Article pubs.acs.org/IECR
Synthesis and Thermomechanical and Rheological Properties of Biodegradable Long-Chain Branched Poly(butylene succinate-cobutylene terephthalate) Copolyesters Yongjian Sun,† Linbo Wu,†,* Zhiyang Bu,† Bo-Geng Li,† Naixiang Li,‡ and Junming Dai‡ †
State Key Laboratory of Chemical Engineering at ZJU, Department of Chemical & Biological Engineering, Zhejiang University, Hangzhou 310027, China ‡ Sinopec Yizheng Chemical Fiber Company Limited, Yizheng, 255000, China S Supporting Information *
ABSTRACT: Biodegradable long-chain branched (LCB) poly(butylene succinate-co-butylene terephthalate) (PBST) copolyesters were prepared via a two-step direct esterification and melt polycondensation process, using a small amount (0− 2 mol %) of diglycidyl 1,2,3,6-tetrahydrophthalate (DGT) as an in situ branching agent (BA). The chemical structures of LCB PBSTs were characterized and the thermal, mechanical, and rheological properties were investigated. With increasing DGT loading, PBSTs with higher branching degree, broader molecular weight distribution, and lower melt flow index were synthesized in shorter polycondensation time. The branching of PBSTs results in a slight decrease in crystallizability, melting, and Vicat softening temperatures, but leads to an obvious decrease in elongation at break. On the other hand, the existence of LCB greatly improved the rheological properties of PBSTs. PBST with higher branching degree possesses higher storage and loss modulus, higher zero-shear viscosity, longer relaxation time, more obvious shear-thinning, and lower loss angle tangent. The Han plot of the rheological data also indicates higher elasticity of LCB PBSTs. polycondensation reaction.13,16 With this method, many LCB polyesters, nonbiodegradable as well as biodegradable, such as LCB PET,17−20 LCB PBT,21 LCB PBS,22−24 LCB PBA,25 and LCB PLA16,26−28 have been synthesized. LCB copolyester like LCB PBAT synthesized by this method has also been reported in many patents.29−33 However, there was little report on the effects of branching on properties of LCB copolyesters. In this work, LCB PBSTs were synthesized by direct esterification and melt polycondensation using diglycidyl 1,2,3,6-tetrahydrophthalate (DGT) as a BA. DGT is a difunctional compound, but it can serve as a potential tetrafunctional BA after reaction with diacids and then with diols. The chemical structures of LCB PBSTs were characterized by triple-detector GPC and 1H NMR. The thermal, tensile, and rheological properties were assessed. The synthesis, chemical structures, and branching/properties relationships of LCB PBSTs are analyzed and discussed.
1. INTRODUCTION Aliphatic-aromatic copolyester poly(butylene succinate-cobutylene terephthalate) (PBST) is biodegradable in a certain composition range. The synthesis, thermal property,1−7 mechanical properties,2 rheological property,1 and biodegradability1,2,8−10 of linear PBST have been extensively studied and reported. In general, PBST has thermo-mechanical properties comparable to poly(butylene adipate-co-butylene terephthalate) (PBAT) which has been commercialized by the BASF Co. with a trademark “Ecoflex”, and therefore may find applications in disposable plastic products like package materials, trash bags, and agricultural mulch film as PBAT does.1,2 Although biodegradable linear copolyesters usually have better film blowing processability than other biodegradable polymers like poly(L-lactic acid), their film blowing processability and cost are much less competitive than polyolefin, especially for agricultural mulch film application. To lower the cost, it is necessary to reduce film thickness and enhance film strength; meanwhile, to produce ultrathin film in a stable way, the melt strength must be greatly enhanced. The most effective and convenient way to improve melt strength is to introduce long chain branching (LCB) into the polymer backbone. The appearance of LCB polymers greatly expands the scope of application of the polymer materials.11−13 Thus, many efforts have been made to modify the linear polymers to branched ones and investigate the effect of LCB on structure and properties of LCB polymers.12−15 The most common method to synthesize LCB (co)polyesters is to introduce multifunctional (≥3) comonomers as branching agents (BAs), such as multifunctional alcohols, acids, isocyanates, phenyl phosphites. and epoxides, in © XXXX American Chemical Society
2. EXPERIMENTAL SECTION 2.1. Materials. Succinic acid (SA, 99.5%, Tianjin Letai Chemical Co.), 1,4-butanediol (BDO, 98%, Shanghai Wulian Chemical Co.), terephthalic acid (TPA, 98%, Zhejiang Hengyi Co.), diglycidyl 1,2,3,6-tetrahydrophthalate (DGT, Ginray), tetrabutyl titanate (TBT, Shanghai Meixing Co.), and lanthanum(III) acetylacetonate hydrate (La(acac) 3·H2O, Shanghai Dibai Chemical Co.) were all used as received. Received: April 10, 2014 Revised: May 28, 2014 Accepted: May 30, 2014
A
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Scheme 1. Schematic Diagram of Synthesis of LCB PBST
2.2. Synthesis. A two-step procedure, namely direct esterification followed by melt polycondensation, was employed to synthesize PBSTs, using a 500 mL glass reactor equipped with an impeller and a condenser. TPA (0.43 mol), SA (0.57 mol), BDO (1.5 mol), DGT (0−2 mol % based on diacids) and TBT (1 mmol) were added into the reactor and then heated to 210 °C under nitrogen atmosphere with slow stirring. After the reactants were mixed well, the stirring rate was raised to 400 rpm. The esterification reaction was carried out at 210 °C until clear point. Then, La(acac)3 (1.0 mmol) was added into the esterification product. The temperature was raised to 250 °C and the absolute pressure was gradually reduced to about 200 Pa to start the polycondensation reaction. The reaction was stopped when an obvious Weissenberg effect was observed at a stirring rate of 20 rpm. The copolyesters thus synthesized are named as PBST43-x, where x is the molar percentage of DGT based diacids, that is, x% = ϕDGT = DGT/(SA+TPA)×100. 2.3. Characterization. The weight-average molecular weight (Mw), polydispersity index (PDI) and intrinsic viscosity ([η]) of PBSTs were obtained from a triple-detector gel permeation chromatography (GPC, PL Co., USA) equipped with a two-angle (45/90) laser light scattering (LS45/90), a differential refractive index (DRI) and a viscosity (CV) detectors. Tetrahydrofuran was used as eluent at a flow rate of 1.0 mL/min. The intrinsic viscosity of branched PBST ([η)B) is measured directly using the viscosity detector and that of linear PBST of the same molecular weight ([η)L) is calculated using the Mark−Houwink relationship (([η)L) = 0.00557M0.432). The “branching index” of LCB PBST defined as g′ = [η]B/[η]L was therefore easily determined from the GPC measurement.34 1H NMR spectra were recorded with a Bruker Advance2B 400 FT-NMR spectrometer (400 M). Deuterated
chloroform was used as solvent and tetramethyl silane as internal standard. The thermal transitions of PBSTs were recorded with differential scanning calorimetry (DSC, Q200, TA Instrument) under nitrogen atmosphere. A standard heating−cooling− heating scanning mode was used. Both heating and cooling rates were 10 °C/min. The thermogravimetric analysis (TGA) of PBSTs was performed on a Pyris-1 thermogravimertic analyzer (PerkinElmer instruments, USA) by heating the sample from 50 to 800 °C at 10 °C/min under N2 atmosphere. The melt flow index (MFI) of PBSTs was determined using a melt flow indexer (CEΛST, Italy). The testing temperature was 190 °C and the load was 2.16 kg. The clipping time was 30 s. The specimens used for heat-resistance, mechanical and rheological testing were prepared using a HAAKE MiniJet II molding machine and then conditioned at 25 °C and 50% relative humidity for over 48 h prior to test. To avoid shrinkage, the specimens were maintained in the mold for at least 30 s after injection. The Vicat softening point (VSP) was measured with a Vicat softening point tester (CEΛST, Italy). Rectangular specimens (80 × 10 × 4 mm3) were heated at a rate of 50 °C/h with a load of 1 kg according to GB-T 1633-1979. Three specimens were tested for each sample. The tensile properties were measured with a Zwick Roell Z020 testing machine at a crosshead speed of 20 mm/min according to GB/T 1040-2006. At least five dumbbell-shaped specimens (80 × 10 × 4 mm3) were tested for each sample. The dynamic rheological measurement was performed at 150 °C on a rotational rheometer (RS6000, HAAKE, Germany) with parallel-plate geometry (diameter 25 mm). Small-amplitude oscillatory shear was performed in the frequency range of 0.01−100 rad/s. A strain of 1% was used, which was in the linear viscoelastic regime of PBSTs. B
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3. RESULTS AND DISCUSSION 3.1. Synthesis and Characterization. Long chain branched (LCB) polyesters or copolyesters are usually synthesized by polycondensation in the presence of a multifunctional comonomer as branching agent (BA).13 In this study, a difunctional monomer, namely, a diglycidyl ester DGT was used as an in situ BA to synthesize LCB PBSTs, as outlined in Scheme 1. At the esterification stage, the diacids (SA and TPA) not only reacted with BDO to form normal esterification products, but also reacted with DGT to form ester bonds and secondary hydroxyls. The secondary hydroxyls acted as in situ formed branching points. They further reacted with diacid to in situ form tri- or tetra-acid, and finally generated trior tetra-functional esterification products. Consequently, LCB PBST was produced via further melt copolycondensation. Linear and LCB PBSTs were synthesized by varying DGT loading (ϕDGT) from 0 to 2 mol % based on the diacids. The presence of DGT did not affect the esterification kinetics. However, with increasing ϕDGT, the viscosity of polycondensation product increased more rapidly and the polycondensation time, namely, the time reaching the Weissenberg effect, shortened. This phenomenon suggested that a branching reaction occurred. The products can be completely dissolved in chloroform, so no gel was formed. It is well-known that an infinite molecular weight polymer network or gel may be formed above a certain multifunctional BA concentration or at a high reaction degree in copolycondensation.14 As DGT can be regarded as a tetrafunctional monomer at most, the gel point can be calculated according to the well-known Carothers’ or Flory’s method. In the ϕDGT range of 0−2 mol %, the calculated gel point is larger than 0.979 (Carother’s, see Supporting Information) or 0.962 (Flory’s). And the actual gel point may be a little higher because branching might be insufficient because the formed secondary hydroxyls were less reactive than primary ones. So no gel was observed under the experimental conditions. The GPC curves of the products are illustrated in Figure 1, and the molecular weight distribution (MDW) parameters,
These results indicate that branching occurred, and the branching degree increased with ϕDGT. At the same time, it should be noted that the branching index of PBST43−0.1 is equal to that of PBST43, indicating GPC characterization is not sensitive enough to low-level branching. The 1H NMR spectra of various PBSTs are shown in Figure 2. The spectra of LCB PBSTs are the same as that of linear PBST except that some weak chemical shifts for DGT moiety (see Scheme 1) appear at 5.69 ppm (h), 5.67 ppm (i), and 3.06 ppm (j). The calculated contents of DGT moiety in PBSTs are basically comparable to ϕDGT, indicating that the branching degree increases with ϕDGT. The intensity of signal i is a little weaker than h, implying that the branching reaction is incomplete possibly because the formed secondary hydroxyls are less active as mentioned above. The intensity of chemical shift (k, 3.7 ppm) of −CH2 adjacent to terminal hydroxyl also increases with ϕDGT because of branching and decrease in Mn. From the 1H NMR spectra, the copolymer composition (molar fraction of butylene terephthalate (BT) unit, ϕBT), the number-average sequence length of BS and BT units (Ln,BS and Ln,BT) and the degree of randomness (R) can be calculated according to literature.4 The copolymer composition is 45.1 mol % for linear PBST at a fixed TPA feed fraction of 43 mol %. The discrepancy between them is attributed to loss of SA and its esterification product by sublimation and reduced pressure distillation during polycondensation at high temperature (250 °C) and low pressure (∼200 Pa). The ϕBT value decreased with ϕDGT because the polycondensation time was shortened and therefore less loss of SA happened. The Ln,BS and Ln,BT are 2.20 ± 0.05 and 1.76 ± 0.03, respectively, and the R value is 1.01 ± 0.004, indicating the copolyesters are random copolymers and the sequence structure at a fixed feed ratio is independent of ϕDGT. 3.2. Thermal Transition and Heat Resistance. The DSC curves of linear and various LCB PBSTs are shown in Figure 3 and the thermal transition data are summarized in Table 2. Linear PBST43 crystallized readily from melt at a cooling rate of 10 °C/min and did not cold-crystallize in the second heating scan, indicating the melt crystallization was completed. After branching, the melt crystallization temperature (Tc) and enthalpy (ΔHc) both decreased with ϕDGT (0−0.5 mol %). The melt crystallization was not completed, so clear cold crystallization was observed in the second heating scan. At higher ϕDGT, however, the melt crystallizability recovered (both Tc and ΔHc increased) to a certain extent and the subsequent cold crystallization weakened (T cc increased and ΔH cc decreased), possibly due to extra influence of broadened MWD. In other words, the low molecular weight part in highly branched PBST had higher crystallizability and therefore contributed to the recovery of crystallizability. For the same reason, the glass transition temperature (Tg) increased at a ϕDGT range of 0−0.5 mol % and then decreased again at higher ϕDGT. Therefore, it can be concluded that the crystallizability of PBST is depressed by branching but can be recovered to a certain extent due to broadening of MWD accompanied by excessive branching. The melting temperature (Tm) decreased monotonously with ϕDGT, from 116 °C of linear PBST43 to 107 °C of PBST43−2 because of combined action of branching and MWD broadening. The melting enthalpy (ΔHm) also exhibited a decrease trend. Consequently, the heat resistance of PBST became somewhat deteriorated. The Vicat softening point (Tvsp) decreased from 85.6 °C of PBST43 to 71.8 °C of PBST43−2.
Figure 1. Molecular weight distribution curves of linear and LCB PBSTs.
branching index, and melt flow index are summarized in Table 1. The linear PBST has unimodal molecular weight distribution (MWD), relatively low polydispersity index (PDI, 2.45), unit branching index and high melt flow index (10.8 g/10 min). For LCB PBST, the MWD broadens, the “branching index” and melt flow index decreases monotonically with ϕDGT. And multipeak MWD curve appears at ϕDGT higher than 0.5 mol %. C
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Table 1. Synthesis Conditionsa and Results of Linear and Long Chain Branched PBSTs 1
sample
ϕDGT (mol %)
PBST43−0 PBST43−0.1 PBST43−0.3 PBST43−0.5 PBST43−1.5 PBST43−2.0
0 0.1 0.3 0.5 1.5 2.0
b
tmpc
(h)
H NMR
triple-detector GPC
ϕBT (mol %)
SA losse (%)
Mn (g/mol)
Mw (g/mol)
PDI
g′f
MFIg (g/10 min)
45.1 44.8 44.4 44.3 43.9 43.7
3.60 3.20 2.53 2.19 1.51 1.18
63 100 50 000 29 400 26 200 19 500 24 000
156 000 138 000 142 000 171 000 171 000 333 000
2.45 2.75 4.84 6.53 8.78 14.0
1.00 1.00 0.90 0.80 0.65 0.53
10.8 7.0 7.0 7.1 5.9 4.3
3.7 3.5 3.2 3.0 2.0 1.5
d
Reaction conditions. (1) Esterification: SA/TPA = 57/43 molar ratio in feed, TBT = 0.1 mol % based on diacids, diol/diacid = 1.5, 210 °C/3 h. (2) Polycondensation: La(acac)3, La/Ti = 1.5/1 molar ratio, 250 °C. bMolar percentage of branching agent DGT based on diacids. cMelt polycondensation time. dCopolymer composition, i.e., molar percentage of butylene terephthalate (BT) unit in PBST. eLoss percentage of SA during polycondensation calculated from the discrepancy of SA content in feed and in PBST. fBranching index (g′ = [η)B/[η)L) defined as the ratio of the intrinsic viscosity of branched PBST to that of linear PBST of the same molecular weight. gMelt flow index. a
3.3. Mechanical Properties. The effect of branching on tensile properties was then investigated. The stress-stain curves of linear and various LCB PBSTs are shown in Figure 4. The tensile properties, namely modulus (E), strength at break (σb), and elongation at break (εb) are summarized in Table 3. The tensile modulus and strength of LCB PBST are determined by many factors including molecular weight and its distribution, composition, branching, and crystallinity. So they do not show clear dependence on ϕDGT. However, the effect of branching on elongation at break seems to be more significant than other factors so that the elongation at break does exhibit clear ϕDGT dependence: it decreases monotonically with ϕDGT. In fact, yielding/necking phenomenon appeared for linear PBST43−0 during the tensile test. Such cold drawing phenomenon and high elongation at break over 400% indicates that it is a tough material. The cold drawing phenomenon gradually weakened with ϕDGT and gradually disappeared. The elongation at break decreased to be less than 100% for PBST43−2.0. In general, the elongation at break depends on the flexibility of macromolecular chains. The presence of long chain branches hindered inner rotation of chains, and consequently weakened chain flexibility. So, the elongation at break decreased with ϕDGT. As elongation at break can be regarded as an indicator of tensile toughness of material, its decrease indicates that the toughness was gradually weakened with ϕDGT. Considering high elongation is desirable for film blowing, the DGT loading of 0.3−0.5 mol % seems to be appropriate. 3.4. Dynamic Viscoelastic Properties. Linear viscoelastic properties of polymers are very sensitive to their topological structure.14 So, the dynamic rheological behaviors of linear and various LCB PBSTs were further investigated at 150 °C. The
Figure 2. 1H NMR spectra of linear and LCB PBSTs.
However, on the other hand, the existence of branching does not clearly affect the thermal stability of PBST. The TGA curves of linear and various LCB PBSTs are almost overlapped (see Figure S1 in Supporting Information). The decomposition temperature at 5% weight loss (Td,5, 384.0 ± 1.4 °C) and at maximum rate (Td,max, 409.0 ± 1.9 °C) are nearly independent of ϕDGT. Therefore, the LCB PBSTs have excellent thermal stability.
Figure 3. DSC curves of linear and LCB PBSTs. D
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Table 2. Thermal Transition Properties and Vicat Softening Point (TVSP) of Linear and LCB PBSTs cooling at 10 °C/min
2nd heating at 10 °C/min
sample
Tc (°C)
ΔHc (J/g)
Tg (°C)
Tcc (°C)
ΔHcc (J/g)
Tm (°C)
ΔHm (J/g)
TVSP (°C)
PBST43−0 PBST43−0.1 PBST43−0.3 PBST43−0.5 PBST43−1.5 PBST43−2.0
57.9 38.9 29.7 20.9 31.1 42.0
17.0 15.8 9.3 0.7 5.4 12.4
−16.4 −16.5 −15.7 −15.2 −15.8 −18.8
nd 23.3 22.8 22.8 25.1 26.1
nd 0.5 5.8 9.9 9.3 1.5
116.1 113.2 113.4 111.2 108.9 107.1
15.1 14.8 14.4 14.9 13.4 12.0
85.6 83.5 79.5 76.2 72.1 71.8
Figure 4. (A) Typical stress-stain curves of linear and LCB PBSTs and (B) dependence of elongation at break on the loading of branching agent DGT (ϕDGT).
Table 3. Tensile Properties and Rheological Parameters of Linear and LCB PBSTs sample PBST43−0 PBST43−0.1 PBST43−0.3 PBST43−0.5 PBST43−1.5 PBST43−2.0
Ea (MPa) 61.4 45.5 57.6 72.4 77.2 70.9
± ± ± ± ± ±
5.4 2.7 6.6 4.8 14.6 5.0
σbb (MPa) 22.0 23.7 21.4 19.8 18.4 18.8
± ± ± ± ± ±
1.4 1.8 0.6 0.4 0.3 0.8
εbc (%)
η0d (Pa.s)
λe (s)
nf
slope of G′g
slope of G″h
± ± ± ± ± ±
5010 5620 9440 8560 10 900 16 000
0.18 0.33 1.15 1.38 5.20 9.86
0.66 0.64 0.53 0.62 0.61 0.61
1.92 1.81 1.69 1.57 1.26 0.98
1.05 1.03 0.98 0.97 0.79 0.73
408.3 358.5 270.7 274.3 116.4 78.9
22.4 12.9 16.6 15.2 11.2 15.1
a
Tensile modulus. bStrength at break. cElongation at break. dZero-shear viscosity. eRelaxation time. fShear-thinning index. gStorage modulus. hLoss modulus.
are very typical for LCB polymers like LCB polypropylene.36 The viscosity-frequency data fit well with Cross equation (eq 1).38 From such a fitting, the relaxation time (λ) and the shearthinning index (n) were obtained, as listed in Table 3. It can be seen that the relaxation time increases gradually with ϕDGT. So, the melt elasticity of PBST increases with ϕDGT.
frequency-dependences of storage modulus (G′), loss modulus (G″), tangent of loss angle (tan δ), and complex viscosity (η*) are illustrated in Figure 5. In general, the high frequency regions primarily reflect the local motion of segments, while the low frequency or terminal region reflect the large-scale rearrangement of chain conformations, such as the movement of main chain and LCB.35 So, the viscoelastic properties at terminal zone are analyzed and discussed with emphasis. In general, linear polymers exhibit a Newtonian zone of complex viscosity and G′ ∝ ω2 and G″ ∝ ω frequency dependences in terminal zone, and tan δ decreases with angular frequency. In this study, PBST43 showed typical rheological properties of linear polymers. The terminal slope of G′ and G″ of PBST43 is 1.92 and 0.95, respectively. The tan δ decreases clearly with angular frequency, and shear thinning phenomenon appears at high frequency zone. After branching, both G′ and G″ increase with ϕDGT in the terminal zone, and the terminal slopes of both G′ and G″ decrease, see Table 3 and inserted plots in Figure 5 panels A and B. The tan δ in the terminal zone decreases with ϕDGT, and a tan δ plateau appears in the whole frequency range of 10−2− 102 rad/s at ϕDGT over 1.5%. With increasing ϕDGT, the LCB PBSTs exhibit a narrower Newtonian-zone, more pronounced shear thinning and higher zero-shear viscosity (η0). At ϕDGT over 1.5%, the Newtonian-zone was not clearly observed in the experimental frequency range. These rheological observations
η*(ω) =
η0 1 + (λω)n
(1)
Although the branching index of PBST43−0.1 given by triple-detector GPC is the same of linear PBST (Table 1), the dynamic rheological properties PBST43−0.1 is much different from linear PBST. Clearly, dynamical rheology can sufficiently identify low-level LCB PBST (i.e., PBST43−0.1) from the linear one because it is more sensitive to low-level branching39 than GPC is. However, the rheological quantities like G′, G″, tan δ, and η* are influenced not only by branching but also by molecular weight and its distribution. It is reported that the socalled Han plot, that is, G′-G″ plot, is independent of temperature and average molecular weight but strongly depends on polydispersity and LCB.37 So, the Han plot seems to be a more useful tool to analyze the effects of the unique structural feature of LCB polymers, that is, branching and broad MWD. From Figure 6, it can be seen that the storage modulus regularly increases with ϕDGT at the same loss modulus in the low frequency region. Clearly, PBST with a E
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Figure 5. (A) Storage modulus (G′), (B) loss modulus (G″), (C) tangent loss angle (tan δ), and (D) complex viscosity (η*) of linear and LCB PBSTs at 150 °C.
loading of DGT (0.3−0.5 mol %) is enough for significant enhancement in melt elasticity.
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ASSOCIATED CONTENT
S Supporting Information *
Details of calculation of the gel point by Carother’s and Flory’s methods and TGA curves of linear and LCB PBSTs. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Tel +86 571 87952631. Fax +86 571 87951612. E-mail:
[email protected].
Figure 6. Han plot (G′ vs G″) of linear and LCB PBSTs (150 °C).
Notes
higher long chain branching density exhibits more notable “solid” character and higher elasticity. Furthermore, a small loading of DGT (0.3−0.5 mol %) is enough for significant enhancement in melt elasticity.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Key Technology R&D Program of China (2012BAD11B03), Sinopec YCF, and PCSIRT.
4. CONCLUSIONS Long-chain branching PBSTs were successfully synthesized via a direct esterification and polycondensation process using DGT as an in situ branched agent. The polycondensation time shortens and the branching degree increases with increasing DGT loading. The molecular weight distribution broadens and the melt flow index decreases with branching degree. Branching leads to slight to moderate reduction in crystallizability, melt temperature, and Vicat softening temperatures, and pronounced decrease in elongation at break. On the other hand, the existence of LCB results in improved rheological properties: higher storage and loss modulus, higher zero-shear viscosity, longer relaxation time, more obvious shear-thinning phenomenon, and lower loss angle tangent. Furthermore, a small
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REFERENCES
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dx.doi.org/10.1021/ie501504b | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX