Chain Dimensions and Entanglement Spacings

Fetters, Lewis J.; Lohse, David J.; Colby, Ralph H.

doi:10.1007/978-0-387-69002-5_25

Cited by 387 publications

(549 citation statements)

References 80 publications

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“…The entanglement mass of PEP at 492 K was estimated to be M e Ӎ 3360 g / mol from the experimental values published in Ref. 27. As can be seen in Table III, the average mean square end-to-end distance and the average mean square radius of gyration of the longest chains approximately obey random walk statistics, i.e., ͗R ee 2 ͘ / ͗R g 2 ͘ =6.…”

Section: Simulated Systemsmentioning

confidence: 85%

“…Following the considerations explained in the previous section, the level of coarse graining was chosen to be ten monomers as a blob, which is one-half of the reported entanglement length. 27 Thus, from the atomistic simulations ͑described in Sec. II A͒, we calculate the center of mass every ten monomers producing a system of 12 chains of eight blobs per chain.…”

Section: Determining the Potential Of Mean Forcementioning

confidence: 99%

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Chain dynamics of poly(ethylene-alt-propylene) melts by means of coarse-grained simulations based on atomistic molecular dynamics

Pérez-Aparicio

Colmenero

Álvarez

et al. 2010

The Journal of Chemical Physics

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We present coarse-grained molecular dynamics simulations of poly͑ethylene-alt-propylene͒ ͑PEP͒ melts, ranging in chain length from about N e ͑the entanglement length͒ to N =6N e . The coarse-grained parameters, potential of mean force and bare friction, were determined from fully atomistic molecular dynamics simulations carried out on a PEP cell containing 12 chains of 80 monomers each and subjected to periodic boundary conditions. These atomistic simulations were previously validated by means of extensive neutron scattering measurements. Uncrossability constrains were also introduced in the coarse-grained model to prevent unphysical bond crossing. The coarse-grained simulations were carried out at 492 K and focus on chain dynamics. The results obtained were analyzed in terms of Rouse coordinates and Rouse correlators. We observe deviations from Rouse behavior for all chain lengths investigated, even when the chain stiffness is incorporated in the Rouse model. These deviations become more important as the chain length increases. The general scenario emerging from the results obtained is that the deviations from Rouse-like behavior are due to correlations among the forces acting upon a chain bead, which seem to be related with the constraint of uncrossability among the chains. As consequence, nonexponentiality of the Rouse correlators and mode-and time-dependent friction are observed. It seems that, in the molecular weight explored, these effects still give not raise to reptation behavior but to a crossover regime between Rouse and reptation. On the other hand, the results obtained are in qualitative agreement with those expected from the so-called generalized Rouse models, based on memory function formalisms.

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Section: Simulated Systemsmentioning

confidence: 85%

Section: Determining the Potential Of Mean Forcementioning

confidence: 99%

Chain dynamics of poly(ethylene-alt-propylene) melts by means of coarse-grained simulations based on atomistic molecular dynamics

Pérez-Aparicio

Colmenero

Álvarez

et al. 2010

The Journal of Chemical Physics

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“…We are not aware of any studies that have determined the entanglement or critical molecular weight of PEHA. However, a comparable acrylate polymer with a linear side-chain also containing eight carbons, poly octyl acrylate (POA), has an M e ∼ 15 kg/mol and an estimated M c ∼ 25 kg/mol [95]. The molecular weights of all our samples (Table I) are below this M c and we thus expect our polymers to be unentangled, meaning that the cross-linking effects of reversible supramolecular side group interactions can be readily identified.…”

Section: Introductionmentioning

confidence: 94%

“…From Table I, we see that as φ UPy increases, N m decreases from 16 for UPyPEHA6 to 6 for UPyPEHA14. Compared with the Kuhn length (∼13 monomers) of a similar polymer (PHA) [95], the segments between two UPy groups are not flexible enough to search for a different partner in a surrounding volume, especially for high φ UPy samples. To relax stresses, cooperative dissociation of several stickers simultaneously is required for segments being flexible enough to search for a new partner.…”

Section: τ S Vs φ U P Ymentioning

confidence: 99%

Linear shear and nonlinear extensional rheology of unentangled supramolecular side-chain polymers

Cui

Boudara

Huang

et al. 2018

Journal of Rheology

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Supramolecular polymers are important within a wide range of applications including printing, adhesives, coatings, cosmetics, surgery and nano-fabrication. The possibility to tune polymer properties through the control of supramolecular associations makes these materials both versatile and powerful. Here, we present a systematic investigation of the linear shear rheology for a series of unentangled ethylhexyl acrylate based polymers for which the concentration of randomly distributed supramolecular side-groups are systematically varied. We perform a detailed investigation of the appplicability of Time Temperature Superposition (TTS) for our polymers; small amplitude oscillatory shear rheology is combined with stress relaxation experiments to identify the dynamic range over which TTS is a reasonable approximation. Moreover, we find that the "stickyRouse" model normally used to interpret the rheological response of supramolecular polymers fits our experimental data well in the terminal regime, but is less successful in the rubbery plateau regime. We propose some modifications to the "sticky-Rouse" model, which includes more realistic assumptions with regards to (i) the random placement of the stickers along the backbone, (ii) the contributions from dangling chain ends and (iii) the chain motion upon dissociation of a sticker and re-association with a new co-ordination which involves a finite sized "hop" of the chain. Our model provides an improved description of the plateau region. Finally, we measure the extensional rheological response of one of our supramolecular polymers. For the probed extensional flow rates, which are small compared to the characteristic rates of sticker dynamics, we expect a Rouse-type description to work well. We test this by modeling the observed strain hardening using the upper convected Maxwell model and demonstrate that this simple model can describe the data well, confirming the prediction and supporting our determination of sticker dynamics based on linear shear rheology. * k.j.l.mattsson@leeds.ac.uk 2

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“…By using the former equations we find C ∞ ≈ 5, 9 and 15 for k = 3, 5 and 8, respectively. The investigated range 5 C ∞ 15 for the semiflexible cases corresponds to the majority of common polymers [22,39]. For each pair (f, k) we generate typically 100-200 realizations of the SCNPs.…”

Section: Model and Simulation Detailsmentioning

confidence: 99%

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

Moreno

Bačová

Verso

et al. 2017

J. Phys.: Condens. Matter

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Abstract.Polymeric single-chain nanoparticles (SCNPs) are soft nano-objects synthesized by purely intramolecular cross-linking of single polymer chains. By means of computer simulations, we investigate the conformational properties of SCNPs as a function of the bending stiffness of their linear polymer precursors. We investigate a broad range of characteristic ratios from the fully flexible case to those typical of bulky synthetic polymers. Increasing stiffness hinders bonding of groups separated by short contour distances and increases looping over longer distances, leading to more compact nanoparticles with a structure of highly interconnected loops. This feature is reflected in a crossover in the scaling behaviour of several structural observables. The scaling exponents change from those characteristic for Gaussian chains or rings in θ-solvents in the fully flexible limit, to values resembling fractal or 'crumpled' globular behaviour for very stiff SCNPs. We characterize domains in the SCNPs. These are weakly deformable regions that can be seen as disordered analogues of domains in disordered proteins. Increasing stiffness leads to bigger and less deformable domains. Surprisingly, the scaling behaviour of the domains is in all cases similar to that of Gaussian chains or rings, irrespective of the stiffness and degree of cross-linking. It is the spatial arrangement of the domains which determines the global structure of the SCNP (sparse Gaussian-like object or crumpled globule). Since intramolecular stiffness can be varied through the specific chemistry of the precursor or by introducing bulky side groups in its backbone, our results propose a new strategy to tune the global structure of SCNPs.

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Chain Dimensions and Entanglement Spacings

Cited by 387 publications

References 80 publications

Chain dynamics of poly(ethylene-alt-propylene) melts by means of coarse-grained simulations based on atomistic molecular dynamics

Chain dynamics of poly(ethylene-alt-propylene) melts by means of coarse-grained simulations based on atomistic molecular dynamics

Linear shear and nonlinear extensional rheology of unentangled supramolecular side-chain polymers

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

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