Abstract
Thermorheological complexity in polyolefins has been reported many times but so far it has not been systematically investigated. Here, a classification of the different types of thermorheologically complex behavior is proposed, which categorize the available data in five different types and describe key characteristics. These definitions are based on polyethylene, but other polymers show similar patterns for materials with comparable branching structure. Linear materials are thermorheologically simple as long as many very long short-chain branches do not introduce phase separation. Sparsely branched materials show the most significant thermorheological complexity, with significant shape changes of rheological functions with temperature, while higher amounts of branching (such as trees or combs) reduce thermorheological complexity and increase Ea at the same time. Low-density polyethylene shows a significant modulus shift at different temperatures probably due to excessive low molecular components.
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Notes
As the shift factors are relatively small and the temperature range is limited for PE, activation energies are especially prone to incorrect values, and therefore, only publications with a range of different samples from reliable sources are considered.
The results indicate that samples with dodecene (C12) or shorter as comonomer (Stadler et al. 2006b) do not show such a phase separation, while samples with octadecene or longer do show phase separation in melt and solid state (Piel et al. 2006a; Stadler 2011). As the amount of available data is limited, it is not possible to specify this threshold clearer.
The term long SCBs seems to be self-contradictory at a first glance. In rheology, classically, LCBs are defined as entangled side chains and have a significant effect on the rheological behavior, while SCBs are unentangled and have little rheological effect except on thermorheological behavior. However, recently, the new group of long SCBs was discovered, which is on one hand unentangled but on the other hand is long enough to phase separate. Therefore, the term “long SCBs” is coined to express that these longer than normal unentangled side chains have an effect on rheology beyond increasing the activation energy.
It should be mentioned that in the future, new chain topographies could lead to new types of thermorheological complexity.
Abbreviations
- WLF relation:
-
Williams-Landel-Ferry relation
- VFTH relation:
-
Vogel-Fulcher-Tammann-Hesse relation
- T g :
-
glass transition temperature
- TTS:
-
time-temperature superposition
- LDPE:
-
low-density polyethylene
- LLDPE:
-
linear low-density polyethylene
- HDPE:
-
high-density polyethylene
- LCB/LCBs:
-
long-chain branch(-ed/-ing/-es)
- SCB/SCBs:
-
short-chain branch(-ed/-ing/-es)
- mPE:
-
metallocenes catalyzed polyethylene
- PP:
-
polypropylene
- PE:
-
polyethylene
- PS:
-
polystyrene
- PI:
-
polyisoprene
- PBd:
-
polybutylene
- hPBd:
-
hydrogenated polybutadiene
- THV:
-
semifluorinated tetrafluoroethylene-hexafluoropropylene-vinylidenfluoride copolymer
- |G*|:
-
magnitude of the complex shear modulus
- G’:
-
storage modulus
- G”:
-
loss modulus
- δ :
-
phase angle
- ω :
-
angular frequency
- a T :
-
temperature dependent shift factor
- γ 0 :
-
oscillatory deformation amplitude
- E a :
-
activation energy determined according to Arrhenius relation
- H:
-
relaxation strength
- τ :
-
relaxation time
- δ c :
-
characteristic phase angle (Trinkle et al. 2002)
- δ max :
-
phase angle at the maximum Ea determined from δ (Stadler et al. 2016)
- η 0 :
-
zero shear-rate viscosity
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Acknowledgements
The authors would like to thank the National Natural Science Foundation of China (21574086), Shenzhen Sci & Tech research grant (ZDSYS201507141105130), and Shenzhen City Science and Technology Plan Project (JCYJ20160520171103239).
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Yan, ZC., Stadler, F.J. Classification of thermorheological complexity for linear and branched polyolefins. Rheol Acta 57, 377–388 (2018). https://doi.org/10.1007/s00397-018-1088-6
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DOI: https://doi.org/10.1007/s00397-018-1088-6