Strain-Induced Crystallization during Relaxation Following Biaxial

Jun 22, 2015 - Stretching of PET Films: A Real-Time Mechano-Optical Study ... dimensions while true stress, true strain, in- and out-of-plane birefrin...
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Strain-Induced Crystallization during Relaxation Following Biaxial Stretching of PET Films: A Real-Time Mechano-Optical Study Mohamed K. Hassan and Mukerrem Cakmak* Polymer Engineering Department, University of Akron, 250 South Forge Street, Akron, Ohio 44325, United States ABSTRACT: The relaxation behavior of simultaneously and sequentially biaxially stretched PET films was studied at the rubbery state stretching temperatures. The primary objective was to investigate the influence of process conditions and the mode of deformation on the structural changes that take place in the stretched films. Using an instrumented biaxial stretcher, the films were stretched and held at the stretching temperature at fixed dimensions while true stress, true strain, in- and out-of-plane birefringences were monitored. The relaxation behavior was found to be dependent on the process prehistory including extent and rate of deformation. The behavior was divided into three regimes: Regime I, where the birefringence and strain always decrease and the material remains in the amorphous state. Regime II, where both the birefringence and strain first decrease while the film remains amorphous; then they start to increase when the first evidence of strain crystallization appears. Regime III, where strain-induced crystallization was already well-established during the biaxial deformation; both strain and birefringence increase during relaxation. This three-regime behavior was directly linked to the formation of strain-induced crystallization. Off-line Raman spectroscopy, DSC measurements, and X-ray WAXS patterns were used to follow the structure evolution and the transitions between these regimes.

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INTRODUCTION The orientation of PET has been extensively investigated in the literature, but there are very few studies that dealt with the relaxation following the orientation processes.1 Normally, three directions represent the dynamics of the stretching process; directions 1, 2, and 3 respectively correspond to machine direction (MD), which is the direction of the main stretching action, transverse direction (TD), which is perpendicular to the MD in the sample 2D plane, and normal direction (ND), which is the sample thickness direction in 3D. The level of orientation obtained at the end of the stretching is modified by relaxation especially if high stretching temperatures and low deformation rates are utilized. The recovery that occurs when the acting force is removed has been attributed to motions of the polymer chains in the amorphous regions,2 particularly in the absence of crystals and entanglements. The oriented chains try to recoil into the isotropic state, as this is the most energetically favorable state. The relaxation process may enhance the crystallization of the polymeric materials particularly when deformation process creates taut chains with unfavorable orientations adjacent to each other. More understanding of the relaxation mechanism should help in the efforts to understand the orientation-induced crystallization during processing. To quantify the relaxation parameters in the molten state, Doi and Edwards3 have used the rheological measurements to postulate the presence of three relaxation steps. The first one corresponds to a Rouse-like relaxation between entanglements in order to re-establish a constant chain density; this is followed by a relaxation, which is associated with the chain retraction © XXXX American Chemical Society

inside the deformed tube. The third step corresponds to the chain disengagement from the tube by a reptation process. These steps are characterized by relaxation times τa, τb, and τc, respectively.4−10 Applying the same technique on amorphous polymers, Tassin and Monnerie 4 have studied the relaxation of polystyrene (PS), using linear infrared dichroism to determine the Rouse, retraction, and reptation times. Boue et al.,8 Walczak and Wool,9 and Abtal and Prud’homme10 have reported for PS Rouse times of the order of 0.5−16 s, and the retraction times are of the order of 230−4000 s, depending on temperature. Going into the relaxation behavior of a semicrystalline polymer like PET stretched in the uniaxial constant width (UCW) mode, Lapersonne11 has estimated the values of τa to be around 10−2 s at 85 °C and 10−4 s at 97 °C. The temperature dependence of the Rouse modes is mainly due to the molecular friction coefficient. Using another approach to describe the relaxation behavior of the polymeric materials, Rui12 described two levels of relaxation: global chain and local segmental relaxation. The relaxation behavior of polymers upon being thermally treated is a rather complicated process for the global chain owing to the inter- and intramolecular interactions such as van der Waals forces, hydrogen bonds, and chain entanglements. It is relatively easy for local segments to relax because of their mobility. So, the relaxation of polymeric materials can be Received: March 6, 2015 Revised: May 2, 2015

A

DOI: 10.1021/acs.macromol.5b00388 Macromolecules XXXX, XXX, XXX−XXX

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that PET behaves as a rubber-like network when deformed at low to moderate draw ratios (λ ≤ 2.5), where PET will follow the Gaussian network model which predicts an increasing slope in the orientation function plotted as a function of λ, as given by Treloar:21

categorized into two: the orientation relaxation of coil as a whole and that of local segment of molecular chains. Upon relaxation at a temperature above the glass transition temperature (Tg), it was found that the birefringence abruptly diminishes. According to Qian,13 the segmental relaxation time of amorphous PET is on the order of seconds or even much shorter, depending on how long the local segment is involved in the molecular motion, while the global chain relaxation time is on the order of minutes or longer at the drawing temperature above Tg. Buckley et al.,14 in explaining the slippage of entanglements (reptation) at high temperatures and long times, argue that conformation stresses can relax by a process of axial diffusion of entire molecules, whereby they disengage from the topological constraint of other molecules. There are three components for the birefringence:36 one inplane, Δn12 = n11 − n22, and two out-of-plane, Δn23 = n22 − n33 and Δn13 = n11 − n33; two out of three are independent. Here n11, n22, and n33 are the principal refractive indices of the film in the machine (MD), transverse (TD), and normal (ND) directions, respectively. In-plane birefringence, Δn12, is calculated from the zero degree retardation values R0(t) and the true thickness d(t) as follows: Δn12 =

R 0(t ) d (t )

f=

(6)

where N is the number of freely jointed links between network entanglement points. But, Clauss and Salem22 have showed that when relaxation effects during the deformation are important (especially at low draw rates and high temperatures), this model is not applicable. Oultache and co-workers1 found that in all cases the relaxation is initially rapid as indicated by the sharp drop of ⟨P2(cos θ)⟩ at short times and then slows down to finally reach a quasi-plateau at longer relaxation times. Pearce et al.23 have stretched PET samples uniaxially at 80 °C at different draw rates, quenched them immediately after drawing in order to freeze in the orientation, and finally studied their relaxation by infrared spectroscopy. They have shown that the relaxation is rapid at low stretch ratios whereas straininduced crystallization prevents the PET relaxation when the polymer is stretched at λ ≥ 3. They also observed that the orientation process is rapid as compared to relaxation. Matthewsa et al.24 stated that for uniaxially drawn PET the development of strain-induced crystallization has a significant impact on the relaxation behavior. Online birefringence measurements, during the relaxation of PET drawn to different draw ratios, showed that at low draw ratios the orientation relaxes over long periods of time, while at higher draw ratios, when significant strain-induced crystallization has occurred, the orientation decreases over short times, of the order of 10 s, and remains constant thereafter. But they have seen also birefringence relaxation even after the onset of strain-induced crystallization. Jarrigeon25 suggested that the decrease of the relaxation time with orientation suggests that the size of the moving units decreases. Rahmat26 correlated the larger value of relaxation time in the rubbery state with better thermal stability or smaller molecular mobility. They also expected a larger relaxed amorphous form upon relaxation from a high stretching rate, where a high stretching rate facilitates molecular relaxation after stretching. Using the stress-birefringence measurements, Ito27 and Ryu28 found that when relaxing the simultaneously biaxially stretched PET samples from deformation levels, where the stress-optical law holds, the birefringence and stress decreased along a straight line. When the relaxation is observed just above the point at which the deviation from the stress-optical law is detected, the stress decreased; however, the birefringence first decreased but eventually increased with time. At high draw ratio λ =3.5, the birefringence increased during the stress relaxation process. In other words, the deviation point represents the starting of spontaneous molecular orientation. The spontaneous molecular orientation is usually associated with the crystallization process. Boyce29 reached the same conclusion that after the strain-induced crystallization there is an arrest in viscous flow, and this arrest correlates with network stretching. Strain-induced crystallization acts to lock-in the highly oriented structure and leads to the extensive permanent deformation upon unloading.

(1)

The out-of-plane birefringence Δn23 is calculated from both the zero degree retardation values, R0(t), and the 45° retardation values, R45(t), using Stein’s equation as follows: Δn23

1 =− d (t )

(

R 0(t ) − R 45(t ) 1 −

sin 2 45 n̅ 2

sin 2 45 n̅ 2

0.5

)

(2)

where 1.57 is taken as the average refractive index n̅ for PET; the 45° retardation was measured at the green light wavelength of 546 nm. The other out-of-plane birefringence, Δn13, is calculated as follows:

Δn13 = Δn12 + Δn23

(3)

Normally, the relaxation is carried out under constrained or fixed dimensions. In investigating the behavior of PET in the unconstrained state, Terada et al.15 and Gupta et al.2 have studied the crystallization and thermal shrinkage of PET at different temperatures and draw ratios. They have shown that beyond a stretch ratio, λ = 3, PET develops a strain-induced crystallization which impedes the shrinkage, where crystals act as physical cross-links, preventing the amorphous chain segments from assuming a random coil configuration, in agreement with previous results reported by Nobbs et al.16 Ward17 and Samuels18 related the birefringence of an amorphous polymer (Δ) to the second moment of the orientation function, ⟨P2(cos θ)⟩, by Δ = Δ0⟨P2(cos θ )⟩

⟨P2(cos θ )⟩ = f =

Δ 3 cos2 θ − 1 = Δ0 2

Δ 3 cos2 θ − 1 1 ⎛⎜ 2 1⎞ = = ⟨P2(cos θ )⟩ = λ − ⎟ ⎝ Δ0 λ⎠ 2 5N

(4)

(5)

where Δ0 is the intrinsic birefringence of the sample, which is equal to 0.275 for amorphous PET,19,20 f is the orientation function, and θ is the angle between the chain axes and fiber axis. Using this approach, several authors15,16,23 have suggested B

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Macromolecules In transferring from the amorphous state into the crystalline state, PET passes through an intermediate unstable mesophase. Havens et al.30 using multiple pulse dipolar decoupling spectroscopy techniques found that three domains, i.e., crystalline, oriented mesophase, and amorphous phase, were present in an oriented sample each with very different chain segment mobilities. On investigating the drawing behavior of semicryatalline PET, Dargent31 confirmed the coexistence of a completely disordered amorphous and an ordered mesomorphic phase. Also, other authors32−34 have considered that three phases, i.e., crystalline regions, are composed entirely of trans conformer, amorphous regions containing a mixture of trans and gauche conformers, and a mesophase which is also composed of trans conformers, only exist in strain-induced crystallized polymers. The relaxation process gives the chance for the amorphous oriented chains to align themselves in a way that favors the formation of the mesophase leading to the subsequent crystallization. During the course of stretching processes such as in the tenter frame, etc., oriented films are transported from station to station while constrained. During these stages, materials undergo stress relaxation and related other physical changes. In all of the above studies, the connection between the mechanical behavior and the optical behavior was missing. This paper will introduce for the first time the connection between the state of chain orientation, mechanical and optical relaxation, crystalline order, stress−strain behavior, and their implications on the overall morphology of PET films undergoing relaxation from the simultaneous and sequential biaxially oriented state above the glass transition temperature.

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WT =

t

σ :D dt

(8)

where σ is the stress tensor and D is the deformation rate tensor. For the case of the biaxial stretching condition, this reduces to

WT =

∫0

t

̇ + σ22ε22 ̇ ) dt (σ11ε11

(9)

where σ11 and σ22 are the true stresses in machine direction (MD) and transverse direction (TD), respectively; ε̇11 and ε̇22 are the strain rates in MD and TD directions, respectively.

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EXPERIMENTAL PROCEDURE FOR OFF-LINE MEASUREMENTS

To characterize the structure at several different length scales, we employed Raman spectroscopy, wide-angle X-ray diffraction, and differential scanning calorimetery techniques. Raman Spectroscopy. Raman spectroscopy using HoloProbe VPT laser Raman system manufactured by Kaiser Optical Systems was used to follow up the intensity of the spectral changes induced by the relaxation process; the excitation laser is operated at 780 nm. The reference peak at 793 cm−1, the peak at 886 cm−1 corresponding to the gauche conformation, and the peak at 998 cm−1 corresponding to the trans conformation were followed up. The ratio of the intensity of the 998 cm−1 to the 793 cm−1 (I998/I793) was taken as a measure for the gauche−trans conformational change and hence the crystallinity evolution and amorphous ordering in the films. A total accumulation time of 1 h was used.37 Differential Scanning Calorimetry. The stretched samples were thermally analyzed using a TA Instruments model 2000 differential scanning calorimeter. The heating was in the temperature range of 20 to 300 °C at the rate of 20 °C/min and equilibration at 35 °C in a dry nitrogen environment. From the DSC heat flowchart for each sample, the midpoints of the glass transition temperature, Tg, the cold crystallization temperature, Tcc, and the melting point, Tm, were determined. Also, the area under the cold crystallization peak, ΔHcc, and the heat of fusion under the melting peak, ΔHm, were determined to evaluate the effect of the relaxation on the crystallinity evolution of the samples. The heat of fusion of 100% crystalline polymer was taken as 120 J/g for PET.38 X-ray Diffraction Studies. The WAXS patterns were taken using a Rigaku R-Axis-IV equipped with image plate detecting the X-ray intensity. This machine was operated at 50 kV and 200 mA. The X-ray was monocromatized with a nickel filter to obtain the Cu Kα radiation (1.542 Å). The sample to image plate distance was kept at 214 mm. The X-ray samples were prepared from the relaxed films by cutting the films into strips then stacking them together using epoxy resin to form a cube of 2 × 2 × 2 mm. The X-ray patterns were taken through the normal direction (ND) to the film surface and through the machine direction (MD) using exposure time of 15 min.

EXPERIMENTAL PROCEDURES

Material. The material used in this study was poly(ethylene terephthalate) (PET) in the form of commercial film provided by M and G polymers with an intrinsic viscosity of 0.80 dL/mg, corresponding to a number-average molecular weight of 28 500. The solvent used was phenol/tetrachloroethane 60/40; using Mark− Houvink relationship, we can calculate the number-average molecular weight as follows:

[η] = kM̅ n a

∫0

(7)

For the solvent system used, k = 7.5 × 10−4 and a = 0.68.35 Film Stretching and Relaxation Procedure. An instrumented custom-built biaxial stretcher was used in this study. The details of this machine were described elsewhere.36 With available imaging sensor as well as visible spectrometers, this machine is able to track true strain, in- and out-of-plane birefringence, and true stresses during the course of deformation history. Using this machine, films were stretched in the simultaneous biaxial, sequential biaxial, and uniaxial constant width (UCW) modes at the temperature of 95 °C (Tg + 15 °C). The stretching rate of 0.125 s−1 (15 mm/s) was used in order to simulate the conditions of the industrial production process. In the simultaneous biaxial condition four stretch ratios were used: 1.5 × 1.5, 2 × 2, 2.5 × 2.5, and 3 × 3. In the sequential biaxial mode the used ratios were 1.5 × 1.5, 1.75 × 1.75, 2 × 1.5, 2 × 2, 2.5 × 1.5, 2.5 × 2, and 3 × 1.25. In the UCW mode, the used ratios were 1.5 × 1, 2 × 1, 2.5 × 1, and 3 × 1. After the completion of the stretching process, the samples were held inside the heating chamber by the clamps at constant temperature and fixed dimensions for 2 h, while the strain, stress in-plane, and out-of-plane birefringences were monitored. After the completion of the relaxation process, the samples were cooled down below the glass transition temperature and then taken out of the clamps for further off-line structural measurements. Work Function. The total work put into the material during stretching is calculated using the relationship

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RESULTS AND DISCUSSION Regime Behavior during Stretching. During stretching of PET films, the initial stress and birefringence behavior is linear, where the stress has a linear relationship with birefringence and the stress optical rule (SOR) holds (regime I). If the films are sufficiently stretched beyond that limit, this linear stress optical behavior gives way to nonlinear behavior that manifested itself as positive deviation (regime II) from the previous regime I. At this stage “chain tautness” begins to establish, and some degree of ordering also observed in the structure and a physical network starts to forma process akin to percolation. Upon further stretching, and once the sufficient “slack“ is taken from the system, the third regime is reached where finite extensibility brings about saturation of birefringence while stress continues to increase (regime III). The relaxation behavior of the PET stretched films depends on the C

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Macromolecules regime from which the relaxation started. Figures 1 and 2 show the stress−birefringence behavior of the simultaneously and

Figure 3. True stress behavior during stretching and relaxation of simultaneous biaxial stretching at different stretch rates and ratios. Figure 1. Stretching behavior and regimes of simultaneously biaxially stretched PET films at the rate of 0.125 s−1 and different stretch ratios.

Figure 4. True stress behavior during stretching and relaxation of sequential biaxial stretching at different stretch rates and ratios. Figure 2. Stretching behavior and regimes of sequentially biaxially stretched PET films at the rate of 0.125 s−1 and different stretch ratios.

sequential biaxial stretching, we could not observe a leveling off in the principal stresses for any stretching rate or ratio, as the stresses relax. Stress Relaxation Time. Brinson39 proposed the modified Bingham model to calculate the stress relaxation time of epoxy adhesive with carrier cloth. In order to investigate the relaxation time behavior at different stretch rates and ratios, the modified Bingham model39 was used to calculate the relaxation times. The relaxation behavior of the Bingham model is described by the equation

sequentially biaxially stretched samples respectively at the rate of 0.125 s−1 and different stretch ratios indicating the end point of each regime (indicated by triangles). Mechanical Behavior. True Stress Behavior. Figures 3 and 4 show the true stress evolution during stretching and relaxation for simultaneously and sequentially biaxially stretched samples, respectively, at different stretch rates and ratios. When relaxing the samples that were stretched at high stretching rates, the stress relaxation is rapid just after the termination of deformation, while this is slower following deformation at low stretching rates. In the case of the simultaneous biaxial stretching before the onset of strain induced crystallization (regime I) the stress relaxation continues throughout the relaxation time observed. After the onset of crystallization has been passed during the stretching step, relaxation stage proceeds with rapid relaxation that levels off quickly. This behavior could be observed in both the 0.125 and 0.0125 s−1 stretching rates. While at the lowest rate of 0.001 25 s−1 the stress continues to relax to zero without showing any sign of leveling off. This is a result of the samples not experiencing a significant crystallization. In the case of the

σ(t ) = (σi − θ )e−(E / μ)t + θ

(10)

where σ(t) is the relaxation stress at any time t and σi is the stress value at the start of relaxation, which is equal to the final value at the end of the stretching phase. E is the elastic modulus, μ is the viscous modulus, and θ is the final stress value at the end of relaxation phase. The value of μ/E is called the relaxation time, T. When μ = E, which means T = 1, the material is said to be relaxed, which indicates that the elastic forces are now equivalent to the viscous forces. This condition gives the following form for calculating the relaxation stress (note: e, the base for the natural logarithm, is equal to 2.72): D

DOI: 10.1021/acs.macromol.5b00388 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules σ (t ) =

σi − θ +θ e

correlated the larger value of relaxation time in the rubbery state with better thermal stability or smaller molecular mobility. Also, they expected a larger relaxed amorphous form upon relaxation from a high stretching rate, which facilitates higher molecular relaxation after stretching, as shown in Figure 5. Two factors that control the stress relaxation time are the stress level and the crystallinity level. The decrease in the relaxation time with the increase of the stretch rate and ratio is most probably due to the fast recovery of the elastic forces upon completion of the stretching process, which represents the spring element in the material. The higher the stretching rate, the less chance for the elastic recovery to occur during the stretching. Upon the stoppage of the deformation process these forces are recovered in a rate comparable to the stretching rate. Also, the higher the stretch ratio, the higher the extension of the elastic components in the system, which also causes the shorter relaxation times. The second factor is the crystallinity level. When the material is transformed into the semicrystalline state, the crystalline regions act as junctions of the network transferring the stresses throughout the material. In the case of the sequential biaxial samples as shown in Figure 6 the two factors, the stress level and the crystallinity level, control the relaxation time according to the weight of each factor in the different stress-optical regimes. The MD relaxation time decreases with the TD stretch, up to the point of the strain-induced crystallization (the end of regime I). Up to that point, the crystallinity plays the dominant role as crystallinity increases with TD stretch, and there is not much change in the stress level. After that point (in regimes II and III), TD stretch causes first increase in the relaxation time (slower relaxation), then decrease (faster relaxation) as a result of first decrease in both the stress level and crystallinity, and then increase in both during further TD stretch. In case of the TD relaxation time, TD stretch causes an increase in the stress level in the TD direction up to the end of regime I (area ratio 2 × 2), where the relaxation time is always decreasing. Beyond the onset of strain-induced crystallization (regimes II and III) relaxation time may be influenced more either by the maximum stress level reached or the maximum crystallinity level reached depending on the final stretch area (λMD × λTD). True Stress−True Strain Behavior. Figures 7 and 8 show the stress−strain behavior of the simultaneously and sequentially

(11)

Relaxation time is the time when the stress is equal to σ(t) calculated from the last expression. Figure 5 shows the

Figure 5. Relaxation time for simultaneous biaxial samples stretched at different stretch ratios and rates.

relaxation time behavior of the simultaneously biaxially stretched then relaxed samples, while Figure 6 shows the relaxation behavior of the sequentially biaxially stretched then relaxed samples in MD and TD directions at different stretch ratios at stretch rate of 0.125 s−1.

Figure 6. Relaxation time for sequential biaxial samples in MD and TD directions at different stretch ratios at stretch rate of 0.125 s−1.

It was shown that for both the simultaneous and the sequential samples increasing the stretch area (λMD × λTD) and/or the stretch rate causes faster relaxation as observed by the drop in the relaxation time, in agreement with Jarrigeon.25 From the stress point of view, the relaxation rate was found to depend on the stress value from which the relaxation process starts; the higher the initial stress value, the faster the relaxation process (shorter relaxation time). The decrease of the relaxation time with orientation suggests that the size of the amorphous segments capable of moving has been decreased. Also, this is in agreement with Rahmat,26 who

Figure 7. Stress−strain relationships for the simultaneously biaxially stretched and then relaxed samples at different stretch rates and ratios. E

DOI: 10.1021/acs.macromol.5b00388 Macromolecules XXXX, XXX, XXX−XXX

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The behavior of the sequential stretching was different. In the case of the in-plane birefringence, after MD stretching, stretching in the TD direction causes a fast drop in the inplane birefringence, suggesting that there is a significant “loosening” of the structure, as shown in Figures 10 and 11.

Figure 8. Stress−strain relationships for the sequentially biaxially stretched and then relaxed samples at different stretch rates and ratios.

biaxially stretched samples, respectively, at different stretch rates and ratios. Relaxing from regime I at low stretch ratios before network formation causes the stress and strain to relax continuously. Going into regime II, the strain first decreases, and when a “connected” network starts to form, we could observe increase in the strain. At high stretch ratios and after the deviation from the stress optical role (regime III), the strain no longer decreases, but slightly increases. In the case of the simultaneous biaxial stretching at the rate of 0.001 25 s−1 a very small increase in strain at the end could be observed if the relaxation process was started at higher stretch ratios, while in sequentially stretched samples at the same rate, strain always decreases for all ratios. Optical Behavior. We have studied the optical behavior of the films during relaxation stage. As shown in Figure 9, in

Figure 10. In-plane birefringence for sequentially biaxially stretched samples at different rates and stretch ratios.

Figure 11. Out-of-plane birefringence for sequentially biaxially stretched samples at different rates stretch ratios.

The density measurements indicated an initial decrease upon TD stretching, following MD stretching that develops sufficient crystallinity.40 Starting the relaxation process after the completion of the TD stretch, the in-plane birefringence either remains nearly constant (regime I) or goes through a minima (saddle) point then increases again (regime II) or increases all the way up (regime III). Time to the saddle point was shorter for the uniaxial constant width (UCW) samples than the biaxial samples for both the in-plane and out-of-plane birefringences. Mechano-Optical Behavior. Stress−Birefringence Relationship. Relaxing from regime I causes a continuous decrease in both the stress and birefringence for all rates and modes (Figures 12 and 13). Relaxing from regime II causes first a decrease in birefringence and then increase, but stress always decreases. In regime III we observe only increase in the birefringence during the relaxation process. When relaxing from regime I, the stress−birefringence relationship follows the linear stress−optical rule observed during the stretching stage.

Figure 9. Out-of-plane birefringence for simultaneously biaxially stretched samples at different rates and stretch ratios.

simultaneous stretching, relaxing in regime I, the out-of-plane birefringence decreases continuously. Relaxing from regime II, which is a deformation level just above the onset of crystallization (2 × 2 condition), we observe first a decrease in the birefringence to a minimum and then starts to increase again. After the onset of crystallization (regime III), the birefringence does not experience any decrease but increases steadily during the whole relaxation time. F

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Figure 12. Stress−birefringence relationships for the simultaneously biaxially stretched and then relaxed samples at different stretching rates and ratios.

Figure 14. Relationship between out of plane birefringence and total work during stretching and relaxation of sequentially biaxially stretched samples at different stretch rates and ratios.

Figure 13. Stress−birefringence relationships for the sequentially biaxially stretched and then relaxed samples at different stretching rates and ratios.

Figure 15. Trans conformation evolution with total work level during stretching and relaxation of the simultaneous biaxially stretched then relaxed samples at different stretch rates and ratios.

Relaxing from regimes II and III, there is always a stress and birefringence shift, causing the material to follow another route than the one during the stretching stage. Work−Birefringence Relationship. Figure 14 shows the relationship between birefringence and total work put into the material during stretching and relaxation for sequentially biaxially stretched samples at different stretch rates and ratios. At low deformation levels there is a nonlinear, yet universal behavior. Deviations do occur at high deformation levels and during relaxation stages. The work−birefringence relationship are in three regimes. Initial nonlinear regime I followed by a linear regime II that ends with the onset of strain-induced crystallization, followed by a linear regime III with a steeper slope. Both the birefringence and work decrease in regime I. When relaxing regime II samples, both the birefringence and work decrease then they start to increase. Relaxing regime III samples causes both the work and birefringence to increase. Off-Line Characterization of the Samples. Spectroscopy Analysis. Figure 15 shows the relationship between the total work put into the material during the stretching and relaxation processes and the evolution of the trans conformation with respect to the reference peak for the simultaneously biaxially

stretched films up to the stretch ratio of 3 × 3 for different rates. Substantial changes in the vibrational spectra with increasing the stretch rate and ratio were detected. It is shown that there is an increasing trend for the I998/I793 ratio with both the stretch ratio and rate. The figure also shows that there is a considerable difference between the rate of 0.125 s−1 and the other two rates. For the rate of 0.001 25 s−1 the change in the trans content was not high as compared with the other two rates between the start of the stretch and the end. The 0.0125 s−1 rate experienced a nearly constant step increase in the trans content with increasing the stretch ratio with a trend to level off at the high stretch ratios. The 0.125 s−1 experienced also a steady increase with the stretch ratio showing a considerable difference between the 1.5 × 1.5 and the 2 × 2 ratios. At the end this rate, the samples showed a high increase in the trans content. Except for minor rate dependency, the overall trans conformer content correlates quite well with the work, signifying that work put into the material plays a significant role in gauche−trans transformation. Comparing the trans content in the as-stretched samples and the relaxed samples, we find the intermediate stretch ratio samples had the highest increase in trans conformers, while the G

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Macromolecules Table 1. Simultaneous Biaxial Samples’ Trans Content in Stretched and Then Relaxed Samples rate (s−1) 0.00125

0.0125

0.125

ratio

stretched

relaxed

% increase

stretched

relaxed

% increase

stretched

relaxed

% increase

1.5 × 1.5 2×2 2.5 × 2.5 3×3

0.14671 0.16244 0.17317 0.21303

0.15232 0.17890 0.18783 0.22734

3.825 10.136 8.463 6.714

0.17908 0.26108 0.36451 0.43823

0.20570 0.36474 0.49864 0.53127

14.867 39.705 36.797 21.231

0.20260 0.44184 0.53670 0.82920

0.21892 0.59159 0.71659 0.85620

8.056 33.893 33.517 3.256

ratio of 2 × 2 (regimes II and III), TD stretch started to cause an increase in the trans content with increasing the work input into the material. An interesting observation is that in regimes II and III and where the total work input into the material is nearly equal at different stretch ratios, the films exhibited nearly the same trans content. Also, as the total work input into the films in the case of the simultaneous biaxial stretching is higher than that in the case of the sequential biaxial stretching, the simultaneous samples contained higher trans isomer than the sequential samples. Thermal Behavior. The DSC thermograms for the simultaneously biaxially stretched samples at different stretch rates and ratios are shown in Figure 17. In the case of the 0.125

low and high stretch ratio samples exhibited smaller increase in trans content as shown in Table 1. The intermediate stretch ratio samples have both the orientation and crystallinity levels that enabled them to go to a higher regime ranking (from I to II) upon relaxation. This is due to the ability of the samples to attain higher crystallinities as not much of their chains crystallized during the stretching process and the high value of orientation gained during stretching. The amorphous low stretch ratio samples lack both the orientation and crystallinity level which can enable them to have higher degree of trans content. In the case of the high stretch ratio samples, the lower increase in the trans content was due to the existence of the already formed crystalline domains during the stretching process, which may lock in a large amount of oriented amorphous chains in unfavorable orientations with respect to neighboring chains. This prevents the amorphous chains from moving into crystalline domains reducing the crystallizability. Figure 16 shows the relationship between the work put into the material and the evolution of the trans conformation with

Figure 17. DSC thermograms for simultaneously biaxially stretched and then relaxed samples at different stretch rates and ratios.

s−1 rate, the films show a large movement in the midpoint of the glass transition temperature, Tg, from around 79 °C in the low stretch ratios to about 90 °C in the 3 × 3 ratio. While in the case of the 0.0125 and the 0.001 25 s−1 rates, there was not much change in Tg. A cold crystallization temperature, Tcc, around 142 °C and a melting temperature, Tm, around 254 °C were observed in the low stretch ratios for all rates. With increasing the stretch ratio, the cold crystallization exotherm moves to lower temperatures approaching Tg, while getting more flattened at the high rates. The peak position of the melting endotherm does not change significantly, but the shape of the peak varies. At the lowest rate of 0.001 25 s−1 the area under the cold crystallization exotherm was the largest compared to the other rates. This exotherm becomes narrower with increasing the stretching rate and ratio. The DSC thermograms for the rate of 0.001 25 s−1 exhibited the widest breadth in the melting endotherm; this breadth became narrower with increasing the rate. Figure 18 shows the DSC

Figure 16. Trans conformation evolution with total work level during stretching and relaxation of the sequentially biaxially stretched and then relaxed samples at different stretch rates and ratios.

respect to the reference peak for the sequentially biaxially stretched films up to the stretch ratio of 3 × 1.25 at different stretch rates and ratios. As shown in the figure, the stretch rate and ratio have a significant effect on the trans content of the films. It is shown that there is an increasing trend for the I998/ I793 ratio with both the stretch ratio and rate. Always MD stretching causes an increase in the trans content. TD stretching caused a continuous decrease in the trans content for the rate of 0.001 25 s−1 for all stretch ratios. While, for the rates of 0.0125 and 0.125 s−1, TD stretch caused a decrease in the trans content up to the stretch ratio of 2 × 2 (regime I). Above the stretch H

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ratio. The highest percentage was for the highest stretching rate. The rates of 0.125 and 0.0125 s−1 show a tendency to level off in the crystalline content, while the 0.001 25 s−1 rate did not show that. As shown in the figure, the higher the work input into the material, the higher the crystalline content in it. The low and intermediate stretch ratio samples exhibited the highest increase in crystallinity, while the high stretch ratio samples exhibited lower degree of crystallinity increase. Figure 20 shows the evolution of the samples’ crystallinity with the work input into the material at different stretch rates

thermograms for the sequentially biaxially stretched and then relaxed samples at different stretch rates and ratios.

Figure 18. DSC thermograms for sequentially biaxially stretched and then relaxed samples at different stretch rates and ratios.

Increasing λMD × λTD causes increase in the melting peak area as an indication of increased crystallinity. Increasing the area stretch ratio causes in general a decrease in the area under the cold crystallization temperature and movement of its peak temperature closer to Tg. In regime I, TD stretch causes the movement of the cold crystallization peak to a higher temperature, while going into regimes II and III we did not observe a significant change in this peak position. Increasing the stretch ratio causes the melting peak to be larger, indicating a higher crystalline fraction. The area under the crystallization exotherm decreases with deformation. Figure 19 shows the percentage crystallinity of the simultaneously biaxially stretched then relaxed samples for different stretch rates and ratios. In general, the crystalline fraction for the relaxed samples is higher than that of the asstretched samples. There is an increasing trend for the percentage of crystallinity with both the stretch rate and

Figure 20. Evolution of samples’ crystallinity with the work input into the material for sequentially biaxially stretched and then relaxed samples at different stretch rates and ratios.

and ratios. For the low stretch ratios TD stretch causes increase in the crystalline content. For the intermediate stretch ratios up to the stretch ratio of 2.5 × 2, TD stretch causes first a decrease in the crystallinity and then increase; after that, more TD stretch causes again increase in the crystalline content. It is shown that there is a significant effect for the stretching rate on the crystallization rate and the percentage of crystallinity in the samples. The higher the stretching rate, the higher the crystallinity increase rate and the higher the percentage of crystallinity. In general, the higher the work input, the higher the crystalline fraction. In both the simultaneous and the sequential samples, the intermediate stretch ratio samples exhibited the highest increase in crystallinity, while the very low and high stretch ratio samples exhibited lower degree of crystallinity increase for the same reasons discussed above for the increase in the trans content. WAXS Studies. WAXS diffraction patterns for the simultaneously biaxially stretched and then relaxed samples at different stretch rates and ratios are shown in Figures 21 and 22. The WAXS patterns are presented for both the as-stretched and the relaxed stages at selected conditions in order to illustrate the key stages behavior. For all stretching rates, the WAXS patterns did not show any sign of crystallization in regime I, where linear stress optical behavior is observed. Relaxing from regimes II and III causes intensification and sharpness in the crystalline peaks, comparing the as stretched and the relaxed patterns. The effect of relaxation was pronounced in the case of the 0.125 s−1. For the rate of 0.001 25 s−1 there was not much change in the WAXS patterns when comparing the as-stretched and the relaxed patterns except for the 3 × 3 ratio, which started to show a very weak crystalline diffractions. The

Figure 19. Percentage of crystallinity of the simultaneously biaxially stretched and then relaxed samples for different stretch rates and ratios. I

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Figure 23. WAXS patterns for the as stretched and the relaxed sequentially biaxially stretched samples at the rate of 0.001 25 s−1 and different stretch ratios.

Figure 21. Structure evolution with stretch ratio for simultaneously biaxially stretched then relaxed samples. Stretched at the rate of 0.001 25 s−1 and 95 °C.

crystalline diffractions upon relaxing the 2 stretch ratio series (2 × 1, 2 × 1.5, and 2 × 2) in the case of the 0.125 s−1 stretching rate and from the 2.5 series in the case of the 0.0125 s−1 rate. This was not seen in the case of 0.001 25 s−1 stretching rate, where the sample experienced only relaxation in both the stress and birefringence. This means a part of regime I could crystallize upon relaxation but just at the high stretching rates. In relaxing from regimes II and III, the crystalline peaks became intensified as a sign of better orientation and higher crystalline order. The X-ray patterns taken at the intermediate stages for the samples that experienced a minima in the birefringence as in the case of the 2 × 1 and 2 × 1.5 samples at the rate of 0.125 s−1 showed no distinct crystalline peaks at those stages, while on further relaxation the samples showed crystalline diffractions while birefringence increased. The samples showed this behavior needed a longer time for the crystallization from the oriented state. The time and relaxation temperature enabled the chains to work cooperatively in registering into crystalline domains. In all films with the lowest rate used 0.001 25 s −1 crystallization did not take place even after relaxation from all ratios. In these samples relaxation dominates the orientation effects.

Figure 22. Structure evolution with stretch ratio for simultaneously biaxially stretched then relaxed samples. Stretched at the rate of 0.125 s−1 and 95 °C.

relaxation helped in better ordering for the crystalline entities in regime II and growth observed in regime III, where the distinct crystalline peaks became more pronounced. In all cases, the patterns taken with the X-ray in normal direction (ND) indicate that these films exhibit in-plane isotropy. The X-ray patterns taken at the intermediate stages for the samples experienced a minima in the birefringence as in the case of the 2.5 × 2.5 sample at the rate of 0.0125 s−1 and the 3 × 3 sample at the rate of 0.001 25 s−1 showed that the original crystalline peaks in the as-stretched samples became diffuse and decrease in sharpness as a sign of decreasing orientation and crystallinity. The WAXS diffraction patterns for the as-stretched and the relaxed sequentially biaxially stretched samples at different stretch rates and ratios are shown in Figures 23 and 24. The through views show better alignment for the (010) planes on the equator, an increase in λTD causes the spreading of those diffractions as observed in the case of 2.5 × 1.5 and 3 × 1.25. Increasing λTD more transfers the diffractions into the equal biaxial form in the shape of rings for both the (010), (01̅1), and (100) planes. The main observation is the appearance of the

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DISCUSSION In the rubbery deformation state, the polymer orientation involves both a viscous flow due to the slippage of molecules and an elastic chain alignment. Stretching at a low rate increases the chain slippage contribution at the expense of the chain alignment, resulting in low orientation values. At high stretching rates, the chain orientation clearly dominate the relaxation, resulting in higher orientation values. At the start of relaxation process, the initial relaxation process is fast, and this is attributed to the segmental disorientation, which relaxes almost totally in less than 1 min when the samples are held in the rubbery plateau. After that the chain extension starts to relax41 as evidenced by the slower decrease in birefringence, stress and strain as a recovery in the length. The relaxation behavior of PET samples stretched in the rubbery region at different rates and stretch ratios can be classified into three regimes: J

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Figure 24. WAXS patterns for the as stretched and the relaxed sequentially biaxially stretched samples at the rate of 0.125 s−1 and different stretch ratios.

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CONCLUSIONS In this study, we confirm that PET films exhibit three distinct regime behavior in their mechano-optical behavior upon stretching from their amorphous precursors at rubbery temperatures. The material remains amorphous in regime I following linear stress optical law during stretching and relaxation stages. At intermediate deformation levels (regime II), the polymer chains may remain amorphous initially, but during relaxation stage they begin to exhibit strain induced crystallization. This occurs as the adjacent oriented amorphous chains become locally aligned relative to each other and form crystalline regions. This phenomenon appears as a demarcation point on evolution of birefringence, and once the crystalline domains start to form, the previously decreasing birefringence starts to increase while stress continues to decrease. We observe that a minimum degree of orientation is required for the chains to start crystallizing during relaxation. When the relaxation starts from a point where the material has developed a well-connected network during deformation (regime III), the birefringence does not experience any relaxation but starts to increase from the point of relaxation.

Regime I. In this regime, birefringence−stress relationship is linear during stretching and relaxation following the linear stress optical law. The material remains amorphous and low levels of trans conformers are observed (∼9%). In this regime the strain recovery is high as the chains retract almost free of constraints. The decreasing level of birefringence accompanies the abrupt decrease of strain. Regime II. The characteristics of regime II are initial decrease in the birefringence and recovery of the strain, after which both the birefringence and strain increase again although the stress continues to relax. The initial decrease in birefringence and strain is primarily caused by the relaxation of the oriented amorphous chains. The onset of crystallization and the generation of the crystalline sites start increasing the population of crystal sites adding to the overall connected physical network that slow down and stop the relaxation of remaining oriented population chains. Regime III. Regime III is characterized by simultaneous increase in birefringence and strain, while the stress decreases. This occurs in the samples stretched to well beyond the onset of the strain-induced crystallization and thus well beyond the validity of the linear stress optical rule. At this stage the relaxation of oriented amorphous chains is highly suppressed by well-developed physical network composed of crystalline domains and entanglements. Many authors observed increase of the orientation function, which indicates greater orientation of the trans units in the draw direction.24 At this stage, the trans content increases but to a lower extent than regime II. It should be noted here that even the amorphous chains may have a little degree of relaxation; the crystalline domains do not experience this relaxation, but they keep on growing in size. Stopping the deformation, which some times frustrates the network formation (especially when stretching at high rates), gives the chance for the oriented molecular chains to work cooperatively on aligning themselves into crystalline domains, leading to formation of oriented amorphous domains and increase in birefringence.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (M.C.). Notes

The authors declare no competing financial interest.

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REFERENCES

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