Branching structure and strain hardening of branched metallocene polyethylenes

Torres, Enrique; Li, Si-Wan; Costeux, Stéphane; Dealy, John M.

doi:10.1122/1.4927919

Cited by 15 publications

(8 citation statements)

References 47 publications

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“…The evolution of the orientation tensor is conveniently described by the auxiliary tensor A with and satisfying equation (4): (4) The stress evolution is given by the following equation:…”

Section: Resultsmentioning

confidence: 99%

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Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension

Huang¹,

Costanzo²,

Das³

et al. 2017

Journal of Rheology

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We present unique nonlinear rheological data of well-defined symmetric Cayley-tree poly(methyl methacrylates) in shear and uniaxial extension. Earlier work has shown that their linear viscoelasticity is governed by the hierarchical relaxation of different generations, whereas the segments between branch points are responsible for their substantial strain hardening as compared to linear homopolymers of the same total molar mass at the same value of imposed stretch rate. Here, we extend that work in order to obtain further experimental evidence that will help understanding the molecular origin of the remarkable properties of these highly branched macromolecules. In particular, we address three questions pertinent to the specific molecular structure: (i) is steady state attainable during uniaxial extension? (ii) what is the respective transient response in simple shear? and (iii) how does stress relax upon cessation of extension or shear? To accomplish our goal we utilize state-of-the-art instrumentation, i.e., filament stretching rheometry (FSR) and cone-partitioned plate (CPP) shear rheometry for polymers with 3 and 4 generations, and complement it with state-of-the-art modeling predictions using the Branch-on-Branch (BoB) algorithm. The data indicates that the extensional viscosity reaches a steady state value, whose dependence on extension rate is identical to that of entangled linear and other branched polymer melts. Nonlinear shear is characterized by transient stress overshoots and the validity of the Cox-Merz rule. Remarkably, nonlinear stress relaxation is much broader and slower in extension compared to shear. It is also slower at higher generation, and rate-independent for rates below the Rouse rate of the outer segment. For extension, the relaxation time is longer than that of the linear stress relaxation, suggesting a strong 'elastic memory' of the material. These results are 2 described by BoB semi-quantitatively, both in linear and nonlinear shear and extensional regimes. Given the fact that the segments between branch points are less than 3 entanglements long, this is a very promising outcome that gives confidence in using BoB for understanding the key features. Moreover, the response of the segments between generations controls the rheology of the Cayley trees. Their substantial stretching in uniaxial extension appears responsible for strain hardening, whereas coupling of stretches of different parts of the polymer appears to be the origin of the slower subsequent relaxation of extensional stress. Concerning the latter effect, for which predictions are not available, it is hoped that the present experimental findings and proposed framework of analysis will motivate further developments in the direction of molecular constitutive models for branched and hyperbranched polymers.

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“…The evolution of the orientation tensor is conveniently described by the auxiliary tensor A with and satisfying equation (4): (4) The stress evolution is given by the following equation:…”

Section: Resultsmentioning

confidence: 99%

“…The use of model polymers of well-defined architecture is important in probing molecular rheology [1][2][3][4]. Indeed, substantial progress has been made in decoding the linear viscoelasticity of model branched polymers (such as combs or pom-pom-like macromolecules), and more recently their nonlinear response in shear and extension.…”

Section: Introductionmentioning

confidence: 99%

Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension

Huang¹,

Costanzo²,

Das³

et al. 2017

Journal of Rheology

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“…In addition, due to the linear structure of LLDPE, the relaxation of its molecular chain is faster, so the nucleation density decreases continuously as it is not enough to keep stretching . Based on these, it can reasonably be inferred that a small amount of freshly generated crystals in Region I are poorly distributed in the bubble . At the same time, considering the relatively linear molecular structure of LLDPE, when the initial crystal nuclei exists, the molecular chain tends to be arranged therein for growth, especially when the average volume per crystal grain is relatively large at the beginning .…”

Section: Discussionmentioning

confidence: 99%

“…It is well known that LLDPE is different from LDPE in its polymerization mechanism, so its long‐chain branching (LCB) is rarely present on the main chains, and only a small number of short‐chain branching exist . Increasing the content of LCB helps to increase the density of the entanglement points in the entangled network of the polymer melt chain, and at the same time it also helps to improve the uniformity of the chain entangling network . This manifestation in blown film processing is to increase the melt strength of the bubble and promote its response to the external field .…”

Section: Discussionmentioning

confidence: 99%

“…Rheological experiments show that the elongational behavior of the polymer is closely related to the stability of the blown film processing, that is, a better bubble stability and a higher homogeneity of the thickness of the films can be correlated with a strain‐hardening behavior . Due to the entanglement of its long branches, LDPE can always exhibit the expected strain hardening during stretching rheology, while LLDPE shows no significant strain hardening at lower strain rates, which may be the reason for the instability of the bubble . Based on this understanding, people have studied the rheological properties of different structures of PE and LLDPE/LDPE blends with different mixing ratios, hoping to find the appropriate relationship to guide the stability of the blown film processing so that the raw material preparation and preselection can be targeted design .…”

Section: Introductionmentioning

confidence: 99%

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A real‐time WAXS and SAXS study of the structural evolution of LLDPE bubble

Zhao

Zhang

Ali

et al. 2018

J Polym Sci B Polym Phys

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The structural evolution during the linear low-density polyethylene (LLDPE) film blowing has been studied with a combination of home-made blown film apparatus and in situ WAXS and SAXS measurements. Analyzing the evolution of orientation parameters and crystallinity of the bubble shows that the blown film process can be divided into four regions. Distinctly different features of LLDPE bubble are observed in first three regions: (a) lower orientation parameters during the blown film process, (b) higher crystallinity is required to form a deformable crystalline crosslinked network, and (c) the weaker stretching effect and the difficulty of reaching equilibrium when the crystal network deforms. These results should provide a basis for understanding the poor blown film stability of LLDPE.

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Review of the hierarchical multi‐mode molecular stress function model for broadly distributed linear and LCB polymer melts

Narimissa

Wagner

2018

Polymer Engineering & Sci

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We developed a novel Hierarchical Multi-mode Molecular Stress Function (HMMSF) model for linear and long-chain branched (LCB) polymer melts implementing the basic ideas of (1) hierarchical relaxation, (2) dynamic dilution, (3) interchain tube pressure, and (4) convective constraint release. With a minimum number of nonlinear free parameters and remarkable quantitative predictions of the rheology of polymer melts, this model is an outstanding option for the simulation of different processing operations in the polymer industry. The excellent predictions of this model were demonstrated in uniaxial, equibiaxial, and planar extensional deformations for linear and LCB melts, as well as in shear flow for a LCB polymer, with a minimum number of adjustable free nonlinear material parameters, that is, one in the case of extensional flows, and two in shear flow. In this contribution, we review the development of the HMMSF model and present a reduced number of welldefined constitutive relations comprising the rheology of both linear and LCB melts. We also extend the comparison of model and data to cover the shear flow of a linear polymer melt. POLYM. ENG. SCI., 59:573-583, 2019. 4. (a) In extensional flow and large strains, any CR effects are compensated by the advection of neighboring topological constraints, leading to a minimum tube diameter a and a maximum molecular stress f max . (b) In shear flow and large strains, the molecule is simply oriented in the flow direction and, due to convective CR above and below the molecular chain, the tube diameter returns to its equilibrium value a 0. Adapted from [15]. FIG.

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Branching structure and strain hardening of branched metallocene polyethylenes

Cited by 15 publications

References 47 publications

Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension

Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension

A real‐time WAXS and SAXS study of the structural evolution of LLDPE bubble

Review of the hierarchical multi‐mode molecular stress function model for broadly distributed linear and LCB polymer melts

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