Letter pubs.acs.org/macroletters
Crystallization of Polyethylene at Large Undercooling Evgeny Zhuravlev,*,† Vadlamudi Madhavi,‡ Arnold Lustiger,‡ René Androsch,§ and Christoph Schick† †
Institute of Physics, University of Rostock, Wismarsche Str. 43-45, 18051 Rostock, Germany ExxonMobil Research & Engineering Company, 1545 Route 22 East, LD 152, Annandale, New Jersey 08801, United States § Center for Engineering Sciences, Martin-Luther-University Halle-Wittenberg, 06099 Halle/S., Germany ‡
ABSTRACT: Extremely fast crystallization of high-density polyethylene and random copolymers of ethylene with up to 16 mol % 1-octene was observed for the first time by ultrafast scanning calorimetry. In order to account for the inherently high crystallization rate of polyethylenes, in nonisothermal and isothermal crystallization experiments cooling rates up to 1 000 000 K/s and crystallization times as short as 10 μs, respectively, were employed. It was possible to supercool the melt of high-density polyethylene down to 57 °C and the melt of a random ethylene/1-octene copolymer with 16 mol % 1-octene down to −33 °C, without prior crystallization. At these temperatures, the characteristic time of the primary crystallization process is of the order of magnitude of 100 μs. Complete vitrification of the liquid would require cooling even faster than 1 000 000 K/s. Compared to the homopolymer, the cooling-rate dependence of the crystallization temperatures and the temperature dependence of the characteristic time of primary crystallization of random ethylene/1-octene copolymers both are nearly parallel shifted to lower temperatures. Fast crystallization under conditions of reduced linear crystal growth rate is possibly caused by boosting homogeneous nuclei density up to 1027 m−3 and urgently requires further investigation.
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change of the semicrystalline morphology, resulting in dramatic changes of application-relevant properties.5 Crystallization experiments are often limited by the maximum possible cooling rate. Fast scanning chip calorimetry (FSC) was developed to overcome this limitation by significant reduction of both the sample mass and heat capacity of the furnaces.6 While the maximum cooling rate in special setups of conventional DSC is around few hundred K/min, state-of-theart FSC permits nonisothermal crystallization studies at rates up to 1 000 000 K/s, owing to the continuous improvement/ miniaturization of the chip sensors.6a,7The Mettler-Toledo Flash DSC 1 with a diameter of the circular heated area of the sensor of about 500 μm allows controlled heating and cooling of samples with a typical mass of about 100 ng up to a few thousand K/s.8For higher scanning rates, custom-made ultrafast FSC devices with even smaller samples and sensor sizes, allowing measurements up to 1 000 000 K/s, can be used. For illustration, in Figure 1 are shown photographs of the rather large UFS 1 sensor of the Flash DSC 1 (a) and the distinctly smaller XI 394 sensor accommodating samples with a typical mass of about 2 ng (b). Both sensors were employed in the present study. Polyethylene is polymorphic and crystallizes at atmospheric pressure in an orthorhombic unit cell.9 The density, equilibrium melting temperature, and enthalpy of melting of orthorhombic
rystallization of polyethylene (PE) is an important industrial and scientific topic as its control by modification of the chain architecture or variation of the thermal pathway allows the generation of largely different semicrystalline morphologies and, with that, property profiles.1 The simple chemical structure of the repeat unit of the PE macromolecule in combination with the high chain flexibility above the glass transition temperature makes it extremely fast crystallizing. Conventional techniques to obtain the crystallization kinetics cover only a narrow temperature range at rather low undercooling of the melt. In this low-undercooling temperature range, crystallization is assumed to proceed via a heterogeneous nucleation mechanism and is well-studied regarding both its kinetics and the resulting semicrystalline morphology.2 However, crystallization at high undercooling of the melt may be evident in industrial processes, as for example in film production or microinjection molding cooling rates can be of the order of magnitude of 10 000 K/s. Though there are available data about the cooling-rate dependence of crystallization of high-density polyethylene (HDPE) in the literature, the effect of variation of the chemical architecture on the crystallization kinetics at application-relevant cooling conditions or at high supercooling is not yet known.3 This includes lack of knowledge about a possible change from heterogeneous to homogeneous nucleation at low and high supercooling of the melt, respectively, as it has been observed in numerous polymers.4 It is worthwhile noting that a change of the nucleation mechanism is connected with a qualitative © XXXX American Chemical Society
Received: December 7, 2015 Accepted: February 16, 2016
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ACS Macro Letters
to HDPE, if measured at similar conditions.1b,15It has been suggested that in such copolymers, due to an ethylene sequence length distribution, there is formation of a broad spectrum of crystals of different size, crystallizing at largely different temperatures. At high temperature formation of the largest crystals occurs, involving the longer ethylene sequences, while the shortest sequences of lengths of a few nanometers may order only in proximity of the glass transition. Besides a large effect of the presence of counits in the chain on the crystallization kinetics, former research also proved a replacement of formation of lamellar crystals by fringed micelles/nodules, disappearance of the spherulitic superstructure, or incomplete segregation of counits at the crystal growth front leading to a loss of the orthorhombic crystal symmetry and formation of pseudohexagonal structures.1b,15a,16 These observations were found to be enforced by either an increase of the counit concentration or an increase of the rate of cooling the melt. It is known that the crystallization temperature of PE is controlled by the branching characteristics. At identical cooling conditions copolymers crystallize at significantly lower temperatures than HDPE. A major reason may be the depression of the equilibrium melting temperature though an unequivocal opinion on whether the hexyl branches are completely or only partially excluded from crystallization does not seem to exist.17 The assumption of slower crystallization in copolymers due to segregation of counits at the crystal growth front, based on the observation of lowered crystallization temperatures at standard DSC experimentation conditions, is a subject of discussion in the present work, in particular in the shed of light that state-of-the-art FSC allows determination of crystallization temperatures and half-times in wide cooling-rate and temperature ranges, respectively, ultimately providing information about an effect of branches on the crystallization kinetics of polyethylenes at comparable supercooling. In the present work the crystallization kinetics of HDPE (Paxon) and metallocene-catalyzed LLDPE (Exact) of different concentrations of 1-octene counits is compared. Polymers were provided by ExxonMobil and are listed in Table 1, including
Figure 1. FSC sensors loaded with samples. Flash DSC UFS 1 sensor (a) and XI394 sensor (b).
crystals are 1.006 g/cm3, 141 °C, and 290 J/g, respectively.10 Among the most common polymers, HDPE was ranked as the second fastest crystallizing polymer, after polytetrafluoroethylene (PTFE).11 As such, quantitative data about the crystallization kinetics, obtained by conventional techniques like DSC, or dilatometry are available only for a narrow temperature range, at temperatures higher than about 120 °C.12 Application of a modified light-depolarizing microscopy technique allowed analysis of nonisothermal crystallization of an 80 μm HDPE thin section between cover glasses during fast ballistic cooling up to an average rate of about 60 K/s (3600 K/ min), leading to a supercooling of the melt before the beginning of crystallization by almost 30 K; an estimation of the crystallization half-time at such supercooling revealed a value of about 0.3 s.13 Further progress regarding analysis of crystallization of HDPE at higher supercooling of the melt was then achieved with the introduction of the first FSC versions, permitting cooling of polymer samples at rates up to 5000 K/s. At such conditions an HDPE sample with a mass of 120 ng began to crystallize at about 100 °C; that is, the melt was undercooled by 40 K.6bIn a more recent work, employing a sample of ultrahigh molecular weight polyethylene (UHMWPE) with a mass of only 5 ng and the XI320 sensor with an active area of 60 × 60 μm2, the cooling-rate range was expanded to 10 000 K/s, achieving a supercooling of the melt by more than 70 K;7b,14 eventually, amorphization of UHMWPE was predicted to take place on cooling at 2 000 000 K/s.7b Measurements on UHMWPE were then done with an analogue of the XI394 sensor with a measurement area of 8 × 6 μm2, allowing cooling of a sample with a mass of 2.5 ng at rates up to 1 000 000 K/s. In extension to earlier investigations, in this study not only new instrumentation has been developed and applied but also random copolymers of ethylene were included with different amounts of 1-octene to probe the effect of constitutional chain defects on the crystallization kinetics. However, it is emphasized that analysis of the mechanism of copolymer crystallization is not the main purpose of this work but the demonstration of the possibility to detect differences of the crystallization behaviors of polyethylenes of different chain architecture, at conditions not assessed before by standard instrumentation. In random copolymers of ethylene with a low amount of 1octene, crystallization deteriorates as counits are excluded from crystallization. The required segregation at the crystal growth front is assumed to slow down the crystallization proportional to the counit concentration, as it is concluded from the often reported lowering of the crystallization temperature compared
Table 1. List of Samples, Including Information about the 1Octene Content, Density, Mass-Average Molar Mass and Polydispersity, and Equilibrium Melting Temperature18
sample
content on 1-octene in mol %
HDPE LLDPE-6 LLDPE-9 LLDPE-16
6.5 9.5 16.0
density in g/cm3
massaverage molar mass in kDa
polydispersity
equilibrium melting temperature in °C
0.953 0.902 0.882 0.860
150 105 105 85
7.9 2.3 2.3 2.3
141 134 129 117
information about the 1-octene content, density, mass-average molar mass and polydispersity, and equilibrium melting temperature. Note that the equilibrium melting temperature was calculated according to Flory, assuming exclusion of the 1octene counits from crystallization.18 A custom-designed power-compensation-type FSC with sensors of different sizes was needed to optimize the signal quality in crystallization experiments using cooling rates between 100 and 1 000 000 K/s.14a,19These instruments were operated in a helium environment at normal pressure and using 366
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Figure 2. FSC experiments for characterization of direct nonisothermal crystallization of HDPE (a) and indirectly probed by reheating after isothermal crystallization of an LLDPE copolymer with 16 mol % 1-octene (b), using in both cases the small XI394 sensor.
a base temperature of −196 °C, in order to maximize the heat transfer from the sample to the surrounding and to cool as fast as possible, respectively. Remaining thermal lag was corrected using indium as calibrant.19 Two sensor types were used in this device; the sensor XI391 with an active area of 60 × 60 μm2 was used to cool at rates up to 100 000 K/s, employing samples with a mass of about 10 ng, and the even smaller XI394 sensor with an active area of 6 × 8 μm2 was used to cover rates up to 1 000 000 K/s with samples with a mass of only 1−2 ng. At this scale the reduction of heterogeneous nucleation sites in the single droplets may occur as in droplet experiments for PE20 where homogeneous nucleation is observed below 90 °C. In our experiments the crystallization kinetics of micron-sized samples was in line with larger samples. Particularly at temperatures below 90 °C heterogeneous nucleation is not playing a significant role, as homogeneous nucleation dominates. The Mettler-Toledo Flash DSC was employed to measure larger samples with a mass of around 100 ng at cooling rates between 10 and 4000 K/s. Conventional DSC at cooling rates 1 and 0.17 K/s was performed employing a PerkinElmer Pyris 1 DSC. Examples of FSC experiments for characterization of nonisothermal and isothermal crystallization, using the smallest available sensor XI394, are shown in Figure 2a and 2b, respectively. In the left plot are presented cooling curves obtained on HDPE, measured at rates between 10 000 K/s (bottom curve, black) and 1 000 000 K/s (top curve, red). It can be seen that cooling at rates between 10 000 (black curve) and 200 000 K/s (orange curve) are linear in the shown temperature range from 150 to −100 °C and that on further increase of the cooling rate to, e.g., 700 000 K/s (green curve) or 1 000 000 K/s (red curve) instrument control is lost at about −60 and −30 °C, respectively. This notwithstanding, the data show that even at these rates crystallization of HDPE can be quantified since onset and peak temperatures can reliably be determined. In Figure 2b are shown FSC heating scans at a heating rate of 100 000 K/s obtained immediately after the sample was crystallized at 17 °C for different times as indicated in the legend. The LLDPE-16 was quenched at 1 000 000 K/s to the crystallization temperature. It can be seen by the absence of a melting peak that annealing of the sample for 0.6 ms at 17 °C (black curve) did not result in crystallization. If the annealing
time at 17 °C, however, is longer than about 1 ms then there is observed formation of crystals, as their fraction can be quantified by the melting-peak area. It is furthermore observed that with ongoing crystallization the stability of crystals increases, as is judged by the shift of the melting peak, including the onset temperature, toward higher values (green arrow in Figure 2b).15a Evaluation of the peak area and plotting it as a function of the crystallization time yields conversion− times curves, allowing the determination of crystallization halftimes, discussed below. Figure 3 shows the cooling-rate dependence of crystallization-peak temperatures of HDPE and LLDPEs, as is indicated in the legend.
Figure 3. Crystallization peak maximum temperature of HDPE and LLDPEs with different content on 1-octene, as is indicated in the legend, as a function of the cooling rate. For comparison, the plot contains with the green circle data on an UHMWPE sample available in the literature.14b The use of different devices is indicated.
Crystallization temperatures obtained on cooling at rates lower than 1 K/s were collected by DSC and confirm knowledge available in the literature. Increasing 1-octene concentration in the LLDPE copolymers decreases the crystallization temperature, both onset and peak, presumably due to smaller maximum crystal sizes limited by the longest 367
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ACS Macro Letters ethylene sequences available, a lowered equilibrium melting temperature, or the segregation of 1-octene counits at the crystal growth front.21The data in Figure 3, obtained on cooling at rates higher than 1 K/s, at least for the copolymers, are new and allow for the first time a comparison of the cooling-rate dependence of crystallization of HPDE and LLDPE. Surprisingly, the various data sets seem only parallel shifted to each other, suggesting that the kinetics of nonisothermal crystallization, with respect to the lowered equilibrium melting temperatures in the copolymers, is similar for all samples. Importantly, the critical cooling rate is not reached for any of the resins. Following Eder’s approximation, critical cooling rate can be estimated by22 qcrit = 13.24
Gmax 3 Nmax kG
where Gmax is the maximum crystal growth rate; Nmax is the nuclei density at the temperature of maximum growth rate; and the parameter 1/kG is the width of the temperature range, in which crystallization occurs. Eder et al. measured Gmax = 2 × 10−5 m s−1, Nmax ∼ 1017 m−3, and kG = 0.1 K−1 resulting in qcrit = 1200 K s−1,22b,c,23 which is at least 3 orders of magnitude apart from the data, measured in this work. Assuming a correct growth-rate determination, the expected nuclei density at qcrit > 106 K s−1 should be at least 1027 m−3. Then the distance between nuclei would be of the order 1 nm, and growth of crystals would be very limited as observed for iPP24 and PBT,25 or PA 11.26 Such tiny crystals are easily formed, and it simplifies exclusion of comonomer units from the crystal. The estimated high nuclei density suggests homogeneous nucleation.27 The effect of entanglements, predicted by Des Cloizeaux and modeled by Sommer, is expected to reduce molecular diffusion on cooling faster than 107 K/s.28 These rates are comparable with maximum possible cooling rates, reached in this work. However, the estimated nucleation density is so high and the crystal size so small (ca. 1 nm) that one can reasonably assume that crystallization does not require long-scale rearrangements and that entanglement distances of order of 10 nm are not important. Figure 4 shows enthalpies of isothermal crystallization of HDPE (top) and LLDPE-16 (bottom) as a function of the crystallization time. Compared to conventional DSC, FSC significantly increases the accessible range of temperatures for such isothermal crystallization studies, ensuring absence of crystallization during the approach of the crystallization temperature. As such, for HDPE, isothermal crystallization experiments were possible at temperatures as low as 72 °C, while in the case of the LLDPE-16 copolymer the minimum crystallization temperature was 17 °C. For all analyzed samples, regardless of the 1-octene concentration and crystallization temperature, the conversion−time curves reveal an initial strong increase of the crystallinity which then is followed by a slower and less pronounced increase. Typically, these processes are related to primary and secondary crystallization.29 It is worthwhile noting that crystallization of shorter ethylene segments in LLDPE’s is not allowed at higher temperatures causing the large increase of the maximum achievable crystallinity with decreasing crystallization temperature (black arrow in Figure 4). Crystallization at higher supercooling, e.g., at 17 °C, then allows crystallization of a much larger fraction of ethylene sequences than at 62 °C, even within the primary crystallization step. For HDPE,
Figure 4. Enthalpy of isothermal crystallization of HDPE (top) and LLDPE with 6, 9, and 16 mol % 1-octene content as a function of the crystallization time. Data points were fitted using a modified Kolmogorov−Johnson−Mehl−Avrami equation.4a
contrarily, the common slight increase of the maximum attainable crystallinity with increasing crystallization temperature is observed. An Avrami-based fit, incorporating primary and secondary crystallization, is shown as solid lines in Figure 4.4a The fit describes the HDPE crystallization reasonably well. A more complex crystallization kinetics is observed for low-temperature crystallization of LLDPEs. A bimodal crystallization behavior was also reported for these materials by van Drongelen et al.30 The data of Figure 4were used to obtain half-times of isothermal crystallization, considering the primary crystallization process only. Such data are shown in Figure 5a as a function of the crystallization temperature. First of all, and most importantly, the results confirm the observation of an unchanged kinetics of crystallization in the various samples of different branch characteristics as was already concluded from the nonisothermal experiments of Figure 3. The comparison of crystallization half-times of HDPE and different LLDPEs manifests that the curves are shifted to lower temperature with increasing content of 1-octene. Though at high temperatures the slope is different, the minor differences in curvature between HDPE and LLDPE suggest a similar kinetics in the very large temperature range covered in these experiments. This notwithstanding, the shift to lower temperature is larger than as is expected from the depression of the equilibrium melting temperature (see Table 1). At the same time, the shift in crystallization temperature seen in Figure 3 parallels the shift of the equilibrium melting temperature. Figure 5b and c are shows that the undercooling below the equilibrium melting temperature from Table 1 alone cannot 368
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Figure 5. (a) Half-time of primary crystallization of HDPE and LLDPE with different content of 1-octene as a function of the crystallization temperature. (b) and (c) Dependency of isothermal and nonisothermal crystallization kinetics on undercooling below equilibrium melting temperature redrawn from (a) and Figure 3 employing melting temperatures from Table 1.
homogeneous nucleation in the studied polyethylenes is therefore suggested.
explain the observed shift of the crystallization half-time and peak-maximum temperature for the copolymers similar to data published by Phillips.31 Differences in the nucleation mechanism may be important too. Summarizing, the crystallization kinetics of high-density polyethylene and random copolymers of ethylene with up to 16 mol % 1-octene was studied by state-of-the-art ultrafast scanning calorimetry. With the use of samples with a mass of only 1 ng it was possible to monitor nonisothermal crystallization at rates up to 1 000 000 K/s and to supercool the melt by roughly 70 K in the case of HDPE and to a temperature of only 10−20 K higher than the expected glass transition temperature in the case of LLDPEs containing 1octene counits. All PE samples studied here crystallized on cooling at 1 000 000 K/s, and isothermal crystallization experiments showed that the minimum crystallization half time is lower than 10−4 s, presumably independent of the PE grade. The experimentally justified extremely high critical cooling rates above 1 000 000 K/s, combined with existing data on linear growth rates, suggest an extremely high density of crystal nuclei of more than 1027 m−3. For the much less flexible chain of PBT a comparable nuclei density of about 1024 m−3 was reported. Under these specific experimental conditions,
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Authors kindly acknowledge ExxonMobil Research and Engineering Company for partial funding of this research and providing materials. EZ acknowledges Functional Materials Rostock e.V. for supplying ultrafast scanning (FSC) calorimeters and for financial support.
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REFERENCES
(1) (a) Mandelkern, L. Polym. J. 1985, 17 (1), 337−349. (b) Bensason, S.; Minick, J.; Moet, A.; Chum, S.; Hiltner, A.; Baer, E. J. Polym. Sci., Part B: Polym. Phys. 1996, 34 (7), 1301−1315. (c) Baeten, D.; Mathot, V. B. F.; Pijpers, T. F. J.; Verkinderen, O.; Portale, G.; Van Puyvelde, P.; Goderis, B. Macromol. Rapid Commun. 2015, 36 (12), 1184−1191. 369
DOI: 10.1021/acsmacrolett.5b00889 ACS Macro Lett. 2016, 5, 365−370
Letter
ACS Macro Letters (2) (a) Wunderlich, B.; Czornyj, G. Macromolecules 1977, 10 (5), 906−913. (b) Albrecht, T.; Strobl, G. Macromolecules 1996, 29 (2), 783−785. (c) Vanden Eynde, S.; Mathot, V. B. F.; Hohne, G. W. H.; Schawe, J. W. K.; Reynaers, H. Polymer 2000, 41 (9), 3411−3423. (d) Marand, H.; Huang, Z. Macromolecules 2004, 37 (17), 6492−6497. (e) Balta-Calleja, F. J.; Santa Cruz, C.; Bayer, R. K.; Kilian, H. G. Colloid Polym. Sci. 1990, 268 (5), 440−446. (3) (a) Minakov, A. A.; Roy, S. B.; Bugoslavsky, Y. V.; Cohen, L. F. Rev. Sci. Instrum. 2005, 76, 043906. (b) Patki, R. P.; Phillips, P. J. Eur. Polym. J. 2008, 44 (2), 534−541. (4) (a) Zhuravlev, E.; Schmelzer, J. W. P.; Wunderlich, B.; Schick, C. Polymer 2011, 52 (9), 1983−1997. (b) De Santis, F.; Adamovsky, S.; Titomanlio, G.; Schick, C. Macromolecules 2006, 39, 2562−2567. (c) van Drongelen, M.; Meijer-Vissers, T.; Cavallo, D.; Portale, G.; Poel, G. V.; Androsch, R. Thermochim. Acta 2013, 563, 33−37. (d) Rhoades, A. M.; Williams, J. L.; Androsch, R. Thermochim. Acta 2015, 603, 103−109. (e) Pyda, M.; Nowak-Pyda, E.; Heeg, J.; Huth, H.; Minakov, A. A.; Di Lorenzo, M. L.; Schick, C.; Wunderlich, B. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 1364−1377. (f) Zhuravlev, E.; Schmelzer, J. W. P.; Abyzov, A. S.; Fokin, V. M.; Androsch, R.; Schick, C. Cryst. Growth Des. 2015, 15 (2), 786−798. (5) (a) Mileva, D.; Androsch, R.; Zhuravlev, E.; Schick, C. Polymer 2012, 53 (18), 3994−4001. (b) Mileva, D.; Kolesov, I.; Androsch, R. Colloid Polym. Sci. 2012, 290 (10), 971−978. (c) Zia, O.; Androsch, R.; Radusch, H. J.; Piccarolo, S. Polymer 2006, 47, 8163−8172. (d) Zia, Q.; Androsch, R.; Radusch, H. J. J. Appl. Polym. Sci. 2010, 117 (2), 1013−1020. (6) (a) Pijpers, M. F. J.; Mathot, V. B. F.; Goderis, B.; Scherrenberg, R.; van der Vegte, E. Macromolecules 2002, 35 (9), 3601−3613. (b) Adamovsky, S. A.; Minakov, A. A.; Schick, C. Thermochim. Acta 2003, 403 (1), 55−63. (c) Adamovsky, S.; Schick, C. Thermochim. Acta 2004, 415, 1−7. (d) Minakov, A. A.; Adamovsky, S. A.; Schick, C. Thermochim. Acta 2005, 432 (2), 177−185. (7) (a) Kolesov, I. S.; Androsch, R.; Radusch, H. J. J. Therm. Anal. Calorim. 2004, 78, 885−895. (b) Minakov, A. A.; Schick, C. Rev. Sci. Instrum. 2007, 78 (7), 073902−10. (8) (a) Mettler, T. Flash DSC. http://au.mt.com/au/en/home/ products/Laboratory_Analytics_Browse/TA_Family_Browse/Flash_ DSC.html (accessed Feb 2016). (b) Mathot, V.; Pyda, M.; Pijpers, T.; Vanden Poel, G.; van de Kerkhof, E.; van Herwaarden, S.; van Herwaarden, F.; Leenaers, A. Thermochim. Acta 2011, 522 (1−2), 36− 45. (9) (a) Bassett, D. C.; Block, S.; Piermarini, G. J. J. Appl. Phys. 1974, 45 (10), 4146−4150. (b) Yasuniwa, M.; Enoshita, R.; Takemura, T. Jpn. J. Appl. Phys. 1976, 15 (8), 1421−1428. (c) Hikosaka, M.; Minomura, S.; Seto, T. Japanese journal of applied physics 1980, 19 (9), 1763−1769. (10) Wunderlich, B. Pure Appl. Chem. 1995, 67 (6), 1019−1026 See on WWW URL: http://www.springermaterials.com/docs/athas.html.. (11) Khanna, Y. P. J. Mater. Sci. Lett. 1988, 7 (8), 817−818. (12) Wunderlich, B.; Jones, L. D. J. Macromol. Sci., Part B: Phys. 1969, 3 (1), 67−79. (13) Supaphol, P.; Spruiell, J. E. J. Polym. Sci., Part B: Polym. Phys. 1998, 36 (4), 681−692. (14) (a) Zhuravlev, E.; Schick, C. Thermochim. Acta 2010, 505 (1− 2), 14−21. (b) Androsch, R.; Lorenzo, M. L. D.; Schick, C.; Wunderlich, B. Polymer 2010, 51 (21), 4639−4662. (15) (a) Androsch, R.; Wunderlich, B. Macromolecules 1999, 32 (21), 7238−7247. (b) Minick, J.; Moet, A.; Hiltner, A.; Baer, E.; Chum, S. P. J. Appl. Polym. Sci. 1995, 58, 1371−1384. (c) Mathot, V. B. F.; Scherrenberg, R. L.; Pijpers, T. F. J. Polymer 1998, 39 (19), 4541− 4559. (16) (a) Kolesov, I. S.; Androsch, R.; Radusch, H. J. Macromolecules 2005, 38, 445−453. (b) Androsch, R.; Kolesov, I.; Radusch, H. J. J. Therm. Anal. Calorim. 2003, 73 (1), 59−70. (c) Scherrenberg, R.; Mathot, V. B. F.; Steeman, P. J. Therm. Anal. Calorim. 1998, 54 (2), 477−499. (d) McFaddin, D. C.; Russell, K. E.; Wu, G.; Heyding, R. D. J. Polym. Sci., Part B: Polym. Phys. 1993, 31 (2), 175−183.
(17) Kim, M. H.; Phillips, P. J.; Lin, J. S. J. Polym. Sci., Part B: Polym. Phys. 2000, 38 (1), 154−170. (18) Flory, P. J. Macromolecules 1978, 11 (6), 1138−1141. (19) Zhuravlev, E.; Schick, C. Thermochim. Acta 2010, 505 (1−2), 1−13. (20) (a) Gornick, F.; Ross, G. S.; Frolen, L. J. J. Polym. Sci., Part C: Polym. Symp. 1967, 18 (1), 79−91. (b) Cormia, R. L.; Price, F. P.; Turnbull, D. J. Chem. Phys. 1962, 37 (6), 1333−1340. (c) Ross, G. S.; Frolen, L. J. J. Res. Natl. Bureau Standards 1975, 79A (6), 10. (d) Price, F. P.; Gornick, F. J. Appl. Phys. 1967, 38 (11), 4182−4186. (21) (a) Mandelkern, L.; Prasad, A.; Alamo, R. G.; Stack, G. M. Macromolecules 1990, 23 (15), 3696−3700. (b) Mandelkern, L.; Alamo, R. G.; Kennedy, M. A. Macromolecules 1990, 23 (21), 4721− 4723. (22) (a) European Conference on Mathematics. Arkeryd, L. In Progress in industrial mathematics at ECMI 98, Stuttgart, 1999; Teubner: Stuttgart. (b) Janeschitz-Kriegl, H.; Eder, G.; Stadlbauer, M.; Ratajski, E. Monatsh. Chem. 2005, 136 (7), 1119−1137. (c) Stadlbauer, M. Rheo-kinetics of polymers in extension; Institue of Chemistry, Linz University, 2001. (23) Stadlbauer, M.; Eder, G.; Janeschitz-Kriegl, H. Polymer 2001, 42 (8), 3809−3816. (24) (a) Mileva, D.; Zia, Q.; Androsch, R.; Radusch, H.-J.; Piccarolob, S. Polymer 2009, 50 (23), 5482−5489. (b) Zia, Q.; Androsch, R.; Radusch, H.-J.; Ingoliç, E. Polym. Bull. 2008, 60 (6), 791−798. (25) Androsch, R.; Rhoades, A. M.; Stolte, I.; Schick, C. Eur. Polym. J. 2015, 66, 180−189. (26) Kolesov, I.; Mileva, D.; Androsch, R. Polym. Bull. 2014, 71 (3), 581−593. (27) Jones, J. B.; Barenberg, S.; Geil, P. H. J. Macromol. Sci., Part B: Phys. 1978, 15 (2), 329−335. (28) (a) Des Cloizeaux, J. Macromolecules 1990, 23 (17), 3992−4006. (b) Luo, C.; Sommer, J.-U. ACS Macro Lett. 2015, 5, 30−34. (29) Rybnikar, F. J. Polym. Sci., Part A: Gen. Pap. 1963, 1 (6), 2031− 2038. (30) van Drongelen, M.; Roozemond, P. C.; Troisi, E. M.; Doufas, A. K.; Peters, G. W. M. Polymer 2015, 76, 254−270. (31) Wagner, J.; Phillips, P. J. Polymer 2001, 42, 8999−9013.
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