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0019933162
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Boué, F.; Nierlich, M.; Leibler, L. Polymer 1982, 23, 29.
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Boué, F.1
Nierlich, M.2
Leibler, L.3
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9
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34249777766
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-
Unwanted inhomogeneities (dusts or bubbles) scatter at low-q; also polydispersity effects are most important there
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Unwanted inhomogeneities (dusts or bubbles) scatter at low-q; also polydispersity effects are most important there.
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-
-
-
10
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0001012487
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Rawiso, M.; Duplessix, R.; Picot, C. Macromolecules 1987, 20, 630.
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Rawiso, M.1
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Picot, C.3
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11
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34249799550
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max = 1/(2χf(1-f)). A generalization of the theory including the effect of finite χ is straightforward.
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max = 1/(2χf(1-f)). A generalization of the theory including the effect of finite χ is straightforward.
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-
-
-
14
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17444415942
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Wittmer, J. P.; Meyer, H.; Baschnagel. J.; Johner, A.; Obukhov, S. P.; Mattioni, L.; Müller, M.; Semenov, A. N. Phys. Rev. Lett. 2004, 93, 147801.
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Mattioni, L.6
Müller, M.7
Semenov, A.N.8
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17
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79051469264
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Johner, A.3
Semenov, A.N.4
Obukhov, S.P.5
Meyer, H.6
Baschnagel, J.7
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19
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18744399271
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Cavallo, A.1
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Wittmer, J.P.3
Johner, A.4
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20
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34247228246
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Curro, J. G.; Schweizer, K. S.; Grest. G. S.; Kremer, K. J. Chem. Phys. 1991, 91, 1359.
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Curro, J.G.1
Schweizer, K.S.2
Grest, G.S.3
Kremer, K.4
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21
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0842330642
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Auhl, R.; Everaers, R.; Grest, G. S.; Kremer, K.; Plimpton, S. J. J. Chem. Phys. 2003, 119, 12718.
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Auhl, R.1
Everaers, R.2
Grest, G.S.3
Kremer, K.4
Plimpton, S.J.5
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23
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0038672658
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Schäfer, L.; Müller, M.; Binder, K. Macromolecules 2000, 33, 4568.
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Schäfer, L.1
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28744431985
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Svaneborg, C.1
Grest, G.S.2
Everaers, R.3
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26
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34249780781
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15.16) of the bath surrounding the chain under consideration. This can be shown to be negligible.
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15.16) of the bath surrounding the chain under consideration. This can be shown to be negligible.
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28
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0003105009
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Paul, W.; Binder, K.; Heermann, D.; Kremer, K. J. Phys. 11 1991, 1, 37.
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J. Phys
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Paul, W.1
Binder, K.2
Heermann, D.3
Kremer, K.4
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29
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4143106160
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Monte Carlo Simulation of Polymers: Coarse-Grained Models
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Computational Soft Matter: From Synthetic Polymers to Proteins; Attig, N, et al, Eds, NIC: Jülien, Germany
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Baschnagel, J.; Wittmer, J. P.; Meyer, H. Monte Carlo Simulation of Polymers: Coarse-Grained Models. In Computational Soft Matter: From Synthetic Polymers to Proteins; Attig, N, et al., Eds.; NIC Series, Volume 23; NIC: Jülien, Germany, 2004; pp 83-140.
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Baschnagel, J.1
Wittmer, J.P.2
Meyer, H.3
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31
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0001557223
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Wittmer, J. P.; Milchev, A.; Cates, M. E. J. Chem. Phys. 1998, 109, 834.
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Wittmer, J.P.1
Milchev, A.2
Cates, M.E.3
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32
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34047213586
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Springer, cond-mat/0604279
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Huang, C. C.; Xu, H.; Crevel, F.; Wittmer, J. P.; Ryckaert, J.-P. Lect. Notes Phys. (Springer) 2006, 704, 379; cond-mat/0604279.
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Lect. Notes Phys
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Huang, C.C.1
Xu, H.2
Crevel, F.3
Wittmer, J.P.4
Ryckaert, J.-P.5
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33
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34249789538
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Note that there is no difference between the annealed and the corresponding quenched polydispersity for infinite macroscopically homogeneous systems as long as equilibrium properties (static rather than dynamic properties) are concerned. This follows from the well-known behavior of fluctuations of extensive parameters (like mean molecular weight, or polydispersity degree) in macroscopic systems: the relative fluctuations vanish as 1/√V as the total V → ∞. Incidently, the macroscopic limit V → ∞ is taken first in our analytical calculations, i.e. we consider systems containing an infinite number of (annealed or quenched) chains. The large chain limit (μ, 1/〈N〉 → 0 or N → ∞) is then taken afterwards to increase the range of the scale free Kratky regime. Taking the second limit simply means that the chain size becomes much larger than the length-scale 1/q probed experimentally
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Note that there is no difference between the annealed and the corresponding quenched polydispersity for infinite macroscopically homogeneous systems as long as equilibrium properties (static rather than dynamic properties) are concerned. This follows from the well-known behavior of fluctuations of extensive parameters (like mean molecular weight, or polydispersity degree) in macroscopic systems: the relative fluctuations vanish as 1/√V as the total volume V → ∞. Incidently, the macroscopic limit V → ∞ is taken first in our analytical calculations, i.e. we consider systems containing an infinite number of (annealed or quenched) chains. The large chain limit (μ = 1/〈N〉 → 0 or N → ∞) is then taken afterwards to increase the range of the scale free Kratky regime. Taking the second limit simply means that the chain size becomes much larger than the length-scale 1/q probed experimentally.
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43
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34249804116
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The full cumbersome expression leading to eq 12 is not given here
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The full cumbersome expression leading to eq 12 is not given here.
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-
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48
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34249816109
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This result has been cross-checked by means of a direct perturbation calculation for monodisperse chains using the Padé approximation of Debye's formula for the effective interaction potential
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This result has been cross-checked by means of a direct perturbation calculation for monodisperse chains using the Padé approximation of Debye's formula for the effective interaction potential.
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49
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34249800617
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As indicated in ref 14, b*2 may be best obtained from the intramolecular (mean-squared) distance R2(s) averaged over all monomer pairs (n, m, n, s) of the chains. As suggested by eq 17 one plots y, R2(s)/s as a function of x -1√s which allows the simple one-parameter fit: y=b*2(1, √24/π3/ρb*3 x) The prefactor-derived in ref 14, eq 2, for monodisperse chains-does also apply to polydisperse systems provided 〈N〉 ≫ s. Note that it is in principle also possible to obtain from the total coil size as indicated by eqs 15 and 16 for the polydisperse case. Due to chain end effects it turns out that this requires much larger (mean) chain lengths than the recommended method above. For details see ref 49
-
3 x) The prefactor-derived in ref 14, eq 2, for monodisperse chains-does also apply to polydisperse systems provided 〈N〉 ≫ s. Note that it is in principle also possible to obtain from the total coil size as indicated by eqs 15 and 16 for the polydisperse case. Due to chain end effects it turns out that this requires much larger (mean) chain lengths than the recommended method above. For details see ref 49.
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50
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34249816753
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Manuscript in preparation
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Wittmer, J. P.; et al. Manuscript in preparation.
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Wittmer, J.P.1
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51
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34249780066
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Since the EP chains break and recombine permanently the relaxation time of the system is not set by the typical EP radius of gyration but rather by the size of a small chain segment which has just about the time to diffuse over its radius before it breaks or recombines.29 The high frequency for the scission-recombination attempts used in our simulations ensures that the effective recombination time is small and the dynamics is, hence, always of Rouse type. It should be emphasized that due to the permanent recombination events a data structure based on a topologically ordered intra chain interactions is not appropriate and straight-forward pointer lists between connected monomers are required.30 The attempt frequency should not be taken too large to avoid useless immediate recombination of the same monomers, and some time must be given for the monomers to diffuse over a couple of monomer diameters between scission-recombination attempts.31
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31
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53
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34249806258
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Schulz, M.; Frisch, H. L.; Reineker, P. New J. Phys. 2004, 6, 77.
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(2004)
New J. Phys
, vol.6
, pp. 77
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Schulz, M.1
Frisch, H.L.2
Reineker, P.3
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54
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34249792325
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We have computed the response function S(qf= 1) for monodisperse polymers over a large range of densities and for a nouvel version of the BFM with finite overlap energies. This has been done to verify the recent prediction of fluctuation induced long-range repulsions between solid objects in polymer media.15,16 This approach suggests a systematic violation of the RPA eq 2 proportional to q3 which we have put to a numerical test. Our findings, complicated by the fact that trivial monomer-monomer correlations of Percus-Yevick type51,52 must be correctly taken into account26-will be presented elsewhere. Please note that these corrections to eq 2 do correspond to higher order deviations which can be shown to be negligible for the questions addressed in this paper
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26-will be presented elsewhere. Please note that these corrections to eq 2 do correspond to higher order deviations which can be shown to be negligible for the questions addressed in this paper.
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