Phys. Rev. E 54, 127–135 (1996)Spherically symmetric random walks. III. Polymer adsorption at a hyperspherical boundaryReceived 8 February 1996; published in the issue dated July 1996 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. © 1996 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.54.127
DOI:
10.1103/PhysRevE.54.127
PACS:
05.40.+j, 05.20.-y, 05.50.+q
See AlsoSee Also: Carl M. Bender, Fred Cooper, and Peter N. Meisinger, Spherically symmetric random walks. I. Representation in terms of orthogonal polynomials, Phys. Rev. E 54, 100 (1996). |
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