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(c) J. M. R. d'Oliveira, J. M. G. Martinho, R. Xu, and M. A. Winnik, ibid. 28, 4750 (1995).
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C. M. Wijmans, F. A. M. Leermakers, and G. J. Fleer, Langmuir 10, 4514 (1994); D. R. M. Williams and F. C. MacKin-tosh, J. Phys. (France) II 5, 1407 (1995).
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Williams, D.R.M.1
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-
-
5544284213
-
-
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
-
-
5544295283
-
-
note
-
⊥|).
-
-
-
-
32
-
-
85086290059
-
-
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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0001856561
-
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edited by C. Domb and J. L. Lebowitz Academic, London
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K. Binder, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8, p. 1.
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Binder, K.1
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0003130040
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H. W. Diehl, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1986), Vol. 10, p. 75.
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Diehl, H.W.1
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5544260028
-
-
note
-
λ(0)〉 and 〈m(y)〉 introduced in Polymers near Surfaces (Ref. [4]), Chap. III.
-
-
-
-
36
-
-
0042643864
-
-
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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Eisenriegler, E.1
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0004245694
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M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972); I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, London, 1965).
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Handbook of Mathematical Functions
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Abramowitz, M.1
Stegun, I.A.2
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0003498504
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Academic, London
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M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972); I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, London, 1965).
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Table of Integrals, Series, and Products
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Gradshteyn, I.S.1
Ryzhik, I.M.2
-
39
-
-
5544298322
-
-
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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0003438193
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McGraw-Hill, New York
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For a table of inverse Laplace transforms see, e.g., Tables of Integral Transforms, edited by A. Erdélyi (McGraw-Hill, New York, 1954), Vol. I.
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(1954)
Tables of Integral Transforms
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Erdélyi, A.1
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43
-
-
5544293490
-
-
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
-
-
5544290912
-
-
note
-
⊥ in that the chain for c
-
-
-
-
45
-
-
5544318234
-
-
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
-
-
5544295284
-
-
note
-
α and Δζ, respectively.
-
-
-
-
47
-
-
0019637073
-
-
⊥ 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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J. Phys. (Paris)
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Vallade, M.1
Lajzerowicz, J.2
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48
-
-
84956273193
-
-
⊥ 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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Europhys. Lett.
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Lipowsky, R.1
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49
-
-
5544261775
-
-
note
-
E for chains with EVI differ from those for ideal chains [see, e.g., Eq. (4.12)].
-
-
-
-
51
-
-
85086289379
-
-
note
-
E for R→∞ is also finite for (D=3, d=2) and shall discuss its behavior for ρ≫1.
-
-
-
-
52
-
-
5544265698
-
-
note
-
∥=1.
-
-
-
-
53
-
-
85086290146
-
-
note
-
d=1=2 in front of the curly bracket in Eq. (3.9) accounts for the two planar surfaces.
-
-
-
-
54
-
-
5544295281
-
-
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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0000303810
-
-
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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Asakura, S.1
Oosawa, F.2
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56
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0000274345
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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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Phys. Rev. E
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Warren, P.B.1
Ilett, S.M.2
Poon, W.C.K.3
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57
-
-
85086288911
-
-
note
-
d-(1/ν).
-
-
-
-
58
-
-
5544305368
-
-
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
-
-
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
-
-
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
-
-
85086290191
-
-
note
-
2/L.
-
-
-
-
64
-
-
0001909227
-
-
edited by C. Domb and J. L. Lebowitz Academic, London
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(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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Cardy, J.L.1
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65
-
-
85086289349
-
-
note
-
2(y) on the rhs of Eq. (4.3c) is dominated by the region where Eq. (4.11) holds.
-
-
-
-
66
-
-
85086288888
-
-
note
-
2 must be an interior point of the half space.
-
-
-
-
68
-
-
0001916662
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H. N. W. Lekkerkerker, J. K. G. Dhont, H. Verduin, C. Smits, and J. S. van Duijneveldt, Physica A 213, 18 (1995);
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Physica A
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Lekkerkerker, H.N.W.1
Dhont, J.K.G.2
Verduin, H.3
Smits, C.4
Van Duijneveldt, J.S.5
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69
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0003703849
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edited by M. Baus, L. R. Rull, and J. P. Ryckaert Kluwer Academic, Dordrecht
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(b) W. C. K. Poon and P. N. Pusey, in Observation, Prediction, and Simulation of Phase Transitions in Complex Fluids, Vol. 460 of NATO Advanced Study Institute, Series C: Mathematical and Physical Sciences, edited by M. Baus, L. R. Rull, and J. P. Ryckaert (Kluwer Academic, Dordrecht, 1995), p. 3;
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Observation, Prediction, and Simulation of Phase Transitions in Complex Fluids, Vol. 460 of NATO Advanced Study Institute, Series C: Mathematical and Physical Sciences
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Poon, W.C.K.1
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5544274481
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(c) H. N. W. Lekkerkerker, P. Buining, J. Buitenhuis, G. J. Vroege, and A. Stroobants, ibid., p. 53.
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Observation, Prediction, and Simulation of Phase Transitions in Complex Fluids, Vol. 460 of NATO Advanced Study Institute, Series C: Mathematical and Physical Sciences
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Lekkerkerker, H.N.W.1
Buining, P.2
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Vroege, G.J.4
Stroobants, A.5
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71
-
-
5544319851
-
-
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
-
-
note
-
L is considered for the special case of a purely repulsive sphere.
-
-
-
-
73
-
-
5544257284
-
-
note
-
4 interaction.
-
-
-
-
74
-
-
5544302672
-
-
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
-
-
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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(1974)
Ann. Phys. (N.Y.)
, vol.83
, pp. 28
-
-
Balian, R.1
Toulouse, G.2
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76
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0004056428
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Pergamon, London
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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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(1958)
Statistical Physics
-
-
Landau, L.D.1
Lifshitz, E.M.2
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80
-
-
5544319848
-
-
note
-
α+ℓ(√μR)] (compare Ref. [24]).
-
-
-
-
81
-
-
5544234487
-
-
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
-
-
(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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0038139050
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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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Ann. Phys. (N.Y.)
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, pp. 559
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-
-
89
-
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0004099776
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-
edited by D. Nelson, T. Piran, and S. Weinberg World Scientific, Singapore
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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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(1988)
Statistical Mechanics of Membranes and Surfaces
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David, F.1
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90
-
-
5544298321
-
-
note
-
m [compare Fig. 1 and Eq. (21) in Ref. [62(e)]].
-
-
-
|