Ring-opening copolymerization thermodynamics and kinetics of γ-valerolactone/ϵ-caprolactone

The general misconception that γ-lactones are not thermodynamically polymerizable has limited the development of all γ-lactone-based copolymers. A few studies have reported copolymerization of these five-membered cyclic esters with more reactive monomers, yet a systematic investigation of kinetics and thermodynamics is still lacking. To explore the feasibility of the reaction, we combined equilibrium and non-isothermal syntheses for the copolymerization of γ-valerolactone with ϵ-caprolactone, initiated with methoxy polyethyleneglycol and catalyzed by Tin(II) 2-ethylhexanoate. Here, we present the polymerization kinetic and thermodynamic parameters for different monomer ratios in the reaction feed. We observed the dependency of enthalpy and entropy of polymerization upon monomer ratio changes, and estimated a linear increase in the activation energy by increasing the γ-valerolactone fraction in the starting monomer mixture. Our data demonstrate that γ-valerolactone can copolymerize with ϵ-caprolactone, but only under specific conditions. The reaction parameters determined in this study will enable preparation of additional γ-valerolactone-based copolymers and development of a family of degradable materials with improved properties in respect to commonly used polyesters.


Introduction
Degradable polymers are attracting increasing attention for their application in the fields of green chemistry, food packaging, agriculture and nanomedicine [1]. Hydrolyzable materials are particularly interesting for their short half-life, complete degradation and favorable clearance of degradation products. Aliphatic polyesters are the most widespread hydrolizable polymers due to their favorable characteristics [2], and cyclic esters lactones are starting reactants for their synthesis.
The majority of short-chain (four-, six-and seven-membered) cyclic esters are useful monomers that easily polymerize via Ring-Opening Polymerization (ROP). The ability of lactones to react via ROP is determined by the ring stability and their aptitude to shift the monomer/polymer equilibrium to the product side. a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 To contribute in this field, we evaluated thermodynamics and kinetics for the copolymerization of GVL with ECL, initiated with methoxy polyethyleneglycol (mPEG) and catalyzed by Tin(II) 2-ethylhexanoate (Sn(Oct) 2 ). To estimate thermodynamic parameters, we performed the equilibrium synthesis of three different copolymer compositions at six different temperatures. Experimental data provided values of ΔH p and ΔS p . Kinetic parameters were computed by experimental data from non-isothermal polymerization at five different heating rates, while major details on copolymerization kinetics were obtained following ROP in a low-monomerconversion range. Results demonstrated that the presence of GVL influenced the polymerization, and copolymerization can occur only within a specific range of feed compositions and working temperature.

Materials
-caprolactone (ECL), γ-valerolactone (GVL), methoxy polyethyleneglycol (mPEG, Mn: 550 Da, initiator) and Tin(II) 2-ethylhexanoate (Sn(Oct) 2 , catalyst) were purchased from Sigma Aldrich. ECL and mPEG were dried at 60˚C for 6 h and stored over molecular sieves before use, GVL and Sn(Oct) 2 were used as received. The molar ratio between mPEG and monomer units was adjusted to obtain a theoretical molecular weight of 10 kDa. The amount of catalyst was in ratio 1/1 with mPEG. Molar monomer ratio ECL/GVL of the starting monomer mixture was varied (90/10, 80/20 and 70/30) to obtain three copolymer compositions. Homopolymer 100/0 was synthesized as reference. Monomer mixtures with lower ECL/GVL ratios and the reference 0/100 gave after ROP only oligomers (M n lower than 1000 Da), and were not considered for this study.

Analytic methods
The GPC apparatus was composed of a Shimadzu Prominence UFLC chromatograph, two ResiPore/PLGel GPC column (Agilent Technology, Italy), a tetra-detector equipped by UV γ-valerolactone copolymerization diode array, refractive index, dual-angle light scattering (15˚and 90˚) and viscometer. Columns and detectors were thermostatted at 40˚C. THF (Sigma Aldrich, Chromasolv 1 , 1 mL min -1 ) was used as eluent. Samples for GPC analysis were dissolved in THF (concentration: 0.1-0.2 mg mL -1 , injection volume: 50 μL). Data analysis was based on a calibration curve obtained with narrow polystyrene standards.
NMR spectra were acquired on polymer solutions in CDCl 3 (Aldrich) with a Bruker 400 MHz spectrometer (Bruker, Italy) at fixed temperature (300 K). Polymers for 1 H-NMR analysis were dried under vacuum, for at least 24 h, before their solubilization in CDCl 3 (0.2 mg mL -1 ).
FTIR analysis was conducted on polymer powders with a Shimadzu IRAffinity-1 spectrometer.
Non-isothermal polymerization was performed in a DSC1 apparatus (Mettler Toledo, Italy). The instrument was calibrated before each analysis session [27]. Polymerization was obtained under dry N 2 flow (80 mL min -1 ) at different heating rates (5, 10, 15, 20 and 30 K min -1 ) in the temperature range from 300 to 525 K.

Ring-opening polymerization procedures
Equilibrium and low-conversion polymerizations were performed in 10 mL one-neck roundbottom glass reactors. mPEG (1.5Á10 −4 mol) and liquid monomers (Table 1) were transferred in the reactor, flushed with dry N 2 for 15 min, then stirred and heated at fixed temperature. The catalyst Sn(Oct) 2 (1.5Á10 −4 mol, dissolved in 50 μL of toluene) was added upon heating. The reactor was connected to a CaCl 2 column and maintained under N 2 flux. Small amounts of crude products were withdrawn and immediately dissolved in cold acetone to stop the reaction. Crude samples were maintained at −20˚C before the GPC analysis, then evaporated, weighted and dissolved in THF. Eventually, the reactor was quenched in cold water, products were dissolved in acetone, precipitated in methanol three times and finally dried under vented oven overnight at room temperature.

ROP thermodynamics
Values of [M] eq were quantified from GPC chromatograms of crude samples from equilibrium polymerization. Due to their similar molecular weight, ECL and GVL monomers were eluted together, allowing only the quantification of the overall concentration. The quantification was based on the coefficient of RI response β i,j (i: ECL molar fraction, j: GVL molar fraction) of monomer mixtures in respect to obtained polymers for each polymer. GPC chromatograms of five monomers/polymer mixtures with known composition gave desired values (Fig C in S1 File).
[M] eq were calculated as [28]: In this equation, [M] 0 is the starting overall concentration, while A m and A p are areas under peaks of UV traces, for monomer and polymer respectively (Fig D in S1 File).
[M] eq were validated by comparing values of predicted and experimental M n values. Predicted M n values were calculated with the following equation: where " M m is the average molecular weight of monomers, [I] 0 is the molar concentration of mPEG (0.1 mol L −1 ) and M I is the molecular weight of mPEG (550 g mol −1 ).
Starting from the fundamental definition of the free Gibbs energy of polymerization ΔG p = ΔH p − TΔS p , the Dainton-Ivin's equation [29] where ΔH p is the enthalpy of polymerization, ΔS p is the entropy of polymerization, R is the ideal gas constant (8.314 J mol −1 K −1 ). In our experiments, the degree of polymerization was comprised between 52 and 83, then Eq ( [ECL] eq and [GVL] eq were estimated from experimental M n and macromolecular composition, resulting: where N ECL,0 and N GVL,0 are ECL and GVL moles in the starting reaction mixtures and N ECL,p and N GVL,p are ECL and GVL moles polymerized. Estimated values were validated by comparing predicted and experimental ΔH p and ΔS p . Predicted thermodynamic parameters were calculated as:

ROP kinetics
Kinetic rates and monomer reactivity ratios were calculated from data obtained from low-conversion ROPs. Kinetic rates derived from fitting of experimental values of M n vs. time. Reactivity ratios were calculated from the copolymerization kinetic equation (more details in SI): Solving Eq (8) we can calculate reactivity ratios and gather information about monomer distribution along the polymer chain.

Non-isothermal ROP
DSC analysis provided information on kinetic rate parameters [31,32]. We assumed the following reaction rate model: In this equation, k(T) is the temperature-dependent kinetic constant, A is the pre-exponential factor, E a is the apparent activation energy (J mol −1 ), T is the absolute temperature (K), and n is the reaction order. The reaction order n is an estimation of reactant concentration effect on the reaction rate. Eq (9) is called nth order model and it is often used for the empirical description of heterogeneous processes affected by diffusion processes; it is derived from the Šesták-Berggren equation [33] dα/dt = k(T)α m (1 − α) n (−ln(1−α)) p setting m = p = 0. This generic model was selected to compute the unknown nth reaction order. Eq (9) contains three unknown parameters (A, E a and n) while the triplet T, α and dα/dt was recorded by DSC. Unknown variables of Eq (9) were calculated with a multi-linear regression. Preliminary values of n, obtained from peak shapes with a geometric method, were used as first-attempt inputs. Assuming n constant over time, the shape index S was calculated from the degree of asymmetry of the peak as (Fig 2): and n was then obtained as: Values of α were normalized on the actual conversion calculated from GPC data. Tests were performed in triplicate.

ROP thermodynamic
Theoretical values of [M] eq were considerably higher in copolymers than in material 100/0 (  (Fig 3a) confirmed that GVL affected the ROP mechanism. Reaction temperature influenced monomer equilibrium only in copolymer synthesis, while its effect was negligible in homopolymer reaction (Fig 3b). We combined GPC and 1 H-NMR data to obtain a theoretical evaluation of single-monomer equilibrium concentration, [ECL] eq and [GVL] eq (Table 2). Single-monomer equilibrium concentration increased with decreasing ECL/GVL ratio.
[ECL] eq values in copolymerization were significantly higher than that calculated in material 100/0 (Fig 3c). This observation confirmed that GVL hindered the reaction, decreasing the ability of ECL to react via a ROP scheme.
[ECL] eq values were 25-30% the ECL concentration in reaction feeds ([ECL] 0 = 7.7, 6.9 and 6.0 mol L −1 in copolymers 90/10, 80/20 and 70/30 respectively). Also [GVL] eq depended on the starting molar composition of the reaction feed (Fig 3d). Its values linearly increased as the GVL concentration in reaction feeds increased. Equilibrium values were close to the starting concentrations (0.9, 1.8 and 2.7 mol L −1 ), indicating low reactivity of this monomer. Calculated and experimental M n values were in reasonable agreement ( Table 2). While M n value for material 100/0 was similar to the theoretical value (10 kDa) fixed in reaction setup, M n values calculated for copolymers showed strong differences. This can be explained considering that GVL reactivity lowered the overall reaction yield while the theoretical starting value of the desired molecular weight was calculated hypothesizing the complete monomers conversion. The data can be used as reference to correct the reaction recipe if higher molecular weights are requested.
Trends of [M] eq by varying T enabled the calculation of thermodynamic parameters (Fig 4  and Table 3), which were used to evaluate ceiling temperatures via the Dainton-Ivin equation (Eq (3)). While ΔS p were not affected by the composition of the reaction feed, ΔH p linearly increased with the GVL concentration. Calculated values indicated that major effects on ROP thermodynamics were given by the contribution of the reaction enthalpy. Higher ΔH p values entailed higher ΔG p and thus a lower aptitude to induce ROP. The results obtained for homopolymer 100/0 were close to those reported in the literature [34], while comparative data for copolymers were not available. Calculated values of T c for the homopolymer was in agreement with the literature [35]. Values of T c linearly decreased as the ECL/GVL ratio decreased, reducing the upper limit of the temperature range in which this ROP can occur.

ROP kinetics
Reaction rates indicate the speed at which monomers are consumed by the polymerization process. In addition to thermodynamic effects of the GVL monomer on this ROP, the kinetic analysis of copolymerization highlighted additional effects on ROP feasibility. Kinetic rates evaluated from residual monomer concentrations in low-conversion reactions (Table 4) confirmed that GVL affects ROP kinetics, slowing down the reaction. Calculated ECL consumption rate was significantly lower in copolymerization than that calculated in material 100/0.  Decreasing trends for both ECL and GVL kinetic rates were registered as the ratio ECL/GVL decreased. The order of reaction n indicates how fast the concentration of reactants falls while the reaction proceeds. For this ROP, calculated values were close to unity in all cases and did not depend on monomer feed compositions. This indicates that reactions proceeded with a stepwise mechanism.
Reactivity ratios, calculated as reported in SI, were r 1 = 0.65 ± 0.06 and r 2 = 0.44 ± 0.02. These values indicated a slightly greater tendency of [−ECL • ] to add the ECL monomer instead of the GVL, but similar reactivity ratios, both lower than 1, ensured the occurrence of the copolymerization, excluding a strong tendency of activated monomers to form homopolymers. Reactivity ratios product corroborate this conclusion. Their product was close to 0.3, indicating the aptitude of both monomers to form alternating or random copolymers [36]. However, lower amounts of GVL in the reaction feed did not allow formation of a perfectly alternating copolymer, as a random configuration is more probable under these conditions.

Non-isothermal ROP
Non-isothermal DSC by varying heating rate provided data on kinetic rate parameters and defined lower values of temperature ranges to obtain significant polymerization rates. The unimodal distribution of DSC thermograms (Fig Ea in S1 File) revealed that the reaction kinetics was not affected by the molecular weight of growing polymer chains. Polymerization proceeded with equivalent chain-growth events, excluding the occurrence of side-reactions (e.g. trans-esterifications or inter-and intra-molecular reactions). The absence of significant sidereactions ensured that final products were linear macromolecules. The observation of equivalent chain-growth events confirmed our previous hypothesis, based on reactivity ratios calculations, which indicated a non-preferential tendency of activated monomers to add ECL or GVL. Monomer conversion α (Fig Eb in S1 File) and reaction rate dα/dt (Fig Ec in S1 File) traces shifted towards higher temperatures as the ECL/GVL ratio decreased. Final monomer conversion lowered in copolymers containing higher amounts of GVL. dα/dt curves were fitted, providing E a , n and A. Peak height increased as the heating rate increased, indicating faster polymerization rates.
Characteristic temperatures were calculated from DSC traces. Onset (Fig 5a) and peak (Fig  5b) temperatures were affected by heating rate and ECL/GVL ratio. Usually, onset temperatures should be not dependent on the heating rate. As for the ROP of ECL [37], we hypothesized that Sn(Oct) 2 catalyst provided a coordination-insertion mechanism, which is governed by kinetics and thus by the temperature. Onset temperatures identified the lowest value to obtain significant reaction rates. At onset temperature, copolymerization was thermodynamically possible, γ-valerolactone copolymerization but kinetics was too slow to be estimated. Peak temperatures identified the conditions to obtain the higher reaction rates. Values increased in copolymers with higher GVL amounts. From non-isothermal ROP we obtained reaction orders and activation energies. Commonly, E a is calculated with semi-empirical methods, based on maximum reaction rate or isoconversional maps. Although these methods have been used to study ROP of ECL [38][39][40][41], they present some restrictions that may limit their reliability. For the reported case, we performed a mathematical modeling of experimental data, avoiding approximations or model restrictions. Results of multi-linear regression are compared with those obtained with semiempirical models in SI.
Orders of reaction n were preliminary evaluated from curves dα/dt vs T with a geometric model. Values of n were close to 1.2 and not affected by feed mixture composition. Data obtained in non-isothermal analysis were in close agreement with those calculated in low-conversion reactions. Data were used as first tentative input of the multi-linear regression of dα/dt vs T. Multi-linear regression provided values of the triplet E a , n and ln(A). Values of n from multi-linear regression analysis confirmed those obtained with the geometric method (Fig 6a). E a and ln(A) (Fig 6b and 6c) depended on the monomer feed composition, the first parameter increased while the second decreased as the ECL/GVL ratio decreased. Reported trends of E a and ln(A) indicated that ROP kinetics was unfavorable in the presence of GVL.

Conclusion
We demonstrated that ring-opening copolymerization of γ-valerolactone and -caprolactone is feasible under specific conditions of temperature and composition of the starting feed. By using different techniques, we identified limit conditions, in terms of temperature and monomer molar ratios, for such reaction. The combination of results from equilibrium, low-conversion and non-isothermal polymerizations enabled analyses of all major aspects related to kinetics and thermodynamics of this specific copolymerization process by varying the starting  γ-valerolactone copolymerization monomer feeds. We found that both kinetics and thermodynamics govern copolymerization and related parameters are affected by the amount of GVL used for the reaction. Equilibrium monomer concentrations and enthalpy of polymerization increased as the GVL concentration increased in the reaction feed. This indicates the existence of a thermodynamic upper limit in the concentration of this monomer. The upper monomer concentration limit explains why it was not possible to obtain homopolymers from GVL with high molecular weights with the proposed approach. The increase of reaction temperature caused the same effect on equilibrium monomer concentration, leading to a linear decrease of the ceiling temperature with the ECL/GVL ratio. Ceiling temperatures represent the upper temperature limit for this ROP, indicating the existence of a temperature range for copolymerization. Non-isothermal analysis identified the onset temperature providing significant copolymerization ratios. These results fix a lower temperature limit for the proposed ROP. Also, onset temperatures increased as the ECL/GVL ratio decreased, restricting the optimal range of temperatures for copolymerization. Overall monomer conversion was limited by the increasing GVL fraction, thus confirming that copolymerization was hampered in the presence of this monomer. While the reaction order n was not affected by monomer concentrations, trends of apparent activation energy and pre-exponential factor of kinetic constants confirmed the effect of GVL, which limited the reaction rate. Reactivity ratios were both smaller than 1 and their product suggested the formation of random copolymers.
Very few studies reported the synthesis of γ-lactone-based polyesters, probably due to the difficult ROP of five-membered rings, but their properties seem to be promising in several aspects, like degradation kinetics, mechanical properties and biocompatibility, even thought some preliminary studies on reaction conditions are needed to perform a controlled polymerization of γ-lactones. This paper clarifies the effects of reaction parameters on this specific copolymerization, and provides a guideline for the optimization of different ROPs in the presence of poorly reactive lactones.