### Abstract

Lattice Monte Carlo simulations are widely used to study the effect of walls on the concentration profile in polymer solutions. The scaling theory predicts that the monomer density at a distance x from the wall, reduced by the bulk density, is proportional to (x/R_{g0})^{1/v} at low concentrations, and the correlation length replaces R_{g0} in the semidilute solution, where R_{g0} is the radius of gyration and v is the Flow exponent for the chain dimension. We conducted simulations for long chains on a cubic lattice to find that a positive penetration depth γ is needed to see an agreement with the theory. The monomers perceive a theoretical wall at an off-lattice position of γ behind the presumed wall on the lattice points. We found γ ∼ 0.13 of the lattice unit at low concentrations but ∼0.36 in the semidilute solution for athermal chains. For Θ solutions, γ was 0.31-0.36 at all concentrations. We ascribe the positive γ to uneven chain segment propagation in the chain update in a nonuniform density profile.

Original language | English (US) |
---|---|

Pages (from-to) | 7121-7126 |

Number of pages | 6 |

Journal | Macromolecules |

Volume | 34 |

Issue number | 20 |

DOIs | |

State | Published - Sep 25 2001 |

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### ASJC Scopus subject areas

- Materials Chemistry

### Cite this

*Macromolecules*,

*34*(20), 7121-7126. https://doi.org/10.1021/ma010158j

**What is the distance to the wall in lattice simulations?** / Teraoka, Iwao; Cifra, Peter; Wang, Yongmei.

Research output: Contribution to journal › Article

*Macromolecules*, vol. 34, no. 20, pp. 7121-7126. https://doi.org/10.1021/ma010158j

}

TY - JOUR

T1 - What is the distance to the wall in lattice simulations?

AU - Teraoka, Iwao

AU - Cifra, Peter

AU - Wang, Yongmei

PY - 2001/9/25

Y1 - 2001/9/25

N2 - Lattice Monte Carlo simulations are widely used to study the effect of walls on the concentration profile in polymer solutions. The scaling theory predicts that the monomer density at a distance x from the wall, reduced by the bulk density, is proportional to (x/Rg0)1/v at low concentrations, and the correlation length replaces Rg0 in the semidilute solution, where Rg0 is the radius of gyration and v is the Flow exponent for the chain dimension. We conducted simulations for long chains on a cubic lattice to find that a positive penetration depth γ is needed to see an agreement with the theory. The monomers perceive a theoretical wall at an off-lattice position of γ behind the presumed wall on the lattice points. We found γ ∼ 0.13 of the lattice unit at low concentrations but ∼0.36 in the semidilute solution for athermal chains. For Θ solutions, γ was 0.31-0.36 at all concentrations. We ascribe the positive γ to uneven chain segment propagation in the chain update in a nonuniform density profile.

AB - Lattice Monte Carlo simulations are widely used to study the effect of walls on the concentration profile in polymer solutions. The scaling theory predicts that the monomer density at a distance x from the wall, reduced by the bulk density, is proportional to (x/Rg0)1/v at low concentrations, and the correlation length replaces Rg0 in the semidilute solution, where Rg0 is the radius of gyration and v is the Flow exponent for the chain dimension. We conducted simulations for long chains on a cubic lattice to find that a positive penetration depth γ is needed to see an agreement with the theory. The monomers perceive a theoretical wall at an off-lattice position of γ behind the presumed wall on the lattice points. We found γ ∼ 0.13 of the lattice unit at low concentrations but ∼0.36 in the semidilute solution for athermal chains. For Θ solutions, γ was 0.31-0.36 at all concentrations. We ascribe the positive γ to uneven chain segment propagation in the chain update in a nonuniform density profile.

UR - http://www.scopus.com/inward/record.url?scp=0035949910&partnerID=8YFLogxK

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U2 - 10.1021/ma010158j

DO - 10.1021/ma010158j

M3 - Article

AN - SCOPUS:0035949910

VL - 34

SP - 7121

EP - 7126

JO - Macromolecules

JF - Macromolecules

SN - 0024-9297

IS - 20

ER -