Dynamic dilution exponent in monodisperse entangled polymer solutions

Shahid, Taisir; Huang, Qian; Oosterlinck, Filip; Clasen, Christian; Ruymbeke, Evelyne Van

doi:10.1039/c6sm01083k

Cited by 49 publications

(116 citation statements)

References 63 publications

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“…(v) Simulation by tube shrinking algorithms convert equilibrated polymer configurations into networks of piecewise linear segments between mutual contact points capturing the impenetrability of chains but deform chains in an ad hoc manner: The results agree with packing models for homopolymer melts [18,19]; Experimentally, the dilation exponent a is very difficult to access; in rheological models the tube size is determined by adjusting its value to reach the best agreement between tube based rheological models and experimental data [10,20]. Rheological results on hierarchical branched polymers find exponents 1 ≤ a ≤ 4=3 [5].…”

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confidence: 68%

“…We note, as shown in the Supplemental Material [21], that the rheological data always reveal a power law exponent between 2. 20 In this work, by applying NSE spectroscopy we measured the dynamic dilution exponent a directly on the scale of the topological constraints, commonly denoted as the tube. The experiments were entirely performed in the highly entangled regime (Z ≥ 40).…”

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confidence: 99%

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Direct Assessment of Tube Dilation in Entangled Polymers

et al. 2019

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A key ingredient within theories focusing on the rheology of entangled polymers is the way how the topological constraints of an entangled chain are lifted by unconstrained segments, i.e., how the constraining tube is dilated. This important question has been addressed by directly measuring the tube diameter d at the scale of the tube by neutron spin echo spectroscopy. The tube diameter d and plateau modulus G 0 N of highly entangled polyethylene oxide (PEO) chains of volume fraction c that are diluted by low molecular PEO show a concentration dependence d ∝ c a=2 and G 0 N ∝ c 1þa with an exponent a close to 4=3. This result allows the clear discrimination between different theoretical models that predict 4=3 or other values between 1 and 2 and provides an important ingredient to tube model theories.

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confidence: 68%

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confidence: 99%

Direct Assessment of Tube Dilation in Entangled Polymers

et al. 2019

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“…The exact value of dilution exponent α for branched polymers depends on the mathematical definition of relaxation mechanisms and moduli considered in the tube theory [22,38,45,52,53] as well as the experimental method to define this value. [54] It should be mentioned that Equation (1) considers combs with a limited number of side chains, 6 ≤ q ≤ Z bb . The upper limit of q in this model is equal to the number of entanglements of the backbone, Z bb , where the branching point spacing is almost equal to one entanglement, Z g ≈ 1.…”

Section: Zero Shear Viscositymentioning

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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“…As shown in ref. [13,14,53], when the CR-activated CLF has a large influence on the relaxation of long chains, an enhanced effect of CR process from the short chains is measured, corresponding to an experimentally determined apparent dynamic dilution exponent exp, which takes values close to 4/3 (as determined based on the evolution of the terminal modulus). Whereas this issue remains unsettled, it has been shown recently that by accounting for CR-CLF process, the viscoelastic properties of all these binary linear blends with well-separated molar masses can be correctly predicted with a (theoretically determined) dynamic dilution exponent = 1.…”

Section: Introductionmentioning

confidence: 99%

“…Whereas this issue remains unsettled, it has been shown recently that by accounting for CR-CLF process, the viscoelastic properties of all these binary linear blends with well-separated molar masses can be correctly predicted with a (theoretically determined) dynamic dilution exponent = 1. 14,53,54 The objective of the present work is to extend the investigation of CR effect in more complex polymer blends, involving branched polymers which display hierarchical relaxation of their different generations of branches in the monodisperse state and a respective tunable nonlinear response (for example, extension hardening). To this end, we investigate the relaxation dynamics of binary mixtures of entangled H-polymer (the probe) 55 in linear polymers (the matrix) of varying molar mass.…”

Section: Introductionmentioning

confidence: 99%

Constraint Release Mechanisms for H-Polymers Moving in Linear Matrices of Varying Molar Masses

et al. 2019

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We investigate the influence of the environment on the relaxation dynamics of well-defined Hpolymers diluted in a matrix of linear chains. The molar mass of the linear chain matrix is systematically varied and the relaxation dynamics of the H-polymer is probed by means of linear viscoelastic measurements, with the aim to understand its altered motion in the different blends, compared to its pure melt state. Our results indicate that short unentangled linear chains accelerate the relaxation of both the branches and the backbone of the H-polymers by acting as an effective solvent.On the other hand, the relaxation of the H-polymer in an entangled matrix is slowed-down, with the degree of retardation depending on the entanglements number of the linear chains. We show that this retardation can be quantified by considering that the H-polymers are moving in a dilated tube at the rhythm of the motion of the linear matrix.

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Dynamic dilution exponent in monodisperse entangled polymer solutions

Cited by 49 publications

References 63 publications

Direct Assessment of Tube Dilation in Entangled Polymers

Direct Assessment of Tube Dilation in Entangled Polymers

Comb and Bottlebrush Polymers with Superior Rheological and Mechanical Properties

Constraint Release Mechanisms for H-Polymers Moving in Linear Matrices of Varying Molar Masses

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