Theoretical and Experimental Approach to Accurately Predict the

Aug 15, 2014 - SABIC T&I, STC-Geleen, SABIC Europe B.V., Urmonderbaan 22, 6160 AH Geleen, The Netherlands. •S Supporting Information. ABSTRACT: ...
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Theoretical and Experimental Approach to Accurately Predict the Complex Molecular Weight Distribution in the Polymerization of Strainless Cyclic Esters Mark P. F. Pepels,† Paul Souljé,† Ron Peters,‡ and Rob Duchateau*,†,§ †

Laboratory of Polymer Materials, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands ‡ DSM Resolve, Urmonderbaan 22, 6167RD, Geleen, The Netherlands § SABIC T&I, STC-Geleen, SABIC Europe B.V., Urmonderbaan 22, 6160 AH Geleen, The Netherlands S Supporting Information *

ABSTRACT: Polyesters obtained by the catalytic ringopening polymerization of macrolactones in many aspects resemble the properties of polyethylene. However, the molecular weight distribution is intrinsically different and equals the molecular weight distribution observed for a stepgrowth process even though macrolactone ring-opening polymerization follows a chain-growth mechanism. The concurrent occurrence of transesterification reactions leading to the formation of cyclic polymers is responsible for the deviation from the molecular weight distribution characteristic for chain-growth polymerization. To explain and extent on the theoretical principles forming the basis of this peculiar molecular weight distribution, in this work the cyclization process during the polymerization of the 17-membered macrolactone ambrettolide has been analyzed. Liquid chromatography under critical conditions has been applied to semiquantitatively analyze the fractions of cyclic and linear products. In addition, low molecular weight size exclusion chromatography has been used to independently quantify the fractions of the smallest cyclics. Using the combination of these techniques it has been shown that cyclics are present during the whole polymerization process. Furthermore, the thermodynamics of the polymerization reaction were determined. The negligible ΔH⊖p = 0.9 ± 1.9 kJ·mol−1 and a positive ΔS⊖p = 38.5 ± 6.5 J·mol−1·K−1 clearly demonstrate the absence of significant ring strain and proofs that the polymerization is driven by entropy. Individual equilibrium concentrations of the cyclics, from monomer to pentamer, were determined and these values were used in combination with the Jacobson and Stockmayer theory to calculate the effective molarity of the cyclic monomer, B = 0.087 M. This value subsequently yields a critical monomer concentration of 0.155 M, for which it was also experimentally determined that polymerizations having a monomer concentration below this value only yield cyclic polymers. Finally, B was used in combination with the monomer and initiator concentration to successfully predict the molecular weight distribution, which shows that real Mn’s are far lower and dispersities far higher than predicted from often-applied theories.

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olefins.4 Although macrolactones can be polymerized using a variety of compounds including enzymes (eROP),11 organometallic (cROP)12−15 and organic catalysts (oROP),16 all polymers show a rather broad molecular weight distribution. Indeed, this is expected for eROP reaction, since they are known to have fast transesterification rates. However, due to their intrinsically living nature, cROP and oROP reactions generally provide good control of the molecular weight and molecular weight distribution. Lack of control during the cROP of macrolactones originates from the absence of ring-strain,17 which results in similar rates for polymerization and transesterification.12

INTRODUCTION Aliphatic long-chain polyesters (ALCPs) have received considerable attention, since they can be made from biobased resources1,2 and have crystalline properties similar to polyethylene.3 The most significant difference compared to polyethylene is the incorporation of ester groups into the crystal lattice, resulting in a decrease of the melting temperature.4 These polymers can be processed using common industrial techniques such as injection molding and film extrusion.5 ALCPs can be made using various methods, which can generally be divided into two categories: polymerizations following a step-growth mechanism, e.g., polycondensation6−8 and ADMET,9 and a chain-growth mechanism, e.g., ringopening polymerization (ROP) of macrolactones10 and ROMP of unsaturated macrolactones optionally together with cyclic © XXXX American Chemical Society

Received: July 27, 2014

A

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Scheme 1. Polymerization of Amb using 1 into lPAmb and cPAmb

Figure 1. (a) LCCC-ELSD chromatograms using different solvent ratios of PAmb obtained by cROP, [Amb] = 1.0 M and [1] = 0.01 M and (b) the MALDI−TOF−MS spectra of the collected fractions A−D for THF/water = 89.5/10.5.

While intermolecular transesterification only leads to a broadening of the molecular weight distribution (increase of dispersity, ĐM), intramolecular transesterification leads to the formation of relatively low molecular weight cyclic products, thereby increasing the total number of chains and significantly broadening ĐM. The presence of cyclics in polycondensates was already mentioned in Flory’s early work on molecular size distributions,18 but a solid theoretical description was only developed in 1950 by Jacobson and Stockmayer (J&S theory).19 This theory describes that for a system in thermodynamic equilibrium, a certain finite amount of cyclics is produced at high conversion, which follows a specific distribution most dominant in the low molecular weight regime. More recent work by Kricheldorf and co-workers suggest that the cyclic fraction for polycondensations is actually much larger at high conversions.20 The formation of cyclic oligomers has been studied for the ROP of strained lactones, e.g., ε-caprolactone (εCL),21−24 and it was shown that depending on the catalytic and initiating system macrocycle formation can be enhanced by stimulating end-to-end cyclization, or reduced by suppressing transesterification.25 In other work, the equilibrium polymerization of propiolactone was investigated by Roelens and co-workers who could describe the cyclic product very well with the J&S theory. However, the focus of these papers was mostly on the cyclic products and not on how the presence of cyclics affects the whole molecular weight distribution. Polymerizations of strained rings like εCL are generally stopped far before thermodynamic equilibrium is reached, thus producing a kinetic product distribution containing only a limited amount of cyclics. Therefore, a theoretical description of the whole distribution is less necessary and the contribution of cyclics oligomers is generally neglected. In contrast, due to the limited

amount of ring strain the ROP of macrolactones is associated with relatively high transesterification rates yielding a distribution close to thermodynamic equilibrium. The presence of a significant amount of cyclic products during the ROP of macrolactones has been reported in several papers, however, a solid quantification (method) for these products has to our knowledge never been developed. Since low molecular weight fractions can influence both the melt- and solid-state properties of a polymer significantly,26 it is desired to develop a practical method to calculate the molecular weight distribution of both the linear and cyclic part of the polymer produced by cROP of macrolactones. Therefore, in this paper we present an extended theoretical approach as a special case of the J&S theory suitable to predict the complete molecular weight distribution of the polymerization of macrolactones, in combination with experimental work.

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RESULTS AND DISCUSSION To allow investigating the formation of cyclic and linear products during the ROP of macrolactones, a polymer system is required that can easily be analyzed, i.e., is soluble in conventional solvents at room temperature. For this reason, the cROP of the 17-membered macrolactone ambrettolide (Amb) was studied, since the ring size and reaction rate are comparable to the often studied pentadecalactone (PDL),12 while the internal double bond significantly lowers the melting temperature of poly(ambrettolide) (PAmb, 55 °C vs 95 °C for PPDL27) resulting in room temperature solubility of the polymer in THF. In order to obtain a polymer mixture containing both significant linear PAmb (lPAmb) and cyclic PAmb (cPAmb), a 1.0 M Amb solution in toluene was polymerized using 0.01 M of aluminum salen (PDO−Al[salen] (1); PDO = pentadecanoxy), which was shown in a previous B

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Figure 2. (a) Low-MW−SEC of PAmb obtained by cROP, [Amb] = 1 M and [PDOH] = 0.01 (solid line) and the individual fractions (dotted lines A−D) obtained from fractionation. (b) MALDI−TOF−MS analysis of the individual fractions.

Figure 3. (a) Conversion versus time of the cROP of Amb, [Amb] = 0.5 M, [1] = 0.005 M. (b) Dotted line representing the calculated conversion using the kinetic parameters from ref 12. LCCC-ELSD chromatograms of the samples taken at 30 and 240 min.

study to be a very suitable catalyst for the cROP of macrolactones (Scheme 1).12 Furthermore, it is expected that there is no difference in the reactivity of a PDO−Amb ester linkage compared to an Amb-Amb ester linkage, excluding any preference for backbiting or end-to-end cyclization. This in contrast to cROPs initiated with water, which, depending on the catalyst, sometimes tend to have a preference for one of both cyclization mechanisms.28 End-Group Separation Using Liquid Chromatography under Critical Conditions. The separation of lPAmb and cPAmb by chromatography can only be achieved if the interactions of the polymer backbone with the column material are eliminated, i.e., using liquid chromatography under critical conditions (LCCC),29 which allows separation purely on end groups excluding molecular weight. In order to achieve critical conditions, the eluent composition was carefully varied while maintaining a constant temperature and flow rate (similar to the approach as described by de Geus et al.30). A stepwise decrease of the THF/water ratio led to the chromatograms shown in Figure 1a, for which the critical conditions were

established to be at a ratio of 89.5% (v/v) THF and 10.5% (v/ v) H2O. Fractionation of the polymer and subsequent MALDI−TOF−MS analysis revealed that the spectra (Figure 1b) of the main peak at 10.8 min and the shoulder at 11.6 min both correspond to lPAmb, while the MALDI−TOF−MS spectra of the peak at 13.2 min correlate to a distribution consisting solely of cPAmb. The cyclic fraction eludes in LCCC mode, while lPAmb elutes in exclusion mode. The observation that the linear fraction develops two peaks can likely be explained by the total exclusion of the high molecular weight fraction of lPAmb, possible in combination with the good solvent (100% THF) in which the samples are prepared, causing faster elution of part of the product (break through). Quantification with an evaporative light-scattering detector (ELSD) is challenging since the intensity is influenced by concentration, molecular weight and molecular structure. This is reflected in the intensity of pure Amb, which barely gives a signal even when measured in high concentrations. Therefore, the LCCC method in this work is only used as a semiquantitative method. It should furthermore be noted that C

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in which R is the gas constant and T the temperature. It can be observed that within the experimental error there is no temperature dependence in [Meq], resulting in a ΔH⊖p = 0.9 ± 1.9 kJ·mol−1 and a ΔS⊖p = 38.5 ± 6.5 J·mol−1·K−1 (Figure 4).

the elution time under critical conditions is very sensitive to variations, resulting in minor shifts when samples were measured at different moments. Quantification of Individual Cyclic Oligomers and Determining the Polymerization Thermodynamics for ROP of Amb Using Low-MW−SEC. The quantification of individual small cyclic oligomers is essential for the application of the J&S theory to the system. Therefore, low molecular weight size exclusion chromatography (low-MW−SEC) was applied to the sample described in the previous section. Various well-defined signals can be obtained in the low molecular weight regime using this method (Figure 2a). A large part of the polymer has a molecular weight higher than the exclusion limit of the system, leading to a narrow peak at 12.6 min. Amb was easily identified as the signal at 20.5 min by direct measurement. The low molecular weight cyclics were individually collected using fractionation of a concentrated sample into fractions A-D. The reinjection of the individual fractions on the low-MW−SEC and MALDI−TOF−MS led to the identification of the cyclic dimer to pentamer (Figure 2b). It is desired to be able to quantify the conversion using lowMW−SEC instead of 1H NMR for two reasons. First, at high dilution the amount of Amb versus solvent is very low resulting in a low signal-to-noise ratio for the monomer and polymer signal in 1H NMR. Second, high dilution gives rise to a third signal in 1H NMR between the monomer and polymer triplets, probably being caused by the cyclic oligomers. This signal makes accurate integration impossible since the monomer and polymer signals overlap. In order to test if low-MW−SEC could be used to determine the conversion of these systems, a polymerization was performed using [Amb] = 0.5 M and [1] = 5.0 mM at 100 °C in toluene. Integration of the polymer and the Amb fraction of samples taken at different time intervals led to the conversion−time profile presented in Figure 3a. When using the reaction rate constant determined in a previous study,12 the dotted line is obtained. It can be seen that this line fits the conversion profile very well, showing the ability of lowMW−SEC to be used as quantitative method for conversion determination. For strained-ring lactones the cROP is generally much faster than transesterifications.21,23,24,31,32 This means that in the initial stages of the polymerization predominantly linear chains are produced and only after prolonged reaction times cyclic chains are formed. Typically, the reaction is stopped before significant transesterification has taken place, yielding polymers with a very narrow ĐM. Analysis of the cyclic content during polymerization of Amb shows that there is no significant difference between the amount of cyclics at intermediate and full conversion (Figure 3b). This again shows that there is hardly a difference between polymerization rate and transesterification rate of Amb and PAmb, respectively. For Amb the thermodynamics of the cROP were investigated by polymerization of a solution containing [Amb] = 0.2 M and [1] = 0.002 M in toluene at temperatures ranging from 70−130 °C for 141 h, which is long enough to reach full thermodynamic equilibrium. Subsequently, the monomer equilibrium concentrations ([Meq]) obtained from low-MW− SEC were used to obtain the enthalpy (ΔH⊖p) and entropy (ΔS⊖p) of polymerization, which follows the relation:17 ln[Meq] =

ΔH p⊖ RT

−

Figure 4. Polymerization thermodynamics of the cROP of Amb, [Amb] = 0.2 M, [1] = 0.002 M. Concentrations were calculated using the measured densities as reported.12

Indeed this shows that the main driving force for the ROP of macrolactones is entropy. As a comparison, for εCL the values are ΔH⊖p = −28.8 kJ·mol−1 and ΔS⊖p = −53.9 J·mol−1·K−1, which makes this polymerization completely enthalpy driven.17 It should be noted that the values on the low-MW−SEC measurements in the monomer regime show some variations due to small overlap of the Amb peak with system peaks, which gives a significant uncertainty in the enthalpy. Nevertheless, it is clear that ΔS⊖p is the determining factor in this type of polymerizations. This means that the cROP of macrolactones is indeed similar to transesterification, which is also an entropydriven process. Theoretical Description of ROP Products in Thermodynamic Equilibrium as a Special Case of J&S Theory. As explained above, since all ester bonds are similar, there is in principle no preference for the system to undergo intra- or intermolecular transesterification. Generally, the average degree of polymerization for a ROP can be predicted using the monomer/initiator ratio, which excludes the formation of cyclics. However, when the reaction mixture is allowed to reach thermodynamic equilibrium, the molecular weight distribution should be similar to the equilibrium obtained from a polycondensation reaction. The initial monomer/initiator ratio in a fully reacted system is basically the same as the number of reacted groups/unreacted groups in a polycondensation reaction. Similar to a polycondensation reaction, the extent of the reaction can be calculated using p=1−

(2)

where [Ini]0 and [Mon]0 are initial concentration of initiator and monomer, respectively. Since the polymerization of macrocyclic esters will generally lead to a product in thermodynamic equilibrium, it possible to apply the theory of macrocyclization under thermodynamic control to this system. This theory was first postulated by Jacobson and Stockmayer,19 after which it has been redefined in a more understandable

ΔSp⊖ R

[Ini]0 [Mon]0

(1) D

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Figure 5. (a) Equilibrium concentration of cyclic oligomers in the cROP of Amb versus total monomer concentration in toluene at 100 °C. (b) Equilibrium concentration of cyclic oligomers for [Mon]0 = 0.2 M versus the cyclic size. Dotted line represents the best fit (B = 0.087 M) using eqs 3−5

manner for nonexperts by Roelens and co-workers.33 For clarity purposes, the overall reasoning of the Roelens paper is described with modifications concerning the ROP of macrolactones. For these systems, the extent of reaction in the linear fraction, x, should be calculated similar as eq 2, replacing [Mon]0 by the concentration of monomers included in the linear part ([Mon]l): [Ini]0 x=1− [Mon]l

At high conversions, this equation diverges to a value representing the so-called critical monomer concentration ([Mon]crit):33 r−1

[Mon]crit = 2.612B +

i=1

Eventhough the value for [Mon]l cannot be directly obtained, it can be calculated using an iterative process (as described in the Experimental Section).34 In the J&S theory, it is stated that the concentration of cyclic chains with length i, [Ci], can be calculated using the molar cyclization equilibrium constant Ki:33

[Mon]l = [Mon]0 − [Mon]c

Ki is both conceptually and operationally identical to the equilibrium effective molarity (EM), which represents the concentration of cyclic chains with size i when x approaches 1. In J&S theory it is furthermore derived that when strainless rings are formed from chain-obeying Gaussian statistics, the EMi is inversely proportional to the power 5/2 and follows the relation:33

Pi = x i − 1(1 − x)

[Li] =

in which B represents the effective molarity of the monomeric ring (EM1) as if it were strainless. Macrocycles with more than 30 atoms are generally strainless,35 but smaller rings often contain some amount of ring strain. Therefore, the total amount of monomers included in cyclic chains ([Mon]c) should be expressed by two terms, of which the first describes the cyclics up to sizes of r − 1, where r is the size of the first strainless cycle:33

[Mon]c =

∑ i EMix i=1

strained rings

+

B ∑ i−3/2x i i=r

strainless rings

Pi [Mon]l ∞ ∑i = 1 Pii

(10)

Application of the Theory to the Polymerization of the Macrolactone Amb. In order to be able to predict the molecular weight distribution of PAmb, the polymerization of solutions containing various concentrations of Amb were performed using 1 in toluene at 100 °C. For all polymerizations a 100/1 Amb/initiator ratio was used. All reactions were allowed to react for 93 h, which theoretically would lead to 99.999% of the theoretically maximum conversion for the lowest amount of catalyst.37 It can therefore be stated that all systems will be in thermodynamic equilibrium. The individual cyclic oligomers were quantified using the low-MW−SEC method described in the previous section. It can be observed that the concentration of cyclics increases until [Mon]0 = 0.2

∞ i

(9)

Finally, from this the concentrations for linear chains with size i, [Li], can be calculated:

(5)

r−1

(8)

The probability distribution (Pi) of the linear part of the system can still be described by the theory for molecular size distribution in linear condensation polymers developed by Flory.18 However, for the extent of the reaction only the linear part should be taken into account, which requires the use of eq 3:

(4)

K i = EMi = Bi−5/2

(7)

This physically means that up to this critical concentration only cyclic chains will be formed. When the concentration increases further, only linear chains will be formed. This concept has been nicely visualized by Di Stefano.36 The linear part of the polymer is therefore made up from the remaining part of the monomers:

(3)

[Ci] = K ix i

∑ (Bi−3/2 − i EM)

(6) E

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results in a further increase of the linear fraction, which consequently becomes larger than the cyclic fraction. In general, polymers are synthesized far above their [Mon]crit. Even though in these polymerizations by weight the vast majority of the product consist of linear chains, the cyclic chains do have a tremendous effect on the Mn and the ĐM of the polymer, since these parameters are strongly influenced by the number of chains. To show the effect of the cyclic polymers on the Mn, Mw, and ĐM, a SEC chromatogram was constructed using the theory described above. Since in the normal SEC chromatograms ambrettolide is excluded from the analysis, Amb is also omitted from the current molecular weight calculations. It should be stressed that for these calculations only three parameters are required, i.e., [Mon]0 and [Ini]0, which are set by the experimenter, and B, which is an intrinsic property of the polymer. A numerical approach (see Supporting Information for details) was used determining the cyclic distribution from the input parameters, subsequently determining the linear distribution, and finally plotting the distribution of all the individual chain fractions as normal distributions. As an example, the polymerization of Amb was both experimentally performed and modeled using [Amb]0 = 1.0 M and [Ini]0 = 0.01 M. This resulted in the measured and calculated molecular weight distribution (Figure 7) with an experimental Mn of 12.1 kg·mol−1 and a ĐM of 6.73, and a calculated Mn of 6.46 kg· mol−1 and a ĐM of 6.04. This discrepancy is the result of the calibration with polystyrene standards, and can be compensated using the Mark−Houwink equation. Transformation of the calculated molecular weights resulted in a good fit with an Mn of 11.9 kg·mol−1 and a ĐM of 6.68. This clearly shows the power of this method, in which the determination of the B value is enough to predict the whole distribution using the modified J&S theory. Predicting the Molecular Weight Distribution with Varying [Mon]0/[Ini]0. For a ROP at full conversion excluding cyclization reactions, the theoretical Mn is easily calculated using ([Mon]0/[Ini]0)·Mmonomer, where Mmonomer is the monomer molecular weight. However, as shown in Figure 7, intramolecular transesterification and the corresponding cyclic distribution have a tremendous effect on the molecular weight distribution. To quantitatively investigate this influence, the developed model was applied to two systems having a [Mon]0 = 1.0 M, which is an experimentally often used concentration for a solution polymerization, and [Mon]0 = 3.6 M, which corresponds to the bulk concentration at 100 °C. For these systems, the [Mon]0/[Ini]0 ratio was varied from 2 to 500, and the corresponding Mn and Mw values for the cyclic, linear and total distribution were calculated, as well as the mol- and weight fractions of cyclics (Figure 8). It can be seen that the linear chains show the expected linear increase in both Mn and Mw with increasing [Mon]0/[Ini]0. However, while the Mw of the total distribution also shows this linear increase, the Mn for [Mon]0 = 1.0 M quickly levels off to 8 kg·mol−1 at high [Mon]0/[Ini]0 ratios. The reason for this is the increasing mole fraction of cyclics resulting from the decreasing concentration of linear chains. When [Mon]0/[Ini]0 appoaches infinite, the Mn,total can be calculated using eq 11 and the Mn converges to 8.3 kg·mol−1 (see Supporting Information for details).

M, after which the equilibrium concentration is reached (Figure 5a). The quantification works well up to the pentamer (C5), after which the overlap of peaks in the low-MW−SEC measurements becomes too large. The equilibrium concentration vs the cyclic oligomer size leads to a profile from which it can easily be seen that C1 (=Amb) does not follow the trend expected for strainless rings (Figure 5b). Indeed, application of eqs 3−5 to C2−C5 leads to a good fit and a B value of 0.087 M. This means that if Amb would consist of a strainless ring, the theoretical concentration of Amb would be 0.087 M. However, since the actual concentration is lower, this means that ambrettolide still has some ring strain, which is possible within the experimental error of the observed ΔH⊖p for Amb. Since C2 does fit the profile well, this cyclic can be considered as the first strainless ring. This furthermore agrees with the theory, which states that rings consisting of 25−30 atoms can safely be assumed to be strainless.35 The practical consequence is that quantification of the cyclic monomer and dimer is enough to quantify the whole cyclic fraction. The critical monomer concentration can be determined using the data above and eq 7, which yields [Mon]crit = 0.155 M. To clarify, this means that in a polymerization where [Mon]0 = 1 M and the [Mon]0/[Ini]0 ratio is high, around 15 wt % of the polymer will consist of cyclics (including unreacted monomer), and for bulk polymerizations ([Mon]0 = 3.6 M at 100 °C) around 4 wt %. The manifestation of a critical monomer concentration can also clearly be observed when the LCCC chromatograms are considered (Figure 6a). It can be seen that the product of the

Figure 6. (a) LCCC chromatograms and (b) SEC chromatograms of the products obtained from cROP of Amb at different concentrations. For all reactions [Mon]0/[Ini]0 = 100.

polymerization having [Mon]0 = 0.1 M, which is lower than [Mon]crit, only shows one peak in LCCC corresponding to cyclic polymers. When the concentration is raised to just above [Mon]crit, a second peak appears which corresponds to the linear fraction. Even though this technique is only semiquantitative, it can be said that the cyclic fraction is much larger than the linear fraction, which is expected since only 0.045 M is converted into linear chains versus 0.155 M into cyclics. A further increase in monomer concentration to [Mon]0 = 0.5 M

Mn , total = F

[Mon]l M 0 + Mn , cyclic ∞ ∑i = 2 [Ci]

(11)

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Figure 7. Calculated SEC chromatogram with input parameters [Amb] = 1.0 M, [Ini] = 0.01 M and B = 0.087 M (red dotted line). Mark−Houwink transformation applied (blue dotted line). Measured chromatogram (green solid line). Monomer concentrations are excluded from molecular weight calculations.

Figure 8. Calculated Mn, Mw, and cyclic fraction values versus [Mon]0/[Ini]0 for [Mon]0 = 1.0 M (a) and 3.6 M (b).

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This shows that the only variable which can be influenced is [Mon]l, since this is directly dependent on [Mon]0. Indeed, calculation of the Mn for a bulk polymerization ([Mon]0 = 3.6 M) yields a maximum Mn of 30.5 kg·mol−1. The Mw of these distribution is mainly dependent on the Mw,linear and can be calculated using (for more details see Supporting Information): M w , total =

[Mon]l [Mon]l 2M 0 [Ini]0 [Mon]0

CONCLUSIONS

An LCCC method was successfully developed to semiquantitatively determine the fraction of cyclic polymer relative to linear polymer from the cROP of ambrettolide. This method shows in combination with low-MW−SEC that during the whole polymerization cyclic oligomers are present, proving that there is no clear preference for ring-opening polymerization or transesterification when polymerizing macrolactones. This is furthermore strengthened by the determined thermodynamic parameters for polymerization, which show that there is a negligible enthalpy and a large entropy of polymerization, proving that the driving force for ROP of macrolactones basically is similar to transesterification. Quantification of the cyclic oligomers, from monomer to pentamer, shows that the cyclic dimer is strainless, while the monomer still shows little ring-strain. Application of a modified version of the J&S theory to the experimental results gave an effective molarity of B = 0.087 M, which corresponds to a critical monomer concentration of [Mon]crit = 0.155 M. Furthermore, the developed

(12)

This function does not converge to a value, and therefore Mw keeps increasing when the amount of initiator is decreased. Consequently, this means that the ĐM increases when the amount initiator is decreased. Therefore, in contradiction to general belief, the dispersity of polymerizations of strainless cyclic esters will not lead to a dispersity around 2, but will increase far beyond this value depending on the used monomer and initiator concentrations. G

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HPLC and SEC respectively. In both cases, fractions were collected in intervals of 0.5 min. Polymerization Procedure. Before polymerization, a catalyst stock solution was prepared by adding an equivalent amount of catalyst precursor, [salen]AlEt, and initiator, PDOH, in a vial, dissolving it in toluene and stirring it for ±12 h at 100 °C. In a typical polymerization of Amb (630 mg, 2.5 mmol) and catalyst stock solution (0.025 mmol) were added to a glass crimp cap vial in a nitrogen filled glovebox and toluene (3000 mg) was added giving concentrations of [Amb]:[Cat]:[Ini] 0.5:0.005:0.005. The vial was capped, taken out of the glovebox and put in a carrousel reactor at 100 °C while stirring with a magnetic stirrer bar for 141 h. After the reaction, the reaction mixtures were cooled to room temperature, subjected to air and stored in the freezer. Before analysis, the samples were put under vacuum overnight after which the samples for SEC and LCCC were prepared. Numerical Procedure for the Calculation of the Molecular Weight Distribution. To calculate the molecular weight distributions, an iterative numerical model was used in which B, [Mon]0 and [Ini]0 were used as input parameters. As initial condition [Mon]l = [Mon]0 was chosen. For every cyclic size i, eqs 3−5 were applied to calculate the absolute concentration of cyclic i. Subsequently, the sum of [Ci]i (eq 6), which represent the amount of monomer included in the cyclic phase, was subtracted from [Mon]0 to calculate [Mon]l (eq 8). These steps were repeated until the difference between iterations was 2 for the ROP of macrolactones. Since for polymers the molecular weight distribution is of key importance for the properties, this method offers an excellent framework for both describing and tuning the desired molecular weight distribution and the fraction of cyclic products.

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EXPERIMENTAL SECTION

Reagents and Methods. All solvents and reagents were purchased from commercial sources (Sigma-Aldrich, BioSolve) unless stated otherwise. Toluene was dried over an alumina column prior to use. Ambrettolide was kindly received from Symrise and freshly distilled from CaH2 under nitrogen prior to use. The aluminum Schiff base complex (1) was synthesized using literature procedure.38 All reactions and preparations were either carried out in an MBraun MB150 GI glovebox or using proper Schlenk techniques. High molecular weight size exclusion chromatography (SEC) was measured on a Waters Alliance system equipped with a Waters 2695 separation module, a Waters 2414 refractive index detector (35 °C), a Waters 2487 dual absorbance detector, a PSS SDV 5m guard column followed by 2 PSS SDV linearXL columns in series of 500 Angstrom (8 × 300 mm) at 40 °C. Tetrahydrofuran (THF stabilized with BHT, Biosolve) with 1% v/v acetic acid was used as eluent at a flow rate of 1.0 mL·min−1. The molecular weights were calculated with respect to polystyrene standards (Polymer Laboratories, Mp = 580 Da up to Mp = 2.25 × 106 Da). Before SEC analysis was performed, the samples were filtered through a 0.2 μm PTFE filter (13 mm, PP housing, Alltech). Low molecular weight size exclusion chromatography (SEC) was measured on a system equipped with a Waters 1515 Isocratic HPLC pump, a Waters 2707 autosampler, a Waters 2414 refractive index detector (35 °C), a Waters 2996 Photodiode Array detector, a PSS SDV 5m guard column followed by 2 SDV 5m, 500 Å (8 × 300 mm) columns in series at 40 °C. Tetrahydrofuran (THF stabilized with BHT, Biosolve) with 1% v/v % acetic acid was used as eluent at a flow rate of 1.0 mL·min−1. The molecular weights were calculated against polystyrene standards (Polymer Laboratories, Mp = 580 Da up to Mp = 21 000 Da). MALDI−TOF−MS analysis was performed on a Voyager DE-STR from Applied Biosystems equipped with a 337 nm nitrogen laser. An acceleration voltage of 25 kV was applied. Mass spectra of 1000 shots were accumulated. The polymer samples were dissolved in THF with Milli-Q water containing 0.1% formic acid at a concentration of 1 mg· mL−1. The matrix used was trans-2-[3-(4-tert-butylphenyl)-2-methyl-2propenylidene]malononitrile (DCTB) (Fluka) and was dissolved in THF at a concentration of 40 mg·mL−1. Solutions of matrix, sodium salt, and polymer were mixed in a volume ratio of 4:1:4, respectively. The mixed solution was hand-spotted on a stainless steel MALDI target and left to dry. The spectra were recorded in the reflection mode. All LCCC experiments were conducted on an Agilent 1100, equipped with a quaternary pump, degasser, autosampler, column oven, a diode-array detector (DAD) with 10 mm cell (Agilent, Waldbronn, Germany) at 40 °C. The mobile phase, 10.5 w/w-% ultrapure water (0.1 vol % formic acid) and 89.5 w/w-% THF, was mixed and pumped with a flow rate of 0.5 mL·min−1. Two Zorbax RXC18 (Agilent, 4.6 × 250 mm) and one Zorbax RX-C18 (Agilent, 4.6 × 150 mm) columns with 5 μm particles were used in series to establish the critical separation. The injection volume was 5 μL. Detection with an Alltech Model 3300 ELSD detector (Grace) was also performed. Fraction collection was performed by coupling an additional fraction collector of Agilent technologies (Series 1200) to the

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ASSOCIATED CONTENT

S Supporting Information *

Additional 1H NMR spectra and SEC chromatograms, derivation of calculations, and Matlab code used to calculate MWDs and SEC chromatograms.This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(R.D.) Telephone: +31 40 247 4918. Fax: +31 40 246 3966. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by SABIC for this work is gratefully acknowledged. The authors thank José Augusto Berrocal (Università di Roma La Sapienza) for the stimulating discussion on J&S theory.

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REFERENCES

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