The growth constant of uniform star polymers in a slab geometry

Chee, Merk‐Na; Whittington, S G

doi:10.1088/0305-4470/20/14/029

Cited by 11 publications

(13 citation statements)

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“…Stars embedded in a slab, infinite in d -1 dimensions and of finite thickness I. , have been considered by Chee and Whittington(1987). They conclude that in three or more dimensions the limit lim X 'lnC&(f)=v(L, f)Pf~oo (b) {c)is independent of f, but in two dimensions the limit depends on f(Chee and Whittington, 1987; see also Soterosand Whittington, 1989).For lattice animals, which may be regarded as models of branched polymers with general topology, the limiting value of the number of lattice animals of X vertices contained in a wedge of angle a obeysFIG. 4.…”

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confidence: 99%

Surface phase transitions in polymer systems

1993

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Self-avoiding walks, lattice trees, and related geometrical models provide a link between the physics of polymers and the study of critical phenomena. In particular, these models in the presence of a surface provide insight into surface adsorption in dilute polymer systems in a good solvent. The theme of this review is the influence of polymer structure (topology) on the critical properties of these models. Emphasis is placed on recent results by rigorous methods, scaling theory, and conformal covariance theory. Numerical results that may be used to test the predictions of scaling and conformal covariance theories are also summarized. Related topics such as the adsorption of directed polymers, the semidilute regime, the theta point and theta solvents, and percolation (polymer gels) are briefly discussed in the final section.

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confidence: 99%

Surface phase transitions in polymer systems

1993

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“…where γ(G) is the entropic exponent of the network and µ d is the self-avoiding walk growth constant [1,2] (see references [3,4], and for lattice stars reference [5]). The best estimates of the growth constants in the square and cubic lattices are obtained from simulations of the selfavoiding walk, and are µ 2 = 2.63815853035(2), [6] (2) µ 3 = 4.684039931 (27).…”

Section: Introductionmentioning

confidence: 99%

“…Uniform lattice star polymers form a particular class of lattice networks that have received significant attention in the literature at least since the 1980s [3][4][5][8][9][10][11]. If s (f ) n is the number of uniform lattice stars in Z d with f arms (these are f -stars) with central node at the origin, then by equation (1),…”

Section: Introductionmentioning

confidence: 99%

Entropic exponents of grafted lattices stars

van Rensburg

2022

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The surface entropic exponents of half-space lattice stars grafted at their central nodes in a hard wall are estimated numerically using the PERM algorithm. In the square half-lattice the exact values of the exponents are verified, including Barber's scaling relation and a generalisation for 2-stars with one and two surface loops respectively. This is the relationwhere γ21 and γ211 are the surface entropic exponents of a grafted 2-star with one and two surface loops respectively, and γ20 is the surface entropic exponent with no surface loops. This relation is also tested in the cubic half-lattice where surface entropic exponents are estimated up to 5-stars, including many with one or more surface loops. Barber's scaling relation and the relation γ3111 = γ30 − 3 γ31 + 3 γ311 are also tested, where the exponents {γ31, γ311, γ3111} are of grafted 3-stars with one, two or three surface loops respectively, and γ30 is the surface exponent of grafted 3-stars.

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“…We model each molecule as a four-armed star; each link on the star is modeled as a hard sphere. There are 21 beads/molecule, a central bead and four arms containing five beads each. The surfaces are modeled as hard walls impenetrable to the centers of the beads on the molecule.…”

Section: Introductionmentioning

confidence: 99%

“…Normal periodic boundary conditions are employed in the other (x and y) directions. The system consists of 40 molecules each containing 21 sites. The walls are 16 apart, and the periodic length is 9.57 .…”

Section: Introductionmentioning

confidence: 99%