Numerical prediction of nonlinear rheology of branched polymer melts

Das, Chinmay; Read, Daniel J.; Auhl, Dietmar; Kapnistos, M.; Doelder, Jaap den; Vittorias, Iakovos; McLeish, Tom

doi:10.1122/1.4869485

Cited by 38 publications

(56 citation statements)

References 35 publications

(65 reference statements)

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“…When the flow rate is much slower than the stretch relaxation time, the geometric criteria for assigning the maximum stretch lead to an over-prediction of the extensional hardening for randomly branched polymers, hence flow-dependent modifications of the priority variables are required in order to describe the experimental data [8,40]. However, the available approximation for this flow modification requires vastly different relaxation times (as in industrial randomly branched low density polyethylene) and is not valid for symmetric model polymers.…”

Section: Resultsmentioning

confidence: 99%

“…In a multimode pom-pom description, a set of such pom-pom molecules is considered, and the stress is calculated by a simple sum over stress from each of the pom-pom modes. The numerical calculation for the linear rheology prediction offers a natural choice to resolve the molecules in terms of multiple independent pom-pom modes [8,40]: the parts of the molecules relaxing at a certain time tc have orientation relaxation time o = tc ; the time at which these parts (segments) can move coherently with the chain ends define the stretch relaxation time s. In addition, the branching topology from the currently relaxing segments define the maximum stretch q as the priority variables [53], and the modulus relaxed in this time interval sets the modulus of the pom-pom mode. Based on the pompom model [13], equating the maximum tension with the tension along the backbone gives a maximum stretch of q.…”

Section: Resultsmentioning

confidence: 99%

“…Recent molecular dynamics results also suggest that entanglement constraints at the branch-points are stronger than those for linear polymers [49]. For this reason, we have decided not to have a cut-off function at order one entanglement like in the hierarchical model [40,41]. Having a zero (as in the original BoB model) or a small value (as in the present work) allows us to predict rheology of branched polymers with segment lengths down to order one entanglement.…”

Section: Ii4 Modelingmentioning

confidence: 99%

“…In view of the lack of mesoscopic models predicting the rheology of generic unentangled (or barely entangled, as here) branched polymers, we used the BoB model [8,24,40] in order to describe the flow properties of the Cayley tree polymers.…”

Section: Ii4 Modelingmentioning

confidence: 99%

See 3 more Smart Citations

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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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Ii4 Modelingmentioning

confidence: 99%

Section: Ii4 Modelingmentioning

confidence: 99%

See 2 more Smart Citations

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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“…An additional piece of physics not included in the present model (nor in the original pom-pom model) is the nested tube structure and different types of stress relaxation suggested by constraint release within the dynamic dilution approximation. In the linear rheological limit, stress is relaxed both by tube escape and by constraint release [Das et al (2014)]. It seems probable that, in nonlinear flow, such effects would couple with the ES identified within the present work.…”

Section: Discussionmentioning

confidence: 77%

Modifying the pom-pom model for extensional viscosity overshoots

Hawke¹,

Huang²,

Hassager³

et al. 2015

Journal of Rheology

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We have developed a variant of the pom-pom model that qualitatively describes two surprising features recently observed in filament stretching rheometer experiments of uniaxial extensional flow of industrial branched polymer resins: (i) Overshoots of the transient stress during steady flow and (ii) strongly accelerated stress relaxation upon cessation of the flow beyond the overshoot. Within the context of our model, these overshoots originate from entanglement stripping (ES) during the processes of normal chain retraction and branch point withdrawal. We demonstrate that, for a single mode, the predictions of our overshoot model are qualitatively consistent with experimental data. To provide a quantitative fit, we represent an industrial melt by a superposition of several individual modes. We show that a minimal version of our model, in which ES due to normal chain retraction is omitted, can provide a reasonable, but not perfect, fit to the data. With regard the stress relaxation after (kinematically) steady flow, we demonstrate that the differential version of tube orientation dynamics in the original pom-pom model performs anomalously. We discuss the reasons for this and suggest a suitable alternative. V C 2015 The Society of Rheology.[http://dx

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Comb and Bottlebrush Polymers with Superior Rheological and Mechanical Properties

2019

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combined with the grafting-to method [1,10] results in comb polystyrenes (PSs) with well-entangled monodisperse backbone and side chains; however, branch points along the backbone are randomly distributed. This random distribution of branch points has no distinct effect on the rheological properties of dense comb topologies; however, it will broaden the backbone relaxation time of loose comb topologies even though the molecular weight distribution is narrow enough. [11] A controlled branching point spacing can be achieved through the coupling of living macroanions; [12] however, this method is prone to slightly high molecular weight distribution, Ð > 1.5. Synthesis of welldefined densely grafted bottlebrushes using ROMP and grafting-through method guarantees the presence of one side chain per repeating unit on the backbone. Bottlebrushes with more than one branch per backbone repeating unit can also be synthesized using ROMP and macromonomers with more bulky groups referred as wedge polymers. [13] These bottlebrushes are similar to that of the dendronized polymer with only one layer of grafting. Loosely grafted bottlebrushes with longer distance between the branching points can be achieved using ROMP technique through copolymerization of macromonomer and a diluent molecule, e.g., racemic endo,exo-norbornenyl diesters, with different ratios. However, different reactivity of macromonomer and diluent leads to a gradient of branching point spacing along the backbone, [14] where the conformations of side chains along the backbone are affected by this gradient. [15] It should be mentioned that the bottlebrushes synthesized with ROMP technique have different repeating units in the backbone than the side chains which might cause microphase separation. However this issue could be ignorable in dense bottlebrushes where the volume fraction of backbone is less than 1 wt%. In order to avoid any microphase separation, Sheiko and co-workers [16] synthesized a series of dense combs and loose bottlebrushes homo poly(n-butyl acrylates) (PBA) with similar side chains and systematically varied grafting density through copolymerization of nonfunctional n-butyl acrylates with trimethylsilyl-protected acrylates by ATRP. However, in order to achieve high degree of polymerization (DP) of backbone (entangled system) for dense bottlebrushes, they had to use slightly different backbones, i.e., poly(n-butyl methacrylate). An organometallic coordinative insertion polymerization of α-olefins results in entangled densely grafted bottlebrushes with rod-like side chains where both backbone and side chains have alkane groups. However the dispersity index of such homopolymer bottlebrushes would Comb and bottlebrush polymers present a wide range of rheological and mechanical properties that can be controlled through their molecular characteristics, such as the backbone and side chain lengths as well as the number of branches per molecule or the grafting density. This review investigates the impact of these characteristics specifically on the zero sh...

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Numerical prediction of nonlinear rheology of branched polymer melts

Cited by 38 publications

References 35 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

Modifying the pom-pom model for extensional viscosity overshoots

Comb and Bottlebrush Polymers with Superior Rheological and Mechanical Properties

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