Model-Based Visualization and Understanding of Monomer Sequence

Article pubs.acs.org/Macromolecules

Model-Based Visualization and Understanding of Monomer Sequence Formation in Gradient Copoly(2-oxazoline)s On the basis of 2‑Methyl-2-oxazoline and 2‑Phenyl-2-oxazoline Paul H. M. Van Steenberge,†,⊥ Bart Verbraeken,‡,⊥ Marie-Françoise Reyniers,† Richard Hoogenboom,*,‡ and Dagmar R. D’hooge*,†,§ †

Laboratory for Chemical Technology (LCT), Ghent University, Technologiepark 914, B-9052 Zwijnaarde (Gent), Belgium Supramolecular Chemistry Group, Department of Organic and Macromolecular Chemistry, Ghent University, Krijgslaan 281-S4, 9000 Ghent, Belgium § Department of Textiles, Ghent University, Technologiepark 907, B-9052 Zwijnaarde (Gent), Belgium ‡

S Supporting Information *

ABSTRACT: For the first time, the formation of monomer sequences of individual macromolecules during cationic ringopening copolymerization (CROcoP) of 2-methyl-2-oxazoline (MeOx) and 2-phenyl-2-oxazoline (PhOx) in acetonitrile (3 mol L−1; 100−140 °C; target degree of polymerization (DP): 50− 400) is visualized via kinetic Monte Carlo simulations with model parameters optimized based on experimental data. It is shown that chain transfer via β-elimination and branching reactions are required to describe the experimental data. At complete monomer conversion for target DPs below 200, at most 5% of the chains are macromonomers and the average number of branches per chain remains below 15%. A higher amount of chains with a defined, steeper MeOx to PhOx gradient is obtained by lowering the polymerization temperature albeit at the expense of polymerization time. The simulations results highlight the great potential of CROcoP of 2-oxazolines for the direct synthesis of welldefined steep gradient copolymers.

1. INTRODUCTION In the last few decades, poly(2-alkyl/aryl-2-oxazoline)s (PAOx) have been put forward as a versatile replacement for poly(ethylene glycol)s (PEG) in for instance biomedical applications.1−7 For poly(2-methyl-2-oxazoline) (PMeOx) and poly(2-ethyl-2-oxazoline), a similar stealth behavior and even improved biocompatibility as compared with PEG has already been well-established.8−10 This can be supplemented with a high flexibility in structural variation of the R substituent of the basic cyclic imino ether 2-oxazoline monomer (Scheme 1; left) creating a wide variety of biocompatible copolymers.11−16 As an example of improved biocompatibility, a stronger hydrophilicity than PEG can be obtained with poly(2methyl-2-oxazoline) (PMeOx), which does not display a lower critical solution temperature.4,17,18 In contrast, poly(2-phenyl-2oxazoline) (PPhOx) is completely insoluble in water and intermediate solubilities can be obtained by selecting the appropriate R group, even excluding the optional copolymers.4,17−19 As illustrated in Scheme 1,20−24 cationic ring-opening polymerization (CROP) can be used as polymerization technique for PAOx synthesis. Upon the nucleophilic attack of the endocyclic nitrogen atom of the 2-oxazoline ring onto © XXXX American Chemical Society

the initiator (e.g., methyl tosylate (MeOTs)) chain initiation (ki), i.e., the incorporation of the first monomer unit, takes place. The resulting oxazolinium species can further propagate (kp), until all monomer is consumed. Note that in general also a covalent mechanism can take place, which can although be neglected upon a careful choice of the combination of monomer and counterion (initiator). Ideally, the resulting chain length of each macrospecies is simply given by the initial molar ratio of monomer to initiator, i.e., the target (number) degree of polymerization (DP). In a final step, termination (kt) can be ensured by the addition of a nucleophile, which can be utilized to incorporate specific functional end-groups (Scheme 1; right) allowing further chemical modification.13,25−28 The living nature of CROP lends itself incredibly well to the synthesis of block copolymers via the addition of the second monomer after complete conversion of the first monomer.29−31 This transition from one monomer type to the other can also be less abrupt by targeting the spontaneous synthesis of the less studied gradient copolymers.32,33 2-Oxazolines offer a high Received: July 22, 2015 Revised: October 8, 2015

A

DOI: 10.1021/acs.macromol.5b01642 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Scheme 1. Principle of Cationic Ring-Opening Polymerizationa (CROP) of 2-Oxazolines20−24

Key: black oval, initiator part; X−, counter ion; grey box, terminator (e.g. water), present work; R, Me or Ph group; covalent mechanism not shown for simplicity. a

flexibility for gradient polymer synthesis, since a variation of the R substituent not only influences the bulk and solution polymer properties, as mentioned above, but also strongly alters the propagation reactivity. For example, at 140 °C, kp can decrease from ca. 10−1 L mol−1 s−1 to ca. 10−3 L mol−1s−1 by switching from MeOx to 2-(perfluoroethyl)-2-oxazoline as monomer.34 Hence, copolymerizations with a “fast” and a “slow” 2-oxazoline can be conducted for many combinations of propagation reactivities.17,35 Under batch conditions the “fast” monomer is dominantly incorporated until the monomer-feed is enriched in the “slow” monomer, due to the concentration drift. The “slow” monomer is thus mostly consumed at the end of the CROP, inherently leading to the spontaneous formation of gradient copolymers.36 Note that this control over the gradient behavior on the level of the chemical variation of the R group is, in practice, more efficient than a fed-batch monomer addition, also referred to as forced gradient copolymer synthesis, in which accurate addition rates and intensive mixing are prerequisites for reproducible synthesis, which is especially important for biomedical applications. Hence, as novel biomedical applications for PAOx are around the corner,1−4 the in-depth analysis of these chemically driven spontaneous gradient formation methods is highly important. A key challenge is the evaluation of the monomer sequences and gradient quality of individual macromolecules for which recently advanced kinetic Monte Carlo (kMC) techniques24,36−38 have been developed. These techniques are complementary to experimental studies, which currently only allow the determination of average copolymer properties. For example, the overall comonomer incorporation rates can be measured but provide only insights in the average monomer consumption profiles. In this work, a combined experimental and kMC modeling study is presented for the batch copolymerization of MeOx and PhOx in acetonitrile, aiming at an in-depth understanding of the gradient monomer sequences and an improved design of gradient copolymers via a detailed tracking of the formation history of the polymer microstructure of individual macromolecules. MeOx and PhOx are selected as comonomers since they are characterized by a vastly different propagation reactivity and are both notorious in the field of 2-oxazolines as “difficult” monomers in terms of achieving low dispersities, therefore representing a worst case scenario for gradient control.39 It is shown that the occurrence of side reactions such as βelimination and subsequent macropropagation, which leads upon further reaction to branch formation, needs to be considered for a complete description of the polymer microstructure. Moreover, model-based design is applied to identify those polymerization conditions that allow a good control over the monomer sequences with a limited impact of side reactions.

2. EXPERIMENTAL PROCEDURE AND ANALYSIS Materials. 2-Methyl-2-oxazoline (MeOx; monomer 1) and barium oxide were purchased from Chemical Point and Acros Organics, respectively. 2-Phenyl-2-oxazoline (PhOx; monomer 2), methyl tosylate (MeOTs), phosphorus pentoxide, acetonitrile (polymerization solvent) and the analytic solvents (HPLC quality) were purchased from Sigma-Aldrich. Acetonitrile was dried over aluminum oxide by means of a custom-made solvent purification system from J.C. Meyer and was tapped directly in the glovebox. MeOx was distilled over barium oxide under inert argon atmosphere and PhOx over BaO under reduced pressure prior to polymerization. MeOTs was distilled over phosphorus pentoxide under reduced pressure. The monomers, acetonitrile and MeOTs were stored in a glovebox. In particular, PhOx was stored in the absence of light and used as freshly distilled as possible. Experimental Procedure. All manipulations were carried out in a VIGOR Sci-Lab SG 1200/750 Glovebox System with a water and oxygen concentration below 0.1 and 0.5 ppm, respectively. For the CROPs, a Biotage Initiator EXP Microwave System with Robot Sixty autosampler was used to obtain isothermal conditions either at 100, 120, or 140 °C. The temperature was monitored via an infrared sensor. The polymerizations were conducted in Biotage vials, which were dried overnight in an oven at 220 °C. The vials were filled with 0.7 mL reaction mixtures from a stock solution, composed of MeOTs, an equimolar ratio of MeOx and PhOx, and acetonitrile, leading to an initial monomer concentration of 3 mol L−1 (with thus 1.5 mol L−1 for each monomer) and an initial monomer to initiator molar ratio of 100. To ensure homogeneity the stock solution was stirred for 10 min before samples were taken to fill the vials. Analysis. The conversions of both MeOx and PhOx, which are respectively denoted as Xm,1 and Xm,2, were determined based on gas chromatography (GC) with acetonitrile as internal standard after dilution of 100 μL of the polymerization mixture with 900 μL chloroform. On the basis of these conversions, the overall conversion Xm, for which no differentiation according to the monomer type is made or thus the contribution of both comonomers is included, is also calculated. For completeness it is mentioned here that at very low Xm the set-temperature is not immediately obtained as a consequence of the heating stage for the microwave reactor, inherently leading to a slight deviation between the experimental and modeling data at very low polymerization times, since the latter assume isothermicity from the start of the polymerization. The GC analysis was performed on an Agilent 7890A system equipped with a VWR Carrier-160 hydrogen generator and an Agilent HP-5 column of 30 m length and 0.32 mm diameter. A flame ionization detector was used and the inlet temperature was set at 240 °C with a split injection ratio of 25. Hydrogen was used as carrier gas at a flow rate of 2 mL min−1. The oven temperature was increased with 20 °C min−1 from 50 to 120 °C, followed by a ramp of 50 °C min−1 to 240 °C. Size-exclusion chromatography (SEC) was performed on an Agilent 1260-series HPLC system equipped with a 1260 online degasser, a 1260 ISO-pump, a 1260 automatic liquid sampler, a thermostated column compartment at 50 °C equipped with two PLgel 5 μm mixedD columns and a guard column in series, a 1260 diode array detector, and a 1260 refractive index detector. The eluent was dimethylacetamide containing 50 mM of lithium chloride at an optimized flow rate B


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Scheme 2. Main (Bottom Part) and Side (Top Part) Reactions in the Kinetic Model for Cationic Ring-Opening Polymerization (CROP) of MeOx and PhOx Initiated by MeOTs in Acetonitrilea

a

Arrhenius parameters are given in Table 1; n″ = n′ + 1; ktrM and kpm are rate coefficients for β-elimination and macropropagation.

Table 1. Reactions and Arrhenius Parameters for the Cationic Ring-Opening Polymerization (CROP) of MeOx (M1) and PhOx (M2) Initiated by MeOTs (I) as well as the Utilized Rate Coefficients at 140 °C (Reference Temperature) and the Corresponding Monomer Reactivity Ratios r1/2a A (L mol−1 s−1)

Ea (kJ mol‑1)

k at 140 °C (L mol−1 s−1)

7

6.67 × 10

75.4

1.94 × 10−2

c

1.49 × 108

84.4

3.15 × 10−3

c

5.00 × 108

75.4

1.45 × 10−1

51

k p22

1.49 × 109

84.4

3.15 × 10−2

51

k p12

9.55 × 107

80.0

7.27 × 10−3

c

k p21

1.23 × 1010

80.0

9.40 × 10−1

c

k trM11

4.14 × 107

85.4

6.54 × 10−4

c

k trM12

7.91 × 107

90.0

3.27 × 10−5

c

5.24b

−4.6

2.00 × 101b

c

0.12b

4.4

3.35 × 10−2b

c

equation chain initiation

k i1

I + M1 → P1,1 + X

−

k i2

I + M 2 → P1,2 + X− propagation

k p11

Pi ,1 + M1 ⎯⎯⎯→ Pi + 1,1

Pi ,2 + M 2 ⎯⎯⎯→ Pi + 1,2 Pi ,1 + M 2 ⎯⎯⎯→ Pi + 1,2

Pi ,2 + M1 ⎯⎯⎯→ Pi + 1,1 chain transfer

Pi ,1 + M1 ⎯⎯⎯⎯⎯→ Di ,1 + P0,1

Pi ,1 + M 2 ⎯⎯⎯⎯⎯⎯→ Di ,1 + P0,2 r1/2

kp11

ref

kp12 kp22 kp21 macro propagation

d

k pm11

5.00 × 106

75.4

1.45 × 10−3

c

k pm21

1.23 × 108

80.0

9.40 × 10−3

c

Pi ,1 + Dj ,1 ⎯⎯⎯⎯⎯→ Pi + j ,1 Pi ,2 + Dj ,1 ⎯⎯⎯⎯⎯→ Pi + j ,1

Chain transfer only if H atom available in β-position. bDimensionless. cThis work. dSubsequent propagation of the reaction product is counted to calculate the average amount of branches per chain.

a

of 0.59 mL min−1. The spectra were analyzed using the Agilent Chemstation software with the GPC add on. Number-average chain length xn and dispersity values were measured against poly(methyl methacrylate) (PMMA) standards from Polymer Standards Service GmbH (PSS). It should be stressed that the obtained experimental data on the control over chain length are thus relative and, hence, a direct comparison with absolute simulation results cannot be made. However, due to the absolute nature of the model, the experimental data can be appropriately improved. The measured xn data have been rescaled with a constant factor to account for the difference in hydrodynamic volume of the standard and the studied PAOx, ignoring for simplicity the impact of the difference in hydrodynamic volume between both comonomers, i.e. an average correction factor is considered. A preliminary comparison of simulation and experimental results in the region

where branching reactions can be safely neglected revealed a correction factor of 0.45 for the measured xn data, which is in agreement with literature data, confirming the relevance of the model parameters and their absolute nature.40 For the dispersity data, no correction factor was introduced, as a limited effect is to be expected at least to a first approximation. The reproducibility of all experimental data (see Supporting Information) was explicitly verified at the reference temperature (140 °C). Error bars were calculated based on these additional measurements, i.e., triplicate polymerizations, triplicate sampling and triplicate analysis, to facilitate the comparison between the modeling and experimental results. C


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3. KINETIC MODEL Van Steenberge et al.36,41 previously developed a kMC model allowing the design of controlled radical copolymerization or reversible deactivation radical copolymerization processes via the explicit calculation of monomer sequences for a representative number of linear copolymer chains. In this stochastic model, reaction events are randomly selected according to the well-established Gillespie algorithm42 and elegantly stored to allow for the a posteriori visualization of monomer sequences. Importantly, this explicit visualization allows a unique classification of copolymers with respect to a targeted microstructure such as a linear gradient36 or block copolymer43 and can also be applied to living polymerization techniques such as CROP, including an explicit tracking of branched chains. In this work, this kMC modeling strategy is applied to CROP of 2-oxazolines in acetonitrile, considering MeOx and PhOx as comonomers (respectively M1 and M2) and MeOTs as initiator (I). The main reactions in the kinetic model are chain initiation and propagation, as illustrated in Scheme 2 (bottom part) and Table 1. No covalent macrospecies17,44 are considered, as literature data45−48 have indicated that the equilibrium is shifted completely toward the cationic macrospecies for the studied initiator/comonomer pair. In agreement with literature reports,39 chain transfer to monomer via β-elimination and macropropagation (Scheme 2 top part) are included as additional reaction possibilities. Note that β-elimination cannot take place with living chains with a PhOx oxazolinium end as no β-hydrogen atom is available. The potential occurrence of a chain transfer reaction for such chains has although been postulated.39 Since no reaction mechanism is currently known, in the present kinetic model chain transfer is only taking into account for living chains with a MeOx oxazolinium end. Importantly, propagation with the macromonomers formed via β-elimination, i.e., macropropagation, leads to branching and an increase of the number-average molar mass of the polymer. For sufficiently high branching rates, a sudden rise of the viscosity can even take place and therefore significantly different polymer properties can result.39 The developed kinetic model can be used to calculate the average number of branches per chain. It should be born in mind that the experimental quantification of branching levels is a tedious task for polymerization processes in general,49,50 highlighting the strength of combined experimental and modeling studies. The Arrhenius parameters of the reactions in Scheme 2 are also specified in Table 1. Those for the homopropagation steps are taken from the work of Wiesbrock et al.,51 in which the effect of the polymerization temperature on the monomer consumption was studied for various 2-oxazolines. The remaining Arrhenius parameters were determined according to the following purely qualitative tuning procedure. The rate coefficients were first optimized at the reference temperature of 140 °C and subsequently the activation energies were assessed based on a comparison with additional isothermal experimental data at polymerization temperatures of 100 and 120 °C. Because of the lack of literature values and in line with general expectations,52 in this assessment, chain transfer reactions were assumed to be more activated than their propagation counterparts. A value of 10 kJ mol−1 was selected, allowing a good description of the temperature variation on the polymerization characteristics. Because of the limited informa-

tion available, a slower macropropagation is mimicked by lowering the pre-exponential factor of the normal propagation only. For simplicity, the possible difference in propagation reactivity of end-chain and mid-chain cationic species is ignored. Furthermore, the activation energies for chain initiation were approximated by those for homopropagation. Hence, it is clear that the reported simulation results are merely of a qualitative nature but sufficient to understand the impact of side reactions on the microstructural control. The resulting activation energies of the cross-propagation reactions, which were assessed based on a comparison of experimental and simulated data at the different temperature studied, are approximately arithmetic averages of the activation energies of the corresponding homopropagation reactions, which indicates the absence of synergistic effects and leads to a weak temperature dependence for the monomer reactivity ratios r1 and r2 in Table 1. In agreement with literature reports, the reactivity ratio of MeOx is much higher than one, whereas that for PhOx is much lower.53 On the basis of Table 1, it follows that with MeOx as monomer at 140 °C ca. one chain transfer event (ktrM11) takes place per 200 propagation steps, in agreement with literature data and neglecting concentration effects.39 For the monomer PhOx (ktrM12), an even lower value of 1 transfer reaction to the MeOx oxazolinium species per 1000 propagation steps is obtained.

4. RESULTS AND DISCUSSION In this section, it is first demonstrated that chain transfer to monomer, i.e., β-elimination, and macropropagation cannot be ignored via a comparison of simulated and experimental data under the following reference conditions: 140 °C; [MeOx]0: [PhOx]0:[MeOTs]0 = 50:50:1; ([MeOx]0 + [PhOx]0) = 3 mol L−1. Next, the effect of the target DP on the microstructural control is discussed. Finally, it is shown that lower polymerization temperatures are beneficial for a suppression of these side reactions. 4.1. Effect of Chain Transfer to Monomer and Macropropagation. The chain growth during the synthesis of PAOx can ideally be described by only chain initiation and propagation; i.e., the reactivity for chain transfer can be assumed to be zero (ktrM = 0 L mol−1 s−1 in Table 1; Scheme 1). For the reference conditions, the corresponding simulated comonomer conversion profiles and the corresponding simulated evolution of xn, the dispersity, the macromonomer fraction, and the average number of branches per chain with Xm are given by the red dashed lines in Figure 1. To evaluate the validity of these ideal simulation results, in the same figure, the recorded experimental data are provided, including their error bars. Clearly, the model assuming an ideal reaction scheme (ktrM = 0 L mol−1 s−1 in Table 1) is incapable of describing the experimental data on average polymer properties (Figure 1b-c), since too high xn values and too low dispersity values are simulated. In the absence of chain transfer reactions, xn would increase linearly with Xm until at complete monomer consumption the initial molar ratio of monomer to initiator of 100 is reached. In addition, already at Xm values as low as 0.25 dispersity values very close to 1 would result, reflecting a better control over chain length than observed experimentally. Note that the comonomer conversion (Xm,i; i = 1,2; Figure 1a) profiles are qualitatively well-described, since chain transfer does not affect the number of active cationic centers. A very fast consumption of MeOx is simulated, whereas PhOx is D


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compensation is accompanied by the formation of branches at high Xm. As demonstrated in Figure 1d at complete monomer depletion the average number of branches per chain is 0.15, i.e. on average 1 out of 7 chains is branched once. The relatively good control over chain length and the steep character of the gradient are confirmed in Figure 2a−c, which

Figure 2. Monomer sequences for a representative number of polymer chains under reference conditions (see caption of Figure 1) at an overall conversion Xm of (a) 0.25, (b) 0.50, and (c) 1, using the full kinetic model with chain transfer CT (Table 1); (d) for comparison with (c) ideal monomer sequences in absence of CT reactions (ktrM = 0 L mol−1 s−1 in Table 1) at Xm = 1. Key: green, MeOx; red, PhOx (blue: background); branches are also represented linearly for simplicity (e.g., long chains at the bottom of part c).

Figure 1. Effect of chain transfer on (a) the comonomer conversion profiles (Xm,I; i = 1 (MeOx), 2 (PhOx)), and the (b) number-average chain length xn, (c) dispersity, and (d) macromonomer (macroM) fraction and average number of branches per chain (br) as a function of overall conversion Xm under reference conditions (140 °C; [MeOx]0:[PhOx]0: [MeOTs]0 = 50:50:1; [MeOx]0 + [PhOx]0 = 3 mol L−1; solvent: acetonitrile): dashed red lines, no chain transfer (CT; Table 1 with ktrM = 0 L mol−1 s−1); full green lines including CT (Table 1); symbols, experimental data with xn rescaled (factor 0.45 to compensate for use of PMMA standards); coinciding lines in Figure 1a for values with and without CT.

show the simulated explicit monomer sequences for a representative number of chains at Xm of 0.25, 0.50 and 1, using the complete kinetic model (Table 1; ktrM ≠ 0 L mol−1 s−1). Note that each time a branch is formed its monomer sequences are stored for simplicity in a linear format but the model takes into account the proper reactivity (see Table 1) upon further propagation. In agreement with Figure 1d (br line), branch formation only occurs at high Xm, since only then chains are present which possess much more units than the target DP of 100. For example, in Figure 2c (Xm = 1) several chains appear at the bottom with up to ca. 300 comonomer units, which is significantly higher than the targeted number of 100. Moreover, in Figure 2c several blue lines are visible in between the different chains which corresponds to the “removal” of macromonomer chains upon macropropagation. Note that at the top quasi homopolymer chains of PhOx can be identified, which is a consequence of the dominant contribution of PhOx in the monomer feed when chain transfer side reactions occur at the later stages of the polymerization (Figure 1a and Figure 1d). For comparison, Figure 2d depicts the monomer sequences at final overall conversion (Xm = 1) in case chain transfer reactions are removed from the kinetic model (ktrM = 0 L mol−1 s−1 in Table 1). Compared to Figure 2c almost all chains are well-tailored in the absence of chain transfer. Only small irregularities are observed with respect to the target DP, which can be mainly attributed to imperfect chain initiation. At first sight, it would thus be recommendable to select initiators with a higher ki, such as nosylates or triflates.54,55 However, this would only lead to a limited improvement of the microstructural control as can be deduced from Figure 3. By artificially taking ki1/2 as high as kp1/2 (dotted black lines; otherwise full kinetic model with ktrM ≠ 0 L mol−1 s−1) a faster chain initiation occurs (Figure 3a) but only a limited decrease of the dispersity (Figure 3b) is obtained. This indicates that the impact of chain transfer reactions is still high even for fast initiation. In other words, the side reactions effectively prevent

incorporated only slowly, indicative of the formation of steep gradient-like monomer sequences. In reality, chain transfer reactions do take place and therefore no perfect control over the polymer microstructure is obtained. Indeed, with the full kinetic model (ktrM ≠ 0 L mol−1 s−1 in Table 1; full green lines in Figure 1), the experimental xn and dispersity profiles are qualitatively in good agreement with the simulations results. Closer inspection shows that at intermediate overall conversions (0.25 < Xm < 0.75) both the modeled and experimental xn data display a significant downward curvature, which is somehow corrected for at the end of the polymerization (Xm > 0.75) as values closer to the red dashed line are again obtained. An opposite observation can be made for the modeled and experimental dispersity profile. At the intermediate Xm values, a weak increase of the dispersity values is obtained with slightly decreasing values at Xm values greater than 0.75. These nonideal effects in the xn and dispersity data along the polymerization can be directly correlated to the occurrence of side reactions. At intermediate Xm, the contribution of chain transfer reactions cannot be ignored, as shown in Figure 1d (macroM line). For example, at Xm equal to 0.50 ca. 20% of the chains are macromonomers, which are directly formed upon chain transfer to monomer. As a consequence, the observed and simulated control over chain length are decreased, resulting in a decrease of the xn and an increase of the dispersity values. On the other hand, at high Xm, macromonomers are also consumed by macropropagation (Figure 1d; br line), as can also be deduced from the additional peak in the SEC traces at low retention times (see Supporting Information). Because of this macropropagation, the previous reduction in control can thus be somewhat compensated. At the end of the CROP, xn is even close to the target DP of 100, the dispersity decreases to a value below 1.1 and only ca. 7% of the chains remain as macromonomers. It should however be stressed that this E


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Figure 5. Effect of initial molar ratio of monomer to initiator or target degree of polymerization (DP) on the (a) initiator (I) concentration and (b) dispersity profiles. Key: target DP = 50 (dashed gray line), 100 (full green line), 200 (dotted purple line), and 400 (dashed dotted brown line); all other reaction conditions as in caption of Figure 1.

Figure 3. (a) Initiator (I) concentration and (b) dispersity as a function of overall conversion Xm under reference conditions (see caption Figure 1) green full line: full kinetic model with chain transfer CT (Table 1); dotted black line: with a faster initiation as mimicked by ki1/2 in Table 1 taken as high as kp1/2.

the uniform distribution of the remaining monomer molecules over all polymer chains after complete initiator consumption. This strong influence of chain transfer reactions on the control over the monomer sequences can alternatively be deduced from Figure 4, in which the average composition as a

Figure 4. Theoretical average chain corresponding with Figure 3c (bottom; with chain transfer (CT)) and Figure 3d (top; without CT); for simplicity only shown until chain position equal to target DP.

Figure 6. Effect of initial molar ratio of monomer to initiator or target degree of polymerization (DP) on (a) conversion profiles of both comonomers (Xm,I; i = 1 (MeOx), 2 (PhOx)), (b) number-average chain length xn, (c) dispersity, and (d) macromonomer (macroM) fraction and average number of branches per chain (br) as a function of overall conversion Xm. Key: target DP = 50 (dashed gray line), 100 (full green line), 200 (dotted purple line), and 400 (dashed dotted brown lines); all other reaction conditions as in caption of Figure 1.

function of the chain position is depicted for Xm equal to 1, in case chain transfer is switched off (top) and switched on (bottom). For simplicity, the maximum chain position is limited to the target DP of 100. Almost exclusively MeOx units (pure green) are obtained at low positions, whereas the opposite is true at the high chain positions with predominantly PhOx units (pure red). For the intermediate positions, a transition zone is obtained, since chains exists with both MeOx and PhOx units at a given position. This compositional heterogeneity is reflected by the color gradient (dashed boxes in Figure 4) and is broader in the presence of chain transfer reactions, consistent with the simulated differences in the explicit monomer sequences (Figure 3c vs Figure 3d). 4.2. Effect of Initial Molar Ratio of Monomer to Initiator. It can be expected that the aforementioned negative effect of noninstantaneous chain initiation on the CROP process is less important if the initial molar ratio of monomer to initiator or equivalently the target DP is increased, in agreement with kinetic modeling results on controlled radical polymerization processes.56 As shown in Figure 5a, a faster initiation on a Xm basis is indeed obtained for a higher target DP and, hence, lower dispersity values should result. Figure 5b shows that this is however only true at low Xm. At intermediate Xm, the beneficial effect on the control over chain length vanishes, since the contribution of chain transfer reactions becomes more dominant, as indicated by the crossing of the dispersity lines in Figure 5b. This higher importance of side reactions for increasing target DP becomes more clear if a detailed analysis of the main CROP characteristics (Figure 6; target DP = 50 (dashed gray line),

100 (full green line), 200 (dotted purple line), and 400 (dashed dotted brown line)) is made for the entire Xm range. It can be seen that for a higher target DP a slower CROP is obtained on a time basis and the xn and dispersity profile (Figure 5, part b or c) are less ideal, since higher macromonomer and branching fractions (Figure 5d) are obtained. In particular, for a target DP of 400 the average number of branches per chain is ca. 0.50 at complete monomer depletion. More side reactions occur for a higher target DP since relatively more MeOx is incorporated compared to PhOx (Figure 6a), aggravating the occurrence of β-elimination and subsequent macropropagation side reactions (Figure 6d). This is also confirmed in Figure 7, in which the final monomer sequences (Xm = 1) are depicted for the four target DPs studied. For the highest target DP of 400, clearly the control over individual macromolecules is even lost, as evidenced by the very high amounts of blue lines indicating the “removal” of a large fraction of macromonomer chains by macropropagation, and the very large scatter with respect to the total number of monomer units. In addition, significantly more homopolymer chains with PhOx units are present, as can be seen at the top of Figure 7d. This reduced microstructural control for increasing target DP can also be inferred from the corresponding theoretical average F


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Figure 7. Effect of initial molar ratio of monomer to initiator or targeted degree of polymerization (target DP) on the final monomer sequences. Target DP = 50, 100, 200 and 400; all other reaction conditions as in caption of Figure 1 (blue: background).

chains, as shown in Figure 8 assuming again a maximum chain position equal to the target DP for visualization purposes.

Figure 9. Effect of polymerization temperature (left 100 °C: gold lines; middle; 120 °C: blue lines; right 140 °C: green lines) for simulated (a−c) conversion profiles of comonomers; (b−f) numberaverage chain length xn, (g−i) dispersity, and (j−k) macromonomer (MM) fraction and average number of branches per chain (br) as a function of overall conversion Xm under otherwise reference conditions (see caption of Figure 1).

Figure 8. Theoretical average chains corresponding with Figure 7; top to bottom. Target DP = 50, 100, 200 and 400; for simplicity, it is only shown until chain position is equal to target DP.

Clearly, for a higher target DP a broader transition zone (larger dashed box) is obtained, indicative of a more ill-defined monomer incorporation. Hence, it is clear that the target DP is an important parameter for the level of microstructural control that can be achieved at a polymerization temperature of 140 °C. On the basis of Figures 6−8, a target DP of 200 can be considered as a practical limit for microstructural control. It can thus be concluded that a combined experimental and modeling study allows to truly identify the potential of gradient copolymer synthesis. 4.3. Effect of Polymerization Temperature. Figure 9 shows the effect of the polymerization temperature on the main CROP characteristics, keeping the other reaction conditions unchanged. A distinction is made between a polymerization temperature of 100 (left), 120 (middle), and 140 °C (right). At each temperature, a comparison is also made between simulated and experimental conversion, xn and dispersity data. Again the same correction factor of 0.45 is used to scale the measured xn data (see section 2), bearing in mind that this factor is mainly accurate up to intermediate Xm at which still linear copolymer chains are mostly obtained. It follows that the Arrhenius parameters in Table 1 allow a good qualitative description of the observed experimental trends. Moreover, the simulation results suggest that for microstructural control the lowest polymerization temperature should be selected, as the

contribution of chain transfer to monomer reactions is less important (Figure 9j−l). This in agreement with postulations in earlier kinetic studies that low polymerization temperatures are beneficial for control.57,58 For example, at Xm = 1, the macromonomer fraction decreases from ca. 7 to 4% and the average number of branches per chain decreases from 0.15 to 0.10 by lowering the polymerization temperature from 140 to 100 °C. In addition, the dispersity lowers from 1.1 to 1.05. On the other hand, upon lowering the polymerization temperature from 140 to 100 °C, the polymerization time (Figure 9a−c) is significantly increased from 1 h to ca. 18 h indicating that in practice the polymerization temperature should not be lowered much more to retain a practically useful polymerization time. The beneficial effect of a lower polymerization temperature on the microstructural control at is also confirmed in Figure 10, which shows the corresponding monomer sequences. For a lower polymerization temperature less PhOx homopolymer chains (top) and branched chains (bottom) are formed and a somewhat steeper gradient is obtained. In particular, at 100 °C a nearly perfect diblock copolymer is obtained, implying a very abrupt transition from MeOx to PhOx units in the majority of the chains. G


Macromolecules

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Article

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01642. Overview of experimental data (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (D.R.D.). *E-mail: [email protected] (R.H.).

Figure 10. Corresponding final monomer sequences for Figure 8: (a) 100, (b) 120, and (c) 140 °C. Blue: background.

Author Contributions ⊥

Hence, for a lower polymerization temperature a less pronounced transition zone can be expected for the corresponding theoretical average chain. Indeed, as shown in Figure 11 at 100 °C (top) a narrower transition zone (smaller

These authors contributed equally

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS P.H.M.V.S., M.-F.R. and D.R.D. acknowledge financial support from the Fund for Scientific Research Flanders (FWO; G.0065.13N). B.V. acknowledges support from the Agency for Innovation by Science and Technology (IWT). D.R.D. acknowledges the FWO through a postdoctoral fellowship. R.H. is grateful to the Special Research Fund of Ghent University (BOF-UGent) and the FWO for funding. The authors also thank the Interuniversity Attraction Poles Program−Belgian State−Belgian Science Policy for financial support.

Figure 11. Theoretical average chains corresponding with Figure 10, parts a (top; 100 °C) and c (bottom; 140 °C). For simplicity, this is only shown until the chain position is equal to target DP.

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REFERENCES

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dashed box) is obtained compared to the one at 140 °C (bottom), as can be also deduced based on the color contrast at the low chain positions (brighter green at 100 °C). Also here it can thus be concluded that the combined used of experimental and modeling results allows to explore the full potential of gradient copolymer synthesis.

5. CONCLUSIONS Kinetic Monte Carlo simulations have been successfully applied to study in detail the formation of individual macrospecies in CROP of MeOx and PhOx, including an explicit visualization of their monomer sequences. On the basis of a comparison with experimental data, it can be concluded that chain transfer to monomer via β-elimination and macropropagation need to be considered for a correct description of the polymer microstructure. β-Elimination is mainly relevant at low to intermediate Xm, whereas macropropagation becomes the dominant side reaction at higher Xm. The disturbance of the microstructure due to side reactions is more pronounced for higher target DPs. Despite the formation of macromonomers and branches, for target DPs below 200, the control over chain length is still preserved with final dispersity values close to 1.1. This control is even enhanced by lowering the polymerization temperature. Under such conditions, more chains are characterized by a defined, steep gradient. On the other hand, this improved microstructural control is accompanied by an increase of the polymerization time. Overall it can be concluded that kinetic Monte Carlo modeling is a powerful tool not only to understand but also to optimize CROP processes and presents a high added value for future kinetic studies. H


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Model-Based Visualization and Understanding of Monomer Sequence

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