2013
DOI: 10.1021/ma302103p
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Determination of Tube Theory Parameters Using a Simple Grid Model as an Example

Abstract: Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs 3 entanglement related parameters, but only 2 combinations of them are relevant for… Show more

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Cited by 22 publications
(31 citation 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%
See 1 more Smart Citation
“…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%
“…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…”
mentioning
confidence: 99%
“…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%