Self-Avoiding Walks on Randomly Diluted Lattices

Lee, Sang Bub; Nakanishi, Hisao

doi:10.1103/physrevlett.61.2022

Cited by 84 publications

(78 citation statements)

References 19 publications

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“…37,38 Theories predict that the scaling exponent at the percolation threshold ͑denoted c ͒ should be different from , although there are discrepancies in the values, with c = 0.678 in field theoretic renormalization group theory 7 and c = 0.612 in MC simulations. 39 Our simulations are for m lower than the percolation threshold, and so we cannot address this point.…”

Section: Resultsmentioning

confidence: 95%

Swelling of polymers in porous media

Sung

Chang

Yethiraj

2009

The Journal of Chemical Physics

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The swelling of polymers in random matrices is studied using computer simulations and percolation theory. The model system consists of freely jointed hard sphere chains in a matrix of hard spheres fixed in space. The average size of the polymer is a nonmonotonic function of the matrix volume fraction, phi(m). For low values of phi(m) the polymer size decreases as phi(m) is increased but beyond a certain value of phi(m) the polymer size increases as phi(m) is increased. The qualitative behavior is similar for three different types of matrices. In order to study the relationship between the polymer swelling and pore percolation, we use the Voronoi tessellation and a percolation theory to map the matrix onto an irregular lattice, with bonds being considered connected if a particle can pass directly between the two vertices they connect. The simulations confirm the scaling relation R(G) approximately (p-p(c))(delta(0))N(nu), where R(G) is the radius of gyration, N is the polymer degree of polymerization, p is the number of connected bonds, and p(c) is the value of p at the percolation threshold, with universal exponents delta(0)(approximately = -0.126+/-0.005) and nu(approximately = 0.6+/-0.01). The values of the exponents are consistent with predictions of scaling theory.

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Section: Resultsmentioning

confidence: 95%

Swelling of polymers in porous media

Sung

Chang

Yethiraj

2009

The Journal of Chemical Physics

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“…Lee and Nakanishi [9], however, pointed out that his result near p, was in error owing to mistakes in data analysis, and should be corrected not to be greater than 0.62, which is much closer to vF. They also presented their own Monte Carlo data on square and simple-cubic lattices and obtained a Flory-exponent value v, similar to the normal-lattice value even for p close to p" for both two and three dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…Lyklema and Kremer [6] presented a qualitative argument that the probability of starting an ¹tep walk at a finite cluster vanishes as N -+~, suggesting that the critical behavior is dominated by walks on an infinite cluster. Recently, Lee et al [9] also argued that the two ensembles are likely to yield identical critical behavior for the following reason. Since the critical behavior of SAW's is governed by asymptotically long walks, and such walks can exist only on the infinite cluster, the contributions of finite clusters diminish as N~~.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo study of self-avoiding walks on a percolation cluster

Woo

Lee

1991

Phys. Rev. A

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We present computer-simulation results of self-avoiding walks (SAW's) on a percolation cluster for a square lattice performed very close to the percolation threshold. We specifically consider the disorder averages of SAW's on all clusters supporting one or more ¹tepwalks and those on a backbone of an infinite cluster and estimate the critical exponents v and y that characterize the disorder averages of the end-to-end distance and the number of SAW's, respectively. Our results for y indicate a behavior rather similar to SAW s on fully occupied lattices for both cases, while for v one of two cases shows diferent behavior.

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“…In the simplest case one can treat these objects as uncorrelated point-like defects. Then, for the small concentrations of obstacles it was proven both analytically [26] and numerically [27][28][29], that conformational properties of polymer macromolecules do not change in comparison with the pure environment, unless the concentration of such impurities reaches the percolation threshold [27,[30][31][32]. Completely different situation occurs when obstacles cannot be treated as point-like objects but form the complex fractal structures (clusters) [33].…”

Section: Introductionmentioning

confidence: 99%