Influence of Flexible Poly(Trimethylene Sebacate) Segments on the

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Influence of Flexible Poly(Trimethylene Sebacate) Segments on the Lamellar Twisting Behavior of Poly(Trimethylene Terephthalate) Ring-Banded Spherulites Jun Li,† Zhen Hu,† Zongbao Wang,‡ Qun Gu,‡,* Yuzhong Wang,§ and Yudong Huang*,† †

School of Chemical Engineering and Technology, State Key Laboratory of Urban Water Resource and Environment, Harbin Institute of Technology, Harbin 150001, China ‡ Ningbo Key Laboratory of Polymer Materials, Ningbo Institute of Material Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China § Center for Degradable and Flame-Retardant Polymeric Materials (ERCEPM), College of Chemistry, Sichuan University, Chengdu 610064, China ABSTRACT: Ring-banded spherulite is an important morphology of polymer crystals, and its formation mechanism is still under debate. In this study, we synthesized poly(trimethylene terephthalate)-co-poly(trimethylene sebacate) copolyesters (PTTco-PTS) by melting copolycondensation and studied the influence of PTS segments on the crystallization and ring-banded morphology of poly(trimethylene terephthalate) spherulites by using a moderate etching technology. It is found that he band spacing of PTT-co-PTS spherulites decreased sharply with PTS segments content. It is confirmed by experiments that there are twofold reasons for the sharp decrease of band spacing in PTT-co-PTS ring-banded spherulites. First, PTS segments acted as diluents for PTT molecules, which intensified the unbalanced surface stress at the fold surfaces for the PTT lamellar twisting. Second, incorporation of PTS segments decreased the thickness of PTT lamellae, and the greater the PTS content, the thinner the lamellae. Both these two changes significantly enhance the helical twisting power of twist PTT lamellae.

1. INTRODUCTION Ring-banded spherulites, an interesting and representative morphological feature of polymer crystalline aggregates, have been attracting considerable attention for fifty years. To reveal the banding mechanism, many investigations on the characterization of lamellar morphology in ring-banded spherulites have been carried out, using scanning electron microscopy (SEM), transmission electron microscopy (TEM), microfocus wideangle X-ray diffraction (WAXD), and atomic force microscopy (AFM).1−5 Different lamellar morphologies have been reported, such as twisted lamellar stacks, consecutive isochiral spiral terraces, individual C- and S-profiled lamellae, and suddenly changed lamellar orientation.6 However, how these twisting crystals develop during growth and organize in a spherulite to form regular bands is still somewhat unclear. Up to now, there have developed several band formation mechanisms. The most popular and accepted explanation for the formation of ring-banded spherulites is coherent periodic twisting of ribbon-like crystalline lamellae along the radial growth direction of the spherulites.7−10 Lotz and Cheng extensively studied the origin of lamellar twisting in a comprehensive review, and they believed that unbalanced surface stresses from structural features was the origin for the twisting of lamellae.6 The rhythmic crystal growth of ringbanded spherulites has been observed experimentally in many polymers,11−16 but such rhythmic crystal growth is generally encountered in thin films of semicrystalline polymers when the diffusion of molecular chains and the growth of spherulites are competitive because of the mass and spatial confinement.17 Gazzano et al.18 and Tanaka et al.19 confirmed the regular © 2013 American Chemical Society

lamellae twisting in poly(3-hydroxybutyrate) (PHB) ringbanded spherulites by microfocus X-ray diffraction. Xu et al.20 found the lamellae twisting during crystals growth of poly(3hydroxybutyrate-co-3-hydroxyhexanoate) (PHBHHx) ringbanded spherulites by real-time atomic force microscopy (AFM) observation in thin films. Ho et al.21 and Wang et al.22 confirmed the periodical continual twisting of lamellar crystals in poly(trimethylene teraphthalate) (PTT) ring-banded spherulites by electron diffraction (ED). Interestingly, polyesters often form ring-banded spherulites at particular crystallization temperatures, and so, they are usually used to study the band formation mechanism of polymer ring-banded spherulites. 23−26 Recently, poly(trimethylene terephthalate) (PTT) have attracted much attention because of its excellent mechanical properties and rich crystal morphologies. It is well-known that PTT shows various crystallization morphologies, such as regular spherulites, weakly banded spherulites,27 banded spherulites,22,28,29 even alternating-layered spherulites,30 which enable it to become a hot topic. Meanwhile, PTT copolymers have also attracted much attention because copolymer microdomains exert tremendous influence on the morphology, properties, and applications of PTT.31−34 However, little work has focused on the ring-banded crystallization morphology of PTT copolymers Received: Revised: Accepted: Published: 1892

September 6, 2012 December 3, 2012 January 11, 2013 January 11, 2013 dx.doi.org/10.1021/ie302406t | Ind. Eng. Chem. Res. 2013, 52, 1892−1900

Industrial & Engineering Chemistry Research

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film of 1 ± 0.2 mm by melting the sample between two pieces of polyimide films under 4 MPa. Then the film was placed on a HCS601 microscope hot/cold stage equipped with an Instec STC200 temperature controller and melted at 40 °C above the melting point for 4 min to eliminate the thermal history. Third, the melt sample was quenched to the crystallization temperature at a rate of −250 °C/min and isothermally crystallized under nitrogen atmosphere for 12 h. Crystal films were treated by a solvent vapor etching using 40% (w/w) methylamine aqueous solution in sealed container at 25 °C before observation of the lamellar twisting in ringbanded spherulites. 2.2. Characterization. Intrinsic viscosities of PTT-co-PTS copolyesters in mixture solvents (c = 5 g/dL) of phenol and 1,1,2,2-tetrachloroethane (3/2 w/w) were examined using a AV370 Ubbelohde viscometer at 25 °C. The chemical structures of PTT-co-PTS copolyesters were characterized using a Bruker AVIII 400 MHz nuclear magnetic resonance (NMR) spectrometer. Trifluoroacetic acid-d was used as the solvent, and all experiments were carried out at 25 °C. METTLER TELEDO-DSC I differential scanning calorimetry (DSC) was employed to detect the heat flow from the samples during isothermal crystallization, nonisothermal crystallization, and melting processes. All the experiments were conducted under a nitrogen atmosphere. Melting temperatures (Tm) were taken at the minima of melting endotherms and glass transition temperatures (Tg) at the inflection point. To study the thermal behaviors, 7 ± 0.2 mg of each sample was held at a temperature 40 °C above the melting point for 4 min to eliminate the thermal history, and then quenched to room temperature at a rate of −10 °C/min, and then heated to the temperature 40 °C above the melting point at a rate of 10 °C/min. The heat flow curves as a function of temperature were recorded to study the melting behaviors. WAXD at room temperature were acquired by using a Bruker D8 diffractometer, using Ni-filtered Cu Ka radiation at 40 kV and 30 mA. WAXD patterns were recorded in the 2θ range of 5−50° at a scanning rate of 2° min−1. The degree of crystallinity was calculated from the relative areas of the resolved peaks. The lamellar thickness of polymer crystal was investigated by SAXS analysis with a Rigaku RU-200 (Rigaku Corp., Tokyo, Japan), working at 40 kV and 200 mA, with Nifiltered Cu KR radiation (λ = 0.154 18 nm). SAXS profiles were recorded in the 2θ range 0.1−2.5°. Each step increased 2θ by 0.04°, and X-rays were collected for 4 s at each step. Films for investigation of spherulite morphologies were observed using an Olympus BX51 polarized light microscopy (PLM) equipped with a CCD camera and a Hitachi TM1000 scanning electron microscopy (SEM) at an accelerating voltage of 15 kV.

while copolymers possess rich morphological textures that are different from PTT homopolymer. To understand how the chain aggregation influence the lamellar twisting structure of polymer ring-banded spherulites, flexible segments, trimethylene sebacate, were incorporated into PTT molecules and the influences of them on the crystallization behavior and lamellar twisting power of PTT ring-banded spherulites was investigated. First, the lamellar morphologies of the PTT ring-banded spherulites were studied by using etching technology. Then, the influences of trimethylene sebacate segments on PTT crystal structures were investigated by SAXS and discussed in detail. Finally, a lamellar twisting structure model is proposed for understanding of the impact of comonomer segments on the lamellar twisting frequency of homopolymer spherulites.

2. EXPERIMENTAL SECTION 2.1. Materials and Methods. Materials. Purified terephthalatic acid (PTA) was obtained from Yangzi Petrochemical Company Ltd. 1,3-Propanediol (PDO) was purchased from Cell Ltd. All the other reagents were purchased from Sinopharm Chemical Reagent Co., Ltd. Synthesis of PTT-co-PTS Copolyesters. First, poly(trimethylene sebacate) (PTS) oligomer was prepared by esterification of sebacic acid (SA) and PDO at 190−195 °C under 0.2 MPa with stannous chloride as the catalyst, and PTT oligomer was synthesized through esterification of PTA and PDO at 250 °C under 0.3−0.4 MPa with zinc acetate as the catalyst. Then, blends of PTT oligomer, PTS oligomer, and composite catalysts composed of titanium dioxide, antimonic oxide, polyphospholic acid, and tetrabutyl titanate were placed in a 1 L rotating steel reactor. The reaction blends were kept at 235−240 °C and under a vacuum of 10 Pa for 3−5 h. Highmolecular-weight PTT-co-PTS copolyesters were obtained. The reaction route for the synthesis of the PTT-co-PTS copolyester was shown as Scheme 1. Scheme 1. Reaction Routine of PTT-co-PTS Copolyester

Post-treating of the Obtained Copolyesters. First, PTT-coPTS copolyester were dissolved in the mixture of chloroform/ trifluoroacetic acid (1/3 v/v) and then filtered to eliminate impurity. Second, the obtained filtered liquor was precipitated by petroleum ether and filtered in order to remove PTS oligomer and PTS homopolymer. This process was repeated for three times and then the last filtered cake was collected and dried at 40 °C under vacuum for 96 h. Specimen for morphologies observation were prepared by casting 15 μL chloroform/trifluoroacetic acid (3/1 v/v) solution (10 mg mL−1) onto a clean glass slide, which has been preheated to 60 °C, and then films were dried at 40 °C under vacuum for 48 h. Specimen for WAXD and SAXS were made through three steps. First, the sample was made into a

3. RESULTS AND DISCUSSION 3.1. Composition and Microstructure. Chemical structures of PTT-co-PTS copolyesters were characterized with NMR spectrometer. As expected, the reactive blends of PTT and PTS oligomers generated new TXS sequences, in addition to TXT and SXS sequences (where X represents trimethylene unit from 1,3-propanediol, T denotes terephthalate unit, and S represents sebacoyl unit) that are present in the initial PTT and PTS homopolymers, respectively. The 1H NMR spectrum of PTT-co-PTS3 and the assignment of each chemical shift are shown as Figure 1.35−37 The actual terephthalate (T)/sebacic 1893

dx.doi.org/10.1021/ie302406t | Ind. Eng. Chem. Res. 2013, 52, 1892−1900


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Figure 2. Comparison of the cooling DSC curves of PTT and PTT-coPTS copolyesters at a heating rate of 10 °C/min.

both the melting temperature (Tm) and heat of fusion (ΔHm) decrease with the sebacoyl unit contents (Figure 3).

Figure 1. 1H NMR spectrum of PTT-co-PTS3 copolyester (a) and the peak assignments (b).

(S) molar ratio of PTT-co-PTS copolyester was determined from the relative intensity of aromatic protons and sebacoyl methylene proton. The average number sequence lengths of TXT segments (LPTT) and SXS segments (LPTS) were calculated from the relative intensity of proton resonances,38 shown in Table 1. It can be seen that LPTS increases with the Figure 3. Comparison of the second heating DSC curves of PTT and PTT-co-PTS copolyesters at a heating rate of 10 °C/min.

Table 1. Composition, Molecular Weight, and Thermal Properties of PTT and PTT-co-PTS Copolyesters sample PTT1 PTT-coPTS1 PTT-coPTS2 PTT-coPTS3

CPTS (mol %)

LPTT

LPTS

R

Tg

Tm

[η]

0 11.5

11.2

0 1.5

0.76

58.5 56.3

228.5 215.6

0.90 0.91

18.1

8.5

1.8

0.67

54.1

189.3

1.11

31.7

5.8

3.1

0.49

51.1

157.4

1.08

To investigate whether PTS segments in the PTT-co-PTS copolyesters crystallize at the setting crystallization temperature windows, PTT-co-PTS samples crystallized at different temperatures were studied by WAXD. From the samples isothermally crystallized at 120 °C and then quenched to 25 °C, it can be seen that all PTT-co-PTS samples show the same crystalline diffraction peaks as PTT homopolymer (Figure 4a). The characteristic peaks are at the scattering angle 2θ of 15.3°, 16.7°, 19.4°, 21.7°, 23.7°, and 24.5°, which correspond to the diffraction planes of (010), (01̅2), (012), (100), (102, 1̅03), and (11̅3) of PTT homopolymer crystals, respectively.41 PTTco-PTS3 copolyester crystallized at different temperatures show the same locations of diffraction peaks, which mean crystal structure of PTT-co- PTS3 does not change with crystallization temperature. The results mentioned above indicate that crystallized PTT-co- PTS has the same crystalline structures as PTT and trimethylene sebacoyl segments are in amorphous state. The primary reason for the absence of PTS crystals in PTT-co-PTS copolyesters is that the number-average sequence length of trimethylene sebacoyl segments are too short and it is difficult for them to form crystals.42,43So it can be concluded that crystallization of PTT decrease with incorporation of sebacoyl units. One reason for this is that the sequence lengths of PTT segments are shortened when the sebacoyl units are incorporated into PTT molecular chains, which slows down the lamellar thickness and lateral size of PTT crystals, and so lowers the melting point and crystallization degree. Furthermore, the

sebacoyl unit content while LPTT decreases with it. The degrees of randomness (R) of the PTT-co-PTS copolyesters are calculated by the equation: R = 1/LPTT + 1/LPTS. It is shown that R is less than 1 for all the copolymers. Therefore, it can be concluded that they are block copolymers.31 3.2. Crystallization. Thermal behaviors of PTT and PTTco-PTS copolyesters were examined by DSC. Each PTT-co-PTS copolyester shows only one glass transition temperature (Tg) and Tg decreases with sebacoyl unit content, which means increasing molecular mobility with the PTS segments. It could be caused by the plasticization effect generated by flexible PTS segments and the decrease of rigid aromatic segments.39,40 During the cooling from melt, the crystallization temperatures of PTT-co-PTS1, PTT-co-PTS2, and PTT-co-PTS3 shift to lower temperature than that of PTT homopolymer and decreased with sebacoyl units (Figure 2). During the second heating from room temperature, it can be seen that only one melting peak probably due to of PTT crystals are observed and 1894



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Figure 4. WAXD patterns of the PTT and PTT-co-PTS copolyesters crystallized at 120 °C (a) and that of the PTT-co-PTS3 copolyester crystallized at different temperatures (b).

chain regularity of PTT segments is damaged with the incorporation of sebacoyl units, which also lowers the crystallinity of PTT.44,45 The relationship among spherulites growth rate, crystallization temperature, and PTS content of PTT-co-PTS copolyesters were investigated by using PLM (Figure 5). It

Figure 5. Temperature dependence of spherulites growth rate of PTTco-PTS copolyesters with different compositions. PTT and PTT-coPTS copolyesters use the right and left longitudinal coordinate, respectively.

Figure 6. Polarized optical micrographs of PTT (a), PTT-co-PTS1 (b), PTT-co-PTS2 (c), and PTT-co-PTS3 (d) ring-banded spherulites that formed at different ΔT: 20 °C (a1, b1, c1, and d1); 30 °C (a2, b2, c2, and d2); 40 °C (a3, b3, c3, and d3).

can be seen that spherulites growth rate of each sample increases with temperature at the earlier stage, and then decreases with it, which comply well with the nuclear control and growth control laws, respectively.46 Moreover, spherulites growth rate of PTT-co-PTS copolyesters decrease with PTS content, which should be attributed to the decreased molecular regularity and chain sequence of crystalline PTT segments.43 3.3. Spherulitic Structures. The spherulitic morphologies of PTT and PTT-co-PTS copolyesters isothermally crystallized at different temperatures were observed by PLM. For PTT and PTT-co-PTS spherulites obtained at special crystallization temperature, the crystalline lamellae aggregates exhibit ringbanded patterns (Figure 6). Both Malltese cross and extinction rings are clearly observed under crossed-polarized light, which is similar to the classical ring-banded spherulites in other different polymeric materials. The appearance of ring-banded spherulite is strongly dependent upon crystallization temperature, and the band spacing increases with crystallization temperature, which is same as the results reported by Ho et al.21 and Wang et al.22 Meanwhile, the size of spherulites

increased with crystallization temperature owing to reduced nucleation density. Importantly, PTT-co-PTS copolyester ringbanded spherulites showed smaller band spacings than that of PTT homopolymer crystallized at the same degree of supercooling (ΔT = Tm − Tc), and band spacing decreased with the content of PTS segments (Figure 7). To identify the orientation of lamellar crystals in the ringbanded spherulites, PTT and PTT-co-PTS films were etched by methylamine vapor and the inner structure structures of spherulites were studied in detail. Figure 8 shows the polarized optical micrographs of PTT ring-banded spherulites etched for 0, 1, and 60 h. It can be seen that the etching starts from the central of the spherulites. The reason for this phenomenon is that the spherulitic eyes at the central part of spherulites are thinner and more easily eroded by methylamine than lamellar crystals in other regions. Similar phenomenon has been found in our previous study on the etching of polyhydroxybutyrate valerate ring-banded spherulites.47 After long time etching, 1895



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with further growth (the bright arrow in Figure 9b). This structure is consistent with the results obtained by Ho et al.21 and Wang et al.22 using transmission electron microscopy (TEM) and ED. In etched PTT-co-PTS ring-banded spherulites, obvious periodical cooperative twisting of lamellar crystals can also be seen, as shown in Figure 9c. The alternating flat-on-to-edge-on morphologies are consistent with the alternating dark-to-bright bands in polarized optical micrographs. Meanwhile, PTT and PTT-co-PTS ring-banded spherulites showed the same twist orientations of lamellar crystals. As suggested by Keith and Padden,7 nonadjacent reentry of chains and loose folds generally introduce overcrowding and inefficient packing in lamellar crystals. The different conditions at the opposite fold surfaces may lead to the difference in the magnitude of compressive stresses, which can result in a bending moment responsible for twisting of lamellar crystals. In our previous work, it has been proved that band spacing of PTT banded spherulites decreased with molecular weight (namely sequence length). Thus, the decreased band spacing of PTT-co-PTS ring banded spherulites with PTS contents could not be caused by the decreased PTT sequence length with incorporation of PTS segments. According to the lamellae twisting theory suggested by Keith et al.,7,17 the formation of the ring-banded spherulites is attributed to the periodical lamellae twisting along the radical growths direction of the spherulites, we speculated that the incorporation of the PTS segments increased the twisting frequency of PTT lamellae and made the twisting of lamellae easier. Similar phenomenon has been reported in several polymer blends by Keith and co-workers,17 and it is found that 0.5 wt % of polyvinyl butyral (PVB) lowers the onset banding temperature of PCL by 15 °C. They believe it is due to the polar action of PVB on polycaprolactone (PCL), which increased the frequency of lamellar branching at screw dislocations and the intercrystalline connectivity of PCL. Another similar phenomenon that introduction of polystyrene (PS) block increased the helical twisting power and decreased the band spacing of poly(lactic acid) (PLA) ring-banded spherulites has been reported in block copolymer of PS-PLA by Ho and co-workers.48 Thus, we speculate that PTT shows greater helical twisting power after incorporation of PTS segments because of the increasing unbalanced surface stress at PTT crystalline lamellar fold surfaces. However, the reason for this phenomenon is still unclear and will be discussed in the following paragraphs. 3.4. Impact of Comonomer on Band Spacing. Typical morphologies of PTT and PTT-co-PTS ring-banded spherulites crystallized at different ΔT show that band spacing decreases with ΔT. Meanwhile, both band spacing and regularity of ring bands decreases with the content of sebacoyl units (Figure 6). It is well-known that band spacing of homopolymer ringbanded spherulites generally decreases with molecular weight, namely sequence length.9,49 However, this trend is opposite in PTT-co-PTS copolyesters, ring-banded spherulites of PTT-coPTS that with smaller PTT sequence length show apparently smaller band spacing than PTT ring-banded spherulites (Figure 7). Importantly, the greater the PTS contents, the smaller the band spacing. For example, the band spacing of PTT ringbanded spherulites crystallized at ΔT of 40 °C was 17.15 μm while that of PTT-co-PTS3 crystals crystallized at the same ΔT was only 1.22 μm. Similar phenomenon has been reported in block copolymer of PS-PLA, in which introduction of PS block increases the helical twisting power and decreases the band

Figure 7. Crystallization temperature dependence of band spacing.

Figure 8. Polarized optical micrographs of PTT ring-banded spherulites, formed at 185 °C, etched by methylamine vapor for different time: (a) 0, (b) 1, (c) 60 h; (d) the optical micrograph of part c.

many slits along the radius direction appear. It is understandable because the amorphous parts between edge-on lamellae are easier to be etched and washed out than the amorphous part between flat-on lamellae. Meanwhile, similar results were obtained in the etched PTT-co-PTS ring-banded spherulites. Etched PTT and PTT-co-PTS ring-banded spherulites showed distinct continual lamellae twisting structures (Figure 9). It can be seen that edge-on lamellae twist after growing to a certain length, protruding from the film surface (the black arrow in Figure 9b) and twisting to the flat-on lamellar crystals

Figure 9. PTT and PTT-co-PTS ring-banded spherulites showed distinctive lamellar twisting morphologies after etching with methylamine vapor. (a and b) SEM images of PTT ring-banded spherulites (crystallized at ΔT of 40 °C) etched for 360 h. (c) PTT-co-PTS1 ringbanded spherulites (crystallized at ΔT of 20 °C) etched for 360 h. 1896



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PTT homopolymer crystallized at a ΔT of 40 °C shows a lamellar crystals thickness of 4.1 nm, which is similar to the results reported by Hong et al.52 The Lc of PTT-co-PTS copolymers were calculated to be 2.2−2.7 nm (Table 2).

spacing of PLA ring-banded spherulites.48 Furthermore, flexibility of comonomer segments also influences the band spacing of PTT ring-banded spherulites. Compared with the results from the previous work,50 it can be seen that PTT-coPTS copolyesters showed greater twisting power than PTT-coPLA copolyesters that with the same comonomer contents. For example, PTT-co-PTS3 spherulites formed at ΔT of 40 °C showed a band spacing of 1.5 μm while that of PTT-co-PLA4 spherulites formed at the same ΔT was 2.2 μm. As mentioned above, the PTT-co-PTS copolyesters possess greater helical twisting power than PTT homopolymer, and the higher the content of PTS segments content, the greater the power. To understand the influence of amorphous PTS segments on PTT ring-banded spherulites, the thickness of lamellar crystals and amorphous layer in PTT and PTT-co-PTS ring-banded spherulites were measured by SAXS. PTT and PTT-co-PTS films with thickness of 175 ± 15 μm, crystallized at ΔT of 40 °C, were used for SAXS. Each sample showed similar ringbanded morphologies but a litter lower degree of crystallinity compared to its solution casting films on the glass slide, but the influence of the slight difference in degree of crystallinity on the calculation of lamellar thickness is in the acceptable range. The first-dimension correlation function method, γ(x), was used to analyze the SAXS results. The crystalline−amorphous structures of PTT and PTT-co-PTS copolyester were analyzed in terms of finite stack model, in which the stacks consist of crystalline lamellae separated by amorphous layers. γ(x) is defined as follows:51 γ (x ) =

1 Q

∫0

∞

I(q)q2 cos(qx) dq

Table 2. Degree of Crystallinity and Thickness of Different Phases in PTT and PTT-co-PTS Ring-Banded Spherulites number

Xv (%)

L (nm)

Lc (nm)

La (nm)

PTT1 PTT-co-PTS1 PTT-co-PTS2 PTT-co-PTS3

44.6 29.0 23.8 19.3

9.2 9.3 10.5 11.9

4.1 2.7 2.5 2.3

5.1 6.6 8.0 9.6

Importantly, Lc of PTT-co-PTS copolyester decreases with the increase of PTS segments, which complies well with the results that the melting temperature (Tm) of PTT-co-PTS decreases with the increase of PTS segments content (Table 1).41,42 The increase of L and La with PTS segments should be attributed to the decreasing PTT sequence length and chain regularity and correlative degree of crystallinity (Xv), which is similar to the influence of poly(ethylene oxide) segments on PTT.53 It is generally believed that the occurrence of ring-banded spherulites is attributed to the periodical cooperative lamellar twisting along the radial direction. Considering a polymer lamellae as a cantilever with thickness of b,9 the disparate compressive stresses on the folding surface, τ, cause a torque of T and a bending with a angular rotation θ per unit. It can be found that the angular rotation between two cross sections per unit distance, θ, can be calculated by eq 3.54

(1)

θ=

where I(q) is the scattered intensity, q = 4π/(λ sin(θ/2)) (θ is the scattering angle) is the scattering vector and the scattering invariant, Q is expressed as Q=

∫0

∞

I(q)q2 dq

T ⎡ 1 b Ghb3⎢ 3 − 0.21 h 1 − ⎣

(

4

b 12h4

⎤ ⎦⎥

)

=

T C1Ghb3 (3)

where G is the elastic modulus, h is the width, b is the thickness, and C1 can be calculated by h/b value (when h/b is more than 10, C1 is less than 0.333). Equation 3 indicates that θ, which is directly proportional to the twisting power, increases with T and decreases with h and b. The θ, in a thin plate with compressed surface layer, is generally proportional to its thickness, which has been observed in thin films of metals.55 According to the mechanism proposed by Keith and Padden, steric hindrance or chain tilt could result in the curvature of polymer crystals.7,9,56 PTT crystal is of two-chain triclinic structure,21 so an unbalanced surface stress, which leads to the crystalline lamellar curvature, is initiated by imbalance of fold geometry or conformation and improved by polymer chains overcrowding and inefficient packing at crystalline lamellar fold surfaces. Therefore, an unbalanced surface stress at the fold surfaces should also be expected in PTT-co-PTS copolyesters and the twisting sense can also be analyzed using eq 3. As mentioned above, only PTT chains crystallize to form crystalline lamellae in PTT-co-PTS ring-banded spherulites, the region between the lamellae is occupied by amorphous PTT and PTS segments. To easily understand the impact of PTS segments on the lamellar twisting frequency, a lamellar twisting structure model of PTT and PTT-co-PTS is proposed (Figure 11). As illustrated, the unbalanced surface stress is initiated by imbalance of fold geometry or conformation. In addition, the unbalanced surface stress is intensified by the effect of diluents due to the existence of dangling amorphous PTS segments. In particular, the PTS random chains, dangling from PTT crystalline lamellar surface via chemical junction, can be

(2)

The correlation function shows the electron density fluctuations at the correlation distance x and can be calculated from the Fourier transform of the observed scattered intensity on a relative scale. The correlation function was interpreted with a suitable morphological model. Herein, the crystalline thickness Lc was determined from self-correlation triangle, i.e. an intercept of the linear portion of g(x) and the tangent line of the first minimum peak, shown as the following Figure 10.

Figure 10. One-dimensional correlation function of PTT film that crystallized at a ΔT of 40 °C. 1897



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Figure 11. Schematic representation of lamellar twisting structures in PTT (a) and PTT-co-PTS (b) ring-banded spherulites. In PTT-co-PTS crystal, PTS segments crowd on the folding surface and increase the unbalanced stress on the opposite sides of the PTT lamellae. Meanwhile, incorporation of PTS units decreases the PTT lamellar thickness.

regarded as the origin for the amplification of the steric hindrance effect due to the formation of phase separation resulting from incompatibility. Thus, we speculate that the stress loaded on the PTT lamellae, τ, is promoted by the incorporation of PTS segments. In addition, incorporation of PTS segments increases the amorphous layer thickness and results in the increase of unbalanced surface stress, as well as decrease of lamellar thickness. As mentioned above (Table 2), the thickness of amorphous layer and crystalline lamellae in PTT-co-PTS3 were increased to 170% and decreased to 54% of that in PTT, respectively. Roughly estimated with eq 3, even if the stress was constant, the angular rotation per unit in the PTT-co-PTS3 lamellae will be increased to about 630% of that in PTT. Moreover, PTS segments show almost the same influence on the lamellar thickness of PTT spherulites as PLA segments, but PTT-co-PTS has much smaller band spacing than PTT-co-PLA. We presume that the difference of lamellar twisting power between PTT-co-PTS and PTT-co-PLA should be attributed to the flexibility difference of comonomer segments, which aggregated on the folding surface and regulated the unbalanced stress. As we known, PLA molecules are rigid because of the steric hindrance effect of methyl groups on the side of PLA molecular backbone. On the other hand, the PTS molecule has no side group and displays excellent flexibility. Therefore, PTTco-PTS molecules form compact molecular coils with small endto-end distances because of flexible PTS segments, and these

coils crowded each other on the lamellar folding surface, for which PTT-co-PTS showed great unbalanced stress. Different from PTT-co-PTS, PTT-co-PLA segments form looser coils on the folding surface because of rigid PLA segments and show smaller unbalanced stress. Consequently, the sharp decrease of the band spacing in PTT-co-PTS ring-banded spherulites can be regarded as the cooperative effect of increasing unbalanced surface stress and the decrease of lamellae thickness. The effect of steric hindrance that causes unbalanced surface stress was intensified by the incorporation of amorphous PTS segments and the decrease of lamellae thickness, which lead to significant lamellar twisting so as to result in the ring-banded spherulites with higher twisting power.

■

CONCLUSION A series of random PTT-co-PTS copolyesters were synthesized by melt condensation of PTT and PTS oligomer, and the expected chemical structures were confirmed by 1H NMR. Crystallization of PTT and PTT-co-PTS copolyesters were studied by using DSC, WXRD, and PLM. It is found that the crystallization rate, crystallinity and crystal regularity decreased with the incorporation of PTS segments, and PTS segments did not crystallize in PTT-co-PTS crystalline films at the setting temperature window. After being etched by mild methylamine steam, the periodical cooperative twisting of lamellar crystals in PTT and PTT-co-PTS ring-banded spherulites was clearly 1898



Article

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observed using SEM. Comparing with ring-banded spherulites in PTT homopolymer, PTT-co-PTS showed much smaller band spacing and the band spacing decreased with the increase of PTS segments content. Furthermore, we demonstrated that flexibility of comonomer segments also influenced the band spacing of PTT ring-banded spherulites, and the more flexible the comonomer segments, the greater the decrease of band spacing. The sharp decrease in the band spacing of PTT ring-banded spherulites with the incorporation of PTS segments was studied by SAXS and two reasons for it were elucidated. One is the intensified unbalanced surface stress at the fold surfaces by PTS segments due to the effect of diluents on the formation PTT lamellae. Another one is the decrease of crystalline lamellae thickness. Both these two changes significantly enhance the helical twisting power of lamellae. Then, the mechanism of band spacing changes was also analyzed by using a mathematical model, on the basis of the theory of unbalanced stress leading to lamellae twisting, proposed by Keith and Padden. Finally, we proposed an understanding structure model to explain the formation of PTT and PTT-co-PTS ring-banded spherulites, which may provide further understanding for the formation of other polymer ring-banded spherulites.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial supports from the Chang Jiang Scholars Program and the National Natural Science Foundation of China (No. 51073047 and No. 91016015).

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