Shear and Elongational Flow Properties of Long-Chain Branched Poly

Publication Date (Web): June 23, 2014. Copyright © 2014 American .... Experimentally Calibrated Random Walk of Branched Polymers: A Pragmatic Approac...
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Shear and Elongational Flow Properties of Long-Chain Branched Poly(ethylene terephthalates) and Correlations to Their Molecular Structure Michael Har̈ th,* Joachim Kaschta, and Dirk W. Schubert Institute of Polymer Materials, Friedrich-Alexander-University Erlangen-Nuremberg, Martensstraße 7, 91058 Erlangen, Germany S Supporting Information *

ABSTRACT: Reactive processing with low-molar-mass modifiers is a well-known method to create long-chain branched (LCB) structures in a poly(ethylene terephthalate) (PET) melt. However, less is known about the elongational flow properties of LCB-PET. Therefore, the aim of this contribution is (a) to generate LCB molecules and (b) to evaluate the influence of the branching level on the transient elongational behavior. For this purpose, a commercial, linear PET and different contents (0.1− 0.3 wt %) of the tetrafunctional modifier pyromellitic dianhydride (PMDA) were reactively processed. All samples were analyzed by size exclusion chromatography coupled with a light scattering device and characterized by shear and elongational rheometry. It was found that the molar mass distribution of the modified materials exhibit a high molar mass shoulder, leading to an increase of the weight-average molar mass and a broadening of the molar mass distribution. Moreover, the Mark−Houwink plot of the modified materials displays deviations from the power law toward lower intrinsic viscosities, which indicate the existence of LCB molecules. The shear viscosity shows a pronounced shear thinning behavior and a remarkable increase at low frequencies compared to the linear PET. Considering the transient elongational viscosity, a distinguished strain hardening is observed, which increases with increasing PMDA content and with increasing strain rate. From the results of the rheological and molecular characterization and by considering the chemical reaction mechanisms, it can be concluded that the PET modified with high PMDA contents has a treelike branch-on-branch architecture, which is well-known from low-density polyethylene melts.

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INTRODUCTION The elongational deformation of a polymer melt is governing in several processing technologies like thermoforming, film blowing, blow molding, or foaming. It is well-known that the behavior of the melt during these elongational processes is strongly affected by the molecular architecture, the molar mass, and the molar mass dispersity. In particular, it was found e.g. for polyethylene,1 polypropylene,2 fluoropolymers,3 and polylactide4 that long-chain branches lead to a significant increase of the transient elongational viscosity at constant deformation rate. This strain hardening behavior results in an improved thickness homogeneity, which was observed e.g. for blown films of low-density polyethylene (LDPE)5 and thermoformed polypropylene (PP) beakers6 or in a higher blow up ratio, observed for a poly(vinylidene fluoride).3 Furthermore, the findings of the rheological measurements of LCB polymers in combination with the molecular characterization by sizeexclusion chromatography (SEC) enable a deeper understanding of the molecule architecture. While several investigations can be found, considering the elongational properties of polyolefins, only a few publications exist for PET melts. The main reasons for that are the inherently low weight-average molar mass, the narrow molar mass distribution, and the linear molecule topography of most © 2014 American Chemical Society

of the commercial PET materials. These molecular properties result in a low melt viscosity and a poor melt strength, which complicate the measurements of the elongational properties. One successful way to create LCB structures and to increase the melt viscosity is reactive processing with polyfunctional low-molar-mass chemicals, so-called chain extenders. The chain extender for PET studied most is PMDA, which is a tetrafunctional modifier that reacts very rapidly with the end groups of the PET chains. Incarnato et al. used PMDA in a concentration regime between 0.25 and 1 wt % to modify high purity recycled PET. They observed a pronounced shear thinning behavior, a lower amount of crystallinity, and a higher melt strength which were ascribed to an increase of the molar mass, a broadening of the molar mass distribution, and branching phenomena. The increase of the molar mass and the broadening of the molar mass distribution could be detected by SEC, but an experimental proof of the branching phenomena was not shown in this study.7 Forsythe et al. used a combination of PMDA and pentaerythriol and pointed out that this coaddition results in gel-free branched PET with higher Received: February 4, 2014 Revised: June 8, 2014 Published: June 23, 2014 4471

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Malvern) with triple detection (refractive index, viscosimeter, light scattering, TDA 305, Malvern). The use of these detectors allows the measurement of the absolute molar mass and the hydrodynamic radius. The measurements were carried out at 35 °C with HFIP and a constant flow rate of 0.8 mL min−1. In order to ensure complete solubility before performing the experiments, the polymer solution with a concentration of 4 g L−1 were heated up to 50 °C for 2 h. Rheological Characterization in Shear. The rheological characterization in shear flow was performed with an ARES rheometer (TA Instruments) in plate−plate geometry at 270 °C. Cylindrical samples of a diameter of 25 mm and a thickness of 2 mm were prepared with a hot press at a temperature of 270 °C under a nitrogen atmosphere. Dynamic mechanical experiments were carried out in a frequency range between 100 and 0.1 rad s−1. The deformation amplitude applied was set to 4% for all measurements, which was proven to be in the linear viscoelastic regime. The thermal stability of the materials was checked by dynamic time sweeps at a constant frequency of 0.2 rad s−1. The reproducibility for all rheological experiments in shear was better than ±10%. Rheological Characterization in Elongation. The transient elongational viscosity was determined with the ARES extensional viscosity fixture (EVF, TA Instruments) under a nitrogen atmosphere at 270 °C. Rectangular samples (10 mm wide, 18 mm long, 1 mm thick) were prepared under the same conditions as the samples for the characterization in shear. Strain rates of 0.01, 0.1, 0.3, 1, and 3 s−1 were applied. The preheating time before the measurements in elongation as well as in shear was set to 8 min to enable comparison of the measurements and to ensure that the material is completely molten.13

melt strength and higher viscosity compared to the addition of PMDA alone.8 Xanthos et al. found an increase of the extrudate swell, a reduction of the melt flow index, and an increase of the melt strength of PET modified with PMDA compared to unmodified PET.9 Furthermore, reactive reprocessing with PMDA could be applied for recycled PET containing some impurities of poly(vinyl chloride) in order to raise the molar mass and to make it suitable for applications requiring high melt viscosities.10,11 In all the investigations described above, the reactive processing of PET with PMDA aims to create materials with high melt strength which are useful for processing technologies where elongational deformation plays a pronounced role. However, no isothermal elongational viscosity measurements of LCB-PET were published up to now. Solely Japon et al. showed elongational viscosity data for a PET modified with a tetrafunctional epoxy-based additive. However, these data were calculated from force measurements with a fiber spinning device under nonisothermal conditions by using simplifying assumptions.12 Therefore, the aim of this paper is to describe the production of LCB-PET with different branching levels and to investigate the transient elongational behavior under isothermal conditions. The LCB polymers were generated by reactive processing with different contents of the chain extender PMDA, and the molecular structures were determined by SEC with coupled light scattering. Furthermore, rheological measurements in shear were performed to get a comprehensive characterization of the materials and to obtain a deeper insight into the influence of the molecular structure on the rheological properties.

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RESULTS AND DISCUSSION Reactive Processing and Chemical Reactions. The torque M and temperature T as a function of residence time t during the reactive processing at a nominal temperature of 270 °C are plotted in Figure 1. The legend displays the different contents of the chain extender in percent by weight. For comparison, the pure PET pellets, named 0 wt %, were kneaded, too.

EXPERIMENTAL SECTION

Materials. The material used in this study was a commercially available PET copolymer (Artenius Care) from La Seda. This resin is a high viscous extrusion type and is usually utilized for blow molding or spinning of monofilaments. The glass transition temperature and the melting temperature of the PET were measured by differential scanning calorimetry to 80 and 247 °C, respectively. The chain extender PMDA was supplied as powder by Sigma-Aldrich. It has a purity of 97% and a nominal melting point of 283−286 °C.a Before reactive processing, the pellets were dry blended with the PMDA in a speed mixer at room temperature in concentrations of 0.1, 0.2, 0.25, and 0.3 wt %, respectively. The mixtures were then dried for 24 h at 130 °C in a vacuum oven. No evaporation of the PMDA powder was observed during the drying period. Reactive Processing. A kneader (Haake PolyDrive, Thermo Scientific) was used for the reactive processing. The residence time was set to 250 s at a rotation speed of 60 rpm and a nominal temperature of 270 °C. During the kneading process, the torque as well as the chamber temperature was recorded. In order to avoid thermo-oxidative degradation, the chamber was purged with nitrogen. The kneaded materials were pelletized and again dried for 24 h at 130 °C in a vacuum oven. Gel Determination. It is well-known that high contents of a highfunctional chain extender can lead to gel formation, which influences the end-product properties, like the elongation at break. Therefore, the modified and unmodified materials were analyzed by the solvent extraction technique. Each material was dissolved in hexafluoroisopropanol (HFIP) and filtered after 24 h using a 1 μm filter. No residue was found after solvent removal, indicating that no or only minor cross-linking reactions occurred during the reactive processing. Molecular Characterization. The information about the molar mass, the molar mass distribution, and the degree of long-chain branching of the raw material as well as the materials with chain extender was obtained by size exclusion chromatography (GPCmax,

Figure 1. Torque and temperature as a function of residence time in the kneader during the reactive processing of PET with various PMDA contents at 270 °C.

The residence time was evaluated in such a way that PET with a concentration of 0.2 wt % PMDA was processed for 500 s at the same processing conditions listed in the Experimental Section. The recorded torque displays a maximum at approximately 250 s. This period of time was used for all materials. It can be seen that the torque decreases for all compositions during the first 70 s while the temperature increases. This behavior indicates the melting of the pellets. After the melting, 4472

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from the rheometer after the frequency sweep, quenched in liquid nitrogen, and afterward analyzed by triple detection SEC. The molar mass distributions of the materials investigated are plotted in Figure 2. The corresponding weight-average molar mass Mw, number-average molar mass Mn, polydispersity Mw/Mn, and the zero shear viscosity η0 at 270 °C are shown in Table 1.

the torque of the neat PET continues to decrease. This can be correlated to a slight viscosity decrease due to the temperature increase and the thermomechanical degradation (see section Molecular Characterization). For the PET with PMDA the torque increases with time after the melting period, which is a result of the chain extension and branching reactions. It is obvious that the highest PMDA content investigated leads to the highest torque as well as to the highest temperature during the reactive process. This indicates a distinguished viscosity increase during the exothermic chemical reactions. The chemical reaction mechanisms between the PET end groups and one PMDA molecule have been first described by Khemani14 and are meanwhile presented several times in the literature.7−10 In Scheme 1, the reaction mechanisms are Scheme 1. Possible Final Molecule Architectures Formed during the Reaction between PET and PMDA

Figure 2. Logarithmic derivative of the cumulative molar mass distribution W(M) as a function of MLS of PET with various PMDA contents. MLS indicates the absolute molar mass determined by light scattering.

Table 1. Weight-Average Molar Mass, Number-Average Molar Mass, Polydispersity, and Zero Shear Viscosity of PET with Various PMDA Contents sample PET 0 wt % 0.1 wt % 0.2 wt % 0.25 wt % 0.3 wt %

Mwa (kg mol−1) 59 54 98 133 332 543

± ± ± ± ± ±

1 1 1 2 3 5

Mna (kg mol−1)

Mw/Mn

η0 at 270 °Cb (Pa s)

± ± ± ± ± ±

1.8 1.9 3.0 4.3 7.7 11.8

1690 1010 7120 20900 58900c 134600c

32 29 33 31 43 46

1 2 1 3 2 6

a

Errors describe the standard deviation of three injections. bFitted with eq 1. cValues contain an uncertainty of maximal 40% (see section Zero Shear Viscosity Dependence on Weight-Average Molar Mass) as the lowest frequency measured is still too high to extrapolate safely to the true zero shear viscosity.

summarized briefly. In a first step, the ring-opening reaction of the two anhydride groups by two hydroxyl end groups of the PET chains take place, leading to chain extension. In a second step a star molecule with four arms is formed by the reaction with two further PET chains. Depending on the PMDA content, different molecule topologies are possible: If two star molecules combine, a pom-pom topology is formed while combinations of more than two PMDA molecules result in a hyperbranched (Cayley) treelike structure. Cross-linking may occur as well. Molecular Characterization. It is described in the literature that compression molding of PET for the rheological material characterization leads to irreversible molar mass degradation.15 Furthermore, Souza et al. performed time sweep tests on a commercial PET fiber grade and found a significant decrease of the viscosity average molar mass during the initial stages of the measurements.16 Taking these findings into account and in order to obtain comparable results of the molecular characterization and the rheological measurements, the SEC was not directly performed after the reactive processing. Instead, a sample of each material was removed

The pure PET is narrowly and monomodal distributed as expected for a commercial PET grade. The processing of the neat PET for 250 s leads to a slight reduction of the weightaverage molar mass, while the polydispersity remains nearly constant. For the materials with chain extender, a broadening of the molar mass distribution with increasing PMDA content is obvious. In particular, a high molar mass shoulder is formed which is much more pronounced for higher PMDA amounts. Instead of that, the low molar mass fraction in the distribution is only slightly influenced by the addition of the chain extender. This results in a remarkable increase of the polydispersity from 1.8 for the unprocessed PET to 11.8 for the 0.3 wt % sample. In Figure 3, the weight-average molar mass and the numberaverage molar mass are plotted as a function of the PMDA content. It can be nicely seen that the number-average remains almost constant, while the weight-average increases exponentially due to the high molar mass shoulder. 4473

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of great importance for an accurate interpretation of the results especially if the material is known to degrade. Therefore, time sweeps were performed for all samples at a constant angular frequency of 0.2 rad s−1 at 270 °C under a nitrogen atmosphere.b For a better comparison of all materials, the measured complex shear viscosity |η*| was normalized to its individual initial value. As illustrated in Figure 5, the relative

Figure 3. Weight-average molar mass and number-average molar mass as a function of PMDA content. The lines are a guide to the eye.

From the double-logarithmic plot of the intrinsic viscosity [η] as a function of molar mass (Figure 4), conclusions can be

Figure 5. Normalized complex shear viscosity as a function of time for PET with various PMDA contents. The gray marked area displays the measuring window used for the rheological characterization.

viscosity of the untreated PET increases with increasing time due to esterification and transesterification reactions.18 This is a well-known behavior of commercial, dried PET under a nitrogen atmosphere, while in air a continuous decrease of the viscosity can be observed (not shown). The kneaded material exhibits a behavior comparable to the unprocessed PET. For the materials with chain extender, it is obvious that the normalized viscosity decreases in the initial stages of the measurements, while for longer times the build-up reactions dominate. The higher the PMDA concentration, the more pronounced is the decrease at the beginning of the measurement. This behavior indicates two features. First, the chain extension and branching reactions of the PET chains with the PMDA are complete; otherwise, the normalized viscosity would increase faster than that of the neat PET. Second, a degradation mechanism dominates the typical esterification and transesterification build-up reactions during the initial stages of the measurements. Such a behavior is typically attributed to hydrolysis reaction in unmodified PET containing a high water content.16 However, all samples are dried equally. Kuhmann et al. reported that in PET films modified with PMDA hydrolysis is by 15% faster than in neat PET films.19 Nevertheless, for all samples the viscosity does not change by more than 8% during the first 300 s compared to the initial measuring value, suggesting that all materials are almost thermally stable during this period of time. The characterization in oscillatory shear flow was therefore performed between 100 and 0.1 rad s−1 with three measuring points per decade, leading to a measuring time below 300 s. The time for the rheological characterization in elongation also does not exceed this limit. Frequency Dependence. Figure 6 shows the complex shear viscosity |η*| as a function of the frequency ω for the neat PET and the modified PET with various PMDA contents.c For the processed and unprocessed PET a comparable characteristic of the viscosity function can be seen, however, with a lower zero shear viscosity for the processed PET, as expected from the results of the molecular characterization. For the materials with

Figure 4. Intrinsic viscosity as a function of molar mass for PET with various PMDA contents.

drawn concerning the branching of the material. The neat PET, as well as the processed PET without PMDA, shows a powerlaw dependency as expected for linear molecules. From a fit, the parameters of the well-known Mark−Houwink equation can be calculated to α = 0.713 and K = 2.3 × 10−4 (for [η] in dL g−1 and MLS in g mol−1), respectively. These parameters belong to a given combination of solvent, polymer, and temperature. Berkowitz used the same solvent and found α = 0.695 and K = 5.2 × 10−4 at 25 °C.17 The deviations can be explained by the temperature difference and by the fact that we used a copolymer in our study. The materials with chain extender are also plotted in Figure 4. For molar masses lower than 104 g mol−1 no deviations can be detected compared to the linear PET, which indicates no or only minor branching in this molar mass regime. For higher molar masses deviations become visible, and a decrease of the slope with increasing PMDA content is obvious. Thus, the hydrodynamic radius is smaller for a LCB sample compared to a linear one of the same molar mass. This coil contraction is typical of LCB polymers as the coils are more densely packed than the linear ones. Comparable results are found for electron-beam-treated PP2 and LDPE.1 Therefore, it can be concluded that all materials with chain extender contain long-chain branches and the degree of branched molecules becomes higher with increasing PMDA content and with increasing molar mass. Rheological Characterization in Shear. Thermal Stability. The thermal stability during the material characterization is 4474

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considering the narrow window of stability, the zero shear viscosity is only accessible for the pure PET as well as the kneaded PET by oscillatory measurements. Therefore, the Carreau-type function (eq 1) was used to extrapolate to the zero shear viscosity of the materials with chain extender. In this equation η0 represents the zero shear viscosity, ωc the critical angular frequency, at which the viscosity function begins to decrease, and m the double logarithmic slope of the shearthinning region. η0 |η*| = m ω 1+ ω

(

c

)

(1)

The fitted curves are shown in Figure 6, and the corresponding zero shear viscosity values are listed in Table 1. . It should be noted that there is an uncertainty of the extrapolated values for the 0.25 and the 0.3 wt % samples, as the lowest frequency measured is still too high to extrapolate safely to the true zero shear viscosity. The fitted zero shear viscosities as a function of the weightaverage molar masses are plotted in Figure 8. The straight line

Figure 6. Complex shear viscosity as a function of angular frequency for PET with various PMDA contents. The lines are fits to eq 1.

chain extender, the Newtonian plateau cannot be reached within the measuring window due to long relaxation times. With increasing PMDA content, the viscosity in the low frequency regime increases by 2 orders of magnitude, and the shear thinning behavior becomes more and more pronounced. For high frequencies the differences between the individual curves become smaller, which is relevant for industrial processing. In order to evaluate the influence of long-chain branching, the polydispersity as well as the high molecular component on the shear rheological behavior, the phase angle δ can be plotted against the complex modulus |G*|. As shown in Figure 7, the

Figure 8. Zero shear viscosity as a function of weight-average molar mass for PET with various PMDA contents. The line corresponds to η0 = 3.2 × 10−14Mw3.5 for the units used in this figure.

represents a power law equation according to the well-known relationship between the zero shear viscosity and the weightaverage molar mass:

η0 = KM w α

Figure 7. Phase angle as a function of complex modulus for PET with various PMDA contents.

(2)

The parameter α depends on the critical molar mass Mc, which is 3300 g mol−1 for PET.22 It was found for several polymers that for molar masses lower than Mc the zero shear viscosity is directly proportional to the weight-average molar mass, while for polymers with a molar mass higher than Mc, the parameter α lies between 3.4 and 3.6.23 Gregory24 and Hudson et al.25 determined α for linear PET melts of molar masses higher than Mc and found experimentally 3.5 and 3.54, respectively. As we have a copolymer in our study, the value of the parameter K differs from the values reported in the literature for the same temperature. Therefore, the line in Figure 8 is the best fit by using the measuring points of the pure and the kneaded PETd and the parameter α = 3.5. This gives a value of K = 3.2 × 10−14 (for η0 in Pa s and Mw in g mol−1). It can be seen in Figure 8 that the points of the 0.1 and 0.2 wt % sample lie slightly below the line for the linear polymers. As the η0−Mw plot is independent of the polydispersity Mw/Mn, this deviation can be attributed to the long-chain branching. Considering the 0.25

unprocessed and processed PET coincide due to equal polydispersity and the linear molecular architecture. Any deviations from this curve can be denoted to the appearance of long-chain branches and/or a broadening of the molar mass distribution.20,21 For the materials with chain extender, a change of the curves’ shape can be observed. The curves are shifted to lower δ values for higher PMDA contents. This can be explained by a growing influence of the long-chain branched structure and an increase of the polydispersity due to the high molar mass shoulder, which both lead to longer relaxation times compared to the linear monomodal PET. Zero Shear Viscosity Dependence on Weight-Average Molar Mass. It is well-known that the plot of the zero shear viscosity as a function of the weight-average molar mass is highly sensitive to long-chain branches. However, by 4475

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and 0.3 wt % samples, the deviation is much more pronounced. In particular, the straight line at the same molar mass is higher by the factor of 11 and 28, respectively, than the fitted zero shear viscosity. Taking the uncertainty of the determination of the zero shear viscosity into account, a deviation of the branched samples to lower values compared to the straight line is nevertheless ensured. This can be proven from the results of the rheological characterization in elongation (next section). As a stationary value without strain hardening is reached for the strain rate of 0.01 s−1, the plateau value can be compared with the 3-fold of the zero shear viscosity according to Trouton’s law. The zero shear rate viscosity can be obtained from the fit of the viscosity data to eq 1 and from the scaling law for linear PET (eq 2). The comparison is shown in Figures 9a and 9b, where these values are indicated by the horizontal dotted (Carreau fit; eq 1) and dashed (scaling law for linear PET; eq 2) lines. The deviation between the 3-fold of the zero shear viscosity from the Carreau fit and the time-independent plateau from the elongational measurements is less than 40%. Therefore, it is proven that the zero shear viscosities of the 0.25 and 0.3 wt % samples are by more than 1 order of magnitude smaller than those of the linear products of the same molar mass.e Comparing these results with investigations on polyethylene samples of various branching structures, conclusions can be drawn concerning the molecular structure of the modified PET samples. It is known from LCB polyethylene that slightly long-chain branched starlike polymers (e.g., LCBLLDPE produced with a metallocene catalyst) lie above the line, whereas highly long-chain branched treelike polymers (e.g., LDPE) are found beneath.26,27 Similar results are reported for LCB-PP2 and for high molecular weight arborescent graft polystyrenes.28 The deviation toward lower values, compared to the linear reference, can be explained by the high branching functionality which reduces the number of entanglements per branch.26 In particular, the branches and the low molar mass molecules relax very quickly, and only a linear or singly branched backbone remain. The relaxed molecules act as a diluent for the backbone, which is responsible for the decrease of the zero shear viscosity.29 Taking these results into account, it can be concluded that a treelike molecule structure for PET modified with high PMDA contents is very probably, which agrees quite well with the expected molecular architecture illustrated in Scheme 1. Rheological Characterization in Elongation. In Figure 9, the transient elongational viscosities ηE+ for the 0.2, 0.25, and 0.3 wt % samples are plotted for different elongation rates. The maximum Hencky strain reached is 2.5 in all experiments. The elongational viscosity of the neat PET, the 0 wt % sample, and the 0.1 wt % sample cannot be determined due to sagging effects prior or during the measurement. For the 0.3 wt % sample, the excellent reproducibility (two measurements for each strain rate) is shown exemplarily in Figure 9a. The reproducibility of all elongational measurements is always better than 10%. According to the linear viscoelastic theory, the envelope of the transient elongational viscosity in the linear range of deformation agrees well with the 3-fold of the complex shear viscosity for all samples. This indicates the validity of the well-known Trouton ratio, which supports the reliability of the measurements. For all PMDA contents, a pronounced strain hardening could be observed for strain rates between 0.1 and 3 s−1. It is obvious that the amount of strain hardening becomes more pronounced with increasing PMDA content. In order to

Figure 9. Transient elongational viscosity at different elongation rates for PET with (a) 0.3 wt % PMDA, (b) 0.25 wt % PMDA, and (c) 0.2 wt % PMDA. Part (a) displays the reproducibility as two measurements for each strain rate are shown. The dotted lines represent the 3fold of the zero shear viscosities from the Carreau fit. The dashed lines correspond to the 3-fold of η0 = 3.2 × 10−14Mw3.5 with the measured Mw (in g mol−1) according to Table 1.

obtain a more quantitative analysis of this strain hardening behavior, it is useful to calculate the strain hardening factor as X=

ηE+(t , ε)̇ lim ηE+(t , ε)̇

ε→0

(3)

The Hencky strain can furthermore be calculated from the strain rate and the measuring time according to εH = εṫ

(4)

which enables an easier comparison of different strain rates. The strain-hardening factor as a function of Hencky strain is 4476

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plotted in Figure 10 for a low (0.1 s−1) and a high (1 s−1) strain rate and for the three PMDA contents. It is obvious that the

This can be explained by an increase of the LCB amount and a broadening of the molar mass distribution. At high frequencies, the viscosities of all samples are close to each other, which is relevant for industrial processing. The zero shear viscosities were examined with a Carreau-type function as the thermal stability window is limited to 300 s, which is too narrow to measure the zero shear viscosity of the LCB samples by oscillatory measurements. The η0−Mw plot shows that the LCB samples lie beneath the line for the linear products. This behavior is known from a LDPE which has a high amount of LCB and a treelike structure. For the first time, isothermal elongational measurements were shown for a LCB-PET. The samples with 0.2, 0.25, and 0.3 wt % PMDA exhibit a distinguished strain hardening behavior during elongation, which is higher for higher PMDA contents. Additionally, an increase of the strain hardening was observed with increasing strain rate for all samples. The behavior of the rate dependence of the strain hardening can also be used as an indicator of the topology of the LCB molecules. An increase of the strain hardening with increasing strain rate which was found for the LCB-PET is also typical for a treelike structure. Summarizing the results from the molecular and rheological characterization and considering (a) the proposed chemical reaction mechanisms shown in Scheme 1, (b) the deviation from the η0−Mw dependency for linear polymers toward lower values (Figure 8), and (c) the increase of the strain hardening with increasing strain rate (Figure 10) lead to the conclusion that a LCB-PET made by reactive extrusion with high amounts of PMDA consist of a treelike branch-on-branch molecular architecture which is well-known from LDPE. Considering the results with respect to industrial processing, the shear viscosity at high shear rates increases only slightly for the modified materials, which is relevant for the pressure during an extrusion process. Moreover, the strain hardening behavior of the LCBPET should lead to an improved homogeneity in thickness for processing applications (e.g., film blowing) where elongation plays a pronounced role and where the strain rates are comparable to ones used during the elongational viscosity measurements.

Figure 10. Strain hardening factor as a function of Hencky strain for two strain rates and for the 0.2, 0.25, and 0.3 wt % PMDA samples.

strain hardening factor at a constant strain rate increases with increasing PMDA content, which can be explained by a rise of the branching level. Furthermore, an increase of the strain hardening factor with increasing strain rate can be seen. This behavior is well-known for a LDPE with a treelike branch-onbranch architecture and a high degree of branching.1,13 However, to discuss the strain hardening factor with respect to the molecular architecture, it must be taken into account that the elongational behavior is also influenced by a gel content30 and by a high molar mass component.1,31 As described in the Experimental Section, gel formations can be excluded as all samples are completely soluble. However, a high molar mass shoulder appeared during the reactive processing which increases with increasing PMDA content. In addition, these high molar mass components contain most of the branched molecules as can be seen in Figure 4. This gives rise to the assumption that the effect of the branching structure on the strain hardening behavior dominates and is maybe slightly amplified by the linear molecules in the high molar mass shoulder.

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ASSOCIATED CONTENT

S Supporting Information *

CONCLUSIONS A linear PET with different contents of the tetrafunctional chain extender PMDA were reactively processed with the aim of creating LCB structures. The dissolution experiments show no gel formation, indicating that no cross-linking occurred. The molecular characterization by SEC coupled with triple detection exhibits an exponential increase of the weight-average molar mass, a broadening of the molar mass distribution, and a high molar mass shoulder with increasing PMDA content. Deviations in the Mark−Houwink plot from the power law for linear molecules clearly demonstrate the incorporation of LCB structures for all samples with PMDA. The amount of LCB structures increases with increasing modifier content, and it was found that the LCB appear particularly in the high molar mass region. The change of the molecular structure as well as the increase of the molar mass results in significantly different shear flow properties of the melts compared to the neat PET. First, the complex viscosity increases in the low frequency region with increasing PMDA content. Second, a pronounced shear thinning behavior was found for the modified PET samples.

Storage modulus G′ and loss modulus G″ as a function of angular frequency ω for PET with various PMDA contents; slope of G′ and G″ in the low- and high-frequency region as a function of PMDA content. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank La Seda for supplying the PET for free of charge. Inge Herzer is thanked for performing the SEC measurements and Jürgen Majewski for carrying out some of the rheological measurements. Additionally, the authors acknowledge Dipl.-Phys. Matthias Bechert, M.Sc. Johannes Krückel, and M.Sc. Peter Kunzelmann for fruitful discussions. 4477

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(30) Yamaguchi, M.; Suzuki, K.; Maeda, S. J. Appl. Polym. Sci. 2002, 86, 73−78. (31) Münstedt, H. J. Rheol. 1980, 24, 847−867.

ADDITIONAL NOTES Values according to the manufacturer. b This is a typical frequency which allows the determination of the zero shear viscosity of the neat PET. c The plot of the storage modulus G′ and the loss modulus G″ as a function of the angular frequency ω is shown in the Supporting Information. d Both are linear materials according to the molecular characterization. e This behavior is supported by the small slope (∼0.4) of the storage and loss modulus in the high frequency regime (see Supporting Information). a

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REFERENCES

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dx.doi.org/10.1021/ma5002657 | Macromolecules 2014, 47, 4471−4478