kinetic analysis of the living ring-opening polymerisation of l -lactide with tin(ii) initiators

FULL PAPER

DOI:10.1002/ejic.201300964

Kinetic Analysis of the Living Ring-OpeningPolymerisation of L-Lactide with Tin(II) Initiators

Lingfang Wang,[a] Manfred Bochmann,*[b] Roderick D. Cannon,*[b]

Jean-François Carpentier,*[a] Thierry Roisnel,[c] and Yann Sarazin*[a]

Keywords: Polymerization / Ring-opening polymerization / Lactide / Tin / Kinetics

A general kinetic model to describe the initiation and mono-mer depletion phases of the metal-catalysed living ring-opening polymerisation (ROP) of cyclic esters is presented.The model allows the description of ROP reactions in terms ofrates of initiation (ki) and propagation (kp) and is in principleapplicable to all metal-mediated ROP reactions. The modelwas validated by curve-fitting of data obtained for the livingROP of L-lactide catalysed by a variety of tin(II) catalysts. Thecatalyst was chosen from tin(II) diisopropoxide or fromheteroleptic complexes of the type (LOx)Sn(OR), in which(LOx) is an amino or aminoether phenolate ancillary ligandand OR is isopropoxide or O-tert-butyl lactate. All tested cat-alysts promote the controlled, living polymerisation of L-lact-ide. No initiation phase was discerned for any of the consid-

Introduction

Poly(l-lactide) (PLLA) is of major academic and indus-trial interest as a bioresourced and biodegradable material,and a large number of catalyst systems for its preparationby ring-opening polymerisation (ROP) have been devel-oped.[1] Although the general mechanistic principles of thepolymerisation reaction are fairly well understood, funda-mental aspects of the ROP kinetics of lactide (LA) andother cyclic esters often remain complicated. A number ofpreliminary investigations with simple tin(II) octanoate ex-ist, but they have not been developed into a comprehensive

[a] Organometallics: Materials and Catalysis, Institut des SciencesChimiques de Rennes, UMR 6226 CNRS – Université deRennes 1,Campus de Beaulieu, 35042 Rennes Cedex, FranceE-mail: [email protected]

[email protected]://scienceschimiques.univ-rennes1.fr/catalyse/carpentier/index.html

[b] Wolfson Materials and Catalysis Centre, School of Chemistry,University of East Anglia,Norwich UK NR4 7TJ, UKE-mail: [email protected]

[email protected]://www.uea.ac.uk/chemistry/people/faculty/bochmannm

[c] Centre de diffractométrie X, Institut des Sciences Chimiques deRennes, UMR 6226 CNRS – Université de Rennes 1,Campus de Beaulieu, 35042 Rennes Cedex, FranceSupporting information for this article is available on theWWW under http://dx.doi.org/10.1002/ejic.201300964.

Eur. J. Inorg. Chem. 2013, 5896–5905 © 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim5896

ered catalysts in polymerisations performed at 60 °C,whereas at 25 °C initiation is an order of magnitude slowerthan propagation and, therefore, the inclusion of ki is re-quired for an accurate kinetic description. Tin diisopropoxideis polymeric in the solid state, but it is dimeric in toluenesolution. [Sn(OiPr)2]2 is an excellent example of an aggre-gated catalyst precursor and is catalytically more active thanthe heteroleptic (LOx)Sn(OR). As dissociation of the inactivedimer into a catalytically active monomeric complex is re-quired, half-order dependence on [metal] is to be expectedand was indeed found. A method to estimate the relatedmonomer–dimer equilibrium constant KD under polymerisa-tion conditions is also provided.

model.[2] The general rate law for catalysed polymerisationsis –d[M]/dt = k[cat]m[M]n (cat = catalyst, M = monomer),and, in the large majority of cases, the reaction is first orderin both catalyst and monomer (i.e., m = n = 1). For in-stance, this was the case in the detailed investigation of thealuminium-catalysed polymerisation of ε-caprolactone byTolman, Hillmyer and co-workers,[3] for the ROP of(macro)lactones described very recently by Duchateau andco-workers[4] and in the stereocontrolled ROP of rac-LAreported by Feijen and co-workers.[5] However, for the ROPof LA, a significant number of cases have been describedthat show very different types of kinetic behaviour and dif-ferent rate dependencies on both the monomer and the cat-alyst concentrations. A number of studies report reactionorders in [monomer]n with n� 1. For example, Lin and co-workers used the diketiminate–zinc alkoxide A (Scheme 1)as a catalyst in CH2Cl2 and found a first-order dependenceon [Zn] but a second-order dependence on lactide concen-tration (but first order for ε-caprolactone!).[6] By contrast,LA polymerisations in chloroform with the binuclear salen–zinc alkoxide B (Scheme 1, M = Zn) were first order in both[Zn] and [LA], whereas the structurally identical magne-sium analogue showed first-order dependence on [Mg] butsecond-order dependence on monomer.[7] A second-orderdependence on [LA] was also found recently for the bulkpolymerisation catalysed by homoleptic bis(alkoxy-Schiffbase)Ti complex C (Scheme 1) at 130–160 °C.[8]

www.eurjic.org FULL PAPER

Scheme 1.

An even greater diversity of empirical rate laws exists forthe dependence on the metal catalyst. For example, for theROP of LA with the monomeric tin alkoxide D (Scheme 2)activated with benzyl alcohol (1:1) in toluene at 80 °C, Tol-man and co-workers reported a fractional order of0.33� 0.02 in [Sn].[9] On the other hand, with the highlyactive binuclear zinc complex E (Scheme 2) in dichloro-methane solution, the same authors reported that plots ofln(kobs) vs. ln[Zn] led to noninteger dependence on [Zn]n,and the values of n = 1.33 at 0 °C and 1.75 at 25 °C suggestpossible catalyst aggregation. However, they also noted that

Scheme 2.


plots of kobs vs. [Zn] were linear and consistent with first-order behaviour in both [LA] and [Zn].[10] This contrastswith the polymerisation of rac-LA by F (Scheme 2) indichloromethane at 25 °C, which was first order in [LA] butshowed an apparent noninteger dependency of 1.56 on[Zn].[11] On the basis of earlier precedence,[12,13] this wasthought to be indicative of catalyst aggregation. Second-order dependence on [catalyst] was reported for LA poly-merisations initiated with the disodium salt of 2,2�-ethyl-idene-bis(4,6-di-tert-butylphenol) (EDBPNa2), whereas thedependence on [LA] was first order.[14] More recently,Mehrkodhavandi and co-workers used the indium alkoxidecatalyst G (Scheme 2) and suggested dependence on [In2](i.e., second order in [In]) and, thus, a binuclear propagatingspecies for the polymerisation of rac-LA.[15] Complex ki-netic behaviour was also found in ε-caprolactone polymeri-sations mediated by FeIII alkoxides: whereas polymerisationcatalysed by H (Scheme 2) was first order in [Fe2], complexI showed a fractional order in [Fe] of 0.55� 0.02, whichwas interpreted as arising from the dimerisation of activepolymer chains with slower propagation of the dimeric spe-cies than that of the nonaggregated form.[16] On the otherhand, the ROP of l-LA with the tetranuclear magnesiumalkoxide J (Scheme 2) was first order in [Mg], and the mo-nonuclear Mg(OR)2(lactide)2 K (Scheme 2) was suggestedas the active species.[17]

We have recently described synthetic, spectroscopic andcatalytic studies on the immortal ROP of l-LA mediatedby a number of tin(II) (pre-)catalysts of types 1–3(Scheme 3) in the presence of excess iPrOH[18] and pro-posed a mechanistic model based on a combined experi-mental and theoretical investigation.[19] Following thiswork, we report here a kinetic investigation into the mecha-nism of the living ROP of lactide with heteroleptic amidotin(II) precatalysts 1 and 3 (combined with 1 equiv. ofiPrOH), the discrete alkoxide 2 and the homoleptic[Sn(OiPr)2]n (4); a mathematical treatment of the kinetics ofthese living polymerisations is included.


Scheme 3.

Results and Discussion

Synthesis and Reactivity

Our initial investigations revealed that the complexes(LO1)Sn[N(SiMe3)2] (1), (LO2)Sn[tBu (R)-lactate] (2) and(LO4)Sn[N(SiMe3)2] [3; (LOx)– = ancillary phenolate of thetype 2-CH2NR2-4,6-tBu2-C6H2O–; NR2 = aza-15-crown-5,x = 1; morpholine, x = 2; N(CH2CH3)2, x = 4] catalysethe living ROP of l-LA and trimethylene carbonate in thepresence of isopropanol as activator (ROH/Sn molar ratio= 1) and chain transfer agent (ROH/Sn molar ratio � 1,

Figure 1. Molecular structure of 4 in the solid state. Ellipsoids are drawn at 50% probability. Hydrogen atoms are omitted for clarity.Selected bond lengths [Å] and angles [°]: Sn(1)–O(1) 2.102(3), Sn(1)–O(11) 2.114(3), Sn(1)–O(1�) 2.446(3), Sn(1)–O(11�) 2.353(3); O(1)–Sn(1)–O(11) 93.61(14), O(1)–Sn(1)–O(11�) 72.58(12), O(11)–Sn(1)–O(11�) 93.43(10), O(1)–Sn(1)–O(1�) 94.07(11), O(11)–Sn(1)–O(1�)70.45(12), O(11�)–Sn(1)–O(1�) 158.72(12), Sn(1)–O(1)–Sn(1�) 106.77(14), Sn(1)–O(11)–Sn(1�) 109.78(14). Symmetry transformations usedto generate equivalent atoms: x – 1/2, –y – 1/2, z.


i.e., immortal reactions).[18,19] The reaction rates show first-order dependence on both monomer and precatalyst con-centrations.

NMR investigations on the reaction of 1 with excess iso-propanol (2–10 equiv.) in the context of immortal ROP re-actions have previously shown not just formation of the cat-alyst (LO1)Sn(OiPr) but also release of the phenolate ligandand eventual formation of the homoleptic tin(II) alkoxide,Sn(OiPr)2 (4).[18] This compound was consequently synthe-sised here from Sn{N(SiMe3)2}2 and iPrOH and recoveredas a colourless powder. Recrystallisation of the powderfrom pentane gave crystals of 4 suitable for X-ray diffrac-tion. In the solid state, the compound has a polymeric chainstructure with doubly bridging isopropoxide ligands (Fig-ure 1); by comparison, the bulkier Sn(OtBu)2 forms a dimerin the solid state.[20] However, NMR diffusion measure-ments indicate that in toluene solution complex 4 also existspredominantly as a dimer (see Supporting Information).

Whereas the amido complexes 1 and 3 require the ad-dition of one equiv. of alcohol to become effective catalystsfor controlled ROP reactions (metal amides sometimes initi-ate fast but poorly controlled ROP reactions and usuallygive polymers with broad molecular weight distributions),[1]

the alkoxide complexes 2 and 4 catalyse the controlled liv-ing ROP of l-LA on their own. Qualitative batch-scalepolymerisations (typically 1.0–1.5 g of monomer in 8–10 mL of toluene) produced monodisperse PLLAs withnarrow molecular weight distributions and good agreementbetween theoretical and experimentally determined molecu-lar weights (Table 1 and Figure 2). End-group analysis(MALDI-TOF MS, 1H NMR spectroscopy) confirmed thepresence of the expected chain termini: iPrOC(=O)– (for 4)or tBuOC(=O)CH(CH3)OC(=O)– (for 2) on one end and–CH(CH3)OH on the other. Size-exclusion chromatography(SEC) and NMR analyses showed that [Sn(OiPr)2]2 gener-


Table 1. Living ROP of l-lactide catalysed by SnII complexes.[a]

Entry Cat. [l-LA]T/[Sn]T Time [min] Conv.[b] [%] Mn,theo[c] [gmol–1] Mn,SEC

[d] [gmol–1] Mw/Mn[d]

1 2 300:1 36 29 12500 10600 1.042 2 300:1 65 49 21300 17900 1.063 2 300:1 95 59 25600 21100 1.074 4 400:1 11 38 11100 10100 1.035 4 400:1 20 59 17100 20200 1.036 4 400:1 30 78 22500 25400 1.057 4 400:1 45 87 25100 27700 1.08

[a] Polymerisation conditions: [l-LA]T = 1.0 m, 1.15 (Entries 1–3) or 1.44 g (Entries 4–7) of l-LA, T = 60 °C, 8 (Entries 1–3) or 10 mL(Entries 4–7) of toluene. [b] Conversion measured by NMR spectroscopy. [c] Calculated according to [l-LA]T/[Sn]T � monomer conver-sion � 144.13 + 60. [d] Determined by size-exclusion chromatography vs. polystyrene standards and corrected by a factor of 0.58.

Figure 2. Plots of monomer conversion vs. reaction time (top) and molecular weight determined by SEC vs. monomer conversion (bottom)for the ROP of l-LA catalysed by 2 (�, 300 equiv. of l-LA; 1.15 g of l-LA in 8 mL of toluene) and 4 (♦, 400 equiv. of l-LA; 1.44 g ofl-LA in 10 mL of toluene). [l-LA]T = 1.0 m in toluene, 60 °C.

ates two polymer chains per metal centre. Monomer con-sumption followed first-order kinetics in [l-LA] in bothcases, and higher apparent rates were observed for [Sn(O-iPr)2]2 (kobs = 1.55� 0.08�10–4 and 7.81 �0.38� 10–4 s–1

for 2 and 4, respectively).

Living ROP with Discrete Alkoxides and in situ Amide/ROH (1:1) Systems

We describe here a kinetic model for l-LA ROP devel-oped from first principles; the model was tested against arange of polymerisation data. The catalysts 1/ROH, 3/ROH


(1:1) and [Sn(OiPr)2]2 (4) polymerise l-LA in a highly con-trolled fashion (for details, see the Supporting Information).In the following, it is assumed that the amide precursors 1and 3 react quantitatively with one equiv. of ROH to gener-ate the corresponding alkoxide catalysts (LOx)Sn(OR)[ROH = iPrOH or methyl (S,S)-lactidate, a good model ofthe growing polymeryl chain].

The living ROP of l-LA (LA/Sn molar ratio = 100:1) in[D8]toluene at 60 °C was monitored by 1H NMR spec-troscopy (Figure 3). The apparent rate constants (kobs)ranged from ca. 3–6�10–4 s–1 for 1 and 3, whereas Sn(O-iPr)2 was approximately an order of magnitude faster


(Table 2). The differences in rates between heteroleptic com-plexes were only marginal, and the nature of the alcoholbore no influence.

Figure 3. Monomer conversion vs. reaction time for the ROP of l-LA in [D8]toluene at 60 °C catalysed by 1/iPrOH 1:1 (�), 1/methyl(S,S)-lactidate 1:1 (Δ), 2 (+), 3/iPrOH 1:1 (�), and 4 (♦). [l-LA]T= 1.0 m, [Sn]T = 10 mm.

In principle, ROP reactions can be described by an initia-tion step followed by a number of propagation steps. Theinitiation step represents the first monomer insertion intothe Sn–OR bond and is characterised by a rate constant ki,whereas we assume that all subsequent insertion steps pro-ceed with the same rate constant kp. The process may thenbe described by Equations (1a–1c):

(L)Sn(OR) + M � (L)Sn(OMR), ki (1a)

(L)Sn(OMR) + M � (L)Sn(OM2R), kp (1b)

(L)Sn(OM2R) + M �{L}Sn(OM3R), kp (1c)

and so on. (L)Sn(OR) is the general form of the tin(II) cata-lyst, (L) can be an alkoxide or an ancillary ligand (e.g., theaminophenolate {LOx} in 1–3) and OR is the initial reac-tive alkoxide (OiPr in the case of 1, 3 and 4, or O-tBu(R)-lactate in the case of 2), M is the monomer (l-LA) andOMnR is the growing polymeryl chain that results from theinsertions of n monomer units into the initial Sn–OR bond.By assuming that the elementary reactions are first order in

Table 2. Kinetic parameters for the ROP of l-lactide with SnII catalysts.[a,b]

Entry Catalyst system T [°C] [l-LA]T [m] kobs[c] [s–1] Initiation[d] Monomer depletion[e]

ki [Lmol–1s–1]) kp [Lmol–1s–1]) kp [Lmol–1s–1])

1 1/Me (R)-lactidate (1:1) 60 1.0 5.47�0.01�10–4 42.7�0.5�10–3[f] 42.7�0.5�10–3 52.2�0.1�10–3

2 1/iPrOH (1:1) 60 1.0 6.25�0.01�10–4 30.6�0.8�10–3 38.9�0.1�10–3 54.3�0.2�10–3

3 2 60 1.0 5.35�0.01�10–4 35.9�0.9�10–3 42.5�0.9�10–3 52.3�0.1�10–3

4 3/iPrOH (1:1) 60 1.0 3.57�0.01�10–4 54.7�9.7�10–3 29.1�0.2�10–3 35.2�0.1�10–3

5 4 60 1.0 31.4�0.3�10–4 –[g] –[g] 337�1�10–3

6 2 25 0.4 0.45�0.01�10–4 1.28�0.08�10–3 4.66�0.16�10–3 4.23�0.01�10–3[h]

7 4 25 0.4 2.37�0.01�10–4 2.66�0.15� 10–3 20.4�0.8�10–3 21.2�0.1�10–3

[a] Reaction conditions: [Sn]T = 10 mm, [D8]toluene. [b] Standard deviations apply to curve-fitting of a given set of data, not to duplicatedexperiments; all curve-fitting plots are available in the Supporting Information. [c] Determined from the semilogarithmic plots of monomerconversion vs. reaction time. [d] For monomer conversion below 25% [Equation (3)]. [e] For monomer conversion between 70–100%[Equation (4)]. [f] Determined by using the simplified version of Equation (3) for ki = kp. [g] 35% of the monomer had already beenconverted at the first point of analysis; hence, the treatment for the initiation could not be applied to the ROP catalysed by 4. [h]Determined for conversion � 65%.


each component, the first of these equations can be solveddirectly to give Equation (2):

[(L)Sn(OR)] = [Sn]Texp(–ki[M]t) (2)

[Sn]T is the total concentration of tin(II) species and re-mains constant throughout the reaction. The concentrationof polymerised monomer [M]P is given by summing over allpropagating events (see Supporting Information for de-tails):

which leads to Equation (3):

[M]P = kp[M][Sn]Tt + [(ki – kp)/ki][Sn]T[1 – exp(–ki[M]t)] (3)

Equation (3) should only be applied to the initial stageof the polymerisation when [M] can be considered constant,typically for conversion below 25%. In the special case ki =kp, Equation (3) simplifies to [M]P = kp[M][Sn]Tt. If ki � kp,there is an initial nonlinear phase, and the time dependenceof [M]P may be extracted to give the curves shown in Fig-ure 4.

Figure 4. Time dependence of monomer consumption for poly-merisations with an initiation phase.

Curve-fitting showed that Equation (3) was an accuratemodel for these polymerisations (Table 2). Except for thoseof 4, for which the polymerisation was too fast at 60 °C torecord accurate data in the early stages, the values of kp andki for the early phase were determined by using the data


points for conversions up to 25% (i.e., [M] was consideredconstant over this time interval). At elevated temperature(60 °C, Table 2, Entries 1–5), the values of ki were essen-tially identical to the propagation rate constants kp. As[Sn]T = 0.01 m, the observed kobs value of ca. 10–2 � kp

(Table 2, Entries 1–4) was in excellent agreement with therelationship kobs = [Sn]T �kp expected for such systemswith first-order dependence upon monomer and catalystconcentrations and for which there is no significant initia-tion phase.[16,17]

Under identical conditions (toluene, 60 °C; [l-LA]T =1.0 m, [Sn]T = 10.0 mm), the ROP is faster with 4 than withthe heteroleptic complexes (1 and 3) treated with one equiv.of iPrOH or methyl (S,S)-lactidate. In control experiments,the rates measured (kobs = 26.6 and 29.5 �10–4 s–1) or deter-mined by curve-fitting (kp = 290 and 275 �10–3 L mol–1 s–1)for 4 in the presence of 2 and 10 equiv. HN(SiMe3)2, respec-tively, were commensurate with those determined without

Figure 5. Plot of monomer conversion vs. time for the ROP of l-lactide in [D8]toluene at 25 °C catalysed by 2. [l-LA]T = 0.4 m,[Sn]T = 10 mm.

Figure 6. Plot of polymerised monomer ([M]P) vs. time during theinitiation phase of ROP of l-LA catalysed by 2 in [D8]toluene at25 °C. The red line shows the fit of the curve to Equation (3).[l-LA]T = 0.4 m, [Sn]T = 10 mm.


amine (Table 2, Entry 5). These data demonstrated that thepresence of HN(SiMe3)2 in the reaction medium has no re-tarding effect in these systems.

The reactions were slower at 25 °C (Table 2, Entries 6–7)and showed a distinct initiation phase (ki � kp, Figure 5).Also in this case, the agreement between the mathematicalmodel and the experimental data was excellent (R2 � 0.99,Figure 6). All curve-fitting plots are available in the Sup-porting Information.

Depletion of Monomer

In the present experiments, the concentration of mono-mer is not constant over time, and after the initiation phase,the monomer conversion is described by the typical rate lawwith a first-order dependence on monomer and catalyst:[M] = [M]T exp(–kp[Sn]Tt).

The monomer conversion, C(t), defined above is given byEquation (4):

C(t) = [M]P/[M]T = ([M]T – [M])/[M]T = 1 – exp(–kp[Sn]Tt) (4)

Curve-fitting was performed with the same set of experi-mental data used before to assess the validity of Equa-tion (4) for catalyst systems 1/iPrOH, 3/iPrOH (1:1) and 2(Table 2). At 60 °C, values of kp from 35.2 �0.1� 10–3 to54.3�0.2 �10–3 Lmol–1 s–1 were determined, and thecurve-fitting was excellent (R2 � 0.99, Figure 7). Consistentwith the aforementioned apparent rate constants, thehomoleptic diisopropoxide complex 4 gave a kp value ap-proximately one order of magnitude greater than those ofthe heteroleptic precursors (Table 2, Entry 5). For 1–3, anexcellent match was found for the kp values determined byusing Equation (3) for initiation and Equation (4) formonomer depletion, both at 25 and 60 °C. Figure 8 displaysthe curve-fitting covering a wide timescale for the polymeri-sation catalysed by 4 at 25 °C (Table 2, Entry 7); again, theagreement between experimental data and curve-fitting wasgood (R2 � 0.99).

Figure 7. Curve-fitting at high monomer conversion for the ROPof l-lactide catalysed by 2. ROP conditions: 60 °C, [D8]toluene,[l-LA] = 1.0 m, [Sn]T = 10 mm.


Figure 8. Curve-fitting at high monomer conversion for the ROPof l-lactide catalysed by 4. ROP conditions: 25 °C, [D8]toluene,[l-LA] = 0.4 m, [Sn]T = 10 mm.

Living ROP of L-Lactide with [Sn(OiPr)2]2 and RelatedSystems

The polymerisation of l-LA catalysed by the homolepticcomplex 4 is first order in [monomer] (Figure 9). Earlierstudies showed that on the addition of several equivalentsof l-LA to a solution of 4 in [D8]toluene at 60 °C, the119Sn{1H} NMR resonance changed from δ119Sn ≈ –200 (for4) to –344 ppm [a bis(polymeryl)SnII species].[18] The corre-sponding 1H NMR spectrum was consistent with the inser-tion of monomer units into the two Sn–OiPr bonds, butno evidence for a lactide adduct “Sn(OiPr)2(lactide)” wasdetected.[18] Although 4 is a dimer in toluene solution, therate law shows that only monomeric Sn(OiPr)2 is the activespecies as the slopes of ln(kobs) vs. ln([Sn]T) plots show ahalf-order dependence on [Sn] (Figure 10). Similarly, a plotof the original kobs values against either [Sn] or [Sn]1/2 givesa better fit for the [Sn]1/2 case (Figure 11).

Figure 9. Monomer conversion vs. time for the ROP of l-LA cata-lysed by 4 in [D8]toluene at 60 °C. [l-LA]T = 1.0 m, [Sn]T = 1.00(♦), 2.50 (�), 5.00 (�), 7.50 (�), 10.0 (*), 14.0 (�) and 18.0 mm (+).


Figure 10. Logarithmic plot of kobs vs. [Sn]T for the ROP of l-lactide catalysed by 4 in [D8]toluene at 60 °C; [l-LA]T = 1.0 m and[Sn]T = 1.00–18.0 mm.

Figure 11. Plots of kobs vs. [Sn]1/2 (top) and kobs vs. [Sn] (bottom)for the ROP of l-lactide catalysed by 4 in [D8]toluene at 60 °C;[l-LA]T = 1.0 m and [Sn] = 1.00–18.0 mm.

As 4 is dimeric in toluene solution, the observed half-order dependence on [Sn] can be accounted for by the rapiddissociation equilibrium [Equation (5)]

(5)

in which Sn2 and Sn are the dimeric and monomeric species,respectively, and KD is the related dissociation constant.The ROP reaction then proceeds from Sn with the rate con-stant k according to:


Therefore, there is the equilibrium KD = [Sn]2/[Sn2],whereas kobs = k[Sn] in the case of first-order dependencein [reactants] as established for l-LA. As [Sn]T = 2[Sn2] +[Sn] and [Sn]2 = KD[Sn2], and by using a linearisationmethod developed earlier in a spectroscopic application,[21]

it follows:

(6)

(7)

and

(8)

and, therefore:

(9)

Therefore, a plot of kobs vs. [Sn]T/kobs should be a straightline that misses the origin by an amount that depends onKD (Figure 12, top). The area of the triangle formed by thisline with the x and y axes is 1/2(k–1)(1/2KDk) = KD/4. Inpractice, the line passes close to the origin (Figure 12, bot-tom), and we obtained an estimate of KD � 10–4 molL–1.This value is below the detection limit of NMR measure-ments, which is consistent with the observations.

Figure 12. A method to estimate the dimer–monomer dissociationconstant KD (illustrated with 4) from the observed rates kobs forthe ROP of l-lactide in [D8]toluene at 60 °C ([l-LA]T = 1.0 m,[Sn]T = 1.0–18.0 mm). Top: theoretical model, bottom: experimen-tal plot.


Beyond the initial splitting of the inert dimeric homolep-tic isopropoxide, the half-order dependency in [Sn]T impliesthat there must be an equilibrium between an active mono-nuclear species and an inactive dinuclear species during theentire course of the polymerisation.

Conclusions

A general kinetic model that describes the initiation andmonomer depletion phases of the living ROP of cyclic estersmediated by metal complexes has been developed and al-lows the description of these polymerisation systems interms of rates of initiation and propagation. Curve-fittingperformed with data obtained for the controlled living ROPof l-LA mediated by tin(II) initiators illustrates the validityof the proposed model. The results and mathematicalmodel presented here complement the pioneering and ex-tensive studies of cyclic ester ring-opening polymerisationscatalysed by Sn(2-ethylhexanoate)2 reported by Penczek,Duda and co-workers.[2] For all the SnII catalyst systemsemployed here, l-lactide polymerisations at 60 °C showedno initiation phase, whereas at 25 °C initiation can be anorder of magnitude slower than propagation, and the ki-netic description requires inclusion of ki.

Tin diisopropoxide is a much more active catalyst thanheteroleptic compounds of the type (LOx)Sn(OR) and itcan generate two polymer chains per metal centre underliving conditions. It is a polymer in the solid state, but formsa dimer in toluene solution and provides an excellent exam-ple of an aggregated catalyst precursor. Fractional ordersin [catalyst] are often cited as a sign of the aggregated na-ture of the complex, yet conclusive evidence is rarely pro-vided. We have shown that in cases in which dissociationof an inactive dimer into a catalytically active monomericcomplex is required, half-order dependence on [metal] is tobe expected. The kinetic results confirm that the actualactive initiator is monomeric Sn(OiPr)2. We have alsoshown a method for estimating the upper limit of the re-lated dimer–monomer dissociation constant KD, which inthis case is not directly detectable by NMR spectroscopy.The lower kp and kobs values for catalysts 1–3 comparedto that of 4 probably reflect lower intrinsic activity for theheteroleptic catalysts, although slow formation of{LOx}Sn(OR) at low alcohol concentration in the case ofheteroleptic complexes cannot be categorically ruled out.Current efforts in our labs are aimed at assessing in detailthe impact of excess alcohol on the catalytic activity of suchsystems. This is relevant not only to simply living polymeri-sation but also to immortal ring-opening polymerisationsystems.[1i,18,19,22]

The kinetic model, demonstrated here for SnII catalysts,is of course generally applicable and can in principle be ex-tended to all metal-based catalysts and cyclic esters, pro-vided quality data suitable for curve-fitting are available. Itwould now be interesting to verify its utility and validitywith other well-known catalysts based on aluminium, zincor rare-earth metals, for example. Faster catalysts require


faster data collection, and optimisation of the reaction con-ditions and the use of in situ FTIR measurements are someof the directions we will explore to alleviate this issue.

Experimental SectionGeneral Procedures: All manipulations were performed under aninert gas atmosphere by using standard Schlenk techniques or in aglovebox. SnCl2 (Acros, 98%) and tert-butyl (R)-lactate (Aldrich,99%) were used as received. HN(SiMe3)2 (Acros) was dried withactivated molecular sieves and distilled prior to use.Sn[N(SiMe3)2]2, {LO1}Sn[N(SiMe3)2] (1), {LO2}Sn[tBu (R)-lactate](2) and {LO4}Sn[N(SiMe3)2] (3) were prepared as described else-where.[18,19,23] Tetrahydrofuran (THF) was distilled from Na/benzo-phenone under argon prior to use. Other solvents were collectedfrom MBraun SPS-800 purification alumina columns. Deuteratedsolvents (Eurisotop, Saclay, France) were stored in sealed ampoulesover activated 3 Å molecular sieves and degassed by several freeze–thaw cycles. l-LA was provided by Total Petrochemicals and puri-fied by recrystallisation from a hot (80 °C) iPrOH solution, fol-lowed by two recrystallisations in hot (105 °C) toluene.

NMR spectra were recorded with Bruker AM-400 and AM-500spectrometers. All 1H and 13C{1H} chemical shifts were determinedby using residual signals of the deuterated solvents and were cal-ibrated to SiMe4. Coupling constants are given in Hertz. 119Sn{1H}and 29Si{1H} NMR spectra were externally referenced to SnMe4

and SiMe4, respectively. Elemental analyses were performed with aCarlo Erba 1108 Elemental Analyser at the London MetropolitanUniversity by Stephen Boyer and were the average of a minimumof two independent measurements. SEC measurements were per-formed with an Agilent PL-GPC50 instrument equipped with twoPLgel 5-Å MIXED-C columns and a refractive index detector. Thecolumn was eluted with THF at room temperature at 1.0 mL min–1

and was calibrated by using 11 monodisperse polystyrene standardsin the range 580–380000 gmol–1. According to the literature recom-mendation, the molecular weights of all PLLAs were corrected bya factor of 0.58.[24] Curve-fitting was performed with the Originsoftware by using exponential fits that were defined manually ac-cording to Equation (3) for the initial period of the polymerisationsor Equation (4) for the phase corresponding to monomer de-pletion; all standard deviations given in Table 2 are the outcomeof the curve-fitting performed by the software on a given set ofpolymerisation data.

[Sn(OiPr)2]n (4): The synthetic procedure was adapted from thatreported by Caulton and co-workers.[25] At room temperature, asolution of iPrOH (0.15 g, 2.58 mmol) in diethyl ether (10 mL) wasadded dropwise to a solution of Sn[N(SiMe3)2]2 (0.45 g, 1.03 mmol)in diethyl ether (10 mL). After the addition was complete, the solu-tion was stirred for another 10 min before the volatiles were re-moved in vacuo. Extraction with pentane (3 � 10 mL) followed byevaporation of the solvent yielded analytically pure 4 as a colour-less air- and moisture-sensitive solid, yield 0.20 g (81%). X-rayquality crystals were obtained by recrystallisation from pentane. 1HNMR ([D8]toluene, 500.13 MHz, 25 °C): δ = 4.58 [m, 2 H,CH(CH3)2], 1.32 [d, 3JH,H = 6.1 Hz, 12 H, CH(CH3)2] ppm.13C{1H} NMR ([D8]toluene, 125.76 MHz, 60 °C): δ = 66.27[CH(CH3)2], 28.75 [CH(CH3)2] ppm. 119Sn{1H} NMR ([D8]tolu-ene, 149.20 MHz, 60 °C): δ = –200.4 ppm. C6H14O2Sn (236.88):calcd. C 30.4, H 6.0; found C 30.2, H 5.9.

Typical Batch-Scale Polymerisation Reactions: In a glovebox, themetal catalyst was placed in a Schlenk flask together with the


monomer. The Schlenk flask was sealed and removed from theglovebox. All subsequent operations were performed on a vacuummanifold by using Schlenk techniques. The required amount of sol-vent (toluene) was added with a syringe to the catalyst and themonomer, followed by the addition of the cocatalyst (iPrOH) whenrequired. The resulting mixture was immersed in an oil bath presetat the desired temperature (25 or 60 °C), and the polymerisationtime was measured from this point. The reaction was terminatedby the addition of acidified MeOH (HCl, 1 wt.-%), and the polymerwas precipitated in methanol and washed thoroughly. The polymerwas then dried to constant weight in a vacuum oven at 55 °C underdynamic vacuum (�5�10–2 mbar). For instance, the followingconditions and measurements correspond to the experiments fromTable 1 and Figure 2: [l-LA]T/[2]T = 300:1, [l-LA]T = 1.0 m in tolu-ene, 60 °C, kobs(2) = 1.60 �0.08�10–4 s–1; [l-LA]T/[4]T = 400:1, [l-LA]T = 1.0 m in toluene, 60 °C, kobs(4) = 7.78�0.38� 10–4 s–1; de-tails are available in the Supporting Information.

Typical NMR Kinetic Measurements: In a typical experiment, thecatalyst and monomer were loaded in an NMR tube in theglovebox. The NMR tube was placed in a Schlenk flask, whichwas then removed from the glovebox and connected to the vacuummanifold. All subsequent operations were performed by usingSchlenk techniques. The appropriate amounts of solvent ([D8]tolu-ene) and cocatalyst (iPrOH) were added to the NMR tube in thisorder at room temperature. The NMR tube was then sealed andbriefly heated to ensure complete dissolution of the monomer (timemeasurement started from this point) and introduced in the spec-trometer preset at the desired temperature (25 or 60 °C). Datapoints were collected at regular intervals (typically 15–60 s, withD1 = 0.5 s and number of scans = 8) until conversion of the mono-mer stopped (this usually coincided with full conversion). The con-version was reliably determined by integrating the methine regionof PLLA (δ1H = 5.00 ppm at 60 °C in [D8]toluene) vs. that of themonomer (δ1H = 4.08 ppm at 60 °C in [D8]toluene). The accuracyof the measurements was corroborated by the good agreement be-tween theoretical (based on the conversion, Mn,theo = 144.13 � [l-lactide]0/[iPrOH]0 �conversion) and experimental (Mn,NMR deter-mined by integration of the resonance of the methine hydrogenatoms vs. that of the chain-ends) molecular weights. ROP reactionswere typically conducted in [D8]toluene at 60 °C with [l-LA]T =1.0 m and [l-LA]T/[Sn]T = 100:1, which corresponds to the datafor Figure 3. At 25 °C, more dilute solutions and lower monomerloadings were used because of poor solubility: [l-LA]T = 0.4 m and[l-LA]T/[Sn]T = 40:1.

X-ray Diffraction Crystallography: Suitable crystals for X-ray dif-fraction analysis of [Sn(OiPr)2]n were obtained by recrystallisationof the purified compound from pentane. The diffraction data werecollected at 150(2) K by using a Bruker APEX CCD diffractometerwith graphite-monochromated Mo-Kα radiation (λ = 0.71073 Å).A combination of ω and Φ scans was performed to obtain at leasta unique data set. The crystal structures were solved by directmethods, and the remaining atoms were located from a differenceFourier synthesis followed by full-matrix least-squares refinementbased on F2 (programs SIR97 and SHELXL-97).[26] Carbon- andoxygen-bound hydrogen atoms were placed at calculated positionsand forced to ride on the attached atom. The hydrogen atom con-tributions were calculated but not refined. All non-hydrogen atomswere refined with anisotropic displacement parameters. The loca-tions of the largest peaks in the final difference Fourier map calcu-lation as well as the magnitude of the residual electron densitieswere of no chemical significance.

CCDC-938898 contains the supplementary crystallographic datafor this paper. These data can be obtained free of charge from The


Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

Supporting Information (see footnote on the first page of this arti-cle): Semilogarithmic plots of monomer consumption for theSchlenk-scale polymerisations of l-LA; diffusion-ordered spec-troscopy (DOSY) measurements and diffusion/formula weight (D–fw) analysis for [Sn(OiPr)2]n; curve-fitting plots and correspondingequations for initiation and monomer depletion phases; polymerend-group analyses (1H NMR, MALDI-TOF MS); details ofmathematical calculations; synthesis and molecular solid-statestructure of (LO4)2Sn; CIF files and table of crystallographic datafor (LO4)2Sn and [Sn(OiPr)2]n.

Acknowledgments

Assistance from Stephen Boyer (elemental analysis, London Metro-politan University) and Jean-Paul Guégan (DOSY and PGSE mea-surements, Institut des Sciences Chimiques de Rennes) is gratefullyacknowledged.

[1] For recent reviews, see, for example: a) A. Buchard, C. M.Bakewell, J. Weiner, C. K. Williams, Recent Developments inCatalytic Activation of Renewable Resources for Polymer Syn-thesis in: Topics in Organometallic Chemistry, vol. 39, Organo-metallics and Renewables (Eds.: M. A. R. Meier, B. M. Weckhu-ysen, P. C. Bruijnincx), Springer, Heidelberg, Germany, 2012;b) M. J.-L. Tschan, E. Brulé, P. Haquette, C. M. Thomas, Po-lym. Chem. 2012, 3, 836; c) P. J. Dijkstra, H. Du, J. Feijen,Polym. Chem. 2011, 2, 520; d) C. A. Wheaton, P. G. Hayes,Commun. Inorg. Chem. 2011, 32, 127; e) J.-C. Buffet, J. Okuda,Polym. Chem. 2011, 2, 2758; f) J. M. Becker, R. J. Pounder,A. P. Dove, Macromol. Rapid Commun. 2010, 31, 1923; g)C. M. Thomas, Chem. Soc. Rev. 2010, 39, 165; h) M. J. Stan-ford, A. P. Dove, Chem. Soc. Rev. 2010, 39, 486; i) N. Ajellal,J.-F. Carpentier, C. Guillaume, S. M. Guillaume, M. Hélou, V.Poirier, Y. Sarazin, A. Trifonov, Dalton Trans. 2010, 39, 8363;j) C. A. Wheaton, P. G. Hayes, B. J. Ireland, Dalton Trans.2009, 4832.

[2] a) J.-P. Puaux, I. Banu, I. Nagy, G. Bozga, Macromol. Symp.2007, 259, 318; b) A. Kowalski, J. Libiszowski, T. Biela, M.Cypryk, A. Duda, S. Penczek, Macromolecules 2005, 38, 8170;c) A. Kowalski, A. Duda, S. Penczek, Macromolecules 2000,33, 7359; d) A. Kowalski, J. Libiszowski, A. Duda, S. Penczek,Macromolecules 2000, 33, 1964; e) H. R. Kricheldorf, I.Kreiser-Saunders, A. Stricker, Macromolecules 2000, 33, 702;f) A. Kowalski, A. Duda, S. Penczek, Macromolecules 2000, 33,689; g) A. Kowalski, A. Duda, S. Penczek, Macromol. RapidCommun. 1998, 19, 567; h) A. Duda, S. Penczek, Macromole-cules 1990, 23, 1636.

[3] a) K. Ding, M. O. Miranda, B. Moscato-Goodpaster, N. Ajel-lal, L. E. Breyfogle, E. D. Hermes, C. P. Schaller, S. E. Roe, C. J.Cramer, M. A. Hillmyer, W. B. Tolman, Macromolecules 2012,


45, 5387; b) L. M. Alcazar-Roman, B. J. O’Keefe, M. A.Hillmyer, W. B. Tolman, Dalton Trans. 2003, 3082.

[4] M. P. F. Pepels, M. Bouyahyi, A. Heise, R. Duchateau, Macro-molecules 2013, 46, 4324.

[5] Z. Zhong, P. J. Dijkstra, J. Feijen, J. Am. Chem. Soc. 2003, 125,11291.

[6] H. Y. Chen, B. H. Huang, C.-C. Lin, Macromolecules 2005, 38,5400.

[7] J. C. Wu, B. H. Huang, M. L. Hsueh, S. L. Lai, C.-C. Lin, Poly-mer 2005, 46, 9784.

[8] C. B. Hu, Y. L. Wang, H. Z. Xiang, Y. Fu, C. H. Fu, J. X. Sun,Y. Xiang, C. S. Ruan, X. Li, Polym. Int. 2012, 61, 1564.

[9] K. B. Aubrecht, M. A. Hillmyer, W. B. Tolman, Macromole-cules 2002, 35, 644.

[10] C. K. Williams, L. E. Breyfogle, S. K. Choi, W. Nam, V. G.Young Jr., M. A. Hillmyer, W. B. Tolman, J. Am. Chem. Soc.2003, 125, 11350.

[11] B. M. Chamberlain, M. Cheng, D. R. Moore, T. M. Ovitt,E. B. Lobkovsky, G. W. Coates, J. Am. Chem. Soc. 2001, 123,3229.

[12] T. Ouhadi, A. Hamitou, R. Jérôme, P. Teyssié, Macromolecules1976, 9, 927.

[13] S. Penczek, A. Duda, T. Biela, Polym. Prepr. (Am. Chem. Soc.Div. Polym. Chem.) 1994, 35, 508.

[14] H. Y. Chen, J. Zhang, C.-C. Lin, J. H. Reibenspies, S. A. Miller,Green Chem. 2007, 9, 1038.

[15] I. Yu, A. Acosta-Ramírez, P. Mehrkhodavandi, J. Am. Chem.Soc. 2012, 134, 12758.

[16] B. J. O’Keefe, L. E. Breyfogle, M. A. Hillmyer, W. B. Tolman,J. Am. Chem. Soc. 2002, 124, 4384.

[17] Y. Wang, W. Zhao, X. L. Liu, D. M. Cui, E.-Y. X. Chen, Mac-romolecules 2012, 45, 6957.

[18] V. Poirier, T. Roisnel, S. Sinbandhit, M. Bochmann, J.-F. Carp-entier, Y. Sarazin, Chem. Eur. J. 2012, 18, 2998.

[19] L. Wang, C. E. Kefalidis, S. Sinbandhit, V. Dorcet, J.-F. Carp-entier, L. Maron, Y. Sarazin, Chem. Eur. J. 2013, 19, 13463.

[20] a) T. Fjeldberg, P. B. Hitchcock, M. F. Lappert, S. J. Smith,A. J. Thorne, J. Chem. Soc., Chem. Commun. 1985, 939; b) M.Veith, F. Töllner, J. Organomet. Chem. 1983, 246, 219.

[21] R. D. Cannon, J. Chem. Soc. A 1968, 1098.[22] a) T. Aida, S. Inoue, Acc. Chem. Res. 1996, 29, 39; b) S. Asano,

T. Aida, S. Inoue, J. Chem. Soc., Chem. Commun. 1985, 1148.[23] C. D. Schaeffer, J. J. Zuckerman, J. Am. Chem. Soc. 1974, 96,

7160.[24] M. Save, M. Schappacher, A. Soum, Macromol. Chem. Phys.

2002, 203, 889.[25] For the synthesis of SnIISnIV[OiPr]6 by reaction of in-situ gen-

erated [Sn(OiPr)2]n with [Sn(OiPr)4]n, see: D. J. Teff, C. D. Mi-near, D. V. Baxter, K. G. Caulton, Inorg. Chem. 1998, 37, 2547.

[26] a) G. M. Sheldrick, SHELXS-97, Program for the Determi-nation of Crystal Structures, University of Göttingen, Ger-many, 1997; b) G. M. Sheldrick, SHELXL-97, Program for theRefinement of Crystal Structures, University of Göttingen, Ger-many, 1997.

Received: July 26, 2013Published Online: October 18, 2013

kinetic analysis of the living ring-opening polymerisation of l -lactide with tin(ii) initiators

Documents