Regulating sequence distribution of polyethers via ab initio kinetics control in anionic copolymerization

Zhichao Wu a, Pei Liu b, Yu Liu a, Wei Wei a, Xinlin Zhang a, Ping Wang c, Zhenli Xu bd and Huiming Xiong *ad
aDepartment of Polymer Science, School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China. E-mail:
bSchool of Mathematical Sciences and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
cDow Chemical (China) Investment Co., Ltd, Shanghai 201203, P. R. China
dCenter for Soft Matter and Interdisciplinary Sciences, Shanghai Jiao Tong University, Shanghai 200240, P. R. China

Received 27th June 2017 , Accepted 30th August 2017

First published on 12th September 2017

A study of the reaction kinetics of the copolymerization of two major categories of epoxy monomers, glycidyl ether (GE) and alkylene oxide (AO) derivatives, via the in situ NMR technique has been performed in a combinatorial strategy. GEs or AOs show similar reactivities when copolymerizing within either category, leading to a special azeotropic copolymerization, while they exhibit distinct reactivities between them. The underlying kinetics along with the living anionic copolymerization mechanism allow the generation of gradient and azeotropic copolymers, azeotropic-gradient terpolymers and double azeotropic-gradient tetrapolymers. Through the quantitative determination of rate constants and reactivity ratios with the aid of a numerical calculation in a simulated annealing scenario, we provide a widely applicable design principle for the sophisticated construction of sequence distribution-regulated, functional polyethers via a simple and efficient one-pot approach.


Multicomponent polymers can be obtained by copolymerization of two or more different types of monomers into a sophisticated primary structure.1,2 In this case, the positional arrangement of monomer units distributed along the polymer chain and the integrated properties or functionalities are anticipated to provide unprecedented opportunities to generate tailor-made and inaccessible materials.3–14 The chain copolymerization strategy through the simultaneous polymerization of different monomers in one pot, which is simple and scalable, is of particular importance. Until now, a few types of copolymer structures such as block, gradient, alternating and random copolymers have been well-established, primarily elaborated in the chain copolymerization of the binary mixture of component monomers.1,2,15

The control over the statistical composition or sequence distribution in the chain copolymerization relies on the intrinsic reactivities of the component monomers and the relevant reaction kinetics, the knowledge of which is usually obtained in the studies of reaction kinetics of various monomer pairs.1,2,15 In particular, living polymerization without termination and chain transfer can offer a precision synthesis of polymers with well-defined end groups and molecular weight.16 Most importantly, chain-to-chain deviation can be potentially relieved due to the initiation and the growth of each single polymer chain at approximately the same time and the same speed, which lays a firm basis for the control of monomer sequence distribution. However, the microstructure prediction of multicomponent polymers comprising more than two types of component monomers in the chain-growth process still remains elusive,1,15 partly due to the grand challenges from both experimental and theoretical aspects regarding the system design, proper characterization and data analysis.

Polyethers, feasible to anionic polymerization, are exceptional in many aspects ascribed to their highly flexible C–O–C bond based backbone in comparison with their C–C counterparts.17 They have been extensively applied in drug delivery,18 biosensors,19 electronic devices,20etc. However, the design of sequence distribution-regulated multicomponent polyether chains is still a great challenge. Herein, the essences of chain copolymerization processes and their kinetics in combinatorial two- and multi-component systems through one-pot synthesis are unravelled by the adaption of the in situ NMR technique and a newly developed numerical method, which opens up new possibilities to improve the understanding of copolymerization principles and allows elaboration of diverse multicomponent polyethers with fine-tuned properties from the bottom-up.



Toluene (Tansoole Chemicals, 99.5%) was stirred with sodium over 24 hours and then distilled into a high-vacuum flask which was freeze–thawed three times on a vacuum line. Potassium tert-butoxide (Acros Organics) at a concentration of 1 M in THF, 18-crown-6 (Sigma-Aldrich, 99%) and dibutylmagnesium (Acros Organics) were used as received. The chemical structures of monomers are shown in Fig. 1. Monomer A containing an azo side group and monomer E were synthesized in our previous work;21,22 the synthesis of monomer C is described in the ESI. The purification of monomer B (1,2-butylene oxide) was performed as previously reported.21
image file: c7py01073g-f1.tif
Fig. 1 The chemical structures of four epoxy monomers and their characteristic 1H NMR resonances in a quaternary mixture in toluene-d8, in which monomers A and E belong to the GE derivative whereas monomers B and C belong to the AO derivative.

General copolymerization procedure

We followed a similar procedure to that described previously for the copolymerization experiments.21,22 Briefly, a specially designed NMR-tube reactor was placed on a high-vacuum line and then flame-dried three times. The monomers were added into the reactor and degassed at 40 °C. A trace amount of 18-crown-6 and the potassium tert-butyloxide (∼2 μL, 1 M in THF) initiator were added into the reactor under a nitrogen atmosphere and freeze–thawed three times. Monomer B was stirred with freshly crushed calcium hydride for 24 h and then distilled into another flask that contained dibutylmagnesium. They were then immediately distilled into the NMR-tube reactor. Deuterated toluene was then distilled into the tube and frozen immediately. Finally, the NMR-tube reactor was flame-sealed and removed from the vacuum line. The tube reactor was warmed to 25 °C immediately once the NMR measurements started.


1H NMR spectra were recorded on a Varian MERCURY spectrometer (400 MHz) at 25 °C and the solvent was deuterated toluene. The in situ technique was used to track the process of copolymerization. A spectrum was recorded every 10 min. Gel permeation chromatography (GPC) was performed on a Malvern Viscotek GPCmax with a differential refractive index detector. THF was used as the eluent at a flow rate of 1.0 mL min−1 and polystyrene was used as the standard. The numerical method and the fitting program to obtain the kinetic parameters of the copolymerization are described in the ESI.

Results and discussion

We choose four epoxy monomers with structures as shown in Fig. 1, and denoted them as A, E, C and B. These four monomers can be grouped into alkylene oxide (AO) and glycidyl ether (GE) derivatives, which represent two major categories of epoxy monomers and are widely used as intermediates for synthesizing diverse polyethers.17 C and B are AOs attached with pendent groups of different sizes. A and E are GEs with alkane segments linking mesogenic moieties. The alkane segment in A, E or C not only serves as a spacer necessary for liquid crystalline behavior, but also decouples the electronic effect from the mesogenic group. Notably, the signals of methine protons in epoxide rings of these four monomers are well-resolved in 1H NMR spectra despite the partial overlap of the resonances of methine protons in A and E, as shown in Fig. 1. As polymerization proceeds, these characteristic resonances disappear due to the ring-opening reaction, which allows us to monitor in situ the consumption of the monomers as a function of reaction time for kinetics study. This on-line technique performed in a sealed NMR tube has been verified to be a reliable method as previously reported.21–24

In the binary copolymerization of two competing monomers, X and Y, the reactivity ratio rX = kXX/kXY of monomer X or rY = kYY/kYX of monomer Y is defined as the ratio of the homopolymerization rate constant (kXX or kYY) and the cross-propagation rate constant (kXY or kYX) in the classic terminal mode for chain propagation.15 Ionic copolymerization generally exhibits ideal behavior,25 that is the propagating chain ends have the same tendencies to incorporate monomers, which leads to rX × rY = 1 or kXX/kXY = kYX/kYY. A special case of ideal copolymerization is rX = rY = 1, or kXX = kXY and kYX = kYY, which means that the monomers have equal probabilities to incorporate into either propagating end during copolymerization (or ideal random copolymerization).15 In this type of azeotrope, the overall composition of the copolymer is always equal to the composition of feed at any feed ratio, which is particularly useful in terms of ease of tuning the microstructure and properties of the copolymer simply by control of the feed ratio.

Interestingly, this azeotropic behavior has been observed in the copolymerization of monomer pairs of A and E as well as C and B. As representatively demonstrated in Fig. 2a, A and E at an equal feed consume at the same speed with simultaneous disappearance of the characteristic resonances of the methine protons in epoxy rings at 2.8–2.9 ppm; meanwhile, the signals at 2.3–2.4 ppm belonging to the formed polyether backbones gradually develop. The instantaneous concentration of each monomer is found to quantitatively follow a similar trajectory over time, as shown in Fig. 2b. This fact suggests that these two monomers have similar reactivities and are indistinguishable in kinetics during the chain propagation. Moreover, the instantaneous conversion of monomer A or E (MX/MX0, or MY/MY0, where MX or MY is the instantaneous monomer concentration, and MX0 or MY0 is its initial concentration) versus total monomer conversion ((MX + MY)/(MX0 + MY0)) is linear along the diagonal as shown in Fig. 2c, which is direct evidence of azeotropic copolymerization with reactivity ratios equal to one. This argument is further supported by the copolymerization conducted at a different feed ratio of 1/3 (A/E). The simultaneous disappearance of the monomer signals (Fig. 2d and e) and a diagonally linear function of the monomer conversion as the total conversion (Fig. 2f) unambiguously suggest the special azeotropic behavior complying with rA = rE = 1 without any need for further calculation. This special azeotropic behavior has also been observed in the copolymerization of C and B belonging to the AO group. As shown in Fig. 3a, the monomer conversion versus the total conversion of C and B follow the diagonal lines, indicating similar activities of C and B despite the fact that the substituent in C is much bigger than that in B. The steric hindrance herein seemingly has a negligible influence. In contrast, distinct reactivities between monomers of the GE and AO groups are observed in their binary copolymerizations as illustrated in Fig. 3a, where the plots of the monomer conversion versus the total conversion are no longer diagonal lines. The GE monomers (A or E) consume much faster than the AO monomers (B or C), as also shown in real-time 1H NMR spectra in Fig. S4–S9. It is worth noting that for the pair of E and C, the only difference in the chemical structure is the existence of an extra oxygen atom next to the epoxy group in E as shown in Fig. 1. This difference leads to the dramatic discrepancy in reactivity as discussed below.

image file: c7py01073g-f2.tif
Fig. 2 (a) Real-time 1H NMR spectra overlay of the copolymerization of A and E at an equal feed in toluene-d8 at room temperature; (b) consumption of A and E versus reaction time according to 1H NMR results at an equal feed; (c) instantaneous A and E conversion versus total conversion at an equal feed; (d) real-time 1H NMR spectra overlay of the copolymerization of A and E at a feed ratio of 1/3 (A/E); (e) consumption of A and E versus reaction time at a feed ratio of 1/3 (A/E); (f) instantaneous A and E conversion versus total conversion at a feed ratio of 1/3 (A/E).

image file: c7py01073g-f3.tif
Fig. 3 (a) Instantaneous monomer conversion versus total conversion for the copolymerization of C and B, E and B, A and B, and E and C, determined from their real-time 1H NMR spectra; (b) schematics of chain composition along the chain growth direction for the copolymers.

How to reliably obtain a reactivity ratio in copolymerization is of fundamental importance. However, this is often challenging and has become a central concern.21–28 Inspired by the recent work adopting a numerical method,24 we develop a computational framework to numerically solve the elementary kinetic differential equations, then compare the evolution of monomer concentrations versus time with the experimental NMR data. The rate constants are obtained as the best fitting parameters. In order to avoid being trapped in a certain local minimum instead of the global one during the numerical calculation, we employ a simulated annealing strategy conjugated with the gradient descent method to guarantee the global convergence of the solution (see the ESI for details).

The fitting curves and the rate constants of five binary mixtures, and consequently their reactivity ratios are thus obtained, as illustrated in Fig. S13 and Table S3. The products of the reactivity ratios of the combinatorial monomer pairs are all close to unity, suggesting an ideal copolymerization behavior. Moreover, the reactivity ratios of the A and E pair and the C and B pair belonging to either the GE or AO group exhibit values close to unity, consistent with the special azeotropic behavior observed in experiments. The negligible influence of the size of the pendent group on the reactivity ratios may suggest a saturated steric effect when the substituent in the epoxy monomers is bulkier than ethyl as in butylene oxide.29 For the monomer pairs from the GE and AO group, the GE monomers are found to be around 6–9 times more active than the AO monomers. These results actually imply that the dominant influence on the reactivity could be solely from the electrophilic substituent to the epoxy ring, which is a useful clue for the design of multicomponent polyethers with diverse pendent moieties.

It is worth stressing that in GEs, the additional electronic effect from the mesogenic group seems to be screened by the alkane spacer. In principle, the electron-withdrawing effect of the oxygen at the 3 position to 1,2-epoxide can lower the electron density of the epoxide ring, thus activating its reactivity towards an alkoxide nucleophilic attack and consequently stabilizing the propagating anions. The inductive effect has been reflected in the chemical shifts of the methine protons of GEs to a lower field in the NMR spectrum compared to AOs (Fig. 1). The additional inductive effect is also implied in GE derivatives attached with allyl or phenyl substituents without spacers.25,30 Indeed, distinct reactivities were observed, which confirms the role of the alkane spacer in tuning the activities of epoxy monomers. As for AOs in the absence of an oxygen atom adjacent to the epoxy ring, similar electrophilicities of the substituents lead to similar reactivity ratios of monomers close to unity.

The molecular weights and their distributions of the copolymers have been characterized by GPC. As demonstrated in Fig. 4, the representative traces of copolymers all exhibit narrow molecular weight distributions (Mw/Mn < 1.10), and their molecular weights were consistent with the theoretical values calculated according to the monomer/initiator mole ratio. These characters are expected for the controlled anionic ring-opening polymerization whose conditions have been readily established to obtain monodispersed, well-defined polyethers.21,22

image file: c7py01073g-f4.tif
Fig. 4 Typical GPC traces of C-co-B (PDI = 1.05, Mn = 10.2 kg mol−1), E-co-B (PDI = 1.06, Mn = 9.7 kg mol−1), A-E-B (PDI = 1.07, Mn = 11.5 kg mol−1) and E-C-B-A (PDI = 1.06, Mn = 12.2 kg mol−1) copolymers.

For the multivariate copolymerization of more than two monomers, sequence control often becomes difficult and unpredictable.16 Herein, it is particularly interesting and suitable to reveal the copolymerization processes of these epoxy monomers and how the relevant kinetics in the two-component copolymerization could be inferred to the multiple-component one. To this end, we have performed a study of the copolymerization of a ternary mixture of A, B and E (Fig. 5a–c), and subsequently a quaternary mixture of A, B, E and C (Fig. 5d–f). The resultant copolymers all exhibit narrow molecular weight distributions as demonstrated in Fig. 4. In the ternary copolymerization, it is found that the conversion of A and E exhibits similar rates, but is much faster than that of B, as shown in Fig. 5b. This phenomenon is consistent with the kinetics study in the binary mixtures, where the pair of A and E shows a special azeotropic behavior while either of them shows an equally high reactivity with respect to B. Each monomer's activity in the ternary copolymerization is in line with that in the respective binary copolymerization. The introduction of one more monomer does not seem to impact the other two monomers’ copolymerization process. This character resulted in the generation of an azeotropic-gradient polymer chain ((A-a-E)-g-B) as schematically shown in Fig. 5c.

image file: c7py01073g-f5.tif
Fig. 5 (a) Consumption of each monomer versus reaction time in the ternary copolymerization; (b) instantaneous monomer conversion versus total conversion for ternary copolymerization; (c) schematics of chain composition along the chain growth direction for the terpolymer; (d) consumption of each monomer versus reaction time in the quaternary copolymerization; (e) instantaneous monomer conversion versus total conversion for quaternary copolymerization; (f) schematics of chain composition along the chain growth direction for the tetrapolymer.

We further conducted the copolymerization of a quaternary mixture of A, B, C and E in one pot. We found that when A and E were fed at an equal initial molar ratio, they followed a similar trajectory in the evolution of concentration versus time (Fig. 5d) as in their binary mixtures (Fig. 2b). The conversion curves of A and E (Fig. 5e) show nearly the same incorporation rates, while B and C consumed at similar but apparently smaller rates. This remarkable observation indicates that adding C into the A, B, and E ternary system does not alter the relative reactivities of the monomers and their copolymerization processes in the ternary mixture. According to the estimated reactivity ratios in Table S3, this behavior can be ascribed to the ideal polymerization nature for any pair of epoxy monomers. Moreover, the reactivity ratios of different monomer pairs constituted by GE and AO derivatives do not show a big difference. These intrinsic characters result in the generation of a double azeotropic-gradient copolymer structure, (A-a-E)-g-(B-a-C), as schematically demonstrated in Fig. 5f. The behavior of each pair of monomers in the quaternary mixture is in line with that in their binary copolymerization. The mutual “immunity” among the epoxy monomers in the multivariate living anionic copolymerization is intriguing and can be practically useful. Indeed, the limit of the usual terminology has to be stretched to describe the variable classes of non-deterministic polymeric sequences.


We have revealed general principles to manipulate the kinetics of the anionic copolymerization of epoxy monomers categorized by GEs and AOs, and eventually to achieve the regulation of sequence distribution of polyethers in a one-pot approach. By examining binary copolymerization in different monomer combinations, we have elucidated the influence of pendent groups on the reactivity and copolymerization kinetics. By using an annealing scenario to numerically solve the kinetic differential equations and fit with the experimental data, we have obtained the rate constants and reactivity ratios. Thereby, a series of gradient copolymers, azeotropic copolymers, and terpolymers and tetrapolymers of azeotropic-gradient and double azeotropic-gradient features have been designed and generated. We hope that this finding and the understanding of the detailed kinetics could provide a toolbox towards the diversification of sequence distribution-regulated polyethers from a variety of readily available epoxy monomers.

Conflicts of interest

There are no conflicts of interest to declare.


This research is supported by the National Natural Science Foundation of China (no. 21374063 and no. 21574082 for x.h.m., and no. 11571236 for x.z.l.). We appreciate the Instrumental Analysis Center of SJTU and the assistance from Dr. Bona Dai with NMR measurements.

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Electronic supplementary information (ESI) available. See DOI: 10.1039/c7py01073g
These authors contributed equally.

This journal is © The Royal Society of Chemistry 2017