Largely Improved Mechanical Properties of a Poly(styrene-b-isoprene

Sep 5, 2014 - State Key Laboratory of Polymer Materials Engineering, College of Polymer Science & Engineering, Sichuan University, Chengdu. 610065, Pe...
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Largely Improved Mechanical Properties of a Poly(styrene‑b‑isoprene‑b‑styrene) Thermoplastic Elastomer Prepared under Dynamic-Packing Injection Molding Yongsheng Zhao,† Bin Su,† Licai Zhong,‡ Feng Chen,*,† and Qiang Fu*,† †

State Key Laboratory of Polymer Materials Engineering, College of Polymer Science & Engineering, Sichuan University, Chengdu 610065, People’s Republic of China ‡ Department of Electrical and Mechanical Engineering, Lanzhou Resources & Environment Voc-Tech College, Lanzhou 730021, People’s Republic of China ABSTRACT: In this work, a poly(styrene-b-isoprene-b-styrene) thermoplastic elastomer was processed via a novel processing technique, dynamic-packing injection molding (DPIM). The shear cessation time is variable during DPIM, and a conventional injection-molded sample (C-sample) was prepared for comparison. For the dynamic-packing injection-molded sample (Dsample) with a short cessation time, a high Young’s modulus was obtained but with no significant enhancement of the break strength relative to the C-sample. However, a significant improvement of the break strength was achieved for the D-sample with longer cessation time. The mechanical performance of both the C-sample and D-samples was interpreted from the contribution of polyisoprene (PI, as the matrix) and polystyrene (PS, as a dispersed phase) segments. It is proposed that a short cessation time (strong shear) can induce the formation of a stretched PI network, while prolonged cessation time (more relaxation) could result in the segregation of PS and PI microdomains and the formation of a perfect parallel orientation of the PS cylinder in a hexagonal lattice.

1. INTRODUCTION Block copolymers usually self-organize into nanoscale microstructures depending on the interblock interaction parameter (χ), degree of polymerization (N), molecular architecture,1,2 and block composition and processing conditions.3−9 As a result of chain-packing frustration, the phase behaviors in these block copolymers at the nonequilibrium state are significantly influenced by the external factors such as the presence of solvents and the rate of solvent evaporation,10 thermal treatment,11 and shear stress field.12−14 The stable nanodomain structures of typical diblock or triblock copolymers are mainly spherical domains, cylinders,15,16 bicontinuous morphology,17 or lamella formed as a consequence of an increase in the level of the minor component or an increase of the segregation power between the blocks.18−22 There are a large number of methods available for inducing domain orientation including flow in a rheometer,23,24 strong pressure-driven flows,25,26 electrical fields,27,28 and magnetic fields.29 Generally speaking, well-developed structures can be achieved in a rheometer through control of the shear strains, shear rates, temperatures, and ease of shear stress.30 It is also reported that extrusion with a channel die can achieve parallel or perpendicular orientation of microdomains under different pressure-driven flows.31 Overall, the block copolymers can be prepared to form diverse dimensional anisotropy and varying degrees of orientation along different directions.32,33 These are indeed convenient and effective approaches to preparing welloriented block copolymer samples. However, the mechanical properties of these samples were rarely reported. As we know, injection molding is one of the most widely used industrial processing techniques for manufacturing polymeric products.34 The thermomechanical conditions imposed during injection © 2014 American Chemical Society

molding can affect the microstructures and molecular orientation.35 In our laboratory, a conventional injectionmolded machine was modified by equipping two mobile pistons onto the mold. Reciprocating shears can thus be introduced to orient block copolymers through the oscillatory motion of pistons during the packing stage. In our study, emphasis is placed on a newly developed instrument to prepare oriented samples for a subsequent mechanical deformation study. In general, the nanodomain structures as well as the order of domain orientation play a key role in the final physical properties of block copolymers.30,36−44 For example, the microstructure of triblock copolymers can be varied using a midblock selective solvent. It was found that hydrogenation of the midblock was responsible for shifts in the morphology stability limits and a higher dynamic elastic shear modulus.45 For styrenic block copolymers, it was shown that the elastic modulus increased with increasing domain continuity as well as trapped polyisoprene (PI) entanglements.46 Furthermore, it was found that the extent of the Mullins effect (during cyclic deformation) was increased with increasing d spacing induced by annealing.47 For triblock and pentablock copolymer blends, little pentablock copolymer favors bridging (possibly knotted looping) configurations, which play significant roles in reinforcing the brittle domains of the lamellar-forming block copolymers. So, the mechanical properties are strongly dependent on the processing histories. Received: Revised: Accepted: Published: 15287

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Figure 1. (a) Schematic drawing for shearing procedures during DPIM. (b) Sketch of the basic elements for DPIM.

Table 1. Processing Conditions for Conventional and Dynamic-Packing Injection-Molded Samples sample name

processing method

cessation time [s]

shear cycles

barrel temperature [°C]

mold temperature [°C]

injection pressure [kg/cm2]

SIS-S SIS-3D SIS-6D SIS-15D

CIM DPIM DPIM DPIM

none 3 6 15

none 10 10 10

200 200 200 200

30 30 30 30

900 900 900 900

injection pressure of 900 kg/cm2 via a SZ 180g injectionmolding machine. Dynamic packing was applied to introduce a shear force field.48,49 The shear rate is approximately 10 s−1. As is reported, stress relaxation for SIS follows a power-law slope of −1/2 at high temperatures. The modulus stays at a constant value (2 × 102kPa) for about 101 s and then gradually decays at T = 90.7 °C.50 In our study, three different shear cessation times were selected for the DPIM process including 3, 6, and 15 s. The number of shear−pause cycles was fixed at 10 cycles. Herein, the time for dynamic packing is nearly 5 min (which means enough time for cooling). The shear process will stop when the melt solidifies completely. For simplicity, the dynamic-packing injection-molded samples with different cessation times were assigned as SIS-3D, SIS-6D, and SIS-15D, respectively. Herein, the conventional injection-molded sample was called the Csample, while the dynamic-packing injection-molded sample was called the D-sample. The detailed processing conditions are listed in Table 1. For example, SIS-6D represents the sample that was subjected to shears with 6 s pause. The introduction of shear will induce molecular orientation, and the cessation of shear will relax the ordered structure. The ordered structure induced by shear can be either maintained or relaxed depending on the cessation time. Thus, controlling the cessation time between shears will induce different structures within the injection-molded SIS samples. In addition, a conventional injection-molded sample was also prepared for comparison. It was called SIS-S. The dimensions of the dumbbell-shaped sample are 114 × 6 × 3.5 mm3, and the gauge length is 40 mm. 2.3. Small-Angle X-ray Scattering (SAXS). SAXS measurements were performed to examine the internal microstructures of these samples. The tests were conducted on a homemade X-ray scattering system located at the University of Science and Technology of China. The details

In this work, we report the mechanical properties of poly(styrene-b-isoprene-b-styrene) (SIS) obtained under a novel processing technology named dynamic-packing injection molding (DPIM), as shown in Figure 1. The main feature of DPIM is to introduce periodic shears during cooling by two hydraulically actuated pistons. The mold cavity and hot runner enclose a fixed volume of the melt. Periodic melt shear was applied on the melt/solid interface by moving the pistons reversibly. A shear cycle consists of two-shear flow in the opposite direction and two periods of pauses. The main advantage of DPIM is the well-controlled shear for inducing molecular orientation. Three dynamic-packing processes with different shear cessation times were selected. So, we can expect some unique structures and mechanical properties for the dynamic-packing injection-molded SIS block copolymer. We will investigate how the structural features correlate with the final mechanical performance of both conventional injectionmolded and dynamic-packing injection-molded SIS thermoplastic elastomers. Finally, the slip-link model is introduced to quantitatively analyze the contributions from different blocks to the whole mechanical performance during tensile deformation. Our research is trying to give an example for achieving high performance of the injection-molded SIS thermoplastic elastomer via structural control.

2. EXPERIMENTAL SECTION 2.1. Materials. The SIS triblock copolymer with the tradename Vector 4211 (Dexco Polymers Co.) was taken as the candidate. Vector 4211 is a linear, symmetric triblock copolymer with an overall molecular mass (Mw) of 118 kg/mol, and the polydispersity index, Mw/Mn, is 1.09. The weight fraction of polystyrene is 30%. 2.2. Sample Preparation. The SIS granules were injectionmolded under a barrel temperature of 200 °C with a fixed 15288

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Figure 2. Mechanical stress−strain curves for the C-sample and D-samples. Inset profiles are the Young’s modulus and magnified stress−strain curve at small strains.

of the X-ray system can be found elsewhere.51 The samples were examined with the X-ray beam along the flow direction (FD) to gain two-dimensional (2D)-SAXS patterns. The injection-molded bar generally possesses typical a skin-core structure, and we mainly probe the core layer structures of the C-sample and D-samples, which determine the overall mechanical performance. The X-ray wavelength (λ) was 0.154 nm, and a CCD detector was employed to collect the 2D-SAXS patterns. The sample-to-detector distance was 2.3 m. The Fit2D software from European Synchrotron Radiation Facility was used to analyze the SAXS patterns. In addition, the background scattering (air scattering) was subtracted. 2.4. Transmission Electron Microscopy (TEM). Ultrathin sections of ca. 80 nm thickness were obtained by cryomicrotoming along the FD of the samples using a Leica EMUC6/FC6 microtome at −100 °C. These sections were then collected and stained for 20 min in a ∼2% aqueous solution of osmium tetroxide (OsO4), which selectively stained the PI microdomains. TEM was performed with a FEI-Tecnai G2 F20 S-TWIN-type transmission electron microscope operating at 200 kV. 2.5. IR Dichroism. For comparison, the thin layers with ∼30 μm thickness were cut at about 1.5 mm from the surface of the injection-molded samples. Measurements were carried out on a Thermo Nicolet Fourier transform infrared (FTIR) spectrometer at a resolution of 4 cm−1 with an accumulation of 64 scans in reflection mode. Polarization of the beam was realized through a ZnSe polarizer. The sample was fixed perpendicularly with the FTIR beam and tested with polarized radiation in the machine and transverse directions (TD), respectively. The measurements were performed with radiation polarized in the directions parallel and/or perpendicular to the FD, respectively. The orientation factor f and structural absorbance A of the corresponding band are deduced as follows: R = A /A⊥

f=

3 cos2 φ −1 ⎛ R − 1 ⎞⎛ 2 cot2 α + 2 ⎞ ⎟⎜ =⎜ ⎟ ⎝ R + 2 ⎠⎝ 2 cot2 α − 1 ⎠ 2

(2)

where A∥ and A⊥ are the parallel and perpendicular absorbances at the same positions, R is the dichroic ratio, and α is the angle between the dipole moment vector and the local chain axis (α = 18°).52 For the molecular orientation function, f = 0 means isotropic, f = 1 means polymer-aligned along the reference axis, and f = −0.5 means perpendicular orientation to the reference axis. 2.6. Tensile Tests. Monotonic tensile tests were performed on a SANS Universal tensile testing machine according to the GB/T 528-2009 standard. All of the tests were conducted at ambient temperature (23 °C) at a fixed crosshead speed of 50 mm/min, and five specimens were tested for each group. 2.7. Dynamic Mechanical Analysis (DMA). DMA was performed with a TA Q-800 type machine to assess the glass transition behavior and viscoelastic properties of the C-sample and D-samples. The measurements were performed under single cantilever mode with a frequency of 1 Hz from −100 to +120 °C at a heating rate of 3 °C/min. The dimensions of the tested samples are 17.5 × 6.2 × 3.5 mm3.

3. RESULTS AND DISCUSSION 3.1. Mechanical Performance of Different Samples. The typical stress−strain curves for the C-sample and Dsamples are illustrated in Figure 2. A main feature of these stress−strain curves is that both the C-sample and D-samples exhibit yielding and necking phenomenon to different extents, while the sample SIS-15D shows a relatively continuous and successive deformation process. On the basis of the curve shape and the whole deformation process, all of the stress−strain curves of different samples can be divided into three main regions, which can be denoted as region I, region II, and region III. Region I is distinguished by a steep increase of the nominal stress for the tensile modulus. Then the end of region I can be apparently recognized by a significant yielding process, and

(1) 15289

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functions in the PI and PS domains, respectively.54 The related orientation function can be calculated from the absorbance at peaks of 838 cm−1 for the PI segments and 1602 cm−1 for the PS segments. As shown in Figure 4, the orientation degree of

region II mainly represents the necking platform when the nominal stress remains at a nearly constant value with increasing uniaxial elongation at a fixed speed. Necking is analogous to localized deformation, which can be attributed to a process in which materials deform in a relatively ductile way rather than an elastic response. Subsequently, completion of the necking period means the onset of region III. With the strain further increasing in region III, the nominal stress gains an additional increase to different extents to a final fracture. For SIS-3D, the Young’s modulus reaches as high as ∼85 MPa and achieves a nearly 41.8% increase to be the highest one among all of these samples. The SIS-3D sample also has the highest yield stress, as depicted in the partial magnified stress−strain curves. For samples obtained by DPIM, the Young’s modulus decreases with an increase of the cessation time. Because of the small macroscopic draw ratio (λ = L/L0), differences of stress response are relatively small at regions I and II, while the mechanical performances of the D-samples differ significantly in region III. The final strength at break of the D-samples increases with the prolonging of the shear cessation time. Apparently, SIS-15D deforms in a continuous way and owns the highest strength at break of about 11 MPa, which is nearly 1.5 times that of SIS-S. Overall, the mechanical performances of the D-samples are more excellent than that of C-sample either for a higher Young’s modulus under short shear cessation or a higher break strength under long shear cessation. 3.2. Understanding the Increased Modulus for a Sample Obtained with Short Shear Cessation Time. Because the modulus of a material is usually related to the property at very small deformation, we think the orientation of the block segments will play a dominate role in determining the modulus. For insight into the chain orientation at a molecular level, the polarized FTIR spectra of the corresponding injection-molded samples are presented in Figure 3. For SIS-

Figure 4. Orientation factor f as a function of the shear cessation times for PS (in black) and PI (in red) segments.

the PI segments is higher than that of the PS segments. PS segments are nearly isotropically distributed in the cylindrical domains, while PI segments of the D-samples possess anisotropy. In addition, the orientation factor of the PI segments is negative, which means that the PI segments align well perpendicular to the FD. For SIS-3D, shearing with a short cessation time freezes a large orientation of the PI segments anchored between the PS cylindrical domains. In consideration of the fact that the melt temperature is far above the glass transition temperature (Tg) of the PI blocks, PI segmental orientation induced by shear can easily relax during longer cessation time, which coincides with a change trend of the orientation factor f, indicating that high-frequency shear (short cessation) can effectively maintain the alignment of the PI chains. The experimental result shows that longer shear cessation is in favor of the recovery of aligned molecular chains, while chain orientation on a molecular scale is solidified when the shear cessation is short. The stretched PI chain in the D-sample could be further proven by the enlarged d spacing. For this reason, the 2D-SAXS patterns of each sample are converted to one-dimensional (1D) profiles, as shown in Figure 5a. The 1D scattering curves for all samples are similar and show several peaks, which indicates the existence of well-ordered structure as expected. For all of these curves, high-order peaks with positional ratios of q-spacing values appear at 1:√3:√4:√7 relative to q* if we denote the q position of the first peak as q*. This sequence of reflections generally indicates a hexagonally packed cylindrical structure. In comparison with the C-sample, reflection peaks of the Dsamples including the first and high-order reflection peaks are inclined to shift toward the low q-spacing zone. High-order reflections of the D-samples change more significantly than the first-order peak but still locate at a fixed positional ratio relative to q*. In addition, reflection peaks of the D-samples are increasing gradually to those of the C-sample with prolonging of the cessation time. The d spacing of block copolymers can be calculated by

Figure 3. Polarized FTIR spectra, parallel (black line) and perpendicular (red line) to the FD, of the CIM and DPIM SIS samples: (1) SIS-S; (2) SIS-3D; (3) SIS-6D; (4) SIS-15D.

3D, significant differences of the absorbances in the parallel and perpendicular directions to the reference axis are observed. Other samples gain no obvious dichroic character and present similarity between the absorbances in the parallel and perpendicular directions. For SIS block copolymers, the PI unit would generate several isomers including peaks at 838 cm−1, which is from two overlapped peaks, 835 cm−1 from cis-1,4 units, and 840 cm−1 from trans-1,4 units.53 Absorption bands at 838 cm−1 for C− H bending, 1004 cm−1 for C−C stretching, and 1602 cm−1 for benzene stretching can be used to determine the orientation

dspacing = 2π /q*

(3)

which covers information on the spacing between (100) planes and on microdomain structures such as the microdomain size 15290

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Figure 5. Combination of graphics: (a) 1D-SAXS profiles for the C-sample and D-samples (all of the profiles have been shifted vertically for clarity); (b) related d spacing of the C-sample and D-samples; (c) schematic showing possible shear-induced stretching of the PI blocks; (d) schematic diagram for PI configurations that contribute effectively to the Young’s modulus.

Figure 6. 2D-SAXS patterns and TEM bright-field images of sample SIS-15D observed from different directions: (a) 2D-SAXS along the TD; (b) 2D-SAXS along the FD; (c) 2D-SAXS along the ND; (d) TEM along the TD; (e) TEM along the FD; (f) structural sketch for SIS-15D. Note: isoprene microdomains appear electron-opaque (dark) because of selective OsO4 staining.

and interdomain distance for hexagonally packed cylindrical PS domains. As is also presented in Figure 5b, the d spacing of the C-sample is about 26.5 nm and is smaller than that of the Dsamples. For the D-samples, the d spacing gradually decreases close to the C-sample with increasing shear cessation time, indicating that periodic shear makes the distance between the cylindrical domains enlarge. It is noteworthy that the whole variation trend of d spacing is similar to that of the Young’s modulus. As a matter of fact,

rubbery PI segments can possess either bridge conformation, whose chain ends connect two different PS domains, or loop conformation.55,56 During simple tension, an independent or dangling PI loop makes no contribution to the mechanical response, while bridges (possibly crossed loops) and PI segments in the trapped entanglement are in great favor of enhancing the Young’s modulus, as shown in Figure 5d. At the same time, shear can stretch the PI segments into an extended state, as presented in Figure 5c. In region I, all PS physical 15291

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cross-links are nearly in no deformation, and the macroscopic deformation of a specimen can be wholly attributed to stretchable PI segments. It is authentic that a stretching PI network inevitably needs larger stress and takes less time to reach the yield point (beginning of PS deformation) than that for a PI network in a relaxed state. It also indicates that a SIS melt possesses a residue stretching effect induced by shear because of the existence of enlarged d spacing in SIS-15D relative to SIS-S. However, the Young’s modulus of SIS-15D is even lower than that of SIS-S. This is possibly due to the decrease of the PI entanglements. When shear induces PI segments to disentangle, the number density of the network chain decreases and thus results in a decrease of the shear modulus. Overall, periodic shear can induce PI segments to change from a relaxed state to an extended state. However, shear can also disentangle PI chains, which can decrease the Young’s modulus. 3.3. Understanding the Increased Break Strength for a Sample Obtained with Prolonged Shear Cessation Time. For the D-sample obtained with long shear cessation time, the shear-induced soft PI networks can be easily relaxed, as discussed above. Thus, for the break strength, it is mainly related to the structure of the PS cylindrical domains. The parallel orientation with high symmetry can be well developed when the cessation time is long enough. As shown in Figures 6a−c, two-point patterns emerge along the TD and along the neutral direction (ND), while six-point patterns with clear highorder reflections emerge along the FD. Meanwhile, TEM images show that bright PS cylinders well pack parallel with each other along the FD (Figure 6d), while PS ends well distribute in the cross section (Figure 6e). Hence, PS nanocylinders of SIS-15D well pack in a hexagonal lattice, as shown in Figure 6f. To our surprise, it is the first time to observe a beautiful six-point pattern for the processed article. It is shown that shear can increase the orientation of the PS nanocylinders. At the same time, the packing order of these nanocylinders increases with prolonging of the cessation time. Previous literature reported deformation of a well-oriented triblock copolymer and demonstrated that mechanical tension is sensitive to the orientation direction of the PS cylinders.30 Therefore, SIS-15D exhibits the highest tensile strength at break mainly because of the parallel orientation of the PS nanocylinders with high spatial symmetry. Figure 7 illustrates the evolution of the loss tan δ for the Csample and D-samples as a function of the temperature from −100 to +120 °C. All samples show two typical glass transitions representing the glass transition of the PI block (TgPI) at about −45 °C and that of the PS block (TgPS) at about 105 °C (slight deviations can be found on the data of TgPI and TgPS because of the differences of the test methods and procedures57). It is interesting to note that TgPS of the D-samples is higher than that of SIS-S. With long cessation time, it can be distinguished that TgPS of SIS-15D shifts to the high-temperature zone, while TgPI of SIS-15D shifts to the low-temperature zone. This phenomenon demonstrates two different blocks in SIS segregated more thoroughly from each other; that is, shear and post relaxation can promote microphase separation. Previous literature reported that an increase of TgPS could be correlated with stronger phase separation while a decrease of TgPS could be attributed to partial “dissolved” PS chains in the PI matrix.58 In addition, an increase of TgPS represents that the PS chain movement decreases and thus reinforces the stiffness of the PS domain. It significantly improves the break strength of

Figure 7. Temperature dependence of loss tan δ of SIS samples processed under quiescent and different shear conditions: (1) SIS-S; (2) SIS-3D; (3) SIS-6D; (4) SIS-15D.

SIS-15D. Above all, it can be concluded that it promotes microphase separation and cylindrical packing order with prolonging of the shear cessation time. 3.4. Quantitative Analysis on the Mechanical Performance. In order to further investigate the relationship between the microphase structure and mechanical response of SIS, the slip-link theory was used.59,60 The slip-link model mainly describes the rubber elasticity of a cross-linked network under consideration of the chain entanglements and finite-chain extensibility. The formula shows that the free energy (F) operates as a function of the stretch ratio (λ) with the parameters of cross-linked chains NC, the density of slip-links NS, the slippage parameter η, and the inextensibility parameter α. F /kT =

⎛ 2 2 1 ⎜ ⎡⎢ λi (1 − α )(1 + η) Ns⎜∑ 2 ⎝ i ⎢⎣ (1 − α 2 ∑i λi 2)(1 + ηλi 2) ⎞ ⎤ + log(1 + ηλi 2)⎥ + log(1 − α 2 ∑ λi 2)⎟⎟ ⎥⎦ ⎠ i 2 2 ⎞ 1 ⎛⎜ ∑i λi (1 − α ) 2 2 ⎟ ∑ + Nc⎜ + − α λ log(1 ) i ⎟ 2 ⎝ 1 − α 2 ∑i λi 2 ⎠ i

(4)

while stress in simple tension can be described as σ=

⎛ ∂F ⎞ ⎜ ⎟ ⎝ ∂λ ⎠T , V

(5)

with λ1 = λ2 = 1/λ3. Figure 8 represents a comparison of the stress−strain curves calculated from slip-link theory with the experimental data. In our experiment, fitting curves were achieved based on the assumption of η with a constant value of 0.8. If η = 0, the slip links are rigid and act as cross-links, while α = 0 means that the cross-link reduces to the classical theory of phantom chains. In a styrenic thermoplastic elastomer system, PS segments act as physical cross-links while entanglements of PI act as slip links. So, we can use the slip-link model to simulate the contribution of different segments to the whole rubber elasticity of SIS 15292

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the cross-link and slip-link contributions. The cross-link contribution accumulates linearly, while there is a turning point for the slip-link contribution curve. Obviously, the crosslink of the D-samples contributes more than that of the Csample. Furthermore, the cross-link contribution of samples increases with prolonging of the shear cessation. As a result, shear can help the PS domain possess a well spatial distribution with high symmetry and high packing order. In addition, trapped entanglement cannot slip, while nonfixed entanglement can disentangle and slip along the PI chain. As can be seen in the right profile, the slip link has more contribution for the Csample than for the D-samples, indicating that shear can also disentangle the PI segments.

4. CONCLUSIONS In summary, periodic shear on the SIS melt is helpful for largely improving the mechanical properties of injection-molded samples. When the cessation is short, shear can induce dspacing enlargement and freeze PI segments in the extended state, which is favorable for an increase of the Young’s modulus. When shear cessation is long enough, it is favorable for parallel orientation as well as packing order within a hexagonal lattice for PS nanocylinders. The break strength was thus significantly improved. Hence, the mechanical performance of injectionmolded samples was dominated by the PI matrix contribution by extended bridging effects and trapped entanglements at small deformation before yielding. Correspondingly, it was dominated by the PS contribution of the nanocylinder orientation and lateral order at large deformation until fracture. Meanwhile, the slip-link model is introduced to separate the contributions of different blocks for the mechanical performance of SIS block copolymers during simple tension. The related theoretical predictions are well consistent with our experimental results.

Figure 8. Fitting curves of different samples using the slip-link model.

samples. Overall, the slip-link model fits well with the experimental curve except some deviations in the vicinity of the yielding and necking platform. The Young’s modulus of all of these samples is higher than the theoretically predicted value. PS cross-links can be destroyed with increasing strains. This fact is different from the ideal assumptions of the slip-link model. The theory is based on the cross-links without change and an isotropic rubber network. So, the deviation is mainly due to physical cross-link (PS domain) deformation and orientation (anisotropy) in our system. Table 2 lists all of the Table 2. Slip-Link Model Fitting Parameters of Stress−Strain Behavior in Different Samples sample

NckT (MPa)

NskT (MPa)

α

SIS-S SIS-3D SIS-6D SIS-15D

0.47 0.46 0.51 0.68

12.8 11.9 10.8 10.2

0.036 0.040 0.045 0.041

■

AUTHOR INFORMATION

Corresponding Authors

*Tel: 0086-028-85461795. E-mail: [email protected]. *Tel: 0086-028-85461795. E-mail: [email protected].

necessary fitting parameters of different samples in the slip-link model including Nc, Ns, and α. As shown in the table, the parameter α of all D-samples is higher than that of C-sample, which also indicates that PI networks are in a tightened state after shearing from a numerical perspective. Figure 9 presents the successful isolation on the effect of the cross-link and slip link upon the total engineer stress during simple tension. There are big differences between the trends of

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants 51173112, 51121001, and

Figure 9. Contribution of the cross-link to the whole mechanical properties (a) and contribution of the slip link (b) to the whole mechanical properties of all injection-molded samples including the C-sample and D-samples. 15293

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51210005) and the Special Funds for Major State Basic Research Projects of China (Grant 2011CB606006). We thank Prof. Liangbin Li for his help with SAXS experiments.

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