Pom-pom-like constitutive equations for comb polymers

Lentzakis, Helen; Das, Chinmay; Vlassopoulos, Dimitris; Read, Daniel J.

doi:10.1122/1.4895606

Cited by 32 publications

(36 citation statements)

References 55 publications

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“…The experimental long-time relaxation is approximately power-law decay (linear in log-log plot). Such a non-exponential behaviour may reflect coupling between different modes (see also discussion on the parameter B above): the stretches in different segments of the dendritic macromolecule are coupled, hence describing them as relaxing independently is not completely correct [15,44]. Once stretched, the stretch of inner segments can only relax once the stretches in the outer segments had already relaxed.…”

Section: Resultsmentioning

confidence: 99%

“…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. The rheological properties of model polymers provide profound implications in finessing molecular models and improving material performance in technological applications [5][6][7][8][9][10][11][12][13][14][15]. Focusing on the nonlinear rheology of comb polymers, one important consequence of the recent progress in experimental extensional and shear rheology is the quantitative assessment of the role of dynamic dilution in transient strain hardening and stress overshoot, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…An important element of the pom-pom model is the branch withdrawal at rates larger than the effective Rouse rate of the polymer. This was worked out for the case of multiple branches along the backbone, and a modified pom-pom model for combs captured the transient extensional data remarkably well [15]. In parallel, whereas experiments with well-defined branched polymers (such as combs) are absolutely necessary in order to elucidate the role of the molecular parameters (number, size and distribution of branches, distance between branch points) in the rheological response, the state of the art BoB model, developed for randomly branched polymers [24], can be adopted to well-defined branching in a straightforward way.…”

Section: Introductionmentioning

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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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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Equation (4) can be simplified to SHF 2 bb 1 bb 1 q Z φ = − − , which shows that for a given backbone and side chain length, SHF scales with q 3 or M 3 . [64] For comb polymers with multiple branching points, equivalent to a pom-pom molecule with 2q, the maximum limiting stretch of the backbone segments hierarchically increases from 1 for the outermost segments of the backbone to almost q for the innermost ones located in the middle of the backbone. The concept of a constitutive equation for the pom-pom model was extended for more complicated branched topologies, e.g., Cayley trees, [61] randomly branched polymers, [62,63] as well as comb structures.…”

Section: Strain Hardening Factormentioning

confidence: 99%

“…The concept of a constitutive equation for the pom-pom model was extended for more complicated branched topologies, e.g., Cayley trees, [61] randomly branched polymers, [62,63] as well as comb structures. [64] For comb polymers with multiple branching points, equivalent to a pom-pom molecule with 2q, the maximum limiting stretch of the backbone segments hierarchically increases from 1 for the outermost segments of the backbone to almost q for the innermost ones located in the middle of the backbone. Therefore, the average maximum stretching of a backbone within a comb should be lower than that of a pom-pom with the same amount of branches.…”

Section: Strain Hardening Factormentioning

confidence: 99%

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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Macromolecular Rheology

Ruymbeke

Vlassopoulos

2022

Macromolecular Engineering

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One of the most important features of polymeric systems is their response to weak external stimuli. Of utmost importance is their reaction to an imposed mechanical load, which reflects their viscoelasticity. The viscoelastic properties of polymers are central to their handling and are responsible for their wide‐ranging applications. In this article, we provide the basic elements of molecular rheology, the science of deformation and flow of matter, which is necessary for understanding polymer viscoelasticity and linking it to molecular characteristics of the studied macromolecules. The presentation is basic and does not require prior knowledge on the topic. It refers to amorphous flexible polymers with emphasis on melts. First, the fundamental aspects of rheological measurements are discussed, followed by a discussion on linear viscoelasticity. Then, the models for the linear viscoelastic response of both unentangled and entangled polymers are presented in detail for different architectures, linear, star, and well‐characterized branched polymers. Subsequently, we focus on the nonlinear viscoelastic regime with particular emphasis on the current state‐of‐the‐art and remaining challenges. Where appropriate, some applications of interest to the industrial practice are briefly discussed. Nonlinear phenomena such as flow instabilities, flow‐induced crystallization, and wall slip are not covered.

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Pom-pom-like constitutive equations for comb polymers

Cited by 32 publications

References 55 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

Comb and Bottlebrush Polymers with Superior Rheological and Mechanical Properties

Macromolecular Rheology

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