Cavitation in Poly(4-methyl-1-pentene) during Tensile Deformation

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B: Glasses, Colloids, Polymers, and Soft Matter

Cavitation in Poly(4-methyl-1-pentene) during Tensile Deformation Ran Chen, Ying Lu, Zhiyong Jiang, and Yongfeng Men J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b00060 • Publication Date (Web): 16 Mar 2018 Downloaded from http://pubs.acs.org on March 19, 2018

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The Journal of Physical Chemistry

Cavitation in Poly(4-methyl-1-pentene) during Tensile Deformation Ran Chen, Ying Lu, Zhiyong Jiang and Yongfeng Men*

State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Renmin Street 5625, 130022 Changchun, P.R. China

*:email: [email protected]

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ACS Paragon Plus Environment

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ABSTRACT ： The poly(4-methyl-1-pentene) sample was used to investigate cavitation induced stress-whitening phenomenon during stretching at different temperatures via the ultra-small-angle X-ray scattering technique. Two modes of cavitation were found, in that mode I cavitation activated around yield point followed by mode II cavitation generated in highly oriented state. The critical strain for initiating the mode II cavitation increases with the increase of stretching temperature whereas the critical stress grew steadily in the lower temperature regime (30~60 °C) and reached a plateau at 70 °C. The appearance of mode II cavitation at large strains was independent of the mode I cavitation. The mode I cavitation was attributed to the competitive process between the formation of cavities and shearing yield of lamellae while the mode II cavitation was proven to be related to the failure of the whole highly oriented entangled amorphous network due to the breaking of interfibrillar load bearing tie molecules. Size distribution of cavities has been successfully calculated using a model fitting procedure. The results showed that the quantity of cavities increased heavily while the size kept nearly constant during the propagation of the mode II cavitation.

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1. INTRODUCTION

Semicrystalline polymers having alternative crystalline lamellae and amorphous phase structure show complicated deformation behavior1. It includes two major processes, namely, shear yieding and cavitation2-7. Two distinctly different arguments have been suggested for shear yieding in the literature. The first argument considered that macroscopic deformation is accomplished by slips inlcuding crystallographic fine slips and coarse slips. Fine slips change the angle between molecular chain axis and the normal to the lamellar surface while coarse slips lead to lamellae fragmentation8-13. The second arguement concluded that the process is governed by stress-induced melting and recrystallization14-19. Much evidence shows that both processes discussed above may be activated at different strains during tensile deformation20-24. The spherulitic structure of semicrystalline polymers starts to elongate at the observed macroscopic yield point and coverts into oriented microfibrils during tensile deformation. In genral, the polymers end up with a highly oriented hierarchical fibrillar structure. Structural model of the fibrescomposed of fibrils was proposed by Peterlin11, 25 and Wardet al26. The fibril is made up of microfibrils being composed of crystalline lamellae with normal parallel to the tensile axis and the amorphous phase in between. Peterlin25 considered the plastic deformation of fibrous material to occur primarily by a sliding motion of fibrils, limited by interfibrillar tie molecules. Nervertheless, Tanget al.27 proposed a different mechanism, that the slippage of microfibrils occurs before the slippage of fibrils. With respect to the cavitation during tensile deformation of semi-crystalline 3



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polymers, there are still many questions which need to be answered, such as the nature of the phenomenon, the moment of cavitation, and so on28. Cavitation in semicrystalline polymers generally leads to strong stress-whitening of the materials due to creation of high light scattering voids in the systems. The cavitation was observed in many drawn polymeric materials such as isotactic polypropylene (iPP)29, polyethylene (PE)30, 31, poly(1-butene) (P1B)18,

32, 33

and Poly(4-methyl-1-pentene)

(P4M1P)34. In general, the ability of polymers for cavitation depends on factors like the preparation method of the materials and the experimental conditons. High crystallization temperature35 and annealing36 can promote the process of cavitation. With slower deformation rate29,

37

and higher deformation temperature,35,

38, 39

cavitation may be suppressed. In most cases, cavitation occurs around the yield point, where the whitening intensity increased and peaked at certain strains followed by a continous decreasing6, 37. The development of extent of stress-whitening around yield point in semicrystalline polymers indicates that such cavitations can be effectively stablized during tensile deformation so that the mechnical properties of the materials are less affected by local cavitation in the systems. Very recently, we reported a different mode of stress-whitening in iPP at large strains during tensile deformation40. This kind of cavitation was confirmed to appear within the highly oriented samples and to be related to the failure of the highly oriented amorphous network induced by the breakage of load bearing interfibrillar tie molecules followed by disentanglements of amorphous network connecting adjacent fibrils. The critical strains for activating such cavitation depend on both the molecular weight of iPP and the deformation

4


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temperature while the stress for this behavior depends only on the molecular weight. Poly(4-methyl-1-pentene) (P4M1P), as a semicrystalline polyolefin, presents good properties like high optical transparency, relatively high thermal stability and chemical resistance41. P4M1P crystallized from melt state has an unusual closeness between the densities of the crystal and the amorphous phase, especially at room temperature and this makes the small-angle X-ray scattering (SAXS) intensity of lamellar structure too weak to be detected42. P4M1P has relatively high melting temperature (about 235 °C) and high glass transition temperature (about 35 °C) which is convient and appropriate for the evaluation of its deformation property. Previously, we investigated the initiation of cavitation around yield point in tensile deformed P4M1P below glass transition temperature. A peculiar two-step cavitation process which involved the initiation of small amount of large cavities at the beginning of stretching followed by extensive occurrence of small cavities on further stretching was discovered and attributed to heterogeneously frozen in internal stress in the samples below glass transition temperature34. In the present work, we set out to learn more about the nature of cavitation in quenched P4M1P during tensile deformation at different temperatures using in-situ ultra-small-angle X-ray scattering (USAXS) measurements. The choice of P4M1P as a model system is due to its high glass transition temperature (about 35 °C) and the low electron density contrast between its amorphous and crystalline phases. This enabled us to investigate the cavitation using SAXS without too much interference of the scattering from crystalline lamellar structures. Macroscopically, we observed as

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above mentioned two different kinds of cavitations during the deformation that the cavitation activated around yield point (mode I) and the second kind generated at large strain away from yield point evidenced by an enhenced stress-whitening at late stage of stretching (mode II cavitation). The study provided more detailed views about the cavitation behaivors of semicrystalline polymers. It turned out that the appearance of mode II cavitation was independent on the appearance of mode I cavitation. The mode II cavitation can be linked to the failure of the whole highly oriented entangled amorphous network.

2. EXPERIMENTAL SECTION

The P4M1P used in this study was purchased from Mitsui Chemicals, Inc., Chiba, Japan (TPX) with a trade name of MX002, whose melt flow rate (MFR) is 21 g/10 min (260 °C, 5 kg). It had molecular weights of Mw=282,496 g/mol, Mn=89,311 g/mol and the polydispersity is 3.16. The pellets were compression molded into about 0.5 mm thick sheets at 280 °C and held in the molten state for 5 min to erase the processing history. The molten sheets were quickly quenched into the ice water for half an hour. Dog-bone tensile bars with dimensions of 10*5*0.5 mm3 were obtained from these sheets with the aid of a punch. Uniaxial tensile deformation was carried out at different temperatures (30, 40, 50, 60, 70 and 80 °C) using a portable tensile testing machine (TST350, Linkam, UK). The cross-head speed during stretching was kept at 20 µm s-1(equal to an initial strain rate of 0.0013 s-1). In order to measure the strain of the deformed area at certain spots 6


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on the samples accurately, optical photo images of the samples were employed during stretching processes. Because of the appearance of necking, the true strain is needed to express the local strain of materials during stretching process instead of engineering strain. Therefore, the Hencky strain εH is used as a basic quantity of the true strain, which is defined as

ε H = 2 ln

b0 b

(1)

where b0 and b are the initial and instantaneous widths of sample during stretching process, respectively. In-situ USAXS experiments were conducted with a modified Xeuss system of Xenocs SA, France. The system is equipped with a multilayer focused Cu Kα X-ray source (GeniX3D Cu ULD, λ=0.154 nm), generated at 50 kV and 0.6 mA. Two pairs of scatterless slits were located 2400 mm apart from each other for collimating the X-ray beam. Scattering data were recorded with the aid of a Pilatus 100 K detector, DECTRIS, Swiss (resolution: 487*195, pixel size=172 µm). The sample-to-detector distance was 6558 mm and the effective range of the scattering vector q (q = 4πsinθ/λ, where 2θ is the scattering angle and λ is the wavelength of the X-ray) was 0.019-0.271 nm-1 in the horizontal direction and 0.019-0.179 nm-1 in vertical direction due to the shape of the detector being rectangular. The collection time for USAXS patterns was set as 300 s after each step. USAXS patterns were background corrected and normalized using the standard procedure. In-situ wide angle X-ray scattering (WAXS) experiments were performed at the beamline 1W2A, BSRF, Beijing. The wavelength of X-ray radiation was 0.154 nm. 7



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The sample-to-detector distance was 166 mm. A 2D MAR CCD X-ray detector with a resolution of 2048*2048 (pixel size = 79 µm) was used to acquire 2D-WAXS patterns. Each WAXS pattern obtained in the center of the sample was collected within 40 s. To investigate the orientation of crystalline and amorphous phases, the "halo method" proposed by Hsiao et al.43, 44 was applied in data analysis of 2D WAXS patterns. Fraser45 method has been used to correct the distortion of the pattern caused by flat-plate detector. The 2D WAXS patterns can be divided into two fractions by standard procedure: isotropic part and anisotropic part. The azimuthal scan was first drawn along the angular axes starting from the center of the WAXS patterns. At each pixel of same scattering angle position, a minimum intensity value was obtained from the azimuthal scan, which eventually yielded the isotropic part. The anisotropic part was obtained by subtracting the isotropic part from the whole WAXD pattern. The anisotropic part was composed of oriented crystals and amorphous phase. And the isotropic part is composed of unoriented amorphous and crystalline phases. The quantitative evaluation of mass fraction of crystalline and amorphous phases (oriented and unoriented) was determined with a peak fitting method. The orientation of the lattice plane was calculated using the Hermans orientation equation46: S hkl =

(3 cos 2 ϑhkl − 1)

2

(2)

Where ϑ is the angle between the normal direction of the corresponding crystallographic plane and the reference axis, and π /2

cos ϑhkl 2

∫ =

0

I hkl (ϑ ) cos 2 ϑ sin ϑdϑ

π /2

∫

0

cos 2ϑ hkl is defined as:

I hkl (ϑ ) sin(ϑ )dϑ

8


(3)

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where I (ϑ ) is the scattering intensity along the angle ϑ . And the cosine of the scattering angle is defined by Polanyi equation47:

cosϑhkl = cos µ * cosθ hkl

(4)

where µ is the azimuthal angle along the Debye circle, and 2θ denotes the Bragg scattering angle. Note that the orientational order parameter in the present case assumes values in the range − 0.5 ≤ S ≤ 0 as the stretching direction was taken as the reference direction and only diffractions from (hk0) crystallographic planes are considered. For perfect orientation of the (hk0) lattice planes with their normal perpendicular to the stretching direction, the order parameter would be S = −0.5 , while for an isotropic sample in the randomly oriented state, the order parameter becomes S = 0 . Dynamic mechanical behavior of materials was studied by using dynamic mechanical analyzer Q-800, TA instruments. Rectangular specimens of 30*5*0.5 mm3 were used for the analysis. The experiments were performed under tensile mode at a frequency of 3Hz. The samples were heated up from -20 to 227 °C at a heating rate of 3Kmin-1. The weight fraction crystallinity was determined using a DSC1 Stare System (Mettler Toledo Swiss). The samples were scanned from 30 to 280 °C under the N2 atmosphere with a heating rate of 10 K/min. The crystallinity was calculated from the area under the melting peak, assuming that the heat of fusion for 100% crystallinity of ∆Hid for P4M1P is 61.7 J/g48.

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3. RESULTS AND DISCUSSION

Figure 1. Selected microphotographs showing the stress-whitening phenomenon of P4M1P sample stretched at different temperatures.

Figure 1 shows the optical photographs of the P4M1P samples at selected strains stretched at different temperatures. At the stretching temperature of 30 °C, a severe stress-whitening phenomenon around the yield point was observed. With increasing stretching temperatures from 30 to 70 °C, the stretched sample became more and more transparent indicating a gradually weakened stress-whitening. This is in line with the general whitening phenomenon reported for polyolefin35 which almost appears near the yield point indicating the occurrence of mode I cavitation. It is worth noticing that the P4M1P samples showed sudden enhanced stress-whitening at large strains at each stretching temperature, especially obvious at higher temperatures. This peculiar behavior can be clearly distinguished from mode I cavitation because the onset strain for the enhanced stress-whitening initiation is much larger than yield 10


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point. This second kind of cavitation at the late stage of stretching has been observed in iPP which showed sudden stress-whitening at large strains during stretching at elevated temperatures40.

Figure 2. Selected USAXS patterns of P4M1P deformed at different temperatures taken at different strains as indicated on the graph. (Deformation direction: horizontal)

USAXS has the advantage of giving access to quite small q-values and provides the possibility to study the large-scale structures in the sample. In order to investigate the evolution of inner structures in P4M1P during stretching, USAXS experiments were carried out. Figure 2 exhibits the selected USAXS patterns of P4M1P samples during stretching. Scattering from crystalline lamellar stacks in the P4M1P cannot be detected due to the low contrast of electron density between crystals and amorphous phase at the deformation temperatures. As a result, the scattering streaks detected on the 2D USAXS patterns could only be ascribed to some structures with much low density which differs from the P4M1P matrix in refractive index, causing obvious whitening of the deformed samples shown in Figure 1. At the stretching temperature of 30 °C, the strong horizontal scattering appeared first, indicating the occurrence of

11



plate-like cavities with their normal orientated along stretching direction. The scattering pattern became "butterfly" shape with increasing strain, which was ascribed to the tilting of cavities with respect to the stretching direction. And then one observed a redistribution of scattering intensity from horizontal to vertical direction, indicating the change of the orientation of cavities with their normal from parallel to perpendicular to the stretching direction, which is termed as "cavitation with reorientation" mode33. With the increase of stretching temperature, a similar scattering intensity distribution was observed but to a much less extent. This behavior is in line with the mode I cavitation around yield point. However, the most significant feature of the results is the appearance of sudden intensified scattering streaks perpendicular to the stretching direction at large strains, which is in accordance with enhanced stress-whitening shown macroscopically in Figure 1. The major reason here is the occurrence of the elongated low density objects along the stretching direction in the highly oriented deformed samples. 10

0.1

Ts 30 °C Ts 40 °C Ts 50 °C Ts 60 °C

-3

Ts 70 °C Ts 80 °C

0.01

1

φ

-1

voids

Q / cm nm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1E-3 0.1

1E-4 0.0

0.5

1.0

1.5

2.0

2.5

0.0

εH

0.5

1.0

1.5

2.0

2.5

εH

Figure 3. Absolute scattering invariant (left) and void volume fraction (right) plotted as a function of deformation. 12


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In order to characterize the evolution of the cavities with deformation quantitatively, the absolute intensity was calibrated49. The scattering invariant Q was calculated with the assumption of cylindrical symmetry of the system along the stretching direction50.

Q= Where

1 ∞ ∞ dΣ (qh , qv )qv dqh dqv 2 ∫− ∞ ∫0 dΩ

(5)

dΣ is the absolute scattering intensity distribution. Actually, considering the dΩ

limit range of effective scattering vector, the intensity distribution along qv is extrapolated to q=0 by Guinier's law and to infinity by Power law. The volume fraction of cavities can be obtained according to51

Q = 2π 2φ AφB ( ρ A − ρ B ) 2

(6)

where φ A and φ B denote the volume fraction of polymer matrix and the cavities and

ρ A and ρ B are the corresponding electron density, respectively. The electron density of polymer matrix is 287.0 e-/nm3 and the one of cavities is assumed to be 0 in the calculation. Figure 3 shows the scattering invariant Q and volume fraction of cavities for P4M1P deformed at different temperatures as a function of strain. It is evident that for lower deformation temperatures the scattering invariant Q increased rapidly with strains and reached a plateau value at certain strain in the softening region followed by a slight drop with further stretching. As was discussed in the introduction section, this result indicates effective stabilization of the mode I cavitation occurred around yield point. For higher deformation temperatures, no obvious change in scattering invariant Q at small strains was observed, indicating a kind of rearrangement of the crystalline lamellar structure without creating cavities before considerable deformations. Clearly, the scattering invariant Q increased significantly for all 13



measured deformation temperatures at large strains before rupture. The strong increase in scattering invariant Q indicates the appearance of new cavities.

500

300

Ts 30 °C Ts 40 °C

250

Ts 50 °C

400

Ts 60 °C 200

Ts 70 °C Ts 80 °C

R /nm

L /nm

300

150

200 100 100

50

2.0 0

1.8

1.8

1.6

1.6

1.4

1.4

1.2

1.2

1.0

1.0

σR

2.0 0

σL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

0.0 0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

2.5

εΗ

εΗ

Figure 4. Fits performed for P4M1P stretched at different temperatures. The length distribution (left) and radius distribution (right).

In order to derive the structure parameters about cavities quantitatively, a direct model fitting to the USAXS patterns was conducted. As discussed in the literatures1, 34, 52, 53

, cylinder is a simple and convenient model for simulating the scattering of voids.

For the oriented voids, we used the model proposed by Fischer52 who assumed that the cylinder-shaped cavities are oriented along the stretching direction and randomly distributed in the sample without interference between each other. The scattering intensity is given by the superposition of aligned cylinders which is written as 2

∞

2

 2 J ( q R )   sin( qh L / 2)  I ( q h , qv ) ∝ ∫ ∫ R L  1 r    D( R, L) dRdL  q r R   qh L / 2  0 4 2

14


(7)

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where qh and qv are the components of scattering vector in the horizontal and vertical directions. J1(x) is the Bessel function of the first kind and first order. D(R,L) is the size distribution function of cylinders having a radius R and a length L. Assuming these two parameters are not correlated, we can make a simplification D(R,L)=D1(R)D2(L). As such, the equation (4) becomes 2

∞

 2 J (q R)  I( qh , qv ) ∝ ∫ R  1 r  D1 ( R )dR  qr R  0 ∞  sin( qh L / 2)  × ∫ L2  D2 ( L) dL  qh L / 2  0 4

(8)

D1(R) and D2(L) are the radius and thickness distribution functions of cylinders which are expressed as the lognormal distribution. Furthermore, it is found that scattering in the qh and qv directions can be separated and evaluated independently. Hence, we took two rectangular slices parallel to the axes at appropriate positions, one perpendicular to the stretching direction for the radius evaluation and the other parallel to the stretching direction for the height evaluation. The initial voids, which are oriented perpendicular to the stretching direction, are described by relatively broad cylinders having a small length. For the tilted cavities with a "butterfly" scattering shape, we used a modified model34. The normal of voids are mainly along the stretching direction but with an orientational distribution h(β).The total intensity of broad cylinders with an orientational distribution is π / 2 2π

I (q, β , γ ) = 4V 2 ρ 02

∫ ∫∫ 0

0

sin 2 (qL / 2 cos φ (β , γ )) J 2 (qR sin φ (β , γ )) D1 (L)dL ∫ 1 D 2 (R )dR h (β ) sin(β )dγdβ (9) 2 (qL / 2 cos φ (β , γ )) (qR sin φ ( β , γ )) 2

where βis the angle between the normal direction n of the broad cylinder and the stretching direction (the x axis). γ is the angle between the projection of the normal

15



direction n of the broad cylinder on the yz plane (perpendicular to the stretching direction)and the y axis. Φ is the angle between q and the normal direction n of the broad cylinder. Several characteristic lines on the image were chosen for fine fitting. Data fitting was done using a nonlinear least-squares algorithm. The scattering intensity distribution profiles, corresponding fitting results and the fitted positions are given in the Supporting Information. Figure 4 shows the fitted results of the log-normal size distributions of cavities. Due to the weak scattering intensity observed for samples deformed at temperatures 50 and 60 °C at moderate strains, the size distribution of cavities was not evaluated. At the very beginning of the cavity formation, the cavity diameter (2R) is larger than the length (L), indicating the disc-like cavities oriented along stretching direction. The length of cavities increases gradually with increasing strains, whereas the radius remains relatively stable. The reorientation of cavities happens turning their normal parallel to the stretching direction. There is a sudden increase of radius value at large strains where enhanced whitening appears, indicating a new kind of cavities with larger radius value is generated. In the final stage of stretching, the sizes of cavities kept nearly constant whereas the volume fraction grew continuously indicating a continuous increase of the cavity quantity. This result indicates that cavitation at the late stage of stretching in the samples proceeds in a sequential manner rather than being initiated simultaneously. The cavitation at this late stage of stretching is due to local failure of the highly orientated inter-fibrillar tie chain network. Some cavities occurred first at some places and grew up quickly to certain size. These cavities can

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be effectively stabilized due to surrounding rigid structures. Further stretching initiated more new cavities to similar size. It must be mentioned that globally, the microstructure within the bulk stretched samples is quite similar providing similar situation for cavities to grow to certain limited size. Nevertheless, the microstructures as well as stress strain fields within bulk sample cannot be very homogenous so that cavities cannot occur simultaneously at every possible place. We thus observed continuous increase in cavities quantity but similar size of the cavities. This also explains the large extent of deformation for the P4M1P sample after enhanced whitening. In an effort to confirm the validity of our USAXS fitting results, SEM measurements were performed to provide the real-space images of the cavities. As the cavities occur mostly within the bulk of the sample, only fractured surfaces could be measured. Macroscopic fracture of the samples after stretching produces two typical surfaces with normal perpendicular or parallel to the stretching direction as was shown in Figure S8 in the Supporting Information. Some selected SEM images for the samples stretched at different temperatures are presented in Figure S9. The observed cavities in the fracture surface with normal parallel to the stretching direction shown in Figure S8 (left) reflect their radial size being in the range of 30~170 nm and the ones in the fracture surface with normal perpendicular to the stretching direction shown in Figure S8 (right) reflect their length being in the range of 300~760 nm. The sizes of detected cavities by SEM deviate slightly from the fitted results by SAXS. The main reason might be that SEM results were obtained for samples that had been

17



fractured and relaxed whereas SAXS data represent structure features within the samples under tensile load. 120

120

Ts 40 °C

Ts 30 °C Ts 40 °C

100

100

Ts 50 °C 80

Ts 70 °C

Ts 60 °C Ts50-Ts70 Ts60-Ts70

Ts 80 °C 60

Ts 50 °C Ts40-Ts70

Ts 60 °C

80

Enhanced Whitening

σ /MPa

σ /MPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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40

60

Ts40-T550 Ts40-Ts60 Ts50-T70-Ts50

40 20 20 0 0.0

0.5

1.0

1.5

2.0

2.5

0 0.0

εH

0.5

1.0

1.5

2.0

2.5

εΗ

Figure 5. True stress-strain curves of P4M1P sample stretched at different temperatures in one-step mode (left) and in multi-step mode (right). The dots and circles represent the positions of initial enhanced whitening of sample on the stress-strain curves.

Figure 5(left) registers the true stress-strain curves of the P4M1P sample stretched at different temperatures in one-step mode, including the initial strains and stresses of enhanced whitening (mode II cavitation) highlighted by red dots. The two critical parameters exhibited different dependencies on the stretching temperature. It can be revealed that the critical strains increased with elevating the deformation temperature while the critical stresses grew steadily in the lower temperature regime (30~60 °C) and reached a plateau value at 70 °C. This phenomenon is different from results40 observed in iPP previously, in which the critical stress kept nearly constant under all stretching conditions. As indicated in Figure 1 and Figure 2, the stress-whitening at small strains disappeared at 70 °C. One might consider that the reduction of critical stress of initiating mode II cavitation at large strains in lower temperature regime can 18


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be probably explained by the existence of voids generated at small strains. In order to clarify the physics behind this phenomenon, further experiments were conducted. The sample was stretched first at 40 °C to a strain just before the enhanced whitening, then heated up to 70 °C and stabilized at this temperature for 10 min under tension. During the heating process, thermal expansion of the sample reduced stress effectively. The sample was then further stretched at 70 °C, which deformed in a homogeneous way without necking. The true stress-strain curve was denoted as Ts40-Ts70, as showed in Figure 5 (right). Meanwhile, the strain and stress values, where the mode II cavitation was initiated, were marked with empty circles. To our surprise, the critical stress is nearly the same as the value stretching only in 70 °C. Two more measurements were conducted in a similar manner. The first stretching was performed at 50 and 60 °C, respectively, then heating up to 70 °C for second step of stretching (denoted as Ts50-Ts70 and Ts60-Ts70) showed similar tendency. These results imply that the existence of voids generated at small strains does not influence the initiation of mode II cavitation at large strain. In order to rule out the effect of the annealing at high temperature (70 °C), the sample was first stretched at 50 °C before enhanced whitening and heated up to 70 °C for 10 min and then stretched at 50 °C again (indicated as Ts50-T70-Ts50). The critical stress is almost the same as the value obtained from stretching the sample only at 50 °C. Additional experiments of stretching at 40 °C in the first step and then stretching at 50 or 60 °C (denoted as Ts40-Ts50 and Ts40-Ts60) in the second step were also performed. The critical stress of initiation of mode II cavitation (enhanced whitening) is in agreement with the value

19



stretching only at 50 or 60 °C. Clearly, the reduction of the critical stress at low temperatures is not caused by the mode I cavitation at small strains.

Figure 6. Selected WAXS patterns of P4M1P deformed at 30, 40, 50 and 70 °C taken at different strains as indicated on the graph. (Deformation direction: horizontal)

20


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Figure 7. The evolution of orientation degree of 200-reflection at different temperature as a function of strains.

WAXS experiments were performed in order to explore the origin of the mode II cavitation at large strains. Selected WAXS patterns of P4M1P deformed at different temperatures are given in Figure 6. The 2D WAXS patterns transform from isotropic rings to sharp spots, indicating the inner structure of the sample was highly oriented at the end of stretching. Figure 7 shows the evolution of the orientation order parameter of 200-diffraction of the samples deformed at different temperatures. The samples before deformation showed slight anisotropic due to the preparation procedure probably. Apart from the difference in the value of orientation degree, the evolution of parameter followed an essentially similar trend during stretching at different temperatures. However, the degree of orientation increased quickly for samples stretched at higher temperature. The variation of mass fraction for unoriented crystalline/amorphous phases (hc/ha) and oriented crystalline/amorphous phases (oc/oa) obtained from WAXS patterns during stretching is given in Figure 8. Apparent decrease of both unoriented parts and increase of both oriented parts illustrated an ordered aggregate structure gradually formed during stretching. The stretched P4M1P samples end up with a highly oriented hierarchical fibrillar structure by transformation of the original isotropic structure with spherulites upon stretching. The occurrence of the enhanced stress-whitening in the middle of the samples is considered as the criterion of the critical strains denoting the beginning of mode II cavitation at large strains, marked by colorful vertical lines in 21



Figure 8. It is worth noticing that the mode II cavitation at large strains appeared when the fraction of oriented amorphous phases grew to a certain extent. After this point, stretching of the fibrillar structure was started, leading to the slippage between adjacent microfibrils. This kind of slippage was limited mainly by the entangled chains and tie molecules connecting adjacent fibrils. The tie molecules can be broken upon further stretching. Such chain scission provided nucleation and growth of mode II cavities between fibrils of the system as they cause eventually the local amorphous network rapture, which further led to the collapse of whole stretched entangled network embedded by highly oriented fibrils However, the critical fraction of oriented amorphous phases was lower for samples stretched at 30 and 40 °C than for samples stretched at higher temperatures, indicating less number of load bearing tie chains at these two temperatures after stretching. Figure 9 shows the temperature dependency of loss factor of isotropic and oriented P4M1P samples measured at 3 Hz. As it has been reported54, there are two glass transitions which are suggested to arise from the presence of different types of amorphous materials. The first peak is associated with the general glass transition which shifts to higher temperatures for the stretched samples. Moreover, the peak position of the sample stretched at 80 °C is higher for the one at 50 °C. The whole glass transition range (20~60 °C) is consistent with the temperature regime of the reduction of critical stress for the initiation of mode II cavitation at large strains. At the temperatures near glass transition, some clusters of chain segments may be formed because of limited mobility. The chain segments within the cluster cannot be

22


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straightened, thus effectively bearing little force, which leads to the reduction of quantity of effective load bearing tie molecules. This results in a much higher stress for each molecule during stretching at glass transition range so that an obvious lower macroscopic critical stress for breaking such molecules was needed. The lower the temperature is, the weaker the mobility of the chain segment is, thus the lower the critical stress. 0.50

0.40 0.35

0.45 0.30

0.35

0.30

0.25

0.25

Ts 30 °C Ts 40 °C Ts 50 °C Ts 60 °C Ts 70 °C Ts 80 °C 0.0

φoa

φha

0.40

0.20 0.15 0.10 0.05

0.5

1.0

εH

1.5

2.0

2.5

0.0

0.5

1.0

0.0

0.5

1.0

εH

1.5

2.0

2.5

1.5

2.0

2.5

0.40

0.4

0.35 0.3 0.30 0.2

φoc

φhc

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.25 0.20

0.1 0.15 0.0

0.10 0.0

0.5

1.0

1.5

2.0

2.5

εH

εH

Figure 8. Change tendency of fraction of unoriented amorphous/crystal phase (left up /left bottom) and oriented amorphous/crystal phase (right up/right bottom) with increasing strains at different temperatures.

23



0.35

isotropic Ts 50 °C

0.30

Ts 80 °C 0.25

0.20

tan δ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.15

0.10

0.05

0.00 0

50

100

150

200

T /°C

Figure 9. Temperature dependency of loss factor of isotropic and oriented P4M1P samples measured at 3 Hz.

On the basis of our experimental findings, the deformation mechanism can be tentatively discussed in the following way. It has been generally accepted that the cavitation triggered around yield point was the mode I cavitation which was due to the competition between shear yielding and cavitation6. The block boundaries within crystalline lamellae with normal perpendicular to the tensile direction opened in width and formed the plate-like cavities passing through amorphous phase connecting several lamellae around yield point. The plate-like cavities changed in shape and tilted against the stretching direction after yield point. As the strain was increased, the polymer chains gradually oriented to the stretching direction, resulting in the reorientation of the mode I cavities with their normal perpendicular to the stretching direction33. These mode I cavities are then stabilized during further stretching. The

24


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extent of the mode I cavitation decreased as the stretching temperature was increased because of the activation of shear yielding as temperature increases35. The mode II cavitation at large strain was activated within highly oriented entangled network of P4M1P sample embedded by highly oriented fibrils. It can be linked to the amorphous network rupture due to breakage of interfibrillar tie molecules followed by disentanglement, which creates interfibrillar voiding. In such case, cavities with their long axis oriented along stretching direction showed up as was measured by USAXS scattering intensity distribution perpendicular to the stretching direction. The almost same value of the critical fraction of oriented amorphous phases indicates the occurrence of microfibrils slippage, leading to the breaking of tie molecules and inducing the collapse of the stretched entangled network. This explains the reason of an almost constant critical stress for the mode II cavitation at higher temperature (70~80 oC). However, the clusters of chain segments are formed near glass transition which leads to lower amount of effective molecules bearing the force. This leads to a much higher stress per interfibrillar tie molecule during stretching at lower temperatures (30~60 °C) so that an apparent lower macroscopic critical stress for breaking such tie molecules.

4. CONCLUSIONS In conclusion, the cavitation induced strain-whitening phenomenon triggered in P4M1P samples stretched at different temperaturewas investigated by in-situ USAXS technique. It was found that strong mode I cavitation activated around yield point appeared followed by mode II cavitation generated in highly oriented state. The 25



existence of mode I cavitation did not influence the occurrence of mode II cavitation. The mode II cavitation was proven to be related to the failure of the whole highly oriented entangled amorphous network initiated by the breaking of interfibrillar load bearing tie chains. The critical strains for activating such cavitation depended on the deformation temperature while the critical stress for this behavior grew steadily and reached a plateau with elevatingstretching temperature. A lower stress was needed for initiation of the mode II cavitation at glass transition temperature range due to the formation of clusters of chain segments which led to less amount of effective load bearing molecules and an apparent lower macroscopic critical stress for breaking such tie molecules. The structural change of cavities was analyzed quantitatively by model fitting. It was found that the quantity of cavities increased heavily while the size kept nearly constant during the propagation of the mode II cavitation indicating effective stabilization of such cavities in the system during stretching.

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected]

ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (51525305, 21134006).

Supporting Information Available: (The position of selected slices used for fitting, the 1D scattering intensity distribution profiles and corresponding fit at different 26


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strains for samples stretched at different temperatures, and the results of SEM measurements.) This material is available free of charge via the Internet at http://pubs.acs.org.

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Cavitation in Poly(4-methyl-1-pentene) during Tensile Deformation

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