Determination of Tube Theory Parameters Using a Simple Grid Model as an Example

Likhtman, Alexei E.; Talib, Mohamad Shukor; Vorselaars, Bart; Ramı́rez, Jorge

doi:10.1021/ma302103p

Cited by 22 publications

(31 citation statements)

References 22 publications

(62 reference statements)

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“…The estimated monomer densities were consistent neither with each other, nor with N pp e . • The works of Uchida et al [86] and Likhtman et al [87] are compatible with our MSMbased PP analysis, which shows that the average number of Kuhn steps per strand (i.e. the parameter β) can be obtained from a purely static property of the multi-chain system: the equilibrium PP-length distribution.…”

Section: Appendix C Relation To Recent Worksupporting

confidence: 88%

“…• Likhtman et al [87] obtained the PP-length distribution for a toy model consisting of a single Rouse chain on a cubic lattice, where the grid lines act as rigid obstacles. From this they calculated N pp e and compared it to estimates from several procedures based on dynamics, in which the monomer density appears as a parameter: fitting the relaxation modulus G(t) with an expression derived from slip-spring simulations [57,88], fitting the mean squared displacement of the middle monomer with tube-model scaling laws in different regimes, and fitting the dynamic structure factor in NSE measurements with an empirical formula [65].…”

Section: Appendix C Relation To Recent Workmentioning

confidence: 99%

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Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models

et al. 2014

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We present a method to map the full equilibrium distribution of the primitivepath (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field 'target' model. Most previous works used the Doi-Edwards tube model as a target. However, the average number of monomers per PP segment, obtained from multi-chain PP networks, has consistently shown a discrepancy of a factor of two with respect to tube-model estimates. Part of the problem is that the tube model neglects fluctuations in the lengths of PP segments, the number of entanglements per chain and the distribution of monomers among PP segments, while all these fluctuations are observed in multi-chain simulations. Here we use a recently proposed slip-link model, which 7 Current address: Dow

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Section: Appendix C Relation To Recent Worksupporting

confidence: 88%

Section: Appendix C Relation To Recent Workmentioning

confidence: 99%

Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models

et al. 2014

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“…This procedure however is affected by some implicit assumptions on the static properties of the tube, and has important shortcomings even in the simplest case of pure linear chains (see the recent discussion in Ref. 67 ). Similar drawbacks are present in the estimation of the tube parameters from scattering functions, 20 and in particular if the chains are far from the limit of high molecular weight (Z ∼ 100).…”

Section: Discussionmentioning

confidence: 99%

“…The dependence on the estimator is consistent with observations in Ref46 for nanocomposites with hard NPs. The dependence on the tube representation was brought up in a study of a simple grid model,67 and we…”

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confidence: 99%

The Role of the Topological Constraints in the Chain Dynamics in All-Polymer Nanocomposites

et al. 2017

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We investigate all-polymer nanocomposites, formed by linear chains and single-chain polymer nanoparticles (SCNPs), by means of large-scale simulations. To distinguish the role of the soft penetrable character of the SCNPs in the topological constraints from other specific contributions present in experiments, the simulations for different compositions of the mixture are performed at constant density, and with identical segmental mobility and monomer excluded volume for the SCNPs and linear chains. Every composition leads to a well-dispersed nanocomposite with fully-penetrated nanofillers. Hence, unlike in the case of hard nanofillers, the SCNPs do not exert confinement effects on the linear chains, and only contribute to the topological constraints. We discuss the intramolecular dynamics of the linear chains in terms of the tube model. We determine the entanglement length of the linear chains by analysing their isoconfigurational mean paths (IMP) and the primitive paths (PP), as a function of the concentration and topology of the SCNPs. In the analysis we use different estimators proposed in the literature. The IMP and PP analysis in the nanocomposites with sparse SCNPs yields values of the entanglement length smaller and larger, respectively, than in the reference pure linear melt, though small variations are observed. A more consistent trend is found in the nanocomposites with globular SCNPs, where both the IMP and PP analysis unambiguously reveal that the linear chains are more entangled than in the pure linear melt. Such differences between the effects of SCNPs with different topologies are presumably related to the much higher fraction of threadable loops in the globular SCNPs, with respect to their sparse counterparts, which effectively lead to more topological constraints.

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“…The determination of the dilated tube diameter a from computer simulations is a delicate issue as addressed by Likhtman et al 29 Tube dilation theory predicts that a depends on φ l according to a = a mono φ −α/2 l where a mono is the tube diameter for the monodisperse system and α = 4/3. The precise value of α is a matter of debate.…”

Section: B Tube Dilationmentioning

confidence: 99%

Reptation and constraint release dynamics in bidisperse polymer melts

Langeloth

Masubuchi

Böhm

et al. 2014

The Journal of Chemical Physics

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Bidisperse melts of linear, entangled polymer chains were studied using dissipative particle dynamics. The entanglement constraints were mimicked with our newly developed slip-spring approach. The compositions cover blends with short matrix chains, slightly above the molecular entanglement weight as well as blends were both chain lengths exhibit distinct entangled dynamics at various weight fractions. The Struglinsky-Graessley parameter Gr, which is the ratio between the relaxation time of the long chains due to pure reptation and the relaxation time of the tube caused by constraint release, ranges between values high above and below unity. We compare our slip-spring model with simulations that use conventional generic polymer models where bond crossings are prevented by excluded-volume interactions and find fairly good agreement in terms of the mean squared displacement. However, the slip-spring approach requires only a fraction of the computational time, making large scale systems feasible. The dynamical interference of the two different chain lengths is discussed in terms of reptation and constraint release dynamics. For bidisperse melt compositions with Gr < 1.0 the relaxation time of the long chain component is not affected by constraint release. However, for compositions where constraint release is supposed to contribute significantly to the relaxation mechanism (Gr > 1.0), we find strong evidence that the long chains reptate inside a dilated tube whose diameter increases with an exponent of 1/2 towards lower weight fraction of the long chains. Furthermore we observe a linear relation between the relaxation time and weight fraction. Therefore, based on the relaxation times, our results support the validity of the tube dilation model as proposed by Doi et al. [Macromolecules 20, 1900-1906 (1987)].

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Determination of Tube Theory Parameters Using a Simple Grid Model as an Example

Cited by 22 publications

References 22 publications

Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models

Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models

The Role of the Topological Constraints in the Chain Dynamics in All-Polymer Nanocomposites

Reptation and constraint release dynamics in bidisperse polymer melts

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