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BY-NC-ND 3.0 license Open Access Published by De Gruyter December 2, 2014

Synthesis, characterization, and crystallization of biodegradable poly(ε-caprolactone)-poly(L-lactide) diblock copolymers

Song Luo, Xinyu Peng, Ying Chen, Ting Su, Jun Cao, Sai Li and Bin He
From the journal e-Polymers

Abstract

Three diblock copolymers of PCL6k-PLLA2k, PCL6k-PLLA4k, and PCL6k-PLLA6k were prepared and their crystallization behaviors were investigated. The molecular weights of the copolymers calculated from 1H nuclear magnetic resonance spectra were equivalent to the designed molecular weights. The gel permeation chromatography spectra of the copolymers showed one peak, which revealed that the copolymers were monodisperse. The crystallization capability of poly(ε-caprolactone) (PCL) decreased and that of poly(L-lactide) (PLLA) increased when the molecular weight of the PLLA block was increased from 2k to 6k. PCL spherulites in the PCL6k-PLLA2k copolymer film were smaller than those in PCL6k-PLLA4k or PCL6k-PLLA6k copolymer film. PCL spherulites in the PCL6k-PLLA2k copolymer film grew fastest within all three diblock copolymers. An obvious phase separation phenomenon was observed on the surface of PCL6k-PLLA6k copolymer film in atomic force microscopy images.

1 Introduction

Biodegradable polyesters such as poly(L-lactide) (PLLA), poly(L-lactide-co-glycolide), and poly(ε-caprolactone) (PCL) have been widely used in biomedical engineering, including implant devices (1), scaffolds in tissue engineering (2–4), and medical instruments (5). The synthesis, characterization, and degradation of biodegradable polyesters were extensively reported (6–11). As semicrystal polymers with high crystallinity, the crystallization of PLLA and PCL homopolymers was investigated by several researchers, and spherulites of PLLA and PCL were observed (12–16).

The crystallization investigations of PLLA- and PCL-based polymers and composites were attractive and interesting research works. The crystal characteristics of PLLA and PCL in different architectures and composites were explored. Wang and Dong (17) studied the spherulitic growth of well-defined star-shaped PCL with different arms and found that both the number of arms and the molecular weight of PCL were the main factors that controlled the spherulitic growth rate and morphology. Liu et al. (18) synthesized a new star-shaped PCL with polyhedral oligomeric silsesquioxane (POSS) as the core and concluded that the increase of POSS concentration would increase both the overall crystallization rate and the spherulitic growth rate of the star PCL. Zhang and Zheng (19) synthesized dendritic star-shaped PLLA and found that the crystallization of PLLA was effectively suppressed by the formation of star topology. Zhang and Qiu (20) prepared PCL/thermally reduced graphene (TRG) nanocomposites and reported that the TRG could enhance the crystallization of PCL due to the heterogeneous nucleation effect. Xiao et al. (21) studied the crystallization behavior of poly(lactic acid)/poly(butylene adipate-co-terephthalate) blends and discovered that the maximum crystallization rate of the blends was dependent on the crystallization temperature and their components. Kim et al. (22) mixed PCL/PLLA/P(LLA-co-CL) together to receive blends and observed that the addition of P(LLA-co-CL) could suppress the crystallization of PLLA and induce the concurrent crystallization of PLLA and PCL. DellErba et al. (23) studied PCL-PLLA blends containing PLLA-PCL-PLLA triblock copolymer and concluded that the PLLA crystallization rate was enhanced in the presence of PCL domains.

The crystallization behavior of PLLA-PCL block copolymers was different from that of PLLA or PCL homopolymer or their blend due to their block architectures. Hamley et al. used X-ray scattering, differential scanning calorimetry (DSC), and polarized optical microscopy (POM) to study the crystallization of PLLA-PCL diblock copolymers; two copolymers with 44 and 60 wt% PLLA (the expected molecular weights of PLLA were 12,400 and 11,100, respectively) were synthesized via controlled “living” sequential block copolymerization initiated by aluminum trialkoxides in toluene solution. Sequential isothermal crystallization was measured at 100°C and 30°C. It was found that PCL block was able to crystallize within PLLA-negative spherulites (24). Zhao et al. synthesized PCL-PLLA-PCL triblock copolymers via sequential ring opening polymerization (ROP) of both L-lactide (LLA) and ε-caprolactone (CL) monomers with ethylene glycol as the initiator. With the adjustment of the compositions, only one melting peak of PCL block was detected, and the presence of PLLA decreased the crystallinity of PCL and retarded the degradation of the block copolymer compared with PCL homopolymer (25). Wang and Dong (26) developed a star-shaped PCL-PLLA block copolymer and found the transition of ordinary spherulites to band spherulites when the arm length ratio of PCL to PLLA was increased. Wei et al. (27) synthesized PCL-PLLA diblock copolymers via melt or solution sequential copolymerization. X-ray diffraction (XRD) and DSC results indicated the coexistence of both PCL and PLLA crystallized in microdomains and the microphase separation appeared in the block copolymers. Casas et al. (28) used transmission electron microscopy to observe the single crystals of double crystallized PCL-PLLA diblock copolymers. Isothermal crystallization was carried out at different temperatures and the crystal morphologies were dependent on crystallization temperatures as well as components.

In this paper, we synthesized PCL-PLLA diblock copolymers using sequential ROP of CL and LLA monomers with benzyl alcohol as the initiator. To investigate the influence of block chain length on the crystallization behaviors, the molecular weight of PCL block was maintained at 6k and that of PLLA block varied from 2k to 6k. The chain length of both PLLA and PCL blocks were much shorter than those of block copolymers previously reported, which was more sensitive for the crystallization investigation. The copolymer films were treated at temperatures of 30°C and 60°C for the crystallization investigation of PCL and PLLA blocks. The copolymers were characterized by 1H nuclear magnetic resonance (NMR), Gel permeation chromatography (GPC), Fourier transform infrared (FTIR), DSC, and XRD. The morphology of PCL and PLLA crystals was observed by atomic force microscopy (AFM) and POM.

2 Experimental section

2.1 Materials

ε-CL (Tianjin Heowns Biochem Technologies LLC, Tianjin, China) was dried by CaH2 and purified via vacuum distillation. LLA (Purac Biochem Co., Gorinchem, The Netherlands) was recrystallized twice in ethyl acetate and dried in vacuum at room temperature before use. Tin(II) 2-ethylhexanoate [Sn(Oct)2; Sigma-Aldrich Co., Steinheim, Germany] was used as received. Benzyl alcohol (Tianjin Reagent Chemical Co., Tianjin, China) was dehydrated under reduced pressure. Diethyl ether and dichloromethane (CH2Cl2; Tianjin Chemreagent Chemical Co., Ltd., Tianjin, China) were distilled before use. All other solvents were purchased from Kelong Chemical Co. (Chengdu, China) and used without further purification.

2.2 Synthesis of PCL-PLLA diblock copolymers

2.2.1 Synthesis of PCL

PCL6k was synthesized and purified as previously reported (29). Briefly, PCL6k was synthesized via ROP of ε-CL monomer, and Sn(Oct)2 and benzyl alcohol were used as the catalyst (mass ratio, 1:1000) and initiator, respectively. ε-CL (15 g, 131.4 mmol) and benzyl alcohol (275.3 mg, 2.55 mmol) were added into the flame-dried polymerization tube, and Sn(Oct)2 (131.4 μmol) in anhydrous CH2Cl2 was added into the mixture. The tube was then connected to the nitrogen gas cylinder, and the exhausting-refilling process was repeated three times. The tube was sealed under reduced pressure and put in an oil bath at 120°C for 48 h. After the reaction, the resulting product was dissolved in CH2Cl2 and precipitated in excess cold diethyl ether twice. The white precipitated powder was dried in vacuum at room temperature for 12 h (yield, 91%).

2.2.2 Synthesis of PCL-PLLA

PCL6k-PLLA6k was synthesized via ROP. The typical synthetic procedure was as follows. PCL6k (4 g, 0.683 mmol) and LLA (4 g, 27.75 mmol) were added into a polymerization tube quickly, and Sn(Oct)2 (27.75 μmol) in anhydrous CH2Cl2 was added in the tube. After purging with nitrogen atmosphere three times, the tube was sealed in vacuum and put into an oil bath at 120°C for 48 h. The crude product was dissolved in CH2Cl2 and precipitated in excess cold anhydrous diethyl ether twice. The purified product was filtered and dried in vacuum at room temperature for 12 h (yield, 88.5%). PCL6k-PLLA4k and PCL6k-PLLA2k copolymers were synthesized according to the procedure mentioned above (yield of PCL6k-PLLA4k, 87.8%; yield of PCL6k-PLLA4k, 90.5%).

2.3 Preparation of PCL-PLLA films and the treatment in different temperatures

The three diblock copolymers films were prepared for XRD and AFM measurements. The copolymers were dissolved in chloroform (5 mg in 2.5 ml chloroform), and the solutions were casted on glass plates. The films were received after the solvent was evaporated. The films were incubated at 30°C and 60°C in vacuum for 24 h and cooled to room temperature for characterizations.

2.4 Characterizations

The solvent for 1H NMR measurement was CDCl3 containing 0.05% TMS as internal standard. 1H NMR spectra were obtained using a Bruker Avance-400 MHz NMR spectrometer at 25°C. GPC (Agilent 1100 Series) measurements were carried out to determine the molecular weights (Mn and Mw), and the molecular weight distributions (Mw/Mn) of the diblock copolymers were tested at 25°C with CHCl3 as eluent at a flow rate of 1.0 ml min-1. The received data were analyzed with GPC-SEC data analysis software. FTIR spectra were measured using the KBr disk method on FTIR spectrometer (Thermo Fisher Nicolet 8700) within the range of 4000–5000 cm-1. The thermal properties of the copolymers were investigated via DSC analysis. The measurements were carried out on a Q2000 (TA instruments), and all experiments were processed under nitrogen atmosphere. The diblock copolymers were heated to 180°C at a rate of 10°C min-1 and maintained for 5 min to eliminate the thermal history. Subsequently, the samples were cooled to -80°C with a cooling rate of 10°C min-1 and held at -80°C for another 5 min. The specimens were finally heated to 180°C at a heating rate of 10°C min-1. XRD characterization of PCL-PLLA film was performed on a DX-1000 XRD (Dandong, China) using CuKα radiation (wavelength, λ=0.154 nm) operated at 40 kV and 25 mA. The scanning rate was 0.06° min-1, and the samples were exposed at a scanning range of 2θ=10°–50°. The surface morphology of the films was observed by AFM (MFP-3D-BIO, Asylum Research, USA) with tapping mode. The crystal morphology of the diblock copolymers was observed by POM (Nikon Eclipse LV 100POL) equipped with an Instec HCS621V hot-stage device. Each copolymer (3–5 mg) sample was melted between the glass slip and the cover slip to form a thick film and cooled to room temperature. The sample was heated to 200°C and maintained at that temperature for 3 min. With the regulation of the hot stage, the temperature was cooled to the preestablished value with a cooling rate of 60°C min-1. To investigate the crystallization behaviors of PCL-PLLA copolymers, 30°C and 140°C were set as the observation temperatures. When the specimens were cooled to the temperatures, the observation of spherulites was started and continued immediately. A digital camera was used to take photographs.

3 Results and discussion

The synthetic route of PCL-PLLA diblock copolymers is presented in Scheme 1. Benzyl alcohol was used to initiate the ROP of ε-CL monomers, and the stannous octoate was used as the catalyst. The received PCL was used as the macroinitiator for the ROP of LLA. The melting temperature (Tm) of PCL block was approximately 60°C, and PCL block could be used as the macroinitiator to initiate the ROP of LLA.

Scheme 1 Synthetic route of PCL-b-PLLA diblock copolymer.

Scheme 1

Synthetic route of PCL-b-PLLA diblock copolymer.

We designed three copolymers of PCL6k-PLLA2k, PCL6k-PLLA4k, and PCL6k-PLLA6k. 1H NMR spectra of PCL and PCL-PLLA block copolymers are presented in Figure 1. It was clear in the spectrum of PCL that the protons in benzyl alcohol appeared at approximately δ=7.4 ppm (a in C6H5) and 5.1 ppm (b in CH2O), respectively (30). The PCL blocks contained five proton sites. The protons in COCH2CH2CH2 and CH2CH2CH2O (d in PCL blocks) were in similar chemical environments and the signal appeared at δ=1.7 ppm. The other three protons of COCH2CH2 (c), CH2CH2CH2 (e), and CH2CH2O (f) produced the signals at δ=2.3, 1.4, and 4.1 ppm. To the spectrum of PCL-PLLA copolymers, two new proton signals were found at δ=5.2 and 1.6 ppm, which were assigned to the protons in PLLA blocks [g in COCH(CH3)O and h in CH3] (31). The integrities of the peaks increased when the designed molecular weight (Mn) of PLLA blocks was changed from 2k to 6k. The integrated areas of the peaks of CH2O (b) in benzyl alcohol moiety and CH2CH2O in PCL at δ=4.1 ppm (f) were used to calculate the molecular weight (Mn) of PCL blocks. The integrated areas of the peaks of CH2CH2O in PCL at δ=4.1 ppm (f) and COCH(CH3)O in PLLA at δ=5.2 ppm (g) were employed to calculate the composition of the copolymer.

Figure 1 1H NMR spectra of PCL-PLLA diblock copolymers.

Figure 1

1H NMR spectra of PCL-PLLA diblock copolymers.

The relative molecular weight and molecular weight distribution of PCL-PLLA diblock copolymers were characterized by GPC (Figure 2). All spectra showed one peak to reveal that there were no PCL and/or PLLA homopolymers in the second ROP. Once the designed molecular weight of the copolymers increased, the eluent time decreased. This result was consistent with the variation of molecular weight.

Figure 2 GPC spectra of PCL-PLLA diblock copolymers.

Figure 2

GPC spectra of PCL-PLLA diblock copolymers.

The calculated molecular weight and molecular weight distribution of PCL-PLLA diblock copolymers are summarized in Table 1. From the molecular weights calculated from 1H NMR spectra, it could be concluded that the molecular weights of the three copolymers were similar to those of designed. The molecular weights of the four polymers from 1H NMR spectra calculation were 5860, 8640, 10,840, and 13,800, whereas the designed molecular weights were 6000, 8000, 10,000, and 12,000. Different from the molecular weights calculated from 1H NMR spectra, the molecular weights (Mn) in GPC spectra were much higher than those of designed, which were 9770, 17,670, 18,720, and 19,070, respectively. It was because the molecular weights tested by GPC were the relative molecular weights to the standard sample of narrow distributed polystyrene. It was interesting that the polydispersities (Mw/Mn) of PCL6k-PLLA2k and PCL6k-PLLA4k copolymers were narrower than that of PCL homopolymer. It was probably because the introduction of PLLA blocks changed the aggregation of copolymer chains in random coils in chloroform eluent and led to the variation of polydispersity.

Table 1

Calculated molecular weights of PCL-PLLA diblock copolymers

SampleMnaMnbMncMwcMw/Mnc
PCL6k6k5860977014,4601.48
PCL6k-PLLA2k8k864017,67023,2301.31
PCL6k-PLLA4k10k10,84018,72026,7701.43
PCL6k-PLLA6k12k13,80019,07028,5501.50

aDesigned molecular weight.

bCalculated from 1H NMR.

cGPC results.

FTIR spectra of the three PCL-PLLA diblock copolymers are presented in Figure 3. As the vibration units in the copolymers were the same in the three copolymers, FTIR spectra of the three copolymers were nearly the same. Two vibration bands of carbonyl in ester moieties were observed at 1760 and 1725 cm-1, respectively. Interestingly, the vibration band at 1760 cm-1 increased with increasing chain length of PLLA blocks. It was previously reported that there were two vibration bands of carbonyl in ester moieties in biodegradable polyesters, and as most biodegradable polyesters were semicrystallized polymers, the lower band was attributed to the vibration of carbonyl groups in crystal areas, and the higher band was assigned to the vibration of carbonyl in amorphous areas (32). The ratio of the band at 1760–1725 cm-1 increased when the PLLA chain length was elongated, which implied that the crystallization capability of the copolymers decreased with increasing PLLA chain length.

Figure 3 FTIR spectra of PCL-PLLA diblock copolymers.

Figure 3

FTIR spectra of PCL-PLLA diblock copolymers.

FTIR results showed that the crystallization of the copolymers was changed when the chain length of PLLA blocks increased. DSC and XRD were used to explore the crystallization of the three copolymers. DSC spectra of the three PCL-PLLA diblock copolymers are shown in Figure 4. Three endothermic peaks were observed during the heating process after the elimination of thermal history. Two endothermic peaks appeared at 40°C and 50°C, which were attributed to the melting of PCL crystals. One of the endothermic peaks of PCL blocks was due to the transition of PCL crystals from metastable to stable state in the heating process, which induced perfect PCL crystals and resulted in another endothermic peak at a higher temperature (33). The third endothermic peak at approximately 160°C was attributed to the melting of PLLA crystals.

Figure 4 DSC spectra of PCL-PLLA diblock copolymers.The spectra were the heating process after the elimination of thermal history, and the heating rate was 10°C min-1.

Figure 4

DSC spectra of PCL-PLLA diblock copolymers.

The spectra were the heating process after the elimination of thermal history, and the heating rate was 10°C min-1.

The thermal properties of PCL-PLLA diblock copolymers are summarized in Table 2. The melting points of PCL and PLLA block crystals were approximately 50°C and 160°C within all three copolymers. The Tm of both PCL and PLLA decreased a little when PLLA chains were elongated. The crystallization capability of PCL blocks was weaken and that of PLLA blocks was strengthened greatly as ΔHms of PCL crystals were changed from 42.8 to 19.5 J g-1 and those of PLLA crystals varied from 3.8 to 18.1 J g-1 when the molecular weight of PLLA blocks was increased from 2k to 6k. These results were consistent with those of FTIR.

Table 2

Thermal properties of PCL-PLLA diblock copolymers.

SampleTm (°C)ΔHm (J g-1)
PCLPLLAPCLPLLA
PCL6k-PLLA2K50.5160.842.83.8
PCL6k-PLLA4K50.6159.130.313.7
PCL6k-PLLA6K47.7156.819.518.1

The properties of the two blocks in PCL-PLLA copolymers were very different. The PCL was an elastic polymer with very low glass transition temperature (Tg; approximately -60°C) and Tm (approximately 50°C). PLLA blocks were rigid polymers with Tg at approximately 50°C and Tm at approximately 160°C. To investigate the movement of the polymeric chains in the two blocks, the copolymer films were treated at 30°C and 60°C for isothermal crystallization. After treatment, the crystallization of the films was measured by XRD. XRD spectra of the three copolymers are presented in Figure 5. The peaks of both PCL and PLLA crystals could be observed in all three copolymer films. In the spectra of the films treated at 30°C, the characteristic crystal peaks of PLLA blocks at 2θ=16.7° and 19.0° were obvious and increased with increasing molecular weight of PLLA (34). The peaks at 2θ=21.5° and 23.8° were attributed to PCL crystals (35), which were weakened with the molecular weight increase of PLLA blocks. The integrities of PLLA peaks were much weaker than those of PCL peaks even when the molecular weight of both blocks was 6k. XRD spectra were changed greatly after the films were treated at 60°C. The peaks of PLLA crystals increased dramatically, which were much stronger than those of PCL crystals in PCL6k-PLLA4k and PCL6k-PLLA6k films. It indicated that the incubation at 60°C accelerated the crystallization of PLLA blocks. These conclusions were consistent with DSC results.

Figure 5 XRD spectra of PCL-PLLA diblock copolymers films.That on the left was treated at 30°C, and that on the right was treated at 60°C.

Figure 5

XRD spectra of PCL-PLLA diblock copolymers films.

That on the left was treated at 30°C, and that on the right was treated at 60°C.

The surface morphology of the films was characterized by AFM (Figure 6). In the photographs of PCL6k-PLLA2k and PCL6k-PLLA4k films treated at 30°C, the surfaces were rough. The surface of PCL6k-PLLA4k film was relatively smoother than that of PCL6k-PLLA2k film. The surface morphologies of PCL6k-PLLA2k and PCL6k-PLLA4k films were similar and were in homogenous phase. However, the surface morphology of PCL6k-PLLA6k film treated at 30°C was very different from that of PCL6k-PLLA2k and PCL6k-PLLA4k films. Dark dots were separated in the light continuous phase, which demonstrated phase separation within the diblock copolymer film. Comparing the surface morphology of the three copolymer films, it could be concluded that the light continuous phase was PCL and the dark separated dot phase was PLLA. In the copolymer films treated at 60°C, the surface morphology of PCL6k-PLLA6k was nearly the same as that of film treated at 30°C. The size of dark dots separated phase in PCL6k-PLLA6k film treated at 60°C was larger than that in PCL6k-PLLA6k film treated at 30°C. It was probably because the thermal treatment enlarged the size of the separated PLLA phase. In PCL6k-PLLA4k and PCL6k-PLLA2k films treated at 60°C, the PLLA phase almost disappeared, which was different from the same samples treated at 30°C.

Figure 6 Morphology of PCL-PLLA diblock copolymers films measured by AFM.

Figure 6

Morphology of PCL-PLLA diblock copolymers films measured by AFM.

The three copolymer films were incubated at 30°C and 140°C to observe the crystal growth of PCL and PLLA spherulites. As the two incubated temperatures were approximately 20°C lower than the Tms of PCL (approximately 50°C) and PLLA (approximately 160°C) crystals, spherulites of PCL and PLLA crystals would grow fast, which could be observed by POM conveniently. The photographs of PCL spherulites growth in the three copolymer films are shown in Figure 7. In PCL6k-PLLA2k film, there were rare PLLA spherulites in the background at the beginning. Many white PCL spherulites appeared at 180 s, and spherulites were small. The spherulites grew very fast and the film surface was covered with PCL spherulites quickly. As the growth of spherulites was limited by each other, PCL spherulites in PCL6k-PLLA2k copolymer film were small. In PCL6k-PLLA4k and PCL6k-PLLA6k films, the growth of PCL spherulites was a little different. PLLA spherulites were observed obviously in the background, and PLLA spherulites in PCL6k-PLLA6k film were bigger than those in PCL6k-PLLA4k film. The white PCL spherulites were observed after incubation for 180 s, and spherulites grew with increasing time. Big perfect PCL spherulites were also observed on the surface of PCL6k-PLLA4k and PCL6k-PLLA6k copolymer films. The growth rate of PCL spherulites in PCL6k-PLLA4k and PCL6k-PLLA6k copolymer films was slower than that in PCL6k-PLLA2k copolymer film due to the affection of PLLA spherulites (24).

Figure 7 POM photographs of the growth of PCL spherulites in PCL-PLLA diblock copolymers films at 30°C.

Figure 7

POM photographs of the growth of PCL spherulites in PCL-PLLA diblock copolymers films at 30°C.

The growth of PLLA spherulites in the copolymer films was also observed by POM at 140°C and the relevant photographs are shown in Figure 8. Because the temperature was higher than the Tm of PCL crystals, no PCL spherulites were observed in the background. In the PCL6k-PLLA2k sample, rare PLLA spherulites were formed even when the incubation time was as long as 810 s. PLLA chains were too short to crystallize during incubation. With the PLLA chain length increasing, the crystallization capability of PLLA blocks was enhanced. PLLA spherulites clearly appeared in PCL6k-PLLA4k and PCL6k-PLLA6k copolymer films, and PLLA spherulites in PCL6k-PLLA6k film was larger than those in PCL6k-PLLA4k film due to the longer PLLA blocks, which promoted the crystallization capability of PLLA chains.

4 Conclusions

Three PCL-PLLA diblock copolymers with different PLLA chain lengths were synthesized via ROP of ε-CL and LLA monomers with benzyl alcohol as the initiator and stannous octoate as the catalyst. The molecular weights of the three copolymers were nearly the same as the designed molecular weight. The crystallization of the blocks in copolymers was investigated. The crystallization capability of PCL blocks decreased with the increase of the molecular weight of PLLA blocks and that of PLLA blocks increased when the molecular weight of PLLA block was changed from 2k to 6k. The morphology of the copolymer films was characterized by AFM, and obvious phase separation phenomenon was observed in PCL6k-PLLA6k films. The POM observation exhibited that the growth of PCL spherulites in PCL6k-PLLA2k copolymer film was much faster, and PCL spherulites were smaller than those in PCL6k-PLLA4k and PCL6k-PLLA6k copolymer films. The growth rate of PLLA spherulites in the copolymers increased with increasing molecular weight of PLLA blocks.

Figure 8 POM photographs of the growth of PLLA spherulites in PCL-PLLA diblock copolymers films at 140°C.

Figure 8

POM photographs of the growth of PLLA spherulites in PCL-PLLA diblock copolymers films at 140°C.


Corresponding author: Sai Li, School of Chemical Engineering, Sichuan University, Chengdu 610065, Sichuan, China, e-mail:

Acknowledgments

This research work was supported by the National Science Foundation for Excellent Young Scholars (No. 51222304), the National Science Foundation of China (No. 31170921), the Doctoral Fund of Ministry of Education of China (No. 20130181110038), and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1163).

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Received: 2014-8-11
Accepted: 2014-10-18
Published Online: 2014-12-2
Published in Print: 2015-1-1

©2015 by De Gruyter

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