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Volumn 54, Issue 2, 1996, Pages 1134-1152

Polymers interacting with spherical and rodlike particles

Author keywords

[No Author keywords available]

Indexed keywords

ADSORPTION; BOUNDARY CONDITIONS; CONFORMATIONS; DESORPTION; FREE ENERGY; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; MOLECULAR DYNAMICS; MONOMERS; PHASE DIAGRAMS;

EID: 0030214492     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.54.1134     Document Type: Article
Times cited : (166)

References (90)
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    • note
    • ⊥ - R from the surface will only be universal if these lengths are much larger than microscopic lengths such as the lattice constant in a lattice based walk model (or the bead size in a freely jointed bead model) and the range of the attractive surface potential.
  • 31
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    • note
    • ⊥|).
  • 32
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    • note
    • 2=2LD involving the root-mean-square end-to-end distance R of the ideal chain in unbounded D-dimensional space as follows from Eq. (1.2) (compare, e.g., Ref. [16]).
  • 33
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    • note
    • λ(0)〉 and 〈m(y)〉 introduced in Polymers near Surfaces (Ref. [4]), Chap. III.
  • 36
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    • For Dirichlet boundary conditions c=+∞ the Gaussian propagator for the interior and exterior of a spherical (d=D) surface in D dimensions has been obtained in E. Eisenriegler, Z. Phys. B 61, 299 (1985).
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    • note
    • Note that for α=-1/2 and α=1/2 (i.e., d=1 and d=3) the Bessel functions reduce to elementary functions so that most of the calculations can be carried out explicitly.
  • 42
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    • McGraw-Hill, New York
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  • 43
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    • note
    • Equation (2.15) reproduces the known result for the planar case d=1 [see, e.g., Eq. (3.77) in Ref. [4]] and for d=3 it contains as a special case the result presented in Eq. (6) in Ref. [9] for a purely repulsive surface ζ=+∞.
  • 44
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    • note
    • ⊥ in that the chain for c
  • 45
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    • note
    • It would be interesting to investigate the adsorption of a single chain onto a cylindrical surface (d=2) if EVI is present (compare the discussion at the end of Sec. V). While we believe that an adsorption transition still exists in this case we do not expect that the transition occurs in the exceptional form of an essential singularity [Eq. (2.19)].
  • 46
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    • note
    • α and Δζ, respectively.
  • 47
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    • ⊥ of a flexible line that unbinds from a cylinder has been observed before by Pincus, Sandroff, and Witten [10] and, within a slightly different context, by M. Vallade and J. Lajzerowicz, J. Phys. (Paris) 42, 1505 (1981) and by R. Lipowsky, Europhys. Lett. 15, 703 (1991).
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    • Vallade, M.1    Lajzerowicz, J.2
  • 48
    • 84956273193 scopus 로고
    • ⊥ of a flexible line that unbinds from a cylinder has been observed before by Pincus, Sandroff, and Witten [10] and, within a slightly different context, by M. Vallade and J. Lajzerowicz, J. Phys. (Paris) 42, 1505 (1981) and by R. Lipowsky, Europhys. Lett. 15, 703 (1991).
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  • 49
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    • note
    • E for chains with EVI differ from those for ideal chains [see, e.g., Eq. (4.12)].
  • 51
    • 85086289379 scopus 로고    scopus 로고
    • note
    • E for R→∞ is also finite for (D=3, d=2) and shall discuss its behavior for ρ≫1.
  • 52
    • 5544265698 scopus 로고    scopus 로고
    • note
    • ∥=1.
  • 53
    • 85086290146 scopus 로고    scopus 로고
    • note
    • d=1=2 in front of the curly bracket in Eq. (3.9) accounts for the two planar surfaces.
  • 54
    • 5544295281 scopus 로고    scopus 로고
    • note
    • This is plausible because a surface that is bent away from the polymer solution leads to an increase of the depletion layer effect (compare the discussion for the corresponding magnetic system near Eq. (2.24) in the reference cited in Ref. [24]). The present situation of free polymers should be distinguished from the case in which a (single) polymer is anchored with one end to the repulsive surface. The latter case favors a bending of the surface away from the polymer [9].
  • 55
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    • S. Asakura and F. Oosawa, J. Polym. Sci. 33, 183 (1958); for a recent application of the phs approximation see P. B. Warren, S. M. Ilett, and W. C. K. Poon, Phys. Rev. E 52, 5205 (1995).
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    • S. Asakura and F. Oosawa, J. Polym. Sci. 33, 183 (1958); for a recent application of the phs approximation see P. B. Warren, S. M. Ilett, and W. C. K. Poon, Phys. Rev. E 52, 5205 (1995).
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  • 57
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    • note
    • d-(1/ν).
  • 58
    • 5544305368 scopus 로고    scopus 로고
    • This effect has also been observed within the approximate treatment of Ref. [12(e)]
    • This effect has also been observed within the approximate treatment of Ref. [12(e)].
  • 59
    • 5544220185 scopus 로고    scopus 로고
    • The "small" radius must, however, be large on a microscopic scale [18]
    • The "small" radius must, however, be large on a microscopic scale [18].
  • 60
    • 5544274482 scopus 로고    scopus 로고
    • note
    • For an appropriate generalization of the Gaussian model [Eq. (1.5)] for chains with EVI see Refs. [1,4,16] and Sec. V.
  • 61
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    • note
    • 2/L.
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    • 0001909227 scopus 로고
    • edited by C. Domb and J. L. Lebowitz Academic, London
    • (c) J. L. Cardy, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1986), Vol. 11, p. 55.
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    • note
    • 2(y) on the rhs of Eq. (4.3c) is dominated by the region where Eq. (4.11) holds.
  • 66
    • 85086288888 scopus 로고    scopus 로고
    • note
    • 2 must be an interior point of the half space.
  • 71
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    • note
    • Actually we have considered a more general "particle," namely, a generalized cylinder K [see Eq. (1.1)], which comprises planar, cylindrical, or spherical boundaries as special cases.
  • 72
    • 5544253780 scopus 로고    scopus 로고
    • note
    • L is considered for the special case of a purely repulsive sphere.
  • 73
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    • note
    • 4 interaction.
  • 74
    • 5544302672 scopus 로고    scopus 로고
    • note
    • In the operator expansion [54] this term could be included as an additional operator-free contact term that contributes only to integrals over correlation functions of low order.
  • 75
    • 5544243108 scopus 로고
    • α(ζ) in Fig. 2 (a) are the corresponding Gaussian approximation; this maximum remains finite in the region τ>0 (compare the reference cited in Ref. [27]).
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    • Balian, R.1    Toulouse, G.2
  • 76
    • 0004056428 scopus 로고
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    • α(ζ) in Fig. 2 (a) are the corresponding Gaussian approximation; this maximum remains finite in the region τ>0 (compare the reference cited in Ref. [27]).
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  • 80
    • 5544319848 scopus 로고    scopus 로고
    • note
    • α+ℓ(√μR)] (compare Ref. [24]).
  • 81
    • 5544234487 scopus 로고    scopus 로고
    • note
    • Analogous to Ref. [60] one can derive the Gaussian propagator for the film geometry. This result is given in Eq. (4.1) in Ref. [22].
  • 84
    • 0038139050 scopus 로고
    • (b) R. Balian and C. Bloch, Ann. Phys. (N.Y.) 60, 401 (1970); 64, 271 (1971); 84, 559 (1974);
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  • 85
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    • (b) R. Balian and C. Bloch, Ann. Phys. (N.Y.) 60, 401 (1970); 64, 271 (1971); 84, 559 (1974);
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  • 89
    • 0004099776 scopus 로고
    • edited by D. Nelson, T. Piran, and S. Weinberg World Scientific, Singapore
    • See, e.g., F. David, in Statistical Mechanics of Membranes and Surfaces, edited by D. Nelson, T. Piran, and S. Weinberg (World Scientific, Singapore, 1988).
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  • 90
    • 5544298321 scopus 로고    scopus 로고
    • note
    • m [compare Fig. 1 and Eq. (21) in Ref. [62(e)]].


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.