Toward Biodegradable Chain-Growth Polymers and Polymer Particles

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Toward Biodegradable Chain-Growth Polymers and Polymer Particles: Re-Evaluation of Reactivity Ratios in Copolymerization of Vinyl Monomers with Cyclic Ketene Acetal Using Nonlinear Regression with Proper Error Analysis Jean-Baptiste Lena and Alexander M. Van Herk*

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Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island 627833, Singapore S Supporting Information *

ABSTRACT: Recycling and biodegradability of chain-growth polymers is an important and growing topic. Introducing ester bonds in polymers via cyclic ketene acetals (CKAs) is an interesting route to create (bio)degradability. Incorporation of CKA monomers is controlled by reactivity ratios. Reactivity ratios of different CKA/vinyl monomer systems published in the literature were re-evaluated with the nonlinear least-squares method, taking into account the error in the 1H NMR measurements of monomer fractions in copolymers. This study confirms that the nonlinear least-squares method should be used instead of Fineman−Ross or Kellen−Tudos methods. Re-evaluated values suggest that reactivity ratios of CKA/vinyl monomer systems follow a family-like behavior. The first stage is breakdown to oligomers (via hydrolysis, so degradation), and the second stage is biodegradation by bacteria. Cyclic ketene acetals (CKAs) are interesting cyclic monomers; if the polymerization is carried out in appropriate conditions, they mainly undergo ring opening polymerization (vs ring retained polymerization), leading to aliphatic polyesters. The mechanism is described in Scheme 1. The copolymerization of CKA with vinyl monomers via the rROP mechanism leads to biodegradable vinyl copolymers.8 For rROP, the use of seven-membered rings CKAs such as 2-methylene-1,3 dioxepane (MDO) or 5,6-benzo-2-methylene1,3-dioxepane (BMDO) is a good choice as they have (i) a greater steric hindrance of the nonring open radical and (ii) a greater stability of the ring opened radical. This leads to complete ring opening polymerization. However, the process is still challenging; as in many cases, the incorporation rate of most CKAs is low in copolymerizations with vinyl monomers. Over the last years, several attempts have been made to copolymerize vinyl monomers with CKA. For instance, styrene (S) and MDO,9 vinyl acetate (VAc) and MDO,10 glycidyl methacrylate (GMA) and MDO,11 or with 4,7-dimethyl-2methylene-1,3-dioxepane (DMMDO),12 methyl methacrylate (MMA) with MDO,13 and with MDPL,14 methyl acrylate (MA) with MDO,15 n-butyl acrylate (nBA) with 5,6-benzo-2-

1. INTRODUCTION Vinyl monomer-based polymers have a wide range of applications (e.g., packaging materials, coatings, adhesives, fishing nets, etc.). Of growing concern is the accumulation of degradation resistant polymers in the environment, including plastic microbeads.1 A widely utilized method of forming chain-growth polymers without the use of organic solvents is emulsion polymerization using water as the continuous phase, and an upcoming technique is miniemulsion polymerization.2 In both areas, Lovell and El-Aaser have been pioneers in the field.2a In emulsion polymerization, the radical polymerization mechanism is often used.3 One of the key challenges with chain-growth polymers like polystyrene or polyacrylates is the resistance of these polymers with a C−C backbone to degradation.1 In both spillage in nature as well as the ease of recycling, this is a challenge. A good way to improve the degradability is the insertion of an unstable chemical linkage such as esters4 in a regular way in the main chain, typically every 10th or 20th unit. After insertion of these ester bonds, the chains can be actively degraded into functional oligomers. These oligomers, when collected, can be reconstituted into new polymer chains with potentially a different purpose than the original polymer (e.g., from packaging material to yarn).5 When not collected, they can be eaten by bacteria.6 Radical ring opening polymerization (rROP) is an interesting way to prepare aliphatic polyesters; with this process, vinyl monomers can be copolymerized with cyclic monomers bearing exomethylene groups, resulting in the insertion of unstable chemical linkages in the vinyl polymer.7 These links will break under long-term exposure, which makes the polymers biodegradable. The biodegradation can occur in two stages. © XXXX American Chemical Society

Special Issue: Mohamed El-Aasser Festschrift Received: Revised: Accepted: Published: A

April 30, 2019 July 31, 2019 August 9, 2019 August 9, 2019 DOI: 10.1021/acs.iecr.9b02375 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research Scheme 1. Mechanism of Radical Ring Opening Polymerizationa

a

I represents a radical initiator.

Table 1. Reactivity Ratios of CKAs with Various Vinyl Monomersa CKA

Vinyl commoner

rCKA

rvinyl

Method

Polymerization conditions

Year

ref

MDPL MDPL MDPL MDO MDO MDO MDO MDO MDO MDO MDO MDO MDO BMDO BMDO BMDO BMDO BMDO BMDO BMDO

MMA MeOEGMA NEtMI St MMA MMA MA GMA NVP NVP VAc VAc VAc St PFS MMA DMAEMA HEMA-TMS nBA NIPAAm

0.01 0 0.022 0.21 0.04 0.057 0.023 6.6 0.014 0.081 0.93 0.47 0.14 1.08 0.35 0.53 0.14 1.2 0.08 0.11

4 6.95 0.199 22.6 3.5 34.12 26.53 26.8 6.31 9.25 1.71 1.53 1.89 8.53 9.9 1.96 6.96 7.6 3.7 7.31

NLLS NLLS NLLS Not given KT NLLS LW FR NLLS NLLS FR KT KT KT KT KT KT KT KT KT

NMP, 90 °C, 50 wt %, toluene NMP, 90 °C, 50 wt %, toluene AIBN, toluene, 70 °C DTBP, 120 °C DTBP, 120 °C, bulk PLP, 40 °C, bulk AIBN, 50 or 112 °C, benzene or C6H3Cl AIBN, 60 °C, bulk AIBN, 60 °C, sCO2, 300 mbar AIBN, 70 °C, sCO2, 300 mbar AIBN, 60 °C, bulk AIBN, 70 °C, bulk PhotoCMRP, 30 °C, bulk ATRP, 120 °C, bulk DTBP, 120 °C, bulk ATRP, 120 °C, bulk DTPB, 70 °C, bulk AIBN, 70 °C, bulk ATRP, 110 °C, bulk DTBP, 120 °C, anisole

2016 2015 2017 1984 2007 1999 2003 2013 2006 2006 2012 2009 2016 2003 2006 2003 2010 2012 2005 2007

14 28 19 27 13b 13a 15 11 29 29 10c 10a 10b 26 30 23 31 22 16 32

a

Taken and adapted from ref 7a. St, styrene; MMA, methyl methacrylate; OEGMA, oligo(ethylene glycol) methacrylate; NEtMI, N-ethyl melamide; MA, methyl acrylate; NVP, N-vinylpyrolidone; VAc, vinyl acetate; PFS, 2,3,4,4,6-pentafluorostyrene; DMAEMA, N,Ndimethylaminoethyl methacrylate; HEMA-TMS, trimethylsilyl hydroxyethyl methacrylate; nBA, n-butyl acrylate; NIPAAm, N-isopropylacrylamide; FR, Fineman−Ross; KT, Kelen-Tüdos; LW, Lewis and Mayo; NLLS, nonlinear least-squares method.

methylene-1,3-dioxepane (BMDO),16 2-hydroxyethyl acrylate with MDO,17 propargyl acrylate with MDO,18 and some alternating systems such as N-ethyl maleimide (NEtMI) with MDPL,19 and MA and acrylonitrile with DMMDO.12 A nonexhaustive list is given in Table 1. In 2018, Gigmes et al. investigated the segment length of oligomers resulting from the degradation of copolymers containing vinyl monomers and CKA units. They demonstrated, using kinetic Monte Carlo simulations, that if experimental conditions are carefully chosen to avoid composition drift it becomes possible to counter balance the difference of reactivity of CKA and vinyl monomers and then obtain a regular insertion of ester linkage, leading to homogeneous degradation.20 The properties of the resulting copolymers (e.g., mechanical properties, glass transition temperature Tg, level of degrad-

ability) strongly depend on the microstructure of the copolymer (degree of incorporation as well as distribution of esters linkages). In general, reactivity ratios are essential to describe copolymerizations. Reactivity ratios for a pair of monomers will determine the type of copolymer that will be obtained. Reactivity ratios both close to zero will lead to alternating copolymers. Reactivity ratios above one will lead to blocky copolymers with longer sequences of the monomers, and reactivity ratios around 1 will lead to random or statistical copolymers. If the reactivity ratios of the two monomers are very different, this usually leads to poor incorporation of one of the monomers in a batch process. In those cases, monomer feeding profiles need to be applied to obtain a homogeneous copolymer. These feeding profiles are based on the reactivity B

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Table 2. Comparison between Reactivity Ratios of CKA/Vinyl Monomers Systems Obtained in Literature and Re-Evaluated with CONTOUR Applied to eq 3 System

Method

Reactivity ratios

ref

Re-evaluated reactivity ratios

MDPL/MMA

NLLS

rMDPL = 0.01 rMMA = 4

14

rMDPL = 0.014 (−0.073, +0.092) rMMA = 3.551 (−0.285, +0.401)

MDPL/NEtMI

NLLS

rMDPL = 0.022 rNEtMI = 0.199

19

rMDPL = 0.021 (−0.069, +0.129) rNEtMI = 0.157 (−0.111, +0.221)

MDO/GMA

FR

rMDO = 6.6 rGMA = 26.8

11b

rMDO = 0.155 (−0.057, +0.132) rGMA = 4.2351 (−0.879, +1.940)

MDO/VAc

FR

rMDO = 0.93 rVAc = 1.71

10c

rMDO = 0.948 (−0.359, +0.759) rVAc = 1.707 (−0.236, +0.500)

BMDO/HEMA-TMS

KT

rBMDO = 1.2 rHEMA‑TMS = 7.6

22

rBMDO = 0.019 (−0.014, +0.016) rHEMA‑TMS = 4.692 (−0.240, +0.305)

BMDO/MMA

KT

rBMDO = 0.53 rMMA = 1.96

23

rBMDO = 0.503 (−0.191, +0.601) rMMA = 1.950 (−0.473, +1.409)

f(xi,r1,r2) is the function that relates the independent (errorless) variable xi to the dependent variable yi and where wi are the weighting factors for the n data pairs, which are

ratios. In the case of cyclic ketene acetals, we often see very different reactivity ratios, and there is a needed for additional profiles to fully incorporate the desired levels of cyclic ketene acetals. Consequently, it is important to have a both an accurate and precise estimate of the value of reactivity ratios for the different copolymerization systems, especially in this particular application of copolymerization. Different methods can be used to determine the reactivity ratios. In all methods, the composition of the copolymer is needed. It is generally determined by 1H NMR spectroscopy at low monomer conversion, with a judicious choice of monomer feed composition. Over the years, it has been realized that utilizing the correct statistical methods to extract the reactivity ratios from the experimental data is important. Using linearization methods like Fineman−Ross (F-R) or Kelen−Tudos is distorting the error structure of the original measurements, and proper weighing of the individual data is not applied.21,18,19 Also, the joint confidence intervals are not of true shape and size if based on an orthogonal approximation. This has led to reporting of incorrect reactivity ratios but often based on good data. In this review, we want to re-evaluate some of the reactivity ratios from the original data given in the literature in order to create a reliable set for copolymerizations in this emerging important field of biodegradable chain-growth copolymers. With the correct nonlinear least-squares approach, it is assumed that the errors are independent and normally distributed with a common variance. If the variance is different for different data points, weighing of the data is required. The method of visualization of the sum of squares space21b (SSS) simply observes the minimum by calculating this SSS over a wide range of a parameters and does not look for the minimum in the sum of squares of the residual space (SSS) by iterative procedures. The sum of squares (ss) of residuals as a function of, for example, the two parameters r1 and r2 is defined as

wi =

∑ wi × (yi − f (xi , r1, r2))2 i=1

(2)

where σi2 is the variance in yi. In this SSS, the optimum set of the parameters is found, e.g., r1opt and r2opt, at a minimum sum of squares ss(r1opt,r2opt).21c The advantage of this method is that when the user defines a proper region where the solutions for the parameters are to be found always the true minimum is found. There is no chance of getting stuck in a local minimum, and the unbiased (exact) joint confidence interval with exact shape for the parameter estimates is given as a contour line in the sum of squares space. The method of visualization of the sum of squares directly identifies the lowest value in the total sum of squares space (by looking in the array of values). Here, we use the copolymerization equation utilized for the terminal model (eq 3). The two parameters to be optimized are r1 and r2. The independent (errorless) variable is f1, and the dependent variable is F1. F1 =

r1f12 + f1 f2 r1f12 + 2f1 f2 + r2f22

(3)

In most previous work, reactivity ratios are calculated but without confidence intervals, and the errors on the experimental measurements is not considered. In this study, we aim to recalculate the reactivity ratio of six different systems of vinyl monomer/CKAs using the nonlinear least-square method, applied to eq 3, taking into account the error on the 1H NMR measurements of the copolymer composition and reporting the correct joint confidence intervals. The systems studied are MDPL with MMA,14 MDPL with NEtMI,19 MDO with GMA,11b MDO and VAc,10c BMDO and 2-hydroxyethylyl methacrylate protected with trimethylsilyl (HEMA-TMS),22 and BMDO and MMA.23

i=n

ss(r1 , r2) =

1 σi2

(1) C

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2. METHOD 2.1. Determination of Experimental Error in Copolymer Composition. As the copolymer composition is measured as a ratio of two integrated 1H NMR signals, the error is based on the experimental error in NMR analyses. The residual standard deviation (RSD) (defined as an estimate of the accuracy of the variable being measured) of 1H NMR measurements was calculated from the signal-to-noise ratio (SNR) of both signals integrated in the copolymer composition measurement according to the following equations RSD (%) =

238 SNR1.28

i I(monomer 1) yz zz RSDjjjj z k I(monomer 2) { = RSD(I(monomer 1)) + RSD(I(monomer 2))

(4) Figure 1. Plot of feed composition (molar fraction) vs copolymer composition for the system MDPL/MMA. Green dots correspond to the values obtained by Tran et al.14 Red and purple lines correspond to the fit using reactivity ratios calculated by Tran et al. and reevaluated here. The blue line indicates the azeotropic points.

(5)

Equation 4 was established for branching measurements in polyethylene by a combination of a derivation from calculation error and empirical results24 and was assessed to be accurate also for branching measurement in hydrophobic polyacrylate.25 These errors are utilized in the fitting procedure as individual weighing factors. 2.2. Reactivity Ratio Calculations. The different reactivity ratios were estimated via nonlinear regression, applied to eq 3, considering individual errors per data point. This was carried out with the CONTOUR software package based on algorithms described earlier.18,19

3. RESULTS AND DISCUSSIONS The re-evaluated reactivity ratios of the six different CKA/vinyl monomer systems are presented in Table 2 and discussed in detail. The Supporting Information contains the error estimates in the composition and a correlation table of all reactivity ratios. 3.1. System MDPL MMA. Tran et al. copolymerized MDPL and MMA in toluene at 90 °C. They determined the reactivity ratios of this system using a nonlinear regression and provided a 95% joint confidence interval.14 The values obtained were rMDPL = 0.01 (−0.01, +0.07) and rMMA = 4.0 (−0.6, +0.9). As expected, our nonlinear regression taking into account the error on the NMR measurement provides very similar results (rMDPL = 0.014 (−0.073, +0.092) and rMMA = 3.551 (−0.285, +0.401)). The main difference is the weighing of the individual data points. The plot of feed composition vs copolymer composition and the 95% joint confidence interval for the reactivity ratios are given in Figures 1 and 2. They concluded that MDPL is more reactive toward PMMA radicals than MDO, which is more commonly used. However, this conclusion must be considered with high caution. Two studies were carried out on MDO/MMA copolymerization, and quite different results were obtained. Roberts et al. copolymerized MDO and MMA in bulk by pulsed laser polymerization (PLP) at 40 °C and obtained reactivity ratios values of rMDO = 0.057 and rMMA = 34.12 using nonlinear regression.13a Agarwal copolymerized MDO and MMA in bulk at 120 °C and obtained rMDO = 0.04 and rMMA = 3.5 with the K-T method.13b None of these results are given with a confidence interval. Tran et al.14 used results from Roberts et al.13a to make a comparison. However, the copolymerization of

Figure 2. The 95% joint confidence interval for the reactivity ratios of MDPL and MMA. The joint confidence interval was truncated to not show the negative parts as reactivity ratios below zero are physically impossible.

Tran et al.14 was carried out at a much higher temperature, and their conclusion is not valid if the 95% confidence interval is taken into account. 3.2. System NEtMI/MDPL. Hill et al. copolymerized NEtMI and MDPL in toluene at 70 °C in the presence of pyridine in order to inhibit the cationic polymerization of CKAs.19 The aim of this study was to obtain alternating copolymers that could be fully degraded. Using nonlinear regression, they obtained rNEtMI = 0.199 and rMDPL = 0.022, confirming an alternating tendency. N-substituted maleimides can be used as acceptor monomers as their vinyl bonds are electron poor and sterically hindered. This lowers the tendency for homopolymerization. On the other hand, MDPL is an electron-rich monomer and can form a pair of donors− acceptors with NEtMI. Our recalculation with CONTOUR, applied to eq 3, taking into account the error in NMR measurement leads to rNEtMI = 0.157 (−0.111, +0.221) and rMDPL = 0.021 (−0.069, +0.129), confirming an alternating system. Figures 3 and 4 show the feed composition vs copolymer composition and the 95% joint confidence interval for the reactivity ratios, respectively. A feed composition vs D

DOI: 10.1021/acs.iecr.9b02375 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 5. Plot of feed composition (molar fraction) vs copolymer composition for the system MDO/GMA. Green dots correspond to the values obtained by Udin et al.11b Red and purple lines correspond to the fit using reactivity ratios calculated by Udin et al.11b and reevaluated here. The blue line indicates the azeotropic points.

Figure 3. Plot of feed composition (molar fraction) vs copolymer composition for the system MDPL/NEtMI. Green dots correspond to the values obtained by Udin et al.11b Red and purple lines correspond to the fit using reactivity ratios calculated by Hill et al.19 and reevaluated here. The blue line indicates the azeotropic points.

The results obtained with a nonlinear regression are quite different. The re-evaluated reactivity ratios were rMDO = 0.155 (−0.057, +0.132) and rGMA = 4.2351 (−0.879, +1.940). Figure 6 shows the joint confidence interval of the reactivity ratios.

Figure 4. The 95% joint confidence interval for the reactivity ratios of MDPL and NEtMI. The joint confidence interval was truncated to not show the negative parts as reactivity ratios below zero are physically impossible.

Figure 6. The 95% joint confidence interval for reactivity ratios of MDO and GMA.

copolymer composition plot with error on the copolymer composition was provided by Hill et al.19 However, there is no indication on how the error was obtained. In Figure 4, the 95% joint confidence interval for the reactivity ratios of MDPL and NEtMI are shown. 3.3. System MDO/GMA. Udin et al. copolymerized MDO and GMA in bulk at 60 °C and obtained the reactivity ratio values using a (F-R) plot.11b The obtained values were rMDO = 6.6 and rGMA = 26.8. This means that both growing radicals prefer homopropagatation over cross propagation. This leads to the formation of block copolymers whose degradation would be difficult as the insertion of caprolactone is not favored. This is quite unusual for vinyl monomer/CKA systems. However, if these estimations were accurate the following would occur: (i) We would observe an azeotrope in the Mayo−Lewis plot, and this is not the case (Figure 5). (ii) A blocky copolymer would have been obtained as each monomer would have a preference for itself rather than the other monomer. Thermal analyses carried out showed that a single Tg was observed.

The re-estimated values are more consistent with what is observed and expected. Both monomers have a preference for GMA, which leads to a nonazeotropic composition. The formation of a radical in GMA is favored due to the conjugation. The based-GMA propagating radical is stabilized. However, reactivity ratio values were obtained with experiments carried out at relatively high conversion, which leads to a composition drift and could bias the results. Consequently, even though the use of the NLLS method has led to more reliable results, there might still be some error in the reevaluated values. 3.4. System MDO/VAc. Udin et al. copolymerized MDO and VAc in bulk at 60 °C.10c They measured the reactivity ratios with the F-R method and obtained rMDO = 0.93 and rVAc = 1.71. Our re-estimation confirmed these results: rMDO = 0.948 (−0.359, +0.759) and rVAc = 1.707 (−0.236, +0.500). Both reactivity ratios are close to unity, and a random copolymer structure is obtained. This can be compared with E

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(±1.6) and rBMDO = 1.2 (±0.4). However, the re-evaluated values are different: rHEMA‑TMS = 4.692 (−0.240, +0.305) and rBMDO = 0.019 (−0.014, +0.016). Both results are consistent with what is observed by Zhang et al.22 in terms of copolymer composition. At the start of the reaction, polymer chains rich in HEMA-TMS are formed, and at higher conversion, BMDOHEMA-TMS sequences are more abundant. However, a much faster incorporation of HEMA-TMS was observed all over the copolymerization process, consistent with both growing radicals having a preference for HEMA-TMS. Moreover, the Mayo−Lewis plot obtained with the re-evaluated reactivity ratio values exactly fit with the data points obtained by Zhang et al.22 This is not the case with the values obtained by the K-T method (Figure 9).

the system CKA/acrylates studied previously, where a greater difference between the reactivity ratios was observed and both propagating radicals had a stronger preference for acrylates. This is likely due to the less-activated nature of VAc. Two other studies with the system MDO/VAc are reported in the literature. Agarwal et al. copolymerized these two monomers in bulk at 70 °C and obtained rMDO = 0.47 and rVAc = 1.53 with the K-T method.10a Ding et al. used a bulk polymerization at 30 °C and obtained rMDO = 0.14 and rVAc = 1.89 with the K-T method.10b All three studies are consistent with a random insertion of MDO. The re-evaluated values, which are very similar to Udin et al.10c values, are compatible with Agarwal et al.’s10a study if the error is taken into account. However, Ding et al. observed a much stronger preference of MDO radicals for VAc than the other groups.10b Figures 7 and 8 show the feed composition vs copolymer composition and the 95% joint confidence interval for the reactivity ratios respectively.

Figure 9. Plot of feed composition (molar fraction) vs copolymer composition for the system BMDO/HEMA. Green dots correspond to the values obtained by Zhang et al.22 Red and purple lines correspond to the fit using reactivity ratios calculated by Zhang et al.22 and re-evaluated here. The blue line indicates the azeotropic points.

Figure 7. Plot of feed composition (molar fraction) vs copolymer composition for the system MDO/VAc. Green dots correspond to the values obtained by Udin et al.10c Red and purple lines correspond to the fit using reactivity ratios calculated by Udin et al.10c and reevaluated here. The blue line indicates the azeotropic points.

Figure 10 shows the 95% joint confidence interval for the reactivity ratios. 3.6. System BMDO/MMA. Wickel et al. copolymerized BMDO and MMA in bulk, at 120 °C, using the ATRP method.23 The reactivity ratios they obtained with the K-T method (rBMDO = 0.53 and rMMA = 1.96) are consistent with the re-evaluated values (rBMDO = 0.503 (−0.191, +0.601) and

Figure 8. The 95% joint confidence interval for the reactivity ratios of MDO and VAc.

3.5. System BMDO/HEMA-TMS. Zhang et al. copolymerized BMDO HEMA-TMS in bulk at 70 °C and determined the reactivity ratios with the K-T method, using low conversion polymerization.22 They obtained values of rHEMA‑TMS = 7.6

Figure 10. The 95% joint confidence interval for the reactivity ratios of BMDO and HEMA. F

DOI: 10.1021/acs.iecr.9b02375 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research rMMA = 1.950 (−0.473, +1.409)). Both growing radicals have preference for MMA, which results into a random incorporation of BMDO in the copolymer. These results are similar to the ones for the system MDPL/MMA, which may suggest that copolymerization of different CKAs with a same vinyl monomer follows a family-like behavior. If this is the case, the results obtained from Agarwal et al.13b on the system MDO/MMA fit more into the family-type behavior than the ones of Roberts et al.13a Figures 11 and 12 show the feed composition vs copolymer composition and the 95% joint confidence interval for the reactivity ratios respectively.

systems MOD/styrene, MDO/MMA and MDO/MA obtained by Bailey et al.,27 Roberts et al.13a and Sun et al.15 respectively might be overestimated. Finally, it is important to note that most polymerizations carried out to measure the reactivity ratios reported in Table 1 were stopped far beyond 5% conversion, which could lead to inaccuracies. These re-evaluation tends to demonstrate that reactivity ratios of CKA/vinyl monomers follow a family-like behavior. It can be confidently affirmed that rCKA < 1 and rvinyl > 1 (except for alternating systems with NetMI, in which both reactivity ratios are close to 0), which means that both CKA and vinyl radicals have a preference for the CKA monomer. This leads to a random insertion of CKA in the copolymers. At the early stage of polymerization, only very few CKA units are inserted, and the polymer chains become richer in CKA at higher conversions. The obtained copolymers should be more or less random which is important for the degradation oligomers when the polymers are hydrolyzed or biodegraded. However, due to composition drift in a batch reaction, we would get chains with different incorporation levels of the CKA monomer leading to nonuniformous oligomer chain length distributions and therefore suboptimal further degradation behavior. In order to avoid composition drift, feeding of monomers should be applied, based on the important reactivity.20,33 This family-like behavior is confirmed by the difference of reactivity of vinyl monomers toward CKA and toward other vinyl monomers. This is shown in Table S7 in the Supporting Information.

Figure 11. Plot of feed composition (molar fraction) vs copolymer composition for the system BMDO/MMA. Green dots correspond to the values obtained by Wickel et al.23 Red and purple lines correspond to the fit using reactivity ratios calculated by Wickel et al.23 and reevaluated here. The blue line indicates the azeotropic points.

4. CONCLUSIONS Reactivity ratios of six CKA/vinyl monomer systems were successfully re-evaluated with the NLLS method using CONTOUR. The re-evaluated values tend to show a familylike behavior. Both growing radicals have a more or less pronounced preference for the vinyl monomer (except when both CKA and vinyl monomers cannot homopolymerize, leading to alternating copolymers). CKA units can be inserted randomly in vinyl monomer-based polymers, leading to biodegradable materials. This work provides relevant information which helps to optimize conditions for biodegradable polymer synthesis in numerous applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b02375. Figure 12. The 95% joint confidence interval for the reactivity ratios of BMDO and MMA.

Table S1: Error on NMR analyses and on the fraction of MDPL in the copolymer MMA/MDPL. Table S2: Error on NMR analyses and on the fraction of NEtMI in the copolymer NEtMI/MDPL. Table S3: Error on NMR analyses and on the fraction of MDO in the copolymer GMA/MDO. Table S4: Error on NMR analyses and on the fraction of MDO in the copolymer VAc/MDO. Table S5: Error on NMR analyses and on the fraction of BMDO in the copolymer BMDO/HEMA-TMS. Table S6: Error on NMR analyses and on the fraction of BMDO in the copolymer BMDO/MMA. Table S7: Reactivity ratios of copolymerization systems containing each monomers included in this study. (PDF)

3.7. Discussion. Six reactivity ratios of systems CKA/vinyl monomers were re-evaluated from the published NMR data with the nonlinear least-squares (NLLS) method using CONTOUR applied to eq 3. Results are presented in Table 2. This study confirms that the NLLS method should be used and that the K-T and F-R methods sometimes provide very different reactivity ratios values from the correct ones. Considering their family-like behavior, other reactivity ratios in Table 1 need to be re-evaluated as well, for example the BMDO/styrene by Wickel et al.26 The values of rvinyl of G

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Alexander M. Van Herk: 0000-0001-9398-5408 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Naraharisetti Pavan Kumar is acknowledged for valuable feedback. A*Star is acknowledged through Grant No. A1786a0030.

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REFERENCES

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DOI: 10.1021/acs.iecr.9b02375 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX