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Volumn 40, Issue 10, 2007, Pages 3805-3814

Intramolecular form factor in dense polymer systems: Systematic deviations from the debye formula

Author keywords

[No Author keywords available]

Indexed keywords

CHAIN SIZE; DEBYE FORMULA; DENSE POLYMER SOLUTIONS; GAUSSIAN CONFIGURATIONS; INCOMPRESSIBILITY;

EID: 34249781990     PISSN: 00249297     EISSN: None     Source Type: Journal    
DOI: 10.1021/ma0626113     Document Type: Article
Times cited : (54)

References (54)
  • 9
    • 34249777766 scopus 로고    scopus 로고
    • Unwanted inhomogeneities (dusts or bubbles) scatter at low-q; also polydispersity effects are most important there
    • Unwanted inhomogeneities (dusts or bubbles) scatter at low-q; also polydispersity effects are most important there.
  • 11
    • 34249799550 scopus 로고    scopus 로고
    • max = 1/(2χf(1-f)). A generalization of the theory including the effect of finite χ is straightforward.
    • max = 1/(2χf(1-f)). A generalization of the theory including the effect of finite χ is straightforward.
  • 26
    • 34249780781 scopus 로고    scopus 로고
    • 15.16) of the bath surrounding the chain under consideration. This can be shown to be negligible.
    • 15.16) of the bath surrounding the chain under consideration. This can be shown to be negligible.
  • 29
    • 4143106160 scopus 로고    scopus 로고
    • Monte Carlo Simulation of Polymers: Coarse-Grained Models
    • Computational Soft Matter: From Synthetic Polymers to Proteins; Attig, N, et al, Eds, NIC: Jülien, Germany
    • 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.
    • (2004) NIC Series , vol.23 , pp. 83-140
    • Baschnagel, J.1    Wittmer, J.P.2    Meyer, H.3
  • 33
    • 34249789538 scopus 로고    scopus 로고
    • 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
    • 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.
  • 43
    • 34249804116 scopus 로고    scopus 로고
    • The full cumbersome expression leading to eq 12 is not given here
    • The full cumbersome expression leading to eq 12 is not given here.
  • 48
    • 34249816109 scopus 로고    scopus 로고
    • 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
    • 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.
  • 49
    • 34249800617 scopus 로고    scopus 로고
    • 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.
  • 50
    • 34249816753 scopus 로고    scopus 로고
    • Manuscript in preparation
    • Wittmer, J. P.; et al. Manuscript in preparation.
    • Wittmer, J.P.1
  • 51
    • 34249780066 scopus 로고    scopus 로고
    • 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
    • 31
  • 54
    • 34249792325 scopus 로고    scopus 로고
    • 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
    • 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.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.