ε-Caprolactone Polymerization Catalyzed by Heteropolyacid

41 mins ago - 2. O], as determined in HPA alone, on the. basis of. P. n. , measured for polymerizations without added initiator (only water present in...
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ε‑Caprolactone Polymerization Catalyzed by Heteropolyacid. Derivation of the Kinetic Equation for Activated Monomer Propagation and Determination of the Rate Constants of Propagation Krzysztof Kaluzynski, Piotr Lewinski, Julia Pretula, Ryszard Szymanski, and Stanislaw Penczek*

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Centre of Molecular and Macromolecular Studies, Polish Academy of Sciences, Sienkiewicza 112, 90-363 Lodz, Poland S Supporting Information *

ABSTRACT: This study demonstrates the method to distinguish between the active chain end (ACE) and the activated monomer mechanism (AMM) in polymerization of cyclic esters using kinetic analysis. The kinetic equation for the AMM was derived and applied for analysis of the polymerization of ε-caprolactone (CL) catalyzed by heteropolyacids (HPA). In contrast to other claims, polymerization of CL catalyzed by HPA proceeds by the AMM and not by ACE. The derived kinetic equation was also used to determine the rate constants of propagation involving activated monomer. Poly(ε-caprolactone) with a molar mass (Mn) greater than 105 g/mol was prepared with HPA.

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INTRODUCTION Poly(L-lactide) (PLA) and poly(ε-caprolactone) (PCL) are biodegradable polymers (PLA is also biobased).1,2 Both are industrially used in several applications. In addition to the general use as commodity thermoplastics (e.g., packaging),3 PLA and PCL are applied to biomedicine, specifically as drug delivery systems4 and biodegradable stents.5 Ring-opening polymerization (ROP) is a method of choice for the synthesis of biodegradable polyesters.6 There is a wide variety of available catalysts, allowing preparation of the related polymers with control of both Mn and the structures.7,8 For example, valuable reviews on ROP appeared in earlier monographs.9−11 The catalysts used led to anionic,12,13 cationic,14−17 or coordinate polymerization.18,19 The most versatile catalyst is still Sn(Oct)2operating in the presence of (usually) alcohols or water by the coordination−insertion mechanism.20−24 Then, there are Brønsted acids, mostly triflic acid (CF3SO3H)25−27 and derivatives of phosphoric acid28−31 (operating also in the presence of alcohols or water), that have been developed in recent decades as organocatalysts. However, acidic catalysts remain understudied compared to the more celebrated organocatalysts such as 4-(dimethylamino)pyridine (DMAP)32 and other strong organic bases, including N-heterocyclic carbenes, extensively studied by Hedrick,33 Waymouth,34−37 and Hillmyer.38−40 Recent comprehensive reviews on organocatalysts have been published by Taton41 and Dove,42 stressing living/controlled features of these systems. In one of the kinetic studies of LA polymerization with 1,8diazabicyclo[5.4.0]undec-7-ene (DBU) as catalyst, it has been postulated that in this particular system a termination reaction occurs.43 The cationic ring-opening, proceeding by AMM, involves propagation based on the addition of the protonated © XXXX American Chemical Society

(activated this way) monomer to the polymer hydroxyl end groupan active species in these polymerizations. These neither ionic nor coordinate active species are a priori less susceptible to side reactions and should be able to provide polymers of high molar mass. AMM was first described for the cationic ring-opening polymerization (CROP) in our earlier works44 and studied for polymerization of cyclic ethers.45 This process may involve competition between AMM and ACE, as has been described in detail.46 Strong acids like heteropolyacids (HPA) or particularly trifluoromethanesulfonic acid (triflic acid) are catalysts of choice in AMM.25 HPA are derivatives of phosphoric acids and often used in various chemical reactions.47 The anions of HPA have cyclic structures, with a phosphorus atom in the center and molybdenum atoms in the outer sphere (phosphomolybdic acid). HPA are commonly used in homogeneous acid catalysis (e.g., hydration of propene to produce propanol). An extensive description of HPA is given in a review paper.48 For the first time, HPA was introduced for ROP in our laboratory as a catalyst of cyclic ether and acetals.49 Polymerization of tetrahydrofuran (THF) and cyclic acetals (1,3-dioxolane, 1,3-dioxepane, and 1,3,5-trioxane) led to polymers of very high molar masses, exceeding 200000 g/ mol. The measurements of Mn demonstrated that one proton produced one macromolecule. It has also been shown that in the polymerization of THF the active species are oxonium ions (tetrahydrofuranium cations). Polymerization proceeds according to the ACE mechanism, despite the use of HPA and with autoacceleration, since the first-formed secondary Received: April 3, 2019 Revised: August 1, 2019

A

DOI: 10.1021/acs.macromol.9b00672 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules oxonium ions are much less reactive than the propagating tertiary oxonium ions.49 The rates of ROP catalyzed by low loadings of HPA rival those of the commonly employed BF3O(C2H5)2 at comparatively higher loadings, indicating that HPA is a more active catalyst than BF3O(C2H5)2. Additionally, Asahi Co. developed a green industrial process for preparing poly-THF oligomers in a two-phase system with HPA.50,51 In the polymerization of THF, HPA supported on mesoporous silica was also used.52 HPAs were applied in the polymerization of other cyclic ethers and cyclic esters. Sato studied polymerization and isomerization of oxetanes with HPA.53 Bregault used HPA (tungsten and molybdenum), e.g., H3[PM12O40] (M = Mo or W), in the polymerization of CL and δ-valerolactone, proposing a rather complicated mechanism of polymerization. It has been postulated that monomer is activated by vanadium (V) species. In the process, oligomers were essentially prepared.54 Chang55 then described polymerization of CL with phosphotungstic acid, assuming an ACE mechanism with acylium cation as active species [···− CH2CH2C+(O)]3[PW12O40]3−. The suggested mechanisms of polymerization in these two latter works are not based on the actual analysis of the processes but on the general knowledge of various reactions catalyzed by HPA. A much simpler proton-catalyzed cationic process, described for THF,49 was not considered in the above works. In the polymerization of CL, catalyzed by protonic acids, usually AMM is postulated, particularly when initiators such as alcohols are added. This was adequately described in the cited works by Bourissou,25 Kakuchi28,29 and Kubisa.26 Nevertheless, it has also been assumed that, with HPA as a catalyst, the active species are not hydroxyl polymer end groups adding an activated monomer, but carbocation (acylium cation). The case of HPA is not the only one suggesting carbocations (acylium ions) at the chain end. For the polymerization of Llactide catalyzed with CF3SO3H, Kubisa proposed56 the formation of mixed anhydride (···−CH(CH3 )C(O)OSO2CF3) at the polymer chain end, which reacts in further propagation steps with the −OH end groups on the other ends of macromolecules. In an attempt to show this occurrence, a reaction with triphenylphosphine was applied (to allow for discrimination of various cationic species).57 However, only protonated phosphine was detected by 31P NMR.56 It is worth noting that the mixed anhydrides of triflic acid are highly reactive compounds, known to be in equilibrium with the corresponding acylium ion, so much reactive that can acylate benzene.58 Thus, there is a difference in opinions regarding whether cationic polymerization of cyclic esters proceeds by AMM or ACE, particularly when strong protonic acids such as HPA are used. Because of the nucleophilic competition between monomer and −OH end-group, these two mechanisms compete with each other, and in some instances it is difficult to distinguish which one dominates. The AMM and ACE mechanisms are schematically illustrated for CL in Schemes 1 and 2 (with protonic acid as an initiator in ACE and as a catalyst in AMM). If an alcohol, for example, is added and the monomer is highly basic, then for the ACE mechanism an alcohol merely acts as a chain transfer agent without influencing the rate of polymerization and the acid becomes an initiator. Alternatively, when a monomer is less basic, then when alcohol is added, the alcohol becomes an initiator, and acid is only a catalyst. Thus, for ROH to preferentially react (to win), it has to be (not taking into the account a steric hindrance) more basic (nucleophilic) than the

Scheme 1. ACE Polymerization of a Cyclic Ester (Schematically)a

a

Anion is omitted for clarity; it may also combine with acylium cation giving mixed anhydride. “H+” is presented in inverted comas, since “free” proton does not exist in solution.

Scheme 2. AMM Polymerization of a Cyclic Ester (Schematically; Anion Is Omitted)

monomer. For example, THF polymerizes according to ACE when catalyzed by protonic acids as it is more basic than simple alcohols.59 The basicity of CL is between THF and, for example, propylene oxide (known to polymerize by AMM). The pKB values of the mentioned monomers are as follows: THF (13.5), CL (14.7), and propylene oxide (15.7).60 To avoid cyclization by backbiting in AMM, it is important that monomer is more basic than the polymer unit. For reference, CL has pKBH+ equal to 1.63, whereas simple linear esters are less basic (pKBH+ from 1.0 to 1.1).61 Although basicity of CL indicates that it could proceed by AMM, whether indeed this is the actual mechanism is not easy to determine. There are several papers on protonic acids as catalysts in the polymerization of cyclic esters, stating that polymerization proceeds by AMM, although we were not able to find the way it was established.25,26,28 Notably, AMM has been experimentally observed only in polymerization of cyclic ethers, namely, in studies of polymerization of glycidol. The ACE mechanism produces primary −OH groups (simple ring-opening) while AMM produces secondary −OH groups (primary −OH attack rings). The presence of the sec-OH was established by silylation and studies of the resulting 29Si NMR spectra.62 The dependence of the proportion of cyclics formed on the monomer concentration is only secondary evidence. In the present work, after establishing that polymerization under study proceeds as controlled/living, the equation for the kinetics of AMM polymerization was derived and used to show that polymerization indeed proceeds by AMM. By use of the same equation, rate constants are determined for the first time for propagation with activated monomer. Because HPA belong to the strongest acids (stronger than perchloric acid) and are not able to form covalent bonds with their anions, these features are facilitating proper determination of the rate B

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Figure 1. Dependence of ln([CL]0/[CL] on time in polymerization of CL catalyzed with HPA and initiated with H2O (a) and i-PrOH (b). Conditions of polymerization: (a) [CL]0 = 9.0 mol L−1, [H2O]0 (added) = 0.44 mol L−1, [HPA]0 = 1.06 × 10−3 mol L−1, ([H+]0 = 3.18 × 10−3 mol L−1). (b) [CL]0 = 9.0 mol L−1, [i-PrOH]0 = 0.39 mol L−1, [HPA]0 = 2.34 × 10−3 mol L−1 ([H+] = 7.02 × 10−3 mol L−1). Both polymerizations were conducted in the bulk at 80 °C. additionally heated in a vacuum at 120 °C for 12 h before CL was finally distilled into the polymerization vessel, which was then sealed off. The water content in HPA was estimated either from the Pn of the resulting polymers or by direct determination by 1H NMR in DMSO (cf. Supporting Information, section 1.2). Acetone (Chempur, pure p.a.) was kept over P2O5 and then distilled from over P2O5. The H2O content was determined by 1H NMR. Chloroform-d (CDCl3, 99.8%, Armar Chemicals) for the NMR experiments was used as received. Dichloromethane (DCM, CH2Cl2; P.P.H. “STANLAB” Sp. J.) was kept over P2O5 for 24 h, filtered, and distilled from over fresh P2O5. Next it was heated and distilled from over CaH2. 2-Propanol (iPrOH; P.P.H. “STANLAB” Sp. J.) was distilled from over sodium chips and then was distilled in a vacuum from over sodium metal chips into the glass ampule with a break-seal. Water was distilled twice. The second distillation was performed in a vacuum, and H2O was distilled into the glass ampule with a break-seal that was then sealed off. 1-Nonanol (n-C9H19OH; Sigma-Aldrich, 98%) was distilled from over sodium chips and then distilled in a vacuum from over sodium chips into the glass ampule with a break-seal. Characterization. The number-average molar mass (Mn) and mass average molar mass (Mw) of PCL samples were determined by using a SEC system composed of an Agilent pump 1260, an Agilent 1260 degasser, an Agilent 1100 Series injector, and a set of two PLGel 5 μm MIXED-C thermostated columns. A Wyatt Obtilab T-Rex differential refractometer and a Dawn Helios II (Wyatt Technology Corporation) multiangle laser photometer were used as detectors. DCM was used as an eluent at a flow rate of 0.8 mL min−1 at 300 K. The refractive index increment (dn/dc), equal to 0.053 mL g−1, was determined for PCL according to Wyatt recommendations and used in calculations of Mn and Mw by Astra 6.0 software. SEC (RI) was calibrated by using polystyrene standards. Matrix-assisted laser desorption ionization time-of-flight mass spectrograms (MALDITOF-ms) were registered by using a Voyager Elite mass spectrometer (PerSeptiveBiosystems, USA), equipped with a N2 laser (337 nm, 4 ns pulse width) and a time-delayed extraction ion source. The PCL samples (∼2 mg) were dissolved in 1 mL of methylene chloride containing 10 mg of dithranol and 1 mg of a salt (KCl). Subsequently, 10 μL of this solution was evaporated in air. One hundred scans were averaged per spectrum. 1H and 31P NMR spectra were acquired on Bruker AV 200 (Bruker BioSpin, Rheinstetten, Germany) with a QNP probe (1H, 13C, 19F, and 31P). All data were acquired and processed with a TopSpin 3.1 program running under the Windows 7 operating system. Polymerization Procedures. All polymerizations were performed in custom glass vessels fitted with small ampules for sample collection (Figure S4) and operated on the high-vacuum line. Polymerization with No Additional Initiator Added. HPA was transferred into the ampule that was next connected to the vacuum

constants of propagation. In several papers, the apparent rate constants of propagation were determined from the semilog kinetic plots.25,56 It will be shown that these apparent rate constants could lead, at least in some systems, directly to the rate constants. Some papers mentioned that polymerization involves activated monomer, which does participate in the elementary reactions, but the rate constants have not been determined accordingly.63,64 It is also insufficient to assume that the rate constant of propagation could be determined from an equation using the activated monomer, namely, −d[M]/dt = kp[M]·[I]·[C], where I is an initiator (e.g., an alcohol) and C is the catalyst (e.g., protonic acid) and assuming that the product [M]·[C] is proportional to [MH+], while not considering that the protonated monomer is in equilibrium with the polymer repeating units.65 The equation derived in our paper starts from the equation (−d[MH+]/ dt)prop = −d[M]/dt = kp·[MH+]·[active species] (taking into account only propagation) and eliminates [MH+] using the equilibrium constant (Keq) that involves [MH+] and the polymer units [PH+]. In the CROP of CL, the reported molar masses (Mn) are usually equal to a few thousand. Only in one paper, recently published by our group (polymerization with aryl derivatives of H3PO4), was a higher molar mass PCL prepared.66 Since the formation of poly-THF and polyacetals with Mn > 100000 g/mol when catalyzed with HPA (230000 g/mol for poly-THF),49 we have decided to use HPA to prepare PCL of similar Mn. Finally, PCL with molar masses greater than 105 g/mol are prepared in the present work.

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EXPERIMENTAL SECTION

Materials. ε-Caprolactone (CL) (Sigma-Aldrich) was placed in a round-bottom flask containing CaH2 (flask protected with a tube containing CaCl2) and stirred overnight. The mixture was then filtered, poured into a flask with fresh CaH2, and distilled (highvacuum conditions) into the round-bottom flask filled with molecular sieves (protected with a Rotaflo stopcock). Next, CL was transferred into an ampule with a sodium mirror and maintained for 2 h (during this time monomer partially polymerizes) and distilled in a vacuum into the glass ampule with a Rotaflo stopcock. Prior to polymerization, CL was distilled in a vacuum into the main polymerization vessel. More details are given in the Supporting Information. 12Molybdophosphoric acid (HPA, H3PMo12O40; BDH Chemicals Ltd., England) was dissolved in boiling H2O. The hot solution was filtered, and HPA was crystallized at room temperature. It was then dried in a vacuum, transferred into the polymerization vessel, and C

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Macromolecules line. The extent of drying was set in such a way that according to the screening experiments the rate of polymerization allowed to get close to near complete conversion within 1 or 2 days by using a sufficiently low concentration of HPA. Next, CL was distilled under vacuum into the vessel. The vessel was sealed off, and after mixing of the reagents, the polymerization mixture was distributed into sample ampules that were next sealed off. Ampules were placed in a thermostat (80 °C) at predetermined times and cooled to room temperature. 1H NMR experiments were performed on the resulting PCL to determine conversion and Pn. Polymerizations with Additional Initiator. HPA was transferred into the ampule with an arm with break-seal containing an initiator (water, C9H19OH, or i-PrOH) attached that was next connected to the vacuum line. The ampule was heated to 120 °C to remove excess water. Next, CL was distilled, in a vacuum, into the vessel. The vessel was sealed off, and then the break-seals were broken; the reagents were mixed, and the polymerization mixture was distributed into the sample ampules which were then sealed off. Ampules were placed in a thermostat (80 °C) and at predetermined times cooled to room temperature, and 1H NMR experiments were performed as described above.

determination of Pn, is given in Figure 3, with the electronic integration of the end-groups ···−CH2CH2OH (e″) and number of repeating units marked as integration of a′ or e′. From this spectrum, the determined Pn for 97% conversion is equal to 23.2 or 21.8, depending on the integration of a′ or e′, respectively. In both instances, the agreement between the calculated and determined values was satisfactory (Figure 2; determined values are 19.4 at 95% and 20.4 for full conversion). The combined tests for both phenomena can be given by an equation encompassing the invariance of the active centers concentration and the absence of the chain transfer to the low molar mass components of the system. This equation which was originally derived for the living anionic polymerization is valid for any living polymerization with the rate of initiation comparable to or higher than the rate of propagation.68 −ln(1 − ([I]0 /[M]0 )Pn) = k papp[I]0 t

(1)

total

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For this study, [I]0 = [ROH]0 and [M]0 = [CL]0. The findings shown in Figures 1−4 indicate that polymerization of CL, at least at 80 °C, catalyzed with HPA and in the presence of ROH (either H2O or i-PrOH), proceeds as a controlled/living process. The application of the 1H NMR data for determination of Pn is only valid if there are linear macromolecules present (the content of macrocycles is insignificant). Thus, the MALDI-ToF-MS results are given for both polymerization initiated with H2O and with i-PrOH as initiators (Figures 5 and 6), and as it follows from these figures, only the traces of macrocycles are present. For the “black peaks” we have been testing a large number of compositions, including, for example, major peaks and macrocycles with attached H3PO4 as well as products of oxidation of PCL. Whatever is the real structure, it would not affect the final conclusions due to the low proportion of the “black peaks”. The MALDI data show that the content of macrocycles is low and the determination of Pn from 1H NMR is justified (giving access to the concentration of active centers in the AMM). The comparison of the calculated and determined m/z values for selected signals is given in the Supporting Information (section 4) The tests described above only indicate that polymerization is controlled/living. However, it is not decided whether polymerization proceeds according to ACE or AMM mechanisms, since both controlled/living ACE and AMM would provide linear plots of ln([M]0/[M]) = f(time) and linear plot for Mn = f(conversion). Kinetics Equation for Polymerization According to AMM. Distinguishing between ACE and AMM. The usual observations are insufficient for making the distinction between ACE and AMM. The presence (1H NMR, MALDI) of the fragments of ROH in macromolecules might result equally well from initiation (AMM) or chain transfer (ACE). Similarly, Pn, given by the ratio of [M]0/[ROH]0 could result from both mechanisms as well as linear dependence of Pn on conversion and linearity of the semilog kinetic plots. Determination of the active chain ends is in principle possible but in effect infeasible, particularly for larger molar mass polymers. However, previous studies have not considered that the rate of polymerization would depend differently on the starting concentration of ROH for both mechanisms. ROH is an initiator in AMM, and its starting concentration is equal to the concentration of the active centers. Therefore, the rate of polymerization is proportional to [ROH]0. For the ACE

RESULTS AND DISCUSSION Several routine experiments were first performed to establish whether polymerization of CL with HPA was under control. Controlled/Living Condition for the Polymerization under Study. The invariance of the concentration of the active centers is usually established, independently of the actual mechanism, on the linearity of the semilog kinetic plots (ln([M]0]/[M]) = f(time)). The absence of the chain transfer (except the reversible chain transfer to polymer with rupture) is based on the linearity of the plot Mn = f(conversion). If these two criteria are met, the use of the terms living/controlled is justified and is in agreement with the IUPAC definitions.67 The corresponding kinetic plots related to the first requirement are given in Figure 1a,b. The linearity of the plots in Figures 1a and 1b means that the concentration of the active centers does not change at the described conditions; i.e., there is no termination. To demonstrate that there is no chain transfer, Mn was studied as a function of conversion, as shown in Figure 2. An example of the 1H NMR spectrum, used for the

Figure 2. Number-average molar mass (Mn) as a function of conversion in polymerization of CL. Conditions of polymerization: [CL]0 = 9.0 mol L−1, [H2O]0 (added) = 0.44 mol L−1, [HPA]0 = 1.06 × 10−3 mol L−1 ([H+]0 = 3.18 × 10−3 mol L−1), in the bulk at 80 °C. The experimental points (black ●) were determined from the 1H NMR spectra (both Mn and conversion), while the calculated values (red ●) were computed from the equation Mn(calcd) = ([CL]0 − [CL]) × 114.14/[H2O]0 (H2O was used as initiator in this experiment; 114.14 g/mol is the molar mass of CL). D

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Figure 3. 1H NMR spectrum (CDCl3) of the CL/HPA polymerization mixture. Conditions: [CL]0 = 9.0 mol L−1, [H2O]0 (added) = 0.44 mol L−1, [HPA]0 = 1.06 × 10−3 mol L−1 ([H+]0 = 3.18 × 10−3 mol L−1), in the bulk at 80 °C. Monomer conversion above 95%.

mechanism acid is an initiator and ROH is a merely chain transfer agent. If the chain transfer to ROH is reversible, then its addition does not influence the rate. Thus, there should be two different kinetic equations for ACE and AMM, which provides a distinction and proof. The kinetic equation for the ACE mechanism is simply −d[M]/dt = kp·[acid]·[M]. For AMM, the activated monomer participates in propagation and protic additives (e.g., water or an alcohol) are initiators, often converted quantitatively into the active species. The pertinent equation is derived below, after discussing some important features of this process. Polymerization of cyclic monomers, cyclic ethers, and cyclic esters by AMM involves consecutive addition of activated (usually protonated) monomer molecules (MH+) to the growing chains, with hydroxyl groups at the chain ends. Thus, there is the following general situation: a certain portion of the used acid is present in the reaction system, and only a certain portion of protons is engaged in protonation of −OH (inactivating reversibly active species), monomer (MH+), and polymer units (PH+) and involving the

Figure 4. Plot according to eq 1 for polymerization of CL with HPA and i-PrOH. Conditions: [CL]0 = 9.0 mol L−1, [i-PrOH]0 = 0.39 mol L−1, [HPA]0 = 2.34 × 10−3 mol L−1 ([H+] = 7.02 × 10−3 mol L−1).

Figure 5. MALDI-ToF-MS spectrum of the CL/HPA/H2O polymerization mixture. Conditions: [CL]0 = 9.0 mol L−1, [H2O]0 (added) = 0.44 mol L−1, [HPA]0 = 1.06 × 10−3 mol L−1 ([H+]0 = 3.18 × 10−3 mol·L−1). x: HO[C(O)CH2CH2CH2CH2CH2O]n-H + K+; y: KO[C(O)CH2CH2CH2CH2CH2O]n-H + K+. The traces of macrocycles appear, for example, at m/z = 2436, 2550, and 2664. The “black peaks” could not be identified with any certainty. E

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Figure 6. MALDI-ToF-MS spectrum of the CL/HPA/i-PrOH polymerization mixture. Conditions: [CL]0 = 9.0 mol L−1, [i-PrOH]0 (added) = 0.39 mol L−1 [HPA]0 = 2.34 × 10−3 mol L−1 ([H+] = 7.02 × 10−3 mol L−1). x: i-PrO[C(O)CH2CH2CH2CH2CH2O]n-H + K+; y: HO[C(O)CH2CH2CH2CH2CH2O]n-H + K+. The traces of macrocycles appear, for example, at m/z = 2436, 2550, and 2664. The “black peaks” could not be identified with sufficient accuracy.

matter of several additional factors not considered in our further treatment. Thus, the kinetic scheme is simpler than would be for the described general mechanism and is shown in Scheme 3. The concentration of the active species is equal to

corresponding equilibrium constants. Thus, at least three pertinent equilibria involving a certain proportion of the introduced protons and still present in the system have to be considered. The only complete determination of the rate constant of propagation (kp) in the CROP by AMM was given in our work with two cyclic ethers, propylene oxide and αepichlorohydrin.69 Similar to the earlier work by Ludvig70 (formally resembling the present treatment, but not related to AMM), equilibrium constants (Keq) were introduced, allowing elimination of the unknown concentration of the activated monomer and giving equations with an access to both kp and Keq. In the work of Ludvig, polymerization of CL was initiated with carbenium ions, leading to acylium cations as the active species (ACE), propagating in the usual way and producing dormant species with monomer and polymer units. Despite the fundamental difference of Ludwig’s mechanism and AMM, in principle the procedure in derivation of the integrated form of the kinetic equation is similar. It is also similar to our derivation for cyclic ethers cited above. However, since in the latter case only the beginning of polymerization was analyzed (the first reaction of the activated monomer with an alcohol used as the initiator), the derivation of the equation is different. We assume that there are no “free” protons in the system because of the high acidity of HPA and excess of monomer over the catalyst (the ratio [CL]0/[HPA] is over 103). Additionally, in the derivation of the final equation, the concentration of the added initiator (ROH), i.e., active −OH end groups, is much lower than the monomer concentration. Moreover, basicities of alcohols are not higher than the basicity of CL.59−61 It follows therefore that protonation of the −OH groups could be disregarded. The concentration of the activated monomer (MH+) is not known a priori in our conditions. However, since monomer is more basic than the hydroxyl group in the active species, and [M] ≫ [−OH], then at the beginning of polymerization [MH+] is equal to the concentration of protonic acidthe catalyst. The concentration changes during polymerization due to the monomer conversion and the protonation of the polymer units. Thus, after initiation, MH+ is in equilibrium with the protonated polymer units, PH+. To facilitate the kinetic treatment, protonic acid (HPA) was chosen as it is sufficiently strong to achieve full ionization. Whether it is and to which extent also dissociated (e.g., from the ion pairs into “free” ions) is a

Scheme 3. Kinetic Scheme of Propagation by AMM

the concentration of the used initiator [−OH]0 (most often alcohol). At the above established conditions of living/ controlled polymerization, the rate of monomer consumption is equal to the rate of consumption of AM in the propagation step as the proton exchange is fast in comparison with the rate of polymerization, and every molecule of MH+ reacted is equal to one molecule of M reacted. The solution of the system from Scheme 3, including the rate equation, mass balance, and protonation equilibria, leads to the differential kinetic equation (2). For the polymerization of CL, the reversibility of propagation could be neglected, at least in the studied temperature range (60−100 °C). For the polymerization of CL, the [M] in the general Scheme 3 is replaced with [CL]. −

[H+]0 [−OH]0 d[CL] = kp dt [CL] [CL](1 − Keq) + Keq[CL]0

(2)

The integrated form of eq 2 is given by eq 3: ln

(1 − Keq)([CL]0 − [CL]) k p[H+][− OH] [CL]0 + = t [CL] Keq[CL]0 Keq[CL]0 (3)

The experimentally observed linearity of the integrated equation (see below, Figure 7a−c) requires that Keq ≅ 1.0. Then, eq 3 is reduced to the very simple integral form of eq 4: F

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Figure 7. Kinetic plots giving access to the rate constants of propagation (kp) for polymerization of CL in bulk at 80 °C, calculated according to eq 4. The calculated values of kp are shown in the figures. The four other similar kinetic plots are given in Figures S10−S12. Conditions of polymerization: (a) HPA/H2O (entry 1, Table 1). Conditions: [CL]0 = 9.0 mol L−1, [HPA]0 = 1.06 × 10−3 mol L−1, ([H+]0 = 3.18 × 10−3 mol L−1), [H2O]0 (added) = 0.44 mol L−1. (b) As in (a); HPA/n-C9H19OH (entry 3, Table 1). Conditions: [CL]0 = 9.02 mol L−1, [HPA]0 = 2.2 × 10−3 mol L−1, ([H+]0 = 6.6 × 10−3 mol L−1), [n-C9H19OH]0 = 0.093 mol L−1. (c) As in (a); HPA/H2O (entry 4, Table 1). Conditions: [CL]0 = 9.0 mol L−1, [i-PrOH]0 = 0.39 mol L−1 [HPA]0 = 2.34 × 10−3 mol L−1 ([H+] = 7.02 × 10−3 mol L−1.

Table 1. Rate Constants of Propagation as Determined According to Eq 4 conditions of polymerization entry 1 2

SI figure

[HPA]0a (mol L−1) −3

Figure S13

1.06 × 10 1.82 × 10−3

3

2.20 × 10−3

4

2.34 × 10−3

5 6 7 8 9

Figure Figure Figure Figure Figure

S14 S15 S16 S17 S18

2.28 1.18 5.97 2.38 2.58

× × × × ×

10−3 10−3 10−4 10−3 10−3

initiator structure b

H2O n-C9H19OH H2Oc n-C9H19OH H2Oc i-PrOH H2Oc H2Oc H2Oc H2Oc H2Oc H2Oc

[−OH]0 (mol L−1)

temp (°C)

kp (mol−1 L s−1)

0.44 0.137

80 80

1.56 1.23

0.093

80

1.32

0.39

80

1.88

0.048 0.029 0.016 0.046 0.050

80 80 80 60 100

2.09 1.70 1.48 0.21 5.44

a [H+]0 = 3[HPA]0. bAdded [H2O]. cWth H2O present in HPA as determined according to the description in Supporting Information (section 1.1).

ln

[CL]0 [H+]0 [−OH]0 t = kp [CL]0 [CL]

trations of HPA (cf. entries 2 and 4 in Table 1) and therefore on the total concentration of active centers taken for determination of kp. The kinetic plots of the two sets of experiments were compared: HPA containing a fixed proportion of water, as determined in the Supporting Information (section 1.1), and HPA with additional external initiator. The water in HPA is equal to α[HPA]0. The coefficient α is constant and was determined from Pn. It was assumed that every molecule of H2O gives one active species. Thus, for systems with no added initiator, the rate of polymerization for AMM should depend on the product α[HPA]0[HPA]0 and as such was used in calculations. Having these data enables comparison of the kinetic results to distinguish whether polymerization proceeds according to the AMM or according to the ACE. In Figure 8, the cumulative plot of rp = {ln([CL]0/[CL])}/t = f([H+]0[−OH]0/[CL]0) for kinetics according to AMM is shown. All experimental points are on one straight line. The slope is an average value of kp and dispersion of all of the experimental results indicates relatively good consistency, as previously calculated. The number of points in the figure are the same as number of entries in Table 1. The value of kp from the slope of the linear regression (Figure 8) is equal to 1.87 ± 0.09. It differs by ∼14% from the value of kp (1.61) calculated as a simple average, since in the regression the weight of the points depends on their position versus the calculated line.

(4)

The plots according to eq 4 are given for three experiments in Figure 7, largely differing in conditions. The linearity of these plots indicates that these polymerizations are correctly described by eq 4. The corresponding kp are determined from the slopes, taking into account concentrations [H+], [−OH], and [CL]0. The kp values, as given from the three kinetic plots and determined with three different initiators, namely, H2O, nC9H19OH, and i-PrOH, are close to one another (1.56, 1.32, and 1.88). The four kp values, namely, equal to 1.23, 2.09, 1.70, and 1.48, as given in Figures 13−16, are also within a rather narrow range. The kp determined at 60 and 100 °C, used for the determination of the Arrhenius plot, are in Figures S17 and S18. All of the measured rate constants and experimental conditions are listed in Table 1. The average kp value calculated from the data obtained at 80 °C is 1.61 ± 0.24 mol−1 L s−1. The average error is 15%, although the 1H NMR and SEC used in our work for the determination of Pn (the monomer conversion and the concentration of the present water) are usually subject to a few percent of uncertainty. Additionally, this concentration of water would have a small but different influence on the concentrations of added initiators depending on the concenG

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It is generally known that kinetics do not provide an absolute proof of the mechanism, although in the present instance the kinetic results give very strong evidence for the AMM. The value for the equilibrium constant Keq ≅ 1.0 is surprising since CL is more basic then the corresponding polymer unit, as described in the Introduction.59−61 Thus, the semilog plot should be concave-up as observed in a few papers, particularly for several lactones in the paper by Hillmyer.71 The computer simulated dependences of ln([M]0/[M]) vs time (details to be published) according to eq 3 and various values of Keq for the calculations show that the deviation from linearity is very small, up to Keq equal approximately to 2.0 (although it depends on the value of kp). Alternatively, there is a possibility of cooperative hydrogen bonding, involving a few units from the polymer backbone. In such a case the pKBH+ value for several polymer units would be higher than for a simple “monomeric” unit, for which pKBH+ was measured, and therefore the basicity of the monomer could be approached by the basicity of the “polymer unit”. Arrhenius Plot. The measurements at 60 and 100 °C were used (plus an average value from 80 °C) for determining the dependence of ln kp on the 1/T (Arrhenius plot). The line constructed thereof (Figure 10) results in an activation energy

Figure 8. Dependence of rp = {ln([CL]0/[CL])}/time as a function of [H+]·[−OH]/[CL]0. The plot is linear eq 4 indicating that polymerization of CL with HPA proceeds via AMM. Points refer to the numbers in Table 1.

Alternatively, when rp (defined as above) is plotted in Figure 9 as a function of [acid] (this plot would have been linear if the

Figure 10. Dependence of the rate constant of polymerization (kp) on the reciprocal of the absolute temperature (Arrhenius plot).

Figure 9. Dependence of rp = {ln([CL]0/[CL])}/time as a function of [H+]. The plot should be linear if polymerization proceeded according to ACE. Points refer to the numbers in Table 1, as in the previous figure.

Ea = 84.8 kJ/mol. The relatively good linearity of the plot indicates that the kp measured are related to the elementary reaction. We do not discuss the thermodynamic parameters of the transition state at the present stage of our knowledge. The derived kinetic equation may permit comparison of the reactivities of various monomers and then structures of the corresponding transition states. General Final Remarks Concerning the Rate Constants. Despite the success in determination of the rate constant on the basis of the kinetic equation derived from the proposed reaction scheme, the kp values may depend on the structure of the acid used. Moreover, additional parameters might be required considering the −OH activation by counterion, as originally proposed by Bourissou72 and other authors.73 This kind of interaction may lead to the modified version of eq 4. Furthermore, additional equilibria constants could be required. Some attempts to analyze AMM kinetics of CL polymerization, taking into account the propagation step with activated monomer, have been undertaken by Kubisa63

studied polymerizations were proceeding according to ACE), the experimental points are highly dispersed and are not in any order. Thus, the kinetic equation for ACE is not compatible with our experimental results. Particularly instructive is the comparison of the points for rp belonging to the polymerizations with the same [acid] and analyzed by equations for ACE and AMM. Obviously, the most visible dispersion, for the treatment according to ACE, appears when there are two largely different concentrations of an alcohol for the same concentration of the acid. These points in the ACE figure (e.g., at [acid] = 0.007 mol L−1) are far from each other whereas for AMM are on the same straight line. This relatively simple test, distinguishing between the ACE and AMM mechanisms, is presented in the literature for the first time. H

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Macromolecules Table 2. High Molar Masses PCL Prepared by AMM Polymerizationa RIc no. 1 2 3 4 5b

−1

[HPA] (mol L ) 6.0 6.68 3.65 2.3 6.68

× × × × ×

10−4 10−4 10−4 10−4 10−4

MALLS

Mn

Mw

Đ

Mn

Mw

Đ

81500 84800 98000 105000 110600

155000 162700 169000 189000 183000

1.91 1.92 1.73 1.79 1.65

86500 84600 91000 104600 110200

154000 145300 146000 159000 168200

1.78 1.72 1.60 1.52 1.53

Conditions: polymerizations in bulk ([CL]0 = 9.0 mol L−1) and HPA as catalyst. Conversions were complete in all the instances: the time chosen was 24 h at 80 °C (in the bulk). Times were chosen arbitrarily. Full monomer conversions could had been obtained earlier. bPrecipitated polymer no 2. cThe values were determined by PS standards and were not altered/corrected by using any correction factor. a

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and then, for several cyclic esters, by Hillmyer.71 In these papers, the rate constants were not explicitly determined, and in the latter work, the semilog kinetic curves were concave-up, complicating the kinetic analysis. Nevertheless, measurements of the polymerization rates gave for the first time an insight into the relationship of reactivity and the structures of several cyclic esters. High Molar Masses of Poly(ε-caprolactone) As Prepared with Heteropolyacid. As mentioned in the Introduction, in our early work on THF and several cyclic acetals polymerizations, catalyzed by HPA, polymers from these monomers were prepared with Mn > 200000 g/mol.49 On the other hand, as indicated above, the majority of PCLs prepared by CROP and presumably driven by AMM were usually up to a few thousand g/mol. The only work describing PCL prepared this way and Mn > 105 g/mol was recently published from our group (catalyzed by aryl derivative of phosphoric acid).66 There is an obvious interest in the preparation of sufficiently high molar mass PCL by CROP, particularly, in the range of molar masses PCL could be used as a thermoplastic material. Thus, after establishing that polymerization of CL catalyzed by HPA appears to be a living/ controlled and proceeding by AMM, preparation of PCL with Mn > 105 g/mol was evaluated. The results are tabulated in Table 2. SEC (MALLS and RI) traces are presented in Figures S5−S9. As shown in Table 2, polymers with molar masses above 105 g/mol were achieved, introducing a method for the preparation of high molar mass homo- and copolymers on an industrial scale that would match the criteria of the general use of thermoplastic materials. We have been surprised that the results from SEC RI and MALLS are so close. The SEC RI data are based on the polystyrene standards, and the actual values of Mn are usually obtained by correcting these results by certain coefficients.74,75 The correcting coefficients were determined for lower molar masses, and perhaps, for such high molar masses this difference between the hydrodynamic volumes between polystyrene and PCL decreases or is even eliminated. Thus, we provide the actual RI data. Dispersities are high (Đ up to 1.78), which most likely stems from transesterification. Our previous work demonstrated that the extent of transesterification depends on reactivity of active species and conversion.76 It was shown that particularly reactive active species lead to advanced transesterification already at lower conversions. For studied system, at 20% conversion (usual conditions of polymerization) Đ = 1.4 was observed (the known limit in living polymerization with transestrification is Đ = 2.0).

CONCLUSION Cationic ring-opening polymerization (CROP) may proceed according to two different polymerization mechanisms, as the active chain end (ACE) or activated monomer mechanism (AMM). In the ACE mechanism, the active species are either carbenium or oxonium ions, both with limited stability. In contrast, in the AMM the active species are hydroxyl groups at the growing macromolecule chain ends, reacting in the propagation step with a protonated monomer. These mechanisms may also coexist and methods are known how to switch from one to another. The knowledge whether CROP proceeds by one of these mechanisms is important for the proper understanding how to choose the conditions for the polymer syntheses. For instance, in the ACE mechanism cyclic oligomers may be formed, whereas practically complete elimination of these often undesired species can be achieved in AMM. This study demonstrated how to distinguish between these two mechanisms using simple kinetic analysis. The other approaches are not conclusive. Indeed, neither the linearity of the semilog kinetic plots nor the linear dependence of molar mass as a function of conversion or the presence of the fragments of protic (e.g., H2O or ROH) additives in the resulting macromolecules provides an answer. The kinetic expression for AMM was derived, taking into account that the activated (most often protonated) monomer is in equilibrium with protonated polymer units. The experimental results of this work could be described by this equation and they are incompatible with the kinetic expression for the ACE mechanism. This equation has also allowed for the determination of the rate constants of the propagation of εcaprolactone and could be used for the determination of the rate constants of polymerization (at certain conditions) of other monomers polymerizing by AMM. Additionally, practical application of heteropolyacid as a catalyst for the CL polymerization was investigated, achieving Mn > 105 g/mol poly ε-caprolactone (PCL).

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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.macromol.9b00672. Experimental section: determination of content of water in HPA and polymerization procedures; SEC data, related to Table 2; analysis of the 1H NMR spectra; MALDI-ToF-MS m/z value calculations; how to distinguish between ACE and AMM; graphs for Table 1 (PDF) I

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. ORCID

Julia Pretula: 0000-0002-7734-5045 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was realized as part of a project of the National Science Centre Poland (Grant DEC-2016/23/B/ST5/02448). REFERENCES

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K

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