Predictive Tool for Design and Analysis of ARGET ATRP Grafting

Oct 6, 2017 - ... optimize the reaction and could save much effort, time and money. These results have severe implications when grafting polymer chain...
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Predictive Tool for Design and Analysis of ARGET ATRP Grafting Reactions John J. Keating IV,† Alexander Lee,† and Georges Belfort*,† †

Howard P. Isermann Department of Chemical and Biological Engineering and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, New York 12180, United States S Supporting Information *

ABSTRACT: Solving a comprehensive, yet simple, reaction model for describing the activators regenerated by electron transfer (ARGET)−atom transfer radical polymerization (ATRP) reaction cascade, we show that the molar ratios of transition metal catalyst to initiator and reducing agent to catalyst are critical parameters in the ARGET ATRP mechanism, with optimal values on the order of 0.1:1 and 10:1, respectively. The model also predicts an optimal molar ratio of reducing agent to initiator of 1:1. The ARGET ATRP reaction cascade is extremely complex with many adjustable species concentrations and reaction parameters. The effect of varying any of these parameters on the resulting temporal conversion trajectory of the polymerization is not straightforward. This analysis greatly simplifies the process allowing one to select the proper conditions to optimize the reaction and could save much effort, time and money. These results have severe implications when grafting polymer chains from surfaces, since the amount of surface-bound initiator is very low relative to the amount of catalyst. This suggests adding a sacrificial initiator to the reaction solution when grafting from surfaces is necessary to prevent loss of control on the polymerization. The most viable parameter for both increasing the polymerization rate and maintaining maximum attainable conversion for the ARGET ATRP system is to increase the reaction temperature. For broad use, the model was developed in MATLAB to predict conversion versus time behavior in the ARGET ATRP reaction cascade using an inexpensive ligand. Utilizing known rate constants and pre-exponential factors to the Arrhenius equations from the literature, the model was able to predict published experimental data for the methyl methacrylate (MMA), styrene (St), and glycidyl methacrylate (GMA) monomers at various temperatures. The main assumptions of the model are that termination reactions occur through radical coupling only and the propagation and termination reaction rates are chain length independent. The resulting model is shown to be very accurate, especially at conversions of 0.4 and lower. Sensitivity analyses were performed on the ARGET ATRP mechanism using MMA as a model monomer to identify key reaction parameters to ensure successful controlled polymerization.

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grown from this initiator.7 The development of reversibledeactivation radical polymerization (RDRP) techniques, such as atom transfer radical polymerization (ATRP)8 and reversible addition−fragmentation chain transfer (RAFT) polymerization,9 has allowed for well-defined polymer chains to be grafted from surfaces when compared with conventional free radical techniques. The introduction of these RDRP techniques was a major development toward materials design, since conventional free radical polymerization could not enable polymer chains to be grafted with narrow dispersity. Furthermore, conventional free radical polymerization is not capable of building advanced grafted polymeric architectures, such as block copolymers. The “livingness” of these RDRP techniques therefore greatly expands the horizon of surface functionalization to include morphologies previously unattainable.

INTRODUCTION The functionalization of surfaces with polymer chains has allowed for the design of materials with enhanced performance for a myriad of applications. Typical applications include hemocompatible devices,1,2 membrane separations,3 chromatography,4 antifouling coatings on ships,5 and stimuliresponsive materials,4 to name a few. Two methods are widely used to covalently attach, or graft, polymer chains to a surface. The “grafting-to” method involves the covalent attachment of preformed polymer chains to a surface through reaction between moieties contained on the free polymer chain and the surface.6 This method allows for precise control over the molecular weight and dispersity of the polymer chains but presents complications when high surface grafting densities are required due to the reduced transport of the relatively large, preformed polymer chains to the surface. In order to circumvent this diffusional limitation, “grafting-from” methods have been developed in which a smaller initiator molecule is reacted with the surface, and polymer chains are subsequently © XXXX American Chemical Society

Received: July 23, 2017 Revised: September 18, 2017

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DOI: 10.1021/acs.macromol.7b01572 Macromolecules XXXX, XXX, XXX−XXX

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In this work, a mathematical model is developed to predict the conversion of various monomers versus reaction time for the ARGET ATRP reaction using the inexpensive PMDETA ligand and, given rate constants and pre-exponential factors to the Arrhenius equations from the literature, verified against published experimental data. The experimental conversion data were obtained from polymer chains grown in solution in parallel with those grown on an added initiator-functionalized surface.16,17 It has been shown that polymer chains grown in solution have nearly identical molecular weights as those grown from surfaces when using the ATRP and ARGET ATRP methods.4,11 Therefore, the mathematical model should also be valid for predicting molecular weights of grafted polymers as well (Figure S1). The molecular weight of the grafted chains can be calculated from the conversion of the chains grown in solution by multiplying the conversion by the targeted degree of polymerization (DP) and the molar mass of a monomer unit. Subsequently, sensitivity analyses of the conversion profiles of the methyl methacrylate (MMA) monomer on key reaction parameters are explored to yield fundamental understanding of the kinetics of the ARGET ATRP mechanism and aid researchers in the optimal design of ARGET ATRP reactions.

The original ATRP method involved the use of an alkyl halide initiator (i.e., dormant species) and transition metal catalyst in a lower oxidation state complexed with a ligand to establish an equilibrium with an alkyl radical and transition metal in a higher oxidation state complexed with the ligand.8 The equilibrium constant for this reaction, KATRP, heavily favors the dormant species, thereby maintaining a very low free radical concentration at all times. This greatly reduces radical termination events, allowing for tighter control on the dispersity of the polymer chains. The radicals formed from this equilibrium reaction can further propagate with monomer to form polymer chains or terminate with one another. The main drawbacks to the ATRP reaction are that the catalyst complex must be handled and the polymerization performed under inert atmosphere. Once the catalyst becomes oxidized, the reaction stops. This reaction would be unfavorable industrially due to the necessity of air-free vessels and also the relative large amounts of copper catalyst needed. Similarly, even on the laboratory scale, specialized glassware and equipment are needed to perform the ATRP reaction. A major advancement in the ATRP saga occurred when activators regenerated by electron transfer (ARGET) ATRP was developed.10 The major change from the original ATRP procedure was that the transition metal complex with ligand could be added in its higher oxidation state and a suitable reducing agent used to generate the lower oxidation state transition metal complex. The reducing agent could also act as an indirect oxygen scavenger as well as continually reduce irreversibly produced higher oxidation state complexes formed through termination reactions. This allowed for the ARGET ATRP polymerization to be carried out in small flasks or vials, without the need for special handling of the transition metal complexes and running the reaction under an inert atmosphere.11−13 It also required much less transition metal catalyst, since the reducing agent could continuously regenerate the lower oxidation state form of the catalyst. The advent of ARGET ATRP, therefore, made available the RDRP technique to many laboratories and industrial scale production. One drawback of the ARGET ATRP reaction is that many authors utilize powerful ligands, such as tris[2-(dimethylamino)ethyl]amine (Me6TREN), which are either very expensive or unavailable commercially and must be synthesized in the laboratory. These powerful ligands have relatively large KATRP values, which is defined as the ratio of activation and deactivation rate constants for the ATRP equilibrium reaction. Access to these specialized ligands can severely limit the use of the ARGET ATRP method. There have been reports, however, of using less powerful and much cheaper ligand species such as N,N,N′,N″,N″-pentamethyldiethylenetriamine (PMDETA).14 Me6TREN is 425 times more expensive than PMDETA from a laboratory chemical supplier.15 Although the PMDETA ligand can be used for ARGET ATRP reactions, there is relatively far less experimental data present in the literature on the polymerization progress of different monomers at various reaction conditions. It is also important to note that PMDETA may not be the best ligand for polymerizing some monomers, such as acrylates, since it has less reactivity compared with other ligands. Furthermore, it is desirable to understand the sensitivity of the ARGET ATRP reaction with PMDETA ligand under various reaction conditions in order for scientists and engineers to develop optimal experimental procedures to target different monomer conversions.

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LITERATURE KINETIC DATA AND KINETIC REACTION MODEL Kinetic Data. Monomer conversions for methyl methacrylate (MMA), styrene (St), and glycidyl methacrylate (GMA) were calculated from data plotted in Hansson et al.16 and Jonsson et al.17 as follows. The kinetic data for the different

( ) vs t in the

ARGET ATRP reactions were plotted as ln

[M 0] [M]

publications, where [M0] and [M] are initial and final monomer concentrations, respectively, and t is time. ImageJ software (National Institutes of Health) with a Figure Calibration plugin was used to analyze images of these published semilogarithmic

( ) vs t data to be extracted

kinetic plots. This allowed the ln

[M 0] [M]

from the figures to be used in subsequent analyses. The monomer conversion, X, was calculated using the known [M0] by solving for [M] and then using the following formula: X=

[M]0 − [M] . [M]0

This allowed X vs t data to be plotted for each

ARGET ATRP reaction. It should be noted that the experimental data reported were conducted in reaction flasks which were purged with nitrogen to deoxygenate the system prior to initiating polymerization. Kinetic Reaction Model. The chemical equations used to build the ARGET ATRP mathematical model are shown in Table 1. The definition of the species in the chemical equations and their role in the ARGET ATRP mechanism are as follows: AsAc (ascorbic acid; reducing agent); Cu(II)Br2/L (copper bromide catalyst in higher oxidation state in complex with ligand (L); deactivator); Cu(I)Br/L (copper bromide catalyst in lower oxidation state in complex with ligand (L); activator); Ox− AsAc (oxidized AsAc; inactive form of reducing agent); R−Br (alkyl bromide compound; initiator); R• (free radical; initiates polymerization); M (monomer, n = 1...n; adds to radicals to form polymer chain); RMn (free radical; propagating polymer chain); RM2n−R (polymer chain; terminated). In these reactions, the ligand (L) is always PMDETA, the alkyl bromide initiator (R−Br) is always ethyl α-bromoisobutyrate (EBiB), and for styrene only the reducing agent is sodium ascorbate B

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Because of a lack of literature data on the deactivation rate constant for ATRP, kdeact, KATRP values were set according to Tang et al.21 for the ligand choice of PMDETA in order to calculate kdeact. KATRP was set to this value of 7.5 × 10−8 for all simulations, except for the temperature sensitivity analysis (where kdeact was set at the initial value corresponding to KATRP of 7.5 × 10−8 and kact was allowed to vary with temperature) and the KATRP sensitivity analysis (where kdeact was set at the initial value corresponding to KATRP of 7.5 × 10−8 and kact was varied arbitrarily). The termination rate constant was chosen to vary only with temperature and be chain length independent, which is a simplification of real termination behavior since termination rates are known to decrease at longer chain lengths leading to an overall acceleration of the polymerization reaction rate.22 Therefore, the model is expected to be less accurate at higher monomer conversions. A further simplification to the model is that all radical species (i.e., R• and RMn•) were modeled as the same species. A consequence of this simplification is that the propagation rate of monomer to the growing polymer chain is independent of the length of the growing chain. These assumptions allow the mathematical model to be simplified significantly while still capturing experimental phenomena, especially at conversions below 0.4. The only parameter used in the model that was manually adjusted to fit the experimental data was the reducing rate constant, kred. This was done since literature data on the reduction rate of the deactivator complexed with PMDETA ligand is lacking and because the reducing agent is generally not fully soluble in solvents used for ARGET ATRP reactions, such as anisole,16 precluding an Arrhenius expression for this rate constant. kred, however, was kept constant in systems with a similar solvent and reducing agent. The values for kred used to fit the experimental data are therefore not true rate constants but lumped parameters estimating the combined effects of reducing agent strength, solubility, and temperature. The “goodness of fit” of the model to the experimental conversion data was quantified using the root-mean-square error (RMSE).

Table 1. Chemical Equations Used To Build Mathematical Model of ARGET ATRP Reactiona k red

AsAc + Cu(II)Br2/L ⎯⎯⎯→ Cu(I)Br/L + Ox−AsAc kact

R−Br + Cu(I)Br/L XoooooY Cu(II)Br2/L + R kdeact

kp

R•+ n M → RM n• • kt

•

(1)

•

(2)

(3)

RM n + RM n → RM 2n−R

(4)

a

AsAc = ascorbic acid; L = ligand; Ox−AsAc = oxidized ascorbic acid; R−Br = initiator; R• = alkyl radical; n = arbitrary number (≥0); M = monomer; RMn• = propagating radical n monomer units long; RM2n− R = terminated polymer chain.

(NaAsc) instead of ascorbic acid (AsAc). Reaction 1 consists of the reduction of the deactivator by the reducing agent with rate constant kred to generate the activator needed for the ATRP equilibrium reaction. Reactions 2 are the forward and reverse reactions that constitute the ATRP equilibrium. The equilibrium constant for the reaction, KATRP, is defined as kact/kdeact. Free radicals formed during the ATRP equilibrium step can react with monomer to from a growing polymer chain with propagation rate constant kp in reaction 3. Growing polymer chains are terminated through a coupling mechanism with rate constant kt as shown in reaction 4. Although several termination reactions are also possible through disproportionation, the termination step was modeled as shown in reaction 4 as an approximation to reduce model complexity. The kinetic rate laws for the ARGET ATRP mechanism are shown in Table 2. All reactions were modeled as bimolecular, so the units of all rate constants are M−1 s−1. Arrhenius expressions of the form

(

E

)

k(T ) = A exp − RTa were used to calculate the temperature

dependence of kact, kp, and kt, where A is the pre-exponential factor (M−1 s−1), Ea is the activation energy (kJ mol−1), R is the gas constant (kJ mol−1 K−1), and T is the temperature (K). Arrhenius parameters for kact were taken from Seeliger et al.18 Propagation and termination reaction Arrhenius parameters were taken from the Polymer Handbook19 for MMA and St where those for GMA were taken from Mavroudakis et al.20

This was calculated as follows:

1 n

n

∑i = 1 (yi ̂ − yi )2 , where n is

the number of experimental data points predicted by the model, ŷi is the conversion of the ith data point predicted by the model, and yi is the ith reported experimental conversion. The rate

Table 2. Kinetic Rate Laws for the ARGET ATRP Reaction Mechanism Summarized in Table 1 d[AsAc] = − k red[AsAc][Cu(II)Br2/L] dt

(5)

d[Cu(II)Br2/L] = − k red[AsAc][Cu(II)Br2/L] + kact[R−Br][Cu(I)Br/L] dt − kdeact[Cu(II)Br2/L][R] d[Ox−AsAc] = k red[AsAc][Cu(II)Br2/L] dt

(6) (7)

d[Cu(I )Br2/L] = k red[AsAc][Cu(II)Br2/L] − kact[R−Br][Cu(I)Br/L] dt + kdeact[Cu(II)Br2/L][R]

d[R−Br] = − kact[R − Br][Cu(I)Br/L] + kdeact[Cu(II)Br2/L][R] dt d[R] = kact[R−Br][Cu(I)Br/L] − kdeact[Cu(II)Br2/L][R] − k t[R]2 dt

d[M] = − k p[M][R] dt

(8) (9) (10)

(11) C

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Figure 1. Variation of DP for MMA monomer. ARGET ATRP polymerization of MMA in a constant volume batch reactor (20 mL) at 30 °C in anisole solvent (50% w/w). MATLAB model fit (red ) to experimental data (●) and fit ± RMSE (- - -) with kred = 22 M−1 s−1 for [MMA]:[EBiB]: [Cu(II)Br2]:[PMDETA]:[AsAc] molar ratios of (A) 800:1:0.1:1:1 and (B) 400:1:0.1:1:1.

Figure 2. Variation of DP for St monomer. ARGET ATRP polymerization of St in a constant volume batch reactor (20 mL) at 100 °C in anisole solvent (50% w/w). MATLAB model fit (red ) to experimental data (●) and fit ± RMSE (- - -) with kred = 2.4 M−1 s−1 for [St]:[EBiB]: [Cu(II)Br2]:[PMDETA]:[NaAsc] molar ratios of (A) 800:1:0.1:1:1 and (B) 400:1:0.1:1:1.

larger deviation is observed. This is expected due to the fact that a chain length independent termination rate constant was used in the model, which does not account for polymerization rate acceleration at higher conversions.22 The same model constructed for MMA with targeted DP = 800 (kred = 22 M−1 s−1) was used to fit the experimental data for MMA with targeted DP = 400. The experimental data16 and the model fit (with ±RMSE values) for MMA with DP = 400 and kred = 22 M−1 s−1 are shown in Figure 1B with experimental conditions. The RMSE = 0.096 for this fit, over twice as large as the RMSE for the DP = 800 case. The conversion at tR = 240 min has the largest deviation from the fit, and the model overpredicts the conversion globally. The experimental data for the MMA conversion as a function of time for the DP = 400 case are virtually identical to the experimental data for the DP = 800 case up to the maximum time of 240 min reported for the DP = 400 case. This is surprising since the reported amount of initiator was doubled while the initial monomer concentration was kept constant in the DP = 400 case compared with the DP = 800 case. Since the experimental initial conditions are different, the

laws for each species were incorporated into an m-file in the MATLAB computational software (MATLAB R2017a, Natick, MA) and solved simultaneously using the ordinary differential equation solver, ode15s, with initial conditions as specified in the publications from which the experimental data were taken. The species concentrations were output to a comma separated value (CSV) file, from which the monomer conversion as a function of time could be plotted alongside the experimental conversion data. A typical m-file used for MMA targeting a degree of polymerization (DP) of 800 is shown in Table S1.

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RESULTS AND DISCUSSION Model Verification. Effects of Varying DP. The conversion of MMA with a targeted DP of 800, where the degree of [R−Br] polymerization is defined as DP = [M] 0 , was modeled as a 0

function of reaction time, tR. The experimental data16 and the model fit (with ±RMSE values) with kred = 22 M−1 s−1 are shown in Figure 1A with experimental conditions. The RMSE = 0.046 for this fit. At conversions below approximately 0.4, the data are within the fit ± RMSE. Above a conversion of 0.4, D

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Figure 3. Variation of solvent for GMA monomer. ARGET ATRP polymerization of GMA in a constant volume batch reactor (20 mL). MATLAB model fit (red ) to experimental data (●) and fit ± RMSE (- - -) for [GMA]:[EBiB]:[Cu(II)Br2]:[PMDETA]:[AsAc] molar ratios of (A) 400:1:0.1:1:0.5 in anisole solvent (50% w/w) at 0 °C with kred = 22 M−1 s−1 and (B) 190:1:0.01:0.2:0.2 in toluene solvent at 30 °C with kred = 1.4 M−1 s−1.

versus time data for St follow different trajectories at DP = 400 and DP = 800. The targeted DP = 400 experimental conversions rise more rapidly with time compared with the DP = 800 data. As explained for the MMA monomer, this is expected since doubling the amount of initiator while maintaining all other molar ratios constant should cause the initiator molecules to react at the same rate in both cases. Therefore, the conversion versus time data should be different at both targeted DPs. The model accurately describes a higher conversion versus time when moving to the DP = 400 case. Effects of Varying Solvent. In order to further evaluate the utility of the model, the experimental conversion data16 of the GMA monomer using AsAc reducing agent (i.e., the same reducing agent as for MMA) was modeled using the same reducing rate constant, kred = 22 M−1 s−1 as for MMA. The only experimental data reported in the paper was for DP = 400. These data and the model fit (with ±RMSE values) are shown in Figure 3A along with experimental conditions. The RMSE = 0.030 for this fit. The ARGET ATRP reaction of GMA was run at a lower temperature and lower molar ratio of reducing agent than for MMA. The model predicts the experimental conversion versus time data very well and captures the effect of using a different monomer, reducing agent concentration, and temperature even though it was originally developed for the MMA monomer. This gives confidence that the model developed for MMA using the PMDETA ligand and AsAc reducing agent can be applied to other monomers and at various reaction temperatures, as shown for the GMA monomer. This will be provided Arrhenius parameters are known for the different monomers to be modeled. It should also be noted that solvents can have a significant effect on ARGET ATRP polymerization rate.23 Experimental conversion data for the polymerization of GMA in toluene using AsAc reducing agent have been reported17 and are modeled using an adjusted kred to encapsulate the solvent effect in Figure 3B. The ARGET ATRP of GMA even at a higher temperature has a lower reduction rate constant in toluene when compared with anisole solvent. RMSE = 0.044 for the fit to the GMA polymerization in toluene with kred = 1.4 M−1 s−1. Therefore, changing the reaction solvent requires an adjustment of the reducing rate constant, since this will alter the solubility of the

model predicts a higher conversion as a function time than the reported experimental data. This is expected since mathematically, supplying different initial conditions to a set of differential equations will result in a different solution trajectory.a Furthermore, since the ratios of copper catalyst, ligand, and reducing agent are all scaled in accordance with the initiator concentration, each initiator molecule would be in a similar environment in both cases of targeted DP. Since the initial monomer concentration was kept constant in both cases, the only way experimentally for the conversion data to be temporally identical in both cases would be if the initiator molecules in the higher targeted DP case (which contains half the initiator) reacted much faster than in the lower targeted DP case. Otherwise, the conversions cannot be identical. The DP = 400 experimental data for MMA seems to be anomalous as will be shown when modeling the conversion for the St monomer. The next monomer to be modeled was St with targeted DP = 800. Besides the temperature difference, NaAsc was used as the reducing agent for ARGET ATRP of St. This reducing agent is known to be weaker than AsAc.16 Experimental data16 and the model fit (with ±RMSE values) for St with DP = 800 and kred = 2.4 M−1 s−1 are shown in Figure 2A with experimental conditions. The RMSE = 0.036 for this fit. The RMSE is ∼22% smaller than the DP = 800 case for MMA. The model fit slightly overpredicts the conversion at lower conversions while it slightly under predicts at higher conversions. The reducing rate constant needed to fit the data is nearly an order of magnitude lower than that for MMA with AsAc. This is expected since NaAsc is a weaker reducing agent than AsAc.16 The model appears to fit the data well for the DP = 800 case. This also verifies the Arrhenius expressions used to predict propagation and termination rate constants at higher temperatures in the model accurately describe the observed experimental kinetics. Experimental data16 for the same ARGET ATRP reaction of St were then modeled with targeted DP = 400. The experimental data and model fit (with ±RMSE values) with kred = 2.4 M−1 s−1 are plotted in Figure 2B. The RMSE = 0.027 for this fit. The model fit is least accurate at the very beginning of the polymerization, and all data are within ± RMSE as the reaction proceeds. Contrary to MMA, the experimental conversion E

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Figure 4. Varying catalyst and initiator concentrations. Simulated effect on conversion profile of (A) catalyst CuBr2 concentration (M): 6.5 × 10−6 (◆); 6.5 × 10−5 (■); 6.5 × 10−4 (●); 6.5 × 10−3 (▲); 6.5 × 10−2 (×) with molar ratios set to 800:1:x:10x:1. (B) Initiator EBiB concentration (M): 6.5 × 10−4 (■); 6.5 × 10−3 (●); 6.5 × 10−2 (▲) with molar ratios set to 800:x:0.1:1:1. (A, B) Inset: monomer conversion (ordinate) at tR = 480 min vs initial [Cu(II)Br2]:[EBiB] ratio (abscissa).

concentration while maintaining all other molar ratios constant is shown in Figure 4A. The Cu(II)Br2 concentration of 6.5 × 10−4 M corresponds to the initial condition in the original model developed in Figure 1. Reducing the copper concentration below 6.5 × 10−4 M results in a decrease in the MMA conversion while increasing the copper concentration results in a much quicker decline in the monomer conversion when compared at tR = 480 min. The fact that a maximum conversion is observed when varying the amount of copper added to the reaction is further illustrated in the inset of Figure 4A. Here, it is shown that a maximum conversion at tR = 480 min is observed when the [Cu(II)Br2]:[EBiB] ratio is set to 0.1:1. The fact the copper catalyst concentration exhibits an extremum in the conversion profile for MMA is not unexpected. Low Cu(II)Br2 concentrations result in too little Cu(I)Br being generated through the reduction reaction, causing the reversible ATRP reaction to produce a small number of radicals needed to consume monomer. High Cu(II)Br2 concentrations are even more detrimental to the conversion of monomer, since the amount of reducing agent available becomes incapable of reducing enough Cu(II)Br2 to Cu(I)Br. This residual Cu(II)Br2 (i.e., deactivator) forces the ATRP equilibrium to lie to the left toward the dormant species, preventing the formation of radicals to propagate with monomer. The effect of varying the initiator concentration

reducing agent and its ability to reduce the copper complex. The activation rate constant also depends on the polarity of the reaction medium. Further experiments will need to be performed in order to develop accurate Arrhenius expressions for the activation rate constant as a function of solvent polarity that may allow this kinetic model to be valid for a larger set of solvents. Parameter Sensitivity Analysis. In order to quantify the effects of the ARGET ATRP reaction parameters on the resulting temporal conversion trajectory to optimize reaction conditions as well as to avoid unforeseen pitfalls that result in a poor reaction outcome, parameter sensitivity analyses were performed. In the following simulations, sensitivity analyses were performed on the MMA monomer with targeted DP = 800 using the model developed in Figure 1. All sensitivity analyses were performed at 30 °C in anisole solvent (50% w/ w). Molar ratios are given in the following order in all analyses: [MMA]:[EBiB]:[Cu(II)Br2]:[PMDETA]:[AsAc]. Varying Catalyst and Initiator Concentrations. One critical parameter affecting the control of an ARGET ATRP reaction discussed in Hansson et al.16 is the concentration of dormant species (i.e., initiator). If initiator concentration is too low with respect to the amount of copper catalyst, control over the reaction can be lost leading to polymer chains with high dispersity. Therefore, the effect of varying the copper catalyst F

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Figure 5. Increasing the reducing agent concentration. Simulated effect on conversion profile of reducing agent concentration (M): 6.5 × 10−5 (■); 6.5 × 10−4 (●); 6.5 × 10−3 (▲); 6.5 × 10−2 (×); 6.5 × 10−1 (◆) with molar ratios set to 800:1:0.1:1:x. Inset: monomer conversion (ordinate) at tR = 480 min vs initial [AsAc]:[Cu(II)Br2] ratio (abscissa). For those reactions which stop before tR = 480 min, the conversion at the time the reaction stopped was used as the conversion at tR = 480 min.

Figure 6. Increasing catalyst concentration. Simulated effect on conversion profile of catalyst CuBr2 concentration (M): 6.5 × 10−6 (◆); 6.5 × 10−5 (■); 6.5 × 10−4 (●); 6.5 × 10−3 (▲) with molar ratios set to 800:1:x:10x:10x. Inset: monomer conversion (ordinate) at tR = 480 min vs initial [Cu(II)Br2]:[initiator] ratio (abscissa). For those reactions which stop before tR = 480 min, the conversion at the time the reaction stopped was used as the conversion at tR = 480 min.

critical for optimum performance in the ARGET ATRP reaction. Effect of Increasing Reducing Agent and Catalyst Concentration. It is also necessary to investigate the effect of reducing agent (i.e., AsAc) concentration on the conversion profile. The results of this simulation are shown in Figure 5. The reducing agent concentration of 6.5 × 10−3 M corresponds to the initial condition in the original model developed in Figure 1. Diminishing the reducing agent concentration below 6.5 × 10−3 M reduces the attainable conversion at tR = 480 min as there is not enough reducing agent present to continuously convert Cu(II)Br2 to Cu(I)Br, which in turn reduces the number of radicals that can be formed upon reaction of Cu(I)Br with initiator. Increasing the amount of reducing agent greatly accelerates the initial reaction rate, since a large reservoir of AsAc can produce copious amounts of Cu(I)Br.24 The initial acceleration of the reaction rate, however, comes at a price of limiting the maximum attainable conversion. This is due to the high number of radicals being present in the reaction medium, which increases

while maintaining all other molar ratios constant is shown in Figure 4B. The initiator concentration of 6.5 × 10−3 M corresponds to the initial condition in the original model developed in Figure 1. Reducing the initiator concentration below 6.5 × 10−3 M reduces the attainable conversion at tR = 480 min, while increasing the initiator concentration causes the monomer conversion to rise more rapidly as well as appear to asymptote more quickly. Again, a maximum in the conversion for [Cu(II)Br2]:[EBiB] ratio of 0.1:1 is observed in the inset of Figure 4B. This can be explained since too low of an initiator concentration limits the number of radicals that can be formed to react with monomer, thereby decreasing the conversion. Increasing the initiator concentration too much, however, causes a higher number of radicals that can be formed initially to propagate with monomer which also increases the potential for radical termination events. These termination events can limit the attainable monomer conversion since the terminated chains can no longer propagate with monomer. It appears from these simulations that a [Cu(II)Br2]:[EBiB] ratio of 0.1:1 is G

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Figure 7. Increasing kred and KATRP values. Simulated effect on conversion profile with molar ratios set to 800:1:0.1:1:1 of (A) kred (M−1 s−1): 0.8 (◆); 2.4 (▲); 7.3 (■); 22 (●), 66 (×); 198 (); 594 (|). (B) KATRP (): 7.5 × 10−10 (▲); 7.5 × 10−9 (■); 7.5 × 10−8 (●); 7.5 × 10−7 (◆); 7.5 × 10−6 (×).

while the kred of 66 M−1 s−1 gave a higher conversion than that at 22 M−1 s−1. Increasing the ATRP equilibrium constant, KATRP, also results in behavior similar to increasing kred shown in Figure 7B. The KATRP value of 7.5 × 10−8 corresponds to the initial condition in the original model developed in Figure 1. Increasing this equilibrium constant favors the formation of radicals, which both increase the propagation and termination reaction rates, resulting in higher monomer conversions at short times and lower attainable conversions at longer times. This is important because using highly active ATRP ligands, which increase KATRP, can cause too much of an acceleration of the propagation and termination reaction rates resulting in a limited attainable conversion. Increasing Reaction Temperature. Increasing the maximum attainable monomer conversion requires an increase in the ratio of the rate of propagation to termination, kp:kt. This can be accomplished through increasing the temperature of the ARGET ATRP reaction. For example the ratio of the propagation and termination rate constants at 363 K to the

both propagation reaction rate with monomer and termination reactions. The consequence of a larger amount of termination reactions is to limit the conversion of monomer as the reaction proceeds and dead polymer chains accumulate. This eventually causes the reaction to come to a halt. The inset of Figure 5 shows that the optimum ratio of [AsAc]:[Cu(II)Br2] is 10:1. It was interesting to investigate the effect of repeating the analysis in Figure 4A in which the Cu(II)Br2 concentration was varied but this time setting the [AsAc]:[Cu(II)Br2] ratio at 10:1. The simulation results are shown in Figure 6. As the Cu(II)Br2 concentration is decreased from the initial 6.5 × 10−4 M (cf. Figure 1), the conversion decreases as a function of time similar to the case when the reducing agent concentration was held constant. The explanation is the same as that for the results in Figure 5. Increasing the Cu(II)Br2 concentration, however, results in an acceleration in the conversion of monomer followed by an abrupt end to the polymerization. This effect was also observed in Figure 5 where the reducing agent produced large amounts of Cu(I)Br, which caused an increase in the propagation and termination reactions leading to a lower attainable conversion. These simulations support the hypothesis proposed by Hansson et al.16 that the concentration of dormant species relative to the concentrations of other species in the ARGET ATRP reaction are critical to maintain control over the polymerization. Low amounts of dormant species on initiator functionalized surfaces have very high [Cu(II)Br2]:[EBiB] ratios, and combined with even modest [AsAc]:[Cu(II)Br2] ratios can cause propagation and termination reaction rates to be very fast, resulting in significantly lower attainable conversion and limiting the duration of the reaction. Increasing the Reduction Rate Constant and ATRP Equilibrium Constant. High levels of termination have been known to increase the dispersity of the polymer chains,8 thereby confirming the loss of control explained by Hansson et al. Increasing the reduction rate constant in Figure 7A also appears to increase the polymerization rate by exhibiting higher monomer conversions at short reaction times with the trade-off of lower attainable conversion at longer reaction times. The reduction rate constant, kred, of 22 M−1 s−1 corresponds to the initial condition in the original model developed in Figure 1,

ratio at 303 K,

( (

kp kt

363 K

kp kt

303 K

) = 2.46. )

The sensitivity of the

monomer conversion profile on the ARGET ATRP reaction is shown in Figure 8. The temperature of 303 K corresponds to the initial condition in the original model developed in Figure 1. As is evident from the conversion profiles, increasing the temperature yields a higher initial rate of polymerization while still allowing for much higher attainable conversions at longer reaction times. This is presumably due to the increase in relative importance of propagation rate constant over termination rate constant as temperature increases, preventing dead chains from accumulating to a greater extent due to irreversible termination events.

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CONCLUSION A mathematical model for the temporal conversion of monomer to polymer using the complex ARGET ATRP reaction system with inexpensive PMDETA ligand was developed and verified against published experimental data for MMA, St, and GMA monomers at various reaction temperatures. The main assumptions of the model are that H

DOI: 10.1021/acs.macromol.7b01572 Macromolecules XXXX, XXX, XXX−XXX

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ADDITIONAL NOTE The authors contacted the senior author of the manuscript from which this experimental data originated, Dr. Eva Malmstrom, regarding the peculiar conversion trajectory of the MMA monomer. Dr. Malmstrom has new preliminary data which suggests the conversion trajectories should in fact be different at the different targeted DP’s. a

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(1) Chang, Y.; Shih, Y.-J.; Ko, C.-Y.; Jhong, J.-F.; Liu, Y.-L.; Wei, T.C. Hemocompatibility of Poly(vinylidene fluoride) Membrane Grafted with Network-Like and Brush-Like Antifouling Layer Controlled via Plasma-Induced Surface PEGylation. Langmuir 2011, 27 (9), 5445− 5455. (2) Chen, S.-H.; Chang, Y.; Lee, K.-R.; Wei, T.-C.; Higuchi, A.; Ho, F.-M.; Tsou, C.-C.; Ho, H.-T.; Lai, J.-Y. Hemocompatible Control of Sulfobetaine-Grafted Polypropylene Fibrous Membranes in Human Whole Blood via Plasma-Induced Surface Zwitterionization. Langmuir 2012, 28 (51), 17733−17742. (3) Keating, J. J., IV; Imbrogno, J.; Belfort, G. Polymer Brushes for Membrane Separations: A Review. ACS Appl. Mater. Interfaces 2016, 8 (42), 28383−28399. (4) Barbey, R.; Lavanant, L.; Paripovic, D.; Schüwer, N.; Sugnaux, C.; Tugulu, S.; Klok, H.-A. Polymer Brushes via Surface-Initiated Controlled Radical Polymerization: Synthesis, Characterization, Properties, and Applications. Chem. Rev. 2009, 109 (11), 5437−5527. (5) Chambers, L. D.; Stokes, K. R.; Walsh, F. C.; Wood, R. J. Modern approaches to marine antifouling coatings. Surf. Coat. Technol. 2006, 201 (6), 3642−3652. (6) Zdyrko, B.; Luzinov, I. Polymer Brushes by the “Grafting to” Method. Macromol. Rapid Commun. 2011, 32 (12), 859−869. (7) Edmondson, S.; Osborne, V. L.; Huck, W. T. S. Polymer brushes via surface-initiated polymerizations. Chem. Soc. Rev. 2004, 33 (1), 14− 22. (8) Matyjaszewski, K.; Xia, J. Atom transfer radical polymerization. Chem. Rev. 2001, 101 (9), 2921−2990. (9) Moad, G.; Rizzardo, E.; Thang, S. H. Living radical polymerization by the RAFT process−a second update. Aust. J. Chem. 2009, 62 (11), 1402−1472. (10) Matyjaszewski, K. Atom transfer radical polymerization (ATRP): current status and future perspectives. Macromolecules 2012, 45 (10), 4015−4039. (11) Matyjaszewski, K.; Dong, H.; Jakubowski, W.; Pietrasik, J.; Kusumo, A. Grafting from surfaces for “everyone”: ARGET ATRP in the presence of air. Langmuir 2007, 23 (8), 4528−4531. (12) Keating, J. J.; Belfort, G.; Kocsis, I.; Sorci, M.; Lee, A. Combined Plasma-ARGET ATRP Method and Materials For Modifying Poly(ether sulfone) Surface to Create a Polymer Brush Grafted Membrane, PCT/US/17/50675, 2017. (13) Keating, J. J. I.; Kocsis, I.; Sorci, M.; Setaro, A.; Underhill, P.; Belfort, G. Atmospheric Pressure Plasma - ARGET ATRP Modification of Poly(ether sulfone) Membranes: A Combination Attack. Manuscript in preparation, 2017. (14) Kwak, Y.; Magenau, A. J.; Matyjaszewski, K. ARGET ATRP of methyl acrylate with inexpensive ligands and ppm concentrations of catalyst. Macromolecules 2011, 44 (4), 811−819. (15) http://www.sigmaaldrich.com/united-states.html. (16) Hansson, S.; Ostmark, E.; Carlmark, A.; Malmström, E. ARGET ATRP for versatile grafting of cellulose using various monomers. ACS Appl. Mater. Interfaces 2009, 1 (11), 2651−2659. (17) Jonsson, M.; Nyström, D.; Nordin, O.; Malmström, E. Surface modification of thermally expandable microspheres by grafting poly (glycidyl methacrylate) using ARGET ATRP. Eur. Polym. J. 2009, 45 (8), 2374−2382. (18) Seeliger, F.; Matyjaszewski, K. Temperature effect on activation rate constants in ATRP: new mechanistic insights into the activation process. Macromolecules 2009, 42 (16), 6050−6055.

Figure 8. Increasing reaction temperature. Simulated effect on the conversion profile of reaction temperatures (K): 273 (■), 303 (●), 333 (▲), and 363 (◆) with molar ratios set to 800:1:0.1:1:1.

termination reactions occur through radical coupling only and the propagation and termination reaction rates are chain length independent. The model accurately describes conversion trajectories especially at conversions of 0.4 and below, in which almost all of the experimental data was within the fit ± RMSE. This simple model can be utilized by researchers to design experiments to target a given conversion for a specific monomer at a specified temperature. Furthermore, we show quantitatively that the [Cu(II)Br2]:[EBiB] and [AsAc]:[Cu(II)Br2] ratios are critical parameters in the ARGET ATRP mechanism, with optimal values on the order of 0.1:1 and 10:1, respectively. From these results, we conclude that adding sacrificial initiator in order to increase the concentration of dormant species when grafting from surfaces is necessary to prevent loss of control and premature halting of the polymerization. Finally, increasing the ARGET ATRP reaction temperature is the most viable way to increase polymerization rate while maintaining high attainable conversions.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b01572. Table S1 and Figure S1 (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*(G.B.) E-mail: [email protected]. ORCID

John J. Keating IV: 0000-0003-0227-9191 Georges Belfort: 0000-0002-7314-422X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the Department of Energy, Basic Energy Sciences Division (DE-FG02-09ER16005), for funding our research on fundamental aspects of brush-modified membranes and JJK thanks Howard P. Isermann for a first-year graduate fellowship. I

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J

DOI: 10.1021/acs.macromol.7b01572 Macromolecules XXXX, XXX, XXX−XXX