Spherically symmetric random walks. III. Polymer adsorption at a hyperspherical boundary

Carl M. Bender, Stefan Boettcher, and Peter N. Meisinger
Phys. Rev. E 54, 127 – Published 1 July 1996
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Abstract

A recently developed model of random walks on a D-dimensional hyperspherical lattice, where D is not restricted to integer values, is used to study polymer growth near a D-dimensional attractive hyperspherical boundary. The model determines the fraction P(κ) of the polymer adsorbed on this boundary as a function of the attractive potential κ for all values of D. The adsorption fraction P(κ) exhibits a second-order phase transition with a universal, nontrivial scaling coefficient for 0<D<4, D≠2, and exhibits a first-order phase transition for D≳4. At D=4 there is a tricritical point with logarithmic scaling. This model reproduces earlier results for D=1 and 2, where P(κ) scales linearly and exponentially, respectively. A crossover transition that depends on the radius of the adsorbing boundary is found. © 1996 The American Physical Society.

  • Received 8 February 1996

DOI:https://doi.org/10.1103/PhysRevE.54.127

©1996 American Physical Society

Authors & Affiliations

Carl M. Bender

  • Department of Physics, Washington University, St. Louis, Missouri 63130

Stefan Boettcher

  • Department of Physics, Brookhaven National Laboratory, Upton, New York 11973

Peter N. Meisinger

  • Department of Physics, Washington University, St. Louis, Missouri 63130

See Also

Spherically symmetric random walks. I. Representation in terms of orthogonal polynomials

Carl M. Bender, Fred Cooper, and Peter N. Meisinger
Phys. Rev. E 54, 100 (1996)

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Vol. 54, Iss. 1 — July 1996

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