### Abstract

The mean dimensions of multichain polymer systems are predicted to follow a scaling relation with scaling variable X=l^{dv-1} ρ, where l is the number of statistical segments on the chain, ρ is the segment density, d is the dimension, and v is the critical exponent for the mean dimensions of an isolated polymer chain. The scaling laws are 〈R^{2}〉≈A(X) l^{2v} for l→∞ with X bounded, and 〈R ^{2}〉≈B(ρ)l for l→_{∞} with X→_{∞}. Moreover, the critical amplitudes behave as A(X)∼X^{-(2v-1)/(dv-1)} as X→_{∞} and B(ρ)∼ρ^{-(2v-1)/(dv-1)} as ρ→0. Simulations of both continuum and lattice systems are reanalyzed and found to be consistent with these scaling relations. Previous naive use of short-chain data has led to misleading results.

Original language | English (US) |
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Pages (from-to) | 3496-3499 |

Number of pages | 4 |

Journal | The Journal of chemical physics |

Volume | 79 |

Issue number | 7 |

State | Published - 1983 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of chemical physics*,

*79*(7), 3496-3499.

**Scaling in multichain polymer systems in two and three dimensions.** / Bishop, Marvin; Kalos, M. H.; Sokal, Alan D.; Frisch, H. L.

Research output: Contribution to journal › Article

*The Journal of chemical physics*, vol. 79, no. 7, pp. 3496-3499.

}

TY - JOUR

T1 - Scaling in multichain polymer systems in two and three dimensions

AU - Bishop, Marvin

AU - Kalos, M. H.

AU - Sokal, Alan D.

AU - Frisch, H. L.

PY - 1983

Y1 - 1983

N2 - The mean dimensions of multichain polymer systems are predicted to follow a scaling relation with scaling variable X=ldv-1 ρ, where l is the number of statistical segments on the chain, ρ is the segment density, d is the dimension, and v is the critical exponent for the mean dimensions of an isolated polymer chain. The scaling laws are 〈R2〉≈A(X) l2v for l→∞ with X bounded, and 〈R 2〉≈B(ρ)l for l→∞ with X→∞. Moreover, the critical amplitudes behave as A(X)∼X-(2v-1)/(dv-1) as X→∞ and B(ρ)∼ρ-(2v-1)/(dv-1) as ρ→0. Simulations of both continuum and lattice systems are reanalyzed and found to be consistent with these scaling relations. Previous naive use of short-chain data has led to misleading results.

AB - The mean dimensions of multichain polymer systems are predicted to follow a scaling relation with scaling variable X=ldv-1 ρ, where l is the number of statistical segments on the chain, ρ is the segment density, d is the dimension, and v is the critical exponent for the mean dimensions of an isolated polymer chain. The scaling laws are 〈R2〉≈A(X) l2v for l→∞ with X bounded, and 〈R 2〉≈B(ρ)l for l→∞ with X→∞. Moreover, the critical amplitudes behave as A(X)∼X-(2v-1)/(dv-1) as X→∞ and B(ρ)∼ρ-(2v-1)/(dv-1) as ρ→0. Simulations of both continuum and lattice systems are reanalyzed and found to be consistent with these scaling relations. Previous naive use of short-chain data has led to misleading results.

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M3 - Article

VL - 79

SP - 3496

EP - 3499

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 7

ER -