### Abstract

Language | English |
---|---|

Pages | 2684-2691 |

Number of pages | 7 |

Journal | Journal of Chemical Physics |

Volume | 110 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Feb 1999 |

### Fingerprint

### Keywords

- conformational space renormalization
- self-avoiding walks
- Monte-Carlo simulation
- excluded-volume
- dimensional regularization
- 2-parameter theory
- pivot algorithm
- 3 dimensions
- chain
- lattice

### Cite this

*Journal of Chemical Physics*,

*110*(5), 2684-2691. https://doi.org/10.1063/1.477991

}

*Journal of Chemical Physics*, vol. 110, no. 5, pp. 2684-2691. https://doi.org/10.1063/1.477991

**Crossover approach to scaling behavior in dilute polymer solutions: theory and simulation.** / Lue, L.; Kiselev, S. B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Crossover approach to scaling behavior in dilute polymer solutions: theory and simulation

AU - Lue, L.

AU - Kiselev, S. B.

N1 - English Article 161ET J CHEM PHYS

PY - 1999/2/1

Y1 - 1999/2/1

N2 - We develop a crossover theory for dilute polymer solutions, analogous to crossover theories for critical phenomena in simple fluids. In this theory, a critical degree of polymerization N∗ is found, which plays a similar role as the Ginzburg number in second-order phase transitions. To test the predictions of this theory, we perform Monte Carlo simulations of polymer chains composed of rigidly bonded hard spheres of various diameters and chain lengths. Various properties of these chains were analyzed, including the end-to-end distance distribution and mean-square radius of gyration. We find that the approach to the asymptotic scaling regime displays two types of crossover behavior, depending on the value of the model parameter ū, which is a measure of the strength of the monomer-monomer excluded volume interaction: (i) ū<1 and (ii) ū>1. In case (i), the system exhibits crossover from a Gaussian chain to the Kuhnian chain, as the degree of polymerization increases. In case (ii), the system exhibits crossover from the rigid rod to a Kuhnian chain. Our crossover theory is found to work well for polymers with ū>1 only near the asymptotic scaling regime. However, for ū<1, the theory works well in all regimes.

AB - We develop a crossover theory for dilute polymer solutions, analogous to crossover theories for critical phenomena in simple fluids. In this theory, a critical degree of polymerization N∗ is found, which plays a similar role as the Ginzburg number in second-order phase transitions. To test the predictions of this theory, we perform Monte Carlo simulations of polymer chains composed of rigidly bonded hard spheres of various diameters and chain lengths. Various properties of these chains were analyzed, including the end-to-end distance distribution and mean-square radius of gyration. We find that the approach to the asymptotic scaling regime displays two types of crossover behavior, depending on the value of the model parameter ū, which is a measure of the strength of the monomer-monomer excluded volume interaction: (i) ū<1 and (ii) ū>1. In case (i), the system exhibits crossover from a Gaussian chain to the Kuhnian chain, as the degree of polymerization increases. In case (ii), the system exhibits crossover from the rigid rod to a Kuhnian chain. Our crossover theory is found to work well for polymers with ū>1 only near the asymptotic scaling regime. However, for ū<1, the theory works well in all regimes.

KW - conformational space renormalization

KW - self-avoiding walks

KW - Monte-Carlo simulation

KW - excluded-volume

KW - dimensional regularization

KW - 2-parameter theory

KW - pivot algorithm

KW - 3 dimensions

KW - chain

KW - lattice

UR - http://dx.doi.org/10.1063/1.477991

U2 - 10.1063/1.477991

DO - 10.1063/1.477991

M3 - Article

VL - 110

SP - 2684

EP - 2691

JO - Journal of Chemical Physics

T2 - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 5

ER -