chains generated by termination or chain transfer to monomer (RMi,r). Tables 2 and 3 show the moments of each type of chain and the average properties of the polymers, respectively. The moment equations for various species are shown in Table S2 (Supporting Information). 2.3. Reactor Model. A general tank reactor model is developed to analyze the ATRcoP process in the batch reactor, semibatch reactor, and single continuous stirred tank reactor (CSTR). The following assumptions were employed in the current study: (1) the reaction system is homogeneous, and thus,
Table 3. Average Properties of Copolymer average properties of copolymer
mathematical expression
number-average chain length
rn =
weight-average chain length
rw =
polydispersity index
∑i (μi1 ∑i (μi 0
Fi =
chain-end functionality (batch and CSTR)
Ft =
chain-end functionality (semibatch)
Ft =
+ λi0)+ϕ0 + ψ 0
∑i (μi 2 + λi2)+ϕ2 + ψ 2 ∑i (μi1 + λi1)+ϕ1 + ψ 1
PDI =
instantaneous copolymer composition
+ λi1)+ϕ1 + ψ 1
rw rn
k in,i[R•][Mi] + ∑j k p, jiμ0j [Mi] ∑i k in,i[R•][Mi] + ∑i ∑j k p, jiμ0j [Mi] [RX] + ∑i λi0 •
[RX] + [R ] + ∑i μi 0 + ∑i λi0 + 2ψ 0 + ϕ0
([RX] + ∑i λi0)V [RX]0 V0
reported. In this overview, the advantages and disadvantages of ATRPs at different feeding modes are described based on varying polymer systems.34 Although each feeding mode has been applied in ATRP stirred tank reactors, no systematic study that assess their copolymerization kinetics within the same system has been conducted, which makes the quantitative understanding of the effect of reactor operating mode on the ATRP characteristics including kinetics remain unclear. Thus, the effect of reactor operating mode on the ATRP characteristics should be investigated further. Moreover, the advantages and disadvantages for the same ATRP system from the reactor engineering viewpoint are still unknown. In this study, we develop a common tank reactor model (i.e., an ATRcoP kinetic model coupled with a reactor model), which is suitable for three different operating modes. The ATRcoP of methyl methacrylate (MMA) and 2-(trimethylsilyl)
Table 4. Mass Balance Equations for Batch Reactor, Semi-Batch Reactor, and Single CSTR type of reactor
volume flow rates
volume change
mass balance equations
batch
dV =0 dt
Q In = Q Out = 0
dCi = r(i) dt
semibatch
dV = Q In dt
Q In ≠ 0, Q Out = 0
Q (Ci0 − Ci) dCi = r(i) + In dt V
single CSTR
dV =0 dt
Q In = Q Out ≠ 0
dCi C − Ci = r(i) + i0 τ dt
B
dx.doi.org/10.1021/ie501467g | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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isothermal conditions to eliminate the need to consider energy balance. On the basis of these assumptions, the mass balance equation for species i in a tank reactor can be described as follows: Q InCi0 = Q OutCi − Vr(i) +
d(VCi) dt
(1)
i.e., dCi 1⎛ dV ⎞⎟ = r(i) + ⎜Q InCi0 − Q OutCi − Ci ⎝ dt V dt ⎠
(2)
where QIn, QOut, Ci0, Ci, r(i), and V represent volume flow rate of input, volume flow rate of output, initial concentration of i, final concentration of i, reaction rate of i, and total volume of the reaction system, respectively. In a batch reactor, no input or output exists of materials (QIn = QOut = 0); therefore, the total volume of the mixture is constant (dV/dt = 0). In a semibatch reactor, materials input is the only factor causing volume change (dV/dt = QIn). In a single CSTR, the volume of the reaction system remains unchanged (dV/dt = 0) because QIn = QOut ≠ 0. The mass balance equations for the three reactors are summarized in Table 4. 2.4. Model Implementation. The ODE23S-function provided in MATLAB 2012b (8.0) software is used to solve the differential moment equations for the different kinds of reactors to obtain various polymer properties such as monomer conversion (Xi), rn, PDI, Fi, and Ft, etc.
3. RESULTS ATRcoP of MMA and HEMA-TMS in batch reactor, semibatch reactor, and single CSTR are systematically studied. MMA, HEMA-TMS, Eib-Br, CuBr, and CuBr2 are represented as MA, MB, RX, C, and CX, respectively. 3.1. Estimation of Kinetic Constants and Model Validation. The values of rate constants are independent from the operating mode of reactor, thus ka,A, ka,B, kda,A, and kda,B can be obtained by fitting to data of batch copolymerization experiments using the method of least-squares. Herein, the obtained kinetic data from the batch experiment are first used to estimate the activation and deactivation kinetic parameters. The fitted curves of corresponding experimental data are shown in Figure 1. Other kinetic parameters are directly obtained from references as shown in Table 5. The semibatch experimental data reported in a previous study were used to validate the present model.27 Figure 2A shows the development of monomer mole versus time. The propagating reactions expend a lot of MMA in a short period of time, because of a high concentration of fast monomer (i.e., MMA) and a negligible amount of slow monomer (i.e., HEMATMS) in the system at the beginning. This reaction results in a high MMA conversion. As the polymerization proceeds, the concentration of MMA decreases, whereas the HEMA-TMS concentration increases gradually; therefore, the consumption of MMA decelerates. Figure 2B shows the evolution of PDI and average chain length. Figure 2 shows that the simulation results agree well with the experimental data, thereby indicating that the developed model can be employed for further simulation regarding the effects of different reactor operating modes, monomer molar ratios, and feeding rates on copolymer properties. 3.2. Model Application in Investigating the Effect of the Reactor Operating Mode: Batch Reactor. The effect of monomer molar ratio on polymer properties is considered in
Figure 1. Experimental data of batch ATRcoP of MMA and HEMATMS and corresponding fitted curves: (A) semilogarithmic kinetic plot of MMA, (B) semilogarithmic kinetic plot of HEMA-TMS, and (C) molecular weight vs time. Experimental conditions: [Eib-Br] = 1.026 × 10−2 mol/L; [CuBr] = 0.5[dNbpy] = 1.342 × 10−2 mol/L; [CuBr2] = 6.709 × 10−4 mol/L; VTotal = 11.7 mL; [HEMA-TMS] = 3[MMA] = 3.846 mol/L for Expt.1; [MMA] = [HEMA-TMS] = 2.564 mol/L for Expt.2.
the concentration of each component is constant in the reactor; (2) volume contributions from the solvent, monomer, and polymer are considered, whereas those of the initiator, activator, and deactivator are neglected; (3) density difference between monomer and polymer is neglected, and thus, the volume change of the reaction system caused by the consumption of monomers and formation of polymer chains can be ignored; and (4) the reactions are assumed to be under C
dx.doi.org/10.1021/ie501467g | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Table 5. Kinetic Rate Constants for the ATRcoP of MMA and HEMA-TMS in Simulationa
a
rate constants
values
refs
kin,A,kp,AA (L/mol s) kin,B,kp,BB (L/mol s) ktc,AA (L/mol s) ktd,AA (L/mol s) ktc,BB (L/mol s) ktd,BB (L/mol s) r1 r2 ktr,AA (1/s) ktr,BB (1/s) kt,AB,kt,BA (L/mol s) ktr,AB,ktr,BA (1/s) ktc,AB,ktc,BA (L/mol s) ktd,AB,ktd,BA (L/mol s) kt,AA (L/mol s) kt,BB (L/mol s) ka (L/mol s) kda (L/mol s) ka,A (L/mol s) ka,B (L/mol s) kda,A (L/mol s) kda,B (L/mol s)
106.427 exp[−22 360/(RT)] 106.954 exp[−21 900/(RT)] 1.0 × 107 ktc,AA × 2.57 × 103 exp[−17 113/(RT)] 0.99 × 106 1.1 × 105 0.86 0.66 0.0198 0.0122 (kt,AA × kt,BB)1/2 (ktr,AA × ktr,BB)1/2 (ktc,AA × ktc,BB)1/2 (ktd,AA × ktd,BB)1/2 (ktc,AA + ktd,AA) = 9.9 × 107 (ktc,BB + ktd,BB) = 1.1 × 106 (ka,A + ka,B)/2 (kda,A + kda,B)/2 1.2853 1.2051 1.2597 × 106 1.2216 × 107
42 43 44 44 45 45 46 46 27 27 47 use the method in ref 47 use the method in ref 47 use the method in ref 47 this work this work this work this work this workb this workb this workb this workb
HEMA-TMS (use parameters of HEMA by analogy). bObtained by experimental data fitting.
Figure 2. Comparisons between simulation results and experimental data from ref 27 for the semibatch ATRP process: (A) mole number of monomer vs time and (B) PDI and number-average chain (rn) vs time.
copolymerization, thereby decreasing monomer conversions. Nevertheless, the final monomer conversions of MMA and HEMA-TMS are still excellent (∼80%) even when the initial proportion of MMA is as high as 0.75. Figure 3B depicts the evolution of molecular weight (MW) and PDI with respect to total monomer conversion (XTotal) in a batch reactor. The simulation result shows that even though a linear relationship between MW and XTotal for each monomer molar ratio is obtained, the PDI value gradually decreases with XTotal and eventually levels at a value
